Theory and efficient computation of differential vibrational spectra

A generalized van't Hoff relation for the temperature dependence of complex-valued nonlinear spectra

The temperature dependence of spectra can reveal important insights into the structural and dynamical behavior of the system being probed. In the case of linear spectra, this has been exploited to investigate the thermodynamic driving forces governing the spectral response. Indeed, the temperature derivative of a spectrum can be used to obtain effective energetic and entropic profiles as a function of the measured frequency. The former can further be used to predict the temperature-dependent spectrum via a van't Hoff relation. However, these approaches are not directly applicable to nonlinear, complex-valued spectra, such as vibrational sum-frequency generation (SFG) or two-dimensional infrared (2D-IR) photon echo spectra. Here, we show how the energetic and entropic driving forces governing such nonlinear spectra can be determined and used within a generalized van't Hoff relation to predict their temperature dependence. The central idea is to allow the underlying energetic profiles to themselves be complex-valued. We illustrate this approach for 2D-IR spectra of water and SFG spectra of the air-water interface and demonstrate the accuracy of the generalized van't Hoff relationship and its implications for the origin of temperature-dependent spectral changes.

Identification of Ion Pairs in Aqueous NaCl and KCl Solutions in Combination with Raman Spectroscopy, Molecular Dynamics, and Quantum Chemical Calculations

This work summarizes a theoretical analysis of the perturbation on Raman spectra in aqueous NaCl and KCl solutions with the aim to detect ion pairs. The experimental Raman spectra, both polarized and depolarized, are perturbed by these ions to a comparable extent or somewhat less by KCl than NaCl. This result appears to be contrary to the molecular dynamics (MD) simulation showing that the isolated and separated ions of KCl should have a larger perturbation than NaCl, as the solvation shell of K⁺ is larger than that of Na⁺. The apparent discrepancy signifies the ion pair formation which is more substantial for KCl than NaCl. The MD simulations and quantum chemical calculations revealed that KCl forms ion pairs more than NaCl and that the ion pair formation reduces the perturbation on the Raman spectra more for KCl. The present analysis shows that the perturbed Raman spectra provide a useful sign to evaluate the ion pair formation in aqueous solutions.

Development of Efficient Computational Analysis of Difference Infrared and Raman Spectroscopies

Computational analysis of difference spectra between two analogous systems is a challenging issue, as reliable estimation of a tiny difference spectrum requires an extraordinary precision of the two original spectra. We have developed an alternative new method to calculate the difference spectra in background-free conditions, which greatly improved the efficiency of computation. In this paper we report further improvement by using efficient parallel implementation and the time correlation formula based on time derivative quantities. As a consequence, the present work achieved further remarkable acceleration in the calculations of difference infrared and Raman spectra in the order of magnitude, and thereby allowed us with analyzing these difference spectra at a practical cost of computation.

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

The temperature derivative of the infrared (IR) spectrum of HOD/D₂O is directly calculated from simulations at a single temperature using a fluctuation theory approach. It is demonstrated, on the basis of an energetic decomposition of the derivative, that the blue shift with increasing temperature is associated with the competition between electrostatic and Lennard-Jones interactions. The same competition gives rise, where their contributions cancel, to a near isosbestic point. The derivative is further used to define an effective internal energy (and entropy) associated with the IR spectrum, and it is shown how a van't Hoff relation can be used to accurately predict the spectrum over a wide range of temperatures. These predictions also explain why a precise isosbestic point is not observed.

Effects of third-order susceptibility in sum frequency generation spectra: a molecular dynamics study in liquid water

When sum frequency generation (SFG) spectroscopy is applied to charged solid/liquid interfaces, the observed SFG signals include both the second-order and third-order polarizations. The latter is called the χ⁽³⁾ effect, which mainly includes induced molecular orientation by electric fields at charged interfaces. We theoretically evaluate the χ⁽³⁾ effect on the SFG spectroscopy of liquid water using molecular dynamics (MD) simulations. The MD simulations enable us to definitely calculate the χ⁽³⁾ susceptibility as a bulk property, and thereby separating it from the usual χ⁽²⁾ effect shown in the SFG spectra. The calculated results of χ⁽³⁾ for liquid water are fairly consistent with the experimental estimates. The present finding is utilized to analyze the spectral change of SFG at the air/water interface under electric fields and at the charged silica/water interface. The present analysis of the spectral changes allows for distinguishing the intrinsic change of the interface structure and the χ⁽³⁾ effect from bulk liquid.