Double-substitution method

Wilson and Smith [21] drived equations for general multiple substitutions that can be used if the coordinates of only one of several substituted atoms arc unknown. Pioce [22] and others [23,24] have introduced the double substitution method to locate nuclei near a principal axis by taking secmid diffoences of ground state moments of inertia. This method has not found widespread application maybe because of the necessity for very precise data for a larger set of isotopomers. A formula to calculate an intemuclear distance in a linear molecule directly from the moments Iq of a parent molecule, two monosubstited species and the disubstituted isotopomer ([25],... 

Two special procedures employed in structure calculations will be mentioned here. One is the double substitution method introduced by Pierce26 and used for the determination of the coordinates of atoms near a principal inertial plane, which is the situation for which the Kraitchman equations become unreliable. In Pierce s method rotational constants must be available for four isotopic species, two of which are... 

The principal drawbacks of the double substitution method are the extra isotopic substitution required and the highly accurate rotational constants required for the second differences. While Pierce s method has been very successful in some cases, it has not had widespread usage. 

In this research, the coupled-cluster single and double substitutions method with a perturbative treatment of triple excitations CCSD(T) [16-18] was adopted based on unrestricted Hartree-Fock reference wave functions. For the CCSD(T) computations, the cc-pVDZ, cc-pVTZ, and cc-pVQZ quality basis sets were used, where cc-pVnZ is an abbreviation for the correlation-consistent polarized valence basis sets of Dunning et al. [19-22]. With the coupled-cluster methods used in this research, the core orbitals are frozen. That is, the Is-like molecular orbital is frozen for O, while the Is2s2p3s3p3d-like molecular orbitals are frozen for Br. 

A theoretical study has been carried out by Morokuma for the mechanism of Pt(0)-catalyzed alkyne and alkene diboration reactions with the B3LYP density functional method. The complexation energy between (0H)2B-B(0H)2 and Pt(PH3)2 has been calculated to be 3.7 kcal/mol, where the B-B and P-Pt-P axes are perpendicular to each other. The next step is the activation of the B—B bond, and the activation barrier has been calculated to be 12.5 kcal/mol, relative to the molecular complex (OH)2B— B(OH)2-Pt(PH3)2 or 8.8 kcal/mol relative to the reactants.In parallel, Sakaki theoretically investigated the insertion of Pt(PH3)2 into X2B—BX2 (X = H or OH) with the ab initio MO/MP4SDQ, SD-CI, and coupled cluster with double substitution methods. They found that this reaction proceeds with a moderate of 15 kcal/mol and a considerable of 20 kcal/mol for (OH)2B—B(OH)2. They noted that the B—B bond undergoes the insertion reaction of Pt(PH3)2 much more easily than does the C—C bond. Nowadays, the Pt-catalyzed diboration of terminal... 

Finally, the Hammett equation has been applied in a few instances to heterocycles of the indole-benzofuran type. The double p method of Eq. (3) was first designed for this type of system and was here applied. When this approach was originally proposed, the only truly hetero-cychc system to which it was apphed was the substituted phthahds 14, and pertinent data on the hydrolysis of these compounds are included in Table IX. 

Quadratic Cl (QCI) and coupled cluster (CC) exemplify more complex methods that are not strictly variational in character, but include physical corrections similar to those of higher-order perturbation theory. Keywords for these methods also include a specification of substitutions from the reference FIF configuration, such as QCISD or CCSD, respectively, for QCI or CC methods with all single and double substitutions. More complete descriptions of these methods are beyond the scope of this appendix. 

A number of methods have been proposed for calculations of the geometries of molecules in excited states. These include CIS (Configuration Interaction Singles) and variations on CIS to account for the effect of double substitutions, as well as so-called time dependent density functional models. Except for CIS (the simplest of the methods) there is very little practical experience. There is also very little solid experimental data on the geometries of excited-state molecules. 

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