Bonded tableau

Z. Qianer, L. Xiangzhu, J. Mol. Struct. (THEOCHEM) 198, 413 (1989). Bonded Tableau Method for Many Electron Systems. 

X. Li, Q. Zhang, Int. J. Quant. Chem. XXXVI, 599 (1989). Bonded Tableau Unitary Group Approach to the Many-Electron Correlation Problem. 

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. 

BONDED TABLEAU VALENCE BOND APPROACH 2.1 Bonded tableau basis... 

In VB theory, all electrons are assigned to localized two-centered bonds, lone pairs and impaired components. Each collective pattern of such components constitutes a VB structure. The corresponding VB structure function can be expressed as < , namely, a bonded tableau (BT) state as mentioned before. The wavefunction for the whole system is defined as the superposition of all possible VB structure functions... 

Of these two schemes, it appears that the standard tableaux functions have properties that allow more efficient evaluation. This is directly related to the occurrence of the J f on the outside of OAfVAf. Tableau functions have the most antisymmetry possible remaining after the spin eigenfunction is formed. The HLSP functions have the least. Thus the standard tableaux functions are closer to single determinants, with their many properties that provide for efficient manipulation. Our discussion of evaluation methods will therefore be focused on them. Since the two sets are equivalent, methods for writing the HLSP functions in terms of the others allow us to compare results for weights (see Section 1.1) of bonding patterns where this... 

The principal configurations in the wave function are shown as HLSP functions in Table 10.8 and as standard tableaux functions in Table 10.9. Considering the HLSP functions, the first is the ground state configuration of the separated atoms, the next two are bonding functions with the s-p hybrid of Be and the fourth contributes polarization to the Be2/ z component. The corresponding entries in the third and fourth columns of Table 10.9 do not include the tableau function with the orbital. 

The results for the standard tableaux functions at the energy minimum are shown in Table 11.16. Structures 1,2, 4, and 5 are different standard tableaux corresponding to two ground state atoms and represent mixing in different states from the ground configurations. The standard tableaux functions are not so simple here since they do not represent three electron pair bonds as a single tableau. Structure 3 represents one of the atoms in the first excited valence state and contributes to s-p hybridization in the cr bond as in the HLSP function case. 

Any elementary inorganic structure book will describe, in MO terms, the tt bonds in O2 as each having a doubly occupied bonding orbital and a singly occupied antibonding orbital. (This is the MO description of a three-electron bond.) We may analyze this description, using the properties of tableau functions, to see how it relates to the VB picture. 

A full valence calculation on CH4 gives 1764 standard tableaux functions, and all of these are involved in the 164 A1 sjmimetry functions. The second and fourth tableaux are also present in the principal constellation and, as with the earlier cases, these are not simple symmetry functions alone. The third tableau is ionic with the negative charge at the C atom. As before, this contributes to the relative polarity of the C—H bonds. 

The standard tableaux function representation is similar. The principal term is the same as the only term at i = oo, and together with the fourth term (the other standard tableau of the constellation) represents the two electron pair bonds of the double bond. The second and third terms are the same as those in the HLSP function representation and even have the same coefficients, since there is only one function of this sort. 

RMS root-mean-square SCVB spin coupled valence bond SDF Slater determinantal functions STF standard tableau function VB valence bond... 

Reviews (9, 63, 64) of the reactions between hydroxylated mineral surfaces and aqueous solutions brought out the richness of variety found in surface phenomena involving natural particles. Isolated surface complexes, the principal topic of this chapter, are expected when reaction times are short and the adsorbate content is low [Figure 6, inspired by Schindler and Stumm 63)]. Thus, surface complexes occupy a reasonably well-defined domain in the tableau of reaction time scale versus sorbate concentration. Localized clusters of adsorbate (47, 48, 65, 66) that contain two or more adsorbate ions bonded together can form if the amount sorbed is increased by accretion or bv the direct adsorption of polymeric species (multinuclear surface complexes). Surface clusters can erase the hyperfine structure in the ESR spectrum of an immobilized adsorbate (33, 67) or produce new second-neighbor peaks from ions like the absorber in its EXAFS spectrum (47, 66). 

It is therefore obvious that the chemistry of pure substances can be defined only on the basis of its objects of inquiry. But it should be noted that in the eighteenth century it were the chemists themselves who distinguished these objects of inquiry from other ones in their practices of classification. We argue that their distinction corresponds exactly with the boundaries of objects of inquiry in the tableau of the Meth-ode. The question raised above was whether the authors of the Methode were the first to see an inner bond among the many different activities with pure chemical substances scattered through all domains of chemistry, or whether their distinction of the particular sphere of the chemistry of pure substances followed a tradition established earlier. Fortunately, there exists unmistakable evidence for such a tradition. The famous tables of chemical affinities testify unambiguously to the existence of this particular chemical practice. The first of these tables was the Table des differents rapports constmctedby Etienne Francois Geoffroy (1672-1731), published in 1718. We can thus even determine when the distinction of operations with pure chemical substances first became manifest, namely approximately seventy years before the Tableau of 1787. 

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