Explicitly Correlated Electronic Structure Calculations with Transcorrelated Matrix Product Operators

Area of Science:

• Quantum Chemistry
• Computational Physics
• Many-Body Methods

Background:

• Accurate electronic structure calculations are crucial in quantum chemistry.
• Conventional methods struggle with electron-electron cusp conditions.
• Matrix product states and DMRG offer a powerful framework for strongly correlated systems.

Purpose of the Study:

• To implement the transcorrelated electronic Hamiltonian within a matrix product states optimization procedure using DMRG.
• To improve the accuracy and convergence of quantum chemical calculations.
• To investigate methods for handling the computational cost of the transcorrelated Hamiltonian.

Main Methods:

• Similarity transformation of the electronic Hamiltonian with a Jastrow factor.
• Density fitting for two- and three-body integrals in the second-quantized representation.
• Encoding the non-Hermitian transcorrelated Hamiltonian as a matrix product operator.
• Optimization of the ground state wave function using imaginary-time time-dependent DMRG.

Main Results:

• Successful implementation of the transcorrelated DMRG approach.
• Demonstration on atoms and first-row diatomic molecules.
• Observed improved convergence rates to the complete basis set limit compared to conventional DMRG.
• Exploration of cost-reduction strategies for the matrix product operator representation.

Conclusions:

• Transcorrelated DMRG provides a more efficient route to accurate electronic structure.
• The method enhances convergence properties for basis set extrapolation.
• Further research can optimize the computational scaling of this promising approach.