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Higher Coordination Numbers of the Typical Elements.

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because the diazo groups in (177) and (179) are
derived from azides.
The author and his co-workers are gratefirl to Professor
Dr. B. Eistert for his interest in and support of this
work. Thanks are also due to the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie
for their generous financial support.
f I 78)
ates ( I 79) from ethoxyacetylene and benzenesulfonyl
azidesI76J. Neither of these reactions involves a CHacidic starting material, but they are mentioned here
[A 589 1EI
Received: September 29th, 1966; revised: June 9th. 1967
German version: Angew. Chem. 79, 786 (1967)
Translated by Express Translation Service, London
[761 P. Griinnngrr, P . V . Finzi, and C . Scotti, Chem. Ber. 98, 623
Higher Coordination Numbers of the Typical Elements‘’*I
The bonding in electron-deficient molecules, e.g. the boron hydrides and certain metal
alkyls, and in molecules which appear to violate the rare gas rule, e.g. hydrogen bonded
complexes, interhalogen compounds and compounds of the typical elements with high
coordination numbers such as PC15 and s F 6 can be described by a simple molecular
orbital treatment involving delocalized ri-bonds. The contribution of d-orbitals to the
bonding in the interhalogen compounds and rare gas fluorides is very small. The sterenchemistry and physical properties of the P X j system are explained readily by the delocalization treatment and it is likely that here also the importance of spd hybridization
has been overemphasized in the past.
1. The Basis of the Octet Rule
The electronic structure of an atom is determined by
two main principles.
a) According to the Pauli principle, no two electrons
may have the same set of quantum numbers, and
hence only a limited set of orbitals is available.
b) In the ground state, the electrons occupy the
lowest levels, and Hund’s rule states that electrons
(which have the same spin) will occupy separate
degenerate levels until such levels are filled.
Spectroscopic examination leads to values of orbital
energies, which enables two fairly distinct kinds of
atom to be recognised:
ii. Transition elements
For example:
i. Typical elements
Here the difference in energy between 3s, 3p, and 3d,
4s levels is very high [ I ] (ca. 8-10 eV) so that the characteristic compounds of these elements use 3s and 3p
orbitals only[***] in most of their compounds. Thus
the typical valency of sulfur is 2, of phosphorus 3, and
of silicon 4 (through 3s
3p promotion). I t is the
size of the 3s + 3d energy difference, such that the 3d
orbitals are close to the continuum, which is responsible for the octet rule.
Here the 4s and 3d levels have similar energies and the
3d levels are partially occupied, leading to spd hybridisation of the orbitals. The use of 3d orbitals and their
importance in determining the stereochemistry and
[*I Dr. R. F. Hudson
- ~.
[I] E. Moore, Atomic Energy Levels, Vol. 1 , Circular 467 Nat.
University Chemical Laboratory, University of Kent
Canterbury, Kent (England)
[**I Based on a lecture given at the Review Symposium on
“Modern Views of Valency and Bonding” at Southampton on
April 21st and 22nd, 1966.
Bur. Standards, 1949.
[***I Excited levels contribute to all bonding orbitals, but this
is a secondary effect and will be neglected at this point. The influence of these orbitals will be considered i n somecases a t a later
Angew. Chem. internal. Edit. 1 Vul. 6 (1967)
Nu. 9
physical properties of transition metal compounds is
beyond doubt.
This review deals solely with typical elements ( i e . nontransition elements) and particularly the electronic
structures of compounds which appear to violate the
octet rule. We shall not consider donor-acceptor
complexes of the kind H20
H, H3N
H and
ClI + C1, since in these cases the electron octet is
maintained around the central atom. It is noted that
the interhalogen cations e.g. IC120, but not the
corresponding anions IC12
conform to the octet
Abnormally high coordination numbers are found
for molecules where too few electrons are available
for electron-pair bonding (so-called electron-deficient
compounds) and also in molecules where more than
4 electron pairs appear to be localized around a
central atom. These two types of compound are
considered further in the following sections.
Electrostatic bonding of a carbanion to two cations could
explain some of these structures, as for example in electrophilic substitution at a saturated carbon atom [71 (4)(shown
The structure of the boron hydrides [21 posed a classical
problem of the nature of bonding in compounds in
which the number of bonding electron pairs is less
than the number of bonds. No progress in understanding their structures was made while the boron
hydrides were regarded as abnormal relatives of
hydrocarbons, and while the 2-electron bond was
assumed to be necessary for o-bonds, although many
kinds of resonance structures were proposed [31. The
first structural determination (of B ~ H I o )by Kasper
et al. [41 established hydrogen bridges of the kind
now known to be present in diborane (1).
The same type of bonding by alkyl groups in certain
metal alkyls was recognized about the same time ‘51,
e.g. the structures of A12(CH3)6 ( 2 ) , [(CH3)2Be]n,
show carbon to be 5-coordinated.
Recent work[61 has shown that the carbon atoms in
lithium alkyls are 6-coordinated in the solid state
(cf. the CH3Li tetramer in Fig. 1). Here the CH3
groups in the bridges play the same role as the hydrogen atoms in boron hydrides, i.e. forming one electron
bonds, e.g. as in (3).
[2] W . N . Lipscomb, “Boron Hydrides”, Benjamin, New York
[3] H . C . Loriguet-Higgins, Quart. Rev. I I , 121 (1957).
[4] J. S. Kasper, C . M . Lucht, and D . Harker, Acta crystallogr.
3, 436 (1950).
[5] R. E. Rundle, J. phys. Chem. 61, 45 (1957); J. chem. Physics
17, 671 (1949).
[6] E. Weiss and E. A. C . Lucken, J. organometallic Chem. 2,
197 (1964).
1.1. Electron-Deficient Compounds
Fig. 1. (a) Unit cell of methyl-lithium. (b) Stuart-Briegleb atomic
model of a tetrameric structural unit (CH3Li)a.
by the observed retention of configuration). Such an explanation can hardly hold for the boron hydrides in view of
the similar electronegativities of boron and hydrogen. It will
be shown that a simple MO description leads to a satisfactory treatment of the bonding in electron-deficient
compounds, as well as “electron-excess’’ compounds which
will now be considered.
1.2. “Electron-Excess” Compounds
1.2.1. T h e H y d r o g e n Bond[*]
The hydrogen atoms in the boron hydrides have the
unusual coordination number 2, although the electrons
around the hydrogen atom can be accommodated in
the Is level. This is not the case for hydrogen bonded
species, as it is quite clear from the Pauli exclusion
principle that two localized electron-pair bonds
cannot be formed by hydrogen. Pauling 191 recognised
the electrostatic nature of the bonding, e.g. as in
structure (S), and Lennard-Jones and Pople 1101 calculated the hydrogen bond energy of water (- 6 kcal/
mole) using a localized point charge model, which
took into consideration the lone pairs, as in (6). In
ice and in the ordered form of water, oxygen is
4-coordinated. In the solid state, ammonia also
assumes a symmetrical structure I l l ] with nitrogen
[7]D. J. Cram: “Fundamentals of Carbanion Chemistry”.
Academic Press, New York 1965.
[8] G . C . Pimental and A. L. McClellan: “The Hydrogen Bond”.
Freeman, San Francisco 1960; D.Hadri: “Hydrogen Bonding”.
Pergamon, London 1959.
191 L. Pauling, Proc. nat. Acad. Sci. U.S.A. 14, 359 (1928).
[lo] J. Lenrrard-Jones and J . A. Pople, Proc. Roy. SOC.205A,
155 (1951).
[ll] I . Olovssoir and D . H. Tenipleton, Acta crystallogr. 12, 832
Angew. Chem. internat. Edit./ Vol. 6 (1967)
/ No. 9
6-coordinated, as in (7) ; in view of the long NH-N
bond length of 3.4 8, compared with the N-H covalent
bond distance of 1.13 A, the bonding is predominantly
The amount of charge transfer varies greatly with the
type of donor as shown for example by the X-X
distances 1191 (Table 1).
Several difficulties are however encountered, e.g. the infrared -OH vibration frequency of water is too high to be
explained by electrostatic factors alone; more recent studies
estimate at least 7-8 % covalent character "21.
The electrostatic model has been applied [I31 to HFzO, but
here the molecule is symmetrical and the additional bond
energy is 26 kcal/mole (i.e. 80 kcal/mole for each bond
compared with 135 kcal/rnole for HF). Considerable covalent
bonding must be present in this molecule, but again we have
the question - what kind?
1.2.2. P o l y h a l o g e n Compounds[14]
There are three kinds of polyhalogen compounds,
a) anionic, e.g. Br30, b) cationic, e.g. IClz", and c)
those made up of neutral molecules. A11 the complexes
have an even number of electrons and with one exception (IF7) [ * ] all the bond angles are 90 ' or 180 '.
The X3Q molecules are linear (which may be conipared with the linear reaction coordinate of a Walden
inversion on carbon [*5l), whereas 1x2 is triangular.
The bond lengths of the triiodide ion[161 in
As @(CgH~)~13
0 are equal, whereas in NH413 and Cs13
one bond is longer than the others[l71, probably due
to crystal field effects.
These compounds may be compared with the so-called
charge-transfer compounds formed by the halogens,
interhalogens, and halogen compounds (e.g. CC4,
CHI,) with electron donors (n or ii). The original
structure (8) proposed by Reid and Mulliken (181 was
shown to be incorrect 1191, as the influence of the ionic
form, D @10, is over-exaggerated[**], and in all the
structures so far examined, the linear form (9) is
[12] C. A. Coulson, Research 10, 159 (1957).
1131 W. G. Schneider, J. chem. Phys. 23, 26 (1955); W . S. Fyfe,
ibid. 21, 2 (1953).
[14] E. E. Havinga and E. H . Wiebenga, Recueil Trav. chirn.
Pays-Bas 78, 724 (1959).
[*] This has usually been represented as a pentagonal bipyramid,
but recent investigations have shown that the actual structure is
very complex.
[15] C. K. Ingold: "Structure and Mechanism in Organic
Chemistry". Bell, London 1953, p. 372.
[16] R . C. L. M . Slater, Acta crystallogr. 12, 187 (1959).
[17] R. C. L. Mooney, Z . Kristallogr. Kristallgeometrie, Kristallphysik, Kristallchem. 90, 143; H. A. Tasman and K . H. Boswijk,
Acta Crystallogr. 8, 59 (1955).
[IS] R . S . Mulliken and C. Reid, J. Amer. chem. SOC.76, 3869
Table 1. Iodine-iodine distances in charge-transfer complexes.
1 ,CDithione-Iz
I ,4-Diselenone-l~
The Br-Br distance in C6H6-Br2 is equal to the
bond distance of Brz within experimental error 1191.
It is obvious therefore that the bonding in these
compounds varies regularly from weak interactions,
which may be described in terms of polarization
forces, to strong interactions, described as covalent
half-bonds. From this point of view the situation is
similar to that encountered in hydrogen bonding. In
connection with this gradual change, it is interesting
to note that the charge on the terminal halogen atom
is small in the case of weakly bonded complexes which
may therefore form bridged structures [211 such as
(10). In these compounds the Br-Br length is 2.31 A
compared with 2.28 8, in Brz. Tertiary arnines, being
better electron donors than ethers, do not form
bridged structures and the Br-Br distance is considerably increased (2.43 &.
In most of these anions the central halogen adopts a
coordination number 2, but in some cases, as for most
neutral interhalogen compounds, higher coordination
numbers are observed (see below). In all these cases,
the more electropositive atom is at the center of the
structure. This will be discussed later when the nature
of the bonding in these compounds is considered from
a simple MO point of view.
As pointed out by Rundle[221, the rare gas fluorides (see
Section 2.1.) are isoelectronic with the corresponding interhalogen anions. Thus XeF2, like IC12@,is linear and X e F 4 ,
like iC14@, is planar. This indicates a similar type of bonding,
which will be discussed in a later section.
1.3. Second Row Typical Elements
[19] 0. Hasseland C. Romming, Quart. Rev. 16, 1 (1962).
In the introduction it was mentioned that the electronic structures of silicon, phosphorus, and sulfur
(and their homologues) predict their typical valencies
of 4, 3, and 2, respectively, if the octet rule is maintained. However, these elements form a considerable
number of compounds with high coordination numbers, in particular octahedral compounds e.g. SF6,
[**I The Mulliken theory gives a good interpretation of CT
spectra, but does not give a satisfactory explanation of CT forces.
b $ b + ~should
be replaThe wave function dD = a $D,A
ced [201 by @ = n $QA+
1201 M. J. S. Dewar, J. Amer. Chern. SOC.,in press.
1211 0. Hassel and J . Hvoslej; Acta chem. scand. 8, 873 (1954).
[221 R. E. Rnndle, J . Amer. chem. SOC.85, 112 (1963).
Angew. Chem. internat. Edit.
/ VoZ. 6 (1967) / No. 9
SeF6, TeF6, PF6s SnC162a, SiF6@,and also FsS-SFs,
and pentacoordinated molecules of phosphorus, arsenic, and antimony, silicon, germanium, and tin.
The structures of oxyanions e.g. s0420, P043p, C103”,
C104S, and higher oxides, such as SO3 and 104, will not be
considered here as these involve a detailed discussion of
bonding[*I (this has been discussed in detail elsewhere). It should be pointed out, however, that these
higher oxides and oxyacids are in general the most stable
ones, and any interpretation of their bonding should bear
this in mind.
In view of the unusual symmetry features of the MX5
system, recent structural investigations of these molecules will be briefly reviewed.
1.4. The Pentacoordinated System
The MX5 system cannot adopt the configuration of a
regular polyhedron, but two geometrical forms, the
trigonal bipyramid and the square pyramid represent
systems of maximum symmetry. Until recently, only a
few 5-coordinated molecules (e.g. PF5, PF3C12, PCl5,
PBr5SbC15) were known, and their structures were
found to be bipyramidal[23] with the axial bonds
significantly longer than the equatorial ones (Table 2).
supporting the cyclized form [***I. The X-ray analysis
of the phenanthrene derivative ( 1 1 ) shows this to be
also pyramidal with one of the axial bonds longer than
the other P -0bonds [271.
Recently the structure of the phosphinimine in the
dimeric form (12) has been determined 1281. Here also
the axial P-CI and P-N bonds are longer than the
corresponding equatorial bonds.
An extensive study has been made of a wide range of
fluoro-phosphoranes [*93, RnPFsWn.As in the case of
F3PC12 the more electronegative atoms occupy the
axial positions. In R3PF2 compounds, the R groups
and F groups are shown to be equivalent, and interatomic exchange was shown to be absent by F-H
coupling of the N M R frequencies. These observations
are in agreement with structure (13).
Table 2. Axial and equatorial bond lengths in PX5 molecules.
P-X (axial) (A)
P-X (equatorial) (A)
j j j ;:::
A range of 1:1 adducts of the tetrahalides of Si, Ge,
and Sn have been reported in recent yearsC231 and
some certainly exist in the ionized state, i.e.
R3NSiC13Cla, the tendency towards ionization increasing in the order Sn < Ge < Si. The structure of
(CH3)3Sn CIC5H5N has been found to be bipyramidal
with the most electronegative ligands, C1 and pyridine
in the axial positions.
The compounds (C,jH5)5P and (C6Hs)sAs also have
the same structure (trigonal bipyramid) [**I, whereas
(C&5)5Sb adopts a square pyramidal form [**I 1241.
SbC15 is however bipyramidalr231 with rax,= 2.34 h;,
req, = 2.29 A. As anticipated, therefore, the energy
differences between the two forms is quite small.
A wide range of cyclic oxyphosphoranes has been
prepared by Ramirez et a1. [251, the 31P-NMR shifts
[*] Their structures can be represented by coordinate bonds, thus
conforming to the octet rule, e.g.
0, /O”
o’ S‘oo
0 4 0 0
The participation of dz-px bonding involves the partial delocalization of the electrons on the oxygen atoms into the d
orbitals of the central atom.
1231 I. R. Beattie, Quart. Rev. 17, 382 (1963).
[**I These refer to X-ray investigations of the solid forms.
[24] P. J. Wheatley and G. Wittig, Proc. chem. SOC. (London)
1962, 251; P . J . Wheatley, J. chem. SOC.(London) 1964, 2206.
[25] F. Ramirer : Organo - Phosphorus Compounds. Butterworths, London 1964, p. 337.
19F-NMR measurements on R2PF3 compounds
indicate the presence of two kinds of fluorine atom,
which is in agreement with structure (14) ; however,
the fluorine atoms are equivalent in (15), except at low
temperatures. All the fluorine atoms are equivalent
in RPF4, indicating either a square pyramidal structure
or rapid interchange of the fluorine atoms. The latter
explanation is supported by the observation that
(C2H&NPF4 shows nonequivalence at low temperatures, and by the temperature effect on ( I S ) . This
positional exchange has been termed I301 “pseudorotation” since it involves the internal rotation of
valency bonds as follows (Fig. 2).
Fig. 2. Schematic representation of pseudorotation in the trigonal
[***I The products obtained from [(CH&N]3P and diethyl
oxomalonate, diphenylpropanetrione, and phenanthrenequinone
are reported to adopt an open zwitterionic form [26].
[26] F. Ramirez, A . V . Patwardhan, and C . R. Smith, J. Amer.
chem. SOC.87, 4973 (1965).
I271 I. Hamilton, S. Laplaca, and F. Ramirer, J. Amer. chem.
SOC.87, 127 (1965).
[28] H . Hess and D. Forst, Z . anorg. allg. Chem. 342, 240 (1966).
[29] R . Schmutzler, Angew. Chem. 77,530 (1965); Angew. Chem.
internat. Edit. 4, 496 (1965).
[30] R . S . Berry, J. chem. Physics 32, 933 (1960).
Angew. Chem. internat. Edit. 1 VoI. 6 (1967) 1 No. 9
Mirefterries and Schnicitzler 1291 have calculated a value
of 1 3 kcal.mole-1 for the activation energy of this
process for ( C 2 H 5 ) 2 N P F 4 . Quite recently [311, the
structures of C H 3 P F 4 and ( C H & P F 3 have been found
by X-ray analysis to be distorted trigonal bipyraniids
with the fluorine atoms in the axial positions and the
axial P-F bonds longer than the equatorial ones. For
C H 3 P F 4 , rp-F(ax) == 1.612 A, rp-F(eq.) = 1.543 A.
For (CH3hPF3, rp--pcax) = 1.643 A, Y ~ - F ( ~ ~ .-)
1.553 A.
1.5. Analogous Systems with Lone Pairs
The P X 5 structure may be regarded from an electronic
point of view [321 as involving the distribution of
electron pairs in five bonds in the trigonal bipyramidal
structure (as for an sp3d hybridized system, although
an alternative view will be presented in the following
section). The same distribution in space readily
explains the somewhat irregular structures of M X 4
molecules with a lone pair on M (e.g. TeC14), and M X 3
molecules with two lone pairs on M (e.g. ClF3).
As already mentioned, the most electronegative
groups tend to occupy the axial positions, so that the
lone pair in M X 4 and the two lone pairs in M X 3 should
occupy the equatorial positions as shown in (16) and
The relatively large X-M-X angles between the axial
bonds may be attributed to repulsion between the
electrons in the M-X bonds and the more diffuse
lone pair. Finally, the trihalide ions (e.g. (18)) are tenelectron systems with the three lone pairs occupying
the equatorial positions, the most electronegative
atoms the axial ones.
The following question is now posed. How can the
bonds in all the structures so far considered be explained in a consistent manner? There are two general
ways, (a) to assume the specific participation of high
energy orbitals to accommodate electron pairs (e.g.
2s in the case of H F 2 e and 3d for B r 3 9 or (b) to
retain the octet rule as the main guide, as in the following section.
2. Theoretical Treatment
Let us take the simple view that the octet rule holds
for typical elements 1331 and that the small contributions
of high-energy orbitals d o not alter the general
[31] L. S. Bartell and W. Hansen, Inorg. Chem. 4 , 1777 (1965).
1321 R . J . Gillespie, J. chem. SOC.(London) 1963, 4672.
Consider the formation of a homopolar diatomic
molecule. The combination of two atomic orbitals,
each containing one electron gives two molecular
orbitals, as shown by the following secular equation I *J.
The two electrons in the bonding orbital produce a
quantum-mechanical stabilization energy of 2P.
This simple treatment provides a theoretical basis for
the stability of two-electron bonds, and of the LewisLangmuir extension ‘341 that a stable atom (other than
hydrogen and transition elements) in a molecule, has
four electron pairs distributed around the cose. It does
not however imply that one-electron bonds (or 11/2electron bonds for that matter) necessarily lead to
unstable structures. On the contrary, x-conjugated
systems in which the bonds may be described by
fractional orders are among the most stable organic
compounds. The principle of electron delocalization
leads to the important conclusion that 2n electrons
are not necessary for the formation of n bonds of a
stable molecule, whether the bonding is of the a- or
x-type [361.
This principle can be examined more closely by
referring to the linear combination of three orbitals
centeredon three atoms [**I. In this case the corresponding secular equation leads to three solutions corresponding to bonding, non-bonding, and anti-bonding
molecular orbitals as follows.
Now, so far, it has not been mentioned that bonding
is only possible by the combination of two orbitals
characterized by wave functions of the correct symmetry. The possible combinations of s and p orbitals to
give resulting 3-center molecular orbitals can be
represented as in Fig. 3.
It is a general principle that the configuration leading
to maximum (bonding) overlap will be preferred,
other things being equal. This can be readily understood in a general way since if two atomic orbitals d o
not overlap a bond cannot be formed.
[*I Of course in a complete treatment of a-bonds, repulsion and
Coulombic terms, changes in electronic kinetic energy, spin-spin
interaction, and the overlap integral must be considered. At the
present time, semiempirical treatments of the Pariser-Parr-Pople
type [35] are being developed, but are beyond the scope of this
1341 G. N . Lewis, J. Amer. chem. SOC.38, 762 (1916); I. Lnngmuir,ibid. 41, 868, 1543 (1919).
1351 R . G. Purr and B. M . Gimarc, Advances physic. Chem. 16,
451 (1965); G. Klopman, J. Amer. chem. SOC.86, 4550 (1964).
[36] R . P . Bell and H . C. Longuet-Higgins, Proc. Roy. SOC.183A,
357 (1945); J. chem. SOC.(London) 1943, 250.
[33] R. E. Rundle, Survey Progr. Chem. I , 81 (1963).
[**I A linear combination of atomic orbitals does not of course
imply that the molecule is linear.
1 No. 9
Angew. Chem. internat. Edit. 1 Vol. 6 (1967)
b) pz- a
a ) px-px
allylic system
1. olefin complexes
2. non-classical carbonium ions
c) pa bonding
d) s or s hybrids
1. Hydrogen bond [*I
2. Xafi compounds
3. Transition states 31\12)
3. Metal alkyls
1. Boron hydrides
2. H3":
4. Transition states ( S E ~ )
[*I Here the central atom is an s orbital.
Fig. 3. Combination of s and p orbitals to give 3-center molecular
orbitals (schematic).
One can see therefore why systems (b), (c), and (d)
adopt these particular configurations in which overlap
is a maximum[*]. In system (a) the configuration is
fixed by the o-bond skeleton.
The orbital energies for these systems show that when
two electrons occupy the bonding orbital (as in the
3-center bonds of electron-deficient compounds [369
the bond energy of the system is 2 I/2p.
This treatment may be extended to more complex
structures e.g. the alkyl-lithium tetramer (see Fig. 1).
The simplest view1371 is a 4-center bond formed by
orbital interaction as shown in Fig. 4. Thus each C-Li
bond is formally a 1/3 bond with significantly greater
bond distances than estimated for a single C-Li bond.
More general treatments cover the whole structure
and introduce Li-Li interactions (of s and p orbitals)
in view of the small Li-C-Li angles (68 in CH3Li).
In this structure, two single electron bonds are formed
with a total energy of 2P. This is equal to the exchange
energy of the X- + X2 system, hence structure (19) has
no stabilization energy. The linear form, with 0.83 9
units of stabilization energy is therefore preferred [*I.
It must be noted, however, that these estimated
stabilization energies are not absolute values - for
the reasons already mentioned. Thus, this procedure
predicts that the H3 molecule and H3 0 ion are stable;
but this is not the case [381. The instability may be due
to interelectronic repulsions, which will be large for
small interatomic distances. On the other hand,
hydrogen bonded molecules (e.g. H F 2 0)are stabilized
by the high Coulomb energies, and electronegativity
differences can be included in the a values in the above
treatment, which then enter into the final bond energy
Havinga and Wiebenga
have applied this simple
treatment to all the known interhalogen compounds,
and by using the approximation that a' = a
where n increases in the order I < Br < C1 < F have
Table 3. Prediction of structures of 17 and BrICl 1141.
Structure of I:
Zero approx
1 s t order approx.
1.66 p
1.66 B
1.49 B
1.46 B
1.23 B
I I-- I
1 1 - 1
11-1 I
2.82 3.17
ti- hybrid
values for
Fig. 4. Simplified energy-level diagram of moIecular orbitals in tetrameric methyl-lithium.
A 4-electron system may adopt structure (c) (of Fig.3),
or the alternative structure, (19), in which two separate
orbitals (px and pv) of the central atom participate in
the bonding.
['I Hydrogen bonded structures adopt configuration (c) in
preference to (d) owing to the strong repulsion between the
negative charges on the terminal atoms (which are highly
[37] E. A . C. Lucken and E. Weiss, J. organometallic Chem. 2,
197 (1964).
Structure of BrICl
1 6 a + 5.04p
16 a 4.06 P
I- Cl- Br
[*] Although the linear form of X30 is stable, a simple consideration of the orbitals in X,e shows the triangular form to
have an exchange energy of 4p if two p orbitals can be used (as in
the interhalogen compounds for example), and this should be
more stable than the linear form. X-Ray measurements [39] on
ICIySbC16 and ICl~.AlC14support this prediction.
1381 J . N . Bradley, Trans. Faraday SOC.60, 1553 (1964); H. C.
Bowen and J. W . Linnett, ibid. 60, 1185 (1965); H. Preuss,
Theoret. chim. Acta 2, 344, 362 (1964).
[39] C. G . Vonk, Dissertation, Groningen, 1957, quoted in [13].
Angew. Chem. internat. Edit.
Vol. 6 (1967) / No. 9
correctly predicted all the structures (with the exception of IF7). Examples of their calculations for
the I s 0 ion and BrICl are given in Table 3.
This treatment shows that the charge is located in the
non-bonding orbital, i.e. on the terminal atoms, so
that in unsymmetrical molecules, the more electronegative atoms (with high n values) occupy these
positions. This conclusion is fully supported by
the available experimental evidence. In particular,
35CI NQR frequencies r401 (which are sensitive to
ionic character) of 19.2 and 22.3 MHz are found for
IClz'-: and ICl4Q. These are approximately one half of
the value for I-Cl, indicating considerable localization
of charge on the terminal chlorine atoms. The extent
of participation of 5d orbitals in these bonds is
thought to be low.
The preparation of stable compounds of xenon
stimulated intense interest in the nature of the bonding
in such compounds [*I. Before the structures had in fact
been determined, Rundle [221 explained the bonding as
involving 5p orbitals by analogy with the interhalogen
compounds of iodine, and subsequent more detailed
calculations, and the measurement of the spectroscopic
properties, have fully supported this interpretation 142,431. As pointed out by Pitzer [441 the energy of
formation, AE, is determined mainly by the ionization
potential of the central atom (see Table 4).
Table 4. Ionization potentials (Ix) of the rare gases and halogens;
tabulation of fluorides formed.
1, (eV)
Fluorides formed
IF, IF,, IF5
BrF, BrF,, BrF5
XeF2, XeF4, XeF6
2.2. Extension to MXs and MX6 Systems
The same explanation given for the polyhalide ions
may be appliedL331 to the molecules PX5, s x 6 , and
their analogues. Thus if we consider three of the
P-Cl bonds in PCls to be in the sp2 state, then the
interaction of the remaining p orbital with two chlorine
atoms, (20), gives molecular orbitals of the kind
discussed for X3 Q.
This is an MO description of the resonance structure,
e e
P X 4 X , proposed originally [*I by Pauling 191.
2.1. Rare Gas Fluorides 1411
alternative treatments invoking spd hybridization. The MO
method is to be preferred for the interpretation of the
spectroscopic properties 1411.
The lower coordination numbers of first row elements [**I may be explained by increased non-bonded
repulsions (and also perhaps by increased repulsion
between bonding electrons) owing to the considerably
smaller radius of first row atoms. Such repulsions are
indicated by the large decreases in stability along the
series C F 4 + C14 and B F 4 e -+ B14Q e.g. CH3I is
quite stable whereas C14 readily dissociates. Various
estimates of non-bonded repulsions have been made,
where usually the ligands are regarded as hard spheres
with a given van der Waals radius, e.g. Rundle 1331 has
calculated coordination numbers in this way (see
Table 5).
These steric factors may also be important in coordination compounds of transition metals.
Table 5. Computed coordination numbers of MX, from steric
dc [bl
Thus assuming an electrostatic model, A E is given by,
A E = Ix - EF+ D F , - B (F-X-F)
where EF is the electron affinity of fluorine, Dp2 its
bond energy and B(F-X-F) the bonding term. As the
last term will be determined mainly by the radius of X,
and the X-F distances for I, Br, Xe, and C1 will be
similar, the stability is' determined mainly by the
value of I,.
A more complete M O treatment by Boudreaux [421 shows
that the 5d, 6s, and 6p orbitals produce only small modifications of the orbital energies, and similarly Coulson 1431 has
concluded that the VB and MO methods which give equivalent descriptions of the systems are more correct than the
[40] C. D. CornweN and R. S.Yamasaki, J. chem. Physics 27,
1060 (1957).
[41] J . G. Malm, H . Sehg, J . Jortner, and S. A . Rice, Chem.
Reviews 65, 199 (1965).
[*] For a complete review see [41].
[42] E. A. Boudreaux, J. chem. Physics 40,246 (1964).
I431 C . A. Couison, J. chem. SOC.(London) 1964,1442.
[44] K. S. Pirzer, Science (Washington) 139, 414 (1963).
Angew. Chem. infernat. Edit. 1 Vol. 6 (1967)
M = Carbon
1 No. 9
n Icl
[a] ry is the van der Waals radius of X.
[b] dc is the M-X
[c] n
& 1/3
distance (sum of covalent radii).
[*] Electrostatic treatments [45], which take into account nonbonded repulsions (see below), show that the bipyramidal form
is slightly more favored energetically than a square pyramidal
form. Kinetic studies with optically active 4-coordinated phosphorus compounds also lead to the same conclusion [46]. Thus
it is not necessary to postulate sp3d hybridization to explain the
[45] J. Zemann, Z. anorg. altg. Chem. 324, 241 (1963).
[46] R. F. Hudson and M . Green, Angew. Chem. 75, 47 (1963);
Angew. Chem. internat. Edit. 2, 11 (1963).
[* *] Except for electron-deficient compounds where a maximum
of eight electrons around each atom is possible. Symmetry
arguments show that d orbitals cannot be used here [47], and the
energy requirements would also limit d-orbital participation
[47] M. J. S. Dewar, J . chem. SOC.(London) 1953,2885.
It might be mentioned at this point that such a
structure as (20) is energetically possible[*] as indicated by the following empirical calculation [491:
P a 3 + C12
E = I - &I+
@ . E + G
D C I ~- IDp-cl+
E f I y 2 eV (experimental
value M 3.3 eV)
where I is the ionisation potential of PCl3, Ecl is the
electron affinity of chlorine, and D p - c ~ is taken as
the P-Cl dissociation energy of PCl3.
Although such a calculation is very crude, the same
conclusion was drawn by Pitzer[5ol, who was also
concerned about the source of the promotion energy
if 3d orbitals are used. The recent experimental
dataC311 on the compounds RPF4 and R2PF3 discussed in Section 1.4.can be explained readily on the
basis of this model. Thus the longer and more polar
axial P-F bonds, and the tendency for the most
electronegative atom to occupy the axial position,
follow directly from the model, but these observations
cannot be explained in an obvious way by treatments
based on extensive sp3d hybridization of phosphorus [4*1. The d-orbital angular functions certainly have
the correct symmetry for hybridization with s and p
orbitals (e.g. the dZzin the case of structure (16) and
d,2-y2 in the case of SF6). From this point of view
therefore, the formation of 5- and 6-coordinated
compounds of second row elements involving ten to
twelve valency electrons, and the inability of first row
elements to form such compounds follows naturally
from 3s3p3d hybridization, which would be more
effective than 2s2p3d hybridization.
The radial functions however present a bigger problem.
If one uses Slater orbitals (which are known to give
rather poor descriptions of orbitals), the 3d’orbitals
are found to be too diffuse for bonding with pa or px
orbitals unless the central atom carries a positive
charger48l. This is equivalent to assunling a partial
ionization of the electrons froni the spd hybrid orbital
onto the electronegative terminal atoms [481. On the
other hand, recent Hartree-Fock calculations (511 using
SCF orbitals suggest that the overlap is appreciable
even for a n uncharged central atom. (The recently
[*] The ionization potential of PH3 ( - 10 eV) and PC13 (- 12.3
eV) lie within the range given in Table 4. Thus if the contribution
of 5 d orbitals in XeF2 is small, the contribution in the less
available 3d orbital in the axial X-P-X
bond, by analogy,
should also be small.
[48] D . P. Craig, A . Maccoll, R. S. Nyholm, L. E. Orgel, and
L. E. Sutton, J. chem. SOC.(London) 1954, 332; H. H . Jaffi, J.
Chem. Phys. 21, 258 (1953).
[49] R. F. Hudson: “Structure and Mechanism in OrganoPhosphorus Chemistry”. Academic Press, New York 1965, p. 50.
[50] K . S. Pitzer, J. Amer. chem. SOC.70, 2140 (1948).
1511 D. W . J . Cruickshank, B. C. Webster, and D . F. Mayers,
J. chem. Physics 40,3733 (1964).
reported stability of the H2S radical anion [521 seems
to lend some support to this view.)
There still remains the problem of the high 3s
promotion energy, and although the 3d level must modify the energy of the NBO to some extent, the contribution may well be too small to determine the physical
properties, in particular bond lengths and stereochemistry. The octahedral SF6 system is simpler to
deal with theoretically than the PCls system and has
been the subject of recent detailed treatments. In an
electrostatic model, Craig and Mugnusson [531 regard
the sulfur atom as surrounded by six positive charges
(representing electronegative ligands). The diffuse 3d
Slater-type orbitals are contracted to become commensurate with the 3s and 3p orbitals, but the 3d
promotional energy is greatly increased by the electrostatic field.
A later treatment by Craig and ZauZir54J replaced the
electrostatic field model by a molecular model with
six fluorine atoms surrounding the sulfur, and Cruickshank [551 has very recently introduced SCF orbitals
into this treatment. The detailed calculations suggest
that the ligand field (in contrast to the electrostatic
field) stabilizes the system through 3d orbital participation to the extent of several electron volts.
2 0
I t is reasonable, o n general grounds, t o suppose t h a t = S s
uses d-orbitals (and other excited levels) more extensively
t h a n = P = ; this is reflected in t h e different properties of
t h e SO group in sulfones a n d sulfoxides (which can probably
be represented satisfactorily by a coordinate bond). Moreover,
t h e stability of molecules such as[56] N s S F 3 seems t o
require t h e participation of strong prr-d, bonds, a n d the
sp3dz hybridization of sulfur.
In conclusion, however, the importance must be
stressed of detailed spectroscopic investigation (particularly NMR, ESR, and NQR studies) in estimating
the extent of participation of excited levels in the
bonding of the types of molecules described here.
Care should be taken in drawing conclusions as to the
nature of bonding from bond length, bond energy,
and stereochemical considerations. Similarly, the
influence of conjugation on the energy of organic
x-bonded systems [571 is difficult to determine from
these properties, as changes in hybridization influence (I bonds to carbon to a considerable extent.
Received: June 14th. 1966
German version: Angew. Chem.
[A 590 IE]
79, 756 (1967)
[52] J . E. Bennett, B. Mile, and A.Thoinas, Chem. Commun.
1966, 182.
[53] D. P . Craig and E. A . Magnusson, J. chem. SOC.(London)
1956, 4895.
1541 D . P. Craig and C . Zauli, J. chem. Physics 37,601,609 (1962).
[55] D . W . J. Cruickshank, paper presented at the Symposium o n
“Modern Views of Valency and Bonding”, Southampton 1966.
[56] W . H. Kirchoff and E. Bright Wilson, J. Amer. chem. SOC.
84,335 (1962).
[57] M. J . S . Dewar and H . N . Schmeising, Tetrahedron 5, 166
Aizgew. Chem. internat. Edit. 1 Vol. 6 (1967) ] No. 9
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