Fundamentals of Computational Chemistry

Computational chemistry is a branch of science that uses mathematical calculations, computer simulations, and theoretical methods to understand, model, and predict the structures, properties, and reactions of chemical systems. Computational chemistry studies the energy levels, dynamics, and interactions of molecular structures based on theoretical foundations such as quantum mechanics, molecular mechanics, and statistical methods. For example, it can be used to study the docking of a drug candidate molecule into the active site of an enzyme. In materials science, it is used to investigate the properties of solids (e.g., plastics) and various nanomaterials, and to study catalysis in reactions that are important in the laboratory or in industry (1). Computational chemistry focuses on obtaining results related to chemical problems rather than directly developing new theoretical methods. There is a strong interaction between theoretical chemistry and computational chemistry. The development of new theoretical models can enable the study of new problems, and computational results can help suggest improvements by revealing the limitations of the theory. Depending on the desired accuracy and the nature of the system under study, it is now possible to obtain useful information for systems containing several thousand particles. One of the major challenges in computational chemistry is to choose the appropriate level of theory for a particular problem and to be able to evaluate the quality of the results obtained (2).

Commonly researched topics in computational chemistry include:

Molecular geometry: Shapes, bond lengths, angles, and dihedral angles of molecules (3).

Energies of molecules and transition states: This describes which isomer is more favorable at equilibrium and (from the transition state and reactant energies) how fast a reaction should occur (4).

Figure 1. A representative image showing the energy of the transition states of molecules. (Image generated using artificial intelligence)

Chemical reactivity: For example, knowing where electrons are concentrated (nucleophilic sites) and where they want to go (electrophilic sites) helps predict where various reactants will attack a molecule. A particularly useful application of this is in elucidating possible mechanisms of action of catalysts, which can lead to improved versions (5).

IR, UV, and NMR spectra: Spectra such as IR, UV, and NMR of molecules can be calculated using computational chemistry methods (6).

Figure 2. Experimental spectrum of the curcumin molecule: (A) FT-IR spectrum. (B) Spectrum calculated with B3LYP/6-311G** level of theory (7).

Substrate-enzyme interaction: Seeing how a molecule fits into the active site of an enzyme is an approach used to design better drugs (8).

Figure 3. Three-dimensional structure of the 1E9Z protein with the molecule N-(2-((2-chloro-4,5dicyanophenyl)amino)ethyl)-4-methylbenzenesulfonamide (ADK-1) (9).

Physical properties of substances: Physical properties depend on the properties of molecules and how they interact in bulk. For example, the strength and melting point of a polymer (plastic, etc.) depend on how well the molecules fit together and how strong the forces between them are (10).

History of Computational Chemistry

Computational chemistry is built on the theories and discoveries of quantum mechanics. In 1927, Walter Heitler and Fritz London performed the first theoretical calculations in chemistry (11). With the development of computer technology in the 1940s, the elaboration of the wave functions of complex atomic systems became an achievable goal. The first semiempirical atomic orbital calculations were performed in the early 1950s (12). In 1956, ab initio Hartree-Fock calculations for diatomic molecules were performed at MIT (13). In the 1950s, Boys and his colleagues performed the first configuration interaction calculations using GAUSSIAN orbitals on the EDSAC computer at the University of Cambridge (13). In 1964, Hückel calculations, or the linear combination of atomic orbitals (LCAO) method, were used on computers at the University of California, Berkeley, and the University of Oxford to calculate the electronic energies of molecular orbitals of π-electrons in conjugated systems (14). In the 1970s, efficient computer programs such as ATMOL, GAUSSIAN, IBMOL, and POLYAYTOM were used to accelerate ab initio molecular orbital calculations (15). Of these four programs, GAUSSIAN is the only one still in widespread use today, but many others have been developed.

In the 1970s, with the emergence of computational chemistry as a discipline, different approaches began to be included in the field. Pople presented methods for describing wave functions in the context of the Schrödinger equation and developed theoretical models for computational chemistry that included increasingly precise approximations that could be systematically checked for accuracy (16). In the 1960s, Walter Kohn proposed that the energy of a quantum mechanical system is determined solely by the electron density. This is a much easier quantity to handle than the complex wave functions in the Schrödinger equation. Kohn also provided a method for deriving an equation for solving for the electron density and the energy of the system. Because of its simplicity and applicability to larger molecules, this method is known as density functional theory (DFT) and is widely used in computational chemistry (17). Walter Kohn and John Pople were awarded the 1998 Nobel Prize in Chemistry for "the development of density functional theory" and "the development of computational methods in quantum chemistry", respectively..

Software and Tools Used in Computational Chemistry

Software and tools used in computational chemistry provide a wide range of services for molecular modeling, simulation of chemical reactions, energy calculations, molecular dynamics analyses, and other theoretical studies.

Gaussian: It is widely used for electron structure theory, molecular optimization, and transition state searches (18).

ORCA: It is an open-source, versatile quantum chemistry software (19).

GAMESS: It is used for calculating molecular structures, energies, and wave functions (20).

Q-Chem: It is a software that supports modern quantum chemistry methods (21).

CP2K: It is suitable for density functional theory (DFT) and molecular dynamics simulations (22).

NWChem: It is a software that supports both classical and quantum mechanical calculations. It is used for density functional theory, ab initio methods, and molecular dynamics studies (23).

Quantum Espresso: Open source software for DFT calculations on periodic systems. It is particularly popular in solid state physics and materials science (24).

References

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2. Jensen, F. (2017). Introduction to computational chemistry (Third edition). John Wiley & Sons, Ltd.

3. Choudhary, V. K., Mandhan, K., Dash, D., Bhardwaj, S., Kumari, M., & Sharma, N. (2022). Density functional theory studies on molecular geometry, spectroscopy, HOMO-LUMO and reactivity descriptors of titanium(IV) and oxidozirconium(IV) complexes of phenylacetohydroxamic acid. Journal of computational chemistry, 43(31), 2060–2071. https://doi.org/10.1002/jcc.27004 

4. Wei, W. X., Li, Y., Wen, Y. T., Li, M., Li, X. S., Wang, C. T., Liu, H. C., Xia, Y., Zhang, B. S., Jiao, R. Q., & Liang, Y. M. (2021). Experimental and Computational Studies of Palladium-Catalyzed Spirocyclization via a Narasaka-Heck/C(sp3 or sp2)-H Activation Cascade Reaction. Journal of the American Chemical Society, 143(20), 7868–7875. https://doi.org/10.1021/jacs.1c04114

5. Rajmohan, V., Deepa, S., Asha, S., Priya, S. V., Sagaama, A., & Raja, M. (2023). Synthesis, solvation effects, spectroscopic, chemical reactivity, topological analysis and biological evaluation of 4-chloro-N-(2, 6-dichlorobenzylidene) benzohydrazide. Journal of Molecular Liquids, 390, 122955. https://doi.org/10.1016/j.molliq.2023.122955

6. Manhas, F. M., Fatima, A., Verma, I., Siddiqui, N., Muthu, S., AlSalem, H. S., ... & Javed, S. (2022). Quantum computational, spectroscopic (FT-IR, NMR and UV–Vis) profiling, Hirshfeld surface, molecular docking and dynamics simulation studies on pyridine-2, 6-dicarbonyl dichloride.Journal of Molecular Structure, 1265, 133374. https://doi.org/10.1016/j.molstruc.2022.133374 

7. Benassi, R., Ferrari, E., Lazzari, S., Spagnolo, F., & Saladini, M. (2008). Theoretical study on Curcumin: A comparison of calculated spectroscopic properties with NMR, UV–vis and IR experimental data. Journal of Molecular Structure, 892(1-3), 168-176. https://doi.org/10.1016/j.molstruc.2008.05.024

8. Arulaabaranam, K., Mani, G., & Muthu, S. (2020). Computational assessment on wave function (ELF, LOL) analysis, molecular confirmation and molecular docking explores on 2-(5-Amino-2-Methylanilino)-4-(3-pyridyl) pyrimidine. Chemical Data Collections, 29, 100525. https://doi.org/10.1016/j.cdc.2020.100525

9. Dege, N., Gökce, H., Doğan, O. E., Alpaslan, G., Ağar, T., Muthu, S., & Sert, Y. (2022). Quantum computational, spectroscopic investigations on N-(2-((2-chloro-4, 5-dicyanophenyl) amino) ethyl)-4-methylbenzenesulfonamide by DFT/TD-DFT with different solvents, molecular docking and drug-likeness researches. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 638, 128311.

10. Minissale, M., Aikawa, Y., Bergin, E., Bertin, M., Brown, W. A., Cazaux, S., ... & Dulieu, F. (2022). Thermal desorption of interstellar ices: A review on the controlling parameters and their implications from snowlines to chemical complexity. ACS Earth and Space Chemistry, 6(3), 597-630. https://doi.org/10.1021/acsearthspacechem.1c00357

11. Heitler, W., & London, F. (1927). Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik. Zeitschrift für Physik, 44(6), 455-472.

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14. Streitwieser, A., Brauman, J. I., Coulson, C. A. (1965). Supplementary Tables of Molecular Orbital Calculations. Oxford: Pergamon Press.

15. Ma, Xiaoyue (2022-12-01). "Development of Computational Chemistry and Application of Computational Methods". Journal of Physics: Conference Series. 2386 (1): 012005.

16. Pople, John A.; Beveridge, David L. (1970). Approximate Molecular Orbital Theory. New York: McGraw Hill.

17. Kohn, W. & Sham, L. J. (1965). "Self-Consistent Equations Including Exchange and Correlation Effects". Physical Review, 140(4A), A1133–A1138.

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19. Neese, F. The ORCA program system Wiley Interdiscip. Rev.: Comput. Mol. Sci., 2012, 2, 1, 73–78 https://doi.org/10.1002/wcms.81 

20. Barca, G. M. J., et al. (2020). "Recent developments in the general atomic and molecular electronic structure system." The Journal of Chemical Physics 152(15): 154102. https://doi.org/10.1063/5.0005188 

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24. Giannozzi, P., Andreussi, O., Brumme, T., Bunau, O., Buongiorno Nardelli, M., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Cococcioni, M., Colonna, N., Carnimeo, I., Dal Corso, A., de Gironcoli, S., Delugas, P., DiStasio, R. A., Jr, Ferretti, A., Floris, A., Fratesi, G., Fugallo, G., … Baroni, S. (2017). Advanced capabilities for materials modelling with Quantum ESPRESSO. Journal of physics. Condensed matter : an Institute of Physics journal, 29(46), 465901. https://doi.org/10.1088/1361-648X/aa8f79