Orbital nomenclature

Orbital Nomenclature. In the preceding discussion we implicitly assumed unique orbital descriptions for excited states. It is clear, however, that even orbital promotional designations may fail whenever a near degeneracy of uncoupled levels occurs. Configuration interaction becomes important, and a zeroth-order coincidence of levels of disparate orbital designations leads to some unusual excited state properties that are observable by emission techniques. 

TABLE 13.1 Molecular-Orbital Nomenclature for Homonuclear Diatomic Molecules ... 

Lmol" cm" are typical of those found in spin-forbidden transitions. The valence structure in SO2 is isoelectronic with that in O3, and we will use the orbital nomenclature in Fig. 7.3 to discuss electronic transitions in SO2. In so doing, we should bear in mind that the 6ai orbital in Fig. 7.3, for example, is not actually the sixth lowest-energy aj MO in SO2 This molecule (unlike O3) has additional inner-shell a MOs arising from SALCs of 2s and 2p AOs centered on the sulfur atom. 

The solution to this problem is to use more than one basis function of each type some of them compact and others diffuse, Linear combinations of basis Functions of the same type can then produce MOs with spatial extents between the limits set by the most compact and the most diffuse basis functions. Such basis sets arc known as double is the usual symbol for the exponent of the basis function, which determines its spatial extent) if all orbitals arc split into two components, or split ualence if only the valence orbitals arc split. A typical early split valence basis set was known as 6-31G 124], This nomenclature means that the core (non-valence) orbitals are represented by six Gaussian functions and the valence AOs by two sets of three (compact) and one (more diffuse) Gaussian functions. 

The simplest molecular orbital method to use, and the one involving the most drastic approximations and assumptions, is the Huckel method. One str ength of the Huckel method is that it provides a semiquantitative theoretical treatment of ground-state energies, bond orders, electron densities, and free valences that appeals to the pictorial sense of molecular structure and reactive affinity that most chemists use in their everyday work. Although one rarely sees Huckel calculations in the resear ch literature anymore, they introduce the reader to many of the concepts and much of the nomenclature used in more rigorous molecular orbital calculations. 

At this point the nomenclature used in XPS and AES should be explained. In XPS the spectroscopic notation is used, and in AES the X-ray notation. The two are equivalent, the different usage having arisen for historical reasons, but the differentiation is a convenient one. They are both based on the so-called j-j coupling scheme describing the orbital motion of an electron around an atomic nucleus, in which the... 

Protonation of the anion [SN2] by acetic acid in diethyl ether produces the thermally unstable sulfur diimide S(NH)2. Like all sulfur diimides, the parent compound S(NH)2 can exist as three isomers (Scheme 5.5). Ab initio molecular orbital calculations indicate that the (cis,cis) configuration is somewhat more stable than the (cis,trans) isomer, while the (trans,trans) isomer is expected to possess considerably higher energy. The alternative syn,anti or E,Z nomenclatures may also be used to describe these isomers. The structures of organic derivatives S(NR)2 (R = alkyl, aryl) are discussed in Section 10.4.2. 

In the 1,3-dipolar cycloaddition reactions of especially allyl anion type 1,3-dipoles with alkenes the formation of diastereomers has to be considered. In reactions of nitrones with a terminal alkene the nitrone can approach the alkene in an endo or an exo fashion giving rise to two different diastereomers. The nomenclature endo and exo is well known from the Diels-Alder reaction [3]. The endo isomer arises from the reaction in which the nitrogen atom of the dipole points in the same direction as the substituent of the alkene as outlined in Scheme 6.7. However, compared with the Diels-Alder reaction in which the endo transition state is stabilized by secondary 7t-orbital interactions, the actual interaction of the N-nitrone p -orbital with a vicinal p -orbital on the alkene, and thus the stabilization, is small [25]. The endojexo selectivity in the 1,3-dipolar cycloaddition reaction is therefore primarily controlled by the structure of the substrates or by a catalyst. 

Organic Polymers, Natural and Synthetic 610 Appendix 1 Units, Constants, and Reference Data 635 Appendix 2 Properties of the Elements 641 Appendix 3 Exponents and Logarithms 643 Appendix 4 Nomenclature of Complex Ions 648 Appendix 5 Molecular Orbitals 650... 

The Relation between the Shell Model and Layers of Spherons.—In the customary nomenclature for nucleon orbitals the principal quantum number n is taken to be nr + 1, where nr> the radial quantum number, is the number of nodes in the radial wave function. (For electrons n is taken to be nT + l + 1.) The nucleon distribution function for n = 1 corresponds to a single shell (for Is a ball) about the origin. For n = 2 the wave function has a small negative value inside the nodal surface, that is, in the region where the wave function for n = 1 and the same value of l is large, and a large value in the region just beyond this surface. 

According to these consideration the diamino-substituted phosphenium (an alternative suggestion for its nomenclature is phosphanylium) cation, 5, and the phosphanetriylammonium (iminophosphenium) cation, 6, possess the largest intrinsic (gas phase) stabihties. Since in the X-ray structures the molecules are to a first-order isolated, this theoretical stability scale determined for the gas phase should also mimic the various trends of the stabilities of the cations and their chelation behaviour. The methylenephosphenium, 7, and the PjH cations, 8, suffer from poor stabihties. On the other hand the phosphirenium cation, 11, is considered to be fairly well stabilized. It is due to n-electron delocalisation of the positive charge in the phosphirenium cation. Intermediate cases in stabihty are the PO+ (9) and PS+ cations (10). Of further interest are the frontier orbital considerations, as shown in Fig. 2. 

The conventional chemical nomenclature for these orbitals is given on the right hand side, and the X-ray nomenclature used in Auger spectroscopy appears on the left. The designation of levels to the K, L, M,... shells is based on their having principal quantum numbers of 1,2,3,... respectively. 

All electrons in atoms can be described by means of these four quantum numbers and, as first enunciated in 1926 by Pauli in his Exclusion Principle, each electron in an atom must have a unique set of the four quantum numbers. A summary of the electron shells and of the corresponding maximum numbers of orbitals, and electrons, is shown in Table 4.2 where each shell is defined by the value of the principal quantum number (K = 1, L = 2, etc. according to X-ray spectroscopy nomenclature). 

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