The investigation aims to identify potential approximative methodologies for expediting repeated calculations of Coulomb integral contributions to single-electron Hamiltonian elements during self-consistent field (SCF) iterations, thereby dramatically accelerating computationally intensive density functional theory (DFT) analyses of massive biomolecular structures. The research addressed several challenges: a) evaluating semi-empirical approaches for quantum chemical examination of enormous molecular systems; b) exploring how numerous distant molecular fragments could facilitate faster computation of Coulomb interaction contributions; c) examining contemporary approaches to fixed-geometry single-point molecular calculations; d) developing innovative methodologies for accelerated Coulomb integral contribution computation in DFT analyses of substantial bi-omolecular entities.
We present a novel suite of approximation techniques designed to substantially expedite calculations of Cou-lomb integral contributions to one-electron Hamiltonian elements in conventional DFT methodologies during SCF iterations-typically the rate-limiting phase of these essential yet computationally demanding calculations for exten-sive biomolecular systems, including thousands of docking complexes comprising thousands of atoms.
Our integrated approach features rapid and precise approximation of contribution modifications across innu-merable 4-center Coulomb integrals between successive SCF iterations through auxiliary density function-mediated transformation into linear combinations of 3-center integrals, subsequently converted to combinations of 2-center integrals. Contribution variations from non-multipole short-range components of these 2-center integrals are swiftly determined by modifying pre-computed spline contributions based on inter-atomic separations. The re-maining multipole-based long-range contributions undergo rapid computation for expansive molecular systems using a fast multipole method (FMM) framework, which strategically partitions extensive spatial domains into hi-erarchical regions (a technique originally pioneered for galactic dynamics simulations).
Each SCF iteration employs sophisticated screening to identify exclusively non-negligible integral combina-tions, particularly accounting for the progressively diminishing density matrix increments characteristic of con-verging SCF processes. The framework accommodates the unique characteristics of specific massive molecular systems or extensive collections thereof, such as thousands of docking arrangements between substantial protein structures and diverse small organic ligand molecules.
All bimolecular components-including approximations of two-center basis function overlaps via linear combi-nations of single-center auxiliary density functions-undergo efficient computation utilizing specialized database-stored inter-nuclear distance splines. For novel basis sets, the reference database can be promptly augmented through decomposition into universal exponential components with corresponding database enrichment.