Full-frequency dynamical Bethe-Salpeter equation without frequency and a study of double excitations

Area of Science:

• Computational chemistry
• Quantum mechanics
• Electronic structure theory

Background:

• The GW approximation combined with the Bethe-Salpeter equation (BSE) is a standard method for calculating electronic excitations.
• The computational cost of the full-frequency dynamical BSE is prohibitively high (O(N^6)) due to the frequency-dependent screened Coulomb interaction.

Purpose of the Study:

• To reformulate the full-frequency dynamical BSE into a computationally tractable form.
• To enable accurate calculations of excited states, including those with significant double excitation character.

Main Methods:

• Reformulation of the dynamical BSE as a frequency-independent eigenvalue problem in an expanded space.
• Application of iterative eigensolvers and density fitting approximations.
• Numerical verification of the O(N^5) computational scaling.

Main Results:

• Achieved an O(N^5) computational scaling for the dynamical BSE, significantly reducing computational cost.
• Developed a method that provides direct access to excited states with dominant double excitation character.
• Demonstrated that the GW/BSE method overestimates excitation energies and underestimates double excitation character for the 2^1Ag states of polyenes.

Conclusions:

• The reformulated dynamical BSE offers a computationally efficient and accurate approach for electronic excitation calculations.
• The method overcomes limitations of the static screening approximation by including full-frequency dependence.
• This advancement is crucial for accurately describing excited states with complex electronic character.