Generalized Energy-Based Fragmentation Approach and Its Applications to Macromolecules and Molecular Aggregates

Abstract

Conspectus The generalized energy-based fragmentation (GEBF) approach provides a very simple way of approximately evaluating the ground-state energy or properties of a large system in terms of ground-state energies of various small "electrostatically embedded" subsystems, which can be calculated with any traditional ab initio quantum chemistry (X) method (X = Hartree-Fock, density functional theory, and so on). Due to its excellent parallel efficiency, the GEBF approach at the X theory level (GEBF-X) allows full quantum mechanical (QM) calculations to be accessible for systems with hundreds and even thousands of atoms on ordinary workstations. The implementation of the GEBF approach at various theoretical levels can be easily done with existing quantum chemistry programs. This Account reviews the methodology, implementation, and applications of the GEBF-X approach. This method has been successfully applied to optimize the structures of various large systems including molecular clusters, polypeptides, proteins, and foldamers. Such investigations could allow us to elucidate the origin and nature of the cooperative interaction in secondary structures of long peptides or the driving force of the self-assembly processes of aromatic oligoamides. These GEBF-based QM calculations reveal that the structures and stability of various complex systems result from a subtle balance of many types of noncovalent interactions such as hydrogen bonding and van der Waals interactions. The GEBF-based ab initio molecular dynamics (AIMD) method also allows the investigation of dynamic behaviors of large systems on the order of tens of picoseconds. It was demonstrated that the conformational dynamics of two model peptides predicted by GEBF-based AIMD are noticeably different from those predicted by the classical force field MD method. With the target of extending QM calculations to molecular aggregates in the condensed phase, we have implemented the GEBF-based multilayer hybrid models, which could provide satisfactory descriptions of the binding energies between a solute molecule and its surrounding waters and the chain-length dependence of the conformational changes of oligomers in aqueous solutions. A coarse-grained polarizable molecular mechanics model, furnished with GEBF-X dipole moments of subsystems, exhibits some advantages of treating the electrostatic polarization with reduced computational costs. We anticipate that the GEBF approach will continue to develop with the ultimate goal of studying complicated phenomena at mesoscopic scales and serve as a practical tool to elucidate the structure and dynamics of chemical and biological systems.

Automated error control in divide‐and‐conquer self‐consistent field calculations

“…[5,6] In the molecular tailoring approach, [7] Gadre and coworkers defined the R-goodness parameter, [8,9] which indicates the quality of a fragmentation scheme based on the distance. The generalized energy-based fragmentation (GEBF) approach [10] can also employ a distance-based accuracy control scheme. [11] In the divide-and-conquer (DC) method, [12][13][14] the size of the buffer region controls primarily the accuracy of the approximation.…”

Three pillars for achieving quantum mechanical molecular dynamics simulations of huge systems: Divide‐and‐conquer, density‐functional tight‐binding, and massively parallel computation

“…Reduction of the computational costs for quantum chemical calculations of huge systems can be accomplished by adopting linear‐scaling technique, which avoids explicitly solving the secular equation of the entire system . Examples of such linear‐scaling approaches that can provide the energy gradient include the density matrix minimization method, the fragment molecular orbital (FMO) method, the molecular tailoring method, the elongation method, the systematic molecular fragmentation method, the generalized energy‐based fragmentation method, and the divide‐and‐conquer (DC) method . Kobayashi, Nakai, and coworkers extended the DC method from the mean‐field theory to correlated wave function theories such as the Møller–Plesset perturbation and coupled cluster theories .…”

Parallel implementation of efficient charge–charge interaction evaluation scheme in periodic divide‐and‐conquer density‐functional tight‐binding calculations

“…The relative errors decrease logarithmically as k increases and the plots level off at some replication level on account of attaining the criterion of multipole expansion. The agreement of force with the Ewald summation is as good as five significant digits using p 5 8 and k 5 4, and it passes some arbitrary acceptable accuracy of 2310 24 . [86] The deviation is likely maintained for larger systems according to the system size dependence shown in Figure S1 in Supporting Information.…”

“…The latter two approaches practically reduce the computational complexity to a nearly linear complexity. Thus, interest in such low‐scaling QM‐MD simulations has become intense …”

“…Thus, interest in such low-scaling QM-MD simulations has become intense. [14][15][16][17][18][19][20][21][22][23][24][25][26] With respect to the above considerations, we recently reported a massively parallel implementation of a divide-andconquer density-functional tight-binding (DC-DFTB) method. [27] The DFTB method [28][29][30][31] can be recognized as the simplified version of the Kohn-Sham DFT.…”