Theoretical MO calculations

In order to consider the inversion of Qx(0,0) and Qy(0,0) electronic transition intensities in NH-tautomers of non-symmetrical free-base porphyrins we calculated the ground-state orbital energies of the investigated molecules by a CNDO/2 method using the symmetrized crystal geometry of porphyrin molecule (37,38). On the basis of the above experimental results we must introduce a motionless system of molecular X and Y axes, identically fixed in both tautomers. Then using theoretical MO calculations and the analysis... 

The detailed studies of the surface of CdS nanocrystallites prepared in N,N-dimethylformamide (CdS-DMF) by means of emission measurements, in-situ Cd K-edge EXAFS analysis, and theoretical MO calculations reveal the correlation of the photocatalysis of CdS-DMF and the formation of sulfur vacancies on its surface. It has been experimentally proved that CO2 interacts with the sulfur vacancies and is converted into its radical anion under irradiation as an intermediate in the photocatalysis. The knowledge on the photocatalysis obtained above has led to the achievement of the photofixation of CO2 into benzophenone, acetophenone and benzyl halides under visible light irradiation in the presence of TEA as an electron donor. 

Not accounting for any correlation energy, theoretical MO calculations heavily overestimate ionization potentials. 

These are all empirical measurements, so the model of the harmonic oscillator, which is pur ely theoretical, becomes semiempirical when experimental information is put into it to see how it compares with molecular vibration as determined spectroscopically. In what follows, we shall refer to empirical molecular models such as MM, which draw heavily on empirical information, ab initio molecular models such as advanced MO calculations, which one strives to derive purely from theory without any infusion of empirical data, and semiempirical models such as PM3, which are in between (see later chapters). 

The molecular and liquid properties of water have been subjects of intensive research in the field of molecular science. Most theoretical approaches, including molecular simulation and integral equation methods, have relied on the effective potential, which was determined empirically or semiempirically with the aid of ab initio MO calculations for isolated molecules. The potential parameters so determined from the ab initio MO in vacuum should have been readjusted so as to reproduce experimental observables in solutions. An obvious problem in such a way of determining molecular parameters is that it requires the reevaluation of the parameters whenever the thermodynamic conditions such as temperature and pressure are changed, because the effective potentials are state properties. 

Neither N -labeling, nor kinetic measurements, nor theoretical reasoning on the basis of MO-calculations enable one to rule out either of these alternatives [cf. Eqs. (3) and (5)]. This problem obviously requires an unconventional approach, and a two-phase experiment seems to provide the basis for discriminating. 

There have, however, been attempts to correlate Q-e values and hence reactivity ratios to, for example, c NMR chemical shifts 50 or the results of MO calculations 51153 and to provide a better theoretical basis for the parameters. Most recently, Zhan and Dixon153 applied density functional theory to demonstrate that Q values could be correlated to calculated values of the relative free energy for the radical monomer reaction (PA + Mn — PA ). The e values were correlated to values of the electronegativities of monomer and radical. 

One may ask whether this problem could have been solved by theoretical work. However, in 1973 no reliable results from MO calculations were available (see Sec. 8.4, particularly the statement by Castenmiller and Buck, 1977). It was not until 19 years later that Glaser s group (Horan et al., 1992) provided a comprehensive theoretical basis for dediazoniation of arenediazonium ions. 

What has been reported in the previous subsections does not amount to an exhaustive review of the existing literature on MO calculations for sulphones and sulphoxides— which is, anyway, not particularly rich. It must be said that the treatment of the S—O bond poses special problems, and is therefore less attractive for the theoretical chemist. A search was nevertheless conducted, and what follows provides nearly all the existing entry points to the theoretical literature of sulphone and sulphoxide compounds. 

In this review, we consider the application of quantum-chemical calculations to a range of sulfur-rich compounds. The empirical, semiempirical and ab initio MO calculations published before 1980 are considered rather inadequate. Therefore, theoretical calculations before 1980 will not be mentioned in detail here. 

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. 

A comprehensive review of the preparation, reactions, and n.m.r. spectra of phosphorus-fluorine compounds has appeared. This year s literature has been notable for the first detailed applications of ab initio SCF-MO calculations to the problems of bonding in halogenophosphines and their derivatives. - Comparison of the results of such theoretical calculations with experimental data obtained from photoelectron spectra shows a good correlation in the case of phosphorus trichloride and phosphoryl chloride, and of phosphorus trifluoride and its borane complex. ... 

As in previous volumes, the abbreviations P" , P, P etc. refer to the co-ordination number of phosphorus. Where convenient the compounds in each section are dealt with in this order. A number of theoretical studies such as MO calculations are briefly discussed. They are placed in the sections where they are of most relevance. 

The reactivity index is the conventional theoretical quantity which is used as a measure of the relative rate of reactions of similar sort occurring in different positions in a molecule or in different molecules. As has already been mentioned in Chap. 2, most reactivity indices have been derived from LCAO MO calculations for unicentric reactions of planar n electron systems as). The theoretical indices for saturated molecules have also been put to use B0>. In the present section the discussion is limited to the indices derived from the theory developed in the preceding sections, since the other reactivity indices are presented in more detail than the frontier-electron theory in the usual textbooks 65,86) jn this field. 

A thiepin is formally isoelectronic with the 8ic-electron 1,3,5,7-cyclooctatetraene and 1,3,5-cycloheptatrienide ion and, if planar, may actually be antiaromatic. Recently, the question of the antiaromaticity of thiepin has been the subject of interest for both synthetic and theoretical chemists. The apparent instability of the thiepin ring system is in good agreement with theoretical calculations. Dewar and Trinajstic 68) have reported that the thiepin is considered to be weakly antiaromatic (RE = — 1.45 kcal mol-1) based on PPP SCF MO calculations. On the other hand, Hess Jr. and Schaad 69) have found it to be substantially antiaromatic (RE = —0.232 J) by using the Huckel MO method. This result was also supported by a graph-theoretical treatment by Aihara 70). 

The electron spin resonance (ESR) spectra of free radicals obtained by electrolytic or microsomal reduction of several potential antiprotozoal 1,2,5-oxadiazoles were characterized and analyzed. Ab initio MO calculations were performed to obtain the optimized geometries, and the theoretical hyperfine constant was carried out using Zerner s intermediate neglect of differential overlap (ZINDO) semi-empirical methodology. DFT was used to rationalize the reduction potentials of these compounds <2003SAA69>. 

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