Theory and efficient computation of differential vibrational spectra

Abstract

We developed a general computational scheme for differential spectra on the basis of time correlation function and perturbation theory. The scheme provides a quite efficient route to evaluate small differential spectra by molecular dynamics simulation instead of the straightforward subtraction of two spectra. Applications of this scheme have demonstrated that the proposed route is accurate and far more efficient in several orders of magnitude. The present method enables us to analyze a variety of experimental differential spectra using molecular dynamics simulation.

Activation Energies and Beyond

“…This expression is sufficiently general that it can be applied to properties including viscosity, conductivity, dielectric relaxation, and even spectroscopy. Indeed, Morita and co-workers have developed similar approaches to calculating the dependence of different vibrational spectra on temperature and other variables. − In the case of a number of the transport coefficients, e.g., viscosity, which is a focus on ongoing work in our group, the key difference with the diffusion and reorientational dynamics examples discussed above is that they involve quantities that are global. That is, the quantities A and B in the TCF depend on the full system configuration and are not obtained individually for each molecule.…”

Removing the barrier to the calculation of activation energies: Diffusion coefficients and reorientation times in liquid water

“…The reorientational TCF C 2 (t) (solid black line) is shown as a function of time along with a tri-exponential fit (dashed black line) to Eq. (12). The TCF including the energy fluctuation, C 2,H (t), is also shown (solid red line) along with the fit (dashed blue line) to Eq.…”

“…Indeed, it has been shown by Dellago and Bolhuis 8 that a) Electronic mail: wthompson@ku.edu this perspective can be used to calculate E a directly from transition path sampling simulations at a single temperature, [9][10][11] and a related approach has been demonstrated by Morita and co-workers for vibrational spectra. 12,13 We have recently generalized this beyond transition path sampling and to other TCFs from which rate constants can be obtained, including those based on a quantum description. 14 The measurement and calculation of activation energies by an Arrhenius analysis can raise significant issues due to the need to consider multiple temperatures.…”

Temperature Dependence of the Water Infrared Spectrum: Driving Forces, Isosbestic Points, and Predictions

“…The behavior of liquid water vibrational spectra with temperature has long been of interest − because of the potential insight it can offer into the underlying driving forces for the liquid structure and dynamics. Among the prominent features observed are isosbestic points found in the IR ,− and Raman ,,,,,− ,, spectra as temperature is varied.…”

“…Specifically, we directly calculate the temperature derivative of the IR spectrum using molecular dynamics (MD) simulations. The theoretical approach is an application of fluctuation theory to dynamics, − similar to that previously described by Morita and co-workers. − This method provides new mechanistic insight into the energetic driving forces (e.g., kinetic energy and Coulombic and Lennard-Jones interactions) behind spectral changes with temperature, including the nature and origin of the isosbestic point. We show that the effects can be characterized by an (effective) internal energy as a function of frequency, which itself can be used to predict the IR spectrum for temperatures spanning at least 80 K.…”