Schematic comparison of mode tracking (left) and intensity tracking (right). In the former case, a guess for a specific normal mode of the molecule under study is created, which is iteratively refined to get the exact normal mode and vibrational frequency. In contrast to this, intensity tracking starts with an unspecific guess for a hypothetical collective motion that contains the entire intensity in the resonance Raman spectrum. A guess for the entire spectrum is then iteratively refined. The intermediate spectra shown on the right are taken from a B3LYP/TZVP resonance Raman calculation on uracil, assuming resonance with the state.
B3LYP/TZVP optimized structure of uracil ( symmetry) and molecular orbitals (B3LYP/TZVP) dominating the transition to the state of uracil.
Comparison of the converged resonance Raman spectrum (B3LYP/TZVP) of uracil from an intensity-tracking calculation (top) and a conventional (reference) gradient spectrum (bottom) assuming resonance with the state.
B3LYP/TZVP optimized structures of skatole and model 1 as well as the BP86/TZVP optimized structure of model 2. Also shown are the molecular orbitals (B3LYP/TZVP) involved in the lowest electronic excitations of skatole.
Resonance Raman spectra of skatole for resonance with the or state obtained by a conventional gradient calculation using B3LYP/TZVP. Also shown are the spectra for the corresponding states of Im7-based model 1 obtained either in a converged intensity-tracking calculation (ITC) or as conventional gradient spectra (CGS). Wavenumbers of important vibrations are given in units of .
Graphical representation of the intense vibrations (B3LYP/TZVP) in the resonance Raman spectrum of skatole (upper row) and of model 1 (lower row).
Convergence of the modes during B3LYP/TZVP intensity-tracking iterations (It.) with standard convergence criteria for the resonance Raman spectrum for the state of model 1 (Converged: black; not converged: red). The total number of basis vectors (bv) is given on the right. The relative intensities have a common scale, only the results for iterations 15, 19, and 22 are magnified by a factor of 2.
Converged spectra for the (left) and (right) state of model 1 for a combination of different root-homing options. A wavenumber selection criterion as mentioned in the main text was applied in all cases. indicates for how many of the modes selected by the intensity criterion new basis vectors were created. The total number of basis vectors (bv) and of converged modes (conv) is given for each spectrum.
Resonance Raman spectra of model 1 assuming resonance with the state ( in case of BP86/BP86/TZVP) obtained by conventional gradient calculations using different functionals. The first of two given functionals was used for the ground-state structure and frequencies and the second for excitation energies and the excited-state gradient. Wavenumbers of intense vibrations are given in units of .
Convergence of the spectra during BP86/TZVP intensity-tracking iterations (It.) for model 2, starting from the (B3LYP/TZVP) gradient of the state. The total number of basis vectors (bv) is given on the left. Lowest panel: conventional (reference) gradient spectrum
Calculated excitation energies, dominant orbital transitions, and corresponding transition dipole moments for skatole and models 1 and 2. The applied functionals are denoted in parentheses. Where two different functionals are denoted, the first one was used for the ground state structure and frequencies and the second one for excitation energies and the excited-state gradient. Note that the transition mentioned in the first column always refers to the corresponding transition in skatole; H denotes HOMO and L denotes LUMO.
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