Implement C6 coefficient calculation via Casimir-Polder integration #619
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This PR implements the calculation of$C_6$ dispersion coefficients between two systems using Time-Dependent Density Functional Theory (TDDFT) or Time-Dependent Hartree-Fock (TDHF).
To support this calculation, a helper function
_solve_full_spectrumhas been added to solve the full eigenvalue problem (Casida equation or TDA) for TDDFT/TDHF.The$C_6$ coefficient is calculated using the Casimir-Polder integral formula:
$$C_6 = \frac{3}{\pi} \int_0^{\infty} \alpha_A(i\omega) \alpha_B(i\omega) d\omega$$ $\alpha(i\omega)$ is the dynamic polarizability at imaginary frequencies. To accurately evaluate $\alpha(i\omega)$ , the full spectrum of excitation energies and oscillator strengths is acquired through full diagonalization.
where