Efficient Implementation of the Second-Order Quasidegenerate Perturbation Theory with Density-Fitting and Cholesky Decomposition Approximations: Is It Possible To Use Hartree-Fock Orbitals for a Multiconfigurational Perturbation Theory?

The high cost of common multireference second-order perturbation theory (MRPT2) methods compared with the single-reference variant (MP2) arises from the expensive complete active space self-consistent field (CASSCF) orbital optimization step. Furthermore, the use of conventional four-index electron repulsion integrals (ERIs) prevents their application to larger molecular systems due to expensive I/O procedures. To address these bottlenecks of the multiconfigurational second-order quasidegenerate perturbation theory (MC-QDPT2), an efficient implementation of QDPT2 with the density-fitting (DF) and Cholesky decomposition (CD) approximations, denoted by DF-QDPT2 and CD-QDPT2, is reported. For the DF/CD-QDPT2 methods, the Hose-Kaldor approach is used. The DF-QDPT2 method, with the cc-pwCVTZ basis set, dramatically reduces the computational cost compared to conventional multiconfigurational QDPT2 (MC-QDPT2, from the GAMESS 2017.R2 package), with a more than 122-fold reduction for the largest member of the diradical test set considered. The DF approximation enables substantially accelerated energies to be obtained for the QDPT2 approach due to the significantly reduced I/O time. The performance of the DF-QDPT2 and CD-QDPT2 methods is compared with that of CASSCF, the multireference second-order perturbation theory (MRMP2), MC-QDPT2, and CASSCF-based second-order perturbation theory (CASPT2) methods for singlet-triplet energy splitting (E-ST) in O-2 and C-2 molecules and for the dissociation energy of F-2. For the O-2 and C-2 molecules, the performance of the DF-QDPT2 and CD-QDPT2 methods is significantly better than that of CASSCF, MRMP2, MC-QDPT2, and CASPT2; while for the F-2 case, the results of DF-QDPT2, CD-QDPT2, MRMP2, MC-QDPT2, and CASPT2 are similar and remarkably better than that of CASSCF, which fails dramatically. Moreover, the DF-QDPT2, CASSCF, CASPT2, and MRCI+Q methods are applied to potential energy curves (PECs) for N-2, CH4, and F-2 molecules. Our results demonstrate that the performance of DF-QDPT2 is substantially better than that of CASSCF and is comparable with that of CASPT2 for the molecules considered. Overall, the present application results demonstrate that the DF-QDPT2 and CD-QDPT2 methods are very promising for electronically challenging molecular systems suffering from (quasi)degeneracy problems, where the single-reference methods cannot provide an accurate electronic description, but the DF-QDPT2 and CD-QDPT2 methods can do so at significantly reduced computational costs.