A formal connection is made between the vibrational density of states (DOS) of a liquid and its approximation by way of instantaneous normal modes (INMs). This analysis leads to a quantum generalization of the INM method (QINM), and to the possibility of evaluating the classical DOS exactly. Further, INM approximations to spectroscopic quantities (e.g., infrared absorption and Raman scattering) follow in a consistent manner by evaluating the appropriate golden rule expressions for harmonic oscillators, using the INM or QINM DOS in place of the true DOS. INM and QINM methods are then applied along with traditional time correlation function (TCF) methods to analyze the entire infrared (IR) spectrum of ambient water. The INM and TCF approaches are found to offer complimentary information. TCF methods are shown to offer an unexpectedly accurate description of the O–H stretching line shape. Further, the 19-fold enhancement in liquid phase absorption compared to the gas phase is also reproduced. INM and QINM methods are used to analyze the molecular origin of the water spectrum, and prove especially effective in analyzing the broad O–H stretching absorption. Further, it is argued that a motional narrowing picture is qualitatively useful in analyzing INM approximations to spectroscopy.

The depolarized reduced Raman and corresponding optical Kerr effect (OKE) spectral density of ambient CS2 have been calculated by way of time correlation function (TCF) and instantaneous normal mode (INM) methods and compared with experimental OKE data. When compared in the reduced Raman spectrum form, where the INM spectrum is proportional to the squared polarizability derivative weighted density of states (DOS), the INM results agree nearly quantitatively (at all but the lowest frequencies) with the TCF results. Both are in excellent agreement with experimental measurements. The INM signal has a significant contribution from the imaginary INMs. Within our INM theory of spectroscopy the imaginary INMs contribute like the real modes, at the magnitude of their imaginary frequency. When only the real modes are allowed to contribute, and the spectrum is rescaled to account for the missing degrees of freedom, the results are much poorer, as has been observed previously. When the spectra are compared in their OKE form, the INM spectrum is found to lack the low-frequency spike which is associated with long time scale rotational diffusion, and it is not surprising that an INM theory would not capture such a feature. The results demonstrate that while the OKE and spontaneous depolarized Raman spectrum contain the same information, they clearly highlight different dynamical time scales. At higher frequencies (ω>25 cm−1) the INM OKE results are in excellent agreement with TCF and experimental results. The TCF results capture the low-frequency spike and are in agreement with experiment everywhere within the precision of the present calculations. The molecular contributions to the OKE signal are analyzed using INM methods.

The ambient pressure, temperature dependent optical Kerr effect (OKE) spectral density of CS2 has been calculated by way of time correlation function (TCF) and instantaneous normal mode (INM) methods and compared with corresponding experimental OKE data [R. A. Farrer, B. J. Loughnane, L. A. Deschenes, and J. T. Fourkas, J. Chem. Phys. 106, 6901 (1997)]. Over this temperature range the viscosity of CS2 varies by more than a factor of 5, and the molecular dynamics (MD) spectroscopic methods employed do an excellent job in capturing the associated changes in molecular motions that lead to the observed spectroscopy. The resulting TCF spectra are also in very good agreement with experimental measurements at all temperatures, and this is remarkable considering the range of conditions considered. When compared in the reduced Raman spectrum form, where the INM spectral density is proportional to the squared polarizability derivative weighted density of states (DOS), the INM results agree very well with the TCF results, and the low frequency OKE feature corresponding to rotational reorientation is suppressed in this form. Interestingly, the INM signal includes a significant contribution from the imaginary INM’s at all the temperatures considered, and these contributions are crucial to the agreement between INM and TCF results. Furthermore, the INM approximation to the signal (OKE or reduced Raman) demonstrates that the contribution (spectral density) of the real INM’s remains nearly unchanged over the temperature range considered, while the imaginary contribution grows with increasing temperature. The signal from the imaginary INM’s is therefore deduced to be responsible for a large part of the temperature dependence of the OKE spectral density. Finally, the molecular motions that contribute to the OKE signal are analyzed using INM methods.

A simple time domain method for the observation of polarization-specific Raman responses in electronically nonresonant materials is demonstrated. When a cutoff filter is placed in the probe beam path before the detector in the conventional pump-probe configuration, the in-phase dichroic optical heterodyne-detected (OHD) response is enhanced as compared to the usual putative corresponding dichroic response observed when the probe is not dispersed. The ultrafast excited OHD responses of CS 2 obtained by this method are reported for parallel, perpendicular, and magic angle relative orientations of pump and probe pulse polarizations. The observed dispersed dichroic signal can be derived from the real part alone of the third-order nuclear response function. The decay of the CS 2 isotropic response is found to be dominated by a ∼500 fs decay process for times longer than ∼0.7 ps. This relaxation time scale matches the nondiffusive exponential decay seen in the birefringent and dichroic anisotropic responses of CS 2 . Calculated instantaneous normal mode (INM) isotropic and anisotropic nuclear response functions are found to exhibit exponential decays in this same 500-600 fs time scale, suggesting that this decay component may be predominantly determined by the distribution of Raman-weighted density of states.

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