Calculation of converged rovibrational energies and partition function for methane using vibrational-rotational configuration interaction

The rovibration partition function of CH4 was calculated in the temperature range of 100-1000 K using well-converged energy levels that were calculated by vibrational-rotational configuration interaction using the Watson Hamiltonian for total angular momenta J = 0-50 and the MULTIMODE computer program. The configuration state functions are products of ground-state occupied and virtual modals obtained using the vibrational self-consistent field method. The Gilbert and Jordan potential energy surface was used for the calculations. The resulting partition function was used to test the harmonic oscillator approximation and the separable-rotation approximation. The harmonic oscillator, rigid-rotator approximation is in error by a factor of 2.3 at 300 K, but we also propose a separable-rotation approximation that is accurate within 2% from 100 to 1000 K.     

Theoretical study of O2-H2O: potential energy surface, molecular vibrations, and equilibrium constant at atmospheric temperatures

The intermolecular potential energy surface of O(2)-H(2)O was investigated at ab initio MP2 and MRSDCI levels using the aug-cc-pVTZ basis set. The vibrational levels were evaluated by numerically solving the Schr?dinger equations for the nuclear motions with the ab initio potential functions using one- to three-dimensional finite-element methods. On the basis of the calculated partition functions, the equilibrium constant of the complex, K(p), was studied. The K(p) values at atmospheric temperatures of 200-300 K were found to be 1-2 orders of magnitude less than previous estimates from the harmonic oscillator approximation.     

乙硼烷的简正振动频率和光谱熵

本文用群论方法讨论了Coriolis微扰,认为950cm~(-1)为ν_9是合理的.按非刚性转子-谐振子模型,采用直接加和法计算转动、振动配分函数.应用Cromemco微处理机计算了100～2500K范围内~(10)B_2H_6和~(11)B_2H_6的光谱熵.     

Interpreting nonlinear vibrational spectroscopy with the classical mechanical analogs of double-sided Feynman diagrams

Observables in coherent, multiple-pulse infrared spectroscopy may be computed from a vibrational nonlinear response function. This response function is conventionally calculated quantum-mechanically, but the challenges in applying quantum mechanics to large, anharmonic systems motivate the examination of classical mechanical vibrational nonlinear response functions. We present an approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent, which establishes a clear connection between classical and quantum mechanical treatments. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom, and suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics, which are widely applied to nonlinear spectroscopy. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function. Calculations of the third-order response function for an anharmonic oscillator coupled to a harmonic solvent are compared to numerically correct classical mechanical results.     

Semiclassical initial value series representation in the continuum limit: application to vibrational relaxation

A recently formulated continuum limit semiclassical initial value series representation (SCIVR) of the quantum dynamics of dissipative systems is applied to the study of vibrational relaxation of model harmonic and anharmonic oscillator systems. As is well known, the classical dynamics of dissipative systems may be described in terms of a generalized Langevin equation. The continuum limit SCIVR uses the Langevin trajectories as input, albeit with a quantum noise rather than a classical noise. Combining this development with the forward-backward form of the prefactor-free propagator leads to a tractable scheme for computing quantum thermal correlation functions. Here we present the first implementation of this continuum limit SCIVR series method to study two model problems of vibrational relaxation. Simulations of the dissipative harmonic oscillator system over a wide range of parameters demonstrate that at most only the first two terms in the SCIVR series are needed for convergence of the correlation function. The methodology is then applied to the vibrational relaxation of a dissipative Morse oscillator. Here, too, the SCIVR series converges rapidly as the first two terms are sufficient to provide the quantum mechanical relaxation with an estimated accuracy on the order of a few percent. The results in this case are compared with computations obtained using the classical Wigner approximation for the relaxation dynamics.     

Ab initio study of free-radical polymerizations: cost-effective methods to determine the reaction rates.

The addition of carbon-centered radicals to ethene, which are important in free-radical polymerization processes, are studied from a theoretical point of view. Experimental data for the rate constants are only available for the addition of methyl, ethyl, propyl and butyl radicals. The latter reactions are taken as model systems to derive a cost-effective method for the addition of alkyl radicals to ethene. The proposed model must be accurate and computationally feasible for additions in which larger radicals are involved. Accuracy is validated by direct comparison of theoretical and experimental rate constants in the temperature range from 300 to 600 K. A variety of electronic-structure methods were tested ranging from Hartree-Fock and post-Hartree-Fock methods to pure and hybrid density functional theory methods. Molecular partition functions were refined by treating large amplitude vibrations beyond the harmonic oscillator approximation.     

Characteristics of atomic vibrational motion in a one-component defective crystal

Vibrations of atoms in a defective argon crystal are considered. Frequencies are calculated in the harmonic approximation and Mie and Einstein approximations. The vibrations are calculated for a set of local clusters differing in the position of a vacancy at different distances from a selected atom. Probabilities for these clusters are calculated within a quasichemical approximation of the lattice gas model. It is shown that when combined contributions from lateral interactions and vibrational motions are allowed for in the free crystal energy, there is an increase in the lattice constant upon a rise in temperature in all approximations. It is found that the frequencies calculated using the Mie model become closer to the frequency distribution in the harmonic approximation as the degree of crystal defectiveness increases.     

Experimental and theoretical determination of rate constants for vibrational relaxation of CO2 and CH3F by He

Rate constants have been measured for the vibrational relaxation of CO₂ and CH₃F in the temperature range 300-150 K by the collision partners ⁴He and ³He. These results are compared with those calculated with a vibrational close-coupling, rotational infinite-order sudden approximation.     

Uniform approximate Franck-Condon matrix elements for bound-continuum vibrational transitions

Franck-Condon matrix elements are calculated approximately for vibrational transitions of a diatomic molecule from a bound electronic potential curve to a purely repulsive curve. The bound states are approached by exactly normalized Miller-Good wavefunctions uniform in both turning points. For the continuum wavefunction a single turning point uniform Airy approximation is taken. The resulting Franck-Condon matrix element is approximately done in closed form with the help of a new canonical integral for a product of harmonic oscillator wavefunctions and Airy functions. The degree of agreement with a closed form exact result is qualitatively discussed for transitions from the ground state of a Morse curve to the continuum of a particular repulse exponential curve.Dedicated to Professor Hermann Hartmann on the occasion of his 65th birthday.     

A simple approximation for the vibrational partition function of a hindered internal rotation

A simple formula is presented for calculating the approximate partition function of a hindered internal rotational mode of a polyatomic molecule. The formula gives useful accuracy over the whole range from harmonic oscillator to hindered rotator to free rotator.     

Efficient configuration selection scheme for vibrational second-order perturbation theory

A fast algorithm of vibrational second-order Moller-Plesset perturbation theory is proposed, enabling a substantial reduction in the number of vibrational self-consistent-field (VSCF) configurations that need to be summed in the calculations. Important configurations are identified a priori by assuming that a reference VSCF wave function is approximated well by harmonic oscillator wave functions and that fifth- and higher-order anharmonicities are negligible. The proposed scheme has reduced the number of VSCF configurations by more than 100 times for formaldehyde, ethylene, and furazan with an error in computed frequencies being not more than a few cm(-1).     

Thermodynamic functions and the enthalpies of formation of gaseous VOX<Subscript>3</Subscript> vanadium oxotrihalides

A critical analysis of experimental and theoretical data on the structure and vibrational frequencies of gaseous VOX₃ vanadium oxotrihalides is performed. The values of molecular constants are selected and the thermodynamic functions are calculated within a “rigid rotator–harmonic oscillator” approximation. Equations that approximate a temperature dependence of heat capacity within the temperature range of 298.15–3000 K are obtained. Analysis of the available experimental data allows the enthalpy of formation to be determined for gaseous VOCl₃ molecules. The enthalpies of formation for VOF₃, VOBr₃, and VOI₃ molecules are determined for the first time using this value and quantum-chemical calculations of energy of exchange reactions involving VOCl₃. The obtained results are added to the database of the IVTANTERMO software.     

A new approach to the exact and approximate anharmonic vibrational partition function of diatomic and polyatomic molecules utilizing Morse and Rosen–Morse oscillators

Exact closed forms of the equilibrium partition functions in terms Jacobi elliptic functions are derived for a particle in a box and Rosen–Morse (Poschl–Teller) oscillator (perfect for modeling bending vibrational modes). An exact form of the equilibrium partition function of Morse oscillator is reported. Three other approximate forms of Morse partition function are presented. Having an exact closed‐form for the vibrational partition function can be very helpful in evaluating thermodynamic state functions, e.g., entropy, internal energy, enthalpy, and heat capacity. Moreover, the herein presented closed forms of the vibrational partition function can be used for obtaining spectroscopic and dynamical information through evaluating the two‐ and four‐point dipole moment time correlation functions in anharmonic media. Finally, a closed exact form of the rotational partition function of a particle on a ring in terms of the first kind of complete elliptic integral is derived. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Theoretical study of structure, vibrational frequencies, and electronic spectra of dibenzofuran and its polychlorinated derivatives

Minimum structures and harmonic vibrational frequencies of dibenzofuran (DF), 2,3,7,8-tetrachlorodibenzofuran (TCDF), and octachlorodibenzofuran (OCDF) were calculated using the multiconfigurational complete active space self-consistent field (CASSCF) and density functional theory (DFT) methods. The electronic transitions in these compounds were studied via the single-state multireference second-order perturbation theory (CASPT2) based on the CASSCF(14,13) references, as well as the time-dependent DFT (TD-B3P86) employing the cc-pVDZ (CASSCF/CASPT2) and 6-31G(d,p) (TD-B3P86) basis sets. The B3P86 geometry and harmonic vibrational frequencies of ground state DF agree very well with the experimental data, and the CASSCF/CASPT2 excitation energies and oscillator strengths are accurate enough to provide a reliable assignment of the absorption bands in the 200-300 nm region. The close agreements with experiment for the parent DF give the present theoretical approaches a valuable credit in predicting the properties of the environmentally toxic polychlorinated congeners, which is all the more important considering the difficulties and hazards in obtaining the experimental data.     

Molecular structure, vibrational, UV and NBO analysis of 4-chloro-7-nitrobenzofurazan by DFT calculations

In the present work, we reported a combined experimental and theoretical study on molecular structure, vibrational spectra and NBO analysis of 4-chloro-7-nitrobenzofurazan (NBD-Chloride). The FT-IR (400-4000 cm(-1)) and FT-Raman spectra (50-4000 cm(-1)) of NBD-Chloride were recorded. The molecular geometry, harmonic vibrational frequencies and bonding features of NBD-Chloride in the ground-state have been calculated by using the density functional B3LYP method with 6-311++G (d, p) as higher basis set. The energy and oscillator strength calculated by time-dependent density functional theory (TD-DFT) result in DMSO and CDCl3 solvents complements with each other. The calculated HOMO and LUMO energies show that charge transfer occurs within the molecule. Finally the calculation results were applied to simulate infrared and Raman spectra of the title compound which show good agreement with observed spectra.     

Upper and lower bounds to partition functions for molecules with double minimum potentials

Upper and lower bounds to the vibrational partition function q for molecules with double minimum potentials are derived. Both the exact lower (Gibbs-Bogoliubov) and upper (Golden-Thompson) bound to q are evaluated analytically for the harmonic oscillator perturbed symmetrically or asymmetrically by a gaussian barrier. For the quadratic-quartic oscillator only the lower bound can be evaluated analytically, whereas the upper bound leads to a strongly divergent series resisting conventional surnmability techniques. In this case the classical partition function is used as an upper bound.     

Franck-Condon matrix elements for bound-continuum vibrational transitions calculated by numerical integration and basis set expansion techniques

Franck-Condon factor distributions for bound-to-continuum transitions of one-dimensional vibrational states are calculated by a) using numerical integration, b) employing a finite number of square integrable harmonic oscillator functions. The methods are generally applicable to any kind of bound or repulsive potential involved. Results are presented and compared to model potential calculations previously reported by Krüger [1].     

Franck-Condon factors based on anharmonic vibrational wave functions of polyatomic molecules

Franck-Condon (FC) integrals of polyatomic molecules are computed on the basis of vibrational self-consistent-field (VSCF) or configuration-interaction (VCI) calculations capable of including vibrational anharmonicity to any desired extent (within certain molecular size limits). The anharmonic vibrational wave functions of the initial and final states are expanded unambiguously by harmonic oscillator basis functions of normal coordinates of the respective electronic states. The anharmonic FC integrals are then obtained as linear combinations of harmonic counterparts, which can, in turn, be evaluated by established techniques taking account of the Duschinsky rotations, geometry displacements, and frequency changes. Alternatively, anharmonic wave functions of both states are expanded by basis functions of just one electronic state, permitting the FC integral to be evaluated directly by the Gauss-Hermite quadrature used in the VSCF and VCI steps [Bowman et al., Mol. Phys. 104, 33 (2006)]. These methods in conjunction with the VCI and coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] method have predicted the peak positions and intensities of the vibrational manifold in the X 2B1 photoelectron band of H2O with quantitative accuracy. It has revealed that two weakly visible peaks are the result of intensity borrowing from nearby states through anharmonic couplings, an effect explained qualitatively by VSCF and quantitatively by VCI, but not by the harmonic approximation. The X 2B2 photoelectron band of H2CO is less accurately reproduced by this method, likely because of the inability of CCSD(T)/cc-pVTZ to describe the potential energy surface of open-shell H2CO+ with the same high accuracy as in H2O+.     

The dependence of low-energy electron attachment to CF3Br on electron and vibrational energy

In a joint experimental and theoretical effort, we have studied dissociative electron attachment (DEA) to the CF3Br molecule at electron energies below 2 eV. Using two variants of the laser photoelectron attachment method with a thermal gas target (T(G) = 300 K), we measured the energy dependent yield for Br- formation over the range E = 3-1200 meV with resolutions of about 3 meV (E < 200 meV) and 35 meV. At the onsets for excitation of one and two quanta for the C-Br stretching mode nu3, downward cusps are detected. With reference to the recommended thermal (300 K) attachment rate coefficient k(A)(CF3Br) = 1.4 x 10(-8) cm3 s(-1), absolute cross sections have been determined for Br- formation. In addition, we studied Br- and (CF3Br)Br- formations with a seeded supersonic target beam (10% CF3Br in helium carrier gas, with a stagnation pressure of 1-4 bars and nozzle temperatures of 300 and 600 K) and found prominent structure in the anion yields due to cluster formation. Using the microwave pulse radiolysis swarm technique, allowing for controlled variation of the electron temperature by microwave heating, we studied the dependence of the absolute DEA rate coefficient on the mean electron energy E over the range of 0.04-2 eV at gas temperatures T(G) ranging from 173 to 600 K. For comparison with the experimental results, semiempirical resonance R-matrix calculations have been carried out. The input for the theory includes the known energetic and structural parameters of the neutral molecule and its anion; the parameters of the resonant anion curves are chosen with reference to the known thermal rate coefficient for the DEA process. For the gas temperature T(G) = 300 K, good overall agreement of the theoretical DEA cross section with the experimental results is observed; moreover, rate coefficients for Br- formation due to Rydberg electron transfer, calculated with both the experimental and the theoretical DEA cross sections, are found to agree with the previously reported absolute experimental values. At T(G) = 300 K, satisfactory agreement is also found between the calculated and experimental attachment rate coefficients for mean electron energies E = 0.04-2 eV. The strong increase of the measured rate coefficients with rising gas temperature, however, could be only partially recovered by the R-matrix results. The differences may result from the influence of thermal excitations of other vibrational modes not included in the theory.