Variational formulation of perturbative explicitly-correlated coupled-cluster methods.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Coupled-cluster methods are essential for accurate electronic structure calculations.
• Basis set incompleteness is a major source of error in these calculations.
• The CCSD(2)(R12) method offers a way to correct for this incompleteness.

Purpose of the Study:

• To present a variational formulation of the CCSD(2)(R12) method.
• To develop a computationally efficient variant of this method.
• To extend the method to approximate CCSD(T) calculations.

Main Methods:

• Variational formulation using a CCSD(2)(R12) Lagrangian.
• Development of a Hylleraas-type functional with screening approximations.
• Extension to include perturbative triples for CCSD(T) approximation.

Main Results:

• The method recovers >94.5% of the complete basis set CCSD(T) correlation energy with standard basis sets.
• Electronic reaction energies for 12 isogyric reactions show a mean absolute deviation of 1.4 kJ/mol from experimental values.
• Achieves accuracy comparable to CCSD(T) with a triple-zeta basis, significantly reducing computational cost.

Conclusions:

• The presented variational method provides an accurate and efficient way to approach the complete basis set limit for CCSD and CCSD(T) calculations.
• It offers a practical alternative to standard high-accuracy methods, requiring less computational resources.
• The method is readily implementable within existing coupled-cluster codes.