Symmetric molecular orbitals

The Jacobi method is probably the simplest diagonalization method that is well adapted to computers. It is limited to real symmetric matrices, but that is the only kind we will get by the formula for generating simple Huckel molecular orbital method (HMO) matrices just described. A rotation matrix is defined, for example. 

According to one classification (15,16), symmetrical dinuclear PMDs can be divided into two classes, A and B, with respect to the symmetry of the frontier molecular orbital (MO). Thus, the lowest unoccupied MO (LUMO) of class-A dyes is antisymmetrical and the highest occupied MO (HOMO) is symmetrical, and the TT-system contains an odd number of TT-electron pairs. On the other hand, the frontier MO symmetry of class-B dyes is the opposite, and the molecule has an even number of TT-electron pairs. 

We will find an excitation which goes from a totally symmetric representation into a different one as a shortcut for determining the symmetry of each excited state. For benzene s point group, this totally symmetric representation is Ajg. We ll use the wavefunction coefficients section of the excited state output, along with the listing of the molecular orbitals from the population analysis ... 

Figure B A qualitative molecular orbital diagram for ferrocene. The subscripts g and u refer to the parity of the orbitals g (German gerade, even) indicates that the orbital (or orbital combination) is symmetric with respect to inversion, whereas the subscript u (ungerade, odd) indicates that it is antisymmetric with respect to inversion. Only orbitals with the same parity can combine.

The electron density in both molecular orbitals is symmetrical about the axis between the two nuclei. This means that both of these are sigma orbitals. In MO notation, the Is bonding orbital is designated as eru. The antibonding orbital is given the symbol An asterisk designates an antibonding orbital... 

This is first illustrated for the two nonbonding -type orbitals n, and n2 of para-benzyne and pyrazine (Fig. 31). These nonbonding orbitals are derived from outer (2s, 2p) sp2 type hybrids which have not been used in any bonding interaction. Although the overlap between n, and n2 is zero each one overlaps with the central CC bond orbitals. All told, there will arise two distinct molecular orbitals in which nj and n2 enter as combinations (symmetric or antisymmetric) and which have different energies, because of selective interactions with the central bonds. 

Unsaturated organic molecules, such as ethylene, can be chemisorbed on transition metal surfaces in two ways, namely in -coordination or di-o coordination. As shown in Fig. 2.24, the n type of bonding of ethylene involves donation of electron density from the doubly occupied n orbital (which is o-symmetric with respect to the normal to the surface) to the metal ds-hybrid orbitals. Electron density is also backdonated from the px and dM metal orbitals into the lowest unoccupied molecular orbital (LUMO) of the ethylene molecule, which is the empty asymmetric 71 orbital. The corresponding overall interaction is relatively weak, thus the sp2 hybridization of the carbon atoms involved in the ethylene double bond is retained. 

As a consequence of the molecular orbital interactions, ferrocene adopts an axially symmetrical sandwich structure with two parallel Cp ligands with a distance of 3.32 A (eclipsed conformation) and ten identical Fe-C distances of 2.06 A as well as ten identical C-C distances of 1.43 A [12]. Deviation of the parallel Cp arrangement results in a loss of binding energy owing to a less efficient orbital overlap [8]. All ten C-H bonds are slightly tilted toward the Fe center, as judged from neutron-diffraction studies [13]. 

Why is the splitting between bonding and antibonding molecular orbitals not symmetrical around the atomic levels ... 

To illustrate this point, the contributions of the occupied molecular orbitals to the total electron density at the nucleus are summarized in Table 5.2 for Fep4 (S - 5/2). It is evident from the table that the contributions coming from the orbitals at —6,966 eV must be assigned to the iron Is orbital, those from orbitals at —816 eV to the iron 2s orbital, and those from orbitals at —95 eV to the iron 3s orbital. In this highly symmetric complex, only two valence orbitals contribute to p(0), i.e. the —25 eV contribution from the totally symmetric ligand-group orbital that is derived from the F 2s orbitals and the —1 eV contribution from the totally symmetric... 

Using the simplest picture (and neglecting the effect of overlap on the normalization), this doubly occupied og spatial molecular orbital can be thought of as being the symmetric linear combination of the two Is atomic orbitals on the left and right hydrogens, HL and Hr... 

In a concerted reaction, orbital and state symmetry is conserved throughout the course of the reaction. Thus a symmetric orbital in butadiene must transform into a symmetric orbital in cyclobutene and an antisymmetric orbital must transform into an antisymmetric orbital. In drawing the correlation diagram, molecular orbitals of one symmetry on one side of the diagram are connected to orbitals of the same symmetry on the other side, while observing the noncrossing rule. 

The 327-670 GHz EPR spectra of canthaxanthin radical cation were resolved into two principal components of the g-tensor (Konovalova et al. 1999). Spectral simulations indicated this to be the result of g-anisotropy where gn=2.0032 and gi=2.0023. This type of g-tensor is consistent with the theory for polyacene rc-radical cations (Stone 1964), which states that the difference gxx gyy decreases with increasing chain length. When gxx-gyy approaches zero, the g-tensor becomes cylindrically symmetrical with gxx=gyy=g and gzz=gn. The cylindrical symmetry for the all-trans carotenoids is not surprising because these molecules are long straight chain polyenes. This also demonstrates that the symmetrical unresolved EPR line at 9 GHz is due to a carotenoid Jt-radical cation with electron density distributed throughout the whole chain of double bonds as predicted by RHF-INDO/SP molecular orbital calculations. The lack of temperature... 

Ohta K, Kamada K (2006) Theoretical investigation of two-photon absorption allowed excited states in symmetrically substituted diacetylenes by ab initio molecular-orbital method. J Chem Phys 124 124303... 

---