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. 153, 164115 (2020)] 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.

52 pages, 6 figures, 4 tables

References in corpus (13)

• The density-matrix renormalization group in the age of matrix product states
• Heat-bath Configuration Interaction: An efficient selected CI algorithm inspired by heat-bath sampling
• From density-matrix renormalization group to matrix product states
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• The density matrix renormalization group for ab initio quantum chemistry
• Generic Construction of Efficient Matrix Product Operators
• Finite automata for caching in matrix product algorithms
• Multi-reference perturbation theory with Cholesky decomposition for the density matrix renormalization group
• Spectroscopic accuracy directly from quantum chemistry: application to ground and excited states of beryllium dimer
• Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
• Transcorrelated Density Matrix Renormalization Group
• Calculation of two-centre two-electron integrals over Slater-type orbitals revisited. III. Case study of the beryllium dimer
• Improved Stochastic Multireference Perturbation Theory for Correlated Systems with Large Active Spaces

Cited by in corpus (16)

• Extension of selected configuration interaction for transcorrelated methods
• Transcorrelated coupled cluster methods. II. Molecular systems
• Studies on the Transcorrelated Method
• Unveiling Intrinsic Many-Body Complexity by Compressing Single-Body Triviality
• Nonunitary projective transcorrelation theory inspired by the F12 ansatz
• Towards Efficient Quantum Computing for Quantum Chemistry: Reducing Circuit Complexity with Transcorrelated and Adaptive Ansatz Techniques
• Orbital optimisation in xTC transcorrelated methods
• Compactification of Determinant Expansions via Transcorrelation
• Complete Active Space Iterative Coupled Cluster Theory
• Shortcut to Chemically Accurate Quantum Computing via Density-based Basis-set Correction
• Striking the Right Balance of Encoding Electron Correlation in the Hamiltonian and the Wavefunction Ansatz
• QCMaquis 4.0: Multi-Purpose Electronic, Vibrational, and Vibronic Structure and Dynamics Calculations with the Density Matrix Renormalization Group
• Non-iterative Triples for Transcorrelated Coupled Cluster Theory
• Towards Balanced Description of Ground and Excited States with Transcorrelated F12 Methods
• Scaling up the transcorrelated density matrix renormalization group
• Partial separability of the Schroedinger equation combined with a Jastrow factor