Analytical gradients of variational reduced-density-matrix and wavefunction-based methods from an overlap-reweighted...

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Variational two-electron reduced-density matrix (2-RDM) methods are crucial for accurately describing electron correlation in molecules.
• Calculating analytical gradients is essential for performing geometry optimizations and understanding molecular structures.
• Current methods often face challenges with the dependence of N-representability conditions on the orbital-overlap matrix.

Purpose of the Study:

• To derive and implement analytical gradients for variational 2-RDM methods.
• To develop a formulation that removes the dependence on the orbital-overlap matrix for N-representability conditions.
• To apply the new gradient method for geometry optimizations of transition metal complexes.

Main Methods:

• Transformation of atomic-orbital reduced-density matrices using Cholesky decomposition.
• Generation of a Hellmann-Feynman-like expression for the gradient.
• Application to variational 2-RDM, full configuration interaction, and complete active-space self-consistent-field methods.

Main Results:

• Successful derivation of analytical gradients for variational 2-RDM methods.
• Demonstrated applicability to various quantum chemical methods.
• Performed geometry optimizations on CrF6 and Ni(edt)2 complexes, validating the approach.

Conclusions:

• The developed analytical gradient formulation provides an efficient and robust tool for electronic structure calculations.
• This method facilitates accurate geometry optimizations, particularly for challenging transition metal systems.
• The approach enhances the utility of variational 2-RDM and wavefunction methods in computational chemistry.