Ab initio potential surfaces

W. Meyer and L. Frommhold. Collision induced rototranslational spectra of H2-Ar from an accurate ab initio potential surface. Phys. Rev., A 34 2936, 1986. 

The ion-neutral reaction that has received the greatest attention from a theoretical viewpoint is the H2+ -He process. This is because of the relative simplicity of this reaction (a three-electron system), which facilitates accurate theoretical calculations and also to the fact that a wealth of accurate experimental data has been obtained for this interaction. Several different theoretical approaches have been applied to the H2+He reaction, as indicated by the summary presented in Table VI. Most of these have treated the particle-transfer channel only, and few have considered the CID channel. Various theoretical methods applicable to ion-neutral interactions are discussed in the following sections. For the HeH2+ system, calculations using quasiclassical trajectory methods, employing an ab initio potential surface, have been shown to yield results that are in good agreement with the experimental results. 

Banichevich, A., Peyerimhoff, S.D., and Grein, F. (1990). Ab initio potential surfaces for ozone dissociation in its ground and various electronically excited states, Chem. Phys. Lett. 173, 1-6. 

In this section, we have shown how the first-principle calculations can be performed to analyze steady state and time-resolved spectra to obtain the rate constants of the processes involved in the experiments and how to employ the ab initio potential surfaces and the interactions between these surfaces to calculate these rate constants. 

Many potential surfaces have been calculated for H + H2. Two of the most recent, an accurate Cl calculation [113] and a superposition of configuration calculation [114], review also the prior work on this problem. Ab initio potential surfaces have been calculated for a number of systems of interest. Some of the more pertinent are He + H2 [115], He+ + H2 [116], Li+ + H2 [117], Li + H2 [118], and Li + HF [119]. 

In order to avoid any mathematical sophistication, we restrict ourselves to the construction of only those functions that are of interest in the application. Many more details can be found in the pioneering work of Ahlberg, Nilson and Walsh and in various textbooks on the subject Some authors already applied spline techniques to various problems in Chemical Physics, either to interpolate ab initio potential surfaces or experimental data or to analytically expand... 

The photolysis of HBr at 193 nm has been used by Kleinermanns and Wolfrum as a source of translationally hot H atoms in a series of investigations of the elementary reactions of H with O2, H2O, and C02. They have provided a summary of these studies which also includes other laser-induced processes. Nascent vibrational, rotational, and fine-structure state distributions of OH(X n) resulting from the H( S) + 02( Sg ) reaction were presented simultaneously with the results of classical trajectory calculations of the total and state-to-state cross-sections for this reaction performed on an ab initio potential surface. OH vibrational and rotational excitation was found to be high and a preference for the tt component of the A-doublets was noted. The latter was taken to indicate that the reaction takes place in a planar configuration at high collision energies. For H+H2O and H+CO2, similar... 

An obvious way for carrying out spectroscopic calculations for an ab initio potential is by fitting the latter to a suitable analytic function. With such an approach, any vibrational spectroscopy method can be used. Indeed, such calculations have been pursued since the first appearance of rehable ab initio potential surfaces, and this continues to be a very active and successful direction of research. There are, however, several problems that strongly limit the applicabihty of this approach. First, the requirements of the quality of the fit are rather stringent. High-quality fitting is essential for spectroscopy of good... 

As an example, our first move in this direction has been to solve for the restricted-rotor energy levels of the CH3-NC/CH3-CN system given a theoretical potential for the torsional motion, and the calculated rate constant is very similar to that given in [80.P1] in this trial [82.C] the remaining molecular frequencies were taken to be the experimental ones, but there is no reason to think that equally acceptable ones could not have been generated from an ab initio potential surface. We expect to... 

One HAB molecule for which a fairly complete ab initio potential surface is available not only in the ground but also in the first excited state as well as for its positive and negative ions is the HSO radical. It is of great interest in atmospheric chemistry, in particular with respect to pollution, and has therefore attracted considerable interest in past years, lie most important data are collected in Fig. 7 and Table XIII. 

Experimental and theoretical analysis of thevihrational spectra and theoretical smdy of the structures of 3,6-dichloropyridazine and 3,4,5-trichloropyridazine Anharmonic vibrational spectroscopy of hydrogen-bonded systems directly computed from ab initio potential surfaces (H20) , n = 2, 3 Cl-lHjO), n = 1, 2 H+(H20) , = 1, 2 H2O-CH3OH ... 

Chakravarty and Clary have also simulated the positions and intensities of features in the ultraviolet excitation spectrum, based solely on the ab initio potential surfaces. All of the experimentally observed members of the OH-Ar stretching progression in the OH A-X 0-0 region are... 

Kudla K, Koures A, Harding LB, Schatz GC (1992) A quasiclassical trajectory study of OH rotational excitation in OH + CO collisions using ab initio potential surfaces. J Chem Phys 96 7465... 

An alternative route is based on time-dependent approaches, where the standard statistical mechanics formalism relies on Fourier transform of the time correlation of vibrational operators [54—57]. These approaches can provide a complete description of the experimental spectrum, that is, the characterization of the real molecular motion consisting of many degrees of freedom activated at finite temperature, often strongly coupled and anharmonic in namre. However, computation of the exact quantum dynamics evolution of the nuclei on the ab initio potential surface is as prohibitive as the quantum/stationary-state approaches. In fact, even a semiclassical description of the time evolution of quanmm systems is usually computationally expensive. Therefore, time correlation methods for realistic systems are usually carried out by sampling of the nuclear motion in the classical phase space. In this context, summation over i in Eq. 11.1 is a classical ensemble average furthermore, the field unit vector e can be averaged over all directions of an isotropic fluid, leading to the well-known expression... 

Without further introduction, it seems appropriate to proceed to a discussion of specific systems for which ab initio potential surface features have been predicted. In the present paper, special emphasis will be placed on the relationship between theoretical predictions and experimental observations. 

Figure 3.11 Orientation dependence of the cross-section for the reaction H + D2(v= /= 0) HD + D at the two indicated values of the collision energy Ej- The ordinate is dff R/dcos y = 2ctr(cos y). The solid curves were calculated from the angle-dependent line-of-centers model, Eq. (3.34), and the (open and filled) points represent dynamical computations (these are quasi-classical trajectory results that have statistical error bars as discussed in Chapter 5) on the ab initio potential surface referred to in Figure 3.10 [adapted from N. C. Blais, R. B. Bernstein, and R. D. Levine, J. Phys. Chem. 89, 20 (1985)].

Kuntz, P.J. (1972) Use of the method of diatomics-in-molecules in fitting ab initio potential surfaces the system hehj. Chem. Phys. Lett., 16 (3), 581-583. 

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