English
Русский 49-63 p.
A set of approximative methods is proposed to radically accelerate the calculation of the contribution of Coulomb integrals in the calculations of DFT giant biomolecules - the limiting stage of such relevant but extremely resource-intensive calculations, including calculations of thousands of docking complexes of thousands of atoms. The proposed complex includes, through a quick and accurate approximation of the contribution of a huge number of 4-center Coulomb integrals through a linear combination of 3-center integrals, and then through a combination of 2-center integrals. The non-multi-complete short-range components of these 2-center integrals are very quickly considered pre-prepared splines from the center-to-center distances. The remaining long-range multipole contributions are quickly calculated for giant molecules in the FMM style (splitting a huge space into regions and subdomains, was originally developed for the dynamics of galaxies). Calculations are saved as much as possible everywhere due to pre-selected combinations of integrals. All two-center components (including the approximation of two-center overlaps of basic functions through linear combinations of single-center auxiliary density functions) are quickly calculated due to splines from internuclear distances from a specially prepared database. For new bases, the database is easily and quickly replenished by decomposing the new basis into a set of universal ex-ponents and a database with them.
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5. Hennemann M., Clark T. EMPIRE: a highly parallel semiempirical molecular orbital program: 1: self-consistent field calculations. Journal of Molecular Modeling. 2014. No. 20:7. P. 2331. https://doi.org/10.1007/s00894-014-2331-4
6. Oferkin I.V., Katkova E.V. , Sulimov A.V., Kutov D.C., Sobolev S.I., Voevodin V.V., Sulimov V.B. Evalua-tion of docking target functions by the comprehensive investigation of protein-ligand energy minima. Advances in Bioinformatics. 2015. No. 2015. P. 126858. https://doi.org/10.1155/2015/126858
7. Anikin N.A., Bugaenko V.L., Kuzminsky M. B., Mendkovich A.S. High-speed method for quantum-chemical calculations of large molecules with DFT Hamiltonian approximation. Izv. AN. Ser.; Khim. 2014. No. 2. P. 346 – 349.
8. Zhang J., Weisman A.L., Saitta P., Friesner R.A. Efficient simulation of large materials clusters using the jaguar quantum chemistry program: Parallelization and wavefunction initialization. Int. J. Quant. Chem. 2016. No. 116:5. P. 357 – 368. https://doi.org/10.1002/qua.25043
9. Horvath I., Jeszenoi N., Balint M., Paragi G., Hetenyi C. A fragmenting protocol with explicit hydration for calculation of binding enthalpies of target-ligand complexes at a quantum mechanical level. Int. J. Molec. Sci. 2019. No. 20:18. P. 4384. https://doi.org/10.3390/ijms20184384
10. Brunk E., Rothlisberger U. Mixed Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simu-lations of Biological Systems in Ground and Electronically Excited States. Chemical Reviews. 2015. No. 115 (12). P. 6217 – 6263. https://pubmed.ncbi.nlm.nih.gov/25880693/ doi:10.1021/cr500628b. PMID 2588069
11. Nemukhin A.V., Polyakov I.V., Moskovsky A.I. Multi-scale supercomputing of large molecular aggregates: A case study of the light-harvesting photosynthetic center. Supercomputing Frontiers and Innovations. 2016. No. 2:4. P. 48 – 54. https://doi.org/10.14529/jsfi150403
12. Le H.A., Shiozaki T. Occupied-orbital fast multipole method for efficient exact exchange evaluation. Journal of Chemical Theory and Computation. 2018. No. 14:3. P. 1228 – 1234. https://doi.org/10.1021/acs.jctc.7b00880
13. Eichkorn K., Treutler O., Ohm H., Haser M., Ahlrichs R. Auxiliary basis sets to approximate Coulomb po-tentials. Chem. Phys. Letters. 1995. No. 240. P. 283 – 290.
14. Berman H.M., Westbrook J., Feng Z., Gilliland G., Bhat T.N., Weissig H., Shindyalov I.N., Bourne P.E. The Protein Data Bank. Nucleic Acids Research. 2000. No. 28:1. P. 235 – 242.
15. Verzhbitsky V.M. Numerical Methods. Mathematical Analysis and Ordinary Differential Equations. Mos-cow. ONIX 21st Century. 2005, Ch. 4.
16. Laikov D.N. Development an economical approach to calculating molecules using the density functional method and its application to solving complex chemical problems: dis. ... candidate of physical and mathematical sciences in the specialty 02.00.17 – quantum chemistry. Moscow, 2000.
17. Anikin N.A., Bugaenko V.L., Frash M.V., Gorb L., Leszczynski J. Localized Basis Orbitals: Minimization of 2-Electron Integrals Array and Orthonormality of Basis Set. J. Comput. Chem. Vol. 24. 2003. No. 9. P. 1132 – 1141.
Anikin N.A. A set of possible approximative methods for effectively accounting for the contribution of Coulomb integrals to dramatically accelerate the calculations of DFT giant biomolecules: reduction to fast-computable short-range two-center splines plus FMM long-range Coulomb. Chemical Bulletin. 2024. 7 (3). P. 49 – 63. https://doi.org/10.58224/2619-0575-2024-7-3-49-63