Nuclear-electronic all-particle density matrix renormalization group

Area of Science:

• Quantum chemistry
• Computational physics
• Theoretical chemistry

Background:

• Accurate quantum mechanical calculations are crucial for understanding molecular behavior.
• Existing multicomponent methods face challenges with larger, complex systems.
• The Schrödinger equation describes quantum systems but is difficult to solve exactly.

Purpose of the Study:

• Introduce a novel method, Nuclear-Electronic All-Particle Density Matrix Renormalization Group (NEAP-DMRG), for solving the time-independent Schrödinger equation.
• Develop a robust approach for simultaneous treatment of electrons and other quantum particles.
• Overcome limitations of current multicomponent quantum chemistry methods.

Main Methods:

• Construct a multi-reference trial wave function using stochastically optimized non-orthogonal Gaussian orbitals.
• Iteratively refine Gaussian orbital positions and widths for a compact wave function expansion.
• Extend the Density Matrix Renormalization Group (DMRG) algorithm to handle multicomponent wave functions and correlations.

Main Results:

• NEAP-DMRG accurately approximates full configuration interaction energies for systems with >3 nuclei and >12 particles.
• Demonstrated the method's capability on small systems (H2, H3+) and a larger system (BH3).
• Successfully incorporated inter- and intra-species correlation effects.

Conclusions:

• NEAP-DMRG offers a powerful new tool for high-accuracy quantum mechanical calculations.
• The method is particularly effective for systems previously intractable for other multicomponent approaches.
• NEAP-DMRG advances the field of computational quantum chemistry.