Molecular-orbital representation

Fig. A. Molecular-orbital representation of the 1-centrc F-Xe-F bond, (a) The possible combinations of colinear p, atomic orbitals, and (b) the energies of the resulting MOs (schematic).

Figure 6.18 Molecular orbital representation of oxidative electron transfer...

Fig. 3. Molecular orbital representations (a), the level diagram for Hjj (6), the MO s formed by the addition and subtraction of 2p-n AO s (c), the level diagram for tr orbitals of ethylene.

There are two main ways of representing the H2O molecule the point-charge model and molecular orbital representation. 

Landauer-Buttiker tunneling time for the rectangular barrier Landauer-Buttiker tunneling time in a molecular orbital representation Timneling time... 

The Landauer-Buttiker time was derived for tunnehng through a rectangular barrier. In the case of a series of electronic levels, such as occur for DNA in the models of Fig. 1, one can generahze the Landauer-Buttiker argument to a molecular orbital representation. In the hmiting case that is appropriate to most DNA-type problems, the time in Eq. 10 holds [88]... 

Fig. 2. Molecular orbital representation of silicon-metal rr-interaction.

Molecular Orbital Representations.—A simpler, but less precise way of describing electronic transitions is in terms of the initial and final... 

Figure 3.25. Molecular orbital representations of the bonding structure of the parent bishomoaromatic dication C4H82+ (604) and cyclobutadiene dication C4H42+ (605).

The emphasis of the theoretical discussion is (1) derivation and interpretation of the sum on states perturbation theory for charge polarization (2) development of physical models for the hyperpolarizability to assist molecular design (e.g., reduction of molecular orbital representations to the corresponding anharmonic oscillator description for hyperpolarizability). 

Canonical transformations from the tight-binding (atomic orbitals) representation to the eigenstate (molecular orbitals) representation play an important role, and we consider it in detail. Assume, that we find two unitary matrices SR and SR, such that the Hamiltonians of the left part Hi and of the right part Hi can be diagonalized by the canonical transformations... 

Valence-bond representation Molecular-orbital representation it bonding and multicenter it bonds Shapes of molecules Coordination compounds Isomerism Bonding in metals... 

A localized molecular orbital representation is the closest approach that can be achieved, for a given determinantal wavefunction, to an electrostatic model of a molecule 44>. With truly exclusive orbitals, electron domains interact with each other through purely classical Coulombic forces and the wavefunction reduces, for all values of the electronic coordinates, to a single term, a simple Hartree product. 

Fig. 9. The silicon-oxygen chain in diopside 48>. Or, a localized molecular orbital representation of a hydrocarbon (see text)...

Fig. 9 may be viewed, also, as a localized molecular orbital representation of, e.g., a hydrocarbon (cf. Fig. 13, ref. 7). Thus, replacement of (i) the domains of the Si4+ cations (the atomic cores of silicon atoms) by the domains of C4+ cations (the atomic cores of carbon atoms r = 0.15 A 2>), (ii) the domains of the bridging (i.e., bonding) oxide ions by the domains of the electron-pairs of aliphatic carbon-carbon single bonds (r 0.6e A 40)), and (iii) the domains of the non-bridging oxide ions by the domains of the protonated electron-pairs of carbon-hydrogen bonds... 

This molecular orbital representation of the allyl anion is consistent with the resonance forms shown earlier, with a negative charge and a lone pair of nonbonding electrons evenly divided between Cl and C3. 

The six overlapping p orbitals create a cyclic system of molecular orbitals. Cyclic systems of molecular orbitals differ from linear systems such as buta-1,3-diene and the allyl system. A two-dimensional cyclic system requires two-dimensional MOs, with the possibility of two distinct MOs having the same energy. We can still follow the same principles in developing a molecular orbital representation for benzene, however. 

Fig. 1. Schematic molecular orbital representation of the dative w-type bond.

Fig. 3. Schematic molecular orbital representation of the ethylene-platinum bond. Reproduced from J. Chatt and L. A. Duncanson, J. Chem. Soc. 2939 (1953), by permission of the Chemical Society.

As noted in [4] and [5], and in the discussion above, the electronic structure of Ti " " has been addressed for both Ti20s [14], and the hydrated ion Ti(H20)6 complex [11]. However it is important understand these two applications are different. The d description applies exactly to each hydrated Ti ion. In contrast, the d designation for the Ti-atoms in Ti203 is based on a SALC molecular orbital representation of the Ti203 electronic structure, in particular on overall and local charge neutrality. 

The inclusion of closed-shell configurations in spin-coupled calculations is most easily accomplished by carrying out a self-consistent field (SCF) (or small multiconfiguration SCF (MCSCF)) step first. The integrals over the basis functions are transformed to the molecular-orbital representation and input to the spin-coupled program. The use of MOs as basis functions also shows directly which of them are significant in the spin-coupled wavefunction. 

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