Vibrational softening of diatomic molecules

An analysis of a model molecular oscillator is presented: a vibrating diatomic molecule carrying N ₀ electrons. The energy derivatives over the number of electron (N) and the deformation (Q), ∂ ⁿ /∂N ⁿ and ∂ ⁿ /∂Q ⁿ have been analyzed up to second order (n=2), including the appropriate mixed derivatives. The effect of coupling between distortion of the electron density induced by ΔN and the vibrational deformation of the molecule has been studied. Anharmonicity of the oscillator has been shown to be a possible result of that coupling; new relations between the parameters characterizing the anharmonicity of the oscillator and the energy derivatives at density functional theory level have been obtained. Ab initio calculations for a set of diatomic molecules have been performed, yielding values for all the derivatives discussed and demonstrating the effect of coupling with vibrations. Received: 1 June 2000 / Accepted: 20 October 2000 / Published online: 21 March 2001     

Vibrational relaxation of diatomic molecules in condensed monatomic media

A model based on binary-like collisions is presented to describe the vibrational relaxation of diatomic molecules in a monatomic medium. For N₂Ar and COAr, it is shown that the oscillatory motion of host atoms undergoing multiquantrum processes is most important in removing vibrational energy. The translational motion of molecules confined to the cell space also contributes to the energy relaxation by removing the energy mismatch.     

The generalized potential energy function for diatomic molecules

A new generalized potential energy function is suggested for diatomic molecules. The Dunham, Simons—Parr—Finlan, Thakkar and Ogilvie potentials are shown to be particular cases of the generalized potential energy function. It is also shown that the function suggested may reproduce the path of the potential curve with sufficient accuracy even for the cases of small expansion length.     

Vibration-to-rotation and vibration-to-vibration energy transfer between diatomic molecules

A classical model for VR and VV energy transfer between two dissimilar diatomic molecules is proposed. For the exponential repulsive potential, in the limit as the rotation of the molecules goes to zero, the present model reduces to the previous results for VT and VV energy transfer. For the hydrogen halides, whose relaxation is generally accepted as being governed by VR energy transfer, the Pr's predicted by the present theory agree reasonably well with the experimental data. In particular, the positive and negative temperature dependence of the VV Pr's for N₂HI and N₂DI are predicted.     

Vibrational energy relaxation of a diatomic molecule in a room-temperature ionic liquid

Vibrational energy relaxation (VER) dynamics of a diatomic solute in ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate (EMI(+)PF(6) (-)) are studied via equilibrium and nonequilibrium molecular dynamics simulations. The time scale for VER is found to decrease markedly with the increasing solute dipole moment, consonant with many previous studies in polar solvents. A detailed analysis of nonequilibrium results shows that for a dipolar solute, dissipation of an excess solute vibrational energy occurs almost exclusively via the Lennard-Jones interactions between the solute and solvent, while an oscillatory energy exchange between the two is mainly controlled by their electrostatic interactions. Regardless of the anharmonicity of the solute vibrational potential, VER becomes accelerated as the initial vibrational energy increases. This is attributed primarily to the enhancement in variations of the solvent force on the solute bond, induced by large-amplitude solute vibrations. One interesting finding is that if a time variable scaled with the initial excitation energy is employed, dissipation dynamics of the excess vibrational energy of the dipolar solute tend to show a universal behavior irrespective of its initial vibrational state. Comparison with water and acetonitrile shows that overall characteristics of VER in EMI(+)PF(6) (-) are similar to those in acetonitrile, while relaxation in water is much faster than the two. It is also found that the Landau-Teller theory predictions for VER time scale obtained via equilibrium simulations of the solvent force autocorrelation function are in reasonable agreement with the nonequilibrium results.     

Structure of molecular energy levels of homonuclear diatomic molecules

A new approach is given for the systematic prediction of the low‐lying electronic states of homonuclear diatomic molecules. The approach is based on the bond order and the energy levels of the separated atoms. The asymptotic wave functions are derived from two atomic wave functions by using new operators defined as linear combinations of certain ladder operators. We show that the low angular moment states tend to have a high bond order in the states derived from an asymptote. The observed low‐lying states of C₂, C, Sc₂, and Ti₂ molecules agree with the predictions. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 597–604, 1999     

Vibrational energy relaxation rates via the linearized semiclassical approximation: applications to neat diatomic liquids and atomic-diatomic liquid mixtures

We report the results obtained from the application of our previously proposed linearized semiclassical method for computing vibrational energy relaxation (VER) rates (J. Phys. Chem. A 2003, 107, 9059, 9070) to neat liquid oxygen, neat liquid nitrogen, and liquid mixtures of oxygen and argon. Our calculations are based on a semiclassical approximation for the quantum-mechanical force-force correlation function, which puts it in terms of the Wigner transforms of the force and the product of the Boltzmann operator and the force. The calculation of the multidimensional Wigner integrals is made feasible by the introduction of a local harmonic approximation. A systematic analysis has been performed of the temperature and mole-fraction dependences of the VER rate constant, as well as the relative contributions of centrifugal and potential forces, and of different types of quantum effects. The results were found to be in very good quantitative agreement with experiment, and they suggest that this semiclassical approximation can capture the quantum enhancement, by many orders of magnitude, of the experimentally observed VER rate constants over the corresponding classical predictions.     

Electron–Electron interaction energy in homonuclear diatomic molecules

The derivative of the electron–electron potential energy U_ee with respect to internuclear separation R is studied for light homonuclear diatomic molecules at equilibrium. It is readily related to nuclear–nuclear potential energy U_nn, the force constant K, and the electron–nuclear potential energy U_en. An approximate expression, based on the simplest form of density functional theory, is then used to eliminate dU_en/dR|_Re. The result thus obtained for dU_ee/dR|_Re transcends an earlier proposal of Kryachko by including a term 2/3R_eK, with K the force constant. Numerical tests at SCF–RHF level are presented for nine homonuclear diatomic molecules.     

Semiclassical three-dimensional model for vibrational energy transfer in diatomic molecules

A semiclassical model for calculation of rate constants for vibrational excitation in diatomic gases at low temperatures (below 1000 K) is suggested. The model has been tested by its ability to predict the relaxation times of hydrogen (τ_H1 in the temperature region 40–1000 K. The agreement with experimental values is excellent. The isotopic ratio τ_D2/τ_H2 as a function of temperature is predicted.     

The thermal dissociation of diatomic molecules at high temperatures

On the basis of a solution of gas-kinetic equations describing the population of molecules (cut-off harmonic oscillators) at various oscillatory levels, the process of thermal dissociation has been analyzed. It has been shown that thermal dissociation, in addition to disturbing the Boltzmann distribution, leads to a reduction in the vibrational temperature compared with the translational one. This affects to a considerable extent the rate of thermal dissociation, and also the process of vibrational relaxation. The question of the applicability of the well-known relation of statistical thermodynamics connecting the rate constants of forward and back reactions has also been analyzed. The results obtained agree qualitatively with the experimental data.     

Rare gas pressure shifts of vibration-rotation lines of diatomic molecules

The semiclassical S-matrix theory including all orders of the interaction recently proposed by Smith et al. for spectral line broadening in linear molecules perturbed by atoms is applied to the shifts after inclusion of vibrational dephasing effects. Although this theory does not take into account the non-commutative character of the interaction at different times, a good consistency between experimental data and the present calculation is obtained for HClAr and HClXe at room and low temperatures and for the 0-0, 0-1 and 0-2 vibrational bands. It is shown why the non-commutation of the interaction, which is of major importance for the diatomic-diatomic molecule case, may be reasonably reasonably disregarded for the diatom-atom case.     

Monte carlo simulation and thermodynamic perturbation theory for mixtures of diatomic molecules

The thermodynamic properties and site—site distribution functions of mixtures of non-spherical molecules are obtained by Monte Carlo simulation. A non-spherical reference-system perturbation theory based on the RISM equation is developed to predict these results. The agreement between theory and simulation for the thermodynamic properties is encouraging. Important differences in the relative peak heights of the site—site distribution functions from theory and simulation are attributed to the role of attractive forces in determining local structure in the fluid mixtures, where the volumes of the components are similar but the well depths differ.     

Vibrational energy relaxation of small molecules and ions in liquids

A theoretical/computational framework for determining vibrational energy relaxation rates, pathways, and mechanisms, for small molecules and ions in liquids, is presented. The framework is based on the system—bath coupling approach, Fermi’s golden rule, classical time-correlation functions, and quantum correction factors. We provide results for three specific problems: relaxation of the oxygen stretch in neat liquid oxygen at 77 K, relaxation of the water bend in chloroform at room temperature, and relaxation of the azide ion anti-symmetric stretch in water at room temperature. In each case, our calculated lifetimes are in reasonable agreement with experiment. In the latter two cases, theory for the observed solvent isotope effects illuminates the relaxation pathways and mechanisms. Our results suggest several propensity rules for both pathways and mechanisms.     

Vibrational energy relaxation in liquid N2CO mixtures

The vibrational energy relaxation rates of the liquid nitrogenCO system have been measured by optically pumping the collision-induced fundamental vibrational absorption band of liquid N₂ with the output of an HBr TEA laser. A radiatively dominated value of 56 ± 10 s is found for the intrinsic nitrogen relaxation time. The CO contribution to the decay rate is explained on the basis of a simple kinetic model and found also to be radiatively dominated at low CO concentrations. The importance of radiative trapping and energy transport in evaluating the lifetimes is demonstrated.     

Estimating correlation energy of diatomic molecules and atoms with neural networks

The electronic correlation energy of diatomic molecules and heavy atoms is estimated using a back propagation neural network approach. The supervised learning is accomplished using known exact results of the electronic correlation energy. The recall rate, that is, the performance of the net in recognizing the training set, is about 96%. The correctness of values given to the test set and prediction rate is at the 90% level. We generate tables for the electronic correlation energy of several diatomic molecules and all the neutral atoms up to radon (Rn). © 1997 by John Wiley & Sons, Inc. J Comput Chem 18 : 1407–1414, 1997     

The dissociation energy of the new diatomic molecules SiPb and GePb

The diatomic molecules SiPb and GePb were for the first time identified by producing high temperature vapors of the constituent pure elements in a "double-oven-like" molecular-effusion assembly. The partial pressures of the atomic, heteronuclear, and homonuclear gaseous species observed in the vapor, namely, Si, Ge, Pb, SiPb, GePb, Pb2, Gen, and Sin (n=2-3), were mass-spectrometrically measured in the overall temperature ranges 1753-1961 K (Ge-Pb) and 1992-2314 K (Si-Pb). The dissociation energies of the new species were determined by second- and third-law analyses of both the direct dissociation reactions and isomolecular exchange reactions involving homonuclear molecules. The selected values of the dissociation energies at 0 K (D0 degrees) are 165.1+/-7.3 and 141.6+/-6.9 kJ/mol, respectively, for SiPb and GePb, and the corresponding enthalpies of formation (DeltafH0 degrees) are 476.4+/-7.3 and 419.3+/-6.9 kJ/mol. The ionization efficiency curves of the two species were measured, giving the following values for the first ionization energies: 7.0+/-0.2 eV (SiPb) and 7.1+/-0.2 eV (GePb). A computational study of the species SiPb and GePb was also carried out at the CCSD(T) level of theory using the relativistic electron core potential approach. Molecular parameters, adiabatic ionization energies, adiabatic electron affinities, and dissociation energies of the title species were calculated, as well as the enthalpy changes of the exchange reactions involving the other Pb-containing diatomics of group 14. Finally, a comparison between the experimental and theoretical results is presented, and from a semiempirical correlation the unknown dissociation energies of the SiSn and PbC molecules are predicted as 234+/-7 and 185+/-11 kJ/mol, respectively.     

Potential energy curves of diatomic molecules from the Hill determinant method

The Hill determinant method is shown to be suitable for constructing potential energy curves of diatomic molecules. Both the Dunham and the perturbed Morse oscillator potentials are used to fit spectroscopic data. Results are shown for ionic and covalent molecules.