Large-Scale Variational Two-Electron Reduced-Density-Matrix-Driven Complete Active Space Self-Consistent Field Methods

Abstract

A large-scale implementation of the complete active space self-consistent field (CASSCF) method is presented. The active space is described using the variational two-electron reduced-density-matrix (v2RDM) approach, and the algorithm is applicable to much larger active spaces than can be treated using configuration-interaction-driven methods. Density fitting or Cholesky decomposition approximations to the electron repulsion integral tensor allow for the simultaneous optimization of large numbers of external orbitals. We have tested the implementation by evaluating singlet-triplet energy gaps in the linear polyacene series and two dinitrene biradical compounds. For the acene series, we report computations that involve active spaces consisting of as many as 50 electrons in 50 orbitals and the simultaneous optimization of 1892 orbitals. For the dinitrene compounds, we find that the singlet-triplet gaps obtained from v2RDM-driven CASSCF with partial three-electron N-representability conditions agree with those obtained from configuration-interaction-driven approaches to within one-third of 1 kcal mol(-1). When enforcing only the two-electron N-representability conditions, v2RDM-driven CASSCF yields less accurate singlet-triplet energy gaps in these systems, but the quality of the results is still far superior to those obtained from standard single-reference approaches.

Role of exact exchange in thermally-assisted-occupation density functional theory: A proposal of new hybrid schemes

“…Similar to previous findings [20,21,45,115,122,124], the ground states of n-acenes are singlets for all the chain lengths investigated.…”

“…Recently, linear n-acenes (C 4n+2 H 2n+4 ), containing n linearly fused benzene rings (see Figure 10), have attracted considerable interest in the research community owing to their promising electronic properties [20,21,[45][46][47][48][109][110][111][112][113][114][115][116][117][118][119][120][121][122][123][124]. The electronic properties of nacenes have been found to be highly dependent on the chain lengths.…”

“…Consequently, the experimental singlet-triplet energy gaps (ST gaps) of n-acenes are only available up to pentacene [109][110][111][112]. On the theoretical side, since n-acenes belong to conjugated π-orbital systems, high-level ab initio multi-reference methods, such as the density matrix renormalization group (DMRG) algorithm [115,122], the variational twoelectron reduced density matrix (2-RDM) method [121,124], and other high-level methods [114,[118][119][120], are typically required to capture the essential strong static correlation effects.…”

Orbital optimisation in the perfect pairing hierarchy: applications to full-valence calculations on linear polyacenes

“…80, and in contrast to the π active space results obtained using e.g. DMRG [55] and VDRM [66,68,69], we show the strong correlation is quenched when all valence orbitals are included in the active space. Furthermore, going beyond the STO-3G basis for the first time with a high-level full-valence method shows that improvement of the basis set leads to even more quenching of the strong correlation for the same active space.…”

“…Famously, DMRG calculations have been used to show that the larger linear polyacenes exhibit strong correlation for their π electrons [55]. Other approaches used have included density functional theory [56][57][58][59][60][61], multiconfiguration pair-density functional theory [62], projected Hartree-Fock theory [63], the random phase approximation [64], configuration interaction [60] (CI), adaptive CI [27], GW theory [65], variational two-electron reduced density matrix (VRDM) theory [66][67][68][69], Møller-Plesset perturbation theory [61,[70][71][72][73], spin-flip methods [74,75], CAS-SCF [53,59,71,72,76] as well as restricted-active space self-consistent field theory [77], valence bond [78] and CC valence bond (CCVB) theory [79,80], CC theory [70][71][72]80] and multireference averaged quadratic CC theory [81,82], an algebraic diagrammatic construction scheme [83], as well as PPH methods with approximate orbitals [50].…”