Vibronics

Vibronic spectrum simulation package

In general, there are a several steps to simulate a vibronic spectrum:

1. Expand the diabatic electronic Hamiltonian in polynomials of normal modes (this is diabatz's job)
2. Generate a vibrational basis with tools/vibration
3. Generate a seed vector with tools/seed
4. Run vibronics to tridiagonalize the vibronic Hamiltonian
5. Process the tridiagonal matrix with tools/eig for the spectrum
6. (optional) Perturbatively add spin-orbit coupling with tools/soc

For details and theories of each module, see into each directories

Theory overview

The time-independent approach to simulate vibronic spectrum is to diagonalize the vibronic Hamiltonian

This program adopts diabatic electronic state and harmonic oscillator direct product vibrational basis, under which framework the vibronic Hamiltonian is written as

H^vibronic = H^harmonic + H^anharmonic

so that H^harmonic is diagonal with harmonic oscillator eigenvalues, while H^anharmonic can be very sparse in usual applications

For integral purpose, the dependency of H^anharmonic on molecular geometry is fitted as a polynomial of normal modes. In usual cases where the polynomial order is low (2nd order + few higher order terms), H^anharmonic is almost a band matrix, making Lanczos algorithm extremely efficient

Cite this work

1. M. S. Schuurman, R. A. Young, D. Yarkony, Chem. Phys. 2008, 347, 57-64
2. M. S. Schuurman and D. R. Yarkony, J. Chem. Phys. 2008, 128, 044119
3. Y. Shen and D. R. Yarkony, J. Phys. Chem. Lett. 2020, 11, 17, 7245–7252