Transition structure computational characterization

Orbital-based methods can be used to compute transition structures. When a negative frequency is computed, it indicates that the geometry of the molecule corresponds to a maximum of potential energy with respect to the positions of the nuclei. The transition state of a reaction is characterized by having one negative frequency. Structures with two negative frequencies are called second-order saddle points. These structures have little relevance to chemistry since it is extremely unlikely that the molecule will be found with that structure. 

The stereochemistry of the reaction between alkenes and isocyanates has been studied experimentally [117] and computationally [109]. It was found that the concerted nature of the reaction should result in retention of configuration of the starting olefin. However, in one case in which a strong Ji-donor was present it was possible to characterize a stepwise mechanism (Scheme 37). Reaction between vinyl alcohol (147) and chlorosulfonyl isocyanate (148) was calculated to proceed at the MP2(SCRF)/6-31G //RHF(SCRF)/6-31G level via zwitterionic intermediate (150), whose rotation about the C4-OH bond through transition structure (151) opens the possibility of a loss of stereoselectivity in this kind of reactions, a phenomenon observed in some cases in the reaction between (148) and vinyl ethers [118]. 

Computational Characterization of Diels-Alder Transition Structures... 

Because of the sharply avoided crossing in the region of the transition state for the [2, + 2 J concerted reaction and of the diradicaloid character of the critical points involved in the non-concerted process, the computation of this surface requires computational methods that transcend the SCF method. Recently this surface, and in particular the transition structure region, has been investigated in detail by ab initio molecular-orbital methods. The calculations have been performed at the MC-SCF level with minimal (STO-3G) and extended (4-31G) basis sets. The various critical points have been fully optimized with MC-SCF gradients and characterized by computing the corresponding Hessian matrices. 

Once a saddle point has been found and characterized by computing the Hessian, it must still be tested to determine that it is the transition structure for the desired reaction. The transition vector may indicate clearly enough that the reaction path connects the desired reactants and products. If not, it may be necessary to follow the reaction path down from the saddle point (perhaps only for a short distance) to be sure that the path leads to the correct reactants and products. 

Cossio et /. studied the aromaticity and regiochemislry of 1,3-dipolar cycloadditions computationally. They investigated the aromaticity of both transition structures and reaction products of the reactions scrutinized via NICS values evaluated at RCPs, which they consider as characterizing rings unambiguously. While the NICS values computed in solution are lower than those obtained in the gas phase, the differences are very smaU. Therefore, aromaticity docs not appear to be very sensitive to solvent effects in the compounds under study. 

A number of reactions of polar organometallics have been studied computationally by searching for transition structures on the path between reactants and products (see Reaction Path Following). Locally stable structures are stationary points on the potential energy surface that are characterized by having all real vibrations transition structures have a single imaginary vibration frequency. 

As discussed above, a number of recombinant Zn- and Cd-MTs from various species expressed as fusion proteins contained varying amounts of inorganic sulfide (S ) (up to 14 mole equiv) [27]. Compared to the absorption and CD spectra of Cd-MTs lacking S , those with present in the cluster structure are characterized by a red shift of the absorption envelope with a shoulder at about 280 nm and a new CD band at the same wavelength [27]. Similar spectral features have also been reported for S containing Zn(II)- or Cd(II)-phytochelatins [54,55]. The computer analysis of CD spectra of proteins between 240-180 nm is often used to determine their secondary structure elements such as the a-helix, 3-sheet, and random coil. However, this method cannot be applied to M -MTs (M = Zn, Cd), due to the presence of strong optically active metal-induced transitions in this spectral... 

Table 10.4 lists the rate parameters for the elementary steps of the CO + NO reaction in the limit of zero coverage. Parameters such as those listed in Tab. 10.4 form the highly desirable input for modeling overall reaction mechanisms. In addition, elementary rate parameters can be compared to calculations on the basis of the theories outlined in Chapters 3 and 6. In this way the kinetic parameters of elementary reaction steps provide, through spectroscopy and computational chemistry, a link between the intramolecular properties of adsorbed reactants and their reactivity Statistical thermodynamics furnishes the theoretical framework to describe how equilibrium constants and reaction rate constants depend on the partition functions of vibration and rotation. Thus, spectroscopy studies of adsorbed reactants and intermediates provide the input for computing equilibrium constants, while calculations on the transition states of reaction pathways, starting from structurally, electronically and vibrationally well-characterized ground states, enable the prediction of kinetic parameters. 

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