Orbital manifold

Photoelectron spectroscopy (PES) has been applied to determine the structure of 1-aza- and 1,4,7-triazatricy-clo[5.2.1.04,10]decane 37 and 40 <1997JMT(392)21>. The PES spectrum of ATQ shows four composite bands in the region 7-17 eV. A first band peaked at 7.80 eV is attributed to the NLPO (nitrogen lone-pair orbital). A second prominent broad band system, extending from 10.5 to 13.0 eV is associated with photoionizations from the cr-orbital manifold. The third composite band is produced by two photoemissions. The second band may be attributed to emissions arising from a sequence of seven near-lying MOs. 

Nevertheless, despite the discouraging predictions of the early calculations, some attempts were made to apply the ligand field model to sandwich complexes. The first approach on these lines, due to Matsen (28), assumed a strong ligand field of D h symmetry, which was shown to split the d-orbital manifold into three levels characterised by the value of m. Unfortunately, the calculated energetic order for the metallocenes was found to be... 

The post-transition metals utilize a four-orbital sp3 valence orbital manifold. 

The post-transition metals use a four-orbital sp valence orbital manifold. The inner shell d orbitals are assumed not to be involved in the bonding but instead comprise nonbonding electron pairs. 

All these systems are isoelectronic with Tt-benzene and 7r-allyl and have topologically identical orbital manifolds. 

Fig. 11.5. Population ratio of the two A-doublet states of OH(2Il3/2) generated in the photodissociation of H2O via the A state in a nozzle beam (T 50 K) and in the bulk (T = 300 K). N = j — 1/2 for the 2n3/2 spin-orbit manifold. The inset illustrates schematically the (approximate) conservation of the antisymmetric pn lobe as one of the OH bonds breaks. Adapted from Andresen and al. (1984).

Statistical and nonstatistical population of spin-orbit manifolds... 

All experimental observations are quantitatively reproduced by the extended Franck-Condon theory outlined above this includes the rotational state distributions for all initial states as well as the population ratios of the two spin-orbit manifolds and the two A-doublet states. 

In thiophene, the 7t-orbital manifold comprises the HOMO la2 (tts) describing C(2)-C(3) bonds, the 2bi(7t2) orbital related to the 3p sulfur lone pair, and the deep Ibi(iti) orbital describing the bonding of all the ring atoms. Among the unoccupied orbitals are two antibonding 7t-orbitals rt 4(bi) and p s(a2). The rt-orbital system of the chlorothio-phenes is closely analogous there are three occupied molecular orbitals, 4a"(%), 3a"(Jt2), and la"(Jti), and two unoccupied 7t (a") orbitals. 

Photoelectron spectroscopy (see Photoelectron Spectroscopy of Transition Metal Systems) has also been apphed to gain information about metal-metal bonding. For example, the metal-metal bonded complexes M2(OR)6 (M = Mo, W) show clearly defined ionizations attributed to the a-orbital as well as to the jr-orbital manifold. ... 

For a given total energy E we can identify a manifold of ion states I/) that all have a momentum profile of the same shape, given by (11.11,11.12,11.14). The shape is characteristic of an orbital a) of the target. The manifold is characterised not only by the symmetry, but by the set of quantum numbers a that includes a principal quantum number. We call it the orbital manifold a. 

Fig. 11.4 illustrates the momentum profiles of the other ion states observed in a later experiment with better energy resolution than that of fig. 11.2. All these states have momentum profiles of essentially the same shape. They are thus identified as states of the same orbital manifold, for which the experiment obeys the criterion for the validity of the weak-coupling binary-encounter approximation. Details of electron momentum spectroscopy depend on the approximation adopted for the probe amplitude of (11.1). The 3s Hartree—Fock momentum profiles in the plane-wave impulse approximation identify the 3s manifold. However, the approximation underestimates the high-momentum profile. 

The principles derived and illustrated in section 11.1 show that electron momentum spectroscopy gives information about orbitals, about orbital manifolds that are split by electron correlations in the ion, and about correlations in the target ground state. We give examples of the kind of information that is obtained. 

Since the ligand-field splitting of the d-orbital manifold of low-valent d metal atoms is relatively large, LF excited states of d -metals occur at higher energy than MLCT states, with the only exception of Fe F Hence, LF states are not involved in electron transfer reactivity but they can provide a non-radiative deactivation pathway for the reactive MLCT state, shortening its lifetime. LF states do not exist for d CuF The only polypyridine complexes with a redox-active LF state are [Cr(N,N)3] +, whose T/ E LF states are strong oxidants [278, 279]. 

Further evidence for the validity of the frontier orbital approach derives from its success in predicting the shift (increase or decrease) in naked cluster IP upon the chemisorption of small reactant molecules. For all metal clusters examined thus far, H2 chemisorption induces an increase in cluster IP. ° This follows directly from interactions (1) and (2), since the creation of the two new metal-hydride bonding orbitals effectively removes two electrons from the cluster valence orbital manifold. Thus with resjiect to the metal cluster, H2 chemisorption can be viewed as an oxidative addition process. If a one-electron (Aufbau filling) approximation is assumed as above, the Fermi level of the cluster is shifted toward lower energy, that is, there is an increase in IP. As the cluster grows larger, the shift in IP diminishes. This is simply a manifestation of cluster-size-dependent variations in the valence orbital density of states, and is again consistent with the frontier orbital model. 

We noted in Section 4 that by introducing non-bonded interactions into the molecular orbital scheme we would also lose the non-bonding character of the non-bonding orbitals involved in the p orbital manifold in a similar sort of way to introduction of a central atom s orbital. We illustrate some cases in Fig. 22. 

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