P.A. Cox - Inorganic chemistry (793955), страница 20
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The two occupied MOs are shown in Fig. 3. There is a 3c bonding MOwhere H 1s is combined with both F pσ AOs, and also a nonbonding MO formed from a fluorine combination that hasthe wrong symmetry to interact with hydrogen. The four electrons in the these MOs give rise to a three-center fourelectron (3c4e) bond. Effectively each F—H bond is only ‘half’ a covalent bond as in the 3c2e case, but unlike thatsituation there are also two electrons localized on the terminal atoms, giving a negative charge there. The result isequivalent to the resonance formulation 2.3c4e bonding models are an alternative to the use of d orbitals in hypervalent compounds with octet expansion. Oneinterpretation of a molecule such as XeF2 with five electron pairs around a central atom would use sp3d hybrids, whichinclude d orbitals in the valence shell of Xe.
Calculations show that this picture greatly overestimates the contribution ofd orbitals to the bonding. An alternative approach considers 3c4e bonds that use only p orbitals on the central atom. Theresult corresponds to the resonance picture 3, which requires only eight electrons in Xe valence shell (see Topics F1 andF10).Section C—Structure and bonding in moleculesC7RINGS AND CLUSTERSKey NotesIntroductionAromatic ringsWade’s rulesRelated topicsRing and cluster molecules and ions arise in many areas of chemistry. Somestructures can be understood using simple two-center bonding models; in othersit is necessary to used delocalized MO models.The Hückel MO model predicts that rings will have aromatic stability if theyhave 4n+2 delocalized π electrons, where n is a whole number. Inorganicapplications include S2N2, which has six π electrons.Borane clusters can be classified as closo, nido or arachno with successively moreopen structures, and respectively 2n+2, 2n+4 and 2n+6 skeletal bondingelectrons, where n is the number of boron atoms.
The rules may be applied to‘naked’ clusters formed by p-block metals, and extended to transition metalcompounds.Molecular orbitals: polyatomicsBoron (F3).(C6)IntroductionRing and cluster compounds arise in many areas of chemistry. Rings are most often formed by nonmetallic elementswith directional covalent bonding. They include homoelement rings such as S8 (1) and benzene C6H6, and ones withheteroelement bonding such as S2N2 (2), borazine B3N3H6 (see Topic F3) and the silicate ion [Si3O9]3− (see Topic D5).Clusters are polyhedral arrangements of atoms found very widely in the periodic table: nonmetals (e.g. P4 3 andboranes discussed below), main-group metals (e.g.
[Pb5]2− 4) and transition metals (often with ligands such as CO; seeTopic H9). Heteroelement bonding is also possible as in the A4B4 structure 5, adopted by S4N4 (where A=S and B=N)and As4S4 (where A=As and B=S).Complex molecular structures do not necessarily require complex bonding models, and indeed much of organicchemistry can be understood using rather elementary ideas. Some inorganic ring and cluster compounds such as S8 and84SECTION C—STRUCTURE AND BONDING IN MOLECULESP4 can be understood in terms of elementary electron pair bonds (Topic C1); the octets are achieved in each case withtwo nonbonding electron pairs for each S atom, and one for each P. Similarly in As4S4, each As forms three bonds andone lone-pair, each S atom two bonds and two lone-pairs. The reverse arrangement of S4N4 is slightly harder tounderstand but may still be accommodated within simple ideas by placing a formal negative charge on each two-bondedN, and a formal positive charge on each three-bonded S; as expected for bonds between formal S+ entities, the S—Sbonds (A—A in 5) are abnormally long and weak.Many rings and clusters, however, cannot be understood within the two-center two-electron bond framework.
Thisis sometimes extended by assuming resonance, for example between the two Kekulé-type structures for benzene (6). Amore natural approach is to extend the molecular orbital (MO) approach (see Topic C6) to many atoms. The so-calledHückel theory of ring systems makes important predictions relevant to inorganic molecules such as S2N2. Clusterssuch as boranes also need a delocalized MO approach.
Wade’s rules provide a useful systematization of the principlesinvolved, and can be extended to other systems.Aromatic ringsThe Hückel MO approach treats the π electrons of rings such as benzene. We imagine a framework of σ bonds formedby sp2 hybrids on each carbon atom (see Topic C6). The six remaining 2p π orbitals overlap to form six delocalizedMOs. Figure 1a shows the pattern of orbital energies predicted. The lowest energy MO is formed by combining all 2porbitals with positive overlap to give full bonding; higher energy MOs are progressively less bonding and more antibonding.Figure 1 shows the assignment of six π electrons as in the ground state of benzene.
Aromatic stability arises becausethe electrons are collectively more stable in these MOs than they would be in three separate double bonds.Fig. 1. Energies of π MOs in (a) benzene, (b) a four-membered ring compound.The arrangement of MO energies for benzene is paralleled with other ring sizes: in each case there is a single orbitalof lowest energy followed by pairs of equal energy. Figure 1b shows the energies for a four-membered ring. Assignmentof four π electrons does not lead to a closed-shell ground state where every MO is either filled or empty, and indeedthe four-π-electron molecule cyclobutadiene C4H4 is very unstable. This type of argument leads to the Hückel 4n+2rule: irrespective of the ring size, aromatic stability requires 4n+2 π electrons, where n is a whole number. Possiblevalues are 2, 6, 10,…but not 4, 8,….
One consequence is that the cyclopentadienyl fragment C5H5 is stable as a 6-πelectron anion [C5H5]−, an important ligand for organometallic compounds (Topic H10).C7—RINGS AND CLUSTERS85There are examples of inorganic rings that conform to the Hückel rule. The heteroatom molecule B3N3H6 isisoelectronic with benzene although much more reactive because of the polarity in the B—N bonds (see Topic F3). TheS2N2 ring (2) is an example of a six-π-electron system although the ring is four-membered. Electrons can be counted byassigning two each to four localized S—N σ bonds, and two electrons to a lone-pair on each atom.
Out of 22 valenceelectrons, six remain for the delocalized π system. The ions [S4]2+ and [Se4]2+ have the same valence electron count asS2N2 and are also square planar (see Topic F8).Wade’s rulesThe apparently bewildering variety of structures adopted by boron-hydrogen compounds (boranes) can be rationalizedby recognizing some major families, illustrated by the series in Figure. 2.• Closo boranes with n boron atoms adopt closed polyhedral structures based on triangular faces such as the trigonalbipyramid (five vertices), octahedron (six) and icosahedron (12); such polyhedra are called deltahedra. The simplestexamples are the ions [BnHn]2− such as [B6H6]2− illustrated.• In nido (‘nest-like’) boranes n boron atoms are found roughly at the positions of the vertices of an n+1-vertexdeltahedron, with one vertex missing. The simplest general formula type is BnHn+4; for example, B5H9, where theboron atoms are placed at five of the corners of an octahedron.• Arachno (‘web-like’) boranes are still more open and can be imagined as deltahedra with two vertices missing.
Theyform a general series of formula BnHn+6 (e.g. B4H10).Wade’s rules provide an electronic rationalization of the regularities, based on the MO prediction that an n atomdeltahedron, with s and p valence orbitals, should have n+1 skeletal bonding MOs. For example, in [B6H6]2− thereare seven such MOs, and electrons may be counted as follows: there are 26 valence electrons; 12 are assigned to‘normal’ two-center B-H bonds, leaving 14 for skeletal bonding. There is no simple way of assigning these 14 electronsto localized two-center or even three-center bonds. In the general case, we see that closo boranes with n atomsshould have 2n+2 skeletal bonding electrons. Isoelectronic replacements of atoms should preserve thestructure; for example, B10C2H12 is based on the same icosahedron as [B12H12]2−.Fig.
2. Three boranes illustrating the closo/nido/arachno relationship (see text).86SECTION C—STRUCTURE AND BONDING IN MOLECULESStarting with the closo ion [BnHn]2− we can imagine removing one [BH]2+ unit and adding 4 H+ to give the n−1 nidoborane Bn−1Hn+3 (e.g. [B6H6]2− gives B5H9). Neither of these operations should alter the number of skeletal bondingelectrons, so B5H9 has 14, the same number as [B6H6]2−, and in general nido boranes with n atoms should have 2n+4 skeletal bonding electrons. The argument may be repeated, starting from nido BnHn+4, removing BH2+ andadding 2 H+, leading to the further conclusion that arachno boranes with n atoms should have 2n+6 skeletalbonding electrons.Wade’s rules may be applied to ‘naked’ clusters formed by p-block elements if it is assumed that each atom has onelocalized nonbonding electron pair.
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