Yves Jean - Molecular Orbitals of Transition Metal Complexes (793957), страница 5
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Yet, for every metal except palladium, the s orbital is at leastpartially occupied in the ground state of the isolated atom (see Table 1.1).A detailed study of the electronic structure of complexes, presented inChapter 2, will show us that the nonbonding electrons on the metal doindeed occupy pure d-type orbitals, or molecular orbitals whose maincomponent is a d-type atomic orbital.1.2. An alternative model: the ionic modelThere is a second method for counting the electrons in a complex anddeducing the metal’s oxidation state and electronic configuration. Thisis the ionic model, in which one supposes that a complex is formed bya metal centre and by ligands which always act as Lewis bases, supplyingone (or several) pairs of electrons.1.2.1.
Lewis bases as ligandsIn the covalent model, neutral ligands L (or Ln ) supply one (or n)electron pair(s) to the metal: for example, one for amines (NR3 ),phosphines (PR3 ), the carbonyl group (CO), and derivatives of ethylene (R2 C==CR2 ), and three for benzene (C6 H6 ) in the η6 coordinationAn alternative model: the ionic modelmode. As these ligands already behave as Lewis bases in the covalentmodel, we shall continue to consider them in their neutral form L (orLn ) in the ionic model.However, an X-type ligand in the covalent model is a radical specieswhich supplies only a single electron to the metal. To ‘transform’ itinto a Lewis base, one must add an electron and therefore consider itin its anionic form X− . In this way, the radical ligands H (hydrogen),Cl (chlorine), and CH3 (methyl radical) of the covalent model becomethe H− (hydride), Cl− (chloride), and CH−3 (methyl anion) ligands inthe ionic model.
Analogously, Xx ligands in the covalent model, whichhave x unpaired electrons, become Xx− ligands in the ionic model. Forexample, O (X2 ) and N (X3 ) are now described as O2− and N3− . Ingeneral, one completes the ligand’s valence-electron shell so that the octet ruleis satisfied.This is generalized for ligands of Lℓ Xx type in the covalent model,which quite naturally become Lℓ Xxx− ligands in the ionic model. Thecyclopentadienyl radical (Cp), a neutral species with five π electrons(an L2 X ligand, 1-5), is therefore considered in its monoanionic form(Cp− with six π electrons).
Table 1.3 presents the numbers of electronsattributed to the principal ligands that have been considered so far in thecovalent and ionic models.The additional electron supplied to an X-type ligand to transformit into a Lewis base comes, of course, from the metal. The metal–ligand ensemble is therefore described as an X− ligand interacting witha metallic cation M+ , thereby giving a purely ionic description of themetal–ligand bond. As a consequence, a complex which was writtenMLℓ Xx in the covalent model is represented, in the ionic model, as ametallic cation of charge x bound to (ℓ + x) Lewis bases (1.5).[MLℓ Xx ] (covalent model) → [M(x)+ (L)ℓ (X− )x ] (ionic model).(1.5)If the complex has an overall charge q, the charge on the metalliccentre in the ionic model becomes (x + q) (1.6).[MLℓ Xx ]q (covalent model) → [M(x+q)+ (L)ℓ (X− )x ] (ionic model).(1.6)This ‘redistribution’ of the electrons within the complex can bejustified by the higher electronegativity of the ligands than of the metals(see Table 1.2): an X-type ligand ‘attracts’ the two electrons of the metal–ligand bond to itself, and becomes X− .
In conclusion, we note that thename given to several complexes is directly linked to the ionic model.Thus, complexes with several H ligands ([ReH9 ]2− , for example) arecalled ‘polyhydrides’.Setting the sceneTable 1.3. Number of electrons supplied by several common ligands according to the covalent andionic modelsCovalent modelLigand (type)H, Cl, OR, NR2 , CR3 , CN(X ligands)CO, NR3 , PR3 , H2 ,R2 C==CR2 (L ligands)O, S, NR (X2 ligands)Ionic modelNumber of electrons1e2e2eLigandH− , Cl− , OR− , NR−2,−CR−,CN3CO, NR3 , PR3 , H2 ,R2 C==CR2O2− , S2− , NR2−4eη4 -diene (L2 ligand)2e4eη4 -diene6eη5 -Cp−η5 -Cp (L2 X ligand)6eµ-O (X2 ligand)2e4e5eη6 -arene (L3 ligand)µ-Cl (LX ligand)Number of electrons6e3eη6 -areneµ-Cl−4e2eµ-O2−4e1.2.2.
Equivalence of the covalent andionic models: examples1.2.2.1. Oxidation state and dn electronic configurationIn the covalent model, the oxidation state of the metal, no, is equal to thecharge left on the metal after having carried out a fictitious dissociationof the complex in which all the ligands take the two bonding electronswith them (§ 1.1.2.2). For a complex whose general formula is [MLℓ Xx ]q ,one therefore obtains no = x + q (see equations (1.2) and (1.3)). In theionic formulation of this same complex, (see equation (1.6)), the chargeon the metal is just equal to x + q, so the ionic and covalent modelslead to the same oxidation state no for the metal.
It follows that thesame electronic configuration dn is obtained by the two models, since nis equal to the number of valence electrons on the metal (m), minus itsoxidation state no (equation (1.4)).An alternative model: the ionic modelExamplesCovalent modelIonic model[Ir(CO)(Cl)(PPh3 )2 ][Ir(L)3 (X)] typex = 1; q = 0 ⇒ no = +1m = 9 ⇒ n = 9 − 1 ⇒ d8(Ir+ )(CO)(Cl− )(PPh3 )2 ]no = +1m = 9 ⇒ Ir+ : d8[Fe(η5 -Cp)2 ][Fe(L2 X)2 ] typex = 2; q = 0 ⇒ no = +2m = 8 ⇒ n = 8 − 2 ⇒ d6[Mn(CO)6 ]+[Mn(L)6 ]+ typex = 0; q = +1 ⇒ no = +1m = 7 ⇒ n = 7 − 1 ⇒ d6[Ni(CN)5 ]3−[Ni(X)5 ]3− typex = 5; q = −3 ⇒ no = +2m = 10 ⇒ n = 10 − 2 ⇒ d8[(Fe2+ )(Cp− )2 ]no = +2m = 8 ⇒ Fe2+ : d6[(Mn+ )(CO)6 ]no = +1m = 7 ⇒ Mn+ : d6[(Ni2+ )(CN− )5 ]no = +2m = 10 ⇒ Ni2+ : d81.2.2.2. Total number of electronsThe equivalence of the two models for the calculation of the totalnumber of electrons in a complex (Nt ) is shown by a further look atthe four examples above.Covalent modelIonic model[Ir(CO)(Cl)(PPh3 )2 ][Ir(L)3 (X)] typeIr1 CO2PPh31 ClNt9e2e4e1e16e[(Ir+ )(CO)(Cl− )(PPh3 )2 ]Ir+8e1 CO2e2 PPh34e1 Cl−2eNt16e[Fe(η5 -Cp)2 ][Fe(L2 X)2 ] typeFe2 CpNt8e10e18e[(Fe2+ )(Cp− )2 ]Fe2+6e2 Cp−12eNt18e[Mn(CO)6 ]+[Mn(L)6 ]+ typeMn6 COChargeNt7e12e−1e18e[Ni(CN)5 ]3−[Ni(X)5 ]3− typeNi5 CNChargeNt10e5e3e18e[(Mn+ )(CO)6 ]Mn+6e6 CO12e18eNt[(Ni2+ )(CN− )5 ]Ni2+8e5 CN−10eNt18eSetting the scene1.3.
Principles of orbital interactionsWhen we use molecular orbital (MO) theory, the term ‘orbital structure’of a complex, or of any molecule, means the shape and the energeticorder of the MO. Usually, these orbitals are expressed as Linear Combinations of Atomic Orbitals (LCAO) of the different atoms that makeup the system being studied.
The shape of an MO is determined by therelative magnitudes and the signs of the different coefficients. The electronic structure is then obtained by placing electrons in these orbitals,filling first those which are lowest in energy.To construct the MO, it is often advantageous to decompose themolecular system being studied into two simpler sub-systems whoseorbitals, either atomic or molecular, are already known. The MO of thecomplete system are then obtained by allowing the orbitals of the twofragments to interact.
In this paragraph, we shall remind the reader ofthe principal rules which control the interaction between two orbitalson two fragments. For simplicity, we shall treat atomic orbitals, butthis limitation will not affect the general nature of our conclusions inany way.1.3.1. Interaction between two orbitals withthe same energyConsider, for example, the interaction between two identical orbitals ofs type, χ1 and χ2 (Figure 1.1).The interaction produces a bonding (φ+ ) and an antibonding MO(φ− ).
The first is the in-phase combination of the two orbitals χ1 andχ2 (coefficients with the same sign), while the second is the out-of-phasecombination (coefficients with opposite signs) of these same orbitals. Ineach MO, the coefficients of χ1 and χ2 have the same magnitude, sincethe interacting orbitals are identical.In energy terms, the bonding MO is lower in energy than the initialAO, but the antibonding MO is higher. It is important to notice thatthe destabilization of the antibonding level (E − ) is larger than thestabilization of the bonding level (E + ). It can be shown that these–1Figure 1.1.
Interaction diagram fortwo orbitals with the same energy.∆E ++∆E –2Principles of orbital interactions6The overlap Sij between two orbitals φiand φj is equal to the integral evaluated overall space of the product of the functions φi∗(the complex conjugate function of φi ) andφj : Sij = φi∗ |φi . For real functions, theintegral of the product of the two functionsis evaluated over all space.7We assume here that the total electronicenergy is equal to the sum of the individualelectronic energies. This relationship, whichhas the advantage of being simple, is obtainedwhen the electronic Hamiltonian is written asa sum of monoelectronic Hamiltonians, as inthe Hückel and extended Hückel methods.This approximate formula has, of course,limited application, but it is acceptable for aqualitative analysis of orbital interactions.Further details may be found in Structureélectronique des molécules, by Y.
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