Ab initio calculations results

At the beginning of this section we noted the fact that the b 3n state is one of a manifold of close-lying excited states. The spin orbit interaction mixes singlet and triplet states and ab initio calculations result in the following wave ftmctions for the fine structure components of the h 3 n state ... 

The same authors published a detailed report on the calculations of the oxygen insertion into unactivated C-H bonds by dioxiranes using DFT theory and on comparison of the transition structures for stepwise routes via radical pairs with the concerted pathway <2003JOC811>. The articles dealing with the mechanism of OH formation from ozonolysis of isoprene and a- and /3-pinene provide DFT and ab initio calculation results also for the dioxirane formation <2001CPL(358)171, 2002JA2692, 2005JCP114308>. 

The calculated harmonic force field given in cartesian coordinates was transformed into a force field defined by symmetry coordinates. A normal coordinate analysis was performed using the geometry and the symmetry force constants from ab initio calculations, resulting in a description of the normal modes by their potential energy distribution (FED). Table 3 presents the potential energy distribution for v SiSi and v, SiCb for both rotamers, and Table 4 summarizes the SiSi, SiCl, and SiC stretching force constants. 

The efficiency of force field approaches allows also to perform calculations in explicit solvent. To demonstrate this, we have solvated the ft[Cl2(6-DPPon)2] complex in deuterochloroform and carried out MD simulations. The force field parameters for CDCI3 are determined by combining ab initio calculation results at the MP2/6-311++G level and suggested values from the literature [86, 87]. 

Studied system 2PY2HP to new ones. The PES morphing presented here is heuristic, and a more sophisticated morphing strategy is currently under investigation. Fitting with a CHARMM/I-Nolls interface [80] is also a possible if sufficient experimental data or high-level ab initio calculation results are available. 

No discussion was made in the original paper on the correction for the shrinkage effect, which should have a strong influence on the C-CsS angle. The barrier to linearity was estimated to be higher than 2 kJ mol but could not be determined precisely. Ab initio calculations resulted in a non-linear skeleton if election correlation was included. The MW spectra demonstrated nearly free internal rotation of the CF3 group. The nozzle was at room temperature. 

Detailed analyses of the above experiments suggest that the apparent steps in k E) may not arise from quantized transition state energy levels [110.111]. Transition state models used to interpret the ketene and acetaldehyde dissociation experiments are not consistent with the results of high-level ab initio calculations [110.111]. The steps observed for NO2 dissociation may originate from the opening of electronically excited dissociation chaimels [107.108]. It is also of interest that RRKM-like steps in k E) are not found from detailed quantum dynamical calculations of unimolecular dissociation [91.101.102.112]. More studies are needed of unimolecular reactions near tln-eshold to detennine whether tiiere are actual quantized transition states and steps in k E) and, if not, what is the origin of the apparent steps in the above measurements of k E). 

A further model Hamiltonian that is tailored for the treatment of non-adiabatic systems is the vibronic coupling (VC) model of Koppel et al. [65]. This provides an analytic expression for PES coupled by non-adiabatic effects, which can be fitted to ab initio calculations using only a few data points. As a result, it is a useful tool in the description of photochemical systems. It is also very useful in the development of dynamics methods, as it provides realistic global surfaces that can be used both for exact quantum wavepacket dynamics and more approximate methods. 

Now, we discuss briefly the situation when one or both of the adiabatic electronic states has/have nonlinear equilibrium geometry. In Figures 6 and 7 we show two characteristic examples, the state of BH2 and NH2, respectively. The BH2 potential curves are the result of ab initio calculations of the present authors [33,34], and those for NH2 are taken from [25]. 

Figure 9. Energy difference (absolute value) between the components of the X II electronic State of HCCS as a function of coordinates p, P2, and y. Curves represent the square root of the second of functions given by Eq. (77) (with e, = —0.011, 2 = 0.013, 8,2 = 0.005325) for fixed values of coordinates p, and P2 (attached at each curve) and variable Y = 4>2 Here y = 0 corresponds to cis-planar geometry and y = 71 to trans-planar geometry. Symbols results of explicit ab initio calculations.

The next question asked is whether there are any indications, from ab initio calculations, to the fact that the non-adiabatic transfonnation angles have this feature. Indeed such a study, related to the H3 system, was reported a few years ago [64]. However, it was done for circular contours with exceptionally small radii (at most a few tenths of an atomic unit). Similar studies, for circular and noncircular contours of much larger radii (sometimes up to five atomic units and more) were done for several systems showing that this feature holds for much more general situations [11,12,74]. As a result of the numerous numerical studies on this subject [11,12,64-75] the quantization of a quasi-isolated two-state non-adiabatic coupling term can be considered as established for realistic systems. 

This chapter centers on the mathematical aspects of the non-adiabatic coupling terms as single entities or when grouped in matrices, but were it not for the available ab initio calculation, it would have been almost impossible to proceed thus far in this study. Here, the ab initio results play the same crucial role that experimental results would play in general, and therefore the author feels that it is now appropriate for him to express his appreciation to the groups and individuals who developed the numerical means that led to the necessary numerical outcomes. 

Semi-empirical methods, such as those outlined in Appendix F, use experimental data or the results of ab initio calculations to determine some of the matrix elements or... 

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