Orbital implications

MaUiotra R. (1995) The origin of Pluto s orbit implications for the solar system beyond Neptune. Astron. J. 110, 420. 

Many authors have drawn attention to the resource implications of ab initio calculations. Schlegel and Frisch (1990) give a particularly comprehensive review. The two resources to be considered are CPU usage and disk usage. A small subset of Schlegel and Frisch s tables are given in Table 11.3 n is the number of basis functions and O is the number of occupied orbitals. 

The Pauli exclusion principle has an implication that is not obvious at first glance. It requires that only two electrons can fit into an orbital, since there are only two possible values of m,. Moreover, if two electrons occupy the same orbital, they must have opposed spins. Otherwise they would have the same set of four quantum numbers. 

I have tried to stress the educational implications of the claims for the observation of orbitals in other articles and will not dwell on the issue here (Scerri, 2000 in Science and Education). 

In the three following sections we will try to sketch the mathematical foundation for the three approaches which are most closely connected with the Hartree-Fock scheme, namely the methods of superposition of configurations (a), correlated wave functions (b), and different orbitals for different spins (c). We will also discuss their main physical implications. 

The structural features and the spectroscopic characteristics of the thiirene dioxide system (22) are of special theoretical interest since, on the basis of analogy with cyclopropenone (23), it is a possible nonbenzenoid aromatic system with all the physical and chemical implications involved. Aromatic and/or conjugative effects, if any, require transmission through the d-orbitals of the sulfur atom. 

Both phenomena attest to the covalency of the chemical bonding in these species. Incidentally, they also highlight the different characters and implications of the spectrochemical and nephelauxetic series. Within either lanthanoid- or (higher oxidation state) J-block species, the ligand orbitals overlap with the metal s functions... 

In a, P-unsaturated carbonyl compounds and related electron-deficient alkenes and alkynes, there exist two electrophilic sites and both are prone to be attacked by nucleophiles. However, the conjugated site is considerably softer compared with the unconjugated site, based on the Frontier Molecular Orbital analysis.27 Consequently, softer nucleophiles predominantly react with a, (i-unsaturated carbonyl compounds through conjugate addition (or Michael addition). Water is a hard solvent. This property of water has two significant implications for conjugate addition reactions (1) Such reactions can tolerate water since the nucleophiles and the electrophiles are softer whereas water is hard and (2) water will not compete with nucleophiles significantly in such... 

It is difficult to give a localized orbital description of the bonding in a period 3 hypervalent molecule that is based only on the central atom 3s and 3p orbitals and the ligand orbitals, that is, a description that is consistent with the octet rule. One attempt to do this postulated a new type of bond called a three-center, four-electron (3c,4e) bond. We discuss this type of bond in Box 9.2, where we show that it is not a particularly useful concept. Pauling introduced another way to describe the bonding in these molecules, namely, in terms of resonance structures such as 3 and 4 in which there are only four covalent bonds. The implication of this description is that since there are only four cova-... 

Evidence has accumulated from various sources which supports the idea that polyenylic cations are implicated in other aspects of PVC degradation. Molecular orbital calculations carried out by Starnes (45) show that the charge is better stabilized at the center of the formal delocalized length of the ion than at the end and that since the process represented by equation 16 becomes more favorable with increasing sequence length, this may provide an explanation for the relatively short sequence lengths. 

The implied implication that even 7r-electrons are independent of each other is grossly unjustified. What saves the day is that all wave functions and the overlap function that is being ignored, have the same symmetry. The shape of the molecular orbital remains qualitatively correct. 

As emphasized by Bent, the LST properly places H and He with the s block and realigns file l shells into the actual sequence of configurational orbital filling. The LST therefore avoids the curious STT-based implication that the d-block elements (i = 2) are somehow the transition between the s block (l = 0) and p block (l = 1). 

It is remarkable that the energy scale given by the chemical potential of an approximate wave function can lead to an energy close to that of the exact wave function. The implications are, of course, very great. But it is by no means certain that these results for a two-electron, single-orbital system, can be generalized. 

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