Analytic energy gradients for orbital‐optimized MP3 and MP2.5 with the density‐fitting approximation: An efficient implementation

Abstract

Efficient implementations of analytic gradients for the orbital-optimized MP3 and MP2.5 and their standard versions with the density-fitting approximation, which are denoted as DF-MP3, DF-MP2.5, DF-OMP3, and DF-OMP2.5, are presented. The DF-MP3, DF-MP2.5, DF-OMP3, and DF-OMP2.5 methods are applied to a set of alkanes and noncovalent interaction complexes to compare the computational cost with the conventional MP3, MP2.5, OMP3, and OMP2.5. Our results demonstrate that density-fitted perturbation theory (DF-MP) methods considered substantially reduce the computational cost compared to conventional MP methods. The efficiency of our DF-MP methods arise from the reduced input/output (I/O) time and the acceleration of gradient related terms, such as computations of particle density and generalized Fock matrices (PDMs and GFM), solution of the Z-vector equation, back-transformations of PDMs and GFM, and evaluation of analytic gradients in the atomic orbital basis. Further, application results show that errors introduced by the DF approach are negligible. Mean absolute errors for bond lengths of a molecular set, with the cc-pCVQZ basis set, is 0.0001-0.0002 Å. © 2017 Wiley Periodicals, Inc.

State‐of‐the‐art computations of dipole moments using analytic gradients of high‐level density‐fitted coupled‐cluster methods with focal‐point approximations

“…In the CBS extrapolations, the DFT functionals were treated as the HF method. All computations were performed with the development version of the PSI4 program package, which includes Bozkaya's DFOCC module …”

“…Tensor decomposition of the electron repulsion integrals (ERIs) has been of remarkable interest in modern computational chemistry . The most common ERI decomposition method is density fitting (DF) . In the DF technique, the four‐index ERIs are written in terms of three‐index DF factors.…”

“…Analytic gradient methods are very helpful to locate stationary points on potential energy surfaces, as well as for the computation of one‐electron properties, such as dipole moments (DMs) . Analytic gradients for the density‐fitted post‐HF methods have been reported for second‐order Møller–Plesset perturbation theory (MP2) with conventional HF reference (RI‐MP2), as well as with the DF‐HF reference, coupled cluster model CC2, local MP2 (DF‐LMP2), complete active space second‐order perturbation theory (DF‐CASPT2), orbital‐optimized MP2 (DF‐OMP2), local time‐dependent coupled cluster response theory (DF‐TD‐LCC2), third‐order Møller–Plesset perturbation theory (DF‐MP3), the DF‐MP2.5 model, linearized coupled‐cluster doubles (DF‐LCCD), and recently for the density‐fitted CCSD (DF‐CCSD), and CCSD(T) methods [DF‐CCSD(T)] . With the help of the DF approach, one can replace the 4‐index integrals and 4‐index two‐particle density matrix (TPDM) with 2‐index and 3‐index integrals and TPDMs for analytic gradients.…”

“…Further, we also evaluate dipole moments using common density functional theory (DFT) functionals, such as B3LYP, BP86, M06‐2X, BLYP . The equations presented have been coded in C++ language and added to the density‐fitted orbital‐optimized CC (DFOCC) module of the PSI4 package …”

Energy and Analytic Gradients for the Orbital-Optimized Coupled-Cluster Doubles Method with the Density-Fitting Approximation: An Efficient Implementation

“…42 One of the most common approximation for the tensor factorization of the electron repulsion integrals (ERIs) is the density fitting (DF) technique. 22,23,[30][31][32][43][44][45][46][47][48][49][50][51][52][53][54][55][56] With the help of the DF technique, one can express the four-dimensional ERIs in terms of three-dimensional tensors. In addition to to DF, the partial Cholesky decomposition (CD) of the ERI tensor is also commonly employed as a tensor decomposition approach.…”