Showing papers on "Vibrational partition function published in 1992"
TL;DR: In this article, the authors studied QCD with nonzero chemical potential on 44 lattices by averaging over the canonical partition functions, or sectors with fixed quark number, and derived a condensed matrix of size 2×3×L3 whose eigenvalues can be used to find the canonical partitions.
113 citations
TL;DR: In this article, the vibration Hamiltonian operator Hvib for a nonlinear triatomic molecule is given in Radau coordinates, and a direct product basis is chosen, and the vibrational matrix is evaluated in the discrete variable representation (DVR) for the symmetrized radau coordinates.
Abstract: Highly accurate quantum‐mechanical calculations are presented for highly excited vibrational states of H2O. The vibration Hamiltonian operator Hvib for a nonlinear triatomic molecule is given in Radau coordinates. A direct product basis is chosen, and the Hvib matrix is evaluated in the discrete variable representation (DVR) for the symmetrized Radau coordinates. Vibrational eigenstates are computed from the DVR Hvib via the successive diagonalization/truncation technique. A comparison of the computed eigenvalues with those observed demonstrate the accuracy of our model. Highly excited vibrational states, up to 30 000 cm−1 above the zero‐point energy, are reported for the potential energy surface (PES) given by Jensen [J. Mol. Phys., 133, 438 (1989)]. Using natural orbital expansions, the eigenfunctions of vibrational states are analyzed to understand the origins of the dynamical mixing of the vibrational modes. The local/normal mode transitions, Fermi resonances, Darling–Dennison interactions, and the mode separabilities are investigated. Statistical studies on the energy level spacings are presented for two different types of PES.
109 citations
01 Jan 1992
TL;DR: In this paper, an approximate rate equation and a corresponding relaxation time from the excited states, compatible with the system of flow conservation equations, are derived for the first time, indicating the weak dependency of the initial vibrational temperature, and is shorter than the previously obtained relaxation time in which only excitation from the ground state was considered.
Abstract: Vibrational relaxation process of N2 molecules by electron-impact is examined for the future planetary entry environments. Multiple-quantum transitions from excited states to higher/lower states are considered for the electronic ground state of the nitrogen molecule N2(X1 S+). Vibrational excitation and de-excitation rate coefficients obtained by computational quantum chemistry are incorporated into the "diffusion model" to evaluate the time variations of Vibrational number densities of each energy state and total vibrational energy. Results show a nonBoltzmann distribution of number densities at the earlier stage of relaxation, which in turn suppresses the equilibration process, but affects little on the time variation of total vibrational energy. An approximate rate equation and a corresponding relaxation time from the excited states, compatible with the system of flow conservation equations, are derived for the first time. The relaxation time from the excited states indicates the weak dependency of the initial vibrational temperature, and is shorter than the previously obtained relaxation time in which only excitation from the ground state was considered. The empirical curve-fit formulas for the improved e-V relaxation time is obtained. The rate equation and the relaxation time, suited for the numerical simulation of the highly ionized planetary entry flowfields, are suggested.
77 citations
TL;DR: A modified version of the optothermal technique has been used to measure photofragment angular distributions resulting from the vibrational predissociation of Ar-CO2 from both members of the (1001)/(0201) Fermi diad as discussed by the authors.
Abstract: A modified version of the optothermal technique has been used to measure photofragment angular distributions resulting from the vibrational predissociation of Ar–CO2 from both members of the (1001)/(0201) Fermi diad. These angular distributions show resolvable structure which can be assigned to individual final states of the resulting fragments. The emphasis of the present paper is on the role of the vibrational degrees of freedom of the CO2 fragment as depositories for the excess energy. The dissociation energy (D0) of the complex has been determined to be 166±1 cm−1. This result is used in conjunction with the spectroscopic data already available in the literature to refine two previously reported two‐dimensional Ar–CO2 potential energy surfaces.
57 citations
TL;DR: A section of the potential energy surface of the benzene-argon complex corresponding to the argon versus benzene intermolecular vibrational modes has been determined by fitting the existing ab initio data with the use of two different empirical potentials.
50 citations
TL;DR: In this article, the effect of vibrational activation on the solvent-dependent reaction dynamics of electron transfer processes is examined by using a slightly modified from of the theoretical treatment due to Sumi, Nadler, and Marcus Allowance is made for the occurrence of nuclear tunneling involving the high-frequency vibrational modes, and for barrier crossing driven by solvent inertial polarization as well as vibrational activations, which enables the emergence of the zero-friction (transition-state theory, TST) limit.
Abstract: : The predicted alterations in the solvent-dependent reaction dynamics of electron-transfer processes brought about by the presence of reactant vibrational (inner-shell) activation in addition to overdamped solvent motion are examined by using a slightly modified from of the theoretical treatment due to Sumi, Nadler, and Marcus Allowance is made for the occurrence of nuclear tunneling involving the high-frequency vibrational modes, and for barrier crossing driven by solvent inertial polarization as well as vibrational activation The latter enables the emergence of the zero-friction (transition-state theory, TST) limit to be included along with providing a unified description in the absence and presence of vibrational activation Attention is focussed on the calculated dependencies of the reaction rate constant, and barrier-crossing frequency, upon the overdamped solvent relaxation time, over a range of parameters and in a format which can be compared directly with experimental solvent-dependent kinetic data
27 citations
TL;DR: In this paper, the authors developed a method of computing the vibrational structure of polyatomic molecules on the basis of the variational approach for an excited electronic state of a molecule.
10 citations
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TL;DR: In this article, the authors show that there is a connection between partition functions and thermodynamic quantities with volume regularization, due to the system having a space-varying density in an external potential.
Abstract: A convenient way to calculate $N$-particle quantum partition functions is by confining the particles in a weak harmonic potential instead of using a finite box or periodic boundary conditions. There is, however, a slightly different connection between partition functions and thermodynamic quantities with such volume regularization. This is made explicit, and its origin explained to be due to the system having a space-varying density in an external potential. Beyond perturbation theory there is a potential pitfall with the method, which is pointed out.
9 citations
TL;DR: In this paper, a microscopic approach for the description of low-lying intrinsic states in deformed odd-odd nuclei is formulated as a generalization of the quasiparticle-phonon model.
Abstract: The microscopic approach for the description of low-lying intrinsic states in deformed odd-odd nuclei is formulated as a generalization of the quasiparticle-phonon model. In comparison with other models used for deformed odd-odd nuclei, the approach proposed in this paper involves vibrational degrees of freedom of the doubly-even core, their coupling to quasiparticle degrees of freedom and then-p interaction between the odd particles. Our model treats all of these modes of nuclear motion on the same microscopic footing. This proposed model is applied to calculate the energies and phonon-quasiparticle structure of the intrinsic states of the odd-odd Ho isotopes withA=160, 162, 164, 166 and 168. It is found that the low-lying intrinsic states in the odd-odd Ho isotopes have only small vibrational components. In general the vibrational states are fragmented over many intrinsic states.
8 citations
TL;DR: The involvement of anharmonic interactions in the vibrational level mixing and IVR in S1 benzene at excess vibrational energy up to ∼5000 cm−1 was theoretically studied in this paper.
Abstract: The involvement of anharmonic interactions in the vibrational level mixing and IVR in S1 benzene at excess vibrational energy up to ∼5000 cm−1 was theoretically studied. The employed procedure is based on certain generally valid regularities governing the magnitude of anharmonic coupling matrix elements combined with detailed analysis of vibrational density computations. Definite conclusions concerning the rule of purely anharmonic interaction mechanisms in the vibrational mixing and redistribution behavior of S1 benzene have been arrived at.
8 citations
TL;DR: In this paper, a method of extracting harmonic information from the inertial defects of non-totally symmetric vibrational states of orthorhombic molecules has been developed.
TL;DR: A vibrational coupling model to treat the solvation effects in chemical reaction rate calculations is proposed and applied to the intramolecular hydrogen transfer reaction CH3O· ·CH2OH in the condensed phase as mentioned in this paper.
Abstract: A vibrational coupling model to treat the solvation effects in chemical reaction rate calculations is proposed and applied to the intramolecular hydrogen transfer reaction CH3O· ·CH2OH in the condensed phase. The effect of solvation is taken into account in two ways: (1) the solvent effect on the activation energy of the reaction is simulated by including 39 surrounding water molecules, represented by fractional charges at the assumed atomic positions, in the potential energy surface calculation; and (2) the vibrational couplings between the 10 nearest solvent molecules and the molecules constituting the reaction system are explicitly included in a vibrational frequency calculation. RRKM theory with Miller's tunneling correction included is employed to calculate the rate constants. The effect of solvation causes a significant change in the chemical reaction rate, mainly through a lowering of the activation energy. The vibrational coupling causes a slight increase of the rate constant in the tunneling region by perturbing the vibrational frequencies of the reactant and transition states, which appear in the rate-constant expression, but has little effect at higher temperatures.
TL;DR: The summed and averaged differential cross section for vibratory excitation of molecules in electron scattering in the framework of the algebraic-eikonal approach using intrinsic wave functions for the vibrational excitations is derived.
Abstract: We derive the summed and averaged differential cross section for vibrational excitation of molecules in electron scattering in the framework of the algebraic-eikonal approach. The additional ingredient is that the {ital T}-matrix elements are derived in the mean-field approximation using intrinsic wave functions for the vibrational excitations.
TL;DR: The well-known cumulant-summation formula is applied to the low-temperature calculation of the quantum-mechanical partition functions for many particle systems and the result is that the expected equivalence of the canonical and grand-canonical ensembles is not found at low temperatures.
Abstract: The well-known cumulant-summation formula is applied to the low-temperature calculation of the quantum-mechanical partition functions for many particle systems. The motivation for this method is to be able to deal with many-particle states directly and avoid the usual starting point of independent single-particle states. The test case chosen for this method was the calculation of the canonical partition function and the grand-canonical partition function for the degenerate free-electron gas. The result is that the expected equivalence of the canonical and grand-canonical ensembles is not found at low temperatures. The role of few-particle fluctuations in the grand-canonical ensemble is shown to be extremely important to the thermal properties of the degenerate free-electron gas and in the difference between the ensembles.
TL;DR: In this paper, a force constant model for the vibrational modes in C60, based on bond-stretching and angle bending interactions, is presented, and the results of this model are compared with the experimental data available from Raman, infrared, and high resolution electron energy loss spectroscopies, as well as neutron inelastic scattering measurements.
Abstract: A force constant model for the vibrational modes in C60, based on bond-stretching and anglebending interactions, is presented. The results of this model are compared with the experimental data available from Raman, infrared, and high resolution electron energy loss spectroscopies, as well as neutron inelastic scattering measurements. Excellent agreement is obtained between the calculated and experimental mode frequencies. The pressure dependence of the Ramanand infrared-active mode frequencies is calculated within a simple model and is compared to available experimental data.
TL;DR: In this article, the atomic vibrational dynamics in silica glass (a-SiO2) using molecular-dynamics (MD) simulations and classical lattice dynamics method were studied.
Abstract: We study the atomic vibrational dynamics in silica glass (a-SiO2) using molecular-dynamics (MD) simulations and classical lattice dynamics method. The SiO2 glasses were generated by molecular-dynamics and steepest-descent quench (SDQ) using an effective interatomic potential consisting of two-body and three-body interactions. The frequency and eigenvectors of vibrational normal modes are obtained by diagonalization of the dynamical matrix. The partial and total vibrational density of states (DOS), bond-projected DOS, participation ratio (PR), and neutron-weighted dynamic structure factor are calculated. The results are compared with inelastic neutron scattering experiments on SiO2 glass.
TL;DR: In this article, the authors used functional integration to make an exact calculation of the quantum partition function of the reduced BCS model in the thermodynamic limit, which is used to estimate the temperature T c of the phase transition in the ordered phase.
Abstract: Functional integration is used to make an exact calculation of the quantum partition function of the reduced BCS model in the thermodynamic limit. The expression for the quantum partition function and the estimate of the temperature T c of the phase transition in the ordered phase agree with the well-known results [1]. In the disordered phase, a singularity with respect to the temperature appears in the quantum partition function, which diverges at temperatures below a certain critical temperature Tffc. This satisfies T~c > T c and the difference 7"fie T c is not small. An interpretation of the temperature 7"fie is given.
TL;DR: In this article, the adiabatic multi-step separation method was used to calculate vibrational energy levels of SO2, which reduced the multidimensional vibrational problem to one-dimensional problems by performing successive adi-abatic separations of the different vibrational modes.
Abstract: The adiabatic multi-step separation method is used to calculate vibrational energy levels of SO2. This method reduces the multidimensional vibrational problem to one-dimensional problems by performing successive adiabatic separations of the different vibrational modes. Results are obtained and compared with those from other approximate methods and variationally converged eigenvalues. The adiabatic energies are found to be the most accurate ones, showing very good agreement with the exactum quantum values.
01 Jan 1992
TL;DR: In this article, the authors propose a new theoretical approach for the observed motional narrowing of the inhomogeneously broadened vibrational spectra of condensed phases, which allows for an experimental determination of the relaxation time distributions of the numerous phenomena involved in the fluctuations of the potential acting on the probe oscillator.
Abstract: We propose a new theoretical approach for the observed motional narrowing of the inhomogeneously broadened vibrational spectra of condensed phases. Introducing a “stretched” exponential as the modulation function of the vibrational dephasing process and attributing this function to the survivor function of an equilibrium vibrational renewal process, allows for an experimental determination of the relaxation time distributions of the numerous phenomena involved in the fluctuations of the potential acting on the probe oscillator. Applications to experimental results are reported for several n-CB liquid crystal molecules at various temperatures.