EHMO

Ozin et al. 107,108) performed matrix, optical experiments that resulted in the identification of the dimers of these first-row, transition metals. For Sc and Ti (4s 3d and 4s 3d, respectively), a facile dimerization process was observed in argon. It was found that, for Sc, the atomic absorptions were blue-shifted 500-1000 cm with respect to gas-phase data, whereas the extinction coefficients for both Sc and Scj were of the same order of magnitude, a feature also deduced for Ti and Ti2. The optical transitions and tentative assignments (based on EHMO calculations) are summarized in Table I. 

For planar unsaturated and aromatic molecules, many MO calculations have been made by treating the a and n electrons separately. It is assumed that the o orbitals can be treated as localized bonds and the calculations involve only the tt electrons. The first such calculations were made by Hiickel such calculations are often called Hiickel molecular orbital (HMO) calculations Because electron-electron repulsions are either neglected or averaged out in the HMO method, another approach, the self-consistent field (SCF), or Hartree-Fock (HF), method, was devised. Although these methods give many useful results for planar unsaturated and aromatic molecules, they are often unsuccessful for other molecules it would obviously be better if all electrons, both a and it, could be included in the calculations. The development of modem computers has now made this possible. Many such calculations have been made" using a number of methods, among them an extension of the Hiickel method (EHMO) and the application of the SCF method to all valence electrons. ... 

In order to explain why the bridging vinylidene group of MoCo2(/r 3-)F-CCH2) (COlsI / -CyHOr" (Fig. 83) leans toward the molybdenum atom rather than a cobalt atom, EHMO calculations have been employed. Results showed that the... 

For calculations of electronic structures of azolides (CNDO, PCILO, EHMO, INDO and Molecular Mechanics Calculation) the interested reader should consult the relevant papers. 481... 

Extended Hiickel molecular-orbital (EHMO) calculations using structural parameters from the X-ray determination of Cp(CO)3Mo 3In (Fig. 29) and ideal symmetry Cih were carried out for this compound in order to investigate the extent of the indium-molybdenum ir-bonding.122 The HOMO of the compound is the 3e molecular orbital, which is In—Mo [Pg.54]

Since the g-matrix has only three principal values and there are almost always many potentially interacting molecular orbitals, there is rarely sufficient information to interpret a g-matrix with complete confidence. When a well-resolved and reliably assigned optical spectrum is available, the energy differences, E0—Em, are known and can be used in eqn (4.11) to estimate the contribution of the corresponding MOs to the g-matrix. Extended Hiickel MO (EHMO) calculations can be useful (but do not trust EHMO energies ), but one is most commonly reduced to arguments designed to show that the observed g-matrix is consistent with the interpretation placed on the hyperfine matrix. 

An extended Hiickel MO calculation supports the assumptions made in the above analysis in that the three t2g orbitals are indeed close together in energy and remain nearly nonbonding metal-based d-orbitals. The detailed agreement is less satisfactory the SOMO is predicted to be primarily dx2 y2 with a small dxz admixture (hybrid 6 of Table 4.13), a result that can be ruled out from our analysis of the ESR results. The EHMO overlap matrix based on the X-ray structure suggests that the molecule is much closer to C2 symmetry than to Cs. If we accept that conclusion, then dxzjdxy hybridization is less likely than dyjdxy, as we tacitly assumed above. 

Photoelectron spectra of bis(dimethylamino) and bis(diisopropylamino) cyclopropenone and bis(dimethylamino) cyclopropene thione have been measured and correlated with EHMO calculations163b ... 

Fig. 11 The scattering properties of a five branches - four electrodes molecular bridge, (a) Detailed atomic structure of the molecule. A central perylene branch was included to mimic an internal measurement branch, (b) EHMO-ESQC calculated T12(E) transmission coefficient (plain) and predicted T12(E) transmission coefficient (dashed), applying the intramolecular circuit rules discussed for the four molecular fragments given in Fig. 12. The dashed (dotted) line is the Ti2(E) variation for the single molecular branch, as presented in the inset, to show the origin of the destructive interference...

A very good example is the conductance of a dianthra[a,c]naphtacene starphenelike molecule presented in Fig. 20, interacting with three metallic nano-pads. The EHMO-NESQC T(E) transmission spectrum per tunnel junction looks like a standard conjugated molecule T(E) with well-identified molecular orbitals and their resonances. For the Fig. 20 case all the T(E) are the same. One can note a small deviation after the LUMO resonance, due to a little asymmetry in the adsorption site between the three branches on the nano-pads [127]. A lot of asymmetric star-like three-molecular-branches system can be constructed, in particular in reference to chemical composition of the central node. This had been analyzed in detail [60]. But in this case, each molecule becomes a peculiar case. The next section presents one application of this central-node case to construct molecule OR and molecule XOR logic gates. 

Fig. 14 The three-branches dianthra[a,c]naphtacene molecule circuit of symmetry formed by three anthracene fragments equivalently bonded to a central phenyl group. The molecule is adsorbed by the three branch ending phenyls onto the Au nano-pads. A semilogarithmic plot of the Tij(E) EHMO-NESQC electron transmission spectra (in valence energy range) per pair of branches. The presented frontier MOs show how the valence n electrons are delocalized on the molecule. At resonance, this provides a good electronic conductance through each pair of molecular branches, almost one quantum of conductance...

Fig. 21 The variation of the balancing tunneling current of the four branches four electrodes monomolecular Wheatstone bridge connected as presented in (a). In (b), the dashed line is for the current intensity 7W (in absolute value) measured by the ammeter A and deduced from the standard Kirchoff laws calculating each molecular wire tunneling junction resistance of the bridge one after the other from the EHMO-ESQC technique. In (b), Hie full line is the same tunnel current intensity but obtained with the new intramolecular circuit rules discussed in Sect. 2. (c) The resistance of the branch used to balance the bridge as a function of its rotation angle. The minimum accessible resistance by rotation is 78 MQ for the short tolane molecular wire used here...

Fig. 25 (A) Tight-binding calculation (dashed) and EHMO (plain) of the electronic conduction, for the naked anthracene (a) when the two NO2 groups are perpendicular to the molecule (b), when one N02 is rotated (c) and when the two N02 are rotated (d). (B) Tunneling current intensity for the NOR gate (a) and the AND gate (b) depending on the orientation angle of the two N02 groups...

The substrate in these studies was restricted to be rigid, and Morse functions were used for the hydrogen-surface and two-body interactions. The parameters in the Morse functions were determined for single hydrogen atoms adsorbed on the tungsten surface by fitting to extended Huckel molecular orbital (EHMO) results, and the H2 Morse parameters were fit to gas-phase data. The Sato parameter, which enters the many-body LEPS prescription, was varied to produce a potential barrier for the desorption of H2 from the surface which matched experimental results. 

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