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Bonding Models EAN   Valence bond theory describes exactly what it means for two atoms to share electrons.   The effec�ve atomic number (EAN) is the number that represents the total number of electrons surrounding the nucleus of a metal atom in a metal complex. It is composed of the metal atom’s electrons and the bonding electrons from the surrounding electron-­‐dona�ng atoms and molecules. Thus the effec�ve atomic number of the cobalt atom in the complex [Co(NH3)6]3+ is 36, the sum of the number of electrons in the trivalent cobalt ion (24) and the number of bonding electrons from six surrounding ammonia molecules, each of which contributes an electron pair (2 × 6 =12).   The English chemist Nevil V. Sidgwick made the observa�on, since known as the EAN rule, that in a number of metal complexes the metal atom tends to surround itself with sufficient ligands that the resul�ng effec�ve atomic number is numerically equal to the atomic number of the noble-­‐
gas element found in the same period in which the metal is situated. This rule seems to hold for most of the metal complexes with carbon monoxide, the metal carbonyls as well as many organometallic compounds. By using this rule it is possible to predict the number of ligands in these types of compounds and also the products of their reac�ons. The EAN rule is o�en referred to as the “18-­‐electron rule” since, if one counts only valence electrons (6 for Co3+ and 2 × 6 = 12 for 6 NH3), the total number is 18. EAN Complex # of electrons # of electrons EAN on Mn+ from ligands Pt(NH3)64+ 78 – 4 = 74 6 X 2 = 12 86 (Rn) Co(NH3)63+ 27 – 3 = 24 6 X 2 = 12 36 (Kr) Fe(CN)64-­‐ 26 – 2 = 24 6 X 2 = 12 36 Fe(CO)5 26 – 0 = 26 5 X 2 = 10 36 Cr(CO)6 24 – 0 = 24 6 X 2 = 12 36 Ni(CO)4 28 – 0 = 28 4 X 2 = 8 36 Ni(NH3)62+ 28 – 2 = 26 6 X 2 = 12 38 Ni(CN)42-­‐ 28 –2= 26 4 X 2 = 8 34 Cr(NH3)63+ 24 – 3 = 21 6 X 2 = 12 33   The EAN concept has been par�cularly successful for complexes of low-­‐valent metals (oxid. # < II); for complexes having high oxida�on numbers (oxid. # > II), EAN can be taken only as a rough guide.   This electron-­‐coun�ng scheme is also called the 18-­‐electron rule, in contrast to the usual octet rule for simple compounds. The octet rule applies to main-­‐group elements for which s and p are the only low-­‐E orbitals that need to be filled. For TMs the five d orbitals are also included in the valence shell since they are comparable in E to the filled s and p orbitals of the same n number. Hybridiza�on and Orbital Occupancy   Coordina�on compounds result from the use of available empty bonding orbitals on the metal for the forma�on of coordinate covalent bonds. The coordina�on number and geometry are determined in part by size and charge effects but also to a great extent by the orbitals available for bonding. 1
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Hybridiza�on and Orbital Occupancy   Magne�c suscep�bility measurements have been widely used to determine the number of unpaired electrons in complexes and from this informa�on the number of d orbitals used for bond forma�on usually can be inferred for ions containing four to eight d electrons. Hybridiza�on and Orbital Occupancy   The terms low-­‐spin (or spin-­‐paired) and high-­‐
spin (or spin-­‐free) describe the electron popula�on of the d orbitals as determined from magne�c proper�es w/o any assump�ons concerning the nature of the bonding. Stabiliza�on of Oxida�on States and Pi Bonding Stabiliza�on of Oxida�on States and Pi Bonding [Co(H2O)6]2+ is difficult to oxidize to [Co(H2O)6]3+ but [Co(NH3)6]2+ is to oxidized to [Co(NH3O)6]3+   The difference in reac�vity with ligand type is not great for other first transi�on ions, but in general, coordina�on, w/
ligand atoms less electronega�ve than O stabilizes the oxida�on state next higher than that of the most stable aqua ion unless other factors such as pi bonding are involved. This is because less electronega�ve ligand atoms are more effec�ve donors toward the more highly charged ions.   Compounds of the highest oxida�on state are strongly oxidizing and are stable only with the most electronega�ve ligands, F and O, as in fluoride complexes and oxoanions. [FeF6]3-­‐, yes, but [FeI6]3-­‐ , no   Excep�ons: CO, CN-­‐ and 1,10-­‐phenanthroline   A ligand such as C could give a predominantly covalent coordinate bond with a TM atom leading to the accumula�on of nega�ve charge on the metal atom. Let us now examine Ni
(CO)4-­‐. 2
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Back Bonding Back Bonding   The Cr-­‐C bond distance is shorter than expected for a single bond sugges�ng what?   The VB representa�on of a contribu�ng structure containing a M-­‐C double bond reveals that par�cular contribu�ng structure to have a C-­‐O double bond instead of a triple bond in the other main contribu�ng structure.   The sketch of orbitals available for L-­‐M π bonding in a molecular orbital (MO) descrip�on reveals that if a metal d orbital of appropriate symmetry is filled, electrons can be donated into the CO π* orbital: a CO double bond.   In either model, the C-­‐O bond is weakened and lengthened while the M-­‐C π-­‐bonding strengthens the M-­‐C bond.   Therefore, CO and CN-­‐ stabilize low oxida�on numbers where metal electrons available for M-­‐C π
bonding. Crystal and Ligand Field Theories Crystal and Ligand Field Theories   Crystal field theory (CFC) was originally concerned with the electrosta�c interac�ons about a given ion in a solid-­‐state ionic la�ce. Hence, it is an ionic theory and is an offshoot of electrosta�c theory. It ignores all covalent bonding effects. It was developed by Hans Bethe in 1929 by applying group theory and quantum mechanics to electrosta�c theory and was further developed by physicists during the 1930s and 1940s. It can be used to predict chemical proper�es, kine�c proper�es, reac�on mechanisms, magne�c and spectral proper�es, and thermodynamic data.   This model was later applied to coordina�on compounds and complex ions-­‐for example, for evalua�ng the repulsions that arise when the electron(s) pairs in a d subshell of a metal ca�on are surrounded by ligand electron pairs in a specific geome�c array.   The five d orbitals are degenerate (of equal E) in gaseous metal ions. The simple electrosta�c model fails to predict differences of bond energies among complexes of different TMs. Crystal and Ligand Field Theories Crystal and Ligand Field Theories   Review of d-­‐orbitals.   Consider an isolated TM ion that has one d e-­‐. _ _ _ _ _ x2 xz yz xy x2-­‐y2 For a d1 metal ion in an Oh field, the e-­‐ can go into one of the lower E d orbitals thereby stabilizinig the complex. The e-­‐ experiences electrosta�c repulsion from these charges. If the charge distribu�on is spherically symme�c, the five d orbitals are destabilized by equal amounts and thus remain 3
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Crystal and Ligand Field Theories   degenerate. For any distribu�on other than spherical, however, the repulsion is different for different orbitals; ie. the d orbital equivalence is destroyed. Crystal and Ligand Field Theories   For example, two point charges on opposite sides of the metal would occupy posi�ons along the z axis according to group theory conven�on. We can approach this as a linear ML2 molecule. _ z2 _ _ xz, yz _ _ xy, x2-­‐y2 Crystal and Ligand Field Theories Crystal and Ligand Field Theories   In a pure CFT we consider that only e-­‐’s belonging to the metal occupy the metal’s d orbitals. The ligand lone pairs are considered to belong en�rely to the ligand and to provide an electric field of the symmetry of the ligand arrangement around the metal. The name ligand-­‐field theory is used to refer to the approach in present use; it is basically the same as the pure crystal field approach, except that covalent interac�on is taken into account as necessary.   The single most common geometry for TM complexes is octahedral.   In an octahedral complex, two of the d orbitals (dz2 and dx2-­‐y2) are directed toward the ligands. The repulsion caused by the e-­‐ pairs of the ligands raises the E of any e-­‐’s occupying these orbitals (eg) more than that of the other three orbitals (dxy, dxz and dyz [t2g]) which are directed at 45o to the axes. The stronger the electric field caused by the ligands, the greater the spli�ng (E gap) of the E levels: Oh = 10 Dq or Δ. Crystal and Ligand Field Theories Crystal and Ligand Field Theories   This spli�ng causes no net change in the E of the system if all five orbitals are occupied equally because a filled or half-­‐filled orbital set is totally symmetrical. The t2g level is lowered by 4Dq (4Δ/10), and the eg level is raised by 6Dq (4Δ/10) rela�ve to the average E of the d orbitals.   What is the net change for a d10 ion with 6t2g and 4eg e-­‐’s?   For all configura�ons other than d0, d5 (high-­‐spin, more on this later) and d10, spli�ng lowers the total E of the system as compared to the spherically symme�c case because e-­‐’s preferen�ally occupy the lower-­‐E orbitals. The decrease in E caused by the spli�ng of the E levels is the ligand-­‐field stabiliza�on E (LFSE). 4
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Crystal and Ligand Field Theories Crystal and Ligand Field Theories   Electrons enter the t2g orbitals in accordance with whose rule?   [Cr(NH3)6]3+ has 3 unpaired e-­‐’s = 3 (-­‐4 Dq) = -­‐12Dq   The LFSE for any octahedral Cr(III) complex is -­‐12Dq but the value of Dq varies with the ligand.   Two configura�ons t31g, e1g and t42g are possible for a d4 ion in the ground state. For t32ge1g the fourth e-­‐ occupies the eg level, giving four unpaired e-­‐’s: LFSE is 3(-­‐4Dq) + 1(6Dq) = -­‐6Dq. For t42g, the LFSE is 4(-­‐4Dq) = -­‐16Dq.   Which one of these configura�ons a given complex adopts depends on the rela�ve magnitudes of the ligand field (Dq) and the unfavorable poten�al E of the repulsion of two e-­‐’s occupying the same orbital with spins paired (the pairing E, PE). If Dq (and therefore 10Dq) is rela�vely small compared to the PE, it will be energe�cally more favorable to expend 10Dq in E to place the fourth e-­‐ in an eg orbital instead of pairing it with another e-­‐ in a t2g orbital: t32ge1g. This referred to as the weak-­‐field case, since the spli�ng is small w/r to PE, or the high-­‐spin case, since there is a maximum number of unpaired spins. Crystal and Ligand Field Theories Spectrochemical Series and Factors Affec�ng Δ   If 10Dq is very large compared to the PE, placing the fourth e-­‐ in a t2g orbital produces the t42g configura�on, the lower E state. This is referred to as the strong-­‐field case, or the low-­‐spin (or spin-­‐
paired) case. The net E gain in the strong-­‐field case is of smaller magnitude than -­‐16Dq by the amount of E required for pairing the e-­‐.   Maximum LFSE if obtained for what configura�on in what field?   The order of ligand-­‐field strength (decreasing Dq) for common ligands is approximately: CN-­‐ > phen ~ NO2-­‐ > en > NH3 ~ py > H20 > C2O42-­‐ > OH-­‐ > F-­‐ > S2-­‐ > Cl-­‐ > Br-­‐ > I-­‐   The high ligand-­‐field effect of CN-­‐ and 1,10-­‐
phenanthroline is atributed to π bonding: therefore, low spin, large D, max. occupancy of the t2g orbitals.   The spli�ng (10Dq) increases as the charge on the metal ion increases, because the ca�on radius decreases with increasing charge and the ligands Spectrochemical Series and Factors Affec�ng Δ Spectrochemical Series and Factors Affec�ng Δ would be more strongly a�racted by the higher charge. The spli�ng, for the same ligands, increases and the PE decreases for the second and third transi�on series compared with the first transi�on series.   Why? 4d and 5d orbitals are larger than 3d orbitals, extend farther from the central atom, and are affected to a greater extent by the the ligands.   Because 4d and 5d orbitals are larger than 3d orbitals, it is less energe�cally unfavorable to pair two electrons in the same orbital: PEs are smaller. PEs for the same number of d electrons also increase with increasing oxida�on number, because of increased electron repulsion resul�ng from the contrac�on of d orbitals with increasing posi�ve charge. Δ ,KJ/mol Complex 274 [Co(NH3)6]3+ 408 [Rh(NH3)6]3+ 490 [Ir(NH3)6]3+ 5