Energy and analytic gradients for the orbital-optimized coupled-cluster doubles method with the density-fitting approximation: An efficient implementation

Abstract

Efficient implementations of the orbital-optimized coupled-cluster doubles [or simply "optimized CCD", OCCD, for short] method and its analytic energy gradients with the density-fitting (DF) approach, denoted by DF-OCCD, are presented. In addition to the DF approach, the Cholesky-decomposed variant (CD-OCCD) is also implemented for energy computations. The computational cost of the DF-OCCD method (available in a plugin version of the DFOCC module of Psi4) is compared with that of the conventional OCCD (from the Q-Chem package). The OCCD computations were performed with the Q-chem package, in which it is denoted by OD. In the conventional OCCD, one needs to perform four-index integrals transformations at each CCD iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD provides dramatically lower computational costs compared to OCCD, there are almost 8-fold reductions in the computational time for the C 6 H 14 molecule with the cc-pVTZ basis set. For open-shell geometries, interaction energies, and hydrogen transfer reactions, DF-OCCD provides significant improvements upon DF-CCD. Further, the performance of the DF-OCCD method is substantially better for harmonic vibrational frequencies in the case of symmetry breaking problems. Moreover, several factors make DF-OCCD more attractive compared to CCSD: (1) for DF-OCCD there is no need for orbital relaxation contributions in analytic gradient computations (2) active spaces can readily be incorporated into DF-OCCD (3) DF-OCCD provides accurate vibrational frequencies when symmetry-breaking problems are observed (4) in its response function, DF-OCCD avoids artificial poles; hence, excited-state molecular properties can be computed via linear response theory (5) Symmetric and asymmetric triples corrections based on DF-OCCD [DF-OCCD(T)] has a significantly better performance in near degeneracy regions.

The versatility of the Cholesky decomposition in electronic structure theory

“…To continue, Bozkaya et al have implemented over the last few years in a collective effort CD and RI/DF for various orbital-optimized schemes (the OMP2, OMP2.5, and OCCSD methods), [53][54][55] quasi-degenerate perturbation theory, 56 as well as energies and analytic gradients for OCCSD, and EOM-CCSD. 57,58 These CD approaches are available 35 in the Psi4 program package. 59 Similarly, Hohenstein et al have presented impressive implementations of CD ERI methods in connection with reduced-rank CC theory on GPUs, 60 combined with tensor hypercontraction of the doubles amplitudes.…”

The versatility of Cholesky decomposition of electron repulsion integrals

“…One can also mention the collective effort by Bozkaya and co-workers who over the last few years implemented CD and RI/DF for various orbital-optimized schemes (the OMP2, OMP2.5, and OCCSD methods), [35][36][37] but also recently in connection with quasi-degenerate perturbation theory, energies and analytic gradients for OCCSD, and EOM-CCSD. [38][39][40] Similarly, Hohenstein et al have presented impressive implementations of CD ERI methods in connection with reduced-rank CC theory on GPUs, 41 and combined with tensor hypercontraction of the doubles amplitudes. 42 To this list of implementations of CD ERIs in ab initio methods one can also add a variational two-particle reduced-density-matrix driven CASSCF method, 43 a self-consistent-field valence bond (VBSCF) method, 44 and an implementation in density matrix renormalization group (DMRG) second-order N -electron valence state perturbation theory (NEVPT2).…”

ManyHF: A pragmatic automated method of finding lower-energy Hartree–Fock solutions for potential energy surface development

“…So far, such endeavors have mostly approached the breakdown of SR correlated methods from the direction of the correlated method, and a vast array of schemes have been proposed to improve the performance of traditional SR methods at geometries with multireference character. [30][31][32][33][34][35][36][37][38] At the same time, the possibility of improving the HF reference itself has seen little attention, especially in the context of PES development, where we could only find a single example. 39 While manually ensuring that all fitting points have converged to the desired electronic state is obviously unfeasible, and the worst case computational complexity of the HF problem (NP-complete 40 ) makes a hypothetical HF solver that has guaranteed convergence to the global minimum impractical, it may still be possible to improve results for chemically relevant systems at an affordable computational cost.…”