Explicitly correlated electronic structure calculations with transcorrelated matrix product operators
arXiv:2202.08709 · doi:10.1021/acs.jctc.2c00167
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.
arXiv comment52 pages, 6 figures, 4 tables
References in corpus (48)
- The density-matrix renormalization group in the age of matrix product states
- Unifying time evolution and optimization with matrix product states
- Time-evolution methods for 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
- Automated Selection of Active Orbital Spaces
- 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
- Tensor product methods and entanglement optimization for ab initio quantum chemistry
- Controlling the accuracy of the density matrix renormalization group method: The Dynamical Block State Selection approach
- An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy
- Stripes in the two-dimensional t-J model with infinite projected entangled-pair states
- Quantum information analysis of electronic states at different molecular structures
- An Efficient Matrix Product Operator Representation of the Quantum-Chemical Hamiltonian
- Time integration of tensor trains
- CASSCF with Extremely Large Active Spaces using the Adaptive Sampling Configuration Interaction Method
- Generic Construction of Efficient Matrix Product Operators
- Finite automata for caching in matrix product algorithms
- Born-Oppenheimer potential for H
- Selected configuration interaction dressed by perturbation
- Multi-reference perturbation theory with Cholesky decomposition for the density matrix renormalization group
- Large-scale quantum-dynamics with matrix product states
- Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems
- The Delicate Balance of Static and Dynamic Electron Correlation
- Density Matrix Renormalization Group with Efficient Dynamical Electron Correlation Through Range Separation
- autoCAS: a program for fully automated multi-configurational calculations
- Spin-adapted Matrix Product States and Operators
- Coupled cluster method with single and double excitations tailored by matrix product state wave functions
- Automated Identification of Relevant Frontier Orbitals for Chemical Compounds and Processes
- Spectroscopic accuracy directly from quantum chemistry: application to ground and excited states of beryllium dimer
- Compact numerical solutions to the two-dimensional repulsive Hubbard model obtained via non-unitary similarity transformations
- Similarity transformation of the electronic Schrödinger equation via Jastrow factorisation
- Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
- Testing quantum electrodynamics in the lowest singlet states of beryllium atom
- Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer
- Complete basis set extrapolation of electronic correlation energies using the Riemann zeta function
- A Density-Based Basis-Set Correction For Wave Function Theory
- Local Matrix Product Operators: Canonical Form, Compression, & Control Theory
- Dynamical phase behavior of the single- and multi-lane asymmetric simple exclusion process via matrix product states
- Transcorrelated coupled cluster methods
- Entanglement structure of the Hubbard model in momentum space
- Tailored Coupled Cluster Theory in Varying Correlation Regimes
- Transcorrelated Density Matrix Renormalization Group
- A basis-set error correction based on density-functional theory for strongly correlated molecular systems
- Calculation of two-centre two-electron integrals over Slater-type orbitals revisited. III. Case study of the beryllium dimer
- Electron Dynamics with the Time-Dependent Density Matrix Renormalization Group
- Coupled Cluster Externally Corrected by Adaptive Configuration Interaction
- Improved Stochastic Multireference Perturbation Theory for Correlated Systems with Large Active Spaces
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- Extension of selected configuration interaction for transcorrelated methods
- Transcorrelated coupled cluster methods. II. Molecular systems
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- 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