Fast quantum chemistry calculations for large molecules and condensed-phase systems: The developments and applications of generalized energy-based fragmentation approach

Abstract

It is a challenge in theoretical chemistry to perform the quantum chemistry calculations for large molecules and condensed- phase systems due to the high scalings of the conventional quantum chemistry methods. In order to treat more and more complicated systems in experiments, the development of linear scaling quantum chemistry methods is an active area in theoretical studies. There are two categories of these methods. One is the category of first-principle base methods, including linear scaling Hartree-Fock (HF) and density functional theory (DFT) methods and local correlation methods. Another is the category of fragment-based methods, including density matrix based methods and energy-based fragmentation methods. The energy-based fragmentation approach has been developed rapidly in the last decade due to its simplicity, effectiveness, and extendibility. In this article, we review the developments and applications of the generalized energy-based fragmentation (GEBF) approach proposed in our research group. The basic idea of the GEBF approach is that the total ground-state energy of a large system can be linearly combined by the corresponding ground-state energies of various subsystems, each of which is embedded in the background charges on the places of those atoms outside the subsystem. In the GEBF approach, the target system is divided into various medium-sized fragments, each of which (called central fragment) is capped by its neighboring fragments to form a primitive subsystem. Then, the inclusion-exclusion principle is applied to all primitive subsystems to generate the derivative subsystems. The point charges, from natural population analysis, on all atoms are iteratively obtained by extracting the charges on the central fragments in primitive subsystems or combining the charges on all subsystems. Then the energies or energy derivatives of the target system could be combined by the corresponding values of all electrostatically embedded subsystems. The GEBF approach could be applied to the ground-state energies (including the relative energies or binding energies) of a broad range of large systems including molecular clusters, supramolecular systems, proteins, nucleic acids, and etc. The computational levels include HF, DFT, second-order Møller-Plesset perturbation theory (MP2), coupled cluster singles and doubles (CCSD), CCSD with triples correction [CCSD(T)], and explicitly correlated MP2-F12 and CCSD(T)-F12x (x=a,b) methods. With the GEBF energy derivatives (including energy gradients, Hessians, and so on), the approaches could be employed for optimizing the molecular geometries, performing ab initio molecular dynamics, computing the vibrational spectroscopies (including the IR and Raman spectroscopies) and nuclear magnetic resonance (NMR) chemical shifts of large systems at the HF, DFT, and MP2 levels. GEBF approach is also extended to the localized excited states by defining those subsystems including local excitation as the active subsystems, which are treated by the excited-state calculations at the time-dependent DFT or approximate equation-of-motion CCSD (CC2) levels. Then the GEBF-TDDFT or GEBF-CC2 could be used to compute electronic absorption spectra of solutions or large molecules with local excitations. The GEBF approach under the periodic boundary conditions (PBC) is also been implemented by constructing the subsystems in a super cell and employing the Ewald summation and compensation field methods to take the effect of the long-range electrostatic interaction of the crystal environment into account. The PBC-GEBF approach has been used to compute the lattice energies, crystal structures, IR and Raman spectra, and NMR chemical shifts of various condensed-phase systems, including molecular crystals, liquids, ionic liquid crystals, and solutions. Thus, the GEBF and PBC-GEBF approaches are expected to be widely applied to the energies, structures, and molecular properties of a broad range of large systems and condensed-phase systems.