Time correlation function approach to liquid phase vibrational energy relaxation: H_{2} and D_{2} solutes in Ar solvent
Abstract
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 lowfrequency, large mass dihalogen solutes is extended to the VER of the highfrequency, small mass molecular hydrogen solutes H_{2} and D_{2} in a LennardJones argonlike solvent. As in Paper I, values of the relaxation times T_{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 LennardJones sitesite potentials derived from macroscopic data can be very inaccurate in the steep repulsive slope region crucial for T_{1}. Thus, the HAr LennardJones diameter σ_{UV} is not taken from literature values but rather is chosen as σ_{UV}=1.39 Å, the value needed to make the theory reproduce the experimental H_{2}/Ar gas phase VER rate constant. Next, by MD simulation it is shown that the vibrational coordinate fluctuating force autocorrelation function <F∼(t)F∼>_{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_{B}T)^{1}∫_{0}∞<F∼(t)F∼>0_{cos} ω tdt, yielding for the H_{2}/Ar and D_{2}/Ar systems at T=150 K physical millisecond values for T_{1}=β^{1}(ω_{l}) despite the high liquid phase vibrational frequencies ω_{l} of H2 and D_{2}. The rapid decay of <F∼(t)F∼>_{0} is due to both the steepness of the repulsive slope of the HAr potential and the small masses of H and D. Thus, the small value chosen for σ_{UV} is needed to avoid unphysically long T_{1}'s. Next, an analytical treatment of the H_{2}/D_{2} isotope effect on T_{1}, based on the theory, is found to predict that the H_{2}/Ar and D_{2}/Ar T_{1}'s are close in value due to the compensating effects of lower ω_{l} but slower decay of <F∼(t)F∼>_{0} for D_{2}/Ar, a result in qualitative agreement with experiments. Applying the theory to numerically study the isothermal ρ dependencies of the VER rate constant k(T,ρ)=T1^{1} at 150 K reveals that for both H_{2}/Ar and D_{2}/Ar, as for the solutions of Paper I, k(T,ρ) can be factorized as in the isolated binary collision (IBC) model. Moreover, the molecular theory and IBC rate isotherms differ only slightly for both solutions, a result interpreted in terms of the form of the HAr pair correlation function. The theoretical and experimental rate isotherms at 150 K are then compared. Agreement is very good for the H_{2}/Ar solution, but for the D_{2}/Ar solution the theoretical rates are about four times too large. Finally, the isochoric T dependencies of k(T,ρ) in the range 2001000 K are found for both solutions to conform to an Arrhenius rate law.
 Publication:

Journal of Chemical Physics
 Pub Date:
 August 2002
 DOI:
 10.1063/1.1490916
 Bibcode:
 2002JChPh.117.2688M
 Keywords:

 hydrogen neutral molecules;
 deuterium;
 rotationalvibrational energy transfer;
 molecular dynamics method;
 LennardJones potential;
 Computerized Simulation;
 Deuterium;
 Energy Transfer;
 Hydrogen;
 Intermolecular Forces;
 LennardJones Potential;
 Liquid Phases;
 Molecular Dynamics;
 Molecular Gases;
 Time Functions;
 Vibration;
 34.50.Ez;
 61.20.Ja;
 34.20.Gj;
 Atomic and Molecular Physics;
 Rotational and vibrational energy transfer;
 Computer simulation of liquid structure;
 Intermolecular and atommolecule potentials and forces