Dual-cone variational calculation of the two-electron reduced density matrix

Abstract

The computation of strongly correlated quantum systems is challenging because of its potentially exponential scaling in the number of electron configurations. Variational calculation of the two-electron reduced density matrix (2-RDM) without the many-electron wave function exploits the pairwise nature of the electronic Coulomb interaction to compute a lower bound on the ground-state energy with polynomial computational scaling. Recently, a dual-cone formulation of the variational 2-RDM calculation was shown to generate the ground-state energy, albeit not the 2-RDM, at a substantially reduced computational cost, especially for higher N -representability conditions such as the T2 constraint. Here we generalize the dual-cone variational 2-RDM method to compute not only the ground-state energy but also the 2-RDM. The central result is that we can compute the 2-RDM from a generalization of the Hellmann-Feynman theorem. Specifically, we prove that in the Lagrangian formulation of the dual-cone optimization the 2-RDM is the Lagrange multiplier. We apply the method to computing the energies and properties of strongly correlated electrons-including atomic charges, electron densities, dipole moments, and orbital occupations-in an illustrative hydrogen chain and the nitrogen-fixation catalyst FeMoco. The dual variational computation of the 2-RDM with T2 or higher N -representability conditions provides a polynomially scaling approach to strongly correlated molecules and materials with significant applications in atomic and molecular and condensed-matter chemistry and physics.

Interplay of Electronic and Geometric Structure Tunes Organic Biradical Character in Bimetallic Tetrathiafulvalene Tetrathiolate Complexes

“…The accurate resolution of the singlet biradical character present in the studied systems requires the use of multireference methods. Here, we performed [4,4] active space CASSCF calculations with NEVPT2 as implemented in PySCF, − while larger CASSCF calculations with active spaces as large as [24,24] were performed with the variational 2-RDM (V2RDM) method − as implemented in the Maple quantum chemistry package. , Additional post-CAS calculations were undertaken on the TTFtt ligand using the ACSE method with the Maple quantum chemistry package, which when seeded with an initial guess from a multireference CAS calculation, allows the resolution of the on-top dynamic correlation with an accuracy comparable to that of coupled cluster with singles, doubles, and perturbative triples (CCSD­(T)). − Geometry optimizations and frequency calculations were performed using density functional theory (DFT) with the B3LYP and MN15 functionals as implemented in Gaussian 16, revision A.03 . The Pople basis sets 6-31G and 6-31G* , were used to treat the light atoms H, C, N, P, S, Fe, Ni, while the heavy atoms Sn, Pd, Pt were treated using the LANL2DZ and LANL2TZ basis sets.…”

“…The accurate resolution of the singlet biradical character present in the studied systems requires the use of multi-reference methods. Here, we performed [4,4] active space CASSCF calculations with NEVPT2 as implemented in PySCF, [58][59][60] while larger CASSCF calculations with active spaces as large as [24,24] were performed with the variational 2-RDM (V2RDM) method [61][62][63][64][65][66][67] as implemented in the Maple Quantum Chemistry Package. 68,69 Additional post-CAS calculations were undertaken on the TTFtt ligand using the ACSE method with the Maple Quantum Chemistry Package, which when seeded with an initial guess from a multireference CAS calculation, allows the resolution of the on-top dynamic correlation with an accuracy comparable to that of coupled cluster with singles, doubles and perturbative triples (CCSD(T)).…”

Beginnings of exciton condensation in coronene analog of graphene double layer

“…In this paper, we computationally examine the beginnings of exciton condensation in a double layer composed of coronene. Utilizing variational 2-RDM theory [47][48][49][50][51][52][53][54][55][56][57][58] , we explore the largest eigenvalue (λ G ) of the modified particle-hole reduced density matrix ( G)-which corresponds to the largest population of excitons in a single particle-hole quantum state-for various coronenebilayer geometries, such that an eigenvalue above the Pauli-like limit of one indicates exciton condensation as more than one exciton is occupying a single state and a larger eigenvalue indicates a higher degree of exciton condensate character. We compare the maximal exciton populations (λ G ) as a function of distance between the layers of coronene and note that, near 2 Å, the population peaks at around 1.8 with interlayer excitons being noted via our visualization technique at this distance.…”

Quantum Simulation of Molecules without Fermionic Encoding of the Wave Function

“…Both the preparation and measurement phases use fermionic encoding of the wave function. Once the 2-RDM is determined, that energy can be computed on the classical computer as in variational 2-RDM theory [44][45][46][47][48][49][50][51][52][53][54] from…”