Showing papers on "Vibrational partition function published in 2005"
TL;DR: The numerical solution of the time-dependent Schrodinger equation for vibrating hydrogen molecules in few-cycle laser pulses shows that high-harmonic generation is sensitive to the laser-induced vibrational motion.
Abstract: The numerical solution of the time-dependent Schrodinger equation for vibrating hydrogen molecules in few-cycle laser pulses shows that high-harmonic generation is sensitive to the laser-induced vibrational motion. More intense harmonics are generated in heavier isotopes, the difference increasing with the harmonic frequency. Analytical theory reveals a dependence of the harmonics on the vibrational autocorrelation function. With the help of a genetic algorithm, the nuclear motion can be reconstructed from the harmonic spectra with sub-fs time resolution.
252 citations
Journal Article•
TL;DR: A unified method of solution that reduces the four coupled second-order differential equations to Helmholtz's and Laplace's equations is described and a qualitative discussion of the ir and Raman activity of the calculated modes is given together with a comparison with the few existing experimental data.
Abstract: A macroscopic continuum model coupling the mechanical vibrational amplitude and electrostatic potential is applied to obtain the optical vibrational modes in quantum-dot structures. A unified method of solution (valid for any type of nanostructure) that reduces the four coupled second-order differential equations to Helmholtz's and Laplace's equations is described. Analytical solutions for the vibrational amplitude and the Frohlich-type electron-phonon interaction are given for quantum dots with spherical geometry. The existence of surface modes and their relation to the matching boundary conditions are studied. A qualitative discussion of the ir and Raman activity of the calculated modes is given together with a comparison with the few existing experimental data.
167 citations
TL;DR: Near 300 K the authors find that vibrational energy transfer due to anharmonicity contributes substantially to thermal transport because of the localization of many thermally accessible normal modes.
Abstract: The rate of vibrational energy transfer and thermal transport coefficients are computed for two structurally distinct proteins, green fluorescent protein (GFP) and myoglobin. The computation of thermal transport coefficients exploits the scaling of the energy diffusion coefficient with the vibrational mode frequency of a protein. Near 300 K we find that vibrational energy transfer due to anharmonicity contributes substantially to thermal transport because of the localization of many thermally accessible normal modes. The thermal diffusivity for the β-barrel GFP is larger than that for myoglobin, particularly at low temperature due to a mean free path for vibrational energy propagation that is twice as large at low frequency. Vibrational energy transfer is also faster in GFP than in myoglobin for most vibrational modes.
98 citations
TL;DR: The computed transitions show in nearly all cases good agreement with experimental data and consistent improvement over the harmonic approximation and the agreement between the calculations and experiment also supports the validity of the MP2/TZP potential surfaces.
Abstract: Vibrational frequencies for fundamental, overtone, and combination excitations of sulfuric acid (H2SO4) and of sulfuric acid monohydrate cluster (H2SO4·H2O) are computed directly from ab initio MP2/TZP potential surface points using the correlation-corrected vibrational self-consistent field (CC-VSCF) method, which includes anharmonic effects. The results are compared with experiment. The computed transitions show in nearly all cases good agreement with experimental data and consistent improvement over the harmonic approximation. The CC-VSCF improvements over the harmonic approximation are largest for the overtone and combination excitations and for the OH stretching fundamental. The agreement between the calculations and experiment also supports the validity of the MP2/TZP potential surfaces. Anharmonic coupling between different vibrational modes is found to significantly affect the vibrational frequencies. Analysis of the mean magnitude of the anharmonic coupling interactions between different pairs of...
89 citations
TL;DR: In this article, a number of different methods for calculation of vibrational energies are reviewed and tested for the calculation of the fundamental vibrational frequencies for ethylene, including vibrational self-consistent field (VSCF), vibrational configuration interaction (VCI), and vibrational coupled cluster (VCC).
Abstract: A number of different methods for calculation of vibrational energies are reviewed and tested for calculation of the fundamental vibrational frequencies for ethylene The methods tested for the description of the vibrational states are vibrational self-consistent field (VSCF), vibrational configuration interaction (VCI), vibrational Moller-Plesset theory (VMP), and vibrational coupled cluster (VCC) The convergence of the different methods toward the full vibrational configuration interaction (FVCI) result is discussed for a modest-sized one-mode basis For larger one-mode basis sets results are presented for selected methods Different representations of the potential energy surface are compared including full and partial quartic force field as well as expansions using up to sixth derivatives of the potential energy surface Using MP2 electronic structure theory, the electronic structure basis set convergence is tested © 2005 Wiley Periodicals, Inc Int J Quantum Chem 104: 667- 680, 2005
63 citations
TL;DR: A formalism utilizing a recently developed second-quantization formulation of many-mode dynamics to define nonredundant parameterizations for different types of approximate vibrational wave functions for response functions for vibrationalWave functions is described.
Abstract: A formalism for deriving and implementing response functions for vibrational wave functions is described. The formalism utilizes a recently developed second-quantization formulation of many-mode dynamics to define nonredundant parameterizations for different types of approximate vibrational wave functions. The derived response functions cover the cases of an exact state, a vibrational self-consistent field state, and a vibrational configuration interaction state. Sample calculations are presented for the linear-response function and response excitation energies for a two-mode model system and for formaldehyde employing a quartic force field. The advantages and disadvantages of the response theoretical approach for describing excitation energies using different parameterizations are discussed.
59 citations
TL;DR: A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced and results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required.
Abstract: A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrodinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational Moller–Plesset perturbation theory). Our results indicate when the conventional Bishop–Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed.
54 citations
Book•
01 Jan 2005
TL;DR: In this paper, the authors present a generalization of the canonical distribution to generalized canonical distributions, and apply it to the case of Bose-and Fermi-statistics.
Abstract: 1. Principles of Statistical Mechanics. Microscopic states. Statistical treatment. The principle of equal weight and the microcanonical ensemble. The thermodynamic weight of a macroscopic state and entropy. Number of states and the density of states. Normal systems in statistical thermodynamics. Contact between two systems. Quasi-static adiabatic process. Equilibrium between two systems in contact. Fundamental laws of thermodynamics. The most probable state and fluctuations. Canonical distributions. Generalized canonical distributions. Partition functions and thermodynamic functions. Fermi-, Bose-, and Boltzmann- statistics. Generalized entropy. 2. Applications of the Canonical Distribution. General properties of the partition function Z( ). Asymptotic evaluations for large systems. Asymptotic evaluations and legendre transformations of thermodynamic functions. Grand partition function . Partition functions for generalized canonical distributions. Classical configurational partition functions. Density matrices. 3. Statistical Thermodynamics of Gases. Partition functions of ideal gases. Internal degrees of freedom and internal partition functions. Mixtures of ideal gases. Molecular interactions. Cluster expansion. 4. Applications of Fermi- and Bose- Statistics. Fundamental formulae of Fermi-statistics. Fermi distribution function. Electronic energy bands in crystals. Holes. Semiconductors. Bose-statistics, liquid Helium. 5. Strongly Interacting Systems. Molecular field approximation. Bragg-Williams approximation. Cooperative phenomena. Average potential in charged particle systems. Debye-Huckel theory. Distribution functions in a particle system. 6. Fluctuations and Kinetic Theories. Fluctuations. Collision frequency. Boltzmann transport equation. Index.
49 citations
TL;DR: This work presents the structural, magnetic, and vibrational properties of H2CN computed using a second-order perturbative approach in which equilibrium values and harmonic frequencies evaluated at the coupled-cluster level are combined with anharmonic and vibratory averaging contributions obtained by hybrid Hartree-Fock/Kohn-Sham methods.
Abstract: We present the structural, magnetic, and vibrational properties of H2CN computed using a second-order perturbative approach in which equilibrium values and harmonic frequencies evaluated at the coupled-cluster level are combined with anharmonic and vibrational averaging contributions obtained by hybrid Hartree–Fock/Kohn–Sham methods. Our computations lead to remarkably accurate results and suggest some revision of the experimental vibrational assignments.
48 citations
TL;DR: Very accurate calculations of the pure vibrational spectrum of the HeH(+) ion are reported, and the motion of both the electrons and the nuclei are treated on equal footing.
Abstract: Very accurate calculations of the pure vibrational spectrum of the HeH+ ion are reported. The method used does not assume the Born–Oppenheimer approximation, and the motion of both the electrons and the nuclei are treated on equal footing. In such an approach the vibrational motion cannot be decoupled from the motion of electrons, and thus the pure vibrational states are calculated as the states of the system with zero total angular momentum. The wave functions of the states are expanded in terms of explicitly correlated Gaussian basis functions multipled by even powers of the internuclear distance. The calculations yielded twelve bound states and corresponding eleven transition energies. Those are compared with the pure vibrational transition energies extracted from the experimental rovibrational spectrum.
33 citations
TL;DR: The modification of internal vibrational modes in a protein due to intraprotein anharmonicity and solvation effects is determined by performing molecular dynamics simulations of myoglobin using a Langevin model of the vibrational dynamics and comparing the Langevin results to a harmonic, normal mode models of the protein in vacuum.
Abstract: The modification of internal vibrational modes in a protein due to intraprotein anharmonicity and solvation effects is determined by performing molecular dynamics (MD) simulations of myoglobin, analyzing them using a Langevin model of the vibrational dynamics and comparing the Langevin results to a harmonic, normal mode model of the protein in vacuum. The diagonal and off-diagonal Langevin friction matrix elements, which model the roughness of the vibrational potential energy surfaces, are determined together with the vibrational potentials of mean force from the MD trajectories at 120 K and 300 K in vacuum and in solution. The frictional properties are found to be describable using simple phenomenological functions of the mode frequency, the accessible surface area, and the intraprotein interaction (the displacement vector overlap of any given mode with the other modes in the protein). The frictional damping of a vibrational mode in vacuum is found to be directly proportional to the intraprotein interaction of the mode, whereas in solution, the friction is proportional to the accessible surface area of the mode. In vacuum, the MD frequencies are lower than those of the normal modes, indicating intramolecular anharmonic broadening of the associated potential energy surfaces. Solvation has the opposite effect, increasing the large-amplitude vibrational frequencies relative to in vacuum and thus vibrationally confining the protein atoms. Frictional damping of the low-frequency modes is highly frequency dependent. In contrast to the damping effect of the solvent, the vibrational frequency increase due to solvation is relatively temperature independent, indicating that it is primarily a structural effect. The MD-derived vibrational dynamic structure factor and density of states are well reproduced by a model in which the Langevin friction and potential of mean force parameters are applied to the harmonic normal modes.
TL;DR: Quantum dynamical simulations of vibrational spectroscopy have been carried out for glycine dipeptide and the resulting wave packet dynamics is found to be strongly nonadiabatic due to the presence of a seam of the two potential energy surfaces.
Abstract: Quantum dynamical simulations of vibrational spectroscopy have been carried out for glycine dipeptide (CH3-CO-NH-CH2-CO-NH-CH3). Conformational structure and dynamics are modeled in terms of the two Ramachandran dihedral angles of the molecular backbone. Potential energy surfaces and harmonic frequencies are obtained from electronic structure calculations at the density functional theory (B3LYP/6-31+G(d)) level. The ordering of the energetically most stable isomers (C7 and C5) is reversed upon inclusion of the quantum mechanical zero point vibrational energy. Vibrational spectra of various isomers show distinct differences, mainly in the region of the amide modes, thereby relating conformational structures and vibrational spectra. Conformational dynamics is modeled by propagation of quantum mechanical wave packets. Assuming a directed energy transfer to the torsional degrees of freedom, transitions between the C7 and C5 minimum energy structures occur on a sub-picosecond timescale (700 ... 800 fs). Vibrationally non-adiabatic effects are investigated for the case of the coupled, fundamentally excited amide I states. Using a two state-two mode model, the resulting wave packet dynamics is found to be strongly non-adiabatic due to the presence of a seam of the two potential energy surfaces. Initially prepared adiabatic vibrational states decay upon conformational change on a timescale of 200 ... 500 fs with population transfer of more than 50 % between the coupled amide I states. Also the vibrational energy transport between localized (excitonic) amide I vibrational states is strongly influenced by torsional dynamics of the molecular backbone where both enhanced and reduced decay rates are found. All these observations should allow the detection of conformational changes by means of time-dependent vibrational spectroscopy.
TL;DR: In this article, a method for computing the effects of large-amplitude torsion on thermochemical properties and reaction rates was presented, which is more suitable for routine computations of partition functions of large polyatomics.
Abstract: Large-amplitude motions, particularly internal rotations, significantly affect thermochemical properties and reaction rates. The conventional method for computing partition functions, developed by Pitzer more than 50 years ago, is based on the assumption of large-amplitude motion being completely separable from other vibrational degrees of freedom. However, no convenient method is available to assess the accuracy of Pitzer's approximation. A precise variational method, suitable for computing the coupling between large- and small-amplitude motions in small molecules, has previously been developed by Tew, Carter, Handy, and co-workers and applied to a few cases. Here, a method is presented for computing the effects of this coupling that is more suitable for routine computations of partition functions of large polyatomics. The couplings of all the vibrational modes to a large-amplitude torsion are analysed in the molecule ortho-chlorotoluene. An approach to defining the internal rotational angle along the to...
Patent•
29 Dec 2005
TL;DR: In this paper, a system and method for monitoring a gap between a vibrational body and a reference is achieved by monitoring the resonant frequency of the vibration of the body, and a quantity standing in known relation to an approximate change in the length of the gap is determined, based upon the resonance frequency.
Abstract: A system and method for monitoring a gap between a vibrational body and a reference is achieved by monitoring the resonant frequency of the vibrational body A portion of the vibrational body is fixed a given distance from the reference by a rigid mounting system A resonant frequency of the vibrational body is received Then, a quantity standing in known relation to an approximate change in the length of the gap is determined, based upon the resonant frequency
TL;DR: In this article, the vibrational term values up to 10000 cm−1 were merged using an effective Hamiltonian with a standard deviation of 022cm−1 and the energy pattern was found to be very similar to the one in C212H2 with additional anharmonic resonances arising from the lack of u∕g character in the asymmetric isotopolog.
Abstract: In C12C13H2 129 vibrational term values up to 10000cm−1 are merged, about 60% of which are newly reported They are fitted using an effective Hamiltonian with a standard deviation of 022cm−1 The vibrational assignments and vibrational constants are listed and discussed The energy pattern is found to be very similar to the one in C212H2 with additional anharmonic resonances arising from the lack of u∕g character in the asymmetric isotopolog
TL;DR: In this article, the authors used principal mode analysis (PMA) to analyze the vibrational energy transfer from the O-H stretching modes in liquid water by using QM/MM simulations.
TL;DR: In this article, a mixed quantum-classical molecular dynamics method has been applied to vibrational relaxation of CN − in water, where coulombic force is predominant in the interaction.
TL;DR: In this article, a relation between inelastic electron tunneling (IET) current and vibrational generation rate, a key source of vibrational heating, was studied on the basis of the adsorbate-induced resonance model for IET using the coupled Dyson and kinetic equations of phonon number for the causal and statistical Keldysh-Green functions.
TL;DR: In this paper, the Schrodinger equation was used to calculate the vibrational states of the first 1 Σ u + state of the F2 molecule and the Rydberg state was found to possess a single vibrational level.
TL;DR: In this paper, a potential energy surface (PES) is developed for C60 to describe vibrational motions valid in the anharmonic limit, which is based on a previously existing one that is fit to the harmonic fundamentals and is then modified to generate anharmonicity of all orders and in all terms, but without additional fitted parameters.
Abstract: A potential energy surface (PES) is developed for C60 designed to describe vibrational motions valid in the anharmonic limit. The PES is based on a previously existing one that is fit to the harmonic fundamentals and is then modified to generate anharmonicity of all orders and in all terms, but without additional fitted parameters. The resulting Cartesian vibrational motions are decomposed into normal modes, and the anharmonic expansion coefficients are calculated including 2-mode couplings and up to 4th order. The resulting PES is used in a vibrational self-consistent field (VSCF) algorithm to calculate the anharmonically corrected fundamental frequencies. The parameters are then fit to fundamental infrared and Raman frequencies. While it is not possible to assign combination and overtone transitions with sufficient experimental accuracy, conclusions about the effects of anharmonic vibrational coupling in C60 are described.
TL;DR: In this paper, the static path approximation plus the random-phase approximation (RPA) treatment can be written as a contour integral form without solving the RPA equations for a separable interaction.
Abstract: The partition function by means of the static path approximation (SPA) plus the random-phase approximation (RPA) treatment can be written as a contour integral form without solving the RPA equations for a separable interaction. This method is an efficient way to evaluate numerically the partition function for realistic calculations. As an illustration, we adopt the pairing model at finite temperature.
TL;DR: An approximate model is tested in order to obtain the vibrational distributions of the Cl2 fragment produced after He2-Cl2(B) predissociation, when the dynamics is simulated by a full-dimensional wave-packet method.
Abstract: An approximate model is tested in order to obtain the vibrational distributions of the Cl2 fragment produced after He2–Cl2(B) predissociation, when the dynamics is simulated by a full-dimensional wave-packet method. The model is intended to overcome the limitations imposed to a rigorous calculation of the vibrational distributions by the use of a finite grid size and absorbing boundary conditions. The good agreement found between the present results and the available experimental data indicates that the model is able to provide realistic estimates for the product vibrational distributions.
Patent•
29 Dec 2005
TL;DR: In this article, a vibrational body is fixed a given distance from the reference by a rigid mounting system, and a quantity standing in known relation to an approximate change in the length of the gap is determined, based upon the resonant frequency.
Abstract: A system and method for monitoring a gap between a vibrational body and a reference is achieved by monitoring the resonant frequency of the vibrational body. A portion of the vibrational body is fixed a given distance from the reference by a rigid mounting system. A resonant frequency of the vibrational body is received. Then, a quantity standing in known relation to an approximate change in the length of the gap is determined, based upon the resonant frequency.
TL;DR: In this paper, both the pure vibrational contribution and the zero-point vibrational averaging contribution have been determined by adopting the perturbation treatment of Bishop and Kirtman at the Hartree-Fock level.
Abstract: Static and dynamic vibrational contributions to the linear polarizability and the first and second nonlinear hyperpolarizabilities of methanol, ethanol and propanol have been calculated Both the pure vibrational contribution and the zero-point vibrational averaging contribution have been determined by adopting the perturbation treatment of Bishop and Kirtman at the Hartree–Fock level The pure vibrational contribution is quite important at the static limit, while in the optical region it varies for different nonlinear optical processes The zero-point vibrational averaging contribution is a quite large correction to the electronic nonlinear optical (NLO) properties, especially for the second hyperpolarizability at finite fundamental frequencies Vibrational analysis shows that the swinging modes at around 300 cm−1 and the C–H stretching modes at around 3160 cm−1 often give large contributions
TL;DR: In this article, the authors compare calculations of the classical third-order nonlinear response function for two models of resonantly coupled anharmonic oscillators and provide connections between quantum and classical pictures of nonlinear spectroscopic processes.
Abstract: The signal in a coherent, nonlinear vibrational spectroscopy measurement such as the vibrational echo, the analog in vibrational spectroscopy of the spin echo of magnetic resonance, may be computed from a third-order nonlinear response function. The challenges of the quantum mechanical calculation of this response function for many coupled anharmonic degrees of freedom motivate the analysis of the response function in classical mechanics. We compare calculations of the classical third-order nonlinear response function for two models of resonantly coupled anharmonic oscillators. Our analysis elucidates the effects on nonlinear molecular vibrational spectroscopy of resonant coupling among molecular vibrations and of anharmonicity, and provides connections between quantum and classical pictures of nonlinear spectroscopic processes.
TL;DR: In this paper, it was shown that for a fixed number of particles in the equilibrium system and a fixed volume V and temperature T, the two-particle partition function fully describes the Gibbs partition as well as the Nparticle system in question.
Abstract: We show that in the equilibrium classical canonical ensemble of particles with pair interaction, the full Gibbs partition function can be uniquely expressed in terms of the two-particle partition function. This implies that for a fixed number N of particles in the equilibrium system and a fixed volume V and temperature T, the two-particle partition function fully describes the Gibbs partition as well as the N-particle system in question. The Gibbs partition can be represented as a power series in the two-particle partition function. As an example, we give the linear term of this expansion.
21 Jun 2005
TL;DR: In this article, a two-phase equilibrium model was developed to explain the discontinuous surface charge decay versus atmospheric pressure of insulators that had been charged triboelectrically.
Abstract: A two-phase equilibrium model was developed to explain the discontinuous surface charge decay versus atmospheric pressure of insulators that had been charged triboelectrically. The two-phase model is an electrostatic form of the Langmuir Isotherm for ions adsorbed on a surface in equilibrium with ions in the gas phase. In this paper, the model was extended to account for vibrational states of the adsorbed surface ions via the vibrational partition function. An analysis is performed that rules out Paschen discharge as the cause of the discharge observed. Also, a numerical simulation is performed using NWChem to calculate the adsorption energies of ions on insulator surfaces for comparison to curve fit adsorption energies developed from the model and experimental data.
TL;DR: In this article, the fullpotential linear muffin-tin orbital (FPLMTO) total energy method combining with a mean-field model of the vibrational partition function was used to evaluate the state of face-centred-cubic (fcc) copper crystals at pressures up to 500 GPa and relative volume to 0.55.
Abstract: The equation of state of face-centred-cubic (fcc) copper crystals at pressures up to 500 GPa and relative volume to 0.55 have been evaluated by using the full-potential linear muffin-tin orbital (FPLMTO) total-energy method combining with a mean-field model of the vibrational partition function. The mean-field is constructed from the sum of all the pair potentials between the reference atom and the others of the system. The calculated properties are in good agreement with the available shock-wave experimental measurements.
TL;DR: In this paper, the authors derived the master equation of a relevant electronic and vibrational system for a special diabatic basis corresponding to vertical processes, and studied the time evolution of excited state population.
Abstract: Master equation of a relevant electronic and vibrational system is derived for a special diabatic basis corresponding to vertical processes. It is shown that bath modes contribute dynamically to the inter-state coupling only at short times. For long times the bath-induced inter-state coupling is static and increases with the contribution of bath modes to the Stokes shift and to the Herzberg-Teller correction of the excited state. Simultaneously, the time evolution of excited state population is studied numerically for the system consisting of two electronic levels interacting with two vibrational modes, coupled to a heat bath. A mutual coupling of the vibrational modes in the excited state is taken into account (Duschinsky effect). Excited state population relaxes faster if interacting vibrational mode dissipates its energy via vibrational mode of a smaller eigenfrequency. Fast component of excited state depopulation cannot be achieved via coherent mode-mode coupling, if the second mode is not directly coupled to the electronic inter-state transition.