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A molecular theory of liquid phase vibrational energy relaxation (VER) [S. A. Adelman et al., Adv. Chem. Phys. 84, 73 (1993)] is applied to study the temperature T and density p dependencies of the VER rate constant k(T,ρ)=T[sup -1, sub 1], where T[sub 1] is the energy relaxation time, of model Lennard-Jones systems that roughly simulate solutions of high-mass, low-frequency dihalogen solutes in rare gas solvents; specifically the I[sub 2]/Xe, I[sub 2]/Ar, and ICI/Xe solutions. For selected states of these systems, the theory's assumptions are tested against molecular dynamics (MD) results. The theory is based on the expression T[sub 1]=β[sup -1](ω[sub l]), where β(ω) and β(ω) are, respectively, the solute's liquid phase vibrational frequency and vibrational coordinate friction kernel. The friction kernel is evaluated as a cosine transform of the fluctuating force autocorrelation function of the solute vibrational coordinate, conditional that this coordinate is fixed at equilibrium. Additionally, the early-time decay of the force autocorrelation function is approximated by a Gaussian function which is exact to order t². This Gaussian approximation permits evaluation of T[sub 1] in terms of integrals over equilibrium solute-solvent pair correlation functions. The pair correlation function formulas yield T[sub 1]'s in semiquantitative agreement with those found by MD evaluations of the Gaussian approximation, but with three orders of magnitude less computational effort. For the isothermal ρ dependencies of k(T, ρ), the theory predicts for all systems that the Gaussian decay time r is nearly independent of ρ. This in turn implies that k(T,ρ) factorizes into a liquid phase structural contribution and a gas phase dynamical contribution, yielding a first-principles form for k(T, ρ) similar to that postulated by the isolated binary collision model. Also, the theory predicts both "classical" superlinear rate... [ABSTRACT FROM AUTHOR]

The theoretical treatment in Paper I [D. W. Miller and S. A. Adelman, J. Chem. Phys. 117, 2672, (2002), preceding paper] of the vibrational energy relaxation (VER) of low-frequency, large mass dihalogen solutes is extended to the VER of the high-frequency, small mass molecular hydrogen solutes H[sub 2] and D[sub 2] in a Lennard-Jones argon-like solvent. As in Paper I, values of the relaxation times T[sub 1] predicted by the theory are tested against molecular dynamics (MD) results and are found to be of semiquantitative accuracy. To start, it is noted that standard Lennard-Jones site-site potentials derived from macroscopic data can be very inaccurate in the steep repulsive slope region crucial for T[sub 1]. Thus, the H-Ar Lennard-Jones diameter σ[sub uv] is not taken from literature values but rather is chosen as σ[sub UV] = 1.39 Å, the value needed to make the theory reproduce the experimental H[sub 2]/Ar gas phase VER rate constant. Next, by MD simulation it is shown that the vibrational coordinate fluctuating force autocorrelation function 〈&Ftilde;(t)&Ftilde;〉[sub 0] of Paper I decays roughly an order of magnitude more rapidly for the molecular hydrogen solutions than for the dihalogen solutions. This result implies a relatively slow decay for the molecular hydrogen friction kernels β(ω) = (k[sub B]T)[sup -1] ∫[sup ∞, sub 0] 〈&Ftilde;(t)&Ftilde;〉[sub 0] cos ω tdt, yielding for the H[sub 2]/Ar and D[sub 2]/Ar systems at T= 150 K physical millisecond values for T[sub 1] =beta;[sup -1](ω) despite the high liquid phase vibrational frequencies ω[sub 1] of H[sub 2] and D[sub 2]. The rapid decay of 〈&Ftilde;(t)&Ftilde;&ran;[sub 0] is due to both the steepness of the repulsive slope of the H-Ar potential and the small masses of H and D. Thus, the small value chosen for σ[sub UV] is needed to avoid unphysically long T[sub 1]'s. Next, an analytical treatment of the H[sub 2]/D[sub... [ABSTRACT FROM AUTHOR]

Algorithms which permit the explicit, albeit approximate, construction of a physically realistic generalized Langevin equation of motion for the energy relaxation dynamics of a specified solute normal mode coordinate y in a monatomic solvent are developed. These algorithms permit the construction, from equilibrium solute–solvent pair correlation functions, of the liquid state frequency ωl of the normal mode and of the Gaussian model approximation to the autocorrelation function 〈F(t)F〉0 of the fluctuating generalized force exerted by the solvent on the normal mode. From these quantities one may compute, from equilibrium solute–solvent pair correlation functions, the vibrational energy relaxation time T1 of the solute normal mode and also related quantities which permit one to assess the relative importance of direct [y coordinate→solvent] and indirect [y coordinate→solute translation–rotational coordinates→solvent] energy flow pathways in solute vibrational energy relaxation. The basis of the construction of T1 is the formula T1=β-1(ωl) where β(ω)=∫∞0 β(t)cos ω dt and where β(t)=[kBT]-1 〈F(t)F〉0 is the friction kernel of the solute normal mode. This formula is valid if T1>T2=vibrational phase relaxation time. The approximate formulas for T1 are worked out in detail for diatomic solutes. The approximations are tested for this diatomic solute case by comparing with molecular dynamics results. [ABSTRACT FROM AUTHOR]

A numerical study of the solute, solvent, and energy flow pathway dependence of the vibrational energy relaxation (VER) time T1 of a harmonic solute vibrational mode is presented for the prototype case of diatomic solutes in monatomic solvents. This study is based on formulas for T1 developed in the preceding paper, especially the relationship T1=β-1(ωl) where β(ω) is the frequency-dependent friction kernel of the solute normal mode and where ωl is its liquid state frequency. These formulas permit evaluation of T1 and its energy flow pathway dependence from equilibrium solute–solvent pair correlation functions. Applications are made to VER of ground electronic state molecular iodine and bromine in the fluids xenon and argon and in model Lennard-Jones solvents designed to simulate ethane and carbon tetrachloride. Satisfactory agreement between the present treatment and experimental and computer simulation results for 15 thermodynamic states is found. The VER rates (∼T-11) were found to increase with increase in the degree of resonance overlap between ωl and the solvent frequency spectrum ρF(ω)∼β(ω). Moreover indirect energy flow pathways, i.e., those which involve solute vibration ↔ solute translation–rotation ↔ solvent energy transfer, are found to play a qualitatively essential role for many of the systems studied here. Finally a study of the temperature and density dependence of T1 for iodine in xenon in the experimentally accessible range is presented. [ABSTRACT FROM AUTHOR]