Velocity gauge for oscillator strength in ΔSCF theory

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Theoretical Physics

Background:

• Delta self-consistent-field (ΔSCF) theory is a common method for calculating electronic excitation energies.
• Calculating oscillator strengths within ΔSCF is challenging due to the non-orthogonality of ground and excited state wavefunctions.
• This non-orthogonality leads to unphysical, origin-dependent transition properties.

Purpose of the Study:

• To explore the use of the velocity gauge for calculating oscillator strengths within ΔSCF theory.
• To address the non-orthogonality issue and achieve origin-independent predictions.
• To improve the accuracy of ΔSCF oscillator strength predictions, particularly for conjugated systems.

Main Methods:

• Investigated the velocity gauge formulation for oscillator strength calculations in ΔSCF.
• Analyzed the inherent handling of wavefunction non-orthogonality by the velocity gauge.
• Compared velocity gauge results with length-gauge results, including those using symmetric orthogonalization.
• Utilized spin-purified singlet excitation energy in conjunction with the velocity gauge.

Main Results:

• The velocity gauge naturally accounts for the non-orthogonality of ΔSCF Kohn-Sham wavefunctions.
• Velocity gauge calculations provide origin-independent predictions without requiring additional correction schemes.
• Velocity gauge results are comparable to length-gauge results obtained via symmetric orthogonalization.
• Incorporating spin-purified singlet excitation energy significantly improves velocity gauge performance for conjugated chromophores.

Conclusions:

• The velocity gauge offers a robust and accurate method for calculating oscillator strengths within ΔSCF theory.
• This approach overcomes the limitations associated with wavefunction non-orthogonality and origin dependence.
• The velocity gauge, especially with spin purification, provides a reliable tool for electronic excitation property predictions.