Frozen Virtual Natural Orbitals for Coupled-Cluster Linear-Response Theory

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• The frozen-virtual natural-orbital (NO) approach uses correlated densities to construct compact wave functions for ground-state properties.
• Occupation numbers in the NO approach guide the truncation of virtual space.

Purpose of the Study:

• To evaluate the frozen-virtual NO approach for calculating higher-order response properties, specifically frequency-dependent dipole polarizabilities.
• To compare the performance of the NO basis with the canonical molecular orbital (CMO) basis for property calculations.

Main Methods:

• Coupled-cluster theory was employed to calculate frequency-dependent dipole polarizabilities.
• The study tested the sensitivity of NO and CMO bases to virtual space truncation.
• Approaches to improve NO space performance, including field-perturbed densities and external-space corrections, were investigated.

Main Results:

• Higher-order response properties are significantly more sensitive to virtual space truncation in the NO basis than in the CMO basis.
• Truncation errors in the NO basis increase linearly with the number of frozen virtual NOs.
• CMO basis truncation resulted in less than 2% error for coupled-cluster dipole polarizabilities, even with 50% virtual space removal.

Conclusions:

• The NO approach shows poor performance for higher-order response properties due to diffuse NOs and amplitude sparsity.
• The CMO basis demonstrates superior performance owing to error cancellation and amplitude sparsity.
• A 'dipole amplitude' criterion is proposed for effective CMO basis truncation in property calculations.