Diatomic molecules closed shells

The following presentation is limited to closed-shell molecular orbital wave-functions. The first section discusses the unique ability of molecular orbital theory to make chemical comparisons. The second section contains a discussion of the underlying basic concepts. The next two sections describe characteristics of canonical and localized orbitals. The fifth section examines illustrative examples from the field of diatomic molecules, and the last section demonstrates how the approach can be valuable even for the delocalized electrons in aromatic ir-systems. All localized orbitals considered here are based on the self-energy criterion, since only for these do the authors possess detailed information of the type illustrated. We plan to give elsewhere a survey of work involving other types of localization criteria. [Pg.33]

There exists no uniformity as regards the relation between localized orbitals and canonical orbitals. For example, if one considers an atom with two electrons in a (Is) atomic orbital and two electrons in a (2s) atomic orbital, then one finds that the localized atomic orbitals are rather close to the canonical atomic orbitals, which indicates that the canonical orbitals themselves are already highly, though not maximally, localized.18) (In this case, localization essentially diminishes the (Is) character of the (2s) orbital.) The opposite situation is found, on the other hand, if one considers the two inner shells in a homonuclear diatomic molecule. Here, the canonical orbitals are the molecular orbitals (lo ) and (1 ou), i.e. the bonding and the antibonding combinations of the (Is) orbitals from the two atoms, which are completely delocalized. In contrast, the localization procedure yields two localized orbitals which are essentially the inner shell orbital on the first atom and that on the second atom.19 It is thus apparent that the canonical orbitals may be identical with the localized orbitals, that they may be close to the localized orbitals, that they may be identical with the completely delocalized orbitals, or that they may be intermediate in character. [Pg.44]

Table VI lists the equilibrium geometries for the selected closed-shell diatomic molecules. It has long been recognized that the HF method gives reduced bond lengths. From Table VI we see that the correlated bond lengths are mostly longer than the experimental values. Exceptions are the bond distances predicted by CCD and NOF methods for the HCl molecule.

Many free radicals in their electronic ground states, and also many excited electronic states of molecules with closed shell ground states, have electronic structures in which both electronic orbital and electronic spin angular momentum is present. The precession of electronic angular momentum, L, around the intemuclear axis in a diatomic molecule usually leads to defined components, A, along the axis, and states with A =0, 1, 2, 3, etc., are called , n, A, , etc., states. In most cases there is also spin angular momentum S, and the electronic state is then labelled 2,s+1 Id, 2,s+1 A, etc. [Pg.26]

It is well known from the Bom-Oppenheimer separation [1] that the pattern of energy levels for a typical diatomic molecule consists first of widely separated electronic states (A eiec 20000 cm-1). Each of these states then supports a set of more closely spaced vibrational levels (AEvib 1000 cm-1). Each of these vibrational levels in turn is spanned by closely spaced rotational levels ( A Emt 1 cm-1) and, in the case of open shell molecules, by fine and hyperfine states (A Efs 100 cm-1 and AEhts 0.01 cm-1). The objective is to construct an effective Hamiltonian which is capable of describing the detailed energy levels of the molecule in a single vibrational level of a particular electronic state. It is usual to derive this Hamiltonian in two stages because of the different nature of the electronic and nuclear coordinates. In the first step, which we describe in the present section, we derive a Hamiltonian which acts on all the vibrational states of a single electronic state. The operators thus remain explicitly dependent on the vibrational coordinate R (the intemuclear separation). In the second step, described in section 7.55, we remove the effects of terms in this intermediate Hamiltonian which couple different vibrational levels. The result is an effective Hamiltonian for each vibronic state. [Pg.316]

The existence of molecular species in interstellar space has been known for almost seventy years. The first observations involved the electronic spectra, seen in absorption in the near-ultraviolet, of the CN, CH [28] and CH+ [29] species. Radiofrequency lines due to hydrogen atoms in emission [30] and absorption [31], and from the recombination of H+ ions with electrons were also known. However, molecular radio astronomy started with the observation of the OH radical by Weinreb, Barrett, Meeks and Henry [32] in 1963 in due course, this was followed by the discovery of CO [33]. In the subsequent years over 110 molecules have been observed in a variety of astronomical sources, including some in galaxies other than our own. Nearly a third of these are diatomic molecules, with both closed and open shell electronic ground states, and some were observed by astronomers prior to being detected in the laboratory. [Pg.713]

Emission spectra from discharge tubes or from mass spectrometric studies containing a single gas or mixtures of pure noble gases give evidence for the presence of diatomic molecules. Usually, it is not clear if these are neutral molecules or ions. Ions are more likely to exist because chemical bond formation seems more likely when the closed-shell arrangement is destroyed by removal of an electron. There is also spectroscopic evidence for diatomic molecules between noble gas atoms and other atoms (e.g. H, O, N, Hg) or molecules (e.g. CO2, N2, SFg, etc.). All these species have exceedingly short lifetimes. [Pg.3123]

The Hg atom has a 6s closed electronic shell. It is isoelec-tronic with helium, and is therefore van der Waals bound in the diatomic molecule and in small clusters. For intermediate sized clusters the bands derived from the atomic 6s and 6p orbitals broaden as indicated in fig. 1, but a finite gap A remains until the full 6s band overlaps with the empty 6p band, giving bulk Hg its metallic character. This change in chemical binding has a strong influence, not only on the physical properties of mercury clusters, but also on the properties of expanded Hg, and on Hg layers on solid and liquid surfaces. For a rigid cluster the electronic states are discreet and not continuous as in fig. 1. Also the term band for a bundle of electronic states will be used repeatedly in this paper, although incipient band might be better. As the clusters discussed here are relatively hot, possibly liquid, any discreet structure will be broadened into some form of structured band . [Pg.25]

Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...