Slater transition state

Ziegler T, Rauk A (1979) CO, CS, N2, PF3 and CNCH3 as donors and acceptors. A theoretical study by the Hartree-Fock-Slater transition state method. Inorg Chem 18 1755 ... 

XAS, on the other hand has a core-excited final state for which the effect of the core-hole must be taken into account. To obtain the full spectrum, i.e., valence, Rydberg and continuum excitations, we use the Slater transition-state approach [22,23] with a half-occupied core-hole. This provides a balanced description of both initial and final states allowing the same orbitals to be used to describe both initial and final states and all transitions are obtained in one calculation [23,24]. Details of the computational procedure can be found in the original papers as referenced in the following sections. In the present chapter, the focus is on the surface chemical bond and the spectra, measured or calculated, will mainly be used to obtain the required information on the electronic structure. 

The interaction of formaldehyde and thioformaldehyde with some group 8 metal-ligand fragments [Ru(CO)4,40 Fe(CO)2(PH3)241] in the rf conformation has been analyzed by the Hartree-Fock-Slater transition-state method... 

T. Ziegler and A. Rauk, Inorg. Chem., 18, 1755 (1979). CO, CS, PF3, and CNCH3 as a Donors and n Acceptors. A Theoretical Study by the Hartree-Fock-Slater Transition-State Method. 

A parameterization method of the Hamiltonian for two electronic states which couple via nuclear distortions (vibronic coupling), based on density functional theory (DFT) and Slaters transition state method, is presented and applied to the pseudo-Jahn-Teller coupling problem in molecules with an s2-lone pair. The diagonal and off-diagonal energies of the 2X2 Hamiltonian matrix have been calculated as a function of the symmetry breaking angular distortion modes and r (Td)] of molecules with the coordination number CN = 3... 

Different practical procedures for computing r) have been proposed, that range from the computation of the difference between the energy values of the highest occupied (HOMO) and the lowest unoccupied (LUMO) molecular orbitals [8,9], to the atom in molecules based models [10, 11], to the charge sensitivity analysis [12, 13], to the use of Slater transition state theory [14], to the Janak s extension of DFT for fractional occupancies [15, 16]. Recently, Neshev and Mineva have proposed a scheme for the construction of the internally resolved hardness tensor in... 

In the last equation X is the Lagrange multiplier and can be interpreted, analogously to the Slater transition state formula [26], as the effective electronegativity, or the negative of the chemical potential. Using the set of equations 31, the response of the charge deviation with respect to the external potential (u) measured relative to... 

Figure 24 Comparison of experimental and calculated IE for 9a0 ferrocene (b) ruthenocene. Orbital energies (—ei) Slater transition state method (STS) ion state calculation (AE) Experimental values (Exp.) Correlation corrections (ADC(3)) ab initio ion state calculations (ASCF) Koopmans theorem (KT)...

Some form of MO theory is required to model photoelectron spectrum energies. Representative examples include the application of (1) HF theory to planar dithiophosphonate complexes of Ni", Pd" and Pt" [127], (2) the DVXa model to [M(Cp)2(CO)2] (M = Zr, Ti) [128], (3) the INDO method to halfopen metallocenes of Fe, Ru and Os [129] and (4) the Fenske-Hall method to [CpPt(CH3)3] and [Cp Pt(CH3)3] [130]. In all cases, reasonable qualitative agreement is found. Large but uniform deviations from Koopmans theorem results are noted in the HF calculations while the relaxation accompanying Slater Transition State calculations for the DVXa study show orbital energy changes of 3-4 eV. 

Table 1. Comparison of the Slater transition state (STS) calculations based on the relativistic Hedin-Ludquist local density potential with the experimental values obtained in the gas phase." All values arc given in eV...

In conclusion, the results described in the present article establish that reliable estimates of p, q and the isoelectronic changes in E, p and q for atoms can be made by using the Slater transition state and the Z-transition state calculations which make use of the fractional occupations and nuclear charges, respectively. These transition state procedures contribute further towards the computational power of the density functional theoretic models. 

MO s are mainly 0 2p lone pair in character, by running preliminary calculations on the model U(OH) li) I.E. s have been explicitly calculated using the Slater transition state formalism only for a few selected ground state MO s. The choice has been made according to the dominant atomic population (mainly ligand, metal 6d, and metal 5d based MO s) to evaluate the effects of differential relaxation energies (Table 2). It turned out, however, that these effects are comparable despite the difference in the atomic compositions of various orbitals (see Section 1.2). The most relevant Xa results are reported in Tables 3 and 4. 

The finite-difference approach becomes a more accurate approximation to the exact derivative if one uses a smaller step size in this case, that means using a fraction of an electron, AN. DFT is well suited for use with noninteger occupations. The Slater transition state formula [31], for example, uses half-integer occupations to approximate the electron affinity. Fractional occupations of orbitals are also commonly employed in the use of charge smearing to improve convergence of the self-consistent field (SCF) [32,33]. 

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