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Molecular Orbital, Valence Bond, and Ligand Field

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Molecular Orbital, Valence Bond, and Ligand Field A comparison of theories Andrew D. Liehr Bell Telephone Laboratories, Inc. Molecular Orbital, Valence Murray Hill, NewJersey Bond, and Ligand Field Before jumping into the intricate details magnetic criterion. [A most recent example of such of the various theories of valency, let us first pause a a blow is the demonstration by McGarvey (4) that hit and try to obtain some historical insight into their the odd electron in square planar CU+=complexes is course of development, their successes, and their in a 3d-like orbital and not a 4p-like orbital.] At the failures. Only in this manner shall we be able to present time the valence bond theory of coordination assess with any assurance the future progress of the compounds is being systematically supplanted by a theory of the chemical bond. molecular orbital-crystal field amalgamation, which Soon after the announcement of the Schrodinger has been aptly dubbed ligand field theory. [Crystal equation for electronic motions, there were proposed field theory was originally an ionic theory of chemical and utilized three approximate means of formulating bonding until modified by Van Vleck. In its modified solutions of this equation as it applied to molecular form it was a highly simplified molecular orbital theory problems: (1) the valence bond technique of Heitler, of the nd, (n + l)s, (n + l)p, and nf electrons in which London, Slater, and Pauling; (2) the molecular orbital orbital energies were of the molecular orbital type, but technique of Hund, Bloch, Mulliken, Lennard-Jones, electron-electron electrostatic repulsion energies and and Hiickel; and (3) the crystal field technique of spin-orbit energies were of the atomic type. Ligand Bethe, Kramers, and Van Vleck. Each of these field theory is a molecular orbital theory of the nd, techniques had its limitations, its strong points, and (n + l)s, (n + l)p, and nf electrons in which both the its weak points. And the years 1930-45 saw a struggle individual orbital energies and the electron-electron among the three for pre-eminence in the minds of repulsion and spin-orbit energies- are of a molecular chemists and physicists, even though Van Vleck had type. I shown in 1935 that they were absolutely equivalent Why has this particular pattern of historical dynam- when carried to completion (2, 3). These years wit- ics evolved? The answer to this question is simple: nessed the adoption of the valence bond and molecular the valence bond theory, although it is by far and away orbital methods by the organic chemist, the valence the superior outlook for ground electronic states, bond method by the inorganic chemist, the molecular becomes hopelessly complex as a description of excited orbital method by the molecular and solid-state electronic states. The jungle of ionic valence bond chemist and physicist, and the crystal field method by struebures nverruns all attempts to describe electronic the magneto-physicist. Each of these adoptions had excitations by this technique. Molecular orbital and the same driving reason: most chemists and physicists crystal field theory on the other hand suffer from the of this era were primarily interested in the ground complementary deficiency: they provide adequate electronic states of chemical systems. pictures of the excited electronic states, hut not of With the end of the war, scientific interest began to the ground electronic state of most molecules (they usu- swing toward a concern over the excited electronic ally introduce too much ionicity into the ground elec- states of molecules. This precipitated a rapid fall tronic state). Therefore as long as ground electronic from favor of the valence bond theory, and a consequent state properties were the vogue, valence bond theory rise in esteem of the molecular orbital and crystal field shone, but when the properties of electronically excited theories. Thus in all fields of chemistry except in- states became the style its gleam was dulled. organic, valence bond ideas concerning the nature of With this historical perspective behind us, let us excited molecnlar states made their exit in the years now see how to extend the ligand field technique to 1945-55. But with the accelerated interest in in- encompass all inorganic compounds. In two frequently organic spectroscopy by inorganic chemists com- overlooked papers by Kimball (5) in 1940 and by mencing around 1955, even this last stronghold of Eisenstein (6) in 1956, there are tabulated the sym- valence bond concepts has begun to fall. Indeed, in metry classifications of the primary atom and ligand the particular area of inorganic chemistry called atom orbitals for most geometries of interest. With coordination chemistry, valence bond theory has these classifications written down once and for all, suffered its most grevious blows; even its descriptions it is a simple matter to construct a molecular orbital of the ground electronic charge distributions have energy level diagram, and with this diagram to predict proved false in many important cases, especially with the number and classification of the excited electronic regard to the much vaunted, but completely specious states. We shall demonstrate this fact explicitly for a few exemplary systems. -- Presented at the Symposium an Ligand Field Theory, 140th In Figure 1 we show the orbitals which are primarily Meeting of the ACS, Chicago, September, 1961. involved in the bonding of a linear MX2 transition Volume 39, Number 3, March 1962 / 135 metal compound (e.g., CuC12). We have written down, of the ligand orbitals and the a.+* and T.* antihonding from Kimball's and Eisenstein's tables, the correct sym- orbitals are composed mostly of the primary atom metry designations of the primary atom and ligand nd+ and nd,,, orbitals, respectively. Hence, for atom orbitals prior to compound formation; that is, CuCI2 we expect the ground electronic state to be a for symmetrically disposed reactants at infinity. Then 2Z,+ state [as there is one unpaired electron in the cg+* orbitarcapital letters denote the over-all state electronic distribution], a state with zero orbital angu- lar momentum along the molecular axis, and the first two excited states to be the so-called nd excitations, TI, and 2Ax,which arise from the one electron jumps s.*-te,+* and 8. - c.+*, each. This is what is actu- ally observed (8). As a second example, we present in Figure 2 the energy levels of a square planar complex such as . .. Figure 1. Molecular orbitals for a linear triotomic transition metal com- pound (Dd. Note that the <-bond strudure is closely approximated by the valence bond hybrids r'p'dl, and nots'p' or pld'alone. recalling that the symmetry quantum numbers,' c.+, c.+, s,, 6,, etc., are exact quantum numbers at all internuclear distances, we allow the reactants to ap- proach one another in a symmetrical fashion to pro- duce the ha1 molecule, and we combine only those primary atom and ligand atom molecular orbitals to form the complete over-all bonding, antibonding, and nonbonding molecular orbitals, which have the self-same symmetry designations (i.e., symmetry quan- PeIMAW ATOM MOLECULAR ORBlTAL5 LlCAND MOLECULAR tum numbers). We can, of course, obtain only so ORBITALS OF THE COMPOUND ORBITALS many complete bonding and antibonding molecular Figure 2. Molecular orbitdr for o square planar transition metal complex orbitals of a given symmetry type as there are primary IDd Observe that the o-bond structure is well approximated by the atom and ligand atom orbitals of this same symmetry volence bond hybridsr'p'ff, ond notr'p2d'orpzd2alone. classification initially present. The ordering of the resultant molecular orbitals of the product molecule PtC14-2.2 The placement of the bonding and anti- is completely based on qualitative concepts: the more bonding orbitals is again accomplished by qualitative the primary atom and ligand orbitals are directed principles and may be subject to reordering. The toward one another, the deeper the consequent bonding location of the a@* orbital, which is primarily nd,, orbitals will lie and the higher the consequent anti- bonding orbitals. will lie. For example, the cs+* %Themolecular symbols corresponding to the atomic s, p, d, f, antibonding orbital lies higher than the s.* antibonding etc., designations for non-linear compounds are a, b, e, and 1 orbital, as the primary atom c.+ orbital, nds2,is direc- (an icosahedral molecule has the additional symbols y. and h, ted more strongly toward the ligand cg+ orbital than which are not to be confused with tho analogous atomic terms). The molecular symbol a corresponds to the atomic s (and the the primary atom s, orbital, nd,,,,,, is toward the linear molecule designation a)-it means that the molecular wave ligand T. orbital (the molecular axis is the z axis). function does not change sign under a rotation of 2rln about the Moreover, as the ligands have a greater affinity for molecular n-fold rotational axis of symmetry (e.g., the four-fold z their electrons than does the primary atom, the c.+ axis of PtCL-2): the symbol b means that it does. (In a very s, direct sense this is equivalent to saying that the molecular a type and bonding molecular orbitals are composed mostly orbitals have a component of angular momentum along the n-fold rotational axis of symmetry (the e axis) whose magnitude is a 'For the linear molecule the Greek letter symbols (G, r, 6, p multiple of n (e.g., 0 or n), and the b type a companmt which is etc., replace the stomic designations a, p, d, j, etc. Just as these an odd multiple of n12.) The symhals e and 1 mean that the Latter symbols denoted orbital angular moments of 0, 1, 2, 3, ete., molecular wave function is degenerate (just as the atomic states respectively, in the atom, the former now indicate the magnitude p, d, f, eto., am degenerate), with two-fold and three-fold do of the component of orbital angular moment 0, 1, 2, 3, etc., along generacy, respectively (the icosahedral g and h symbols indicate the internuclear axis (thez axis) of the moleoule.
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