Theoretical modeling of UV-Vis absorption and emission spectra in liquid state systems including vibrational and conformational effects: The vertical transition approximation

Abstract

In this paper we describe in detail a general and efficient methodology, based on the perturbed matrix method and molecular dynamics simulations, to model UV-Vis absorption and emission spectra including vibrational and conformational effects. The basic approximation used is to consider all the chromophore atomic coordinates as semiclassical degrees of freedom, hence allowing the calculation of the complete spectral signal by using the electronic vertical transitions as obtained at each possible chromophore configuration, thus including the contributions of vibrations and conformational transitions into the spectrum. As shown for the model system utilized in this paper, solvated 1-phenyl-naphthalene, such an approximation can be rather accurate to reproduce the absorption and emission spectral line shape and properties when, as it often occurs, the vertical vibronic transition largely overlaps the other non-negligible vibronic transitions.

Theoretical-computational modeling of charge transfer and intersystem crossing reactions in complex chemical systems

“…These last approximations furnish a very simple model of the reaction kinetics with a trivial exponential decay for R 1 and R n , respectively, as typically observed experimentally (note that eqn (70)- (73) (77) clearly show that within the irreversible reaction step approximation when U y 1 and thus 1 À a G y 1 À a e and a G y a e , no explicit vibrational effect is present in the complete reaction kinetics and hence for such a condition in the limit a e / 1 eqn (70)-(77) reduce essentially to the expressions we derived and used in previous papers (ref), based on assuming fully adiabatic ET reactions when neglecting any explicit vibrational effect. Such a result well explains the accuracy of the simpler purely electronic approach utilized previously, indicating that in most typical ET reactions U z 1 and a e z 1 thus providing a kinetic behavior equivalent to adiabatic reactions involving purely electronic diabatic states.…”

“…[Z 1 ] j,j 0 ¼ ÀE$hF 0 e,j |m|F 0 e,j 0 i (19) where f H e 0 is the unperturbed electronic Hamiltonian matrix (diagonal within the chosen basis set), q T andm are the QC total charge and dipole operator, V and E are the electric potential and eld as exerted by the environment on the QC centre of mass and F 0 e,j (x c , b) becoming parametrically functions of only the QC conformational x c coordinates when considering also the b coordinates as relaxed to their x c -dependent energy minimized position as obtained in a reference eigenstate (e.g. the ground state), thus disregarding any explicit quantum vibrational effect 73 (note that the use of electronic coordinates within the internal QC reference of frame requires that bothm and E must be also expressed within the internal QC reference of frame or, equivalently, that hF 0 e,j |m|F 0 e,j 0 i be expressed in the reference of frame providing E). Finally, DV includes all the other terms treated as a simple short range potential andĨ is the identity matrix.…”

Adiabatic-Molecular Dynamics Generalized Vertical Hessian Approach: A Mixed Quantum Classical Method To Compute Electronic Spectra of Flexible Molecules in the Condensed Phase

“…For larger ones, like flexible molecules in condensed phase, a number of approximated protocols to mix classical MD sampling and vibronic computations have been proposed. 7,37,48,[58][59][60][61][62] In the simplest approaches, the vibronic spectrum of the solute has been considered independent of the specific MD snapshot. [58][59][60][61] A way to go beyond this approximation, explicitly accounting for the coupling of intra-molecular and inter-molecular vibrations, is to use in vibronic calculations spectral densities extracted from classical MD trajectories.…”

“…7,37,48,[58][59][60][61][62] In the simplest approaches, the vibronic spectrum of the solute has been considered independent of the specific MD snapshot. [58][59][60][61] A way to go beyond this approximation, explicitly accounting for the coupling of intra-molecular and inter-molecular vibrations, is to use in vibronic calculations spectral densities extracted from classical MD trajectories. 37,51,53,63 The potentiality of such approach has been recently illustrated by Loco et al; 64 its partial limitation is that the spectrum is computed with reference to vibronic harmonic models that only account explicitly for linear couplings.…”

Toward a general mixed quantum/classical method for the calculation of the vibronic ECD of a flexible dye molecule with different stable conformers: Revisiting the case of 2,2,2‐trifluoro‐anthrylethanol

“…MQC approaches are attractive because they combine the usual procedures based on the harmonic approximation to describe the stiff quantum coordinates and simpler classical methods for the flexible modes, provided the associated frequencies are low. Different simple MQC schemes have been recently proposed in literature, for standard absorption and emission properties . The major challenge for these approaches is how to account, at least approximately, for the couplings between rigid and flexible coordinates.…”