Showing papers on "Vibrational partition function published in 1993"

Density matrix description of ultrafast dissipative wave packet dynamics

Abstract: Density matrix theory is applied to incorporate environmental effects and, thus, dephasing and relaxation into the description of vibrational wave packet dynamics on an ultrashort time scale. Instead of calculating the density matrix in the space of vibrational coordinates, the theory is formulated in vibrational eigenstates of appropriately chosen diabatic potential energy surfaces. Although a linear coupling between the vibrational degrees of freedom of the molecular system and those of the environment has been considered in detail, any type of coupling can be studied within the presented approach. The interplay of wave packet motion on the potential energy surfaces and energy dissipation into the environment is demonstrated for two simple one-dimensional examples

The accuracy of second order perturbation theory for multiply excited vibrational energy levels and partition functions for a symmetric top molecular ion

Abstract: The vibrational energy levels and partition functions of the nonrotating H3+ molecular ion have been calculated by using second order perturbation theory, including constant, linear, and quadratic terms in the vibrational quantum numbers. Energy levels have been assigned to A’1, A’2, and E’ symmetry species up to 29 244 cm−1, and perturbation theory energy levels have been compared with the results of accurate quantum calculations. The root‐mean‐square error in 141 energy levels is 4.0 cm−1, as compared to 11.7 cm−1 in the harmonic approximation. Furthermore, perturbation‐theory partition functions have errors of 7.4% or less over the factor‐of‐20 temperature range from 200 to 4000 K. The effect of the constant term in perturbation theory is also discussed; it improves the vibrational partition functions by ∼4% at 200 K.

Vibrational frequencies and dephasing times in excited electronic states by femtosecond time-resolved four-wave mixing

Abstract: Time-resolved degenerate four-wave mixing (TRDFWM) for an electronically resonant system in a phase-matching configuration that measures population decay is reported. Because the spectral width of input light exceeds the vibrational Bohr frequency of a strong Raman active mode, the vibrational coherence produces strong oscillations in the TRDFWM signal together with the usual population decay from the excited electronic state. The data are analyzed in terms of a four-level system: ground and excited electronic states each split by a vibrational quantum of a Raman active mode. Absolute frequencies and their dephasing times of the vibrational modes at ≈590 cm−1 are obtained for the excited as well as the ground electronic state. The vibrational dephasing rate in the excited electronic state is about an order of magnitude faster than that in the ground state, the origin of which is speculated upon.

Vibrational Relaxation of Anharmonic Oscillators in Expanding Flows

Abstract: Although the Landau-Teller vibrational model accurately predicts vibrational excitation process in post-shock and compressing flows, it under-predicts the rate of de-excitation in cooling and expanding flows. In the present paper, detailed calculations of the vibrational relaxation process of N2 and CO in cooling flows are conducted. A coupled set of vibrational transition rate equations and quasi-one-dimensional fluid dynamic equations is solved. Multiple quantum level transition rates are computed using SSH theory. The SSH transition rate results are compared with available experimental data and other theoretical models. Vibration-vibration exchange collisions are responsible for some vibrational relaxation acceleration in situations of high vibrational temperature and low translational temperature. The present results support the relaxation mechanisms proposed by Bray and by Treanor Rich and Rehm.

Approximate path integral methods for partition functions

Abstract: We review several approximate methods for evaluating quantum mechanical partition functions with the goal of obtaining a method that is easy to implement for multidimensional systems but accurately incorporates quantum mechanical corrections to classical partition functions. A particularly promising method is one based upon an approximation to the path integral expression of the partition function. In this method, the partition‐function expression has the ease of evaluation of a classical partition function, and quantum mechanical effects are included by a weight function. Anharmonicity is included exactly in the classical Boltzmann average and local quadratic expansions around the centroid of the quantum paths yield a simple analytic form for the quantum weight function. We discuss the relationship between this expression and previous approximate methods and present numerical comparisons for model one‐dimensional potentials and for accurate three‐dimensional vibrational force fields for H2O and SO2.

Potential energy surface and vibrational analysis along the stretching vibrations of XeHXe+ ion

Abstract: An analytical potential energy surface (PES) along the stretching coordinates of a linear XeHXe+ ion is presented. Ab initio calculations within the effective core potential approach are used as input for the PES. The present vibrational analysis indicates extensive mixing of the zeroth‐order harmonic oscillator vibrational states, and a rather complete collapse of the normal mode picture already near the bottom of the potential well. At higher vibrational energies, and elongated Xe–Xe distances, development of a double minimum in the PES is observed. The simulated absorption spectrum consists of a strong vibrational progression near 1000–1700 cm−1, and is in qualitative agreement with the previous matrix isolation data. The intensity distribution of the vibrational progression is mostly due to the potential terms rather than nonlinear contributions in the Taylor series expansion of the electric dipole moment. Due to the highly anharmonic potential, and subsequent breakdown of selection rules, the emissio...

Vibration-rotation Hamiltonians of linear molecules

Abstract: The construction of the molecular vibration-rotation Hamiltonian is considered, with particular reference to two alternative treatments of molecules with linear reference configurations. These can be considered to have either (i) 3N - 5 vibrational and 2 rotational degrees of freedom or (ii) 3N - 6 vibrational and 3 rotational degrees of freedom. In either case the classical kinetic energy consists of vibrational, rotational and translational parts given by The rotational part contains the angular velocity ω and the modified moment of inertia tensor I' of Wilson and Howard, which also occurs in the relation J α - πα = Σβ I'αβωβ involving the total (J) and vibrational (π) angular momenta. In case (i), I′ has a vanishing z row and column, where z is the axis of the molecule. This is associated with the Sayvetz condition that the total angular momentum about the axis is purely vibrational. These equations therefore contain only the two components ωx and ωy of ω, which can be eliminated to give the Hamiltonia...

Vibrational nonequilibrium effects on diatomic dissociation rates

Abstract: The collision-induced dissociation rate of diatomic molecules from a ladder of rotational and anharmonic vibrational states is developed, and the correction for vibrational nonequilibrium is considered. The result is similar to an analytic correction derived by Hammerling et al. (1959) for harmonic oscillators. An empirical correction algorithm suggested by Park (1987, 1990) gives similar results when vibrational temperature is comparable to kinetic temperature but underestimates the dissociation rate when vibrational temperature is small compared with the kinetic temperature. This algorithm uses an effective temperature in the experimentally determined Arrhenius expression for the rate coefficient, which is a weighted average of the vibrational and kinetic temperature, whereas theory indicates that kinetic temperature should appear only in the exponential term of the Arrhenius expression. Nevertheless, an effective temperature can always be found that will numerically duplicate the proper rate coefficient at any given condition, but a constant weighting factor cannot be expected to provide this. However, the algorithm can he adjusted to give reasonable results over a range of conditions if the geometric weighting factor is taken to be a simple linear function of the ratio of vibrational to kinetic temperature in the gas.

Partition function zeros and the three-dimensional Ising spin glass

Abstract: We have computed the exact partition function of the 3D Ising spin glass on lattices of effective size 3×3×Lz, 4×4×Lz, and 5×5×Lz forL z up to 9, and several random bond configurations. Studying the distribution of zeros of the associated partition functions, we find further evidence that these systems have a singularity in the thermodynamic limit.

The vibrational modes of vitreous B2O3

Abstract: The vibrational density of states of vitreous B2O3 has been studied over its full energy range by the use of two different inelastic neutron scattering spectrometers. Its general features may be described in terms of four bands of modes centred at 6.8, 15.1, 88 and 171 meV. A simple model for the vibrational density of states based on a single triangular BO3 structural unit shows the character of the modes for each of the four bands. There is evidence in the vibrational density of states for low energy modes in excess of the sound wave contribution. The above model suggests that the excess may be due to rotational modes, although this explanation might be invalidated by frustration due to the high concentration of boroxol rings.

Partition Functions in the Dynamical Symmetry Limits of the Interacting-Boson Model

Abstract: In the large boson number (N) limit, analytical formulae for the partition functions are derived in the three dynamical symmetry limits (U(5), SU(3), and O(6)) of the interacting-boson model (IBM). In the U(5) limit the partition function is that of a five-dimensional oscillator and in the SU(3) limit it decomposes into rotational and vibrational parts. These are similar to the geometric-model results. In addition IBM gives an expression for O(6) nuclei; in the O(6) limit the partition function decomposes into O(6) (one-dimensional oscillator) and O(5) (γ-unstable vibration) parts. Finite-boson-number effects are studied numerically and they are found to be important for temperatures T 1 MeV.

The temperature dependence of fast vibrational energy transfer processes in methyl fluoride

Abstract: The temperature dependencies of two fast vibrational energy transfer processes in methyl fluoride (CH3F) have been measured between 120K and 400 K by means of time-resolved millimetre/submillimetre-infrared double resonance spectroscopy. The first of these processes, a resonant vibrational swapping process between the ground vibrational state and the v 3 = 1 (v 3) vibrational state, effectively transfers population between states of A and E symmetry. A rapid increase in cross section with decreasing temperature was observed for this process, a result in excellent quantitative agreement with semiclassical theory of near resonant vibrational collisions. The second process, which transfers population between the v 3 and v 6 = 1 (v 6) vibrational states, was found experimentally to have a much weaker temperature dependence. From this result and from additional experimental observations of symmetry type-sensitive energy transfer into v 6, the energy transfer between v 3 and v 6 was demonstrated to result from ...

An efficient method for optimal modes analysis of vibration: application to acetylene-d

Abstract: The quantitative analysis of vibrational spectra of polyatomic molecules in the high-energy regime requires a determination of the modes which optimally describe the vibrational motions of the nuclei at these energies. Observed vibrational spectra in small polyatomics indicate substantial regularity in the vibrational motion, implying that such a set of «optimal modes» should exist, but the experiments do not provide a direct means of characterizing these modes. We present here a computationally efficient theoretical method for optimal modes analysis of exact multimode vibrational eigenstates. This algorithm consists of direct numerical integration of selected projection coefficients which reveals the extent of zeroth-order character of these eigenstates

Evaluation of Vibrational Energies by Means of Neural Networks

Abstract: A program for neural networks was developed to evaluate many vibrational energies of harmonic oscillators, Morse oscillators and diatomic molecules The tests of all the vibrational levels of SiH (A state) and HF (B state) with vmax equal to 8 and 31, respectively, yielded results in excellent agreement with semi-empirical Morse results The program was also applied to the three vibrational modes of H2O accurately

Influence of electron-electron interaction on the vibrational frequency in one-dimensional dimerized conjugated systems.

Abstract: We apply the correlated-basis-function approach to study the vibrational stretching mode in a one-dimensional dimerized conjugated system modeled as a Kronig-Penney square-well lattice. Polyacetylene is taken as prototypical example. Various potential parameters are considered in the one-dimensional energy-band calculations. We find that the one-electron theory is unable to afford simultaneously reasonable descriptions of the electronic and vibrational properties, which indicates the importance of electron-electron interaction in the vibrational modes (and lattice relaxation). Our parameters are selected according to the ionization potential value in polyacetylene