Paired-permanent-determinant

A spin-free approach for valence bond (VB) theory, based on symmetric group techniques, is introduced in this chapter. Bonded tableaux (BT) are adopted to represent VB structures, and a paired-permanent-determinant algorithm is developed to solve the so-called IV problem in the nonorthogonal VB method, followed by the introduction of our ab initio VB program, Xiamen-99. Furthermore, applications of ab initio VB method to the resonance effect, chemical reactions, and excited states are carried out by the Xiamen package. 

The arrangement of this chapter will be as following. Firstly, we discuss the construction of the bonded tableau basis and its properties. Secondly, the paired-permanent-determinant method is derived, followed by the introduction of our Xiamen-99 ab initio VB program. Then we show the applications of the ab initio VB method to the resonance effect, chemical reactions, as well as to excited states. Finally, we give a brief summary and an outlook for our future work. 

PAIRED-PERMANENT-DETERMINANT ALGORITHM FOR NONORTHOGONAL VALENCE BOND METHOD... 

In this section, a new function, called paired-permanent-determinant (PPD), is introduced, which is an algebrant. An overlap matrix element in the spin-free VB method may be obtained by evaluating a corresponding PPD, while the Hamiltonian matrix element is expressed in terms of the products of electronic integrals and sub-PPDs. 

The first group of tests is carried out on specimens generally fabricated into a dumb-bell shape, with forces applied uniaxially. The usual apparatus consists of a machine with a pair of jaws, which during the test are moved relative to each other, either together or apart, in a controlled manner. A chart recorder is employed to give a permanent record of the results obtained, so that the force at fracture can be determined. Whether this kind of set up measures tensile, compressive, or flexural strength depends on how the sample is oriented between the jaws, and on the direction that the jaws are set to travel relative to one another. 

In cases where only enantiomers are formed, the absolute configuration needs to be determined. This situation occurs when the reaction does not involve the permanent attachment of a group containing a chiral unit to the substrate (e.g., use of a chiral reagent52 or a chiral catalyst53) and only one chiral unit is created or in cases where more than one chiral unit is formed, the mechanism of the reaction ensures that only one pair of enantiomers can result (cf. the Sharpless epoxidation, p 403). 

In water, four valence electrons form two lone pair orbitals that have been determined (Pople, 1951) to point above and below the plane formed by the three nuclei (H—O—H) of the molecule. The shared electrons with the protons give the molecule two positive charges, and the lone pair electrons give the molecule two negative charges. The result is a molecule with four charges and a permanent electric dipole (McCelland, 1963) of 1.84 Debye. 

Electron transfer induced by charge-transfer irradiation (Eqs 12-14) might or might not lead to permanent chemical transformations that yield isolable photoproducts. The fate of the initial electron-transfer intermediate (viz., ion-radical pair or radical pair) is mainly determined by the competition of two pathways, i.e. back electron transfer or the follow-up reaction (see Scheme 1). If the former pathway predominates and the follow-up reaction cannot efficiently compete, the ion-radical or radical pair returns back to the original EDA complex and no net reaction is observed. On the other hand, if the rate of the follow-up reaction is in the same range as that of the back electron transfer, new intermediates and ultimately photoproducts will be formed that do not convert back to the starting materials, and thus an electron-transfer activated reaction is obtained. 

It has been seen in Section III,B,2 that in general more than 80% of the whole dissipated energy appears at a given moment as electronic excitation. The excited states have generally short lifetime they are therefore considered here as transient, compared to the lattice defects, which are indeed quasi-permanent. The influence of these various electronic imperfections upon the properties of solids, and more specially upon their catalytic properties is still little known. However, a simplified view of the problem results when considering only the pairs of excess free carriers produced in the course of irradiation. These tend to recombine and then stationary concentration depends simultaneously on both the recombination time and the intensity of the incident radiation. As soon as the irradiation ceases, this stationary concentration rapidly recovers the thermal equilibrium value. The problem hence reduces to the determination of the conditions under which the stationary concentration of the free carriers under irradiation will differ notably from the thermal equilibrium value. 

In general, in dispersions of fine particles in a liquid, frequent encounters between particles occur through Brownian motion. Whether such encounters result in permanent contact or whether the particles rebound and remain free is determined by the forces between them. A dispersion is colloidally stable when its particles remain permanently free. In dilute dispersions it is sufficient to consider only interactions between pairs of particles (Overbeek, 1977). This would be the case for cloudy apple juice (CAJ) where the volume fraction of particles is less than 0.5% (Genovese and Lozano, 2000). 

Determine which are definite solvents (clear solutions) and non-solvents for the polymer at a given % weight concentration (say, 10-15%w) and note down examples of borderline solvent (turbid solutions). Very often this gives a clue to the area where solvency can be expected on a solubility map (Figure 2.10). Pairs of solvents and diluents are then selected which make cross-sections through this area. Approximately lOg of solution are weighed out accurately and titrated to a permanent turbidity with a diluent (or mixture of diluents). 

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