Xa-Scattered Waves

Let us briefly comment on the Xa scattered-wave (SW) method [174,175] which does not involve MuUiken s population analysis. 

B. Self-consistent Field-Xa-Scattered-Wave Calculations... 

The procedure for calculating energy level diagrams by the self-consistent field Xa scattered wave (SCF-Xa-SW) method is as follows (Sherman, 1984, 1991). An octahedral cluster such as [FeO6]10 is partitioned into a set of (overlapping) spheres centred about divalent iron and each oxygen atom, and these are surrounded by an outer sphere. Within each atomic sphere the one-electron Schrodinger equation... 

In the Xa scattered wave approximation, the exchange potential for spin-up electrons may be different from that for spin-down electrons. In particular, when unpaired electrons are present, the exchange potentials, and hence the spin-up and spin-down orbitals and their energy levels, are different. Thus, MO calculations are performed using a spin-unrestricted formalism so that separate orbital energy levels are given for spin-up (a) and spin-down (p) electrons. 

Vaughan, D. J., Tossell, J. A. Johnson, K. H. (1974) The bonding of ferrous iron to sulfur to sulfur and oxygen in tetrahedral coordination A comparative study using SCF-Xa-scattered wave molecular orbitals calculations. Geochim. Cosmochim. Acta, 38, 993-1005. 

The SCF-Xa Scattered-wave Method.—An alternative to the LCAO-MO method for molecules is the Xa scattered wave or multiple-scattering Xa method, which was suggested less than 10 years ago114 and now has an extensive literative. The basic theory has been refined in several directions115 and there are several excellent reviews.116-180 The method is based on the scattered-wave method in solids181 and aims to solve the Fock equation,... 

Results obtained by this method have been compared with the Xa scattered-wave results for FeCU anions.144 Results for ferrocene compare well with ab initio results and experiment.145 They appear to give better ionization potentials than the ab initio results of Veillard.83 This method has several clear advantages. The use of the LCAO form avoids the muffin-tin potentials and may make the method more easily visualizable for chemists. The numerical integration imposes no restriction on the form of the basic functions. STOs can be used as readily as CGTOs. The Ni problem is avoided since only N2 matrix elements need be stored. 

The cluster approach is, like the extended-surface approach, characterized by many different calculational schemes. A recent review stresses electronic aspects of bonding. In this review we have chosen to concentrate on geometric aspects. We shall discuss a number of major techniques in order of increasing computational complexity the extended H uckel theory, self-consistent Xa scattered wave calculations, and self-consistent ab initio Hartree-Fock and valence bond methods. In that order these techniques allow increasing accuracy. However, the cluster size must decrease simultaneously due to calculational complexity, ultimately reducing the degree of analogy with surfaces. 

SCF-Xa-SW self-consistent field, Xa, scattered wave (form of MO theory)... 

I Extended Hiickel (9), Xa Scattered Wave (15), semiempirical SCF methods 16)) gave way to more sophisticated treatments, based both on ab initio Hartree-Fock SCF (17), Cl (18-20)) and on local density methods (DVM-Xa, 22), LCGTO-Xa (23), LCGTO-LSD-MP (24))- These more elaborate studies furnish structural and energetic information on chemisorption bonds -within the restriction of a local cluster model (9), of course. 

Table I summarizes the results of our calculations, along with previous work on two- and three-iron clusters. As we have noted before, the general tendency of the Xa scattered wave method is to overestimate J for example, the experimental estimate of J for the oxidized linear three-iron cluster (18) is 300 cm, about 45% lower than the value we estimate. Estimates for J in oxidized two-iron clusters are smaller than our estimates by similar amounts (6). We expect the behavior to be about the same for the reduced species, but that the qualitative trends should be correct. We have discussed the results of the oxidized three-iron clusters in our previous paper (9), showing that the Xa calculations predict a ground state for the...

A detailed analysis of the UV-VIS spectrum of (spinach) plasto-cyanin in the Cu(II) state has been reported (56). A Gaussian resolution of bands at 427, 468, 535, 599, 717, 781, and 926 nm is indicated in Fig. 7. Detailed assignments have been made from low-temperature optical absorption and magnetic circular dichroic (MCD) and CD spectra in conjunction with self-consistent field Xa-scattered wave calculations. The intense blue band at 600 nm is due to the S(Cys) pvr transition, which is intense because of the very good overlap between ground- and excited-state wave functions. Other transitions which are observed implicate, for example, the Met (427 nm) and His (468 nm) residues. These bonds are much less intense. The low energy of the d 2 orbital indicates a reasonable interaction between the Cu and S(Met), even at 2.9 A. It is concluded that the S(Cys)—Cu(II) bond makes a dominant contribution to the electronic structure of the active site, which is strongly influenced by the orientation of this residue by the... 

TTie three methods that have been most widely adopted to calculate DOS curves for clusters are (/) the semi-empirical extended-Huckel (EH) method, (n) the complete-neglect-of-differential-overlap (CNDO) method, and iii) the self-consistent-field Xa scattered-wave (Xa-SW) method. Calculations of electronic structures of many transition- and noble-metal clusters have been reported over the last decade. No attempt is made to summarize them all, because there appears to be a disparity of view among the expert practitioners as to the validities of the various methods of calculation. However, the story to date is as follows. 

We next inquire whether this result is consistent with other physical properties of uranocenes. Bulk magnetic susceptibility measurements at low temperature on several substituted uranocenes appear to suggest that within experimental error the magnetic properties of all uranocenes are essentially identical and equal to 2.4 0.2 B.M. (Table VII). This result is consistent with the idea confirmed by Xa Scattered Wave (47) and Extended Huckel MO (48) calculations that the magnetic properties of uranocenes are determined principally by the two unpaired electrons that are primarily metal electrons. 

The ease with which the geometry of the metal-carbene complexes can adjust to accommodate the incoming olefin may be an important factor in determining the rate and stereoselectivity in a given metathesis reaction (Lee, J.B. 1981). Extended Hiickel MO calculations on Ti(=CH2)L2, where L = H, Cl, Cp, have shown that the completely planar molecule is easily distorted into a flattish pyramid with Ti at the apex, ready to receive the incoming donor olefin (Gregory 1985). Similarly, calculations employing the self-consistent-field-Xa-scattered-wave method on Mo(=CH2)(=NH)(OMe)2 show that the reaction with ethene at the COO faee to... 

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