Analytic energy gradients in closed-shell coupled-cluster theory with spin-orbit coupling

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Relativistic Effects

Background:

• Coupled-cluster (CC) theory is a high-accuracy quantum chemical method.
• Spin-orbit coupling (SOC) is vital for heavy elements but often neglected in standard CC calculations.
• Analytic energy gradients are essential for predicting molecular properties.

Purpose of the Study:

• To implement analytic energy gradients for closed-shell coupled-cluster methods including spin-orbit coupling.
• To assess the computational cost of these new gradient methods.
• To investigate the impact of SOC on the structures and vibrational frequencies of heavy-element compounds.

Main Methods:

• Implementation of analytic energy gradients at the coupled-cluster singles and doubles (CCSD) and CCSD(T) levels.
• Inclusion of spin-orbit coupling within the post-Hartree-Fock treatment.
• Calculation of equilibrium structures, harmonic frequencies, and dipole moments for selected heavy-element compounds.

Main Results:

• The computational overhead for analytic gradients with SOC is comparable to ground-state energy calculations for CCSD and doubled for CCSD(T).
• Spin-orbit coupling demonstrably influences equilibrium geometries and harmonic vibrational frequencies.
• Calculated properties show significant deviations when SOC is omitted.

Conclusions:

• Analytic energy gradients incorporating spin-orbit coupling are computationally feasible.
• Spin-orbit coupling is indispensable for accurate structural and vibrational predictions in heavy-element systems.
• The developed methods provide reliable tools for studying relativistic effects in molecules.