Normal mode theory of two step relaxation in liquids: Polarizability dynamics in CS2

Abstract

An instantaneous normal mode description of relaxation in supercooled liquidsInstantaneous normal mode theory of quantum time correlation functions: Raman spectrum of liquid CS2 An instantaneous normal mode ͑INM͒ theory is given for relaxation in liquids by a fast ␤ process followed by a slow ␣ process. The ␤ process is harmonic dynamics in the wells of the N-body potential, while the ␣ process is structural relaxation coincident with barrier crossing to a neighbor well. The theory introduces a new parameter, the ''harmonic fraction'' denoted F H , which is the fraction of the mean-square fluctuations of a dynamical variable capable of being relaxed by the harmonic ␤ process. Theory and computer simulation are compared for the polarizability correlation function, PC(t), and the polarizability time derivative correlation function, DPC(t), in a model of CS 2 including internal degrees of freedom. Agreement is good, with the INM theory clearly showing the ''signature'' time dependence of a correlation function undergoing ␣␤ relaxation in a low temperature liquid; there are no adjustable parameters in the theory. The polarizability is calculated in the ''point atomic polarizability approximation'' ͑PAPA͒ which is sensitive to molecular vibrations, so a preliminary classical INM treatment of Raman scattering is obtained. The PAPA overestimates the derivative of the polarizability with respect to the internal coordinates, and in reality the vibrations behave quantum mechanically, so the Raman intensities are inaccurate, but otherwise a plausible description is obtained for several features of the spectrum. It is explained how an improved PAPA will be combined with a quantum INM theory in future Raman calculations.

Polarizability response in polar solvents: Molecular-dynamics simulations of acetonitrile and chloroform

“…6,16 In the former liquid, the PAPA model has also been used to investigate the mechanisms of light scattering in combination with instantaneous normal-mode ͑INM͒ theory. [17][18][19][20][21] In all cases the PAPA model brings the calculated values of the optical properties into closer agreement with experimental data. With a similar spirit, in order to investigate the depolarized Rayleigh spectra of liquid ortho-terphenyl by MD simulations, Mossa et al 22 have used a simpler site-site DID scheme in which they assign to each of the six sites of each aromatic ring the polarizability tensor of a benzene molecule divided by six, neglecting contributions from atoms in the same ring.…”

Calculating the hopping rate for diffusion in molecular liquids: CS2

“…[8][9][10][11][12][13] INMs are obtained by diagonalizing the matrix of second derivatives of the potential energy surface. Since the instantaneous configurations are not necessarily at the local minima, and since liquids contain anharmonicities, some of the INM frequencies will be imaginary.…”

“…The first approach attempts to calculate the hopping time from a static property-the fraction of imaginary frequency instantaneous normal modes. [8][9][10][11][12][13][14][15][16] The other approach is to measure the decorrelation of atomic surroundings by associating the hopping rate (1/) with the long-time decay rate of the cage correlation function. 2…”

An instantaneous normal mode analysis of solvation: Methyl iodide in high pressure gases

“…However, such relaxation processes may be added to the INM description by the incorporation of lifetime effects as demonstrate recently by Keyes in the calculation of the polarizability of CS 2 . 3 Additionally, the failure of this INM treatment to quantitatively capture the solvation response beyond 150 fs can also be attributed to a breakdown of the harmonic description of the solvent motion This study also highlights the connection offered by this INM framework between spectroscopic and solvation dynamics analyses. The solvation autocorrelation function, which has been primarily considered within the experimental context of time dependent fluorescence Stokes shift measurements, is also known as the energy correlation function in spectral line shape theories.…”

“…1 Larger scale structural relaxation of the many body potential is taken to occur on a longer time scale and thus limits the time range of the applicability of this description unless additional relaxation considerations are incorporated. 2,3 This INM framework has been used to describe transport properties of glasses, clusters, and supercooled liquids, 1,4,5 the low frequency intermolecular motions of water, 6,7 the Raman line shapes of CS 2 , 3 and the vibrational line shape of a diatomic in solution. 8 The solvation of a model diatomic in acetonitrile 6 and I 2 in liquid CO 2 , 9 based on model potentials, has also been given by an INM treatment.…”