Energy surfaces reaction

Fig. 4.7 Reaction energy surfaces for the first and second aquation reactions of cisplatin starting from (a) the syn arrangement of the initial reactant complex and (b) the...

Graphical pre- and postprocessor for semiempirical molecular orbital programs extended Hiickel, MOPAC, and ZINDO. Structure building from library of fragments and molecules manipulation. Stick, ball-and-stick, and space-filling display. Orbital, electron density, and electrostatic maps. Reaction energy surfaces. IR and UV spectra. MM2 energy minimization. Dynamics. 

The specific topic of interest here, i.e. the search for methodologies which are able to describe with the necessary accuracy both conformational and reaction energy surfaces in hybrid QM/MM models for relatively large molecules, has given rise to a considerable number of papers. Some have been already quoted we report here a further selection Singh and Kollman (1986), Eckert et al. (1990), Kawamura-Kuribayashi (1992), Ferenczy et al. (1992), Thery et al. (1994), Maseras and Morokuma (1995), to which all papers referred to the above quoted combined QM/MM methods must be added. 

Within a valence bond approach (Chapter 7), the reaction energy surface can be considered as arising from the interaction of two diabatic surfaces. The adiabatic surface can be generated by solving a 2 x 2 secular equation involving the reactant and product... 

The reaction apparently involves no hydrogen shifts or interchange of carbons and appears to be the result of a 1,3-shift of carbon/" However, subsequent work has revealed that the reaction energy surface is rich in complexity. 

Figure Al.6.10. (a) Schematic representation of the three potential energy surfaces of ICN in the Zewail experiments, (b) Theoretical quantum mechanical simulations for the reaction ICN ICN [I--------------...

Because of the general difficulty encountered in generating reliable potentials energy surfaces and estimating reasonable friction kernels, it still remains an open question whether by analysis of experimental rate constants one can decide whether non-Markovian bath effects or other influences cause a particular solvent or pressure dependence of reaction rate coefficients in condensed phase. From that point of view, a purely... 

Syage J A, Felker P M and Zewail A H 1984 Picosecond dynamics and photoisomerization of stiibene in supersonic beams, ii. Reaction rates and potentiai energy surface J. Chem. Phys. 81 4706-23... 

There are significant differences between tliese two types of reactions as far as how they are treated experimentally and theoretically. Photodissociation typically involves excitation to an excited electronic state, whereas bimolecular reactions often occur on the ground-state potential energy surface for a reaction. In addition, the initial conditions are very different. In bimolecular collisions one has no control over the reactant orbital angular momentum (impact parameter), whereas m photodissociation one can start with cold molecules with total angular momentum 0. Nonetheless, many theoretical constructs and experimental methods can be applied to both types of reactions, and from the point of view of this chapter their similarities are more important than their differences. 

The above discussion represents a necessarily brief simnnary of the aspects of chemical reaction dynamics. The theoretical focus of tliis field is concerned with the development of accurate potential energy surfaces and the calculation of scattering dynamics on these surfaces. Experimentally, much effort has been devoted to developing complementary asymptotic techniques for product characterization and frequency- and time-resolved teclmiques to study transition-state spectroscopy and dynamics. It is instructive to see what can be accomplished with all of these capabilities. Of all the benclunark reactions mentioned in section A3.7.2. the reaction F + H2 —> HE + H represents the best example of how theory and experiment can converge to yield a fairly complete picture of the dynamics of a chemical reaction. Thus, the remainder of this chapter focuses on this reaction as a case study in reaction dynamics. 

Many potential energy surfaces have been proposed for the F + FI2 reaction. It is one of the first reactions for which a surface was generated by a high-level ab initio calculation including electron correlation [47]. The... 

At the time the experiments were perfomied (1984), this discrepancy between theory and experiment was attributed to quantum mechanical resonances drat led to enhanced reaction probability in the FlF(u = 3) chaimel for high impact parameter collisions. Flowever, since 1984, several new potential energy surfaces using a combination of ab initio calculations and empirical corrections were developed in which the bend potential near the barrier was found to be very flat or even non-collinear [49, M], in contrast to the Muckennan V surface. In 1988, Sato [ ] showed that classical trajectory calculations on a surface with a bent transition-state geometry produced angular distributions in which the FIF(u = 3) product was peaked at 0 = 0°, while the FIF(u = 2) product was predominantly scattered into the backward hemisphere (0 > 90°), thereby qualitatively reproducing the most important features in figure A3.7.5. 

Figure A3.7.7. Two-dimensional contour plot of the Stark-Wemer potential energy surface for the F + H2 reaction near the transition state. 0 is the F-H-H bend angle.

Wliat is left to understand about this reaction One key remaining issue is the possible role of otiier electronic surfaces. The discussion so far has assumed that the entire reaction takes place on a single Bom-Oppenlieimer potential energy surface. Flowever, three potential energy surfaces result from the mteraction between an F atom and FI,. The spin-orbit splitting between the - 12 and Pi/2 states of a free F atom is 404 cm When... 

In the statistical description of ununolecular kinetics, known as Rice-Ramsperger-Kassel-Marcus (RRKM) theory [4,7,8], it is assumed that complete IVR occurs on a timescale much shorter than that for the unimolecular reaction [9]. Furdiemiore, to identify states of the system as those for the reactant, a dividing surface [10], called a transition state, is placed at the potential energy barrier region of the potential energy surface. The assumption implicit m RRKM theory is described in the next section. 

To calculate N (E-Eq), the non-torsional transitional modes have been treated as vibrations as well as rotations [26]. The fomier approach is invalid when the transitional mode s barrier for rotation is low, while the latter is inappropriate when the transitional mode is a vibration. Hamionic frequencies for the transitional modes may be obtained from a semi-empirical model [23] or by perfomiing an appropriate nomial mode analysis as a fiinction of the reaction path for the reaction s potential energy surface [26]. Semiclassical quantization may be used to detemiine anliamionic energy levels for die transitional modes [27]. 

Variational RRKM calculations, as described above, show that a imimolecular dissociation reaction may have two variational transition states [32, 31, 34, 31 and 36], i.e. one that is a tight vibrator type and another that is a loose rotator type. Wliether a particular reaction has both of these variational transition states, at a particular energy, depends on the properties of the reaction s potential energy surface [33, 34 and 31]- For many dissociation reactions there is only one variational transition state, which smoothly changes from a loose rotator type to a tight vibrator type as the energy is increased [26],... 

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