A general time-dependent route to Resonance-Raman spectroscopy including Franck-Condon, Herzberg-Teller and Duschinsky effects

Abstract

We present a new formulation of the time-dependent theory of Resonance-Raman spectroscopy (TD-RR). Particular attention has been devoted to the generality of the framework and to the possibility of including different effects (Duschinsky mixing, Herzberg-Teller contributions). Furthermore, the effects of different harmonic models for the intermediate electronic state are also investigated. Thanks to the implementation of the TD-RR procedure within a general-purpose quantum-chemistry program, both solvation and leading anharmonicity effects have been included in an effective way. The reliability and stability of our TD-RR implementation are first validated against our previously proposed and well-tested time-independent procedure. Practical applications are illustrated with some closed-and open-shell medium-size molecules (anthracene, phenoxyl radical, benzyl radical) and the simulated spectra are compared to the experimental results. More complex and larger systems, not limited to organic compounds, are also feasible, as shown for the case of Tris(bipyridine)ruthenium(II) chloride.

Multiconfigurational Effects in Theoretical Resonance Raman Spectra

“…[75] Consistent with these findings,t he mosts ignificant, intense bands in the experimental RR spectrumo fu racil at frequencies highert han 1000 cm À1 have been identifieda sr ing stretches coupled to primarily C5ÀH11a nd C6ÀH12 bending modes at 1235 cm À1 ,aring stretchingb and at 1388 cm À1 ,a nd aC 5 =C6 stretching mode at 1623 cm À1 . [75] Interestingly,t he second most intense band in the experimental spectrum at 1664 cm À1 corresponds predominantly to aC 4 =O10 stretching mode, [75] which does not appear to be of any relevance for thep hoto- (30,26), and DMRG-SCF (18,23). Frequencies for the ground state are taken from our PBE0/augcc-pVTZcalculation and scaled by 0.9776 (frequenciesl ower than 1000 cm À1 )a nd 0.9568 (frequencies highert han 1000cm À1 ), see Ref.…”

“…The resulting CAS(18,23)c omprises the eight p/p*o rbitals( which have the largest s i (1) values), the lone-pair of the carbonyl C4=O10 oxygen (from which the excitation occurs in the n!p*S 1 state), six s/s*o rbitals corresponding to the skeleton C4=O10, C4ÀC5, C5ÀC6 bondinga nd anti-bonding orbitals (as indicated by I ij values > 0.01) as well as eight additional Rydberg-type orbitals. Although still yielding too high vertical excitation energies (see Ta ble 1), the excited-state gap D S 2 ÀS 1 for DMRG-SCF (18,23) is the smallest one (1). The line connecting two orbitals denotestheir mutual information value I ij where darker (from green to black) and thicker lines correspond to an increasing value of the mutual information.…”

“…Concerning the mosti ntense vibrational bands lower than 1000 cm À1 corresponding to the ring bending modes #7 (551 cm À1 )a nd #12 (765 cm À1 ), we find that, with the exception of PBE0, none of the methods compiled in Figure 4y ields aq ualitatively correctr elative intensity ratio in comparison to the experimentalb ands. All wave-function based approaches overestimate (underestimate) the intensity of the bending mode #7 (#12) among which DMRG-SCF (18,23) shows the best relative intensity ratio of both. By contrast, CASPT2 andi np articular HF/CIS, which, in previous works, [7,8,10] yielded witha6-31G* basis set aq ualitatively correct intensity ratio, appear to wronglyp redict an early zero intensity for the bending mode #12.…”

“…In our DMRG-SCF calculations, we therefore augmented the startingC AS(14,10) active orbitals pace with eight Rydbergtype (3p-like) orbitals and 16 Rydberg-type(3p-and 4p-like) orbitals,w hich we denote as DMRG-SCF (14,18) and DMRG-SCF (14,26) in Ta ble 1, respectively.E nlarging the CAS not only significantly improves the absolute vertical excitation energy for the S 2 state while only slightly increasing the S 0 !S 1 transition energy but also reduces for DMRG-SCF (14,26) the gap D S 2 ÀS 1 to more than half of its CASSCF value. Interestingly,t he optimized orbitals from these two DMRG-SCF calculations show as light mixing of the p and s orbitals, whichc ould indicate that some of the skeleton s/s*o rbitals play a( minor) role in the electronice xcitationprocess.…”

“…[3,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Starting out from the Kramers, Heisenberg,and Dirac expression for the Ramanp olarizability tensor, [21,22] the calculation of RR intensities proceeds usually in either at ime-independent or time-dependent framework, see, for example, Refs. [1,10,11,14,18,20] (and literature references in these papers) and Refs. [7,23,24].I nt his work, we follow the time-independenta pproach where we exploit the Kramers-Kronig (KK) transform relationship,w hich provides ac onnection between the polarizabilitya nd optical absorptions pectrum.…”