Symmetry orbitals description

These simple molecular orbital pictures provide useful descriptions of the structures and spectroscopic properties of planar conjugated molecules such as benzene and naphthalene, and heterocychc species such as pyridine. Heats of combustion or hydrogenation reflect the resonance stabilization of the ground states of these systems. Spectroscopic properties in the visible and near-ultraviolet depend on the nature and distribution of low-lying excited electronic states. The success of the simple molecular orbital description in rationalizing these experimental data speaks for the importance of symmetry in determining the basic characteristics of the molecular energy levels. 

In this section we shall first treat the simple molecular orbital description of pyridine. Each molecular energy level corresponds to a configuration, specified by the occupancy of individual molecular orbitals. Each molecular orbital has the symmetry species of an irreducible representation of the symmetry group, C2v The spatial symmetry of the overall molecular wave function is the direct product of the symmetry species of the occupied orbitals. 

Pyridine, symmetry group C2v, has six electrons in a system delocalized around the ring, and two lone-pair electrons in an orbital localized at the Nitrogen atom. The Is electrons, as well as the electrons in orbitals describing the a bonds, need not be considered explicitly in describing the resonance stabilization and low-lying excited states of pyridine. The simple molecular orbital description has the following characteristic assumptions ... 

In cases where there are no electronically driven distortions, the orbital description provides no better account of the chemistry than the bond valence model. Rather it tends to make an essentially simple situation more complex. For example, consider the phosphate and nitrate anions, and NOJ. In orbital models the P atom is described as sp hybridized and the N atom as sp hybridized, but these descriptions are just representations of the spherical and cylindrical harmonics appropriate to the observed geometries. They provide no explanation for why P is four but not three coordinate, or why N is three but not four coordinate. The bond valence account given in Chapter 6 is simpler, more physical, and more predictive. The orbital description is merely a rather complicated way of saying that the ions obey the principle of maximum symmetry but implying that the constraints are related in some unspecified way to the properties of one-electron orbitals rather than to the ionic sizes. 

Molecular Orbital Descriptions. In addition to the localized bond descriptions, molecular orbital (MO) descriptions of bonding in boranes and carboranes have been developed (4). Early work on boranes helped develop one of the most widely applicable approximate MO methods, the extended Htckel method. Molecular orbital descriptions are particulady useful for c/oso molecules where localized bond descriptions become cumbersome because of the large number of resonance structures that do not accurately reflect molecular symmetry. Such descriptions show that the highest occupied MO (HOMO) is degenerate for most deltahedral B H molecules, but that a closed shell is obtained for the corresponding [B H l2 anions. After... 

The molecular orbital description for the nitrite ion just presented was developed without the aid of symmetry considerations and as a starting point, it assumed that a bonds were formed from sp2 hybrid orbitals on the nitrogen and oxygen atoms. Lei us now see how we could have obtained a similar end result by using a method that involves a more formal application of symmetry and does not invoke hybridization. (For a review of symmetry in bonding, see Chapter 3.)... 

Boron trifluoride has a trigonal-planar structure. Formulate the bonding in terms of molecular orbitals for the Dsjj symmetry. In addition, construct wave functions for three equivalent sp2 hybrid orbitals, using the 2px, 2p, and 2s boron valence orbitals, which may be used to form three localized bonds with the three fluorines. Compare and contrast the molecular-orbital and the hybrid-orbital descriptions. 

The carbon-oxygen double bond in aldehydes and ketones is similar and can be described in either of these two ways. If we adopt the iocalised-orbital description, formaldehyde will have two directed lone pairs in place of two of the C-H bonds in ethylene. In this case the axes of these hybrid orbitals will be in the molecular plane (unlike the oxygen lone pairs in water). Either the components of the double bond or the lone pairs can be transformed back into symmetry forms. The alternative description of the lone pairs would he one er-type along the 0-0 direction and one jr-type with axis perpendicular to the 0-0 bond hut in the molecular plane. It is the latter orbital which has the highest energy, so that an electron is removed from it in. ionisation or excitation to the lowest excited state. 

The potential curves derived from such calculations can often be empirically improved by comparison with so-called experimental curves derived from observed spectroscopic data, using Rydberg-Klein-Rees (RKR) or other inversion procedures. It is often found, particularly for the atmospheric systems, that the remaining correlation errors in a configuration interaction (Cl) calculation are similar for many excited electronic states of the same symmetry or principal molecular-orbital description. Thus it is often possible to calibrate an entire family of calculated excited-state potential curves to near-spectroscopic accuracy. Such a procedure has been applied to the systems described here. 

The alkene metathesis reaction was unprecedented - such a non-catalysed concerted four-centred process is forbidden by the Woodward-Hoffmann rules - so new mechanisms were needed to account for the products. Experiments by Pettit showed that free cyclobutane itself was not involved it was not converted to ethylene (<3%) under the reaction condition where ethylene underwent degenerate metathesis (>35%, indicated by experiments involving Di-ethylene) [10]. Consequently, direct interconversion of the alkenes, via an intermediate complex (termed a quasi-cyclobutane , pseudo-cyclobutane or adsorbed cyclobutane ) generated from a bis-alkene complex was proposed, and a detailed molecular orbital description was presented to show how the orbital symmetry issue could be avoided, Scheme 12.14 (upper pathway) [10]. 

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 summary, the molecular orbital description of Mo(RC=CR)2L4 includes a nonbonding n combination of b2 symmetry, alkyne donation of two electrons each from 7T to metal a orbitals, and one filled bonding orbital from overlap of both tt orbitals with the lone vacant dn orbital. 

The aromaticity of benzene is linked, in spin-coupled theory, to the particular mode of coupling of the electron spins, and so it seems reasonable to suppose that the orbital descriptions of Dih cyclobutadiene and of benzene could be fairly similar, but for these to be associated with very different modes of spin coupling. To a first approximation, this indeed turns out to be the case. With benzene-like orbitals ordered a,b,c,d around the ring, the symmetry requirements of an overall Bu state are such that the electron spins associated with each diagonal (ale and bid) must be strictly triplet coupled. These two triplet subsystems combine to a net singlet. A characteristic feature of antiaromatic situations in spin-coupled theory is the presence of such triplet-coupled pairs of electrons. 

Symmetry Orbitals Orbitals from Hydrogen Atoms Description... 

The symmetry projection of the wavefunction is equivalent to a particular orbital transformation among the occupied orbitals of the wavefunction. If the CSF expansion is full within these sets of symmetry-related orbitals, no new CSFs will be generated by this orbital transformation. This type of wavefunction could have been computed directly in terms of symmetry orbitals with no loss of generality. (In fact, the CSF expansion expressed in terms of symmetry orbitals will usually result in fewer expansion terms because the symmetry blocking of the individual CSFs allows those of the incorrect symmetries to be deleted from the expansion.) However, if the CSF expansion is not full within these orbital sets, it is possible that the symmetry transformation of the orbitals will generate new CSF expansion terms. The coefficients of these new CSF expansion terms are determined by the old expansion coefficients and the symmetry transformation coefficients. For example, consider the case of two H2 molecules, described in terms of localized orbitals, separated by a reflection plane. Assume that the localized description of the two H2 molecules is of the form... 

This increase of CSF expansion length upon transformation to symmetry-adapted orbitals potentially affects any of the expansion forms that attempt to describe electron correlation in terms of localized orbitals and that are not invariant to transformations that mix the different localized orbitals. All of the product and direct product expansion forms (including the RCI, PPMC, PPGVB and SOGVB expansions) are potentially of this type. It often happens that these wavefunctions do have the full molecular symmetry even though they are described in terms of localized orbitals and not symmetry-adapted orbitals. The localized orbital description that results from these wavefunction optimizations is therefore both an asset and a liability it aids the chemical interpretability and results in more compact CSF expansions but the computations must be performed in an orbital basis that does not possess the full molecular symmetry. This is computationally important since many steps of the MCSCF wavefunction optimization can exploit such orbital symmetry when it is present. 

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