Linear scaling density matrix perturbation theory for basis-set-dependent quantum response calculations: an...

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Electronic Structure Theory

Background:

• Linear scaling density matrix perturbation theory is crucial for efficient quantum response calculations.
• Handling nonorthogonal basis sets in these calculations presents significant challenges.
• Existing methods for nonorthogonal basis sets can be computationally intensive.

Purpose of the Study:

• To extend linear scaling density matrix perturbation theory to handle basis-set-dependent quantum response calculations with nonorthogonal basis sets.
• To develop a method that simplifies the treatment of nonorthogonal basis sets in perturbation theory.
• To provide an efficient alternative to existing approaches for basis-set-dependent response calculations.

Main Methods:

• A perturbation-dependent congruence transform is employed to generalize the theory.
• The inverse overlap matrix is factorized to facilitate the transform.
• The generalized eigenvalue problem is converted into an orthogonal, standard form.
• Basis-set-dependent perturbations in the overlap matrix are incorporated into the orthogonalized Hamiltonian.

Main Results:

• The extended theory successfully incorporates basis-set-dependent perturbations within an orthogonal framework.
• The method allows the application of existing density matrix perturbation theory for orthogonal representations to nonorthogonal settings.
• This approach offers a computationally viable alternative to purely nonorthogonal methods.

Conclusions:

• The developed method provides an effective extension of linear scaling density matrix perturbation theory for nonorthogonal basis sets.
• This generalization simplifies complex quantum response calculations.
• The approach enhances the applicability and efficiency of perturbation theory in computational chemistry.