Quantum calculations, collision-induced

Glaz et calculated collision-induced hyper-Rayleigh (CIHR) for HeNe at temperatures of 95 and 295 K. Both quantum mechanical and classical approached were applied, for frequency shifts up to 1000 cm The calculations were based on ab initio data obtained at the SCF and MP2 level of theory with atom-specific basis sets for He = [6s4p3dlf] and Ne = [9s6p5dlf]. These basis sets yield SCF values for the dipole polarizability otHe= 1-322 and otNe = 2.368, to be compared to the numerical... 

Line shapes of a great many collision-induced absorption spectra have been obtained in recent years, using classical and quantum formalisms. These will be discussed in Chapters 5 and 6. Line shape calculations require the same input as the moment calculations, namely the dipole moment and interaction potential. They offer the advantage of generating certain parts of the spectra with remarkable precision, for example the... 

Early numerical estimates of ternary moments [402] were based on the empirical exp-4 induced dipole model typical of collision-induced absorption in the fundamental band, which we will consider in Chapter 6, and hard-sphere interaction potentials. While the main conclusions are at least qualitatively supported by more detailed calculations, significant quantitative differences are observed that are related to three improvements that have been possible in recent work [296] improved interaction potentials the quantum corrections of the distribution functions and new, accurate induced dipole functions. The force effect is by no means always positive, nor is it always stronger than the cancellation effect. 

Despite the obvious power of quantum line shape calculations for the analysis of measured collision-induced absorption spectra, a need persists for simple but accurate model line profiles, especially for extrapolating experimental spectra to both low and high frequencies for an accurate determination of the spectral moments. Reliable model profiles are also useful for line shape analyses, i.e., for representing complex spectra as a superposition of lines (where this is possible). 

Crude estimates of the absorption spectra of hydrogen-helium mixtures at temperatures from 2,000 to 20,000 K were attempted [110, 111]. The motivation for that work was to better understand the effects of highly rotovibrationlly excited molecules on the collision-induced absorption spectra. Since small basis sets were used for the quantum chemical calculations of the induced dipole components, the results should not be used for comparisons with measurements. Theoretical estimates of the emission of colliding high-speed ( 10 km/s) neutral atoms, based on classical trajectories and certain quantum corrections, were reported [112]. 

F.D. Colavecchia, F. Mrugala, G.A. Parker, and R.T. Pack, Accurate quantum calculations on three-body collisions in recombination and collision-induced dissociation, ii. the smooth variable discretization enhanced renormalized numerov propagator. J. Chem. Phys., 118 10387-10398,2003. 

Recently, the sapt approach has been applied (32) to compute the interaction-induced polarizability for the helium diatom. The computed polarizability invariants have been analytically fitted, and used in quantum-dynamical calculations of the binary collision-induced Raman spectra. The results of the dynamical calculations are summarized in Fig. 1. 

This book describes the proceedings of a NATO Advanced Research Workshop held at CECAM, Orsay, France in June, 1983. The Workshop concentrated on a critical examination and discussion of the recent developments in the theory of chemical reaction dynamics, with particular emphasis on quantum theories. Several papers focus on exact theories for reactions. Exact calculations on three-dimensional reactions are very hard to perform, but the results are valuable in testing the accuracy of approximate theories which can be applied, with less expense, to a wider variety of reactions. Indeed, critical discussions of the merits and defects of approximate theories, such as sudden, distorted-wave, reduced dimensionality and transition-state methods, form a major part of the book. The theories developed for chemical reactions have found useful extensions into other areas of chemistry and physics. This is illustrated by papers describing topics such as photodissociation, electron-scattering, molecular vibrations and collision-induced dissociation. Furthermore, the important topic of how to treat potential energy surfaces in reaction dynamics calculations is also discussed. 

Bancewicz et al have discussed colKsion-induced HRS spectra of gaz-eous H2-Ar mixture on the basis of ab initio calculations of the collision-induced first hyperpolarizability tensor, Ap. The independent spherical components of the Ap values, evaluated at the MP2 level using the [%s6p5dAf and [6sAp2d[ basis sets for Ar and H atoms, have been fitted to analytical formulas expressing their dependence on the intermolecular distance and then employed as input data to analyze the HRS data. The good agreement between the quantum and semiclassical approaches can be treated as a benchmark proof of both the method s feasibility and accuracy. 

Quantum chemical calculations (Kirby 1980, Kirby et al. 1980) have shown that the products of this reaction are predominantly C and H" " under interstellar conditions. However, in his work on 5 Oph, Draine (1986) assumed the products to be C" " and H (cf. Table 6 of Draine and Katz 1986a). Whilst, at first sight, this may appear to be a minor error, in reality, it is significant and accounts for most of the residual discrepancies to which reference has been made. This may be seen from Table 2, by comparing model A of Draine (1986) with the results of our own calculations in which the products of reaction (2) are supposed to be C and H (row (c) of Table 2). The agreement with Draine s model is much more satisfactory, from the viewpoint of N(CH" ), N (OH), and of N[H2(J)J, considering that the rate coefficients for collision-induced rotational transitions in H2 are not identical in the two models. 

The use of gas-phase biomolecule spectroscopy for structural characterization rehes strongly on the interplay between experiment and theory. Structural properties can usually only be extracted from experimental spectra with the use of high-level quantum-chemical calculatirms. The chapter Theoretical Methods for Vibrational Spectroscopy and CoIUsirai Induced Dissociation in the Gas Phase reviews some recent advances in the theoretical methods applied to predict vibrational spectra, including molecular-dynamics-based methods to model photo-dissociation spectra and DFT-based molecular dynamics to predict spectra in the far-infrared region. The use of trajectory calculations on a semi-empirical potential is investigated as an alternative to transition-state calculations for the modeling of collision-induced dissociation of protonated peptides. 

Maroulis et calculated the interaction-induced dipole moment and (hyper)polarizability of the HeAr heterodiatoms. The calculations were performed at the SCF and MP2/[6s4p3dlf/8s6p5d3f] level of theory. The obtained R-dependence of the interaction properties was subsequently applied to the calculation of the collision-induced hyper-Rayleigh (CIHR) spectra both quantum mechanically and semi-classically for the frequency shifts up to 1200 cm The R-dependence of the mean and the anisotropy of the interaction-induced first hyperpolarizability is given in Figs. 12 and 13. It is observed that electroc correlation effects are particularly significant for short internuclear separations. 

The second dielectric virial coefficient b(T) is 2 orders of magnitude smaller than the density virial coefficient but the existing absolute uncertainties in the values of these coefficients are expected to be similar. Calculations of b(T) were performed by Moszynski et al. using a fully quantum mechanical approach [164,165] and the collision induced polarizability from SAPT calculations with a moderately large orbital basis set. However, more recent calculations from [166] and [167] disagree with this work to such an extent... 

The purpose of this paper was to illustrate the use of a completely classical model to study the laser enhancement of chemical reactions via a collision induced absorption. It is found that the model is easy to apply to a wide range of collinear and three-dimensional examples. It is interesting to note that the quantum mechanical calculation is in qualitative agreement with the classical calculation in the collinear A + BC examples and that a very simple calculation (as in Fig. 3) can predict the Franck-Condon structure in the quantum mechanical reaction. A further study of three-dimensional systems is necessary to see if the low-energy structure in the reaction probability is always weak or whether this is an artifact of the particular model. Other preliminary calculations have illustrated the laser inhibition of chemical reactions with very small field strengths as well as isotopic effects in these systems. Further work is necessary to explore these interesting possibilities. 

A proper analysis of the troposphere requires accurate collision-induced absorption (CIA) coefficients for the various relevant gases. Once quantum-mechanical calculations for N2-CH4 CIA became available (Borysow Tang, 1993), accurate atmospheric models became feasible. In order to suppress synthetic spectra sufficiently between 200 and 300 cm to fit the data, it was necessary to fill the upper... 

Prof. Troe has presented to us the capture cross sections for two colliding particles, for example, an induced dipole with a permanent dipole interacting via the potential V(r,0) = ctq/2rA - ocos 0/r2 (see Recent Advances in Statistical Adiabatic Channel Calculations of State-Specific Dissociation Dynamics, this volume). The results have been evaluated using classical trajectories or SAC theory. But quantum mechanically, a colliding pair of an induced dipole and a permanent dipole could never be captured because ultimately they have to dissociate after forming some sort of a collision complex. I would therefore like to ask for the definition of the capture cross section. ... 

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