Atomic orbitals overlap populations

In summary, the electron density for HF as described by Eq. (3.15) includes the effects of charge transfer between atoms, atomic orbital overlap, and preferential population of lone-pair orbitals, which are neglected in the independent-atom scattering formalism. 

Molecular orbitals are characterized by energies and amplitudes expressing the distribution of electron density over the nuclear framework (1-3). In the linear combination of atomic orbital (LCAO) approximation, the latter are expressed in terms of AO coefficients which in turn can be processed using the Mulliken approach into atomic and overlap populations. These in turn are related to relative charge distribution and atom-atom bonding interactions. Although in principle all occupied MOs are required to describe an observable molecular property, in fact certain aspects of structure and reactivity correlate rather well with the nature of selected filled and unfilled MOs. In particular, the properties of the highest occupied MO (HOMO) and lowest unoccupied MO (LUMO) permit the rationalization of trends in structural and reaction properties (28). A qualitative predictor of stability or, alternatively, a predictor of electron... 

It is now clear that the apparatus of densities of states and crystal orbital overlap populations has served to restore to us a frontier orbital or interaction diagram way of thinking about the way molecules bond to surfaces, or the way atoms or clusters bond in three-dimensional extended structures. Whether it is 2t CO with d of Ni(100), or e of CR with some part of the Pt(lll) band, or the Mn and P sublattices in Mn2P22, or the Chevrel phases discussed below, in all of these cases we can describe what happens in terms of local action. The only novel feature so far is that the interacting orbitals in the solid often are not single orbitals localized in energy or space, but bands. 

DOS = Density of states BO = Bloch orbital IBZ = Irreducible Brillouin zone BZ = Brillouin zone PZ = Primitive zone COOP = Crystal orbital overlap population CDW = Charge density wave MO = Molecular orbital DFT = Density functional theory HF = Hartree-Fock LAPW = Linear augmented plane wave LMTO = Linear muffin tin orbital LCAO = Linear combination of atomic orbitals. 

Finally, we study the atom-atom and orbital-orbital interactions by evaluation of the crystal orbital overlap population (COOP) and the overlap population (OP) corresponding to bonds and atomic orbitals, in order to analyze... 

In the previous paper (13), we have discussed the chemical bonding nature of uranyl nitrate dihydrate and found that the bonding interaction is mainly due to the U 5f, 6d - O 2p components. In the present work, we carry out orbital overlap population analysis to understand contribution of each atomic orbital to the chemical bonding. The orbital overlap populations indicate strength of covalent bonds (19,20). 

The An 5f and An 6d electrons mainly contribute to the covalent bonding between the actinide and actinyl oxygen atoms, as shown in Table 3(a). The orbital overlap populations for both the water molecules and the nitrate groups are found to be smaller. As shown in Table 2, as atomic number changes, the positive effective charge on An slightly decreases and the orbital population of the An 5f electrons increases from 2.94 to 5.14. The increased An 5f electrons... 

Around -10 eV, the overlap population increases with actinide atom in the order U < Np < Pu. This corresponds to the increase of the An 5f population which is shown in Fig. 3. That is, the lowering of the An 5f level enhances the covalency in this energy region. The next prominent change is found at the HOMO where the electrons in the An 5f MO level produce an antibonding character. In Table 3, the decrease in the overlap population of An-OH, is attributed to the decrease in the orbital overlap population of An 5f - O 2p. this arises from the An 5f HOMO level though it is not obvious in Fig. 5 that the... 

Figure 7. Total density of states (DOS) for BaSiNbioOi9 and atomic orbital projections (AOP) for (a) the Nb atoms of the Nb60i2 clusters (b) the Nb atoms of the NbjOn clusters (c) the Nb atoms of the Nb06 octahedra and (d) crystal orbital overlap population (COOP) for the Nb-centered orbitals of the NbjOn clusters.

Fig. 2.19 Semiempirical (extended Huckel theory) band structure, density-of-states, and crystal orbital overlap population for a one-dimensional chain of hydrogen atoms spaced at 2.0 A. Due to a Gaussian smoothing, DOS and COOP plots appear slightly...

Chemical bonding in several transition metal carbides was theoretically investigated by quasi self consistent augmented-plane-wave (APW) calculations [71-73] and by the extended Hiickel method [74]. These calculation indicated a charge transfer from the early transition metal to the carbon atoms. A crystal orbital overlap population analysis (COOP) revealed strong bonding T—T and T-C... 

The Mulliken scheme places the negative charge more or less evenly on the three carbons, and splits the positive charge among the hydrogens. Mulliken population analysis computes charges by dividing orbital overlap evenly between the two atoms involved. 

Equation (10.3) is fulfilled when c2 ss 1 and c 0 in this case the electron is localized essentially at atom 1 and the overlap population is approximately zero. This is the situation of a minor electronic interaction, either because the corresponding orbitals are too far apart or because they differ considerably in energy. Such an electron does not contribute to bonding. 

The information obtainable upon solution of the eigenvalue problem includes the orbital energies eK and the corresponding wave function as a linear combination of the atomic basis set xi- The wave functions can then be subjected to a Mulliken population analysis<88) to provide the overlap populations Ptj ... 

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