Fast method for quantum chemical calculations of large molecules with the approximation of the DFT Hamiltonian

Abstract

The fundamentally new method NESE is proposed for quantum chemical calculations of large molecules, which employs the approximation of the Hamiltonian of the commonly used DFT method and is as fast as the AM1 and PM3 semi empirical methods or the DFTB method. The parameters for the new method were chosen by the least squares method based on the comparison of its matrix elements with the reference DFT/PBE Hamiltonian. The initial non iterative version NESE 0 was computer implemented and approved on many thousands of various molecules containing H, C, N, and O atoms. The NESE 0 method moderately outper forms the DFTB approach and is an order of magnitude better than the AM1, PM3, and PM6 levels in reproducing the one electron energies calculated in terms of the DFT/PBE. Key words: approximate DFT Hamiltonian, fast quantum chemical methods, large mole cules, selection of parameters.The computer modeling of large biological molecules and nanostructures at the quantum chemical level allows researchers to reduce the time of the design of such ob jects, as well as the time of obtaining adequate informa tion on the quantum electronic properties (as opposed to those obtained by molecular mechpanics) and the spatial structures of the newly designed and the already available bio and nanostructures. Experiments for such structures become more and more expensive, while the cost of calcu lations being rapidly reduced. This promising field of high performance calculations is very important, for example, in solving problems of the computer drug design. In the latter case, it is necessary to perform calculations of giant molecules, which requires large computer resources even when employing commonly used and reasonably accurate density functional theory (DFT) methods, not to mention more precise and sophisticated approaches. Hence, semi empirical methods, such as AM1, 1 PM3, 2 and PM6, 3 as well as the approximate DFT method SCC DFTB (self consistent charge density functional tight binding) meant for fast calculations of large systems, 4 were em ployed as alternative approaches.Earlier, we have achieved the record speed for a num ber of simple semi empirical quantum chemical meth ods. 5,6 This allows one to perform large scale calculations (thousands of complexes, each consisting of thousands of atoms) using standard computers. However, the need arises for fast calculations with an accuracy of modern DFT methods widely used in far less large scale calculations. In the present work, we propose a new quantum chemical method for calculations of large molecules, which is al * On the occasion of the 80th anniversary of the N. D. Zelinsky Institute of Organic Chemistry of the Russian Academy of Sciences.