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

Abstract

We present a general mixed quantum classical method that couples classical Molecular Dynamics (MD) and vibronic models to compute the shape of electronic spectra of flexible molecules in condensed phase without, in principle, any phenomenological broadening. It is based on a partition of the nuclear motions of the solute+solvent system in "soft" and "stiff" vibrational modes, and an adiabatic hypothesis that assumes that stiff modes are much faster than soft ones. In this framework the spectrum is rigorously expressed as a conformational integral of quantum vibronic spectra along the stiff coordinates only. Soft modes enter at classical level through the conformational distribution that is sampled with classical MD runs. At each configuration, reduced-dimensionality quadratic Hamiltonians are built in the space of the stiff coordinates only, thanks to a generalization of the Vertical Hessian harmonic model and an iterative application of projectors in internal coordinates to remove soft modes. Quantum vibronic spectra, specific for each sampled configuration of the soft coordinates, are then computed at the desired temperature with efficient time-dependent techniques, and the global spectrum simply arises from their average. For consistency of the whole procedure, classical MD runs are performed with quantum-mechanically derived force fields, parameterized at the same level of theory selected for generating the quadratic Hamiltonians along the stiff coordinates. Application to N-methyl-6-oxyquinolinium betaine in water, dithiophene in ethanol, and a flexible cyanidine in water are presented to show the performance of the method.

The role of chlorine position in the electronic circular dichroism of chlorophenyl‐ethanol investigated by vibronic calculations

“…The above observations highlight the need for new methodologies able to combine MD simulations to fully describe the richness of solvent interactions with flexible solutes and vibronic models to compute the spectral shapes. In this spirit, for instance, we recently introduced a novel method, Ad‐MD|gVH 25 . The results obtained in this contribution indicate that the PhEtOH derivatives and, in particular, the para isomer of ClPhEtOH stand as optimal training pools for these new computational developments in the field.…”

“…To investigate in further detail the effect of this anharmonic vibration, we computed the ECD spectrum of all the conformers of p‐ClPhEtOH using a reduced dimensionality model where θ Ph (and therefore ν 1 ) is projected out from the vibrational space. To that end, we used the novel procedure available in FCclasses 3 and presented in Cerezo et al 25 Figure 4 shows the ECD spectra in reduced dimensions. For the EqSolv model, p‐M01 and p‐M02 spectral shape remarkably changes with respect to the full dimension results.…”

“…For obtaining fully converged vibronic spectra, we used the time‐dependent formalism described in Avila Ferrer et al, 37 whereas for the assignment of the main vibronic bands, we employed the time‐independent prescreening method reported in Santoro et al 33,34 For clusters of the solute + 2 methanol molecules, the harmonic PESs were generated using energy gradients and Hessians of the whole cluster in PCM and projecting out the solvent degrees of freedom as we did in Cerezo et al 25 This approach allows us to obtain normal coordinates that involve only the solute degrees of freedom but, at the same time, “feel” the electronic effects due to existence of the explicit solvent molecules. The Cartesian coordinates of all the ground state optimised structures are given in the Supporting Information.…”

“…It may become possible in the near future with novel methodologies. Among those, we recently proposed a method we named the Adiabatic MD generalised Vertical Hessian (Ad‐MD|gVH) that combines MD and vibronic models, 25 but extensions are needed to include HT transitions and how they are modulated by solute–solvent interactions.…”

Combined Spectroscopic and TD‐DFT Analysis to Elucidate Substituent and Acidochromic Effects in Organic Dyes: A Case Study on Amino‐ versus Nitro‐Substituted 2,4‐Diphenylquinolines

“…For this reason, a very detailed agreement of such calculations with experiment is not expected. Finally, in the following, solvent effects are treated implicitly through PCM; this may be insufficient for a quantitative, extensive description for the absorption properties of protonated species, [42][43] but sufficient as a first approximation as it is required for fast screening as intended in the present work.…”