11.5.2 Visualization of Natural Transition Orbitals

For excited states calculated using the CIS, RPA, TDDFT, EOM-CC, and ADC methods, construction of Natural Transition Orbitals (NTOs), as described in Sections 7.13.2 and 11.2.6, is requested using the $rem variable NTO_PAIRS. This variable also determines the number of hole/particle NTO pairs that are output for each excited state and the number of natural orbitals or natural difference orbitlas. Although the total number of hole/particle pairs is equal to the number of occupied MOs, typically only a very small number of these pairs (often just one pair) have significant amplitudes. (Additional large-amplitude NTOs may be encountered in cases of strong electronic coupling between multiple chromophores.⁵²²)

When NTO_PAIRS $>0$, Q-Chem will generate the NTOs in MolDen format. The NTOs are state-specific, in the sense that each excited state has its own NTOs, and therefore a separate MolDen file is required for each excited state. These files are written to the job’s scratch directory, in a sub-directory called NTOs, so to obtain the NTOs the scratch directory must be saved using the –save option that is described in Section 2.7. The output files in the NTOs directory have an obvious file-naming convention. The “hole” NTOs (which are linear combinations of the occupied MOs) are printed to the MolDen files in order of increasing importance, with the corresponding excitation amplitudes replacing the canonical MO eigenvalues. (This is a formatting convention only; the excitation amplitudes are unrelated to the MO eigenvalues.) Following the holes are the “particle” NTOs, which represent the excited electron and are linear combinations of the virtual MOs. These are written in order of decreasing amplitude. To aid in distinguishing the two sets within the MolDen files, the amplitudes of the holes are listed with negative signs, while the corresponding NTO for the excited electron has the same amplitude with a positive sign.

Due to the manner in which the NTOs are constructed (see Section 7.13.2), NTO analysis is available only when the number of virtual orbitals exceeds the number of occupied orbitals, which may not be the case for minimal basis sets.