Band orbital

As orbitals spread into bands, orbitals oriented for a or a bonds spread into the widest bands. 7t orbitals form narrower bands and 5 bonding orbitals form the narrowest bands. 

Jorgensen, C. K. Partly Filled Shells Constituting Anti-banding Orbitals with Higher Ioniza tion Energy than their Bonding Counterparts. Vol. 22, pp. 49—81. 

In a similar fashion, it usually sufiices to consider a single band of the solid. If the band orbitals are 1 Xk > (fc = 1, . N) with energies e, that part of Jff which refers to the band before it interacts with the atom is... 

The second type of time-dependent term, which couples 0> to the band orbitals and is therefore responsible for charge transfer, is... 

To solve (12) uniquely, we must impose the initial conditions which arise from the original state of the system (r = — oo)>. Considering a case where, initially, the valence orbital 0> of the atom is empty, then d>(— oo)> must represent a situation where the n band orbitals of lowest energy are doubly occupied by electrons, i.e. 

Further, the contact adsorption may reduce the reorganization energy, ) , of redox particles in electron transfer the distribution of electron levels of adsorbed redox particles may be narrower than that of simply hydrated redox particles as shown in Fig. 8-36. Furthermore, the contact adsorption of redox particles produces (1) an increase in the effective cross section for electron capture due to the overlapping of the frontier oihital of adsorbed particles with the band orbital of... 

Extrapolation of the rules for the sign of the superexchange interaction, eqs. (9) and (10), to itinerant-electron magnetism leads to the following rules for bands containing n electrons per band orbital (0 < n < 2 because of spin degeneracy) ... 

Bands with 0 < < 1/2 or 3/2 half-metallic ferromagnets with full magnetization M = Nn/j,b or N(2 — n)fxb per band orbital, where N is the number of transition-metal atoms per unit volume if narrow enough for total removal of the spin de-... 

Fig. 7. The valence Ss and 5p orbital densities of Sn 5s25pz. Shown are free atom densities (solid lines) free atom densities renormalized to the Wigner-Seitz cell of a—Sn (dashed curves) and a schematic plot (dot-dash) of the way in which the 5p conduction band orbital character deviates from simple renormalization. The Wigner-Seitz radii, rws. of a and j8 Sn are indicated...

A further aspect is worthwhile to be mentioned The lower part of Fig. 9 gives the percentage of admixture of the orbitals of a2 parentage to the valence band orbitals. This... 

Fig. 9. Energy bands of tetracyanoplatinates with different intrachain Pt-Pt distances R. The results are obtained from a two-band model in the limit of an one-electron calculation82. The upper and lower structures represent the conduction and the valence bands, respectively, k is the absolute value of the wavevector in the chain direction. P is the percentage of admixture of the orbitals of a2u parentage to the valence band orbitals...

The valence-band orbitals include nonbonding oxygen orbitals such as the lt g, 6tiu, l 2u. and 5t, and those orbiteds with appreciable metal and oxygen character (2 g, 6a,g, lt2g)- The atomic compositions of the latter are given in Table 4.20 along with the compositions of the crystal-field... 

Table 6.6 Theoretical atomic subshell photoionization cross-sections for MoVTeNb-related valence band orbitals at different photon energies, according to the calculations ofYeh and Lindau [177].

Let us explore the electronic stracture of the bare supported island [Ptbuik-XsJ-Pts in some more detail. The oibital resolved d-DOS of the Pts island supported on CosPt (1), Co (2), Pt (3), Ni (4) and Fe (5) reveals that the i-band orbitals without z-component,... 

Fig. S a and b. Schematic representation of local bonding for the c(2 x 2) and, c and d structures of sulfur adsorbed on Ni(lOO). 1 bj represents the lone-pair orbital, 3 ai the banding orbital (after Fischer, 1977...

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