Saddle point geometries

As we noted in the beginning of this section, single-reference-based techniques are not expected to be quantitative, but they can still be very useful in preliminary calculations. In this regard, we note that although the CPF method is quite accurate for the barrier height and saddle-point geometry, it is significantly poorer than the MRCI for the exothermicity. 

Theoretical Studies of the Classical Saddle-Point Geometry (oo) Energetics (kcal/mole) for... 

The saddle-point geometries in parentheses have not been optimized. 

The saddle point geometries are taken from the MRCI(2p)+Q and MRCI+Q calculations in this basis set. 

Inorganic Compounds. - Hamilton216 characterised the proton transfer in the isoelectronic species HO and HF2+. Electron densities were calculated at the QCISD/6-311 + +G(2d, 2p) level for the nonlinear equilibrium geometry and the C2v saddle point and linear saddle point geometries. AIM is applied to partition p into its atomic components and atomic and molecular properties are calculated. These quantities are used to characterise the proton dynamics as similar to internal rotation. 

Hutter et al. concluded from their DFT calculations that the fully symmetrical cumulene structure is the most stable planar ring structure, although it turned out to be a saddle-point geometry [236]. 

There is little empirical information about the C2h saddle point with which to compare. The most reliable empirical estimates are probably those derived from the model potential surface of Barton and Howard. They obtained itf = 2.70 A, 6hff = 61.5 deg, = 4.0 kcal/mol, and = 0.9 kcal/mol. The fit of Hancock et to their out-of-plane bend potential gives 04 = 522 cm-l at the ACCD/TZ(d,p) saddle point geometry. 

Table VIII. Theoretical studies of the classical saddle-point geometry eind barrier for the F-1-H2 reaction.

The first basis set was employed in most of the calculations, and, particularly, in the determination of the saddle point geometry and the minimun energy path (see Sec.4). The second basis set was used mainly to improve the calculated barrier height and the exoergicity of the reaction (see Sec.5). 

The Complete Active Space SCF (CASSCF) method [9] was used in most of the calculations. For Coov symmetry, the H surface was obtained considering as active the orbitals 2<7, 3(7-, 4(t, Itt, and 5o-, while the active electrons in six active orbitals. Analytical gradient calculations using the CASSCF wave-function were performed in order to evaluate the saddle point geometry and the minimum energy path. 

Although the SE surface was used for the various theoretical studies described above, the actual fit of this surface to the saddle point properties derived from the WD data [126] is not very accurate. In fact, harmonic TST rate constants for reaction (Rl) computed from the ab initio saddle point properties differ somewhat from the corresponding values obtained with the SE surface. These differences, which range from 29% to 46% over the temperature range 200 to 4000 K, are primarily due to errors in the saddle point geometry for the SE surface [16]. To obtain a PES that more closely fits the WD data as well as one that yields rate constants that are more quantitatively consistent with experiment, we constructed two improved PESs [135] (called Nos. 3 and 4) for reaction (Rl) by fitting to the ab initio reactant, product, and saddle point properties derived from the WD points. The saddle point and reactant properties were taken directly from [126] (except for the saddle point frequencies, which were taken from [165]), while the H2O properties were obtained by a least-squares fit of the equilibrium geometry (Re, ) and the three force constants k, k e, and koQ in the potential function... 

Figure 1. OH + H2 saddle point geometry [126] (drawn to scale) and definitions of the internal coordinates (reproduced with permission from [176]).

Newton search to reproduce fee WD saddle point geometry, barrier height, and imaginary frequency as closely as possible. Specifically, a Newton search for simultaneous zeros for the relative errors in V, , a, 0, and R weighted by factors of 50, 50, 10, 1, and 10, respectively, was run for several (typically 10) iterations. (3) For each choice of the five constants in (2), the values of fee five constants Cj, tj, g, f , and z were determined by a converged Newton search so feat fee WD frequencies for the five bound vibrational modes at fee saddle point are reproduced. (4) As a final independent step, the values of the five constants fp, Pp, Rp, h, and R were chosen as a group by trial and error to ensure that the a" frequency behaves as reasonably as possible along the reaction path. (The value of z was then readjusted to yield the WD value for fee a" frequency at the saddle point.)... 

With the origin defined as the center of mass of the saddle point geometry, the MEP from the saddle point to the product-side complex was determined by the Euler single-step method with step sizes between gradient and hessian calculations of 0.005 A and 0.025 A,... 

The more limited geometry and vibrational analyses employed in standard ab initio thermodynamics schemes, such as G3, while typically suitable for thermodynamic evaluations of stable species, lack the accuracy required for quantitative a priori kinetic predictions. In essence, kinetic predictions depend much more strongly on the vibrational analyses than do low temperature thermodynamic predictions. Furthermore, saddle point geometries are more strongly dependent on the electronic structure methodology than are equilibrium geometries. 

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