Quantum chemical calculations energy surfaces

Quantum chemical calculations need not be limited to the description of the structures and properties of stable molecules, that is, molecules which can actually be observed and characterized experimentally. They may as easily be applied to molecules which are highly reactive ( reactive intermediates ) and, even more interesting, to molecules which are not minima on the overall potential energy surface, but rather correspond to species which connect energy minima ( transition states or transition structures ). In the latter case, there are (and there can be) no experimental structure data. Transition states do not exist in the sense that they can be observed let alone characterized. However, the energies of transition states, relative to energies of reactants, may be inferred from experimental reaction rates, and qualitative information about transition-state geometries may be inferred from such quantities as activation entropies and activation volumes as well as kinetic isotope effects. 

Clearly a quantum chemical calculation of the energy surface for this reaction would have to be based on a multiconfigurational wave function, with four active orbitals, the k orbitals of the two ethene molecules, and four active electrons. However, a complication appears cyclobutane is a quadratic molecule with all four carbon-carbon bonds equal. Our wave function does not have this property. The CC bonds between atoms A and B are treated using... 

Quantum chemical calculations at MP2/6-31G(d) level for SiHg-substituted model structures predict that only the 3-ewrfo-silylbicyclobutonium cation structure 433 is at a minimum on the potential energy surface, while the 3-exo cation structure exo-433 has one imaginary frequency and thus corresponds to a transition state. The calculated structures of endo- and exo-433 are given in Figure 23. 

Other theoretical studies discussed above include investigations of the potential energy profiles of 18 gas-phase identity S 2 reactions of methyl substrates using G2 quantum-chemical calculations," the transition structures, and secondary a-deuterium and solvent KIEs for the S 2 reaction between microsolvated fluoride ion and methyl halides,66 the S 2 reaction between ethylene oxide and guanine,37 the complexes formed between BF3 and MeOH, HOAc, dimethyl ether, diethyl ether, and ethylene oxide,38 the testing of a new nucleophilicity scale,98 the potential energy surfaces for the Sn2 reactions at carbon, silicon, and phosphorus,74 and a natural bond orbital-based CI/MP through-space/bond interaction analysis of the S 2 reaction between allyl bromide and ammonia.17... 

Once the thermodynamic parameters of stable structures and TSs are determined from quantum-chemical calculations, the next step is to find theoretically the rate constants of all elementary reactions or elementary physical processes (say, diffusion) relevant to a particular overall process (film growth, deposition, etc.). Processes that proceed at a surface active site are most important for modeling various epitaxial processes. Quantum-chemical calculations show that many gas-surface reactions proceed via a surface complex (precursor) between an incident gas-phase molecule and a surface active site. Such precursors mostly have a substantial adsorption energy and play an important role in the processes of dielectric film growth. They give rise to competition among subsequent processes of desorption, stabilization, surface diffusion, and chemical transformations of the surface complex. 

Let the lifetime of particles in the surface layer be sufficiently long for equilibrium in activationless association processes to be established. For this, not very strict, approximation, the concentration of any particle is estimated based on the Gibbs energy. The latter can be extracted from quantum-chemical calculations. These calculations allow one to determine the moments of inertia and vibrational frequencies and, hence, not only the internal energy but also the enthalpy and entropy of a system. 

In view of the accuracy of today s quantum chemical calculations, it is typically necessary to adjust the initial estimates of the potential energy surface to describe the observed kinetics of a catalytic process. Accordingly, the theoretical results presented in Table V provide only initial guesses for the entropies and enthalpies of the stable species and reactive intermediates involved in ethane hydrogenolysis on platinum. 

The quantum-chemical calculations play an important role in investigation of electronic structure and stability of fullerenes. The relative positioning of the pentagons which set the surface curvature of fullerene molecule, presence of condensed hexagons, electronic effects - all of these factors define a total energy of a fullerene molecule and its stability or instability. The analysis has shown that the most stable fullerenes have minimal total energies among their isomers. Nevertheless, the reasons of why some fullerenes can be obtained and others cannot are not clear yet. 

In this section we will present results of ab initio molecular dynamics simulations performed for more complex chemical reactions. Catalytic copolymerization of a-olefins with polar group containing monomers, chosen here as an example, is a complex process involving many elementary reactions. While for many aspects of such a process the standard approach by static quantum chemical calculations performed for the crucial reaction intermediates provides often sufficient information, for some aspects it is necessary to go beyond static computations. In the case of the process presented here, MD was priceless in exploring the potential energy surfaces for a few elementary reactions that were especially difficult for a static approach, due to a large number of alternative transition states and thus, alternative reaction pathways.77... 

X-ray structure determination is used as a constant in the quantum chemical calculation (and all other parameters fully optimized), the energy is only 1.5 kcal/mol higher than that of the free optimized molecule as a consequence of the flat potential energy surface for the B-N bond. 

In this section we shall discuss the results of quantum-chemical calculations of the chemisorption interaction of the surface terminal hydroxyl groups in silicas with water and ammonia molecules. Two types of one-center coordination of H20 molecules by a hydroxyl group of Si02 are presented in Fig. 3. CNDO/BW calculations using these clusters gave adsorption energies... 

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