COSMOplex: Self-consistent simulation of self-organizing systems

Abstract

A method for simulating, in particular computerizing, at least one physical property of a system of one or more chemical substances, said system comprising at least one chemical substance dissolved in at least one inhomogeneous distribution of chemical substances, using quasi-chemical calculations based on statistical thermodynamics of pairwise interactions of molecular surface fragments. According to the invention, the pressure caused by the statistical thermodynamic population excess or population deficiency of a spatial region interacts with the atomic volume as an additional continuum response function, thereby affecting the thermodynamic weights of the molecular states in the system during iterative calculations of the statistical thermodynamic distribution of molecules in a 1-, 2- or 3-dimensional structured simulation volume of the liquid system.

Description

[0001] The present invention relates to a method for simulating, in particular computerizing, at least one physical property of a system of one or more chemical substances, comprising at least one chemical substance dissolved in at least one inhomogeneous distribution of chemical substances, using quasi-chemical calculations based on statistical thermodynamics of pairwise interactions of molecular surface fragments. Field of the Invention

[0002] The simulation of materials at the molecular level has acquired great technological importance because it allows the selection of optimal material components without the need for previous experimental work and because it provides mechanistic insights that are very important for controlling and improving the material or system under consideration. Liquid materials and soft quasi-liquid substances, such as emulsions and thermoplastic polymers, are of particular importance in general chemistry, pharmaceutical, agrochemical, biochemical, petrochemical and cosmetic industries, as well as in cleaning products. While the understanding and simulation of molecules in homogeneous bulk liquids remains of great importance for a wide range of chemical fields, inhomogeneous liquid systems, such as micelles, emulsions, molecules adsorbed to solid interfaces, liquid-liquid interfaces and liquid-air interfaces, as well as liquid crystals and confined liquids, are of increasing technological importance, especially in the technological, pharmaceutical, agrochemical, biological, petrochemical and cosmetic industries. Background Art

[0003] While the mainstream approach to the simulation of liquid systems is molecular dynamics (MD) or Monte Carlo (MC) simulations, in which the huge clusters of molecules in the simulation volume and all their 3D interactions are explicitly simulated, quasi-chemical models based on the statistical thermodynamics of pairwise interactions of molecular surface fragments [1], such as UNIFAC [2] or COSMO-RS [3,4], have proven to be very effective tools for simulating bulk, homogeneous, liquid systems, saving about four orders of magnitude of computer time and providing about twice the accuracy of MD / MC simulations for the free energies of molecules in solution [5,6]. However, quasi-chemical methods seem to be limited to homogeneous liquids, while inhomogeneous liquids seem to remain the domain of MD / MC simulations.

[0004] This situation changes in the COSMOmic approach adopted by Klamt et al. [7,8], when the COSMO-RS method is extended to simulate the distribution and partitioning of solutes in one-dimensional heterogeneous liquid systems such as micelles and biological membranes. COSMOmic treats the heterogeneous liquid as a layer of homogeneous liquids, applies the COSMO-RS method to each layer, and calculates the solute in all possible states, that is, the conformation, position and orientation in front of the layered liquid background. However, COSMOmic is limited by the fact that it can only simulate the behavior of infinitely diluted solute molecules in heterogeneous (mainly micellar) liquids, and it relies on external information about the structure of the heterogeneous system, which usually has to be generated by a previous expensive MD simulation. Summary of the invention

[0005] The present invention involves generalizing the COSMOmic concept to the self-consistent simulation of inhomogeneous, self-organizing systems by introducing a pressure-energy penalty that compensates for other energy contributions, especially quasi-chemical energy, of molecules in certain states within the inhomogeneous system. This pressure penalty reduces the probability that molecules will be in crowded spatial regions. Thus, similar algorithms used in COSMOmic to calculate solute distributions can now be applied to components of inhomogeneous systems, such as surfactant molecules and water. This overcomes the limitation of infinite dilution of COSMOmic and eliminates the need for expensive external information. DETAILED DESCRIPTION

[0006] The COSMO-RS method is based on the idea that all molecules that make up a liquid system convey information about their surface properties to the continuum description of the liquid. In its simplest version, the relevant surface properties are the surface polarization charge density calculated in a quantum chemical COSMO calculation, as well as atomic weight information derived from the same calculation. Based on the resulting total surface continuum composition, i.e., in its simplest version, the σ-profile of the solvent is calculated by solving the quasi-chemical equation, the thermodynamic response function σ-potential. The free energy of each molecule X in the solvent continuum S is then calculated by summing the individual σ-potentials of all surface fragments of the molecule.

[0007] In the COSMOmic approach, an inhomogeneous, one-dimensionally structured liquid system, such as micelles, biomembranes or liquid-liquid interfaces, is treated as a layered homogeneous liquid, i.e., each layer with a typical width of 1-2 angstroms is itself treated as homogeneous, but the composition of the layer, and therefore the response function, varies along the direction of the inhomogeneity, which we will further denote as the z-direction. External information, usually generated by molecular dynamics simulations, is required, which provides the probabilities of different atomic types in different layers. The atomic probabilities are then multiplied by the σ-profiles of their atoms and in this way a continuum composition, i.e., a layer σ-profile, is generated for each layer. Next, the thermodynamic response function is calculated for each layer, as in the bulk liquid. In order to calculate the free energy of a solute X in a simulated inhomogeneous system, all possible states of the solute in the system, or more precisely a reasonably dense grid representation of all states, are sampled, i.e., all center positions and orientations. If the solute X has multiple conformations, each combination of conformation, center position and orientation is sampled. For each individual state, the state-specific free energy of the molecule is calculated by determining the position of each surface fragment, multiplying its area by the local layer σ-potential, and summing these products for all fragments. From this, a state-specific thermodynamic weight, the Boltzmann factor, is calculated for each state. The Boltzmann factors for all states are summed up as the partition function for the compounds in the system. The free energy is fundamentally calculated as -RT In(partition function), where R is the ideal gas constant and T is the temperature.

[0008] The object of the present invention is to improve methods for simulating molecules in 1-, 2- or 3-dimensional structured simulation volumes of liquid systems by eliminating the need for external information.

[0009] The method of the present invention is used to simulate, in particular computerize, at least one physical property of a system of one or more chemical substances using quasi-chemical calculations based on statistical thermodynamics of pairwise interactions of molecular surface fragments, wherein the system includes at least one chemical substance dissolved in at least one non-uniformly distributed chemical substance, and the method includes the following technical teachings: the pressure caused by the statistical thermodynamic over- or underpopulation of a spatial region interacts with the atomic volume as an additional continuum response function, thereby affecting the thermodynamic weights of the molecular states in the system during iterative calculations of the statistical thermodynamic distribution of molecules in a 1-dimensional, 2-dimensional or 3-dimensional structured simulation volume of the liquid system.

[0010] The method of the present invention (referred to as COSMOplex) involves including the layer-specific transverse system pressure and the resulting interaction energy with the atomic volume as additional energy contributions in the calculation of state-specific free energies and Boltzmann factors for molecules in a simulated inhomogeneous system, supplementing the energy contributions due to quasi-chemical interactions of surface fragments. The system pressure is calculated from the spatial filling fraction, i.e. the ratio of the atomic volume probability to the available geometric volume in each layer. The atomic volume probability is calculated from the mole fraction of the compounds in the system and the Boltzmann probabilities of the possible states of the molecules in the system. Since population excess results in a higher pressure penalty, the Boltzmann probabilities in regions of population excess are reduced. Thus, starting from a reasonable distribution of compounds in the simulation volume, an initial layer σ-profile, layer charge and layer volume occupancy can be calculated, yielding an initial σ-potential, layer electrostatic potential and layer pressure. These yield the state-specific free energies of all molecules in the system and the corresponding distribution of the molecules in their possible states, i.e. conformations, positions and orientations. In this way, we obtain a new distribution of the molecules, yielding an updated layer σ-profile and layer volume occupancy. These are mixed with the σ-profile of the previous layer, the layer charge and the layer volume occupancy according to the damping factor. This closes the first iteration cycle of the COSMOplex method. By repeating the same cycle many times, the system minimizes its total free energy and converges to a realistic, self-organized structure. The final output therefore includes the self-organized distribution of all molecules in the entire simulated system and the corresponding free energies of the components.

[0011] The calculation requirements of the method of the present invention are roughly as follows:

[0012] - Typical computation time is 0.5–4 hours on a single CPU,

[0013] - The new optimized implementation will reduce this by 2-5 times,

[0014] - Memory requirement is about 0.5GB.

[0015] To improve performance, parallelization and extreme damping, which are often required for stepwise compression functions (pressure), should be very effective, but there is still room for improvement in damping strategies.

[0016] In any case, it is expected that simulations performed using the methods of the present invention will be at least 1000 times, or even 10,000 times, more efficient than corresponding MD simulations.

[0017] The method of the invention can also be used for calculations of liquid crystals. In order to create conditions for this calculation, it is particularly required to add an external electric field to the energy calculation of the state during the iterative calculation.

[0018] To allow the phases to automatically order according to their density, as one observes in a laboratory or in a centrifuge, external gravitational or centrifugal forces can be used in the energy calculation of the states.

[0019] By calculating the pressure due to a statistical thermodynamic excess or deficiency of population in a region of space, the pressure profile of the system can be calculated.

[0020] Furthermore, the inventive method allows calculations of at least pure and mixed surfactant systems and biofilms with limited solute loading, ionic surfactants with self-consistent ion distribution, molecular and surface tensions at liquid-air interfaces, molecular and adsorption constants at liquid-solid interfaces or confined liquids.

[0021] Another approach to the method of the invention can be to simulate a solid surface at one end of a rectangular box, or even simulate a solid at both ends or in a cylindrical nanotube, i.e. to deal with a confined liquid. In this way, it is possible to study how a liquid phase arranges (adsorbs) on a solid surface by the following method steps:

[0022] - calculation of the σ-surface of a solid (either by periodic COSMO or by cluster COSMO calculation),

[0023] - define this σ surface as being at the outermost layer and having a normal vector (DIRPLEX) in the direction of the interior of the box,

[0024] - Defines Lennard-Jones-like solid penetration penalties for surface fragments penetrating into solids.

[0025] Additionally, the inventive method can be used to simulate macroscopic distances (μm, mm, cm, m) using exponential grid spacing.

[0026] In general, the method of the present invention can perform self-consistent simulation of self-organizing systems based only on COSMO files, and is more efficient than MD simulation (speed increased by 10 3 Up to 10 4 ), and produced very promising initial quantitative results.

[0027] In a preferred embodiment of the invention, the method according to the invention, preferably the simulation method and / or the calculation method according to the invention, is run on a computer device, preferably in the form of computerized software, preferably, wherein the calculation according to the method according to the invention comprises computer-implemented steps, preferably computerized calculations, particularly preferably as algorithms in programming software, preferably as computer software for use on a computer device. The programmed software can be stored on a storage medium, for example on a removable storage medium, on a client computer and / or on a server computer for processing, storage, and input / output devices for executing application programs, etc.

[0028] Preferably, in the present invention, the simulation can be visualized as a computerized model on a display device, and / or the computerized model can be printed or drawn, such as a 3D model printed using a 3D printer. Therefore, another aspect of the present invention is a computerized model for visualizing the simulation of the present invention and / or the calculation of the present invention.

[0029] In order to avoid repeating further advantages of the computer device according to the invention, reference is made to the description of advantageous developments of the method according to the invention, and this description is adopted in its entirety.

[0030] Example

[0031] For example, the figure shows the volume distribution of additives in the oil-surfactant-water system (decane-C8E3-water) calculated by the COSMOplex program.

[0032] Further measures to improve the invention are described in more detail below by describing preferred embodiments of the invention using the accompanying drawings. All previous features and / or advantages of the claims, description or drawings, including design details, spatial configurations and process steps, are essential to the invention, both by themselves and in various combinations. It should be noted that the drawings are merely descriptive and do not limit the invention in any way.

[0033] It is shown schematically:

[0034] Figure 1 is a computerized model of acetone-water mixtures using the COSMORS method,

[0035] Figure 2 It is a computerized model calculated using the COSMOmic method.

[0036] Figure 3 : The conception of the method of the present invention in the workflow diagram,

[0037] Figure 4 is a diagram showing the volume distribution of additives in an oil-surfactant-water system (decane-C8E3-water) calculated by the method of the present invention,

[0038] and

[0039] Figure 5 It is a computerized model calculated using the COSMOplex method of the present invention.

[0040] Figure 1A computerized model of the sigma potential calculated using the COSMORS method for a 50% water, 50% acetone mixture is shown with an acetone-water mixture having a sigma profile of the solvent. The solid line indicates the σ-profile of the mixture, which is constructed from the surface fragments of the components. The dashed line is the resulting σ-potential. The arrows indicate that surface fragments of different polarity are added to different parts of the σ-profile, and then the σ-potential corresponding to the polarity of each fragment is placed back on the surface of the molecule in order to represent the free energy of the surface fragments.

[0041] Figure 2 Schematic diagram of the COSMOmic method showing three different states (position and orientation) of a solute in front of a background of a DMPC biofilm. In each state, different fragments of the solute surface are located in different layers and therefore have different σ-potentials. The background is a snapshot of an MD simulation proposed by Tieleman et al. [9].

[0042] exist Figure 3 In FIG. 1 , the concept of the method 100 of the present invention, called COSMOplex, is shown as a workflow diagram.

[0043] Since a population excess generates high pressure energy, the Boltzmann probability is reduced in regions of population excess. Thus, starting from a reasonable distribution of compounds in the simulation volume, initial layer σ-profiles, layer charges and layer volume occupancy can be calculated, resulting in initial σ-potentials, layer electrostatic potentials and layer pressures. Thus, in a first step 1, the method 100 of the present invention begins by establishing a reasonable starting distribution of the compounds under consideration in a rectangular box, sphere or cylinder with mirrored or periodic boundaries (supported by an automatic box script).

[0044] From the distribution established in step 1, the layer σ-profile, layer charge, layer average molar area and volume, and layer space filling fraction (occupied molar volume divided by geometric layer volume) are calculated in a second step 2, yielding initial σ potentials, layer electrostatic potentials, and layer pressures. These yield state-specific free energies for all molecules in the system and the corresponding distribution of molecules over their possible states, i.e., conformations, positions, and orientations. In this way, we have a new distribution of molecules, yielding updated layer σ-profiles and layer volume occupancy.

[0045] In the third step 3, the layer continuum response function is calculated by a Lennard-Jones-like compression function: μ(σ,z) is calculated from p(σ,z), the combined response is calculated from the average volume and area, the electrostatic response V(z) is calculated from the layer charge, and the pressure response is calculated from the space filling.

[0046] In a fourth step 4, they are mixed with the previous layer σ-profile, layer charge and layer volume occupancy according to the damping factor.

[0047] Thus, in a fourth step 4, all states (conformations, positions, orientations) of each compound are sampled and local, state-specific free energies are calculated as usual based on the local μ(σ,z), the local combinatorial contribution, the local electrostatic potential, and including the pressure contribution of each atom times the product of the atomic volume*pressure(z). This produces a new partition function, a new distribution, a new free energy, and ultimately a converged distribution and free energy of the self-organized compounds, thus closing the first iterative cycle of the COSMOplex method 100. By repeating the same cycle many times, as indicated by the curved arrow 5, the system minimizes its total free energy and converges to a realistic, self-organized structure. Thus, the final output includes the self-organized distribution of all molecules in the entire simulated system, as well as Figure 4 and Figure 5 The corresponding free energies of the components are shown in the computerized model.

[0048] Figure 4 The volume distribution of additives in the oil-surfactant-water system (decane-C8E3-water) calculated by the method of the present invention is shown. The additives are butane, tetradecane, 1-decyne, 1-dodecane, decane at T = 338K, pinane, cyclohexane, dodecane, 1-dodecene, 1-decene, 1-hexanol, hexane, hexyne, decane at T = 298K, 1-octanol, octane, decane at T = 298K, 2-butanol, decane at T = 318K, and 1-methyl-4-isopropylbenzene. The figure shows the distribution of the molecules of the additives in the system and the effect of the additives on the system. For example, 1-hexanol behaves similarly to a surfactant and therefore has only a small effect on the system.

[0049] Figure 5 A schematic diagram of the COSMOplex method is shown. It shows the pressure profile at the cyclohexane-water interface calculated self-consistently using COSMOplex.

[0050] The foregoing examples are provided by way of illustration only and are not intended to limit the scope of protection of the present invention.

[0051] List of cited references

[0052] [1]Guggenheim, EAMixtures; Clarendon Press: Oxford, 1952.

[0053] [2] Fredenslund,J.Gmehling,P.Rasmussen:Vapor-Liquid Equilibria UsingUNIFAC-A Group Contribution Method.Elsevier,Amsterdam 1977.

[0054] [3]A.Klamt,Conductor-like screening model for real solvents:a newapproach to the quantitative calculation of solvation phenomena,J.Phys.Chem.99(1995)2224–2235.doi:10.1021 / j100007a062.

[0055] [4]Klamt,A.;Krooshof,G.J.P.;Taylor,R.COSMOSPACE:Alternative toConventional Activity-Coefficient Models.AIChE J.2002,48(10),2332–2349.

[0056] [5]Zhang,J.;Tuguldur,B.;van der Spoel,D.Force Field Benchmark ofOrganic Liquids.2.Gibbs Energy of Solvation.J.Chem.Inf.Model.2015,55(6),1192–1201.

[0057] [6]Zhang,J.;Tuguldur,B.;van der Spoel,D.Correction to Force FieldBenchmark of Organic Liquids.2.Gibbs

[0058] [7]A.Klamt,U.Huniar,S.Spycher,J.Keldenich,COSMOmic:a mechanisticapproach to the calculation of membrane-water partition coefficients andinternal distributions within membranes and micelles,J.Phys.Chem.B.112(2008)12148–12157.doi:10.1021 / jp801736k.

[0059] [8]Bittermann,K.;Spycher,S.;Endo,S.;Pohler,L.;Huniar,U.;Goss,K.-U.;Klamt,A.Prediction of Phospholipid-Water Partition Coefficients of IonicOrganic Chemicals Using the Mechanistic Model COSMOmic.J.Phys.Chem.B 2014,118(51),14833–14842.

[0060] [9]A DMPC micelle consisting of 54 lipids and a few thousand watermolecules(schematically),http / / indigo1.biop.ox.ac.uk / tieleman / projects.html#micelles

Claims

1. A method for computerized calculation of at least one physical property of a system of one or more chemical substances using quasi-chemical calculations based on statistical thermodynamics of pairwise interactions of molecular surface fragments, the system comprising at least one chemical substance dissolved in at least one inhomogeneous distribution of chemical substances, characterized in that The pressure caused by the statistical thermodynamic population surplus or shortage in a spatial region interacts with the atomic volume as an additional continuum response function, thereby affecting the thermodynamic weights of the molecular states in the system during the iterative calculation of the statistical thermodynamic distribution of molecules in a 1-dimensional, 2-dimensional or 3-dimensional structured simulation volume of the liquid system. The method includes: introducing a pressure energy penalty, supplementing other energy contributions, and reducing the probability of molecules being in crowded spatial regions, and the method includes: establishing a reasonable starting distribution of compounds; generating a new distribution of molecules, an updated layer σ-profile and layer volume occupancy; calculating the layer continuum response function through a compression function; and generating a new distribution function, a new distribution, a new free energy, and a convergent distribution and free energy of self-organized compounds.

2. The method according to claim 1, characterized in that The pressure and the energy contribution due to the molecular surface interaction are used by the quasi-chemical calculation as additional energy contributions in the thermodynamic weights of the molecular states in the system.

3. The method according to claim 1, wherein: The structures of the chemical species are calculated self-consistently by the method without the need for external information.

4. The method according to claim 1, characterized in that: The chemical system simulated is either a micelle or a membrane.

5. The method according to claim 1, characterized in that Surfactant systems and biofilms with finite solute loading, either pure or mixed, can be calculated.

6. The method according to claim 1, characterized in that Able to calculate ionic surfactants with self-consistent ionic distribution.

7. The method according to claim 1, characterized in that Ability to calculate molecular and interfacial tensions at liquid-liquid interfaces.

8. The method according to claim 1, characterized in that Ability to calculate molecular and surface tension at liquid-air interfaces.

9. The method according to claim 1, characterized in that: Ability to calculate molecules and adsorption constants at liquid-solid interfaces.

10. The method according to claim 1, characterized in that Ability to calculate confined liquids.

11. The method according to claim 1, characterized in that: Able to calculate liquid crystals.

12. A computer device for computerizing the calculation of at least one physical property of a system of one or more chemical substances using a quasi-chemical calculation involving a pressure calculation according to a method as described in any one of claims 1 to 11, wherein the system includes at least one chemical substance dissolved in at least one non-uniformly distributed chemical substance, the pressure being caused by a statistical thermodynamic population excess or population deficiency in a spatial region.

Images