Electron domain

Although the electron domain model is, as we shall see, a very useful model, we must remember that it is just that, a model—indeed a very approximate model. We cannot observe the individual domains of electrons but only the total electron density distribution. 

Gillespie, R.J. Robinson, E.A. (1996). Electron domains and the VSEPR model of molecular geometry. Angewante Chemie International Edition in English, 35, 495-514. 

VT > Ronald J. Gillespie, James N. MJI Spencer, and Richard S. Moog, "Demystifying Introductory Chemistry Part 2. Bonding and Molecular Geometry Without Orbitals-The Electron Domain Model," /. Chem. Educ., Vol. 73,1996,622-627. 

Fig. 3. Graphic formula and electron-domain model of methane. Not shown is the relatively small electron-domain of the carbon atom s Is electrons...

It is a small step from van der Waals, electron-domain models of the C—H bonds of, e.g., biphenyl, cyclohexane, or methane (Figs. 1—3), to molecular models in which to a first, and useful, approximation each valence-shell electron-pair is represented by a spherical, van der Waals-like domain 7h (Non-spherical domains may be useful for describing, e.g., lone pairs about atoms with large atomic cores, -electrons, and the electron-pairs of multiple bonds vide infra.)... 

Fig. 4 is a drawing of an all-valence-shell-electron-domain model of ethane superimposed on the molecule s conventional graphic formula. Not shown are the electron-domains of the carbon atoms Is electrons. In Fig. 4, each valence-stroke, i.e. each valence-shell electron-pair of ethane, protonated ("C—H") or unprotonated ( C—C"), is represented by a van der Waals sphere. 

The analogy between electron-domain models of hydrocarbons and the experimental facts — particularly the length, but, also, the low... 

A localized molecular orbital representation is the closest approach that can be achieved, for a given determinantal wavefunction, to an electrostatic model of a molecule 44>. With truly exclusive orbitals, electron domains interact with each other through purely classical Coulombic forces and the wavefunction reduces, for all values of the electronic coordinates, to a single term, a simple Hartree product. 

A striking analogy exists between localized molecular orbital, electron-domain models of organic and other covalently bonded molecules (Figs. 3—8) and ion-packing models of inorganic compounds 47). 

The chief content of the isomorphism displayed in Table 1 is embodied in the phrase "electride ion . By introducing at the outset in the electronic interpretation of chemistry the wave-like character of electrons and the Exclusion Principle through the concept of van der Waals-like electron-domains or electride ions , whose sizes indicate the magnitudes of the electrons kinetic energies, whose impenetrability8) simulates, at least approximately, the operation of the Exclusion Principle, and whose charges yield within the framework of the model easily foreseeable effects, one transforms the complex treatment of the covalent bond in quantum mechanics into a simpler, if less precise, exercise in classical electrostatics. 

Below are five illustrative examples of the explanatory power of classical physics in structural chemistry. In these examples, classical electrostatic interactions are used with the electron-domain representation of molecules to explain or to derive The New Walsh Rules , the Langmuir-Pauling and Hendricks-Latimer Occupancy Rule, the s-character Rule, the Methyl Group — Tilt Rule, and the Octet Rule. 

Fig. 10. Tangent-circle, two-dimensional electron-domain models illustrating Walsh s New Rules ...

Fig. 11 is a drawing of a two-dimensional analogue of the electron-domain model of ethane. Large circles represent valence-shell electron-domains (superimposed on them are the valence strokes of classical structural theory). Plus signs represent protons of the "C—H bonds. The nuclei of the two carbon atoms are represented by small dots in the trigonal interstices of the electron-pair lattice. While these nuclei would not necessarily be in the centers of their interstices, exactly, it can be asserted that an (alchemical) insertion of the two protons on the... 

Fig. 11. Tangent-circle, two-dimensional electron-domain model of ethane and methyl fluoride illustrating the rule that the 5-character of an atom tends to concentrate in orbitals the atom uses toward electropositive substituents 4)...

Fig. 13 is a drawing of electron-domain models of some Group VI hexafluorides. Open circles represent the electron-pairs of four of the six bonds to fluorine atoms in a Lewis, single-bond formulation of these molecules. Solid circles represent the atomic cores of oxygen, sulfur, selenium, tellurium, tungsten, and uranium (core radii, in hundreths of A, 9, 29, 42, 56, 62, and 80 2>, respectively). These hexafluorides are, in order, non-existent, extra-ordinarily unreactive, hydrolyzed slowly, hydrolyzed completely at room temperature in 24 hours, hydrolyzed readily, and hydrolyzed very rapidly. 

Fig. 16. Two-dimensional, tangent-circle representation of an electron-domain model of a coordinated fluoride ion...

Fig. 17. Two-dimensional, tangent-circle representation of an electron-domain model of CF4. Open circles represent valence-shell electron-domains. Smaller filled circles represent atomic cores. Valence strokes pass through shared electron domains. Note mutual overlap of the ligands conventional van der Waals domains...

Fig. 18 A—C. LMO-electron-domain models of (A) NH3, (B) C2H4, and (C) C3H3. Unprotonated domains with sufficient exposure to exhibit nucleophilic activity are...

Fig. 19. Saturation of primary affinity. Two-dimensional representation of an electron-domain model of the formation of a conventional chemical bond the reaction of a Lewis base (NHg) with a relatively strong Lewis acid (BH3).

Fig. 21. Saturation of residual affinity. Schematic, tangent-circle representations o( electron-domain models of the molecular complexes Me N 1 L> and MesN -111...

It would appear that localized molecular orbital, electron-domain models will prove useful in interpretative studies of the structural chemistry of electron-pair donor-acceptor interactions. 

Fig. 22 A and B. Electron-domain models of a water molecule sharing with a metal cation (solid circle) (A) one and (B) two electron pairs...

A drawing of a two-dimensional, electron-domain model of a conventional Lewis lone pair is shown in Fig. 23. The lone pair and bonding pairs are structurally equivalent they have identical van der Waals envelopes. Such seems to be nearly the case for lone pairs in the valence-shells of small-core, non-octet-expanding atoms (carbon, nitrogen, oxygen and fluorine). 

Fig. 23. Two-dimensional reprisi ntation of an electron-domain model of an angularly-localized, I ew is-type lorn >,m...

There is some evidence in support of the view that an electron-domain s effective volume, if not its shape, is approximately transferable from one system to another. Compress a Sidgwick-type unshared electron on one side and it appears to expand elsewhere, particularly on the opposite (trans) side of the kernel, much as one might expect from the form of the kinetic energy operator and the energy minimization principle, which, taken together, require smooth changes in electron density, within a domain. 

Square-planar, four-coordinate tellurium(II) complexes, whose structural chemistry has recently been summarized by Foss 89>, offer illustrations of this highly approximate, constant-volume rule. Fig. 27 is a drawing, approximately to scale, of a schematic, electron-domain representation of a section through the 1 1 complex of benzenetellurenyl chloride with thiourea 90>. Shown are the electron domains of the tellurium kernel (largest, nearly centrally located solid circle) the ligands kernels (two chlorine kernels, a sulfur kernel of thiourea, and a carbon kernel of benzene) and the domains of the tellurium atom s shared valence-shell electrons (open circles) and, most schematically of all, the tellurium atom s unshared valence-shell electrons (shaded region). 

VIII. Further Uses of Localized Electron-Domain Models... 

Estimation of Interatomic Distances. The notion of transferable interference radii — that, e.g., a hydrogen atom is approximately the same size whether it is attached to a phenyl ring (Fig. 1) or to a cyclohexane ring (Fig. 2) or that a sodium ion is approximately the same size whether it is surrounded by chloride ions in NaCl or by, say, bromide ions in NaBr — has found wide application in the estimation of distances between (i) adjacent atoms in adjacent molecules in molecular solids and (ii) adjacent atoms in ionic solids. Extension of these results to the estimation of interatomic distances within covalent molecules through use of the localized electron-domain model and one, new, two-parameter relation (but no new empirical radii) is illustrated in Fig. 28. 

Multicenter Bonding. While the valence stroke of classical structural theory is for many purposes a useful representation of an electron-domain created by the fields of two atomic cores (for every line-segment... 

Fig. 30 A—C. The Berry mechanism for electron-pair-coordination-number 5. (A) Trigonal bipyramidal coordination. Ligands bonded through shaded electron-domains are in axial positions. (B) Tetragonal pyramidal coordination. A slight distortion of structure A. (C) Trigonal bipyramidal coordination. A slight distortion of structure B. Ligands bonded through shaded electron-domains are now in equatorial positions...

On the right in Fig. 32 is an electron-domain representation of Lin-nett s model of an Octet-Rule satisfying atom in field-free space. For domains of (i) fixed size and distribution of charge, (ii) fixed distances from the nucleus, and (iii) fixed tetrahedral disposition with respect to other domains of the same spin-set, three of the four contributions to the total energies of the two structures in Fig. 32 are identical, namely the energies arising from (i) electronic motion, (ii) nuclear-electron attractions, and (iii) electron-electron repulsions between electrons of the same... 

Fig. 32. Electron-domain representation of (left) strong-field and (right) weak-field models of an octet, after Linnett 12 6>...

The upper drawing in Fig. 34 is a schematic, electron-domain representation of the spin-density in a plane through two neighboring comer atoms and the adjacent center atom in Slater s model of the alkali metals. Solid circles represent the atoms kernels (M+ cations). The Pauli Exclusion Principle permits domains occupied by electrons of opposite spin to overlap (comer atoms with the central atom), but prohibits overlap between domains occupied by electrons of the same spin (comer atoms with comer atoms). 

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