Theoretical calculation method for solid formation enthalpy of energetic material
Through the calculation method based on density functional theory, the solid-state generation enthalpy of energy-containing materials is directly calculated using periodic boundary conditions and appropriate reference molecules, solving the problem of calculation accuracy and empirical parameters in the prior art, and achieving high-precision calculation effect.
Patent Information
- Application Number
- CN202510122161.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-26
- Publication Date
- 2025-06-03
AI Technical Summary
It is difficult for the prior art to accurately calculate the solid-state formation enthalpy of energy-containing materials, and the calculation method relies on empirical parameters and experimental data, so the accuracy of the results is difficult to guarantee.
A calculation method based on density functional theory is used to calculate the enthalpy of the crystal structure through periodic boundary conditions, and select appropriate reference molecules to reduce system errors, and directly calculate the solid-state generation enthalpy of energy-containing materials.
The calculation of solid-state generation enthalpy is realized with high precision and independent of empirical parameters and experimental data, reducing the systematic error in density functional theory calculation, and being able to directly calculate the solid-state generation enthalpy of any CHON structure.
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Figure CN120089223A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of chemical engineering, and particularly relates to a theoretical calculation method for the solid formation enthalpy of energetic materials. Background Art
[0002] The formation enthalpy of energetic materials is a key parameter and an important factor determining the performance of energetic materials. For example, for an ideal explosive, given the composition, density, and formation enthalpy, the detonation velocity, detonation pressure, detonation heat, detonation temperature, and detonation volume can be calculated. Currently, the formation enthalpy of energetic materials can be measured experimentally or calculated theoretically. The formation enthalpy is a state function and can be deduced based on Hess's law through a series of consecutive reactions, which can be real or virtual.
[0003] Experimentally, the combustion heat is mainly measured by a calorimetric bomb. If the combustion products and the heat released during combustion are known, the formation enthalpy of the energetic material can be deduced according to the combustion reaction equation of the energetic material. In terms of calculation, the formation enthalpy is decomposed into two steps: sublimation enthalpy and gas formation enthalpy. Among them, the sublimation enthalpy refers to the enthalpy change of sublimating a solid energetic material into gas molecules, which mainly depends on the semi-empirical fitting of experimental data or machine learning; the gas formation enthalpy refers to the formation enthalpy of a single energetic material molecule. Currently, there are three types of calculation methods: atomization energy, atom / group assignment, and isodesmic reaction calculation.
[0004] Among them, the atomization energy is calculated by a high-precision method for the enthalpy change of a molecule splitting into isolated atoms one by one, and then the formation enthalpy of the molecule is deduced. The atom / group assignment regards the formation enthalpy of a gas molecule as the sum of the formation enthalpies of each atom or group in the molecule. Here, the formation enthalpy of the atom or group is not the real formation enthalpy, but an equivalent value, which comes from data fitting or machine learning. The isodesmic reaction calculation refers to calculating the formation enthalpy of the target molecule by constructing an isodesmic reaction. Since the bonding type and quantity of each atom before and after the isodesmic reaction are the same, the error in the calculation can be reduced.
[0005] Currently, the experimental measurement or theoretical calculation of the formation enthalpy of energetic materials is difficult, and the accuracy of the results is difficult to guarantee. In short, a calculation method for the solid formation enthalpy of energetic materials that does not rely on empirical parameters and experimental data is urgently needed in the field of energetic materials, but it still cannot be achieved currently. Summary of the Invention
[0006] The present invention provides a theoretical calculation method for the solid formation enthalpy of energetic materials. This theoretical calculation method has the characteristics of simplicity and high precision. It does not rely on any empirical parameters, does not require a high-precision density functional basis set, does not require fitting or machine learning, does not require experimental measurement data, can directly calculate the solid formation enthalpy of any CHON structure, and can be easily extended to other systems.
[0007] In order to achieve the above object, the present invention adopts the following specific technical solutions:
[0008] A theoretical calculation method for the solid state formation enthalpy of energetic materials, the theoretical calculation method comprising the following steps:
[0009] Step 1, calculate the enthalpy H of the energetic material EM ;
[0010] Step 2, calculate the enthalpies of reference molecules with different coordination numbers of each element in the energetic material;
[0011] Step 3, calculate the equivalent enthalpy values H of each element in the energetic material at different coordination numbers according to the enthalpies of the reference molecules X-N ;
[0012] Step 4, calculate the solid state formation enthalpy ΔH of the energetic material using the following formula (1) f,solid :
[0013]
[0014] In the above formula, M X-N is the number of X atoms with a coordination number of N in each molecule or structural unit of the energetic material, X represents different elements, and N represents the coordination number.
[0015] Furthermore, in Step 1, to calculate the enthalpy H of the energetic material EM , the following specific steps are included:
[0016] Adopt periodic boundary conditions to perform density functional theory calculations and structural optimizations on the crystal structure of the energetic material;
[0017] Perform static calculations on the optimized crystal structure to obtain the Kohn-Sham density functional energy U, and perform vibration calculations to obtain the enthalpy correction terms based on the quasi-harmonic approximation: zero-point vibrational energy ZPE and volume work PV;
[0018] Calculate the enthalpy H of the unit cell using the following formula (2):
[0019] H = U + ZPE + PV (2);
[0020] The enthalpy per molecule or structural unit on average is H / n, where n is the number of molecules or structural units in the unit cell.
[0021] Furthermore, in Step 2, to calculate the enthalpies of reference molecules with different coordination numbers of each element in the energetic material, the following specific steps are included:
[0022] Select a series of gas small molecules as reference molecules for the calculation of the formation enthalpy;
[0023] Calculate the density functional energy U, zero-point vibrational energy ZPE and volume work PV of each reference molecule respectively;
[0024] The enthalpy H of each reference molecule is calculated respectively using the following formula (3):
[0025] H = U + ZPE + PV – H f (3);
[0026] In the above formula, H f is the standard molar enthalpy of formation of the reference molecule, which is obtained by querying the standard database.
[0027] Furthermore, the selection of the reference molecule is based on the atomic coordination number.
[0028] Furthermore, in step four, before calculating the solid-state enthalpy of formation of the energetic material, it also includes counting the number M of X atoms (X-N) with a coordination number of N in each molecule or structural unit of the energetic material. X-N .
[0029] Furthermore, when performing density functional theory calculations and structural optimizations on the crystal structure of the energetic material using periodic boundary conditions, for molecular crystals, van der Waals corrections are used to consider intermolecular interactions.
[0030] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:
[0031] The theoretical calculation method of the present invention directly calculates the solid-state enthalpy of formation of the energetic material, and directly calculates the enthalpy of the crystal structure using periodic boundary conditions, while the previous calculation methods only calculate isolated molecules and ignore intermolecular interactions. By selecting appropriate reference molecules, the coordination numbers of the reference molecules and the energetic material molecules are made consistent, reducing the systematic error in density functional theory calculations. Description of the Drawings
[0032] Figure 1 It is a flow chart of the theoretical calculation method for the solid-state enthalpy of formation of the energetic material of the present invention. Detailed Embodiments
[0033] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.
[0034] The present invention proposes a new, simple, high-precision density functional theory calculation method for the solid-state formation enthalpy of CHON energetic materials, which does not rely on any empirical parameters. This calculation method does not require a high-precision density functional basis set, does not require fitting or machine learning, and does not require experimental measurement data. It can directly calculate the solid-state formation enthalpy of any CHON structure and can be easily extended to other systems.
[0035] As Figure 1 shown in the structure, an embodiment of the present invention provides a theoretical calculation method for the solid-state formation enthalpy of energetic materials. As Figure 1 shown, this theoretical calculation method includes the following steps:
[0036] Step 1, calculate the enthalpy H of the energetic material EM ; Using periodic boundary conditions, perform density functional theory calculations and structural optimizations on the crystal structure of the energetic material. For molecular crystals, van der Waals corrections are used to consider intermolecular interactions; perform static calculations on the optimized crystal structure to obtain the Kohn-Sham density functional energy U, and perform vibration calculations. Based on the quasi-harmonic approximation, obtain the enthalpy correction terms - zero-point vibrational energy and volume work. The zero-point vibrational energy is represented by ZPE, and the volume work is represented by PV. Thus, the enthalpy of the unit cell can be obtained: H = U + ZPE + PV. Then, the enthalpy per molecule or structural unit on average is H / n, where n is the number of molecules or structural units in the unit cell.
[0037] Step 2, calculate the enthalpies of reference molecules with different coordination numbers of each element in the energetic material; Select a series of gas small molecules as reference molecules for the calculation of formation enthalpy. The selection of reference molecules is based on atomic coordination numbers. For example: For carbon (C) atoms, in the actual material, it may be tetracoordinated, tricoordinated, and dicoordinated, and the corresponding reference molecules are methane (CH 4 ), ethylene (CH 2 =CH 2 ), and acetylene (CH≡CH). For nitrogen (N) atoms, in the actual material, it may be tricoordinated, dicoordinated, and monocoordinated, and the corresponding reference molecules are ammonia (NH 3 ), diimide (NH=NH), and nitrogen (N≡N). For oxygen (O) atoms, in the actual material, it may be dicoordinated and monocoordinated, and the corresponding reference molecules are water molecules (H 2 O) and oxygen (O=O). For hydrogen (H) atoms, in the actual material, it is monocoordinated, and the corresponding reference molecule is hydrogen (H-H). In a similar manner as in Step 1, calculate the density functional energy U, zero-point vibrational energy ZPE, and volume work PV of each of the above reference molecules respectively. Then calculate the enthalpies of each reference molecule: H = U + ZPE + PV – H f , where H fis the standard molar enthalpy of formation of the reference molecule, which can be obtained by querying the standard database.
[0038] Step 3: Calculate the equivalent enthalpy value H of each element in the energetic material at different coordination numbers according to the enthalpy of the reference molecule. X-N ; Calculate the equivalent enthalpy value of each element at different coordination numbers according to the enthalpy of each reference molecule in Step 2. The equivalent enthalpy value is represented by H X-N , where X represents different elements and N represents the coordination number, and:
[0039] H H-1 = 0.5H(H 2 );
[0040] H O-1 = 0.5H(O 2 );
[0041] H O-2 = H(H 2 O) – 2H H-1 ;
[0042] H N-1 = 0.5H(N 2 );
[0043] H N-2 = 0.5H(N 2 H 2 ) – H H-1 ;
[0044] H N-3 = H(NH 3 ) – 3H H-1 ;
[0045] H C-2 = 0.5H(C 2 H 2 ) – H H-1 ;
[0046] H C-3 = 0.5H(C 2 H 4 ) – 2H H-1 ;
[0047] H C-4 = H(CH 4 ) – 4H H-1 .
[0048] Step 4: Calculate the solid-state enthalpy of formation of the energetic material. Count the number of X atoms (X-N) with a coordination number of N in each molecule or structural unit of the solid energetic material, denoted as M X-N , based on the enthalpy H of each molecule or structural unit of the target energetic material in Step 1 EMAnd the equivalent enthalpy value H at different coordination numbers of each element in step three X-N , the solid formation enthalpy ΔH of the energetic material is calculated using the following formula f,solid :
[0049]
[0050] In the above formula, M X-N is the number of X atoms with a coordination number of N in each molecule or structural unit of the energetic material, where X represents different elements and N represents the coordination number.
[0051] The above theoretical calculation method is carried out using the above steps, which can directly calculate the solid formation enthalpy of the energetic material, rather than obtaining the solid formation enthalpy by adding the gaseous formation enthalpy and the sublimation enthalpy in the traditional method. The enthalpy of the crystal structure is directly calculated using periodic boundary conditions, while the previous calculation methods only calculate isolated molecules and ignore the intermolecular interactions. Moreover, by selecting appropriate reference molecules, the coordination numbers of the reference molecules and the energetic material molecules are made consistent, reducing the systematic error in the density functional theory calculation.
[0052] In the above theoretical calculation method, the main consideration is enthalpy. For other thermodynamic state functions, such as free energy, it can be converted with enthalpy. Regarding the selection of the reference molecule in step two, it is not unique. Other molecules can also be selected on the premise of considering the coordination number and the bonding type. For the solid energetic material to be calculated, it is not limited to molecular crystals and can be extended to other types of crystals. And the composition is not limited to CHON elements and can be extended to other elements.
[0053] Obviously, those skilled in the art can make various changes and modifications to the embodiments of the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention also intends to include these changes and modifications.
Claims
1. A theoretical calculation method for solid-state formation enthalpy of energetic materials, characterized in that: The following steps are involved: Step 1: Calculate the enthalpy H of the energetic material EM ; Step 2, calculating the enthalpy of reference molecules with different coordination numbers of each element in the energetic material; Step 3: Calculate the equivalent enthalpy H of each element in the energetic material at different coordination numbers based on the enthalpy of the reference molecule. X-N ; Step 4: Calculate the solid-state formation enthalpy ΔH of the energetic material using the following formula (1): f,solid : In the above formula, M X-N It is the number of X atoms with a coordination number of N in each molecule or structural unit in the energetic material, where X represents different elements and N represents the coordination number.
2. The theoretical calculation method according to claim 1, characterized in that: In step 1, calculate the enthalpy H of the energetic material EM , specifically including the following steps: Density functional theory calculations and structural optimization of the crystal structure of energetic materials are performed using periodic boundary conditions; Static calculations were performed on the optimized crystal structure to obtain the Cohen-Shen Lüjiu density functional energy U, and vibration calculations were performed to obtain the enthalpy correction terms based on the quasi-harmonic approximation: zero-point vibration energy ZPE and volume work PV; The enthalpy H of the unit cell is calculated using the following formula (2): H = U + ZPE + PV (2); The average enthalpy per molecule or structural unit is H / n, where n is the number of molecules or structural units in the unit cell.
3. The theoretical calculation method according to claim 2, characterized in that: In step 2, the enthalpy of reference molecules with different coordination numbers of each element in the energetic material is calculated, which specifically includes the following steps: A series of small gas molecules are selected as reference molecules for the calculation of formation enthalpy; Calculate the density functional energy U, zero-point vibrational energy ZPE and volume work PV of each reference molecule respectively; The enthalpy H of each reference molecule is calculated using the following formula (3): H=U+ZPE+PV–H f (3); In the above formula, H f is the standard molar enthalpy of formation of the reference molecule, obtained by querying a standards database.
4. The theoretical calculation method according to claim 3, characterized in that: Reference molecules were selected based on atomic coordination numbers.
5. The theoretical calculation method according to claim 4, characterized in that: In step 4, before calculating the solid-state formation enthalpy of the energetic material, it also includes counting the number M of X atoms (XN) with a coordination number N in each molecule or structural unit in the energetic material. X-N .
6. The theoretical calculation method according to any one of claims 2 to 5, characterized in that: When density functional theory calculations and structural optimization of the crystal structure of energetic materials are performed using periodic boundary conditions, van der Waals corrections are used to consider intermolecular interactions for molecular crystals.