Local random phase approximation with projected oscillator orbitals

Abstract

An approximation to the many-body London dispersion energy in molecular systems is expressed as a functional of the occupied orbitals only. The method is based on the local-RPA theory. The occupied orbitals are localized molecular orbitals and the virtual space is described by projected oscillator orbitals, i.e. functions obtained by multiplying occupied localized orbitals with solid spherical harmonic polynomials having their origin at the orbital centroids. Since we are interested in the long-range part of the correlation energy, responsible for dispersion forces, the electron repulsion is approximated by its multipolar expansion. This procedure leads to a fully non-empirical longrange correlation energy expression. Molecular dispersion coefficients calculated from determinant wave functions obtained by a range-separated hybrid method reproduce experimental values with less than 15% error.

Selected Columns of the Density Matrix in an Atomic Orbital Basis I: An Intrinsic and Non-Iterative Orbital Localization Scheme for the Occupied Space

“…[13][14][15] More recently, LMOs have also been used to quantum mechanically justify the "curly arrow" notation used to denote the movement of electrons when discussing chemical reactions. [16][17][18] In addition to their analytical utility, LMOs can also be used to reduce the computational cost associated with wavefunction theory (WFT) [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] and density functional theory (DFT) [37][38][39][40][41][42][43][44][45][46][47][48] methods, thereby providing an avenue towards linear-scaling algorithms 49 to treat large-scale systems. This follows from the invariance of the mean-field Hartree-Fock (HF) and Kohn-Sham (KS) groundstate energies with respect to unitary (orthogonal) transformations of the occupied canonical molecular orbitals (CMOs), 50 i.e., the eigenfunctions of the Fock (or effective Hamiltonian) matrix.…”

“…[33][34][35][36] In particular, the use of LMOs allows these methods to define and take advantage of local correlation domains, which significantly decrease the number of excitations that must be considered to capture subtle electron correlation effects. In addition, LMOs can also be used in post-DFT methods such as the random phase approximation (RPA) 41,42 and GW-based approaches, 38,40 which explicitly account for higher-order many-body effects at a fraction of the computational cost.…”