Mixed quantum-classical molecular dynamics simulation of vibrational relaxation of ions in an electrostatic field

The vibrational relaxation of ions in low-density gases under the action of an electrostatic field is reproduced through a molecular dynamics simulation method. The vibration is treated though quantum mechanics and the remaining degrees of freedom are considered classical. The procedure is tested through comparison against analytic results for a two-dimensional quantum model and by studying energy exchange during binary ion-atom collisions. Finally, the method has been applied successfully to the calculation of the mobility and the vibrational relaxation rate of O2+ in Kr as a function of the mean collision energy using a model interaction potential that reproduces the potential minimum of a previously known ab initio potential surface. The calculation of the steady mean vibrational motion of the ions in (flow) drift tubes seems straightforward, though at the expense of large amounts of computer time.     

Effect of ions on the vibrational relaxation of liquid water

We study the relaxation of the O-H stretch vibration of water in aqueous salt solutions using femtosecond two-color pump-probe spectroscopy. The vibrational lifetimes are measured for a series of salts consisting of the anions Cl(-), Br(-), and I(-) and the cations Li(+), Na(+), and Mg(2+), for a range of concentrations from 0.5 M up to 6 M (chloride salts), 9 M (bromide salts), and 10 M (iodide salts). In addition to the previously found dependence of the vibrational lifetime on the nature of the anion, the lifetime is found to depend on concentration and is observed to show a small but significant dependence on the nature of the cation. We present a model in which all the effects of ions on the vibrational relaxaton of liquid water are accounted for.     

A semiclassical model for the vibrational excitation of spherical-top molecules in collisions with ions

A simple theory is presented to explain the previously observed single-mode vibrational excitation of the spherical-top molecules CH₄, CF₄ and SF₆ in collisions with H⁺ and Li⁺. The theory is based on a three-dimensional forced-oscillator model which has been modified to take account of many independent harmonic oscillators. For small-angle collisions the linear driving forces are the dipole-, polarizability- and quadrupole-derivatives taken from IR, Raman spectroscopy and simple estimates, respectively. To explain the results at larger angles near and beyond the rainbow it has been necessary to introduce short-range repulsive forces between the ions and the outer atoms of the molecule. For small angles both the predicted first moment of the energy transfer and the time-of-flight spectra agree quantitatively with the experimental results. At large angles, for which only the first moment of the energy is available, good qualitative agreement is obtained after a slight adjustment of the potential parameters. The energy transfer as a function of time is calculated and shows a different oscillatory behavior for the proton and Li⁺-ion systems. Also the effect of intra-mode coupling is investigated and shown to have only a small effect on the overall energy transfer. The paper closes with a discussion of the implications of these experiments and the possible role of rotational excitation. The field strengths in these ion scattering experiments are shown to be greater than in the strongest focused Q-switched laser pulses.     

Microviscosity effects on the vibrational relaxation rates in molecular liquids

The isotropic Raman band of the CO stretching mode of the N,N-dimethylformamide (DMF) molecule has been studied as a function of solvents' hydrodynamic properties. The effect of solvent viscosity on linewidth (Γ_iso) has been studied in detail, particularly using the theory of microviscosity. Modifications have been made in the ƒ(ϱ, η, n) parameter which relates the vibrational relaxation rate with viscosity, density and dispersion energy on the basis of microviscosity.     

Effects of vibrational relaxation on the optical lineshapes in molecular spectra

We derive general expressions for the time dependent optical lineshape of a molecule undergoing vibrational relaxation in a dense medium.     

Electronic spectroscopy and relaxation of gas phase molecular ions

Techniques for obtaining electronic spectra of singly charged cations are described. Jahn-Teller effects in the spectra of polyhalobenzene cations are discussed. Experimental and theoretical methods for studying radiationless transitions in molecular ions are presented. Recent work on the spectroscopy and intramolecular relaxation of doubly-charged cations is reviewed.     

Molecular orbital predictions of the vibrational frequencies of some molecular ions

Recent spectroscopic advances have led to the first determinations of infrared vibration-rotation bands of polyatomic molecular ions. These initial detections were guided by ab initio predictions of the vibrational frequencies. The calculations reported here predict the vibrational frequencies of additional ions which are candidates for laboratory analysis. Vibrational frequencies of neutral molecules computed at three levels of theory, HF/3-21G, HF/6-31G*, and MP2/6-31G*, were compared with experiment and the effect of scaling was investigated to determine how accurately vibrational frequencies could be predicted. For 92% of the frequencies examined, uniformly scaled HF/6-31G* vibrational frequencies were within 100 cm-1 of experiment with a mean absolute error of 49 cm-1. This relatively simple theory thus seems suitable for predicting vibrational frequencies to guide laboratory spectroscopic searches for ions in the infrared. Hence, the frequencies of 30 molecular ions, many with astrochemical significance,were computed. They are CH2+, CH3+, CH5+, NH2+, NH4+, H3O+, H2F+, SiH2+, PH4+, H3S+, H2Cl+, C2H+, classical C2H3+, nonclassical C2H3+, nonclassical C2H5+, HCNH+, H2CNH2+, H3CNH3+, HCO+, HOC+, H2CO+, H2COH+, H3COH2+, H3CFH+, HN2+, HO2+, C3H+, HOCO+, HCS+, and HSiO+.     

A study of molecular vibrational relaxation mechanism in condensed phase based upon mixed quantum-classical molecular dynamics. I. A test of IBC model for the relaxation of a nonpolar solute in nonpolar solvent at high density

In order to investigate vibrational relaxation mechanism in condensed phase, a series of mixed quantum-classical molecular dynamics calculations have been executed for nonpolar solute in nonpolar solvent and polar solute in polar solvent. In the first paper (Paper I), relaxation mechanism of I2 in Ar, where Lennard-Jones force is predominant in the interaction, is investigated as a function of density and temperature, focusing our attention on the isolated binary collision (IBC) model. The model was originally established for the relaxation in gas phase. A key question, here, is "can we apply the IBC model to the relaxation in the high-density fluid?" Analyzing the trajectory of solvent molecule as well as its interaction with the solute, we found that collisions between them may be defined clearly even in the high-density fluid. Change of the survival probability of the vibrationally first excited state on collision was traced. The change caused by collisions with a particular solvent molecule was also traced together with the interaction between them. Each collision makes a contribution to the relaxation by a stepwise change in the probability. The analysis clearly shows that the relaxation is caused by collisions even in the high-density fluid. The difference between stepwise relaxation and the continuous one found for the total relaxation in the low-density fluid and in the high-density one, respectively, was clarified to come from just the difference in frequency of the collision. The stronger the intensity of the collision is, the greater the relaxation caused by the collision is. Further, the shorter the collision time is, the greater the resultant relaxation is. The discussion is followed by the succeeding paper (Paper II), where we report that molecular mechanism of the relaxation of a polar molecule in supercritical water is significantly different from that assumed in the IBC model despite that the density dependence of the relaxation rate showed a linear correlation with the local density of water around the solute, the linear correlation being apparently in good accordance with the IBC model. The puzzle will be solved in Paper II.     

Ultrafast vibrational spectroscopy and relaxation in polyatomic molecules: Potential for molecular parallel computing

The feasibility of controlled ultrafast pumping in the mid IR and the probe of the subsequent intramolecular dynamics is illustrated for vibrational excitation of the two metal carbonyls W(CO)₆ and Mn(CO)₅Br in solution. Pumping and probing is performed by short, 130 fs, pulses centered at about 2000 cm⁻¹. Frequency resolved measurements of the time delayed probe pulse are performed. Measured two dimensional spectra are fitted by a kinetic scheme that models the vibrational dynamics. Fast relaxation is solvent induced with the solvent acting also as a heat bath. The (several) probe signals in the experiment can be thought of as the response of a finite state logic machine. This suggests that the molecular machine can act as an ultrafast (petaHertz) processor. The number of internal (memory) states of the machine is determined by the number of vibrational states in the kinetic scheme that can fit the observed relaxation. The number of outputs of the machine is the number of the several different available probe signals. It is shown that the machine is massively parallel because in each (sub ps) time step it produces an entire vector as an output and that each component of the output vector is, by itself, a transform over the input. Beyond that, the machine can produce a (finite number of) different output vectors in sequential time steps.     

Vibrational energy relaxation of small molecules and ions in liquids

A theoretical/computational framework for determining vibrational energy relaxation rates, pathways, and mechanisms, for small molecules and ions in liquids, is presented. The framework is based on the system—bath coupling approach, Fermi’s golden rule, classical time-correlation functions, and quantum correction factors. We provide results for three specific problems: relaxation of the oxygen stretch in neat liquid oxygen at 77 K, relaxation of the water bend in chloroform at room temperature, and relaxation of the azide ion anti-symmetric stretch in water at room temperature. In each case, our calculated lifetimes are in reasonable agreement with experiment. In the latter two cases, theory for the observed solvent isotope effects illuminates the relaxation pathways and mechanisms. Our results suggest several propensity rules for both pathways and mechanisms.     

Two-stage model for molecular orientational relaxation in liquid crystals

Abstract

The molecular reorientation in anisotropic fluids is considered as twostage process—fast single molecule rotation in the volume restricted by close neighbours and slow collective relaxation of the local surrounding. The theoretical results are applied to explain the discrepancy between the rotational diffusion coefficients D_⊥ ^r obtained by infrared bandshape analysis and polarized fluorescence techniques.     

Two-stage model for molecular orientational relaxation in liquid crystals

The molecular reorientation in anisotropic fluids is considered as twostage process—fast single molecule rotation in the volume restricted by close neighbours and slow collective relaxation of the local surrounding. The theoretical results are applied to explain the discrepancy between the rotational diffusion coefficients D_⊥^r obtained by infrared bandshape analysis and polarized fluorescence techniques.     

Anomalously small jet-cooling of benzene: Absence of efficient low-energy collision-induced vibrational relaxation

Benzene, compared to other supersonic jet-cooled molecules, including ring-substituted benzene derivatives, appears to show a general lack of vibrational cooling in seeded He or Ar supersonic expansions. The general extent of vibrational non-cooling suggests that He or Ar collisions may simply be relatively ineffective in cooling benzene. A number of other gases were also seeded into He-benzene expansions but the vibrational cooling of mode 6, which was monitored carefully, was not substantially improved.     

Improved relations for vibrational relaxation in gases

Explicit expressions are presented for calculating vibration-to-translation (VT) energy conversion probabilities, essential in molecular laser isotope separation. VT conversions in molecular collisions occur by two mechanisms: (1) high-energy impact transfers prevailing at higher temperatures, and (2) Van der Waals-bonding encounters followed by (pre-)dissociations at lower temperatures. While mechanism (1) has been studied for over fifty years culminating in the Schwartz–Slawsky–Herzberg relation, a useful analytic expression for (2) has so far been lacking. An improved dimer formation theory developed by the author together with molecular pre-dissociation physics now provides a VT conversion relation for mechanism (2), which correctly predicts observations.     

A study of molecular vibrational relaxation mechanism in condensed phase based upon mixed quantum-classical molecular dynamics. II. Noncollisional mechanism for the relaxation of a polar solute in supercritical water

Mixed quantum-classical molecular dynamics method has been applied to vibrational relaxation of a hydrophilic model NO in supercritical water at various densities along an isotherm above the critical temperature. The relaxation rate was determined based on Fermi's golden rule at each state point and showed an inverse S-shaped curve as a function of bulk density. The hydration number was also calculated as a function of bulk density based on the calculated radial distribution function, which showed a good correlation with the relaxation rate. Change of the survival probability of the solute vibrational state was analyzed as a function of time together with the trajectory of the solvent water and the interaction with it. We will show that the solvent molecule resides near the solute molecule for a while and the solvent contributes to the relaxation by the random-noiselike Coulombic interaction only when it stays near the solute. After the solvent leaves the solute, it shows no contribution to the relaxation. The relaxation mechanism for this system is significantly different from the collisional one found for a nonpolar solute in nonpolar solvent in Paper I. Then, the relaxation rate is determined, on average, by the hydration number or local density of the solvent. Thus, the density dependence of the relaxation rate for the polar solute in supercritical water is apparently similar to that found for the nonpolar solute in nonpolar solvent, although the molecular process is quite different from each other.     

A virtual vibrational self-consistent-field method for efficient calculation of molecular vibrational partition functions and thermal effects on molecular properties

A new method is described for the calculation of molecular vibrational partition functions and thermal effects on molecular properties including an explicit account of anharmonicity. The approach is based on the vibrational self-consistent-field method. Partition functions and thermal averages of the energies calculated with the new method are generally in good agreement with the result of more accurate methods. At lower temperatures the method gives in addition good results for thermal averages of dipole moments and polarizabilities. The new method is much more efficient than explicit sum-over-states approaches previously used for calculation of thermal averages. Unlike the standard sum-over-states approach, the newly developed method is feasible for larger systems despite the formal exponential increase in the number of states with the size of the system. Thus, it is presently the only practical way for including an explicit treatment of anharmonicity in vibrational wave function based calculations of molecular vibrational partition functions and thermally averaged properties of larger molecules.     

Tube relaxation: A quantitative molecular model for the viscoelastic plateau of entangled polymeric media

The relaxation of an entangled polymeric medium in the viscoelastic plateau is investigated theoretically by using the slip-link representation of topological constraints. In addition to the chain retraction process introduced by Daoudi and investigated theoretically by Doi, we show that two processes contribute significantly to the relaxation: The first, “equilibration across slip-links,” is a longitudinal reequilibration between parts of the chain which have been differently extended or compressed, depending on their initial orientation relatively to the strain tensor. The second, “tube relaxation,” is a mean-field representation of the loss of topological constraints on one chain due to the retraction of the others. Closed analytical expressions for the stress accounting for these three processes are derived and compared with previous theories: the relaxation should be much more progressive than previously predicted, and the terminal time for retraction is reduced significantly by tube relaxation.     

Vibrational amplitude profile of molecular vibrational modes for vibrational mode assignment

Ultrashort pulse lasers with 6- and 20-fs durations were utilized for phthalocyanine thin film sample to induce several vibrational modes and vibration amplitude spectra were determined by multi-wavelength measurement technique. From the spectra we could identify the electronic states, which couple to two vibrational modes with frequencies of 670 and 750 cm⁻¹. It was shown that the vibrational amplitude profile obtained by the method can be used for providing information for the assignment of the vibrational mode.