P.A. Cox - Inorganic chemistry (793955), страница 19
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There is no reason why an MO must be confined to just twoatoms. In Fig. 1a the two orbitals shown are formed respectively from a 2s and a 2p atomic orbital (AO) on beryllium,combined with hydrogen 1s AOs of appropriate sign to give a bonding MO. It is also possible to form antibondingcombinations (not shown). The four valence electrons in the ground state of BeH2 can be regarded as occupying the twothree-center (3c) or delocalized MOs shown. Bonding stabilization is provided, as in the diatomic case, by acombination of increased electron density in the overlap regions between atoms, and a transfer of electrons to the moreelectronegative hydrogen atoms.The alternative picture in Fig.
1b is based on sp hybrid orbitals on the central atom, pointing in opposite directions asin the MO description of BH (see Topic C5). Each hybrid is combined to form a two-center (2c) or localized MO withthe appropriate hydrogen AO; again, antibonding MOs can be made but are not shown. In this description of BeH2 twoelectrons occupy each of the 2c MOs, giving a picture similar to that assumed in VSEPR theory where two electronpairs around an atom adopted a linear configuration (see Topic C2).80C6—MOLECULAR ORBITALS: POLYATOMICSFig. 1. Bonding MOs for BeH2. (a) 3-center, (b) 2-center representations. In each case both MOs are doubly occupied.The 3c and 2c bonding descriptions look different, but so long as both orbitals are doubly occupied in each case, theyare in fact equivalent.
In the orbital approximation any set of occupied orbitals may be replaced by a linearcombination of them without changing the overall many-electron wavefunction. The two 2c MOs of Fig. 1b can be formedby making linear combinations of the 3c MOs in Fig. 1a. and conversely the 3c MOs could be reconstructed bycombining the 2c MOs.
The two pictures show different ways of ‘dissecting’ the total electron distribution intocontributions from individual pairs, but as electrons are completely indistinguishable such dissections are arbitrary anddo not predict any observable differences.The two MO approaches to polyatomic systems, localized and delocalized, are useful in different circumstances.When localized descriptions are possible, they correspond more closely to the simple chemical pictures of electron-pairbonds provided by the Lewis and VSEPR models.
Such descriptions are not always possible, and 3c or other delocalizedmodels provide an alternative to the resonance approach (see below and Topic C7). Delocalized MO theory is alsomore useful for interpreting electronic spectra of molecules.Directed valenceThe localized 2c MO picture depends on hybrid AOs that point towards other atoms and provide directed valence.Combining s with one p orbital in a valence shell gives two sp hybrids directed at 180° apart.
Two p orbitals with smake sp2 hybrids directed at 120° in a plane. These can be used to describe a trigonal planar molecule such as BF3.Combining s with all three p orbitals gives sp3 hybrids directed towards the corners of a tetrahedron. These are thegeometrical arrangements assumed by VSEPR for two, three and four electron pairs, respectively (see Section C2).
Inthe 2c MO description of methane CH4, each of the sp3 hybrids on carbon is combined to make a bonding MO with onehydrogen 1s orbital. The four equivalent bonding MOs are occupied by two electrons each.Nonbonding electron pairs can also be assumed to occupy hybrids on the central atom. Thus in ammonia NH3, threehybrids on nitrogen are directed towards hydrogen atoms and form bonding combinations.
The fourth does not overlapwith a hydrogen atom and remains nonbonding. In water H2O there are two bonding MOs and two nonbonding. Thebond angles in these molecules (107° in NH3, 104.5° in H2O compared with the ideal tetrahedral angle of 109.5° foundin CH4) suggest that the hybrids used for bonding and nonbonding MOs are not quite equivalent. A smaller bond anglecorresponds to more p character and less s in the hybrid.
(The angle between pure p orbitals is 90°; see Topic A2.)Valence s orbitals are more tightly bound to an individual atom than are p orbitals and so do not contribute as much tobonding MOs (see the discussion of HF in Topic C5). On the other hand, hybrid AOs with some s character are morestrongly directed than are pure p orbitals and so can overlap more strongly with neighboring atoms. The degree ofhybridization therefore depends on a balance of factors. NH3 and H2O have angles fairly close to the ideal sp3prediction, although the bonding orbitals have slightly more p character and the nonbonding MOs will havecorrespondingly more s.
In PH3 and H2S the angles are closer to 90°, showing that the balance has changed and thatbonding MOs are constructed mostly with valence p orbitals with s remaining largely nonbonding. This trend can beSECTION C—STRUCTURE AND BONDING IN MOLECULES81attributed to the weaker bond strengths (compared with s-p energy separations) for elements lower in a group (seeTopic C8). The explanation of bond angles provided by VSEPR is very different.Multiple bondingAs with diatomics (see Topic C4) multiple bonds are provided by the overlap of pπ orbitals perpendicular to thedirection of the bond, in contrast to the σ orbitals, which point in the bond direction. A simple example is ethene,C2H4, Fig. 2a. where the planar structure of the molecule results from sp2 bonding with each carbon forming two σbonds to hydrogens, and one to the other carbon.
The p orbitals not involved in the hybrids are directed perpendicularto the molecule, and can overlap to form the π bonding MO shown, which is occupied by two electrons. Thecombination of σ+π MOs gives a double C=C bond. Maximum bonding overlap of the π orbitals depends on thecoplanar arrangement of atoms, and there is a significant barrier to rotation about double bonds, unlike single bondswhere groups can rotate fairly freely.
Triple bonds (e.g. in C2H2) are provided by the overlap of two sets ofperpendicular pπ orbitals, as in diatomics such as N2 and CO (see Topics C4 and C5).In some cases where a localized description of σ bonding is possible this is not so for the π bonds. An example is thecarbonate ionwhere a resonance picture is necessary in simple models (see Topic C1, Structure 11). Figure 2bshows the planar framework, with sp2 bonding in the central atom. The pπ AOs of the four atoms can overlap togetherto form a delocalized MO as shown. Out of the three orbital combinations possible for the three oxygen πAOs only onecan overlap and bond with carbon in this way. There are two others (not shown), which remain nonbonding on theoxygen.
Thus one π bonding MO is distributed over three C—O bonds, with nonbonding charge density correspondingto two MOs distributed over the three oxygen atoms. This is essentially similar to the resonance picture.Three-center bondingAn example of where the 2c bonding picture is not possible is in diborane B2H6 (see Topic C1, Structure 16).
Theterminal B—H bonds can be described in simple 2c terms, but the number of electrons available suggests that eachbridging hydrogen forms part of a 3c bond involving the two boron atoms. The MO method provides a simpleinterpretation (1). Four H atoms are disposed roughly tetrahedrally around each boron; this arrangement shows that sp3hybrids are used. Two such hybrids form normal 2c bonds by overlap with the 1s AO on the terminal hydrogens. Theothers are combined as in 1 to form two 3c bridge bonds (only one shown). In addition to B—H overlap there is somedirect overlap between the boron hybrids, which provides some B—B bonding as well.
The result is known as a threecenter two-electron (3c2e) bond. 3c2e bonds with bridging hydrogen occur in other circumstances, for examplethe normal form of BeH2, which has a polymeric chain structure with all H atoms in bridging positions (see Topic G3).Other groups such as methyl CH3 can do this, for example in dimeric aluminum methyl, Al2(CH3)6, which has a structureessentially similar to B2H6 with CH3 in place of H (see Topic G4).Fig. 2. π bonding MOs in (a) C2H4, (b) CO32−.82C6—MOLECULAR ORBITALS: POLYATOMICSFig.
3. Occupied MOs in the 3c4e description of [FHF]−.Another type of bridging hydrogen occurs in the symmetrical ion [FHF]− formed by hydrogen bonding between F− andHF (see Topic F2). To understand this, first count electrons and orbitals as follows: F 2s AOs have two electrons each,too tightly bound for bonding (as in HF); the 2pπ AOs on each F are too far apart to overlap, thus forming nonbondingorbitals holding a total of eight electrons. This leaves four electrons (out of a total valence count of 16) to occupy MOsformed from the two F pσ and the H 1s AO.
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