Higher order alchemical derivatives from coupled perturbed self-consistent field theory

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory are fundamental in computational chemistry.
• Calculating higher-order energy derivatives with respect to nuclear charge (alchemical derivatives) is computationally demanding.
• Understanding molecular responses to changes in nuclear charge is crucial for predicting chemical properties.

Purpose of the Study:

• To develop an analytical method for calculating higher-order alchemical derivatives of HF and KS energies.
• To derive working equations for second and third derivatives of HF/KS energy and first/second derivatives of orbital energies.
• To assess the accuracy of predicted molecular energies and orbital energies using Taylor series expansion.

Main Methods:

• Utilized modified coupled perturbed self-consistent field (SCF) theory to model molecular response to perturbations.
• Derived analytical expressions for second and third-order alchemical derivatives of HF/KS energies.
• Computed alchemical derivatives for isoelectronic molecular series and applied Taylor series expansion for energy prediction.

Main Results:

• Successfully derived and calculated second and third derivatives of HF energy and second derivatives of KS energy.
• Analytical forms for first and second derivatives of orbital energies were reported.
• Predicted molecular energies using Taylor series expansion showed good agreement with direct HF/KS calculations, with errors <1% for valence orbitals.

Conclusions:

• The developed analytical approach for alchemical derivatives provides an efficient and accurate method for theoretical chemistry.
• This method enables reliable prediction of energies for 'surrounding' molecules within isoelectronic series.
• The approach significantly improves the prediction accuracy of orbital energies, particularly for valence orbitals.