Yves Jean - Molecular Orbitals of Transition Metal Complexes (793957), страница 52
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[CrL6 ], no = 0, d6 , Nt = 18; [RuL]5 , no = 0, d8 , Nt = 18.2. The two compounds are 18-electron complexes. An η6 coordination of the two ligands in the ruthenium complex would lead to a 20-electron organometallic (and thusstrong-field) complex.3. (i) η5 ; (ii) η3 ; (iii) η1 .1.6. The borohydride ligand is of L-type in η1 -coordination, L2 -type inη2 -coordination, and L3 -type in η3 -coordination. In each case, thecoordination mode of this ligand allows an 18-electron complexto be formed.1.7.
(1) no = 0; (2) no = 3; (3) no = 2; (4) no = 2 (each bridgingCl acts as an X-type ligand towards one metallic centre and as anL-type ligand towards the other); (5) no = 2 (SR = ligand of XLtype (or LX), like Cl).1.8.1. The s orbitals have spherical symmetry, so their overlap is nonzero for any relative positions of the metal and the ligand. Thebonding orbital is mainly concentrated on the ligand and theantibonding orbital on the metal.M–L bonding MOM–L antibonding MOAnswers to the exercises (in skeletal form)2. (i) On the x-axis; (ii) in the nodal plane yz: S = 0.3. xy: the overlap is largest when the ligand is placed on thebisectors of the x- and y-axes, and smallest if it is in the xz or yznodal planes (S = 0); z2 : largest overlap along the z-axis andsmallest (S = 0) when the ligand is on the nodal cone.SmaxSmaxS= 0S= 0Chapter 2: Principal ligand fields: σ interactions2.1.
1–3MScTiVCrMnFeCoNiCuZndnd1d2d3d4d5d6d7d8d9d106362625242313030201Electronic configuration t2g eg t2g eg t2g eg t2g eg t2g eg t2g eg t2g eg t2g eg t2g eg t2g eg4Unpaired electrons12345432102.2.(1) d6 ;6 ;(2) Strong-field complex (organometallic): t2g(3) The anion would be a 19-electron complex (d7 ) with a veryhigh-energy d MO (strong field) containing an electron.Dissociation gives a 17-electron ML5 complex (d7 ).2.3.egt1ua1gAnswers to the exercises (in skeletal form)2.4. The xy and x 2 −y2 orbitals are interchanged compared to thedescription given in § 2.2.1.xyzyxMz2yzxzx2–y22.5.
(1) A fourteen-electron d8 complex; (2) and (3) Two emptynonbonding MOs:2.6. (1) and (2) For the orbitals of the square-planar complex, see § 2.2.The z2 orbital becomes strictly nonbonding (ligands on the nodalcone).and90°z125°pzx2–y2s–pzx2–y2yz, xzz2xy, xz, yzxy, z22.7.1. See § 2.3.1.1, Figure 2.7.2. (a) A low-spin d7 complex with electronic configuration(xy)2 (xz)2 (yz)2 (z2 )1 . Compared to d6 low-spin complexes, there is an additional electron in the z2 orbital.Answers to the exercises (in skeletal form)This orbital is particularly antibonding towards the apicalligand ⇒ substantial lengthening of this bond.(b) Two electrons in z2 (low-spin d8 ): even greater lengthening of the apical bond.3.
A high-spin d4 complex with electronic configuration−Cla bond will be longer than(xy)1 (xz)1 (yz)1 (z2 )1 . The M−−Clb , due to the electron in z2 (exp: M−−Cla = 2.58 Å,M−−−M Clb = 2.30 Å).4. (xy)2 (xz)2 (yz)2 (z2 )2 → (xy)2 (xz)2 (yz)2 (z2 )1 (x 2 −y2 )1 . Loss−La antibonding) shortens theof an electron from z2 (M−−Lb−La bond. Addition of an electron to x 2 −y2 (M−M−−−antibonding) lengthens the M Lb bonds.
Compared to the−La > M−−Lb ), the bondcase of a low-spin complex (M−lengths tend to become equal in a high-spin complex.2.8.1. See § 2.2.1, Figure 2.6 and § 2.3.1, Figure 2.9.2. Low-spin d8 (b2g )2 (eg )4 (a1g )2 for square-planar; d8 high-spin(e)4 (t2 )4 for the tetrahedron, with two unpaired electrons inthe t2 block.3. Square-planar: six electrons in nonbonding orbitals, and twoin very weakly antibonding orbitals, in the d block; tetrahedron: four electrons in nonbonding orbitals and four inweakly antibonding orbitals.
The bonds are weaker in thetetrahedron.2.9.1.z2z2xyx2–y2xyxzyzx2–y2xzyzAnswers to the exercises (in skeletal form)2. Compare with Figure 2.15 (right-hand side): the x 2 −y2 orbital(1a1 ) is slightly antibonding, since the two ligands are not−M−−L2 =exactly on the nodal planes, as they are when L1 −◦90 . However, the xy orbital (b2 ) is less antibonding, as in thiscase the three ligands are no longer pointing exactly towardsthe regions of greatest amplitude for xy. The gap betweenx 2 −y2 and xy therefore becomes smaller.2.10.
For the ML4 complex, use the orientation given in Exercise 2.4.The result obtained is exactly the same as that established in§ 2.8.4 (Figure 2.16), since the bond angles are 90◦ in bothcases.2.11. (1) and (2) The symmetry-adapted orbitals on the ligands have a1and t2 symmetries (Chapter 6, § 6.6.2). Due to the (weakly) bonding overlaps, the a1 orbital is lower in energy than the t2 orbitals.The character table for the Td point group (Chapter 6, § 6.6.2,Table 6.20) shows the symmetries of the metal orbitals: a1 (s), t2(p), e ⊕ t2 (d). The following interaction diagram is obtained, characterized by a two-orbital interaction (a1 ), interactions involvingtwo sets of three orbitals (t2 ), and nonbonding e orbitals (theorder of the antibonding MOs 2a1 and 3t2 is not obvious, and maydepend on the particular system considered):3t 22a1*MOp(t 2)s (a 1)2t 2d-blockd (e, t 2)e1t 2 MO1a1t2a1Answers to the exercises (in skeletal form)2.12.
Trigonal-planar ML3 complex3e⬘3a1⬘a2⬙p (e⬘, a⬙2)σ* MOpure nonbondingp orbitals (a⬘1)2e⬘2a1⬘d blockd (a1⬘, e⬘, e⬙)e⬙1e⬘e⬘a1⬘ MO1a1⬘2.13.1. The s orbital, which is totally symmetric like z2 (a1 symmetry).2. The interaction between the s orbital on the metal and theligand orbitals is bonding. As a result, the amplitude of z2decreases in the plane of the complex (xy) but increases alongthe z-axis. The metal–ligand interactions are therefore lessantibonding after the polarization.Chapter 3: π -type interactions3.1.1.
See Figure 2.6 (right-hand side)2. (a) z2 is unchanged (overlap zero by symmetry with the lonepairs (pCl ) on the chloride ligands); one orbital (xy) isdestabilized by four antibonding interactions with pCl ;two orbitals (xz and yz) are destabilized less strongly byAnswers to the exercises (in skeletal form)two antibonding interactions with pCl . Without detailedcalculations, the position of z2 with respect to the threeother orbitals is not clear.xy–4pClz2xyz2yzxzxz–2pClyz–2pCl(b) xy is now stabilized by four bonding interactions with the∗ orbitals (CN is a double-face π-acceptor, like CO), xzπCNand yz by two bonding interactions.z2z2yzxzxyyz + 2*CNxz + 2*CNxy + 4*CN(c) z2 and one of the three nonbonding MO are unchanged,but the two others are destabilized by an antibondinginteraction with one pCl .zyxz2ClMxyxzyzz2xy–pClxz–pClyz3.2. 1.
See Figure 2.10.2. 1a: Large overlaps between yz (nonbonding) and πy∗ , andbetween xz (nonbonding) and πx∗ ; very small overlapsbetween x 2−y2 and πy∗ (one bonding and one antibonding interaction, which do not completely cancel due to theAnswers to the exercises (in skeletal form)polarization of x 2 −y2 (see question 1)); the same situationfor xy and πx∗ .1b: By symmetry (the xy and yz planes), there are interactions between yz (nonbonding) and πz∗ , and betweenxy (antibonding) and πx∗ .CO y*zxyCO x**z x*x2–y2xyxzyz1a1bThere are two stabilizing interactions in each case. Thestrongest interaction involves xy (antibonding) and πx∗ (theseorbitals are closest in energy, and the overlap is larger due tothe polarization of xy).3.
The most favourable site for substitution so far as the π interactions are concerned is axial for a d4 complex and equatorialfor a d8 complex.4. The same type of interactions, but antibonding (a double-faceπ-donor ligand).5. d4 : equatorial substitution (one destabilizing interactioninstead of two for axial substitution); d8 : two destabilizinginteractions in both isomers, but axial substitution is favouredsince one of the overlaps is larger for equatorial substitution.3.3.1. See Chapter 1, § 1.1.1.22. (i) a nonbonding σ orbital, concentrated on C; (ii) seeChapter 1, Figure 1.7; (iii) a π acceptor; (iv) through carbon.3. The MO are similar to those in [M(CO)6 ] (see Scheme 3-35).4.
The bonds are shorter in [Fe(CN)6 ]4− (an Fe(II) complex,with six electrons in π -bonding MO in the d block) than in[Fe(CN)6 ]3− (an Fe(III) complex with only five electrons inπ -bonding MO).Answers to the exercises (in skeletal form)5. No, since the Fe3+ cation is smaller than the Fe2+ cation.6. (i) d3 for each of them; (ii) CN is a π acceptor, F a π donor (seeFigure 3.8).3.4.1. xz(P1 ) and xy(P2 ).2. x 2 −y2 : SS; xz: SA; yz: AA3.MMMMSAAASSAS4.
Three.5. and 6.AASASSASAASASS7. (i) 12; (ii) 18.3.5.1. Two, xz and yz.∗ orbitals for axial2. (a) Two bonding interactions with the πCOsubstitution, only one for equatorial substitution;(b) axial.3.6. Use the orbitals established in Exercise 6.13 (questions 4 and 6), butfor [Pt(CN)4 ]2− , the p orbitals on the ligands should be replaced∗ orbitals. The interaction diagram may be obtained byby the πCNconsidering the symmetry properties of these orbitals and of theAnswers to the exercises (in skeletal form)metal d orbitals (see Table 6.18). There are three interactions: twoinvolve eg orbitals, and one concerns b2g orbitals.3.7.1.
See Chapter 2, Figure 2.11.2. Use Figure 6.11.3. Two interactions between e′ orbitals and two between e′′orbitals.4. It is not possible to establish easily the two-fold degeneracy ofthe orbitals.Chapter 4: Applications4.1.1. Structure 2 (the same analysis as in § 4.1.1).2. and 3.: See T. A. Albright, R. Hoffmann, J.
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