Harmonic Oscillator Approximation Research Articles

Chemical and Electronic Branching Ratios in the Chemiluminescent Reactions of Hyperthermal Ca(3P) Atoms with CF2Cl2 and CF2CCl2

Chemiluminescent reactions of hyperthermal Ca( 3 P) with CF 2 Cl 2 and CF 2 =CCl 2 were studied in a beam-gas arrangement under single collision conditions. Emissions associated with the A( 2 Π Ω ) → X( 2 Σ + ) and the B( 2 Σ + ) → X( 2 Σ + ) transitions from CaCI and CaF were observed for both reactions. The chemical and electronic branching ratios were determined for these reactions, and different results were obtained for each one. The different behavior was rationalized by a simple MO pictures. For the case of the reaction with CF 2 Cl 2 it was assumed that an electron from Ca( 3 P) is transferred to a σ*(C-Cl) orbital in CF 2 Cl 2 which, at higher translational energies can also enter into a σ*(C-F) orbital of the same molecule. In both cases the molecular anion produced is short-lived and will undergo fast decay to Cl - or F - to yield CaCl and CaF. For the reaction with CF 2 =CCl 2 the electron from Ca( 3 P) is transferred to a π* orbital of the reagent molecule that generates a relatively stable molecular anion with 2 Π symmetry. This anion subsequently cross over several repulsive 2 Σ surfaces associated with σ* orbitals of the C-Cl and the C-F bonds, to dissociate into Cl - or F - to produce CaCI and CaF. The electronic branching ratios are in good agreement with statistical distribution based on information theory approach, assuming the rigid rotor harmonic oscillator (RROH) approximation for the reaction with CF 2 Cl 2 and the formation of a collision complex for the reaction with CF 2 =CCl 2 .

Computational method for calculating multidimensional Franck–Condon factors: Based on Sharp–Rosenstock’s method

Normal mode coordinates of vibrational states associated with one electronic state are generally different from those of vibrational states associated with other electronic states in polyatomic molecules (normal coordinate mixing). This has prevented the multidimensional Franck–Condon integrals from being widely used in spite of their importance. We introduce a simple, noncumbersome numerical computer method for calculating those integrals despite including a mixing of the normal coordinates in the harmonic oscillator approximation on the basis of the expressions by Sharp and Rosenstock. We also introduce more simple expressions of Sharp–Rosenstock’s formulas.

Torsional path integral Monte Carlo method for calculating the absolute quantum free energy of large molecules

A new technique for evaluating the absolute free energy of large molecules is presented. Quantum-mechanical contributions to the intramolecular torsions are included via the torsional path integral Monte Carlo (TPIMC) technique. Importance sampling schemes based on uncoupled free rotors and harmonic oscillators facilitate the use of the TPIMC technique for the direct evaluation of quantum partition functions. Absolute free energies are calculated for the molecules ethane, n-butane, n-octane, and enkephalin, and quantum contributions are found to be significant. Comparison of the TPIMC technique with the harmonic oscillator approximation and a variational technique is performed for the ethane molecule. For all molecules, the quantum contributions to free energy are found to be significant but slightly smaller than the quantum contributions to internal energy.

Theoretical study of the conversion of sulfonyl precursors into chains of poly(p-phenylene vinylene).

The elimination and side reactions involved in the thermal conversion of sulfonyl precursor chains into poly(p-phenylene vinylene) (PPV) have been studied in detail, using Density Functional theory, along with the MPW1K functional. The performance of the MPW1K functional for describing radical dissociation and internal conversion reactions of sulfonyl precursors has been assessed against the results of benchmark CCSD(T) calculations. Enthalpies as well as entropies are calculated at different temperatures at the level of the rigid rotor-harmonic oscillator approximation. Entropy effects on internal elimination reactions are very limited. In sharp contrast, at the temperatures under which the conversion is usually performed (550 K), entropy contributions to the activation energies are found to be very significant and to strongly favor direct radical dissociations of the precursors. Further radical side reactions following an E(i) conversion through an alkyl substituent may also significantly contribute to the formation of sp(3) defects and/or cross-linked structures in the polymer-an advantageous feature for the making of materials with improved photoluminescence efficiencies.

Ultraviolet and visible dispersed spectroscopy for the photofragments produced from H2O in the extreme ultraviolet

The photofragmentation of H2O has been studied by fluorescence spectroscopy at photon energies between Ehν=16.9–54.5 eV. The primary photon beam was monochromatized undulator radiation supplied from the UVSOR synchrotron radiation facility. The fluorescence in the wavelength range of 280–720 nm was dispersed with an imaging spectrograph. The dispersed spectra exhibit the hydrogen Balmer lines of H*[n2LJ′′→2 2LJ″″(n=3–9)] and the emission band systems of H2O+[Ã 2A1(0,v2′,0)→X̃ 2B1(0,0,0)], OH+(Ã 3ΠΩ,v′→X̃ 3Σ−,v″), and OH(Ã 2Σ+,v′→X̃ 2ΠΩ,v″). The fluorescence cross sections for these transitions have characteristic dependences on Ehν and vibrational quantum numbers. The cross section summed over the Balmer lines takes a minimum value at Ehν=21.7 eV and is very small even at 24.9 eV beyond which it steadily increases with increasing Ehν. This behavior is understood as that the superexcited states correlating with H*(n⩾3)+OH(Ã 2Σ+) are too repulsive to be accessible below Ehν∼30 eV by the Franck–Condon transitions from H2O(X̃ 1A1) and as that the Balmer emission below 30 eV is mainly due to the H*(n⩾3)+H(n=1)+O(3Pg) channel. The appearance energy of the OH+(Ã 3ΠΩ,v′→X̃ 3Σ−,v″) transitions is found to be ca. 25.5±0.3 eV. This value is much higher than the dissociation limit of 21.5 eV for the OH+(Ã 3ΠΩ)+H(n=1) channel, but is consistent with the vertical ionization energy to H2O+[(1b1)−2(4a1)1 2A1] that has been assumed to correlate with the above dissociation limit in the literature. The vibrational distribution of OH+(Ã 3ΠΩ) evaluated from the OH+(Ã 3ΠΩ,v′→X̃ 3Σ−,v″) band intensities is similar to the prior distribution in the rigid-rotor harmonic-oscillator approximation.

Analytical time-dependent Hartree–Fock schemes for the evaluation of the hyper-Raman intensities

Two analytical procedures based on the time-dependent Hartree–Fock (TDHF) scheme are elaborated to evaluate the first derivatives of the dynamic first hyperpolarizability with respect to atomic Cartesian coordinates. In the first scheme, the mixed third-order TDHF equations are solved iteratively to obtain the third derivatives of the linear combination of atomic orbitals coefficients twice with respect to external dynamic electric fields and once with respect to atomic Cartesian coordinates. The second takes advantage of the 2n+1 rule and interchange relations to express the first derivatives of the dynamic first hyperpolarizability with respect to atomic Cartesian coordinates in terms of lower-order derivatives. Both procedures have been implemented in the GAMESS quantum chemistry package. Applications focus on the characterization of the frequency dispersion of the first derivatives of the first hyperpolarizability with respect to vibrational normal coordinates of H2O, NH3, and CH4 as well as on the determination of nonresonant hyper-Raman intensities within the double harmonic oscillator approximation.

Torsional path integral Monte Carlo method for the quantum simulation of large molecules

A molecular application is introduced for calculating quantum statistical mechanical expectation values of large molecules at nonzero temperatures. The Torsional Path Integral Monte Carlo (TPIMC) technique applies an uncoupled winding number formalism to the torsional degrees of freedom in molecular systems. The internal energy of the molecules ethane, n-butane, n-octane, and enkephalin are calculated at standard temperature using the TPIMC technique and compared to the expectation values obtained using the harmonic oscillator approximation and a variational technique. All studied molecules exhibited significant quantum mechanical contributions to their internal energy expectation values according to the TPIMC technique. The harmonic oscillator approximation approach to calculating the internal energy performs well for the molecules presented in this study but is limited by its neglect of both anharmonicity effects and the potential coupling of intramolecular torsions.

Application of artificial neural networks and genetic algorithms to modeling molecular electronic spectra in solution

A novel approach is presented for finding the vibrational frequencies, Franck–Condon factors, and vibronic linewidths that best reproduce typical, poorly resolved electronic absorption (or fluorescence) spectra of molecules in condensed phases. While calculation of the theoretical spectrum from the molecular parameters is straightforward within the harmonic oscillator approximation for the vibrations, “inversion” of an experimental spectrum to deduce these parameters is not. Standard nonlinear least-squares fitting methods such as Levenberg–Marquardt are highly susceptible to becoming trapped in local minima in the error function unless very good initial guesses for the molecular parameters are made. Here we employ a genetic algorithm to force a broad search through parameter space and couple it with the Levenberg–Marquardt method to speed convergence to each local minimum. In addition, a neural network trained on a large set of synthetic spectra is used to provide an initial guess for the fitting parameters and to narrow the range searched by the genetic algorithm. The combined algorithm provides excellent fits to a variety of single-mode absorption spectra with experimentally negligible errors in the parameters. It converges more rapidly than the genetic algorithm alone and more reliably than the Levenberg–Marquardt method alone, and is robust in the presence of spectral noise. Extensions to multimode systems, and/or to include other spectroscopic data such as resonance Raman intensities, are straightforward.

Thermochemical Properties of Si2F6 and SiF4 in Gas and Condensed Phases

The available data for determining the thermochemical parameters for Si2F6 and SiF4 has been assembled. With this information, the thermochemical functions for Si2F6 and SiF4 have been calculated as ideal gases in the harmonic oscillator approximation. These results are presented in the format of the NIST–JANAF Thermochemical Tables, as well as in the format of the CHEMKIN Thermochemical Database. Using the vapor pressure data, the thermochemical parameters for Si2F6 in the solid phase and SiF4 in both the solid and liquid phases have been calculated. These results are compared with available experimental and calculated data. The earlier results are in good agreement with our results. However, the Si2F6 results were not previously available in the JANAF format, and the results for both species are on a much firmer footing with the new experimental data we used. The anharmonicity constants measured earlier for SiF4 permitted a determination of the effect of anharmonicity on the thermochemical properties for this species. For this species at least, the harmonic oscillator approximation is very good. Differences between the harmonic and anharmonic calculations were only significant at temperatures above 1000 K.

The Near-Infrared 3Φ → (1)3Δ Transition of LaF

Rotational analyses of 32 subbands of the near-infrared 3Φ → (1)3Δ system of LaF have been carried out, involving the levels v = 0–7 of the two states. The three subsystems were first treated as separate singlet systems, directly at equilibrium. Perturbations were revealed in the lower state, ascribed to spin–uncoupling interactions between (1)3Δ3(v) and (1)3Δ2(v + 1) levels. A 21 × 21 matrix representation at equilibrium of the complex of interacting levels (v = 0–6) was then constructed, each diagonal v-block corresponding to a triplet model of the rovibrational 3Δ Hamiltonian. The observed perturbations were completely reduced in the harmonic oscillator approximation with an experimental value of the interaction parameter BΔ0,1 = 0.01322(2) cm−1. The wavenumbers of some 4500 lines of the system were fitted with an rms error of about 0.005 cm−1. (Line lists are available in electronic form via http://www-obs.univ-lyon1.fr/~ABernard/index.html.)

Analytical Models for Electron-Vibration Coupling in Nitrogen Plasma Flows

A model for the electron-vibration energy exchange in nitrogen based on a Landau-Teller-type rate equation is presented. Analytical expressions of relaxation times are derived for cutoff harmonic oscillator and Morse oscillator approximations, assuming that the relaxation proceeds by way of a continuous series of Boltzmann distributions over the vibrational states. Comparisons with the direct numerical integration of the master equation have shown that the use of a a two-temperature relaxation time allows accurate modeling of the nitrogen vibrational energy relaxation rate for various conditions encountered in high-enthalpy flows with electron and vibrational temperatures up to 40,000 K.

Transverse dynamics of hard partons in nuclear media and the QCD dipole

We derive the non-abelian generalization of the Furry approximation which describes the transverse dynamical evolution of a hard projectile parton inside a spatially extended colour target field. This provides a unified starting point for the target rest frame description of the nuclear dependence of a large class of observables. For the case of the virtual gamma -> q-qbar photoabsorption cross section, we investigate then in detail under which conditions the nuclear dependence encoded in the Furry wavefunctions can be parametrized by a q-qbar QCD dipole cross section. The important condition is colour triviality, i.e., the property that for arbitrary N-fold rescattering contributions the only non-vanishing colour trace is N_c C_F^N. We give proofs for the colour triviality of the inelastic, diffractive and total photoabsorption cross section measured inclusively or with one jet resolved in the final state. Also, we list examples for which colour interference effects remain. Colour triviality allows us to write the gamma -> q qbar contribution to the DIS nuclear structure function F_2 for small Bjorken x in terms of a path integral which describes the transverse size evolution of the q-qbar pair in the nuclear colour field. This expression reduces in an opacity expansion to the N=1 result of Nikolaev and Zakharov, and in the eikonal approximation to the Glauber-type rescattering formulas first derived by Mueller. In the harmonic oscillator approximation of the path integral, we quantify deviations from the eikonal limit. Their onset is characterized by the scales L/l_f and E_t L which relate the longitudinal extension L of the nuclear target to the coherence length l_f and the total transverse energy E_t accumulated by the q-qbar pair.

Fourier transform Raman spectrum and ab initio and density functional computations of the vibrational spectrum, molecular geometry, atomic charges and some molecular properties of the anticarcinogenic drug 5‐fluorouracil

FT Raman study of 5-fluorouracil, an anticarcinogenic drug, was carried out. Ab initio and density functional computations of the vibrational spectrum, the molecular geometry, the atomic charges, the total energy, the zero point energy, the rotational constants, the room temperature entropy, (translational, rotational and vibrational) and dipole moment were carried out. The observed Raman wavenumbers were analysed in light of the computed vibrational spectrum. Thermodynamic functions, namely, the enthalpy, the entropy, the heat capacity and the free energy were also computed in the temperature range 200–1000 K using the rigid-rotor harmonic oscillator approximation. For this purpose the fundamental wavenumbers were taken from the present FT-Raman spectrum and the structural parameters were taken from the present theoretically computed geometry. Copyright © 2000 John Wiley & Sons, Ltd.

Large vibrational nonlinear optical properties ofC60:A combined Hartree-Fock/density-functional approach

Vibrational contributions to the nonlinear optical properties of an isolated buckminsterfullerene molecule have been computed within the double harmonic oscillator and infinite optical frequency approximations. In our treatment, normal coordinates from density-functional theory are combined with Hartree-Fock electrical properties. Values obtained for the ratio of vibrational to static electronic contributions vary from 0.01 for second-harmonic generation to 0.64 for the electro-optic Kerr effect to 1.26 for degenerate four-wave mixing.

Absolute band intensities in the ν19/ ν23 (530 cm −1) and ν7 (777 cm −1) bands of acetone ((CH 3) 2CO) from 232 to 295 K

Absolute band intensities of acetone ((CH 3) 2CO) in the ν 19/ ν 23 and ν 7 band systems near 530 and 777 cm −1, respectively, were measured at temperatures of 232, 262 and 295 K, using a Fourier transform infrared (FTIR) spectrometer. No evident temperature dependence for the band intensities was observed. The dipole moments and the fundamental band intensities were derived in the harmonic oscillator approximation. The results are useful for the spectroscopic retrieval of acetone concentrations in the upper atmosphere.

Dissociative grazing scattering of [formula omitted] on metal surfaces: Analysis of the high-energy parts of the spectra of the scattered molecule constituents

In the present work we calculated the high energy tails of the energy distributions for hydrogen molecule constituents scattered from metal surfaces at grazing incidence of H2+, supposing the dissociative capture process to contribute mainly to H2+. No effect of the straggling on the high energy tails formation was considered. The harmonic oscillator approximation was employed for the calculation of the centre-of-mass distributions of the kinetic energy released in the dissociation process, “vibrational temperature” being the only free parameter of the theory. The comparison of the calculations with the experimental high-energy tails of the H spectra from the scattering of H2+ off Pt and Ag shows good agreement. The calculations yield information on the vibrational excitation of the molecules during the scattering process.

Interactions of Molecular Hydrogen with Alkali Metal Halides in Argon Matrices: A Computational Model

MP2 calculations have been performed in order to understand the behavior of molecular hydrogen in gas matrices containing alkali metal halide ion pairs. Calculations that model interactions between H2 and LiCl, NaCl, KCl, KF, and NaF were augmented by the addition of argon atoms. Interactions between CuCl and dihydrogen were also modeled for comparison purposes. The conformational space of H2 with NaCl was explored extensively with and without Ar atoms. The frequency of the H−H stretch is sensitive to the orientation and position of H2 relative to NaCl, with frequency shifts spanning nearly 60 cm-1. Zero-point corrections were scaled differently depending on the nature of the vibrational modes. For modes that are characterized by deep potentials, a scaling factor of 0.93 was used. For the low-energy vibrations that result from the associations of two weakly bound particles, a scaling factor of only 0.26 was used to compensate for the inappropriateness of a harmonic oscillator approximation. KF binds H2 mo...

Theoretical determination of the vibrational and electronic (hyper)polarizabilities of C4H4X (X=O, S, Se, Te) heterocycles

Electronic, pure vibrational and dispersion contributions to the linear polarizability, α, and first hyperpolarizability, β, of the group 16 chalcogenides C4H4X (X=O, S, Se, Te) have been studied by ab initio calculations using the 6-31G*, the Sadlej POL, correlation consistent Dunning and aug-CEP-31G basis sets. Electron correlation was introduced through the MP2 theory. Vibrational (hyper)polarizabilities, evaluated within the double harmonic oscillator approximation, were analyzed in terms of single normal mode contributions. They were found to be a fraction of the electronic counterpart. βv does not show a clear dependence on the heavy atom, contrary to βe, which steadily increases along the series. The βv/βe ratio is very dependent on the basis set, decreasing and also changing sign in the presence of diffuse functions. Frequency-dependent electronic (hyper)polarizabilities were evaluated in the 0.02–0.16 a.u. frequency range. In the low-frequency range they can be fitted into a power series expansion in ω. In accord with the theory, the second-order coefficients of the β expansion are the same for both the SHG and EOPE non-linear optical processes, while in the α expansion they can be related to the lowest electronic excitation energy.

Fourier transform Raman spectrum andab initio and density functional computations of the vibrational spectrum, molecular geometry, atomic charges and some molecular properties of the anticarcinogenic drug 5-fluorouracil

FT Raman study of 5-fluorouracil, an anticarcinogenic drug, was carried out. Ab initio and density functional computations of the vibrational spectrum, the molecular geometry, the atomic charges, the total energy, the zero point energy, the rotational constants, the room temperature entropy, (translational, rotational and vibrational) and dipole moment were carried out. The observed Raman wavenumbers were analysed in light of the computed vibrational spectrum. Thermodynamic functions, namely, the enthalpy, the entropy, the heat capacity and the free energy were also computed in the temperature range 200–1000 K using the rigid-rotor harmonic oscillator approximation. For this purpose the fundamental wavenumbers were taken from the present FT-Raman spectrum and the structural parameters were taken from the present theoretically computed geometry. Copyright © 2000 John Wiley & Sons, Ltd.

Monte Carlo Simulation Approach to Internal Partition Functions for van der Waals Molecules

The calculation of the internal partition function Qint, and the density of states N, is an important topic which has a vast range of applications. In fact, its accurate determination for a nonseparable potential is a long standing problem which goes back to the foundations of statistical mechanics. The density of states is required for the evaluation of reaction rate constants in transition state theory (conventional or variational), while the calculation of Qint is important, e.g., to study the equilibrium properties of bound systems. In turn, its temperature dependence is necessary to evaluate various thermodynamic quantities, such as the Gibbs enthalpy and the Helmholtz function, which are used as standard input for many models in astrophysics; see ref 1. For example, the solution of the equation of state for cool stellar atmospheres requires very accurate values of Qint. 2,3 However, the calculation of Qint becomes particularly difficult for systems involving weakly bound states such as van der Waals (vdW) molecules. Indeed, the application of approximate methods like the harmonic oscillator and rigid rotor (HO+RR) approximation (which has been widely used to build up the JANAF 4 tables of thermodynamic functions) is expected to give poor results for such floppy (anharmonic) molecules. Recently, we have been interested in the study of thermolecular association reactions of the general type