Semiclassical simulations
UV/vis spectrum simulations using semiclassical methods [49] were recently implemented in the Newton-X program [23] for simulations with the MRCI, CASSCF, TDDFT, CC2, ADC(2) and DFT/MRCI methods. These simulations can also be used for initial conditions generations for excited-state dynamics starting from multiple electronic states [57].
The spectrum is simulated by sampling the ground state nuclear geometries either by a statistical distribution (for instance, a Wigner distribution) or by a trajectory run. Then, for each of such geometries Rk, the excitation energies DE and the oscillator strengths f into the states of interest are computed. With these results, the absorption cross section can be computed [49]
,
which is related to the extinction coefficient by
.
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The spectra computed in this way can be directly compared to experiments in absolute units.
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Simulation costs about 500 single point calculations (no gradients needed).
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In general, a good qualitative agreement is observed, although no vibrational progression can be simulated.
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Simulated and experimental UV spectra of nucleobases.[49] |
Vibronic couplings
The semi-classical approach is a post-Condon approximation. Therefore, vibronic couplings are naturally included. We have shown in Ref. [61] that weak vibronically coupled peak of azomethane can be obtained with a quality similar to that obtained with full quantum mechanical methods (if vibrational progressions are neglected). Spectrum simulations with symmetry restrictions were computed in Ref.[68] for Cr(CO)6, allowing the assignment of several vibronic coupling features.
Tautomeric effects
When multiple tautomers are present, it is possible to estimate their effects on the final spectrum by averaging the spectrum for each tautomer according to [66]
where kB is the Boltzmann constant, T is the temperature and the sums run over each of the Ntaut tautomers included in the average. σi is the absorption cross section computed for tautomer i, whose ground state Gibbs free energy lies ΔGi above the ground state Gibbs free energy of the most stable tautomer included in the average.
Tautomeric effects are specially important for urocanic acid, one of the main UV chromophores in our skin. As shown in the figure below, there is two tautomers giving important contributions to the total spectrum. The spectral shift between these two contributions has been recently invoked to explain the anomalous photophysics of this molecule.[66]
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Simulated and experimental UV spectra of urocanic acid. The two most relevant spectral contribution from two tautomers are also shown.[66] |
