The NEO-TDDFT method
J. Phys. Chem. Lett.
(2018), 9, pp. 1765. is a multicomponent extension of the TDDFT method within the NEO framework. It allows the simultaneous calculation of the electronic and proton vibrational excitation energies. In the NEO-TDDFT method, the linear response of the NEO Kohn-Sham system to perturbative external fields is computed. The NEO-TDDFT working equation is
Here, the occupied electronic orbitals are denoted with indices and , whereas the unoccupied electronic orbitals are denoted with indices and . The analogous upper case indices denote protonic orbitals. The solution of Eq. (13.44) provides the electronic and proton vibrational excitation energies , as well as the transition excitation and de-excitation amplitudes, and , respectively. Analogous to the TDDFT method, the Tamm-Dancoff approximation (TDA) can be imposed within the NEO framework, defining the NEO-TDDFT-TDA method that is represented by
The extension of the NEO-TDDFT and NEO-TDDFT-TDA approaches to open-shell electron systems is straightforward.
J. Chem. Phys.
(2019), 150, pp. 201101. NEO-TDHF and NEO-CIS have similar forms as NEO-TDDFT and NEO-TDA without electron-proton, electron-electron, or proton-proton correlation. The analytical gradients for NEO-CIS/NEO-TDA/NEO-TDHF/NEO-TDDFT are available, 1179 J. Chem. Theory Comput.
(2021), 17, pp. 5110. enabling geometry optimizations on the excited state vibronic potential energy surfaces. For NEO-TDA and NEO-TDDFT, analytical gradients are available for the epc17-2 functional or when no electron-proton correlation functional is used. The transition densities can be analyzed to determine the percentages of electronic and protonic character for each vibronic excited state.