Symmetry degenerate molecular orbitals

A Straightforward answer to the above question would be a consideration of molecular symmetry. According to group theory, doubly degenerate molecular orbitals, denoted by the symbol e, can arise if a given molecule has one three-fold or higher axis of rotation, or if it has Djj symmetry. It is well... 

A symmetry-based molecular orbital description of the unusual four-coordinate C3v W(RC=CR)3(CO) series of molecules was presented by King in 1968 (32). The tt orbitals of the three alkynes yield linear combinations of A2 and E symmetry. Since there is no metal orbital of A2 symmetry only the degenerate E combination of n orbitals finds metal orbital mates for bonding and antibonding combinations. The three alkyne 7T orbitals serve as er donors [(Ax + E) symmetry] as does the fourth ligand (Al symmetry). Thus the total metal electron count adheres to the effective atomic number rule [W(0)(6) + 37T j(6) + 2ir (4) + lo-(2) = 18 electrons]. 

In the cyclopropenyl radical with three Ti-electrons, the third electron has to be accommodated in one of the two degenerate molecular orbitals causing the Jahn-Teller distortion, which results in a change in symmetry from Dj, to C2,.. The ab initio (STO-3G 4-31G), as well as semi-empirical (CNDO/2), molecular orbital calculations demonstrate that the odd electron is incorporated in the pyramidalized rr-type orbital giving rise to loss of resonance stabilization in the three-membered ring. Thus, the cyclopropenyl radical is considered to be a highly unstable, short-lived species. 

Another classical non-Kekule molecule is triangulene 23 ( CZar j hydrocabon ) which so far has escaped detection. With two half-filled degenerate molecular orbitals 23 should possess a triplet ground state and be paramagnetic. As a first derivative of triangulene, the trianion 24 has recently been prepared. According to its ESR spectrum it is a triplet molecule with threefold symmetry [20]. 

The BS formalism was developed by Noodleman and Norman [5h,i] to compute singlet-triplet splitting using single determinants with either HF or DFT calculations. Let us consider the simplest case of two electrons in two non-degenerate molecular orbitals, (t>i and ( )2, having different symmetries. 

The molecnlar orbitals for the jr-electrons are given by Eqn. (13-1), with g = L = 1. For systems such as with symmetry, the molecular orbitals /2 and /j are degenerate, as are the excited configurations... 

In the case of the cyclopentadienyl cation, there are only two electrons in the e" tt molecular orbitals that are degenerate in Dji, symmetry. The MO heatments... 

Wong and coworkers37 studied a series of both symmetrical and unsymmetrical tetraalkyltin compounds with different alkyl substituents, focusing their attention on the effect of these on the ionization energy of the highest occupied MOs. It is useful to recall the type of molecular orbitals deriving from the triply degenerate HOMO in the symmetrical R4M (local symmetry Td) upon substitution of one or more R ... 

TPP (45, 46), as well as data for octaalkyl and octathioalkyl porphyrazines. As with the phthalocyanines and porphyrins, the electronic spectra of porphyrazines can be rationalized using Gouterman s four-orbital model, shown in Fig. 5 (47, 48). All of these macrocycles, when symmetrically substituted and with a metal ion incorporated in the central hole, for example, the M[pz(A4)] or B4, have D4h symmetry, with a doubly degenerate lowest unoccupied molecular orbital (LUMO) (eg) and two highest lying highest occupied molecular orbitals (HOMOs) that complete the four Gouterman orbitals with alM and a2u symmetry. 

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