Computer Simulation Study of the Density and Temperature Dependence of Fundamental and Overtone Vibrational Dephasing in Nitrogen:  Interplay between Different Mechanisms of Dephasing

Abstract

Vibrational phase relaxation of the fundamental and the overtones of the N−N stretch of nitrogen in pure nitrogen has been studied by extensive molecular dynamics simulations. The thermodynamic state points simulated include states near the melting point, the boiling point, and the critical point, a normal liquid away from the transition, and also supercritical nitrogen. The simulations provide the following results. (1) The well-known result of Clouter and Kiefte (J. Chem. Phys. 1977, 66, 1736) on the pronounced insensitivity of vibrational phase relaxation of the fundamental to the change in thermodynamic conditions from the triple point (TP) to beyond the boiling point (BP) is found to originate from a competition between density relaxation and resonant energy transfer terms. The latter becomes increasingly important as the melting point is approached. (2) It is found that the experimentally observed sharp rise in the relaxation rate near the gas−liquid critical point (CP) can be attributed at least partly to the sharp rise in the contribution of vibration−rotation coupling. (3) The sharp rise in the vibration−rotation coupling in turn leads, in an unusual way, to a substantial subquadratic quantum number dependence of the overtone dephasing rate near the critical point and in supercritical fluids. The quantum number dependence, however, is found to be quadratic in the condensed phase. (4) The quantum number dependence of overtone dephasing is found to be critically dependent on the separation of time scales between the relaxations of the frequency modulation time correlation function and the normal coordinate time correlation function. The two decays must overlap to observe a significant subquadratic quantum number dependence. The latter is found to occur in the supercritical fluid state. (5) In the absence of a clear separation of time scales between the frequency modulation and the normal coordinate time correlation functions and because of the pronounced Gaussian decay of the latter, the Kubo−Oxtoby method of correlating the motionally narrowing limit with a homogeneous line shape becomes ambiguous. (6) An interesting crossover behavior across the liquid−gas phase transition region is observed in the density−temperature dependencies of the overtone dephasing rate. This crossover is most pronounced for higher overtones. (7) Although the simulation results reproduce the experimental data semiquantitatively (within 40% in most cases) and get the trends correct, quantitative agreement has not been achieved. We attribute this to the large number of terms (correlations and cross-correlations) which contribute to dephasing. In addition, the change of pair intermolecular potential with the thermodynamic state may itself play an increasingly important role, particularly in supercritical fluids.

Isotropic Raman line shapes of N2 and O2 along their liquid–gas coexistence lines

“…1 by the solid squares. As with nitrogen, 24,29 in this case the shift has the wrong sign. 26 When ␥ and ␦ are treated as fit parameters, the theoretical results are given by the solid circles, and are in good agreement with experiment.…”

“…v(⑀,,r) is the site-site potential, which we take ͑as have others before us 24,25,29,37 ͒ to have the simple Lennard-Jones form,…”

“…Note that in the harmonic limit k→ϱ, and that for nearly harmonic systems q 01 2 is greater than q 11 q 00 and q 00 2 by on the order of k. In this case it is a good approximation to neglect q 11 q 00 Ϫq 00 2 compared to q 01 2 , which is what is usually done. 24,29 It can be shown 40-42 that 1/aͱk ϭͱប/2, where is the harmonic ͑angular͒ frequency of the Morse potential, i.e., ϭ2c e . This together with the above leads to the asymptotic expansions,…”

A general method for implementing vibrationally adiabatic mixed quantum-classical simulations

“…However, the error in any transition energy is never larger than 1.5 ϫ10 Ϫ6 %. ͑For reference, the errors in the E 01 , E 12 , and E 23 transition energies with N PO ϭ10, not shown, are less than 8ϫ10 Ϫ7 %, 3ϫ10 Ϫ6 %, and 9ϫ10 Ϫ5 %, respectively.͒ Thus, the PO-DVR and Lanczos scheme provide a very accurate solution of the vibrational Schrödinger equation in these simulations.…”

“…This approach has been widely and successfully used for weakly coupled solute-solvent systems. [9][10][11][12][13] A vibrationally adiabatic QC simulation directly provides the fluctuating frequencies of a quantum-mechanical solute from dynamics that include response from the quantum mode͑s͒ onto the classical coordinates. Further, an explicit calculation of the vibrational energy levels is accurate even for strong solute-solvent coupling, unlike perturbation theory approaches.…”