1. B. Brill University of Delaware Newark, 19711
d Orbitals in Main Group
Does the existence of such species as SiF62-, PCls-, SFe, and PF5 indicate a large d orbital contribution to main group element a-bonding? Does the difference in products upon acid hydrolysis of NC13 compared to PC13 HC1, respectively) demon(NH3 + HOCl and Hap03 strate the importance of phosphorus d orbitals in the kinetic transition state? Is N(SiH3)a planar and N(CH& pyramidal because silicon, unlike carbon, has empty lowlying d orbitals to accept the lone pair electron density from nitrogen? Questions of this type arise frequently in chemistry teaching and can be attributed quite satisfactorily to d orbital involvement in the main group elements. In point of fact, however, there is a dichotomy among chemists as to whether the outer d orbitals are really needed or not (1-9). Definite answers have been elusive in spite of the inundating amount of research data available. By no means is the pretense made here of resolving the d orbital issue. Rather an exposition of some of the reasons why the problem exists in the first place together with several alternative explanations for supposed d orbital usage is intended.
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Techniques for Study A survey of the physical and theoretical arsenal used to examine d orhital effects is an informative starting point since it is from these sources that data are gathered upon which interpretations are based. The ideal instrumental technique that does not disturb electrons in the course of their study and provides an absolute measurement of electron density at various points in a molecule does not, of course, exist. Some spectroscopic interpretative methods attempt to approximate this ideal, but because they are approximations, there is a substantial degree of sport associated with their use. Spectroscopic Techniques X-ray, neutron, and electron diffraction and microwave spectroscopy are the most powerful tools available for molecular structure studies. They mainly provide atom positions, however, and speculation enters in deciding the electron distribution that might give rise to those positions. UV-visible, photoelectron, ir, nmr, esr, nqr, Mossbauer and X-ray spectroscopy give information about electron distribut~on,but it is not always clear to the operator how the information relates to the actual distribution and to what extent such a distribution affects the observed parameters. The higher energy techniques, such as X-ray and uv spectroscopy, yield excited state information that is not always transferable to the ground state orbital participation. ESR, nmr, nqr, Mossbauer, and, within reasonable limits, ir spectroscopy are ground state techniques. Unfortunately, simplified models must usually be invoked to interpret the spectra and as a result, no one technique is completely reliable. Nor can one expect a combination of these methods to give a correct description of the molecular electronic structure because each is sensitive to different parameters. The datum from one technique will not necessarily correlate with that of another. All of these methods have been used to derive information 392
/ Journal of Chemical Education
about d orbital participation. Because the effects are small and because of the aforementioned difficulties, d orbital usage could easily be misjudged. Definitive distinctions and separations of valence shell electrons seem imphssible using the available physical methods because of these natural limitations. Theoretical Methods Semi-empirical and non-empirical calculations related to outer d orbitals are in great abundance. Information from these data, although frequently intriguing, must be treated with caution, because once again, the inherent assumptions are often drastic. As calculations become more sophisticated the concept of d orbitals as we think of it will be lost. The orbitals used a t the present time in sophisticated calculations bear little resemblance to their hydrogen-like counterparts. d Orbitals
Rightly or wrongly, hydrogen-like s, p, d, f, . . . orbitals are mentioned frequently when discussing multielectron systems. In this classification. main m o u ~elements make extensive use of their ns and electrons in bonding. The unfilled high energy nd orbitals occasionally are brought in to account for valence shell expansion and to rationalize differences between first and second row elements. Valence shell expansion using nd orbitals in a-bonding was introduced by Pauling (10) to account for the existence of five and six coordination. In 1954, Craig, et al. (II), formalized arguments for the use of nd orbitals in a-bonding in certain circumstances. Perhaps the best justification for the hydrogen-like model in multielectron atoms is that the angular moment a of electron configurations can be correctly predicted in observable atomic spectroscopic states (12). Historically and more popularly, this atomic consideration has been carried over to molecules and assumed to be a valid anproximation there. One electron wavefunctions do provide a pictorial formalism for rationalizine a broad sDectrum of chemical facts that might otherwisegppear r a h e r mysterious. This latter context is a recognized oversimplification because, in reality, electron-electron repulsion and configuration interaction between states greatly affect the atomic and molecular description (13). It is extremely difficult to ascertain the true characteristics of orbitals, particularly unfilled high energy nd orbitals in atoms, not to mention in molecules. Jorgensen has suggested consideration of the continuum of energy states lying above the ionization potential, rather than d orbitals, to account for the "softness" of second row main group elements compared to their first row congeners (14). The continuum idea is conceptually difficult to grasp; i t does intimate, however, that a t least part of the d orbital fray may be due to the semantic question of how to describe high energy states that are essentially devoid of electron densitv. For the purpose i f pointing out alternate explanations. the existence of orbitals will be a c c e ~ t e dhere. The d orbitals having proper symmetry for a-and s-bonding evolve directly from group theory (15). For octahedral
F Q.re 1 A p ctor a representauon bl r overlap of a d l > . o , , or dn arD m wlth a s.osl !.en1 p orb ra m an aclaneora rnoecr e The dolled n5811 s q n f e s tne etiect on tne d orola at a n ahlv e ectroneaat " re s ~ b -
stitueni (see text).
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to molecules. The presence of a highly electronegative substitnent field, such as that created by N, 0 , or F, could greatly reduce the energy differences (11). This is because electron 'density is drained off the central atom. The subsequent increase in the atom's effective nuclear charge lowers the orbital energies. Secondly, if the radial maximum of the d orbital is large with respect to the bond lengths, they can make only a small contribution to atom-atom overlap in the bonding region. SCF estimates place the 3d orbital radial maximum of sulfur as large as 5.6A (18). A highly polarizing field, however, could contract the d orbitals into the range of covalent bond lengths (11, 20). Although involution of orbital contraction by substituent field effects has been deemed unnecessary (2lJ, it makes the use of d orbitals more plausible. Thus, three factors, proper symmetry, similarity in size and similarity in energy are necessary conditions for significant mixing and bond formation between orbitals. The presence of a highly electronegative substituent field could enhance outer d orbital usage. d Orbitals in a-Bonding
Figure 2. r overlap of the dx2-pand ds? orbital with substituent p arbitals in a tetrahedral molecule. The projection shown is somewhat distorted (seeref. ( 3 1 ) )
complexes, such as SFe, PC16-, and SiFs2-, the d,2 and d*-,2 orbitals on the central atom have e, symmetry and can enter into a-bonding (eg, sp3d2 hybridization); the d,,, d,,, and d,, orbitals have tz, symmetry and can be used for r-bonding with the appropr~ateligand orhitals (Fig. 1). In tetrahedral main group molecules, such as SiCl4, PC14+, and S042-, the a framework is adequately described as an spa hybrid 5et.l The d,=-,z and d , ~orbitals have * symmetry according to Figure 2. The traditional description of trigonal hipyramid hybridization in say PF5 is sp3d, although other sets, such as m ( n + l)sp3, m(n + l)spd2, nd(n + l)dp3, nd3(n 1)dp and spd3 also satisfy symmetry requirements (15). In the spad set, a pad,* hybrid is commonly used to form the axial orbitals with a separate sp2 set making up the equatorial plane. However, in terms of hydrogen-like orbitals this separation is not complete (16). The remaining d orbitals can ?r bond in trigonal bipyramidal molecules. Note that the m(n + l)sp3 hybrid set for a D3h symmetry molecule does not involved orhitals. The possibility of overlap by symmetry arguments is a necessary but not a sufficient condition for mixing and honding. The two crucial factors neglected in the foregoing symmetry survey pertain to the energy and radial diffuseness of the d orhitals. First, if the i ~ dorbitals are energetically too far above the m and np orhitals, they will not mix to any great extent to form either a or s honds (11). For example, the promotion energy to the 3s23p43d1(2P) state in free chlorine is 11.2eV (17), and achieving the sp3dZ(TF) state in sulfur has been estimated to require 24.8 eV (18). The sp3d state in phosphorus is about 16eV above the s2p3 configuration (19). In consequence, little mixing of d states with s and p states would be expected in those atoms; the energies, however, are not representative of the promotion energies that might apply
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Some chemical facts easily attributed to the importance of d orbitals in a-bonding may also be related to the purely practical question of packing efficiency. For example, the non-existence of CFe2-, NFs and OF6 in light of the stable species, SiFe2-, PF5 and SF6, may be due to an insufficient amount of space around the first row atom kernels for a large number of fluorine atoms (22) rather than the absence of d orbitals in the valence shell. The suggestion that n orbitals are needed for n honds has lost favor in chemistry (3). The use of five carbon orbitals to form CH5+ (=),as an example, is regarded as energetically unreasonable. Further, the use of two full outer d orbitals to form sp3d2 hybrids in MX6n- compounds has been questioned (24). Only al, + tl, e, AO's have proper symmetry to mix and form six equivalent octahedrally disposed orbitals (15), but this does not say that the entire orbital must enter in the proportion prescribed by sp3d2. Rundle (24) suggested that 3d orhitals, and 3s orbitals for that matter, are not needed a t all to describe SF6 if three-center molecular orhitals are introduced. Considering a linear FSF linkage along the r axis in SFe, the 3p, orbitals on each atom may mix according to Figure 3. The four electrons in this set of MO's will occupy the bonding and non-bonding orbitals. The two other FSF units on the y and z axes combine in the same way t o give a complete picture of SF6 using only p orbitals. A similar model can be developed for the axial bonds in a trigonal bipyramidal structure obviating the need for d orbitals there as well. Because only two electrons are bonding in each three-center four-electron unit, the bond lengths should be longer than the two-center two-electron equatorial bonds. This is true of the axial bonds in the trigonal bipyramidal structure. It is interesting to note that in SFe, however, the S-F bonds are a few hundreths of an A less than the Shoemaker-Stevenson corrected sum of the covalent radii (5). If some 3s character were mixed into the pure p honds, they could become shorter (25) giving better agreement with experiment.2 Thus, the SF6 molecule and any MXen- species can be described in MO formalism without the use of d orbitals. In fact, i t is thought that the 4s level of sulfur and perhaps even the 4p level is lower in energy than the 3d level (26). If this is the case, 4 s 4 p partial contribution would he more reasonable before 3d. Additional sustenance for
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'The d,,, d,,, and d,, orbitals have proper symmetry far sd3 o-bonding hybridization but are inappropriate by themselves because of their inversion center (see Wiser (63)) Volume 50, Number 6, June 1973 / 393
ENERGIES FSF
S
3P
2F
,-
;K'
t
Figure 3. Three-center four-electron molecular orbitals formed by three p, orbitals. The MO's shown are not normalized.
this model comes from the vacuum uv spectrum of SFe. The high energy absorption bands look more like 4p Rydhergstates rather than 3d states (27). These emnirical arguments contrast somewhat with SCF calculations on sF6which emphasize the importance of ~- 3d -~ orbitals (20. , ~21. ., 281., It is thought that the 4s orbital could he quite competitive in bonding with 3d, however (28). If 3d orhitals are used in these compounds, it may well be that they enter with the weight which is less than that implied by sp3d2 hybridization. It should be mentioned that in light of the high promotion energy to the 3d level, Pauling (10) suggested the use of ionic resonance forms to describe many main group element molecules ~
A simple electron count in some halogen and interhalogen compounds, such as ICl3 and Is-, based on their nqr spectra implies that d orbitals are not used to any great extent in bonding (29) even though the d,l2 orbital has the proper symmetry. From microwave data in CIF it has been suggested that some 3d character in the CIF bond may he needed to account for the unusual molecular quadmpole moment (30). Undoubtedly 3d character exists in the CIF wavefunctions, but 4s and/or 4p character could also account for the observations. d Orbitals in T-Bonding
The same energy, symmetry, and radial diffuseness arguments that apply to orbitals in a-bonding also apply to a-bonding. However, orbital contraction need not be quite as great because the bonding interaction takes place in regions off the internuclear axis. X04n- ions (X = Si, P, S, C1) have been extensively studied (31, 32). The electronegative field of the oxygen atoms could enhance X atom d orbital utilization. A paper favoring substantial X - 0 a-bonding has been presented by Cruicksbank (31) based largely on the shortness of X - 0 bond lengths and t h e sizeable 0 - X - 0 bond angles in several polynuclear species. The evidence is qualitatively convincing hut several poignant questions have It is an empirical observation that as the percent s character in a bond increases, the bond becomes shorter and stronger (25). This is contrary to the hybridization prediction (see Coulsan 2
(64)). 394 /Journal
of Chemical Education
been asked about the assertions (3); namely, how large is the 3d(X) - 2p(0) energy mismatch, and how long would the X - 0 bonds he without the use of d orbitals on X? Jorgensen has also expressed the opinion that the first excited state in S O P and C l O 4 does not involve d states (3). Urch (33), on the other hand, claims to have direct evidence of 3d - 2p a-bonding in XO4"- ions from their X-ray fluorescence spectra. Regretfully, the X-ray data were interpreted in terms of a very simplified MO model. The shortness of X - 0 bonds and the desirability of reducing the potentially high charge on X favor X - 0 a-bonding, but the bonding in S Z O ~ ~and - , Sz0+, and S ~ 0 6 ~has been accounted for quite adequately using only s and p orbitals (34). Truter was led to conclude that no theory yet can satisfactorily account for bond lengths and angles in all 0x0 compounds of sulfur (35). Classic examples of compounds in which dpr-bonding is supposed to occur contain group IV-V atom bonds. Considering group IV atom geometry about tricoordinate group V atoms (Table I), Si3N and Ge3N frameworks are planar implying ideal r overlap of N(2p) and Si or Ge d orbitals (11, 36). The remaining molecules are pyramidal with suhstituent angles between 94" and 99". Much less multiple bond character can occur a t these smaller angles (37). However, the abruptness of the change from N to P and As is curious if attributed solely to dpr-bonding, particularly since N(CH3)3. where there is no multiple bond character, has a C-N-C angle of 111" (38). Additional effects may be operative and possibly overriding. The high electronegativity of the nitrogen atom can polarize Si to a relatively positive charge. Core-core repulsions could force the silicon atoms apart thereby enhancing r-bonding (4). Also, as the Si-N-Si angle increases, the percents character in the Si-N bond and the percent p character in the lone pair increases. These changes tend to shorten the Si-N bond (25) and enhance d p r overlap. Thus three factors, i.e., core-core repulsions, Si-N a bond character, and the p character of the lone pair, in addition to r-bonding, may he important in determining the geometry of (H3Si)sN and (H3Ge)sN. Bonds between group IV atoms and P or As will not be nearly so polarized. Hence, corecore repulsions and lone pair p character will not be as great, and retention of the more common pyramidal geometry is more likely. Similar effects are found in Group IV-VI atom bonds (31, 39). Si-0-Si angles are found to vary from 125-165" depending on the environment (31). This contrasts with the C-0-C unit which varies little from a tetrahedral angle (40). The flexibility of the linkage involving silicon means that the oxygen atom is able to rehybridize readily. Table 1. Substituent Bond Angles in Compounds Containing Group IV-V Atom Bond@
Compound
Angle
dBartell, L. S., and Brockway, L. O., J. Chem. Phys., 32, 512
(1960).
'Beagley, B., Robiette, A. G., and Sheldrick, G. M., J Chem. Soc., A, 3002.3006 (1968). r Rankin, D. W. H., Robiette, A. G., Sheldrick, G. M., Beagley, B., and T. G. Hewitt, J. Inorg. Nuel. Chem., 31,2351 (1969). gSpringall, H. D., and Brockway, L. O., J. Amer Chem. Soc., 60,996 (1938).
The Si-0 bonds are also shorter than the Shoemaker-Stevenson corrected sum of the covalent radii. These ohservations have been interpreted as evidence of S i - 0 dpn bonding (31). However, as the Si-0-Si angle increases, the percent s character in the S i - 0 bond increases, this will also lead to bond shortening. Further, the:Al-F-Alw,> ,."..,.
(477) Mathieso", A. M., Mellor. D. P.. and Stephenson. W. D.. *
