Cluster perturbation theory. XI. Excitation-energy series using a variational excitation-energy function

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Excitation energies in coupled-cluster (CC) theory traditionally rely on solving the CC Jacobian eigenvalue equation.
• This study builds upon recent work to reformulate excitation energy calculations.

Purpose of the Study:

• To propose a new method for calculating excitation energies as a conventional molecular property.
• To introduce an excitation-energy function and Lagrangian for variational calculations.
• To develop and assess new excitation-energy series.

Main Methods:

• Introduced an excitation-energy function dependent on the CC Jacobian and eigenvectors.
• Formulated an excitation-energy Lagrangian incorporating cluster-amplitude equations.
• Derived two quadratically convergent excitation-energy series: total-order cluster-perturbation (tCP) and variational cluster-perturbation (vCP).

Main Results:

• The variational property of the Lagrangian enabled the derivation of tCP and vCP series.
• Calculations on three small molecules demonstrated the preference for the vCP series over tCP.
• vCP series achieved high accuracy, with mean deviations of ~0.04 eV (S(D) space) and 0.001 eV (SD(T) space) from reference CC values.

Conclusions:

• The proposed method offers a variational approach to calculating excitation energies in CC theory.
• The variational cluster-perturbation (vCP) series provides accurate excitation energies with quadratic convergence.
• This reformulation offers a promising alternative to traditional Jacobian eigenvalue equation methods.