And transition state geometry

Aj ala P Y and H B Schlegel 1997. A Combined Method for Determining Reaction Paths, Minima and Transition State Geometries. Journal of Chemical Physics 107 375-384. 

Once HyperChem calculates potential energy, it can obtain all of the forces on the nuclei at negligible additional expense. This allows for rapid optimization of equilibrium and transition-state geometries and the possibility of computing force constants, vibrational modes, and molecular dynamics trajectories. 

Fig. 19 Ground state and transition state geometries for the bimolecular reaction of Af-methylaniline and A -acetoxy-A -alkoxyamides.

Several monographs2-5 have detailed discussions dealing with heavy-atom and primary and secondary hydrogen-deuterium kinetic isotope effects. The monograph by Melander and Saunders5 covers the entire area particularly well. For this reason, only a brief summary of the theory of kinetic isotope effects as well as their important uses in the determination of reaction mechanism and transition-state geometry will be presented. 

Glad, S.S. and Jensen, F. (1997). Kinetic isotope effects and transition state geometries. A theoretical investigation of E2 model systems. J. Org. Chem. 62, 253-260... 

Despite the fact that numerical integration is involved, pseudoanalytical procedures have been developed for calculation of first and second energy derivatives. This means that density functional models, like Hartree-Fock models are routinely applicable to determination of equilibrium and transition-state geometries and of vibrational frequencies. 

All three models show broadly similar behavior. Errors associated with replacement of exacf reactant and transition-state geometries by AMI geometries are typically on the order of 2-3 kcal/mol, although there are cases where much larger errors are observed. In addition, AMI calculations failed to locate a reasonable transition state for one of the reactions in the set, the Cope rearrangement of 1,5-hexadiene. 

Both 3-21G and 6-3IG Hartree-Fock models provide better and more consistent results in supplying reactant and transition-state geometries than the AMI calculations. Also the two Hartree-Fock models (unlike the AMI model) find reasonable transition states for all reactions. With only a few exceptions, activation energies calculated using approximate geometries differ from exact values by only 1-2 kcal/mol. 

The recommendations are clear. While semi-empirical models appear to perform adequately in most cases in the role of supplying reactant and transition-state geometries, some caution needs to be exercised. On the other hand, structures from small-basis-set Hartree-Fock models turn in an overall excellent account. The 3-2IG model, in particular, would appear to be an excellent choice for supplying transition-state geometries for organic reactions, at least insofar as initial surveys. 

A second set of comparisons assesses the consequences of use of approximate reactant and transition-state geometries for relative activation energy calculations, that is, activation energies for a series of closely related reactions relative to the activation energy of one member of the series. Two different examples have been provided, both of which involve Diels-Alder chemistry. The first involves cycloadditions of cyclopentadiene and a series of electron-deficient dienophiles. Experimental activation energies (relative to Diels-Alder... 

In terms of mean absolute error, choice of reactant and transition-state geometry has very little effect on calculated relative activation energies. Nearly perfect agreement between calculated and experimental relative activation energies is found for 6-3IG calculations, irrespective of whether or not approximate geometries are employed. Somewhat larger discrepancies are found in the case of MP2/6-31G calculations, but overall the effects are small. 

Chapter 1 introduces Potential Energy Surfaces as the connection between structure and energetics, and shows how molecular equilibrium and transition-state geometry as well as thermodynamic and kinetic information follow from interpretation of potential energy surfaces. Following this, the guide is divided into four sections ... 

Scheme 11 Carbenium-iminium ion conversion of 22 into 17 schematic representation of the computed reactant and transition state geometries as well as reaction energies. The trigonal planar environments of the carbenoid carbons are shaded in gray. The water molecule participating in the transition state is circled by a dotted line...

P. Y. Ayala and P. B. Schlegel, A combined method for determining reaction paths, minima and transition state geometries, J. Chem. Phys., 107 (1997) 375. 

Endo and exo additions require different approach and transition state geometries as shown below ... 

Ab initio MO Theory Good if large basis sets of orbitals are used and post-FI-F calculations are performed Equilibrium and transition state geometries reaction energy calculations Poor Medium to high depends on basis set if post-FI-F calculations are done, cost is very high Upto 50 atoms... 

Calculations using conventional TST and the Bigeleisen-Wolfsberg [16] treatment for isotope effects have demonstrated that thd = 1-44 is a useful benchmark for primary hydrogen isotope effects. Using empirical harmonic force fields and various reactant-state and transition-state geometries, More O Ferrall and Kouba [30] found, for proton-transfer models, that the exponents were within 2% of the 1.44 value, and similar computational approaches gave Xhd = 1.43-1.45 (343 K)... 

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