Analytical energy gradient for the two-component normalized elimination of the small component method.

Area of Science:

• Computational chemistry
• Relativistic quantum mechanics

Background:

• The two-component Normalized Elimination of the Small Component (2c-NESC) method provides a Dirac-exact approach for electronic structure calculations.
• Accurate modeling of spin-orbit coupling (SOC) is crucial for understanding molecular properties, especially in heavy elements.

Purpose of the Study:

• To present the analytical gradient for the 2c-NESC method.
• To investigate the influence of SOC on molecular geometries, including bond lengths.
• To analyze the role of frontier orbitals and SO couplings in these geometric changes.

Main Methods:

• Implementation and application of the analytical gradient for the 2c-NESC method.
• Modeling of two-electron SOC effects using a screened nucleus potential with effective nuclear charges.
• Analysis of frontier orbital properties and calculated SO couplings.

Main Results:

• The 2c-NESC method yields exact Dirac spin-orbit splittings for one-electron atoms.
• SOC can either lengthen or shorten molecular bond lengths, depending on the interplay of occupied antibonding and unoccupied bonding orbitals.
• Generally, SOC effects on bond lengths are minor (≤5% of scalar relativistic changes), except for van der Waals complexes like Hg2 and Cn2.

Conclusions:

• The analytical gradient of the 2c-NESC method is a valuable tool for studying SOC effects.
• Significant geometric changes due to SOC in specific systems (e.g., Hg2, Cn2) highlight the importance of considering these interactions.
• The findings provide insights into the complex relationship between electronic structure, SOC, and molecular geometry.