Signatures of Nonequilibrium Solvation Dynamics on Multidimensional Spectra

Abstract

Multidimensional electronic and vibrational spectroscopies have established themselves over the last decade as uniquely detailed probes of intramolecular structure and dynamics. However, these spectroscopies can also provide powerful tools for probing solute-solvent interactions and the solvation dynamics that they give rise to. To this end, it should be noted that multidimensional spectra can be expressed in terms of optical response functions that differ with respect to the chromophore's quantum state during the various time intervals separating light-matter interactions. The dynamics of the photoinactive degrees of freedom during those time intervals (that is, between pulses) is dictated by potential energy surfaces that depend on the corresponding state of the chromophore. One therefore expects the system to hop between potential surfaces in a manner dictated by the optical response functions. Thus, the corresponding spectra should reflect the system's dynamics during the resulting sequence of nonequilibrium solvation processes. However, the interpretation of multidimensional spectra is often based on the assumption that they reflect the equilibrium dynamics of the photoinactive degrees of freedom on the potential surface that corresponds to the chromophore's ground state. In this Account, we present a systematic analysis of the signature of nonequilibrium solvation dynamics on multidimensional spectra and the ability of various computational methods to capture it. The analysis is performed in the context of the following three model systems: (A) a two-state chromophore with shifted harmonic potential surfaces that differ in frequency, (B) a two-state atomic chromophore in an atomic liquid, and (C) the hydrogen stretch of a moderately strong hydrogen-bonded complex in a dipolar liquid. The following computational methods are employed and compared: (1) exact quantum dynamics (model A only), (2) the semiclassical forward-backward initial value representation (FB-IVR) method (models A and B only), (3) the linearized semiclassical (LSC) method (all three models), and (4) the standard ground-state equilibrium dynamics approach (all three models). The results demonstrate how multidimensional spectra can be used to probe nonequilibrium solvation dynamics in real time and with an unprecedented level of detail. We also show that, unlike the standard method, the LSC and FB-IVR methods can accurately capture the signature of solvation dynamics on the spectra. Our results also suggest that LSC and FB-IVR yield similar results in the presence of rapid dephasing, which is typical in complex condensed-phase systems. This observation gives credence to the use of the LSC method for modeling spectra in complex systems for which an exact or even FB-IVR-based calculation is prohibitively expensive.

Relation of exact Gaussian basis methods to the dephasing representation: Theory and application to time-resolved electronic spectra

“…Besides applications in electronic spectroscopy, 14,15,18,19 correlation function (7) proved useful, e.g., in nuclear magnetic resonance spin echo experiments 39 and theories of quantum computation, 37 decoherence, 37,38,40 and inelastic neutron scattering. 22 The fidelity amplitude was also used as a measure of the dynamical importance of diabatic, 23 nonadiabatic, 20 or spin-orbit couplings, 21 and of the accuracy of quantum molecular dynamics on an approximate potential energy surface.…”

“…7, which shows the dependence of the condition number κ of the overlap matrix S on N. Monte Carlo basis is generated with an algorithm 59, 69, 70 sampling the coherent-state basis functions from the absolute value of the overlap χ := γ , q, p| , Q, P of the initial state (B7) with a basis state |γ , q, p of Eq. (15). The absolute value of this overlap, understood as a function of q and p, is…”

“…11,12 In electronic spectroscopy, the DR and closely related approximations are known as phase averaging, 13 Wigner-averaged classical limit, or linearized semiclassical initial value representation 14,15 a) Electronic mail: jiri.vanicek@epfl.ch (LSC-IVR, 16 in the generalized sense 17 ), and have been used by several authors. 14,15,18,19 Although the original formulation of the DR pertains to a single electronic potential energy surface, a generalization to multiple surfaces exists.…”

“…11,12 In electronic spectroscopy, the DR and closely related approximations are known as phase averaging, 13 Wigner-averaged classical limit, or linearized semiclassical initial value representation 14,15 a) Electronic mail: jiri.vanicek@epfl.ch (LSC-IVR, 16 in the generalized sense 17 ), and have been used by several authors. 14,15,18,19 Although the original formulation of the DR pertains to a single electronic potential energy surface, a generalization to multiple surfaces exists. 20,21 The DR has many other applications: e.g., in inelastic neutron scattering, 22 as a measure of the dynamical importance of diabatic, 23 nonadiabatic, 20 or spin-orbit couplings, 21 and as a measure of the accuracy of quantum molecular dynamics on an approximate potential energy surface.…”

Generalized dephasing relation for fidelity and application as an efficient propagator

“…Average position plotted versus time of a displaced wavepacket oscillating under the highly anharmonic Hamiltonian H = 1 2 p 2 + 1 2 ω 2 q 2 − 0.1q 3 + 0.1q4 with ω = √ 2. The DR curves were calculated from the expression d…”