Symmetry-adapted perturbation theory based on multiconfigurational wave function description of monomers

Abstract

We present a formulation of the multiconfigurational (MC) wave function symmetryadapted perturbation theory (SAPT). The method is applicable to noncovalent interactions between monomers which require a multiconfigurational description, in particular when the interacting system is strongly correlated or in an electronically excited state. SAPT(MC) is based on one-and two-particle reduced density matrices of the monomers and assumes the single-exchange approximation for the exchange energy contributions. Second-order terms are expressed through response properties from extended random phase approximation (ERPA) equations. SAPT(MC) is applied either with generalized valence bond perfect pairing (GVB) or with complete active space self consistent field (CASSCF) treatment of the monomers. We discuss two model multireference systems: the H 2 • • • H 2 dimer in out-of-equilibrium geometries and interaction between the argon atom and excited state of ethylene. In both cases SAPT(MC) closely reproduces benchmark results. Using the C 2 H * 4 • • • Ar complex as an example, we examine second-order terms arising from negative transitions in the linear response function of an excited monomer. We demonstrate that the negative-transition terms must be accounted for to ensure qualitative prediction of induction and dispersion energies and develop a procedure allowing for their computation. Factors limiting the accuracy of SAPT(MC) are discussed in comparison with other second-order SAPT schemes on a data set of small single-reference dimers.

Towards the simulation of large scale protein–ligand interactions on NISQ-era quantum computers

“…At the lowest order this gives rise to SAPT(HF) (or SAPT0), where each term is evaluated using Hartree-Fock density matrices [20]. Another popular approach is to use density functional theory SAPT(DFT) [24,25] to account for intramonomer electron correlation, but this approach is naturally limited by the performance of the chosen density functional [26].…”

“…The first order SAPT expressions can then be evaluated using only the ground state unperturbed wavefunctions of the individual monomers, i.e., |Ψ 0 = |Ψ A ⊗ |Ψ B . We will use the density matrix formulation of SAPT [27] systematized by Korona [28][29][30] and recently fully implemented for complete active space self consistent field (CASSCF) wavefunctions by Hapka and et al [26] This formalism allows for the evaluation of the terms appearing in Eq. ( 4) using just the ground state one-and twoparticle reduced density matrices of the monomers with additional response terms for the second order terms.…”

“…We will modify these systems to ensure one of the monomers in question has some multi reference character that cannot be well described by SAPT(RHF). Note that previous studies of SAPT(CASSCF) have found little benefit of the method for single-reference problems in the S22 benchmark set [26], so we only focus on more challenging multi-reference problems. In all examples we will benchmark our results against classical SAPT(CASCI) that employs the same active space as the SAPT(VQE) computations.…”

Towards the Simulation of Large Scale Protein-Ligand Interactions on NISQ-era Quantum Computers

“…The first order SAPT expressions can then be evaluated using only the ground state unperturbed wavefunctions of the individual wavefunctions, i.e., |Ψ 0 = |Ψ A ⊗ |Ψ B . We will use the density matrix formulation of SAPT [27] systematized by Korona [28][29][30] and recently fully implemented for complete active space self consistent field (CASSCF) wavefunctions by Hapka and et al [26] This formalism allows for the evaluation of the terms appearing in Eq. (4) using just the ground state one-and twoparticle reduced density matrices of the monomers with additional response terms for the second order terms.…”