Efficient implementation of one- and two-component analytical energy gradients in exact two-component theory

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Relativistic Calculations

Background:

• Accurate calculation of molecular properties requires efficient methods for handling relativistic effects.
• The exact two-component (X2C) approach provides a balance between accuracy and computational cost for relativistic quantum chemistry.
• Analytical energy gradients are crucial for geometry optimization and exploring potential energy surfaces.

Purpose of the Study:

• To develop and implement an efficient algorithm for analytical energy gradients within the X2C framework.
• To generalize existing spin-free methods for calculating gradients in X2C.
• To assess the accuracy and computational efficiency of the new gradient method.

Main Methods:

• Generalization of the spin-free ansatz for calculating perturbed Hamiltonians via first-order response equations.
• Application of the diagonal local approximation to the unitary decoupling transformation (DLU) to the X2C Hamiltonian.
• Implementation within the TURBOMOLE program package, including support for the finite nucleus model.

Main Results:

• The developed algorithm efficiently computes one- and two-component analytical energy gradients.
• The use of the DLU approximation drastically reduces computational costs.
• Optimized structures exhibit a mean absolute error of only 0.01 pm, indicating high accuracy.
• Computational effort scales cubically with molecular size, while storage scales quadratically.

Conclusions:

• The presented X2C/DLU gradient method offers a computationally efficient and accurate approach for relativistic electronic structure calculations.
• The method is suitable for large molecular systems, as demonstrated by applications to silver clusters and iridium complexes.
• This work enables more precise structural predictions and reaction pathway investigations in relativistic chemistry.