Explicitly Correlated Electronic Structure Calculations with Transcorrelated Matrix Product Operators

Abstract

In this work, we present the first implementation of the transcorrelated electronic Hamiltonian in an optimization procedure for matrix product states by the density matrix renormalization group (DMRG) algorithm. In the transcorrelation ansatz, the electronic Hamiltonian is similarity-transformed with a Jastrow factor to describe the cusp in the wave function at electron–electron coalescence. As a result, the wave function is easier to approximate accurately with the conventional expansion in terms of one-particle basis functions and Slater determinants. The transcorrelated Hamiltonian in first quantization comprises up to three-body interactions, which we deal with in the standard way by applying robust density fitting to two- and three-body integrals entering the second-quantized representation of this Hamiltonian. The lack of hermiticity of the transcorrelated Hamiltonian is taken care of along the lines of the first work on transcorrelated DMRG [J. Chem. Phys.2020153164115] by encoding it as a matrix product operator and optimizing the corresponding ground state wave function with imaginary-time time-dependent DMRG. We demonstrate our quantum chemical transcorrelated DMRG approach at the example of several atoms and first-row diatomic molecules. We show that transcorrelation improves the convergence rate to the complete basis set limit in comparison to conventional DMRG. Moreover, we study extensions of our approach that aim at reducing the cost of handling the matrix product operator representation of the transcorrelated Hamiltonian.

Density Matrix Renormalization Group for Transcorrelated Hamiltonians: Ground and Excited States in \emph{ab initio} Systems

“…Although in principle it may not be possible to treat all non-Hermitian Hamiltonians in this way, in practice we found this simple scheme to work well with the non-Hermitian TC Hamiltonian, and we observe no significant numerical issues across a wide range of benchmark systems. In contrast with the ITE approach used by Baiardi and coworkers, 42,57 we show that our approach can be easily extended for treating both the ground and excited states. In the remainder of the paper, we refer to timeindependent TC-DMRG and conventional DMRG as TC-DMRG and DMRG, respectively, and to imaginary-time evolution TC-DMRG as ITE-TC-DMRG.…”

“…For comparison, we also show the curve obtained by ITE-TC-DMRG from Ref. 57 . We note in passing that at large separations, the TC-DMRG curve in cc-pVDZ basis trends downwards slightly, while in cc-pVTZ basis, this trend is largely gone.…”

“…55 The former study reveals that by optimizing the correlator parameters the right groundstate eigenvector can be made much more compact, ac-celerating convergence of the FCIQMC calculations with respect to walker population. Subsequent studies combining TC and other various methods, such as CC 55,56 and DMRG, 42,57 exhibit improvements in both efficiency and accuracy (at fixed excitation level in the CC ansatz) thanks to this property.…”

“…Very recently, they have further shown that the ITE based TC-DMRG approach is equally applicable to ab initio systems for computing ground state energies. 57 Some other approaches 63 have been reported for more general non-Hermitian Hamiltonians where eigenvalues are allowed to have imaginary parts, but such cases are beyond the scope of the TC framework.…”

Extension of selected configuration interaction for transcorrelated methods

“…Applications of the similarity transformation for Hubbard model Hamiltonians with the Gutzwiller Ansatz for the correlation factor 74,75 were carried using FCIQMC 53 and density matrix renormalization group 76 . Adaptations of the TC equations to matrix product state methodology have been also reported 72,77 .…”