Density functional transition states

Stanton, R. V., Merz, K. M., Jr., 1994, Density Functional Transition States of Organic and Organometallic Reactions , J. Chem. Phys., 100, 434. 

Density functional transition states and activation energies have their problems. Merrill et al. found that for the fluoride ion-induced elimination of HE fromCH3CH2F none of the 11 functionals tested (including B3LYP) was satisfactory, by comparison with high-level ab initio calculations. Transition states were often looser and stabler than predicted by ab initio, and in several cases a transition state could not even be found. They concluded that hybrid functionals offer the most promise, and that the ability of density functional methods to predict the nature of TSs demands a great deal more attention than it has received to date. [34]. Note that it is assumed here that... 

Figure 7 Quantum transmission coefficient for a symmetric double well potential interacting with a generic dissipative medium as a function of friction strength y. The barrier height is denoted b and (Ob is the imaginary frequency at the top of the potential barrier. Solid squares QUAPI results. Dashed line results of centroid-density quantum transition state theory, (a) Eb/kbT = 10 (activated regime with tunneling contributions), (b) Eb/kbT = 30 for the first six data points (at small friction) the temperature is below crossover. Data from Ref. 51...

A number of types of calculations can be performed. These include optimization of geometry, transition structure optimization, frequency calculation, and IRC calculation. It is also possible to compute electronic excited states using the TDDFT method. Solvation effects can be included using the COSMO method. Electric fields and point charges may be included in the calculation. Relativistic density functional calculations can be run using the ZORA method or the Pauli Hamiltonian. The program authors recommend using the ZORA method. 

Freezing transitions have been examined in recent years by density functional methods [306-313]. Here we review the results [298] of a modification of the Ramakrishnan-Yussouff theory to the model fluid with Hamiltonian (Eq. (25)) a related study of phase transitions in a system of hard discs in two dimensions with Ising internal states which couple anti-ferromagnetically to their neighbors is shown in Ref. 304. First, a combined... 

Ab initio Hartree-Fock and density functional theory calculations were performed to study the transition state geometry in intramolecular Diels-Alder cycloaddition of azoalkenes 55 to give 2-substituted 3,4,4u,5,6,7-hexahydro-8//-pyrido[l,2-ft]pyridazin-8-ones 56 (01MI7). 

By ab initio MO and density functional theoretical (DPT) calculations it has been shown that the branched isomers of the sulfanes are local minima on the particular potential energy hypersurface. In the case of disulfane the thiosulfoxide isomer H2S=S of Cg symmetry is by 138 kj mol less stable than the chain-like molecule of C2 symmetry at the QCISD(T)/6-31+G // MP2/6-31G level of theory at 0 K [49]. At the MP2/6-311G //MP2/6-3110 level the energy difference is 143 kJ mol" and the activation energy for the isomerization is 210 kJ mol at 0 K [50]. Somewhat smaller values (117/195 kJ mor ) have been calculated with the more elaborate CCSD(T)/ ANO-L method [50]. The high barrier of ca. 80 kJ mol" for the isomerization of the pyramidal H2S=S back to the screw-like disulfane structure means that the thiosulfoxide, once it has been formed, will not decompose in an unimolecular reaction at low temperature, e.g., in a matrix-isolation experiment. The transition state structure is characterized by a hydrogen atom bridging the two sulfur atoms. 

The molecular interpretation of major topics in catalytic kinetics will be highlighted based on insights on the properties of transition-state intermediates as deduced from computational chemical density functional theory (DFT) calculations. 

The gas phase partition function Qg s of the atom is the same however, since the atoms are immediately immobilized on a two-dimensional surface, we need to take the configuration of the adsorbed atoms into account in the transition state. Again we consider a surface containing M sites each with an area of a. The density of sites per area is Nq = M/A = 1 /a. The M sites are not necessarily free as some could be occupied already hence, the number of free sites will be M and 0 = M /M = (1-0a)-If we have N atoms adsorbed on these sites (we again use for the transition state Airmobile), the partition function for this system is given by... 

---