Quantum Chemistry Density Matrix Renormalization Group in the Discrete Variable Representation.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Accurate quantum mechanical simulations are crucial for understanding molecular behavior.
• Traditional methods face challenges with large or complex systems.
• Developing efficient and accurate computational techniques is an ongoing need.

Purpose of the Study:

• To present a novel numerical implementation of the density matrix renormalization group (DMRG) algorithm.
• To utilize a hybrid discrete variable representation (DVR)/Gaussian basis set for enhanced computational efficiency.
• To apply this method to model hydrogen chain systems.

Main Methods:

• Discretization of real space along the z-axis using a DVR basis set.
• Representation of transversal planes using eigenstates of the transversal core Hamiltonian in a Gaussian basis.
• Computation of kinetic energy operator matrix elements exactly using local DVR basis sets.
• Reduction in the computation of two-electron repulsion integrals.

Main Results:

• The hybrid DMRG/DVR method was successfully applied to a one-dimensional pseudo-hydrogen chain under screened Coulomb potential.
• The method was further validated on a realistic hydrogen chain.
• Results obtained showed accuracy comparable to full configuration interaction (FCI) calculations.

Conclusions:

• The hybrid DVR/Gaussian basis set offers an efficient and accurate approach for quantum chemistry calculations.
• This implementation provides a robust tool for studying electronic structure in molecular systems.
• The method demonstrates potential for simulating more complex chemical and physical systems.