Fully variational incremental CASSCF

Abstract

The complete-active-space self-consistent field (CASSCF) method is a canonical electronic structure theory that holds a central place in conceptualizing and practicing first principles simulations. For application to realistic molecules, however, the CASSCF must be approximated to circumvent its exponentially scaling computational costs. Applying the many-body expansion—also known as the method of increments—to CASSCF (iCASSCF) has been shown to produce a polynomially scaling method that retains much of the accuracy of the parent theory and is capable of treating full valence active spaces. Due to an approximation made in the orbital gradient, the orbital parameters of the original iCASSCF formulation could not be variationally optimized, which limited the accuracy of its nuclear gradient. Herein, a variational iCASSCF is introduced and implemented, where all parameters are fully optimized during energy minimization. This method is able to recover electronic correlations from the full valence space in large systems, produce accurate gradients, and optimize stable geometries as well as transition states. Demonstrations on challenging test cases, such as the oxoMn(salen)Cl complex with 84 electrons in 84 orbitals and the automerization of cyclobutadiene, show that the fully variational iCASSCF is a powerful tool for describing challenging molecular chemistries.

Taming the Sign Problem in Auxiliary-Field Quantum Monte Carlo Using Accurate Wave Functions

“…The genuinely multireference Mukherjee’s CCSD (MR-MkCCSD­(T)) yields a barrier height within about 1 kcal/mol of the fp-AFQMC result. Multireference configuration interaction with the Q correction (MRCI+Q) and incremental complete active space configuration interaction (iCAS-CI) also give energy gaps close to the fp-AFQMC value. Finally, despite the poor performance of CCSD­(T), it provides a remarkably accurate basis set correction for fp-AFQMC.…”

“…CCSD­(T) overestimates the gap substantially due to its poor description of the transition state. An iterative treatment of triple excitations in CCSDT or its cheaper approximation CC­(t;3) almost entirely corrects this error, signaling the failure of perturbative treatment of triples to describe the biradical transition state. Tailored CCSD (TCCSD) with a small (2e, 2o) active space reference overestimates the barrier height, while the perturbative triples correction overcorrects this error.…”

Taming the sign problem in auxiliary field quantum Monte Carlo using accurate trial wave functions

“…The minima correspond to a D 2h rectangular geometry, while the transition state has a square D 4h geometry (figure 5). Some geometry optimization studies find slightly bent transition state structures, 59 but due to the flatness of the energy surface near the transition state, energy differences between different geometries used for transition states in various studies are tiny (less than a mH in most cases). Carbon 1s orbitals were frozen, leading to correlation spaces of size (20e, 72o) and (20e, 172o) in the cc-pVDZ and cc-pVTZ basis sets, respectively.…”

“…Full details of the wave functions can be found in the SI. 58 9.4 12.9 TCCSD(T) (2, 2) 58 4.6 7.0 TCCSD (12, 12) 61 -9.2 MR-MkCCSD(T) 62 7.8 8.9 MRCI+Q 61 -9.2 fp-AFQMC/CCSD(T) -10.9(4) fp-AFQMC 8.4(4) 10.2(4) iCAS-CI (6-31+G** basis) 59 11 Experiment 63 1.6-10…”

Cluster many-body expansion: a many-body expansion of the electron correlation energy about a cluster mean-field reference

“…77,78 The incremental FCI (iFCI) method by Zimmerman et al 79,80 used SHCI 14 as a solver for higher order calculations and has also been extended to do orbital optimization. 81,82 Eriksen and Gauss proposed the many-body expansion full configuration interaction (MBE-FCI) method by expanding over virtual orbitals [83][84][85] . A generalized MBE-FCI was later proposed 86 and has been extended to excited states.…”