MONTE CARLO METHOD FOR AUTOMATED AND HIGHLY EFFICIENT CALCULATION OF KINETIC DATA OF CHEMICAL REACTIONS

Description

[0001] The present invention relates to a computer-implemented method for calculating transition states of a chemical reaction, as well as a data processing system comprising means for carrying out the method, a computer program comprising instructions that cause a computer to carry out the method, and the use of the computer program. The invention further relates to a system, a method, and means for the automated and efficient determination of kinetic data of chemical reactions.

[0002] During a chemical reaction, the atoms involved change their geometry, bonds are broken, and new bonds are formed. The energy of the atoms also changes, reaching a state of maximum energy, the so-called transition state, as the reaction progresses. The transition state represents a potential barrier or activation barrier that separates the reactants from the products of the chemical reaction. Once the activation barrier is overcome, the product is formed. The energy during a chemical reaction can be represented using a potential energy surface, which depicts the potential energy of the atoms involved in the reaction as a function of their geometry. The potential energy surface also represents states in which no products are formed.The direct reaction pathway, in which products are formed by overcoming the transition state, can be represented as a curve where the distances between individual atoms of the molecules are plotted against the energy. Using quantum chemical methods and mathematical approximation techniques, the energy of the geometry of a molecule or a system of several molecules can be calculated, with the functional space encompassing the degrees of freedom of the molecule. These methods allow the determination of the geometry at the transition state and permit predictions about the reaction kinetics of a chemical reaction.

[0003] A well-known method for determining the geometry of transition states is the Newton-Raphson method. However, calculating transition states using this method has several disadvantages. First, a Newton-Raphson algorithm cannot be applied to just any initial molecular geometry, but only to molecular geometries that already closely approximate the geometry of the transition state. This is computationally expensive because the approximation of a molecular geometry to the geometry of the transition state is usually done manually; that is, bond lengths are manually set on the computer. Methods also exist in which potential energy surfaces are first calculated using other methods, from which possible saddle points are identified. These methods also require the initial determination of a geometry that is already very close to the geometry of the transition state.For these reasons, calculating transition states using Newton-Raphson algorithms is particularly time-consuming and expensive with current computer technology, especially for molecules with more than 100 atoms. Furthermore, applying Newton-Raphson procedures and related approximations necessitates calculating second derivatives of the energy with respect to the nuclear coordinates of the molecule under consideration. The computational effort required for these second derivatives scales quadratically with the size of the molecule and is therefore rate-limiting for calculating activation energies.

[0004] Lin et al. ("A flexible transition state searching method for atmospheric reaction systems," Chemical Physics 450-451, 2015, pp. 21-31) disclose a method for investigating atmospheric chemical reactions in the gas phase. The method begins with a Monte Carlo-based screening of potential energy surfaces using force field methods to identify approximate saddle-point-like regions. The observable used in the corresponding Monte Carlo method is the value of an energy function. Building on this, Newton-Raphson methods are then used to attempt to locate chemical transition states. With the Monte Carlo method disclosed here, the entire potential energy surface must first be simulated before any approximate saddle-point-like regions can be identified. Consequently, this Monte Carlo method cannot be used to specifically optimize saddle-point-like regions.For this reason, efficient use of the available computing resources for locating the required saddle points is not possible. With current computer technology, the application of the method disclosed here is limited to small molecules with 7 to 30 atoms. Furthermore, mathematically simplified methods are used.

[0005] E. Martínez-Núñez et al., "An automated transition state search using classical trajectories initialized at multiple minima", Phys Chem Chem Phys, June 14, 2015, 17(22):14912-21; "tsscds2018: A code for automated discovery of chemical reaction mechanisms and solving the kinetics", J. Comp. Chem., September 24, 2018, 39(23):1922-1930) reveal a method for investigating chemical reaction pathways. Potential energy surfaces of chemical molecules are calculated using mathematically simplified methods. Subsequently, attempts are made to calculate the chemically relevant transition states using conventional pseudo-Newton-Raphson methods. A disadvantage of this method is that the entire potential energy surface must first be calculated, which is time-consuming and computationally intensive. Furthermore, this method can only be applied to smaller molecules.

[0006] Jacobson et al. ("Automated Transition State Search and Its Application to Diverse Types of Organic Reactions", J. Chem. Theory Comput. 13, 11, 5780-5797) disclose a method for the automated calculation of chemical transition states. This method calculates chemical transition states from chemical equilibrium states. However, this approach requires a separate calculation of chemical equilibrium states before an interpolation of the resulting geometries can be performed to approximate the transition state. In a further step, an attempt is then made to calculate a transition state geometry based on this approximation. Creating the required equilibrium states necessitates additional work by a person skilled in the art. The interpolation used in the disclosed method cannot be successfully applied to arbitrary molecular geometries.

[0007] Hu et al. ("A gradient-directed Monte Carlo method for global optimization in a discrete space: Application to protein sequence design and folding" J Chem Phys. 2009 Oct 21; 131(15): 154-117) disclose a method for calculating protein structures. This method calculates the folding of protein structures using Monte Carlo techniques. To accelerate the convergence of the Monte Carlo procedures, gradients are calculated that take into account the direction and magnitude of atom position displacements. The publication does not indicate a possible application of this method for the targeted calculation of saddle points.

[0008] There is therefore a need for a method for calculating transition states that allows the molecular geometry of a chemical reaction transition state to be approximated using a simple procedure, particularly a computer-implemented one. Specifically, there is a need for a method that can determine transition states without having to first calculate a potential energy surface. Currently, methods are used that are computationally expensive and less accurate. In particular, the use of methods that involve calculating second derivatives of energy with respect to atomic coordinates, such as Newton-Rapson or pseudo-Newton-Rapson methods, should be avoided as much as possible. These either yield poor success rates in locating transition states or are prohibitively resource-intensive, especially for large molecules.This way, the utilization of resources such as processors and storage media can be reduced.

[0009] The object of the present invention is to provide a computer-implemented method for calculating the geometry of a transition state using an easily applicable, and in particular a computer-implemented, method with the aid of a quantum chemical technique. Preferably, a quantum chemical method that requires calculating the second derivative of the energy with respect to the nuclear coordinates of the molecule under consideration in order to calculate the transition state should not be used. In particular, the molecular geometry for a transition state of a chemical reaction should be determined without first calculating the potential energy surface of the chemical reaction. Specifically, a computer-implemented method for calculating the transition state for molecules with preferably more than 100 atoms should be provided.

[0010] This task was solved by a computer-implemented method for calculating transition states of a chemical reaction, comprising the steps A. Generating a starting geometry A1 Provision of a three-dimensional representation of at least one molecule in its energetic ground state, A2 Selection of at least one bond of the at least one molecule and selection of a bond length, wherein the selected length does not correspond to the length of the bond in the energetic ground state of the molecule, so that a starting geometry for the chemical reaction is obtained, A3 Three-dimensional representation of the starting geometry in Cartesian and / or internal coordinates, B Determining an optimized starting geometryB1 Definition of a function space which includes the at least one bond from step A2 and the atoms connected by this bond, B2 Geometry optimization of the function space selected in step B1 using a quantum chemical method and with the boundary condition that the length of the at least one bond selected in step A2 is kept constant, so that an optimized initial geometry is obtained, B3 Determination of the gradient norm B3 for the optimized initial geometry, wherein the gradient norm is obtained by the first derivative of a function E = f(x) of the quantum chemical method, with E = total energy of the optimized initial geometry and x = nuclear coordinates of the molecule in the optimized initial geometry, B4.1 if the gradient norm B3 ∇ 0 ≤ ∇ ≤ 0.03 E ha 0 -1<, then classification of the optimized initial geometry as a precursor for the transition state of the chemical reaction and continuation of the procedure with step D1, or B4.2 if the gradient norm B3 ∇ > 0.03 E ha 0 -1<, then determination of the precursor for the transition state of the chemical reaction starting from the optimized initial geometry by a procedure comprising the following steps: . C Determination of the precursor for the transition state of the chemical reactionC1 Variation of the optimized starting geometry using a Monte Carlo algorithm, wherein C1.1 at least one atom is randomly selected from the function space selected in step B1, C1.2 a vector for a displacement of the atom selected in step C1 is randomly selected, wherein the randomly selected magnitude of the vector is weighted with the gradient norm B3, C1.3 the atom selected in step C1.1 based on the vector from step C1.2 is deflected from the position of the atom in the optimized starting geometry, so that a precursor for a transition state of the chemical reaction is obtained, C2 Geometry optimization of the precursor for the transition state using the quantum chemical method and with the boundary condition that the at least one bond from step A2 has the length determined in step C3, C3 Determination of the gradient norm C3 for the precursor for the transition state from step C2, where the gradient norm is obtained by the first derivative of the function E = f(x) of the quantum chemical method and with E=total energy of the precursor for the transition state and x=nuclear coordinates of the molecule in the precursor for the transition state, C4.1 if the gradient norm C3 ∇ 0 ≤ ∇≤ 0.03 E ha 0 -1< then continuation of the procedure with step D1, or C4.2 if the gradient norm C3 ∇ > 0.03 E ha 0 -1< E ha 0 -1< then repeat steps C1 to C3 until a gradient norm C3 ∇ 0 ≤ ∇≤ 0.03 E ha 0 -1< is obtained, wherein (a) if steps C1 to C3 have been performed once, in step C1 the geometry of the precursor for the transition state is varied if the value of its gradient norm C3 is lower than the value of the gradient norm B3 of the optimized initial geometry, or (b) if steps C1 to C3 have been performed more than once, in step C1 the geometry of the optimized initial geometry or of that precursor for the transition state from the previous repetitions is varied which has the lowest value for the gradient norm C3 or B3 compared to all gradient norms C3 and B3 obtained so far, . D Determination of the transition stateD1 Variation of the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps for an atom within the function space defined in B1: D1.1 Selection of an atom from the function space selected in step B1, D1.2 Selection of a vector for a displacement of the atom selected in step D1.1, D1.3 Displacement of the atom selected in step D1.1 from its position in the precursor based on the vector from step D1.2, wherein the position is displaced once by a positive value of the magnitude of the vector and once by a negative value of the magnitude of the vector, such that when performing steps D1.1 to D1.2.3. Two displaced precursors are obtained, D2. Geometry optimization of the two displaced precursors from step D1 using the quantum chemical method under the boundary condition that the bond distances obtained in D1 are kept constant, so that two optimized precursors (i) and (ii) are obtained, D3. Calculation of the energy of the two optimized precursors (i) and (ii) from step D2 using the quantum chemical method, D4. Comparison of the energy value of the two optimized precursors with the value of the gradient norm C3 or B3 of the precursor used in step D1, D4.1. If the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are each smaller than the energy value C3 or B3 of the precursor used in step D1, then the precursor used in step D1 is classified as a transition state, D4.2.If the value of the energy of the optimized precursor (i) or the value of the energy of the optimized precursor (ii) is not less than the value of energy C3 or B3 of the precursor used in step D1, then repeat the procedure from step C1.

[0011] It was surprisingly found that the problem can be solved by varying different molecular geometries using a suitable Monte Carlo method and approximating a geometry for a transition state with the aid of a quality criterion. Furthermore, it was surprisingly found that the problem can be solved by using the gradient of the direct reaction path curve as the observable in the Monte Carlo method. This allows the functional space to be treated, which is intended to represent the molecular geometry at the transition state of the chemical reaction, to be reduced to such an extent that the calculation of saddle points is made possible without first calculating a potential energy surface or manually searching for molecular geometries. It was also surprisingly found that the method according to the invention makes it possible to calculate saddle points in high-dimensional functional spaces without using Newton-Raphson-based methods.Instead of calculating second derivatives of the energy with respect to the nuclear coordinates, the region around the saddle point is verified by infinitesimal displacements and subsequent geometry optimization. The displacement along the bond dissociation must result in a decrease in the total energy. In this way, the computationally intensive calculation of second derivatives of the energy with respect to the nuclear coordinates, as required in Newton-Raphson-based methods, can be completely avoided. With current computer technology, the inventive method can calculate transition states for molecules with more than 100 atoms much more quickly and efficiently, primarily due to the reduction in the personnel effort required for corresponding conventional processes. This also saves computer resources.

[0012] In Step AIn the process according to the invention, a starting geometry is first generated by providing, in step A1, a three-dimensional representation of at least one molecule in its energetic ground state. Then, in step A2, a bond of the molecule is selected, and a bond length that differs from the length of the bond in the energetic ground state is chosen, so that a starting geometry is obtained. The selected bonds are preferably those bonds that are formed or broken in the chemical reaction under consideration. The bond length that differs from the length of the bond in the energetic ground state is 10 to 90%, preferably 20% to 40%, greater than the bond in the energetic ground state.

[0013] Preferably, the at least one molecule from step A1 has a size of more than 100 atoms, more preferably more than 80 atoms, more preferably more than 60 atoms and / or the length of the molecule in step A1 is greater than 100 atoms.A2 selected bond at most 230 pm, preferably at most 200 pm, more preferably at most 180 pm, more preferably 150 pm.

[0014] Preferably, step A is performed by a user who enters the three-dimensional representation of a molecule in its energetic ground state in step A1, as well as the selection of a bond and the length of the bond in step A2 and the representation of the starting geometry in step A3 into an input mask for the computer-implemented procedure.

[0015] In a further preferred embodiment of the method according to the invention, in step A1 at least two molecules I and II provided and in step A2Alternatively or in addition to the at least one bond, at least one distance between at least one atom from molecule I and at least one atom from molecule II, as well as the length of the at least one distance, can be selected, wherein the length of the distance is in particular at most 230 pm, preferably at most 200 pm, more preferably at most 180 pm, and more preferably 150 pm. If the process is carried out with at least two molecules I and II and the length of the distance between atoms of the different molecules is selected, the transition state of a synthesis reaction can preferably be calculated using the process.Preferably, molecule I and molecule II have a size of 2 to 1000 atoms; more preferably, molecule I and molecule II have a size of 2 to 800 atoms; even more preferably, molecule I and molecule II have a size of 2 to 600 atoms. Preferably, the sum of the atoms in molecule I and molecule II is more than 100 atoms.

[0016] Preferably, molecule I is a catalyst for the chemical reaction, particularly for a polymer synthesis, and molecule II is a reactant of the chemical reaction. In this embodiment, the polymer synthesis is preferably a polyurethane synthesis. The chemical reaction in this embodiment also preferably includes syntheses of monomers for polymerization reactions, industrially required basic chemicals, additives, surfactants, and pharmacological agents. In particular, the chemical reaction is a synthesis for basic chemicals obtained with catalysts or reactants for chemical syntheses. Additives are generally understood to be additives for plastics such as plasticizers, antioxidants, and strengthening agents, as well as fuel additives, in the synthesis of which catalysts are used.

[0017] In step A3, the starting geometry selected in step A2 is represented in Cartesian and / or internal coordinates. Internal coordinates describe the spatial arrangement of the atoms relative to each other using bond lengths, bond angles, and torsion angles.

[0018] In Step BIn the process according to the invention, an optimized starting geometry is determined. For this purpose, a functional space is first defined in step B1. The functional space comprises the spatial coordinates of selected atoms, wherein the spatial coordinates span a subspace in the vector space of all atomic coordinates contained in the molecule. The selected atoms for the functional space are a set of atoms that are involved in a bond dissociation or, preferably, in a synthesis reaction. Furthermore, the functional space includes the at least one bond from step A2. In the preferred embodiment with at least two molecules I and II, the functional space includes the distance between at least one atom from molecule I and at least one atom from molecule II.

[0019] In the following step B2, the initial geometry is subjected to geometry optimization using a quantum chemical method with the constraint that the length of the at least one bond selected in step A2 is kept constant, so that an optimized initial geometry is obtained. The geometry optimization encompasses all atoms of the molecule selected as the initial geometry. In the preferred embodiment with at least two molecules I and II, the distance between at least one atom from molecule I and at least one atom from molecule II is kept constant during the geometry optimization, so that an optimized initial geometry is obtained.

[0020] In boundary-condition geometry optimization, the total energy of the molecule is minimized as a function of the nuclear coordinates of the atoms contained in the molecule using a quantum chemical method. To obtain a local energy minimum, the energy is minimized along gradients (e.g., steepest descent), minimizing the energy as far as the boundary condition allows.

[0021] In step B3, the gradient norm B3 for the previously obtained optimized initial geometry is determined. The gradient norm is obtained by taking the first derivative of a function E = f(x) using the quantum chemical method, where E = total energy of the optimized initial geometry and x = nuclear coordinates of the molecule in the optimized initial geometry. The same quantum chemical method is used in step B3 as in step B2. The Euclidean norm of this vector is the gradient norm. In other words, the gradient vector of the energy is calculated. The gradient vector spans the same vector space as the molecule. Each component of the vector consists of the partial derivative of the energy in the xi coordinates. ∂ ∂ x i E x ) and extends in the direction of the unit vector of the xi coordinates. Then the (Euclidean) norm of this vector is determined.

[0022] The further continuation of the procedure depends on the magnitude of the obtained gradient norm B3. If the gradient norm B3 ∇ 0 ≤ ∇ ≤ 0.03 E ha 0 -1<, then the optimized starting geometry can be classified as a precursor to the transition state of the chemical reaction, and step C of the procedure can be omitted, continuing with step D1. If the gradient norm B3 ∇ > 0.03 E ha 0 -1<, then step C of the procedure is carried out, and a precursor to the transition state of the chemical reaction is determined, starting from the optimized starting geometry. Here, E h represents the Hartree energy, where 1 E h = 4.3597 × 10⁻¹⁸ < J, and a 0 represents the Bohr radius, where 1 a 0 = 5.29 × 10⁻¹¹ < m.

[0023] In Step CThe precursor to the transition state of the chemical reaction is determined. For this purpose, the optimized starting geometry is varied using a Monte Carlo algorithm by randomly generating displacements of atoms in an ensemble consisting of a molecule or, preferably, a geometry of at least two molecules I and II.

[0024] Monte Carlo algorithms or methods are simulation techniques that solve mathematical problems that are difficult or impossible to solve analytically using numerical approximations. They describe the most probable outcome of an experiment through a large number of randomly arranged individual experiments.

[0025] In the Monte Carlo algorithm applied in step C according to the invention, randomly generated displacements of atoms in an ensemble consisting of a molecule or a geometry of at least two molecules I and II are performed, and the change in an observable is observed. This observable is a gradient norm. The method according to the invention varies only a subspace that is significantly lower dimensional than the entire functional space of the ensemble and considers the change in the observable of the entire ensemble as a function of the reduced functional space.

[0026] In step C1.1, at least one atom is selected from the function space chosen in step B1. This is done using a random number Z1. The direction of the displacement of the atom selected by Z1, or the direction of the displacement vector, is selected in step C1.2 by another random number Z2. The direction is preferably defined by selecting, in the preferred step C1.2a, the position of an atom other than the one selected in step C1.1 from the reduced function space, and then, in the preferred step C1.2b, selecting the direction of the displacement, where the position of the atom selected in step C1.2a determines the direction of the vector. The amplitude of the displacement is preferably determined by a third random number Z3 in the preferred step C1.2c.

[0027] In a preferred embodiment of the method according to the invention, step C1.2 comprises the following further steps: C1.2a Determination of another atom from the functional space selected in step B1 that does not match the atom selected in step C1.1, C1.2b Selection of the direction of the vector, wherein the position of the atom selected in step C1.2.a determines the direction of the vector, C1.2.c random selection of the vector length, where the value for the vector length can take positive or negative values.

[0028] The weighting of the randomly selected magnitude of the vector in step C1.2 is preferably carried out by multiplying the numerical value of the randomly selected magnitude of the vector by the numerical value of the gradient norm B3.

[0029] Because the position of the atom selected in step C1.2 determines the direction of the vector, the functional space is restricted as much as possible, and this approach also leads to the primary variation of bond lengths that have lengths very likely to be actually achieved during a reaction.

[0030] In step C1.3, the atom selected in step C.1.1 is deflected from its position in the optimized starting geometry using the vector from step C1.2, so that a precursor for the transition state of the chemical reaction is obtained.

[0031] The resulting precursor for the transition state undergoes geometry optimization in step C2 using a quantum chemical method, with the constraint that at least one bond from step A2 has the length determined in step C1.3. The same quantum chemical method is used in step C2 as in steps B2 and B3. Then, in step C3, the gradient norm C3 for the transition state precursor from step C2 is determined. This gradient norm is obtained by taking the first derivative of the function E = f(x) using a quantum chemical method, where E = total energy of the transition state precursor and x = nuclear coordinates of the molecule in the transition state precursor. The same quantum chemical method is used in step C3 as in steps B2, B3, and C2.

[0032] The further continuation of the procedure depends on the magnitude of the obtained gradient norm C3. If the gradient norm C3 ∇ 0 ≤ ∇ ≤ 0.03 E ha 0 -1<, then step D1 of the procedure can be carried out with the preliminary stage for the transition state. Here, E h represents the Hartree energy, where 1 E h = 4.3597 · 10 -18 < J, and a 0 represents the Bohr radius, where 1 a 0 = 5.29 · 10 -11 < m.

[0033] If the gradient norm C3 ∇ > 0.03 E ha 0 -1<, then steps C1 to C3 are repeated in step 4.2 until a gradient norm C3 ∇ 0 ≤ ∇ ≤ 0.03 E ha 0 -1< is obtained. Repeating steps C1 to C3 constitutes an iterative procedure aimed at minimizing the gradient norm. Therefore, the starting point for each iteration should be a molecular geometry that already exhibits the lowest possible gradient norm. Thus, when repeating steps C1 to C3, not only can the optimized starting geometry be varied in step C1, but also a precursor for the transition state, provided that the value of its gradient norm C3 is smaller than that of the optimized starting geometry. Preferably, the optimized starting geometry and the obtained precursor(s) for the transition state, as well as the values ​​of the respective gradient norms C3, are stored.

[0034] If steps C1 to C3 have been performed once, the molecular geometry with the lowest gradient norm can be selected from two options for the repetition: either the optimized starting geometry or the transition state precursor obtained in the first run. In step C1, the geometry of the transition state precursor is varied if its gradient norm C3 is lower than the gradient norm B3 of the optimized starting geometry.

[0035] If steps C1 to C3 have already been performed, the molecular geometry with the lowest gradient norm can be selected from more than two possible geometries for the repetition. This can be either the optimized starting geometry or the (more than one) precursor for the transition state obtained in the repetitions. If steps C1 to C3 have been performed more than once, in step C1 the geometry of the optimized starting geometry or the precursor for the transition state from the previous repetitions is varied to determine which has the lowest gradient norm value for C3 or B3 compared to all gradient norms C3 and B3 obtained so far.

[0036] The preferred method is in step C4.1 the gradient norm C3 ≤ 0.02 E ha 0 -1< , preferred C3 ≤ 0.01 E ha 0 -1< , and step C4.2is carried out until a gradient norm C3 ≤ 0.02 E ha 0 -1< , preferably C3 ≤ 0.01 E ha 0 -1< , is obtained.

[0037] The preferred step C4.2 at most 50 times, preferably at most 40 times, more preferably at most 30 times, even more preferably at most 10 times, and in particular at most 3 times. Preferably, when performing step C4.2 when repeating step C1 A different atom is selected than in the previous execution of the procedure.

[0038] An advantage of the method according to the invention is that, when varying the process using a Monte Carlo algorithm, only the atomic coordinates of the selected functional space are spanned—that is, the subspace of the atoms involved in the bond dissociation or, preferably, synthesis reaction under consideration—within the vector space of all atomic coordinates contained in the molecule or molecular ensemble. This means that the Monte Carlo algorithm according to the invention operates only in this subspace, since its functions are defined only within it. Thus, the subspace of coordinates involved in the dissociation or, preferably, synthesis reaction constitutes the functional space of the Monte Carlo algorithm. While the calculation of the energies and the gradient vectors (or their norm) do depend on the total coordinates in the molecule, the Monte Carlo algorithm according to the invention considers these only as a function of the coordinates of the subspace.To ensure that the function value, the gradient norm to be minimized, remains unique in this analysis, the entire molecular structure is relaxed by a geometry optimization with boundary condition(s) before each consideration of the function value. The boundary condition(s) are the bond distances generated by the Monte Carlo algorithm.

[0039] If the gradient norm is sufficiently minimized, the property of negative curvature in the region of the obtained stationary point is addressed by infinitesimal displacements and subsequent geometry optimization. Step D verified. The displacement along the bond dissociation must result in a decrease in the total energy. A further advantage of the present invention is that the complex calculation of the second derivatives of the energy with respect to the nuclear coordinates can be completely avoided in this way.

[0040] The preferred method is to proceed in step D3The energy of the two optimized precursors (i) and (II) is represented in the unit E ha 0 -1<.

[0041] A preliminary stage is performed in step D4.1 A step is classified as a transition state if both the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are less than the energy value C3 or B3 of the precursor used in step D1. If either energy value of the optimized precursor (i) or (ii) is greater, or if both energy values ​​of the optimized precursors (i) and (ii) are greater than the energy value C3 or B3 of the precursor used in step D1, the process is repeated from step C. Preferably, the process is repeated from step C at most 10 times, more preferably at most 3 times.

[0042] In the steps B2, B3, C2, C3, D2 and D3The same quantum chemical method is used in each case. The quantum chemical method consisting of steps is preferred. B2, B3, C2, C3, D2 and D3 A semi-empirical method, a density functional theory method, or an approximation of the Schrödinger equation is preferred; in particular, density functional theory methods are preferred, such as the TPSS density functional with a def2-SVP basis set, as implemented by default in the Turbomole software package. In a preferred embodiment, the quantum mechanical calculations are performed using the Turbomole software package. Preferably, a computer with 16 core processors with a clock frequency of 3.20 GHz and 25 MB of cache memory with 128 GB of DDR4 2400 rg ECC RAM is used for the calculation.

[0043] Preferably, the chemical reaction is a synthesis selected from the group consisting of polymer syntheses, in particular polyurethane syntheses, syntheses of monomers for polymerization reactions, industrially required basic chemicals, additives, surfactants, and pharmacological agents. In particular, the chemical reaction is a synthesis for basic chemicals obtained with catalysts or starting materials for chemical syntheses. Additives are generally understood to be additives for plastics such as plasticizers, antioxidants, and strengthening agents, as well as fuel additives, in the synthesis of which catalysts are used.

[0044] In the preferred embodiment of the method, at least two molecules of I and II Those provided can preferably be those listed under the letters AWAY, and CThe steps of the procedure are repeated, with each repetition comparing the previous execution of the procedure to the previous one. Molecule I is changed or a different molecule than Molecule I is provided, and Molecule II is not changed and no different molecule than Molecule II is provided, and the additional step D0 is performed: D0 Comparison of the gradient norm C3 obtained in the repetitions for the different precursors for the transition state and selection of the precursor for the transition state with the lowest gradient norm C3 and performance of step D1 and / or D2 with the selected precursor for the transition state.

[0045] In this previously described preferred embodiment of the method, the gradient norm C3 is first calculated for different combinations of molecules and the results are stored. Then, in a preferred step D0, the obtained values ​​for the gradient norm C3 can be compared and the combination of molecules with the lowest gradient norm C3 can be selected. This preferred embodiment of the method thus enables the direct comparison of different combinations of molecules.

[0046] Another object of the invention is a data processing system comprising means for carrying out a method according to the invention.

[0047] Furthermore, the invention includes a computer program and a computer-readable storage medium, comprising instructions which, when the program is executed by a computer, cause it to perform the following steps of a method: A. Generating a starting geometry A1 Provision of a three-dimensional representation of at least one molecule in its energetic ground state, A2 Selection of at least one bond of the at least one molecule and selection of a bond length, wherein the selected length does not correspond to the length of the bond in the energetic ground state of the molecule, so that a starting geometry for the chemical reaction is obtained, A3 Three-dimensional representation of the starting geometry in Cartesian and / or internal coordinates, B Determining an optimized starting geometryB1 Definition of a function space which includes the at least one bond from step A2 and the atoms connected by this bond, B2 Geometry optimization of the function space selected in step B1 using a quantum chemical method and with the boundary condition that the length of the at least one bond selected in step A2 is kept constant, so that an optimized initial geometry is obtained, B3 Determination of the gradient norm B3 for the optimized initial geometry, wherein the gradient norm is obtained by the first derivative of a function E = f(x) of the quantum chemical method, with E = total energy of the optimized initial geometry and x = nuclear coordinates of the molecule in the optimized initial geometry, B4.1 if the gradient norm B3 ∇ 0 ≤ ∇ ≤ 0.03 E ha 0 -1<, then classification of the optimized initial geometry as a precursor for the transition state of the chemical reaction and continuation of the procedure with step D1, or B4.2 if the gradient norm B3 ∇ > 0.03 E ha 0 -1<, then determination of the precursor for the transition state of the chemical reaction starting from the optimized initial geometry by a procedure comprising the following steps: . C Determination of the precursor for the transition state of the chemical reactionC1 Variation of the optimized starting geometry using a Monte Carlo algorithm, wherein C1.1 at least one atom is randomly selected from the function space selected in step B1, C1.2 a vector for a displacement of the atom selected in step C1 is randomly selected, wherein the randomly selected magnitude of the vector is weighted with the gradient norm B3, C1.3 the atom selected in step C1.1 based on the vector from step C1.2 is deflected from the position of the atom in the optimized starting geometry, so that a precursor for a transition state of the chemical reaction is obtained, C2 Geometry optimization of the precursor for the transition state using the quantum chemical method and with the boundary condition that the at least one bond from step A2 has the length determined in step C3, C3 Determination of the gradient norm C3 for the precursor for the transition state from step C2, where the gradient norm is obtained by the first derivative of the function E = f(x) of the quantum chemical method and with E=total energy of the precursor for the transition state and x=nuclear coordinates of the molecule in the precursor for the transition state, C4.1 if the gradient norm C3 ∇ 0 ≤ ∇≤ 0.03 E ha 0 -1< then continuation of the procedure with step D1, or C4.2 if the gradient norm C3 ∇ > 0.03 E ha 0 -1< E ha 0 -1< then repeat steps C1 to C3 until a gradient norm C3 ∇ 0 ≤ ∇≤ 0.03 E ha 0 -1< is obtained, wherein (a) if steps C1 to C3 have been performed once, in step C1 the geometry of the precursor for the transition state is varied if the value of its gradient norm C3 is lower than the value of the gradient norm B3 of the optimized initial geometry, or (b) if steps C1 to C3 have been performed more than once, in step C1 the geometry of the optimized initial geometry or of that precursor for the transition state from the previous repetitions is varied which has the lowest value for the gradient norm C3 or B3 compared to all gradient norms C3 and B3 obtained so far, . D Determination of the transition stateD1 Variation of the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps for an atom within the function space defined in B1: D1.1 Selection of an atom from the function space selected in step B1, D1.2 Selection of a vector for a displacement of the atom selected in step D1.1, D1.3 Displacement of the atom selected in step D1.1 from its position in the precursor based on the vector from step D1.2, wherein the position is displaced once by a positive value of the magnitude of the vector and once by a negative value of the magnitude of the vector, such that when performing steps D1.1 to D1.2.3. Two deflected precursors are obtained, D2. Geometry optimization of the two deflected precursors from step D1 using the quantum chemical method under the boundary condition that the bond distances obtained in D1 are kept constant, so that two optimized precursors (i) and (ii) are obtained, D3. Calculation of the energy of the two optimized precursors (i) and (ii) from step D2 using the quantum chemical method, D4. Comparison of the energy value of the two optimized precursors with the energy value C3 or B3 of the precursor used in step D1, D4.1. If the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are each smaller than the energy value C3 or B3 of the precursor used in step D1, then the precursor used in step D1 is classified as a transition state, D4.2.If the value of the energy of the optimized precursor (i) or the value of the energy of the optimized precursor (ii) is not less than the value of energy C3 or B3 of the precursor used in step D1, then repeat the procedure from step C1.

[0048] Preferably, the computer program and / or the computer-readable storage medium includes instructions that, when the program is executed by a computer, cause it to perform steps B to D of the procedure.

[0049] Furthermore, the invention is directed to the use of the computer program or the computer-readable storage medium according to the invention for evaluating transition states of a chemical reaction, in particular a polymer synthesis.

[0050] The invention relates in particular to the following embodiments: In a first embodiment, the invention relates to a computer-implemented method for calculating transition states of a chemical reaction, comprising the steps A. Generating a starting geometry A1 Provision of a three-dimensional representation of at least one molecule in its energetic ground state, A2 Selection of at least one bond of the at least one molecule and selection of a bond length, wherein the selected length does not correspond to the length of the bond in the energetic ground state of the molecule, so that a starting geometry for the chemical reaction is obtained, A3 Three-dimensional representation of the starting geometry in Cartesian and / or internal coordinates, B Determining an optimized starting geometryB1 Definition of a function space which includes the at least one bond from step A2 and the atoms connected by this bond, B2 Geometry optimization of the function space selected in step B1 using a quantum chemical method and with the boundary condition that the length of the at least one bond selected in step A2 is kept constant, so that an optimized initial geometry is obtained, B3 Determination of the gradient norm B3 for the optimized initial geometry, wherein the gradient norm is obtained by the first derivative of a function E = f(x) of the quantum chemical method, with E = total energy of the optimized initial geometry and x = nuclear coordinates of the molecule in the optimized initial geometry, B4.1 if the gradient norm B3 ∇ 0 ≤ ∇ ≤ 0.03 E ha 0 -1<, then classification of the optimized initial geometry as a precursor for the transition state of the chemical reaction and continuation of the procedure with step D1, or B4.2 if the gradient norm B3 ∇ > 0.03 E ha 0 -1<, then determination of the precursor for the transition state of the chemical reaction starting from the optimized initial geometry by a procedure comprising the following steps: . C Determination of the precursor for the transition state of the chemical reactionC1 Variation of the optimized starting geometry using a Monte Carlo algorithm, wherein C1.1 at least one atom is randomly selected from the function space selected in step B1, C1.2 a vector for a displacement of the atom selected in step C1 is randomly selected, wherein the randomly selected magnitude of the vector is weighted with the gradient norm B3, C1.3 the atom selected in step C1.1 based on the vector from step C1.2 is deflected from the position of the atom in the optimized starting geometry, so that a precursor for a transition state of the chemical reaction is obtained, C2 Geometry optimization of the precursor for the transition state using the quantum chemical method and with the boundary condition that the at least one bond from step A2 has the length determined in step C3, C3 Determination of the gradient norm C3 for the precursor for the transition state from step C2, where the gradient norm is obtained by the first derivative of the function E = f(x) of the quantum chemical method and with E=total energy of the precursor for the transition state and x=nuclear coordinates of the molecule in the precursor for the transition state, C4.1 if the gradient norm C3 ∇ 0 ≤ ∇≤ 0.03 E ha 0 -1< then continuation of the procedure with step D1, or C4.2 if the gradient norm C3 ∇ > 0.03 E ha 0 -1< E ha 0 -1< then repeat steps C1 to C3 until a gradient norm C3 ∇ 0 ≤ ∇≤ 0.03 E ha 0 -1< is obtained, wherein (a) if steps C1 to C3 have been performed once, in step C1 the geometry of the precursor for the transition state is varied if the value of its gradient norm C3 is lower than the value of the gradient norm B3 of the optimized initial geometry, or (b) if steps C1 to C3 have been performed more than once, in step C1 the geometry of the optimized initial geometry or of that precursor for the transition state from the previous repetitions is varied which has the lowest value for the gradient norm C3 or B3 compared to all gradient norms C3 and B3 obtained so far, . D Determination of the transition stateD1 Variation of the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps for an atom within the function space defined in B1: D1.1 Selection of an atom from the function space selected in step B1, D1.2 Selection of a vector for a displacement of the atom selected in step D1.1, D1.3 Displacement of the atom selected in step D1.1 from its position in the precursor based on the vector from step D1.2, wherein the position is displaced once by a positive value of the magnitude of the vector and once by a negative value of the magnitude of the vector, such that when performing steps D1.1 to D1.2.3. Two deflected precursors are obtained, D2. Geometry optimization of the two deflected precursors from step D1 using the quantum chemical method under the boundary condition that the bond distances obtained in D1 are kept constant, so that two optimized precursors (i) and (ii) are obtained, D3. Calculation of the energy of the two optimized precursors (i) and (ii) from step D2 using the quantum chemical method, D4. Comparison of the energy value of the two optimized precursors with the energy value C3 or B3 of the precursor used in step D1, D4.1. If the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are each smaller than the energy value C3 or B3 of the precursor used in step D1, then the precursor used in step D1 is classified as a transition state, D4.2.If the value of the energy of the optimized precursor (i) or the value of the energy of the optimized precursor (ii) is not less than the value of energy C3 or B3 of the precursor used in step D1, then repeat the procedure from step C1.

[0051] In a second embodiment, the invention relates to a method according to embodiment 1, characterized in that the at least one molecule from step A1 has a size of more than 100 atoms and / or that the length of the molecule in step A1 is greater than 100 atoms. A2 The selected bond is at most 230 pm.

[0052] In a third embodiment, the invention relates to a method according to one of embodiments 1 or 2, characterized in that step C1.2 the following steps include: C1.2a Determination of another atom from the functional space selected in step B1 that does not match the atom selected in step C1.1, C1.2b Selection of the direction of the vector, wherein the position of the atom selected in step C1.2.a determines the direction of the vector, C1.2.c random selection of the vector length, where the value for the vector length can take positive or negative values.

[0053] In a fourth embodiment, the invention relates to a method according to one of the preceding embodiments, characterized in that the weighting of the randomly selected amount of the vector in step C1.2 by multiplying the numerical value of the randomly selected magnitude of the vector with the numerical value of the gradient norm B3.

[0054] In a fifth embodiment, the invention relates to a method according to one of the preceding embodiments, characterized in that in step C4.1 the gradient norm C3 ≤ 0.02 E ha 0 -1< , preferably ≤ 0.01 E ha 0 -1< , is and step C4.2 is carried out until a gradient norm C3 ≤ 0.02 E ha 0 -1< , preferably ≤ 0.01 E ha 0 -1< , is obtained.

[0055] In a sixth embodiment, the invention relates to a method according to one of the preceding embodiments, characterized in that step C4.2is repeated at most 50 times, preferably at most 30 times, and in particular at most 3 times.

[0056] In a seventh embodiment, the invention relates to a method according to one of the preceding embodiments, characterized in that during the execution of step C4.2 when repeating step C1 A different atom can be selected than in the previous execution of the procedure.

[0057] In an eighth embodiment, the invention relates to a method according to one of the preceding embodiments, characterized in that the quantum chemical method consists of steps B2, B3, C2, C3, D2 and D3 a semi-empirical method, density-functional-theoretical method or an approximation of the Schrödinger equation, in particular the quantum chemical method consisting of steps B2, B3, C2, C3, D2 and D3 a density functional theory method.

[0058] In a ninth embodiment, the invention relates to a method according to one of the preceding embodiments, characterized in that the chemical reaction is a synthesis selected from the group consisting of polymer syntheses, in particular polyurethane syntheses, syntheses of monomers for polymerization reactions, industrially required basic chemicals, platform chemicals, additives, surfactants and pharmacological agents.

[0059] In a tenth embodiment, the invention relates to a method according to one of the preceding embodiments, characterized in that in step A1 at least two molecules I and II are provided and in step A2Alternatively or in addition to the at least one bond, at least one distance between at least one atom from molecule I and at least one atom from molecule II, as well as the length of the at least one distance, may be selected, wherein the length of the distance is in particular at most 230 pm .

[0060] In an eleventh embodiment, the invention relates to a method according to embodiment 10, characterized in that the elements listed under letters AWAY and C The steps of the procedure are repeated, with each repetition comparing the previous execution of the procedure to the previous one. Molecule I is changed or a different molecule than Molecule I is provided, and Molecule II is not changed and no other molecule than Molecule II is provided, and encompassing the additional step D0Comparison of the gradient norm C3 obtained in the repetitions for the different precursors for the transition state and selection of the precursor for the transition state with the lowest gradient norm C3 and performance of step D1 and / or D2 with the selected precursor for the transition state.

[0061] In a twelfth embodiment, the invention relates to a method according to one of embodiments 10 or 11, characterized in that molecule I is a catalyst for the chemical reaction, in particular for a polymer synthesis, and molecule II is a reactant of the chemical reaction.

[0062] In a thirteenth embodiment, the invention relates to a method according to one of embodiments 10 to 13, characterized in that molecule I has a size of 2 to 1000 atoms and molecule II has a size of 2 to 1000 atoms, preferably the sum of the atoms from molecule I and from molecule II should be more than 100 atoms.

[0063] In a fourteenth embodiment, the invention relates to a data processing system comprising means for carrying out a method comprising the steps A. Generating a starting geometryA1 Provision of a three-dimensional representation of at least one molecule in its energetic ground state, A2 Selection of at least one bond of the at least one molecule and selection of a bond length, wherein the selected length does not correspond to the length of the bond in the energetic ground state of the molecule, so that a starting geometry for the chemical reaction is obtained, A3 Three-dimensional representation of the starting geometry in Cartesian and / or internal coordinates, B Determining an optimized starting geometryB1 Definition of a function space which includes the at least one bond from step A2 and the atoms connected by this bond, B2 Geometry optimization of the function space selected in step B1 using a quantum chemical method and with the boundary condition that the length of the at least one bond selected in step A2 is kept constant, so that an optimized initial geometry is obtained, B3 Determination of the gradient norm B3 for the optimized initial geometry, wherein the gradient norm is obtained by the first derivative of a function E = f(x) of the quantum chemical method, with E = total energy of the optimized initial geometry and x = nuclear coordinates of the molecule in the optimized initial geometry, B4.1 if the gradient norm B3 ∇ 0 ≤ ∇ ≤ 0.03 E ha 0 -1<, then classification of the optimized initial geometry as a precursor for the transition state of the chemical reaction and continuation of the procedure with step D1, or B4.2 if the gradient norm B3 ∇ > 0.03 E ha 0 -1<, then determination of the precursor for the transition state of the chemical reaction starting from the optimized initial geometry by a procedure comprising the following steps: . C Determination of the precursor for the transition state of the chemical reactionC1 Variation of the optimized starting geometry using a Monte Carlo algorithm, wherein C1.1 at least one atom is randomly selected from the function space selected in step B1, C1.2 a vector for a displacement of the atom selected in step C1 is randomly selected, wherein the randomly selected magnitude of the vector is weighted with the gradient norm B3, C1.3 the atom selected in step C1.1 based on the vector from step C1.2 is deflected from the position of the atom in the optimized starting geometry, so that a precursor for a transition state of the chemical reaction is obtained, C2 Geometry optimization of the precursor for the transition state using the quantum chemical method and with the boundary condition that the at least one bond from step A2 has the length determined in step C3, C3 Determination of the gradient norm C3 for the precursor for the transition state from step C2, where the gradient norm is obtained by the first derivative of the function E = f(x) of the quantum chemical method and with E=total energy of the precursor for the transition state and x=nuclear coordinates of the molecule in the precursor for the transition state, C4.1 if the gradient norm C3 ∇ 0 ≤ ∇≤ 0.03 E ha 0 -1< then continuation of the procedure with step D1, or C4.2 if the gradient norm C3 ∇ > 0.03 E ha 0 -1< E ha 0 -1< then repeat steps C1 to C3 until a gradient norm C3 ∇ 0 ≤ ∇≤ 0.03 E ha 0 -1< is obtained, wherein (a) if steps C1 to C3 have been performed once, in step C1 the geometry of the precursor for the transition state is varied if the value of its gradient norm C3 is lower than the value of the gradient norm B3 of the optimized initial geometry, or (b) if steps C1 to C3 have been performed more than once, in step C1 the geometry of the optimized initial geometry or of that precursor for the transition state from the previous repetitions is varied which has the lowest value for the gradient norm C3 or B3 compared to all gradient norms C3 and B3 obtained so far, . D Determination of the transition stateD1 Variation of the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps for an atom within the function space defined in B1: D1.1 Selection of an atom from the function space selected in step B1, D1.2 Selection of a vector for a displacement of the atom selected in step D1.1, D1.3 Displacement of the atom selected in step D1.1 from its position in the precursor based on the vector from step D1.2, wherein the position is displaced once by a positive value of the magnitude of the vector and once by a negative value of the magnitude of the vector, such that when performing steps D1.1 to D1.2.3. Two deflected precursors are obtained, D2. Geometry optimization of the two deflected precursors from step D1 using the quantum chemical method under the boundary condition that the bond distances obtained in D1 are kept constant, so that two optimized precursors (i) and (ii) are obtained, D3. Calculation of the energy of the two optimized precursors (i) and (ii) from step D2 using the quantum chemical method, D4. Comparison of the energy value of the two optimized precursors with the energy value C3 or B3 of the precursor used in step D1, D4.1. If the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are each smaller than the energy value C3 or B3 of the precursor used in step D1, then the precursor used in step D1 is classified as a transition state, D4.2.If the value of the energy of the optimized precursor (i) or the value of the energy of the optimized precursor (ii) is not less than the value of energy C3 or B3 of the precursor used in step D1, then repeat the procedure from step C1.

[0064] In a fifteenth embodiment, the invention relates to a computer program comprising instructions which, when the program is executed by a computer, cause it to perform the following steps of a method. A. Generating a starting geometryA1 Provision of a three-dimensional representation of at least one molecule in its energetic ground state, A2 Selection of at least one bond of the at least one molecule and selection of a bond length, wherein the selected length does not correspond to the length of the bond in the energetic ground state of the molecule, so that a starting geometry for the chemical reaction is obtained, A3 Three-dimensional representation of the starting geometry in Cartesian and / or internal coordinates, B Determining an optimized starting geometryB1 Definition of a function space which includes the at least one bond from step A2 and the atoms connected by this bond, B2 Geometry optimization of the function space selected in step B1 using a quantum chemical method and with the boundary condition that the length of the at least one bond selected in step A2 is kept constant, so that an optimized initial geometry is obtained, B3 Determination of the gradient norm B3 for the optimized initial geometry, wherein the gradient norm is obtained by the first derivative of a function E = f(x) of the quantum chemical method, with E = total energy of the optimized initial geometry and x = nuclear coordinates of the molecule in the optimized initial geometry, B4.1 if the gradient norm B3 ∇ 0 ≤ ∇ ≤ 0.03 E ha 0 -1<, then classification of the optimized initial geometry as a precursor for the transition state of the chemical reaction and continuation of the procedure with step D1, or B4.2 if the gradient norm B3 ∇ > 0.03 E ha 0 -1<, then determination of the precursor for the transition state of the chemical reaction starting from the optimized initial geometry by a procedure comprising the following steps: . C Determination of the precursor for the transition state of the chemical reactionC1 Variation of the optimized starting geometry using a Monte Carlo algorithm, wherein C1.1 at least one atom is randomly selected from the function space selected in step B1, C1.2 a vector for a displacement of the atom selected in step C1 is randomly selected, wherein the randomly selected magnitude of the vector is weighted with the gradient norm B3, C1.3 the atom selected in step C1.1 based on the vector from step C1.2 is deflected from the position of the atom in the optimized starting geometry, so that a precursor for a transition state of the chemical reaction is obtained, C2 Geometry optimization of the precursor for the transition state using the quantum chemical method and with the boundary condition that the at least one bond from step A2 has the length determined in step C3, C3 Determination of the gradient norm C3 for the precursor for the transition state from step C2, where the gradient norm is obtained by the first derivative of the function E = f(x) of the quantum chemical method and with E=total energy of the precursor for the transition state and x=nuclear coordinates of the molecule in the precursor for the transition state, C4.1 if the gradient norm C3 ∇ 0 ≤ ∇≤ 0.03 E ha 0 -1< then continuation of the procedure with step D1, or C4.2 if the gradient norm C3 ∇ > 0.03 E ha 0 -1< E ha 0 -1< then repeat steps C1 to C3 until a gradient norm C3 ∇ 0 ≤ ∇≤ 0.03 E ha 0 -1< is obtained, wherein (a) if steps C1 to C3 have been performed once, in step C1 the geometry of the precursor for the transition state is varied if the value of its gradient norm C3 is lower than the value of the gradient norm B3 of the optimized initial geometry, or (b) if steps C1 to C3 have been performed more than once, in step C1 the geometry of the optimized initial geometry or of that precursor for the transition state from the previous repetitions is varied which has the lowest value for the gradient norm C3 or B3 compared to all gradient norms C3 and B3 obtained so far, . D Determination of the transition stateD1 Variation of the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps for an atom within the function space defined in B1: D1.1 Selection of an atom from the function space selected in step B1, D1.2 Selection of a vector for a displacement of the atom selected in step D1.1, D1.3 Displacement of the atom selected in step D1.1 from its position in the precursor based on the vector from step D1.2, wherein the position is displaced once by a positive value of the magnitude of the vector and once by a negative value of the magnitude of the vector, such that when performing steps D1.1 to D1.2.3. Two deflected precursors are obtained, D2. Geometry optimization of the two deflected precursors from step D1 using the quantum chemical method under the boundary condition that the bond distances obtained in D1 are kept constant, so that two optimized precursors (i) and (ii) are obtained, D3. Calculation of the energy of the two optimized precursors (i) and (ii) from step D2 using the quantum chemical method, D4. Comparison of the energy value of the two optimized precursors with the energy value C3 or B3 of the precursor used in step D1, D4.1. If the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are each smaller than the energy value C3 or B3 of the precursor used in step D1, then the precursor used in step D1 is classified as a transition state, D4.2.If the value of the energy of the optimized precursor (i) or the value of the energy of the optimized precursor (ii) is not less than the value of energy C3 or B3 of the precursor used in step D1, then repeat the procedure from step C1.

[0065] In a sixteenth embodiment, the invention relates to a computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to perform the following steps of a method. A. Generating a starting geometryA1 Provision of a three-dimensional representation of at least one molecule in its energetic ground state, A2 Selection of at least one bond of the at least one molecule and selection of a bond length, wherein the selected length does not correspond to the length of the bond in the energetic ground state of the molecule, so that a starting geometry for the chemical reaction is obtained, A3 Three-dimensional representation of the starting geometry in Cartesian and / or internal coordinates, B Determining an optimized starting geometryB1 Definition of a function space which includes the at least one bond from step A2 and the atoms connected by this bond, B2 Geometry optimization of the function space selected in step B1 using a quantum chemical method and with the boundary condition that the length of the at least one bond selected in step A2 is kept constant, so that an optimized initial geometry is obtained, B3 Determination of the gradient norm B3 for the optimized initial geometry, wherein the gradient norm is obtained by the first derivative of a function E = f(x) of the quantum chemical method, with E = total energy of the optimized initial geometry and x = nuclear coordinates of the molecule in the optimized initial geometry, B4.1 if the gradient norm B3 ∇ 0 ≤ ∇ ≤ 0.03 E ha 0 -1<, then classification of the optimized initial geometry as a precursor for the transition state of the chemical reaction and continuation of the procedure with step D1, or B4.2 if the gradient norm B3 ∇ > 0.03 E ha 0 -1<, then determination of the precursor for the transition state of the chemical reaction starting from the optimized initial geometry by a procedure comprising the following steps: . C Determination of the precursor for the transition state of the chemical reactionC1 Variation of the optimized starting geometry using a Monte Carlo algorithm, wherein C1.1 at least one atom is randomly selected from the function space selected in step B1, C1.2 a vector for a displacement of the atom selected in step C1 is randomly selected, wherein the randomly selected magnitude of the vector is weighted with the gradient norm B3, C1.3 the atom selected in step C1.1 based on the vector from step C1.2 is deflected from the position of the atom in the optimized starting geometry, so that a precursor for a transition state of the chemical reaction is obtained, C2 Geometry optimization of the precursor for the transition state using the quantum chemical method and with the boundary condition that the at least one bond from step A2 has the length determined in step C3, C3 Determination of the gradient norm C3 for the precursor for the transition state from step C2, where the gradient norm is obtained by the first derivative of the function E = f(x) of the quantum chemical method and with E=total energy of the precursor for the transition state and x=nuclear coordinates of the molecule in the precursor for the transition state, C4.1 if the gradient norm C3 ∇ 0 ≤ ∇≤ 0.03 E ha 0 -1< then continuation of the procedure with step D1, or C4.2 if the gradient norm C3 ∇ > 0.03 E ha 0 -1< E ha 0 -1< then repeat steps C1 to C3 until a gradient norm C3 ∇ 0 ≤ ∇≤ 0.03 E ha 0 -1< is obtained, wherein (a) if steps C1 to C3 have been performed once, in step C1 the geometry of the precursor for the transition state is varied if the value of its gradient norm C3 is lower than the value of the gradient norm B3 of the optimized initial geometry, or (b) if steps C1 to C3 have been performed more than once, in step C1 the geometry of the optimized initial geometry or of that precursor for the transition state from the previous repetitions is varied which has the lowest value for the gradient norm C3 or B3 compared to all gradient norms C3 and B3 obtained so far, . D Determination of the transition stateD1 Variation of the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps for an atom within the function space defined in B1: D1.1 Selection of an atom from the function space selected in step B1, D1.2 Selection of a vector for a displacement of the atom selected in step D1.1, D1.3 Displacement of the atom selected in step D1.1 from its position in the precursor based on the vector from step D1.2, wherein the position is displaced once by a positive value of the magnitude of the vector and once by a negative value of the magnitude of the vector, such that when performing steps D1.1 to D1.2.3. Two deflected precursors are obtained, D2. Geometry optimization of the two deflected precursors from step D1 using the quantum chemical method under the boundary condition that the bond distances obtained in D1 are kept constant, so that two optimized precursors (i) and (ii) are obtained, D3. Calculation of the energy of the two optimized precursors (i) and (ii) from step D2 using the quantum chemical method, D4. Comparison of the energy value of the two optimized precursors with the energy value C3 or B3 of the precursor used in step D1, D4.1. If the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are each smaller than the energy value C3 or B3 of the precursor used in step D1, then the precursor used in step D1 is classified as a transition state, D4.2.If the value of the energy of the optimized precursor (i) or the value of the energy of the optimized precursor (ii) is not less than the value of energy C3 or B3 of the precursor used in step D1, then repeat the procedure from step C1.

[0066] In a seventeenth embodiment, the invention relates to the use of a computer program according to embodiment 15 or a computer-readable storage medium according to embodiment 16 for evaluating transition states of a chemical reaction, in particular a polymer synthesis.

[0067] In an eighteenth embodiment, the invention relates to methods according to one of the first to thirteenth embodiments, characterized in that information about the transition state determined according to step D.1 and / or the equilibrium state determined according to step D.2 is communicated to a user.

[0068] In a nineteenth embodiment, the invention relates to methods according to one of the first to thirteenth embodiments, characterized in that information about the transition state determined according to step D.1 and / or the equilibrium state determined according to step D.2 is received by a user.

[0069] In a twentieth embodiment, the invention relates to methods according to one of the ninth to thirteenth embodiments, characterized in that the molecule I is synthesized after step D.1 and / or after step D.2.

[0070] In a twenty-first embodiment, the invention relates to methods according to one of the ninth to thirteenth embodiments, characterized in that after step D.1 and / or after step D.2 a chemical reaction is carried out with the molecule I as a catalyst.

[0071] In a twenty-second embodiment, the invention relates to a process according to one of the ninth to thirteenth or twenty-first embodiments, characterized in that, after step D.1 and / or after step D.2, a chemical reaction is carried out with molecule II as a reactant.

[0072] The following examples are intended to illustrate the invention, without, however, being limited to them.

[0073] The activity of various catalysts for the reaction of a prepolymer containing terminal isocyanate groups with water was investigated. First, the activation energies for reaction with each catalyst were calculated using the method according to the invention. The calculated values ​​were then compared with the results of laboratory experiments of the previously calculated reactions. The reaction temperature above which the catalysts showed activity was used as a measure of their activity in the laboratory experiments. Whether the catalysts showed activity was determined in the laboratory experiment by the release of gases and the foaming of the reaction mixture. The laboratory tests were carried out as follows: Synthesis of an HDI prepolymer with terminal isocyanate groups

[0074] Since commercially available prepolymers contain catalyst residues that could distort the experimental results, a prepolymer was synthesized specifically for this purpose. For this, 20.00 g (48.193 mmol; 1.0 equivalents) of a polypropylene glycol (PET1004) with an average molecular weight of 415 g / mol were added under countercurrent argon, followed by 16.212 g of hexamethylene diisocyanate (2.0 equivalents). The mixture was heated to 80°C for 3 hours with stirring. After cooling to room temperature and storing the product at room temperature for one week, a viscous, transparent substance was obtained.

[0075] The number-averaged molecular weight of the HDI prepolymer was determined by gel permeation chromatography. The sample was measured in THF with polystyrene as a standard on a PSS SDV 5 µm linear S THF GPC column. A molecular mass of Mn = 789.7 was determined.

[0076] (The theoretical molecular masses are 751.4 g / mol for a 2-fold elongation of the polypropylene glycol used with HDI and 583.2 g / mol for a single elongation of the polypropylene glycol used with HDI). Test reactions

[0077] The following catalysts were used for the reaction of the HDI prepolymer with water: DBN: 1,5-diazabicyclo[4,3,0]non-5-ene; NEt 3 : triethylamine; DMA: Dimethylaniline.

[0078] In a test tube equipped with a magnetic stirrer, 1.0 equivalent of HDI prepolymer and 2.0 equivalents of water were placed. The contents of the test tube were thoroughly mixed, and 0.1 equivalents of the respective catalyst were added while stirring. The temperature of the mixture was slowly increased using an oil bath with a thermostat until significant gas evolution was observed. Table 1: Molar masses and amounts of substance of the substances used component M [g / mol] n [mol] m [mg] Äq d [g / ml] V [ml] HDI prepolymer 751,4 1)< 5,857 4401 1,0 - - H₂O 18,015 11,720 211 2,0 1,00 0,21 DBN 124,18 0,586 73 0,1 1,01 0,07 Net 3 101,19 0,586 59 0,1 0,73 0,08 DMA 121,18 0,586 71 0,1 0,96 0,07 1) Theoretical molecular weight for a prepolymer consisting of two equivalents of HDI and one equivalent of the polypropylene glycol used. Performing the quantum mechanical calculations

[0079] The quantum mechanical calculations were performed using the Turbomole software package. The density functional theory method employed was the TPSS density functional with a def2-SVP basis set, as implemented by default in the Turbomole package. The computer used was an Intel Xeon E5-2667v4 with 16 core processors running at 3.20 GHz and 25 MB of cache, with 128 GB of DDR4 2400 rg ECC RAM. The calculations were performed on two processors simultaneously, with a total memory volume of 8000 MB allocated.

[0080] For each reaction investigated, a starting geometry was chosen as the basis for determining a transition state. The time required to calculate the respective activation energies was up to 36 hours.

[0081] To simulate the activation energies, the reaction of a prepolymer containing two terminal, HDI-based isocyanate groups and a syntactic polypropylene glycol with seven repeating units based on propylene oxide, consisting of a total of 121 atoms, one molecule of water, and the respective catalyst (a total of between 144 and 146 atoms) was considered. To generate the initial geometries of the exemplary embodiments in Table 3, in the example of DBN, according to process step A1, one molecule of the prepolymer, one molecule of the DBN catalyst, and one molecule of water were drawn using a suitable program for visualizing three-dimensional molecular structures.The position of the carbon atom of the isocyanate group under consideration was moved to a distance of 175.5 pm from the oxygen atom of the water molecule under consideration, according to procedure step A2, and one of the hydrogen atoms in the water molecule was moved to a distance of 117.4 pm from the oxygen of the water molecule. The molecular geometry thus generated was stored in a Cartesian coordinate representation according to procedure step A3, and the atoms involved in the bond distances thus arranged were used to define the functional space according to procedure step B1.

[0082] Using the method according to the invention, the in Table 2 The activation energies shown can be obtained.

[0083] Using the prior art pseudo-Newton-Raphson-based method for optimizing transition states, it was not possible to obtain a transition state and thus an activation energy in any of the cases shown under the same conditions, i.e., with the same starting geometries for the transition state. Table 2: Summary of experimental and calculated activation energies catalyst Activation energy calculated [Kcal / mol] Temperature at which catalyst activity was observed in the laboratory test [°C] Gradient norm of the optimized starting geometry [E ha 0 -1< ] Gradient norm of the transition state [E ha 0 -1< ] DBN 13,2 23 0.024810 0.009638 Net 3 16,8 40 0.019049 0.006762 DMA 20,4 110-174 1)< 0.029652 0.008176 1) Temperature point is very difficult to determine. Reaction is only weakly discernible.

[0084] The data from Table 2 show that, using the method according to the invention, the molecular geometry of a transition state of a chemical reaction can be calculated with very little user effort and with such precision that an accurate statement about the kinetics of the chemical reaction can be made based on the calculated activation energy.

[0085] The number-averaged molecular weight of the HDI prepolymer used in the laboratory experiments is in the same range as the theoretically calculated mass of a polypropylene glycol extended by a factor of 2 with HDI. The laboratory experiments thus closely resemble the reaction conditions used to simulate the reaction for calculating the activation energy and realistically represent the simulation.

[0086] The activation energy calculated for DBN based on the inventive process was somewhat lower than for NEt3 and significantly lower than that for DMA. From the calculated results, it can be concluded that DBN as a catalyst enables a transition state in the reaction of the HDI prepolymer with water that exhibits a lower energy than when using NEt3 or DMA as a catalyst. Consequently, when carrying out the reaction with DBN as a catalyst, less or no energy (starting from room temperature) would need to be supplied for the reaction to proceed and products to be obtained.

[0087] These conclusions drawn from the calculated activation energies are reflected in the results of the laboratory experiments. While the reaction of the HDI prepolymer with water and DBN as a catalyst proceeded at 23 °C, the reaction mixture had to be heated to 40 °C when using NEt3 as a catalyst. The calculated activation energies already indicated that a higher activation energy would be required to carry out the reaction with NEt3.

[0088] The same applies to the use of DMA as a catalyst. Here, the calculated activation energy was significantly higher than with NEt3 as a catalyst. This result was verified by laboratory tests. When using NEt3 as a catalyst, a reaction could only be detected at temperatures above 100 °C, and even then only weakly.

Claims

1. Computer-implemented method of calculating transition states of a chemical reaction, comprising the steps of: A generating a starting geometry A1 providing the three-dimensional representation of at least one molecule at ground state energy, A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, where the selected length does not correspond to the length of the bond at ground state energy of the molecule, such that a starting geometry for the chemical reaction is obtained, A3 representing the starting geometry in three dimensions in Cartesian and / or internal coordinates, B ascertaining an optimized starting geometry B1 defining a function space encompassing the at least one bond from step A2 and the atoms joined by this bond, B2 optimizing the geometry of the function space selected in step B1 by means of a quantum-chemical method and with the boundary condition that the length of the at least one bond selected in step A2 is kept constant, such that an optimized starting geometry is obtained, B3 ascertaining the gradient norm B3 for the optimized starting geometry, where the gradient norm is obtained via the first derivative of a function E = f(x) of the quantum-chemical method, with E = total energy of the optimized starting geometry and x = nuclear coordinates of the molecule in the optimized starting geometry, B4.1 when the gradient norm B3 V is 0 ≤ V ≤ 0.03 Eh a0-1, classifying the optimized starting geometry as a precursor to the transition state of the chemical reaction and continuing the method with step D1, or B4.2 when the gradient norm B3 V is > 0.03 Eh a0-1, ascertaining the precursor to the transition state of the chemical reaction proceeding from the optimized starting geometry by a method comprising the following steps: C ascertaining the precursor to the transition state of the chemical reaction C1 varying the optimized starting geometry using a Monte Carlo algorithm, wherein C1.1 at least one atom from the function space selected in step B1 is selected at random, C1.2 a vector for a deflection of the atom chosen in step C1 is selected at random, weighting the randomly chosen magnitude of the vector by the gradient norm B3, C1.3 the atom selected in step C1.1 is deflected from the position of the atom in the optimized starting geometry using the vector from step C1.2, so as to obtain a precursor to a transition state of the chemical reaction, C2 optimizing the geometry of the precursor to the transition state by means of the quantum-chemical method and with the boundary condition that the at least one bond from step A2 has the length that was ascertained in step C1.3, C3 ascertaining the gradient norm C3 for the precursor to the transition state from step C2, where the gradient norm is obtained via the first derivative of the function E = f(x) of the quantum-chemical method, with E = total energy of the precursor to the transition state and x = nuclear coordinates of the molecule in the precursor to the transition state, C4.1 when the gradient norm C3 V is 0 ≤ V ≤ 0.03 Eh a0-1, continuing the method with step D1, or C4.2 when the gradient norm C3 V > 0.03 Eh a0-1, repeating steps C1 to C3 until a gradient norm C3 V of 0 ≤ ∇ ≤ 0.03 Eh a0-1 is obtained, wherein (a) if steps C1 to C3 have been performed once, the geometry of the precursor to the transition state is varied in step C1 when the value of its gradient norm C3 is lower than the value of the gradient norm B3 of the optimized starting geometry, or (b) if steps C1 to C3 have been performed more than once, the geometry of the optimized starting geometry or that precursor to the transition state from the preceding repetitions that has the lowest value for the gradient norm C3 or B3 compared to all the gradient norms C3 and B3 previously obtained is varied in step C1, D ascertaining the transition state D1 varying the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps for one atom within the function space defined in B1: D1.1 selecting an atom from the function space selected in step B1, D1.2 selecting a vector for a deflection of the atom chosen in step D1.1, D1.3 deflecting the atom selected in step D1.1 using the vector from step D1.2 from its position in the precursor, wherein the position is deflected once by the positive value of the magnitude of the vector and once by the negative value of the magnitude of the vector, such that two deflected precursors are obtained when steps D1.1 to D1.3 are conducted, D2 optimizing the geometry of the two deflected precursors from step D1 by means of the quantum-chemical method under the constraint that the bond distances obtained in D1 are kept constant, such that two optimized precursors (i) and (ii) are obtained, D3 calculating the energy of the two optimized precursors (i) and (ii) from step D2 by means of the quantum-chemical method, D4 comparing the energy values of the two optimized precursors with the value of the gradient norm C3 or B3 of the precursor that was used in step D1, D4.

1. if the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are each smaller than the energy value C3 or B3 of the precursor that was used in step D1, classifying the precursor that was used in step D1 as the transition state, D4.

2. if the energy value of the optimized precursor (i) or the energy value of the optimized precursor (ii) is not smaller than the energy value C3 or B3 of the precursor that was used in step D1, repeating the method from step C1.

2. Method according to Claim 2, characterized in that the quantum-chemical method from steps B2, B3, C2, C3, D2 and D3 is a semiempirical method, density functional theory method or an approximation of the Schrödinger equation, the quantum-chemical method from steps B2, B3, C2, C3, D2 and D3 especially being a density functional theory method.

3. Method according to Claim 1 or 2, characterized in that the chemical reaction is a synthesis selected from the group consisting of polymer syntheses, especially polyurethane syntheses, syntheses of monomers for polymerization reactions, industrially required commodity chemicals, platform chemicals, additives, surfactants and active pharmacological ingredients.

4. Method according to any of the preceding claims, characterized in that, in step A1, at least two molecules I and II are provided and, in step A2, alternatively or additionally to the at least one bond, at least one distance between at least one atom from molecule I and at least one atom from molecule II and the length of the at least one distance is also selected, where the length of the distance is especially not more than 230 pm.

5. Method according to Claim 4, characterized in that molecule I is a catalyst for the chemical reaction, especially for a polymer synthesis, and molecule II is a reactant in the chemical reaction, where molecule I is preferably to have a size of 2 to 1000 atoms and molecules II is preferably to have a size of 2 to 1000 atoms, where the sum total of the atoms from molecule I and from molecule II is especially to be more than 100 atoms.

6. Method according to any of Claims 1 to 5, characterized in that information as to the transition state ascertained in step D.1 and / or the equilibrium state ascertained in step D.2 is communicated to a user.

7. Method according to any of Claims 1 to 5, characterized in that information as to the transition state ascertained in step D.1 and / or the equilibrium state ascertained in step D.2 is received by a user.

8. Method according to Claim 5, characterized in that the molecule I is synthesized after step D.1 and / or after step D.2.

9. Method according to Claim 5, characterized in that after step D.1 and / or after step D.2, a chemical reaction is performed with molecule I as catalyst.

10. Method according to Claim 5 or 9, characterized in that after step D.1 and / or after step D.2, a chemical reaction is performed with molecule II as co-reactant.

11. System for data processing, comprising means of executing a method comprising the steps of: A generating a starting geometry A1 providing the three-dimensional representation of at least one molecule at ground state energy, A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, where the selected length does not correspond to the length of the bond at ground state energy of the molecule, such that a starting geometry for the chemical reaction is obtained, A3 representing the starting geometry in three dimensions in Cartesian and / or internal coordinates, B ascertaining an optimized starting geometry B1 defining a function space encompassing the at least one bond from step A2 and the atoms joined by this bond, B2 optimizing the geometry of the function space selected in step B1 by means of a quantum-chemical method and with the boundary condition that the length of the at least one bond selected in step A2 is kept constant, such that an optimized starting geometry is obtained, B3 ascertaining the gradient norm B3 for the optimized starting geometry, where the gradient norm is obtained via the first derivative of a function E = f(x) of the quantum-chemical method, with E = total energy of the optimized starting geometry and x = nuclear coordinates of the molecule in the optimized starting geometry, B4.1 when the gradient norm B3 V is 0 ≤ V ≤ 0.03 Eh a0-1, classifying the optimized starting geometry as a precursor to the transition state of the chemical reaction and continuing the method with step D1, or B4.2 when the gradient norm B3 V is > 0.03 Eh a0-1, ascertaining the precursor to the transition state of the chemical reaction proceeding from the optimized starting geometry by a method comprising the following steps: C ascertaining the precursor to the transition state of the chemical reaction C1 varying the optimized starting geometry using a Monte Carlo algorithm, wherein C1.1 at least one atom from the function space selected in step B1 is selected at random, C1.2 a vector for a deflection of the atom chosen in step C1 is selected at random, weighting the randomly chosen magnitude of the vector by the gradient norm B3, C1.3 the atom selected in step C1.1 is deflected from the position of the atom in the optimized starting geometry using the vector from step C1.2, so as to obtain a precursor to a transition state of the chemical reaction, C2 optimizing the geometry of the precursor to the transition state by means of the quantum-chemical method and with the boundary condition that the at least one bond from step A2 has the length that was ascertained in step C1.3, C3 ascertaining the gradient norm C3 for the precursor to the transition state from step C2, where the gradient norm is obtained via the first derivative of the function E = f(x) of the quantum-chemical method, with E = total energy of the precursor to the transition state and x = nuclear coordinates of the molecule in the precursor to the transition state, C4.1 when the gradient norm C3 V is 0 ≤ V ≤ 0.03 Eh a0-1, continuing the method with step D1, or C4.2 when the gradient norm C3 V > 0.03 Eh a0-1 Eh a0-1, repeating steps C1 to C3 until a gradient norm C3 V of 0 ≤ V ≤ 0.03 Eh a0-1 is obtained, wherein (a) if steps C1 to C3 have been performed once, the geometry of the precursor to the transition state is varied in step C1 when the value of its gradient norm C3 is lower than the value of the gradient norm B3 of the optimized starting geometry, or (b) if steps C1 to C3 have been performed more than once, the geometry of the optimized starting geometry or that precursor to the transition state from the preceding repetitions that has the lowest value for the gradient norm C3 or B3 compared to all the gradient norms C3 and B3 previously obtained is varied in step C1, D ascertaining the transition state D1 varying the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps for one atom within the function space defined in B1: D1.1 selecting an atom from the function space selected in step B1, D1.2 selecting a vector for a deflection of the atom chosen in step D1.1, D1.3 deflecting the atom selected in step D1.1 using the vector from step D1.2 from its position in the precursor, wherein the position is deflected once by the positive value of the magnitude of the vector and once by the negative value of the magnitude of the vector, such that two deflected precursors are obtained when steps D1.1 to D1.3 are conducted, D2 optimizing the geometry of the two deflected precursors from step D1 by means of the quantum-chemical method under the constraint that the bond distances obtained in D1 are kept constant, such that two optimized precursors (i) and (ii) are obtained, D3 calculating the energy of the two optimized precursors (i) and (ii) from step D2 by means of the quantum-chemical method, D4 comparing the energy values of the two optimized precursors with the energy value C3 or B3 of the precursor that was used in step D1, D4.

1. if the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are each smaller than the energy value C3 or B3 of the precursor that was used in step D1, classifying the precursor that was used in step D1 as the transition state, D4.

2. if the energy value of the optimized precursor (i) or the energy value of the optimized precursor (ii) is not smaller than the energy value C3 or B3 of the precursor that was used in step D1, repeating the method from step C1.

12. Computer program comprising commands that, on execution of the program by a computer, cause it to perform the following steps of a method: A generating a starting geometry A1 providing the three-dimensional representation of at least one molecule at ground state energy, A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, where the selected length does not correspond to the length of the bond at ground state energy of the molecule, such that a starting geometry for the chemical reaction is obtained, A3 representing the starting geometry in three dimensions in Cartesian and / or internal coordinates, B ascertaining an optimized starting geometry B1 defining a function space encompassing the at least one bond from step A2 and the atoms joined by this bond, B2 optimizing the geometry of the function space selected in step B1 by means of a quantum-chemical method and with the boundary condition that the length of the at least one bond selected in step A2 is kept constant, such that an optimized starting geometry is obtained, B3 ascertaining the gradient norm B3 for the optimized starting geometry, where the gradient norm is obtained via the first derivative of a function E = f(x) of the quantum-chemical method, with E = total energy of the optimized starting geometry and x = nuclear coordinates of the molecule in the optimized starting geometry, B4.1 when the gradient norm B3 V is 0 ≤ V ≤ 0.03 Eh a0-1, classifying the optimized starting geometry as a precursor to the transition state of the chemical reaction and continuing the method with step D1, or B4.2 when the gradient norm B3 V is > 0.03 Eh a0-1, ascertaining the precursor to the transition state of the chemical reaction proceeding from the optimized starting geometry by a method comprising the following steps: C ascertaining the precursor to the transition state of the chemical reaction C1 varying the optimized starting geometry using a Monte Carlo algorithm, wherein C1.1 at least one atom from the function space selected in step B1 is selected at random, C1.2 a vector for a deflection of the atom chosen in step C1 is selected at random, weighting the randomly chosen magnitude of the vector by the gradient norm B3, C1.3 the atom selected in step C1.1 is deflected from the position of the atom in the optimized starting geometry using the vector from step C1.2, so as to obtain a precursor to a transition state of the chemical reaction, C2 optimizing the geometry of the precursor to the transition state by means of the quantum-chemical method and with the boundary condition that the at least one bond from step A2 has the length that was ascertained in step C1.3, C3 ascertaining the gradient norm C3 for the precursor to the transition state from step C2, where the gradient norm is obtained via the first derivative of the function E = f(x) of the quantum-chemical method, with E = total energy of the precursor to the transition state and x = nuclear coordinates of the molecule in the precursor to the transition state, C4.1 when the gradient norm C3 V is 0 ≤ V ≤ 0.03 Eh a0-1, continuing the method with step D1, or C4.2 when the gradient norm C3 V > 0.03 Eh a0-1, repeating steps C1 to C3 until a gradient norm C3 V of 0 ≤ V ≤ 0.03 Eh a0-1 is obtained, wherein (a) if steps C1 to C3 have been performed once, the geometry of the precursor to the transition state is varied in step C1 when the value of its gradient norm C3 is lower than the value of the gradient norm B3 of the optimized starting geometry, or (b) if steps C1 to C3 have been performed more than once, the geometry of the optimized starting geometry or that precursor to the transition state from the preceding repetitions that has the lowest value for the gradient norm C3 or B3 compared to all the gradient norms C3 and B3 previously obtained is varied in step C1, D ascertaining the transition state D1 varying the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps for one atom within the function space defined in B1: D1.1 selecting an atom from the function space selected in step B1, D1.2 selecting a vector for a deflection of the atom chosen in step D1.1, D1.3 deflecting the atom selected in step D1.1 using the vector from step D1.2 from its position in the precursor, wherein the position is deflected once by the positive value of the magnitude of the vector and once by the negative value of the magnitude of the vector, such that two deflected precursors are obtained when steps D1.1 to D1.3 are conducted, D2 optimizing the geometry of the two deflected precursors from step D1 by means of the quantum-chemical method under the constraint that the bond distances obtained in D1 are kept constant, such that two optimized precursors (i) and (ii) are obtained, D3 calculating the energy of the two optimized precursors (i) and (ii) from step D2 by means of the quantum-chemical method, D4 comparing the energy values of the two optimized precursors with the energy value C3 or B3 of the precursor that was used in step D1, D4.

1. if the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are each smaller than the energy value C3 or B3 of the precursor that was used in step D1, classifying the precursor that was used in step D1 as the transition state, D4.

2. if the energy value of the optimized precursor (i) or the energy value of the optimized precursor (ii) is not smaller than the energy value C3 or B3 of the precursor that was used in step D1, repeating the method from step C1.

13. Computer-readable storage medium comprising commands that, on execution by a computer, cause it to perform the following steps of a method: A generating a starting geometry A1 providing the three-dimensional representation of at least one molecule at ground state energy, A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, where the selected length does not correspond to the length of the bond at ground state energy of the molecule, such that a starting geometry for the chemical reaction is obtained, A3 representing the starting geometry in three dimensions in Cartesian and / or internal coordinates, B ascertaining an optimized starting geometry B1 defining a function space encompassing the at least one bond from step A2 and the atoms joined by this bond, B2 optimizing the geometry of the function space selected in step B1 by means of a quantum-chemical method and with the boundary condition that the length of the at least one bond selected in step A2 is kept constant, such that an optimized starting geometry is obtained, B3 ascertaining the gradient norm B3 for the optimized starting geometry, where the gradient norm is obtained via the first derivative of a function E = f(x) of the quantum-chemical method, with E = total energy of the optimized starting geometry and x = nuclear coordinates of the molecule in the optimized starting geometry, B4.1 when the gradient norm B3 V is 0 ≤ V ≤ 0.03 Eh a0-1, classifying the optimized starting geometry as a precursor to the transition state of the chemical reaction and continuing the method with step D1, or B4.2 when the gradient norm B3 V is > 0.03 Eh a0-1, ascertaining the precursor to the transition state of the chemical reaction proceeding from the optimized starting geometry by a method comprising the following steps: C ascertaining the precursor to the transition state of the chemical reaction C1 varying the optimized starting geometry using a Monte Carlo algorithm, wherein C1.1 at least one atom from the function space selected in step B1 is selected at random, C1.2 a vector for a deflection of the atom chosen in step C1 is selected at random, weighting the randomly chosen magnitude of the vector by the gradient norm B3, C1.3 the atom selected in step C1.1 is deflected from the position of the atom in the optimized starting geometry using the vector from step C1.2, so as to obtain a precursor to a transition state of the chemical reaction, C2 optimizing the geometry of the precursor to the transition state by means of the quantum-chemical method and with the boundary condition that the at least one bond from step A2 has the length that was ascertained in step C1.3, C3 ascertaining the gradient norm C3 for the precursor to the transition state from step C2, where the gradient norm is obtained via the first derivative of the function E = f(x) of the quantum-chemical method, with E = total energy of the precursor to the transition state and x = nuclear coordinates of the molecule in the precursor to the transition state, C4.1 when the gradient norm C3 V is 0 ≤ V ≤ 0.03 Eh a0-1, continuing the method with step D1, or C4.2 when the gradient norm C3 V > 0.03 Eh a0-1 Eh a0-1, repeating steps C1 to C3 until a gradient norm C3 V of 0 ≤ V ≤ 0.03 Eh a0-1 is obtained, wherein (a) if steps C1 to C3 have been performed once, the geometry of the precursor to the transition state is varied in step C1 when the value of its gradient norm C3 is lower than the value of the gradient norm B3 of the optimized starting geometry, or (b) if steps C1 to C3 have been performed more than once, the geometry of the optimized starting geometry or that precursor to the transition state from the preceding repetitions that has the lowest value for the gradient norm C3 or B3 compared to all the gradient norms C3 and B3 previously obtained is varied in step C1, D ascertaining the transition state D1 varying the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps for one atom within the function space defined in B1: D1.1 selecting an atom from the function space selected in step B1, D1.2 selecting a vector for a deflection of the atom chosen in step D1.1, D1.3 deflecting the atom selected in step D1.1 using the vector from step D1.2 from its position in the precursor, wherein the position is deflected once by the positive value of the magnitude of the vector and once by the negative value of the magnitude of the vector, such that two deflected precursors are obtained when steps D1.1 to D1.3 are conducted, D2 optimizing the geometry of the two deflected precursors from step D1 by means of the quantum-chemical method under the constraint that the bond distances obtained in D1 are kept constant, such that two optimized precursors (i) and (ii) are obtained, D3 calculating the energy of the two optimized precursors (i) and (ii) from step D2 by means of the quantum-chemical method, D4 comparing the energy values of the two optimized precursors with the energy value C3 or B3 of the precursor that was used in step D1, D4.

1. if the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are each smaller than the energy value C3 or B3 of the precursor that was used in step D1, classifying the precursor that was used in step D1 as the transition state, D4.

2. if the energy value of the optimized precursor (i) or the energy value of the optimized precursor (ii) is not smaller than the energy value C3 or B3 of the precursor that was used in step D1, repeating the method from step C1.

14. Use of a computer program according to Claim 12 or of a computer-readable storage medium according to Claim 13 for evaluating transition states of a chemical reaction, especially a polymer synthesis.