Inclusion of nuclear quantum effects for simulations of nonlinear spectroscopy

Abstract

The computation and interpretation of nonlinear vibrational spectroscopy is of vital importance for understanding a wide range of dynamical processes in molecular systems. Here, we introduce an approach to evaluate multi-time response functions in terms of multi-time double symmetrized Kubo transformed thermal correlation functions. Furthermore, we introduce a multi-time extension of ring polymer molecular dynamics to evaluate these Kubo transforms. Benchmark calculations show that the approximations are useful for short times even for nonlinear operators, providing a consistent improvement over classical simulations of multi-time correlation functions. The introduced methodology thus provides a practical way of including nuclear quantum effects in multi-time response functions of non-linear optical spectroscopy.

Nonlinear Spectroscopy in the Condensed Phase: The Role of Duschinsky Rotations and Third Order Cumulant Contributions

“…This harmonic QCF can be derived by establishing a link between the full quantum correlation function and its Kubo-transformed analogue 80,81 that possesses the same symmetries as the classical correlation function. Recently, a similar expression has been derived for the two-time quantum correlation function C {3} through a double-Kubo transform, 65 where the quantum correlation function can then be approximated via:…”

“…The results also highlight the importance of including Duschinsky rotation effects in modeling 2DES signals, which has been made possible by using the one-and two-time correlation functions for the GBOM derived in our previous work. 55 Although the QCF for the two-time correlation function 65 introduces some errors when computing nonlinear spectra from purely classical input, these errors are relatively small and the QCF captures the most important features of the exact third order cumulant contribution.…”

“…55,56 Some of the authors have recently shown that the effect of both Duschinsky mode mixing and changes between the ground-and excited state PES curvature, as well as moderate anharmonicities, on linear absorption spectra can be approximately captured by a cumulant expansion truncated at third order. 55 The third order cumulant correction can be constructed to good accuracy from a purely classical two-time correlation function of energy gap fluctuations using a recently derived QCF, 65 opening up the possibility of capturing effects beyond the second order cumulant approximation in complex condensed phase systems. A harmonic model system termed the generalized Brownian oscillator model (GBOM) has been extensively used in the context of linear spectroscopy.…”

Multi-time formulation of Matsubara dynamics

“…This expression represents an exact (smoothed) path integral Fourier representation of the statistics of three operators and is equivalent (in the limit of large M ) to previously derived expressions. 44,45 IV. GENERALIZATION TO MULTI-TIME Following the derivation of the previous sections, it is possible to perform a generalization of the Matsubara dynamics approximation to any order of the symmetrized Kubo transformed multi-time correlation function.…”

On the “Matsubara heating” of overtone intensities and Fermi splittings

“…Imaginary-time path-integral dynamics methods [1][2][3][4][5][6][7][8][9][10][11] can be used to include zero-point energy in simulations of vibrational spectra. 9,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] When used within their range of applicability, 9,[28][29][30] these methods give typically slightly blueshifted estimates of the fundamental band origins, 31 and good estimates of the intensities. However, path-integral methods fail badly when applied to overtone and combination bands.…”