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On the “pentavalent” nitrogen atom and nitrogen pentacoordination
Journal of Molecular Structure, 300 (1993) 245-256 0022-2860/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved
On the “pentavalent” pentacoordination
245
nitrogen atom and nitrogen
Richard D. Harcourt School of Chemistry, University of Melbourne, Parkville, Vie. 3052, Australia
(Received 22 March 1993) Abstract Hydrazoic acid (HNs) is an example of a molecule whose bond lengths suggest that the central nitrogen atom is apparently pentavalent, as indicated in the classical valence bond structure (I). H&l&_&:
HGNEN: .
HN-kN: x’ (1)
(In
W)
However, unless the nitrogen atom expands its valence shell, the r bonds of this structure are fractional electronpair bonds. The increased-valence structure (II) with fractional electron-pair ?r and rr’ bonds, and l-electron rr and $ bonds, also involves an apparent pentavalence. Some of the properties of these two VB structures are used to restate the nature of the origin of the apparent electronic pentavalence for nitrogen, namely appreciable contribntions of Dewar-type structures such as (III) to the component Lewis structure resonance scheme. It is shown that although the valence of the central nitrogen atom of structure (II) is able to exceed a value of 4, it can never attain a value of 5. Increased-valence structures for the Cz isomer of N6 are also presented, and the bond lengths that are associated with the most stable of these structures are in accord with those calculated using ab initio techniques. The results of some ab initio VB calculations, with minimal basis sets, are reported for: (a) Nz, to demonstrate the effect of variation in d bond atomic orbital hybridization on the lengths of the N”-N”’ bonds of HN3 (as HN’N”-N”‘) and the N-N bond of Nz; (b) trigonal bipyramidal NH3F2 and PHsFz, to suggest that the unwillingness of nitrogen to form stable pentacoordinate compounds is associated with some reluctance by nitrogen to participate in the formation of axial 4-electron 3-centre D bonding units.
Introduction
When discussing the electronic structures of HNs and Ns, Glukhovtsev and Schleyer [l] (G. and S.) have made the sensible distinction between geometric hypervalence and electronic
aFor
reasons that are discussed here and elsewhere [4-81, thin bond lines are used to represent the two N-N T bonds in structure (I), and other fractional bonds that arise in structures (VI), VIII), (IX) and (XV)-(XVIII). True pentavalence for nitrogen can only arise when the nitrogen atom utilizes five distinct atomic orbitals (AOs), for example, an n = 3 A0 as well as the four n = 2 AOs, for covalent bonding.
hypervalence. Thus, G. and S. have calculated N’-N’ and N”-N” bond lengths of 1.250 and 1.158 A for HNs [l]. These lengths are similar to the G. and S. estimates of 1.265 and 1.13OA for the N-N double and triple bonds of HNNH and N2 respectively [l]. Therefore the presence of double and triple bonds in VB structure I with a pentavalent nitrogen atoma is more immediately in accord with this data than is resonance between the familiar Kekule-type Lewis octet structures (II)(IV) [2]. However, as indicated by G. and S., the calculated valence indices for HNs reported in their paper give no evidence for electronic hypervalence. The latter result is as expected; it is a consequence
246
R.D. HarcourtjJ.
n’
(III)
(IV)
of the use of molecular orbital (MO) definitions of valence for each of the bonds (see ref. 3). On several occasions, aspects of the origin of the phenomenon of (apparent) electronic pentavalence for the nitrogen atom’have been discussed by the author [4-81. One purpose of the present paper is to show the relevance of this discussion to the pentavalence considerations of G. and S. Consideration is given to the apparent pentavalence of the central nitrogen atom (N”) of HN3, via minimal basis sets. (An extension to double zeta basis sets is provided in ref. 7.) Further development of the definition of atomic valence for increasedvalence structures [4-81 is then presented, and consideration is given to types of increasedvalence structures for the C, isomer of Ng, whose geometry has also been calculated by G. and S. [l]. Related to the phenomenon of apparent pentavalence of nitrogen is the non-existence to date of pentacoordinate covalent NF5, as well as 0F4, and FF3, when their second row homologues have been well-characterized. In this paper, consideration is given to a hypothesis that could account for this phenomenon via the results of some ab initio VB calculations for NH3F2 and PH3F2.
bonding unit, for which six S = 0 spin canonical Lewis structures may be constructed, namely (l)(6) of Fig. 1. The wavefunctions for the electron-pair bonds in structures (l)-(3) are of the Heitler-London type - for example Qi = I(ffaabPI( + Ily”yPboa”llfor structure (1). In the “hypervalent” VB structure (7) of Fig. 1, the electrons occupy the localized MOs (LMOs) #& = y + k’a, c& = y + k”a, & = b + l’a and #gU= b + i”a, to give the (S = 0 spin) LMO configuration (cf. refs. 3 and 9-12 with k’ = k” and 1’ = I”) of Eq. (1): Q7MW
II@,4;! +b”, &‘:I1
=
+ II@ 4;; 4; da - II cghg4~~;:ll - It+;<4;: & 4211
(1)
In (7), thin bond lines are used to indicate the fractionality of the bond orders, which is a consequence of the non-orthogonality of the #,,= and &, terms [ll]. The Q7(LMO) may be expressed as a linear combination of the (S = 0 spin) wavefunctions XlX,-Q6for the Lewis structures (l)-(6), according to Eq. (2): a7 = 2(1’ + I”)Q, + 2(k’ + k”)$ + 2(/k’/” + k”I’)$
+ 4Q4
+ 41’1”KlQ + 4k’k’%& .y.
iAB
.A
(2) ‘B’
+--.
Y (1)
(2)
.. YA;
Dewar-type Lewis structures and the origin of apparent nitrogen pentavalence
Y
(4)
---,A ----
b
(3)
FiiB (5)
Y-A-B
HN3 was used to restate and elaborate on aspects of the theory of the origin of apparent pentavalence that have been described elsewhere [4-81. The ground-state of HN3 has four rr electrons distributed amongst three overlapping pr AOs, designated y, a and b. These electrons therefore form a particular example of a 4-electron 3-centre
Mol. Struct. 300 (1993) 24.5-256
..
..
A
B
(6)
Y:A:B 17
.. Y
A
:
B
Y
(8) l -.
Y
Aok (10)
.. B
:A (9)
;
.
A--i (11)
Fig. 1. Valence bond structures for 4-electron 3-centre bonding units.
241
R.D. HarcourtjJ. Mol. Struct. 300 (1993) US-256
As indicated previously in refs. 6-8, the contribution of the Dewar-type structure (3) to the canonical structure resonance scheme is responsible for the apparent hypervalence of atom A in the VB structure (7). This is demonstrated again here. With k’ = k” = 0 and I’ = 1’ = 0 respectively, we obtain
(3)
Qp(LM0) = I14&#f%PII + I#3@fbPII = (k’ + k”)$
+ 2Qd + 2k’k”\E6
(4)
for which the associated VB structures (8) and (9) do not indicate apparent hypervalence. Inspection of Eqs. (3) and (4) shows that resonance between structures (8) and (9) is equivalent to resonance between the Lewis structures (l), (2) and (4)-(6). Consequently, it is the contribution by the Dewartype Lewis structure (3) which is responsible for the (apparent) hypervalence in VB structure (7). For HNs, the Kekule-type Lewis VB structures (II) and (III) have x electron distributions of types (1) and (2) if the x bonds are of the HeitlerLondon type, and (8) and (9) if the rr bonds involve electron occupation of LMOs. The Dewar-type Lewis VB structure is (V):
..--__ . “v-----N-N-N: .. 69
which involves zero formal charge separation. Therefore according to the electroneutrality principle, this structure should make a significant contribution to the canonical structure resonance scheme. As discussed in ref. 7 for example, where a comparison is also made with the conclusions obtained from spin-coupled VB calculations [ 131, the results of VB calculations from a variety of laboratories indicate that for other 1,3-dipolar molecules, analogous Dewar-type canonical Lewis structures, as well as the familiar Kekuletype zwitterionic structures (such as (II)-(I
are important ground-state structures. Thus for the four x electrons of HNs, Hiberty [14] has calculated STO-3G and 4-31G weights of 0.293,0.252 and 0.316, and 0.337,0.211 and 0.304 for structures (II), (III) and (V). Consequently, a VB structure of type (7) which, as shown already, includes both types of structures in the resonance scheme for its component canonical Lewis structures, may be used to represent the R electron distribution of HNs, as is done in the VB structure (I), with an apparent pentavalent nitrogen atom. A second 4-electron 3-centre bonding unit also exists for HN+ It involves the 7r’ electrons of the N’-N” bond, and the lone-pair of electrons on the N’ atom of VB structures (I). Their orbitals overlap (but due to the orientation of the lone-pair hybrid A0 on N’, the y’-d overlap integral is smaller than the y-a overlap integral for the r electrons). As a consequence of some y’-d overlap, the lone-pair electrons are able to delocalize, and this delocalization manifests itself in the familiar VB resonance scheme of (II)+$III)c*(IV). However if the LMO representation of (7) is used to represent the d as well as the r electron distribution, the associated VB structure for HNs is (VI),
(VU
**-___.....-’
(VII)
which is equivalent to resonance between 36 canonical Lewis structures [15], one of which is the Dewar-type structure (VII) with two long bonds. The N” atom of VB structure (VI) is apparently hexavalent, and this is a consequence of using LMOs (as in structure 7) to accommodate the electrons of each of the 4-electron 3-centre bonding units for the rr and i electrons. To retain an apparent pentavalence, and to ensure that both the 7~’and the rr electrons delocalize, resonance between the LMO structures (I) and (VIII) could be used.
248
This resonance scheme is equivalent to resonance between 27 canonical Lewis structures. However the Dewar structure (VII) is not a member of this set of Lewis structures. Increased-valence structures with l-electron bonds
An alternative approach to apparent pentavalence for the nitrogen atom involves the simultaneous formation of l-electron bonds and fractional electron-pair bonds, via l-electron delocalizations of lone-pair electrons in Kekulttype Lewis structures [4-8, 15, 161. For example, one r electron and one sp’ electron that occupy the y and y’ AOs of the N’ in structure (II) may be delocalized into the N’-N” LMOs &,= = y + la and +fd = y’ + l/a’, for which I and 1’ are polarity parameters, as indicated below,
to afford the VB structure (IX) [17]. The latter structure is an example of an “increased-valence” structure [4-8,11,15-221, and it is equivalent to resonance between the canonical Lewis structures (II), (V), (VII) and (X), when the wavefunctions for the N’-N”rr and r’ bonds of structure (II) are formulated using the Heitler-London procedure. When LMOs are used to accommodate the electrons of these bonds, (IX) is equivalent to resonance between 25 canonical Lewis structures [15], which include (II)-(V), (VII) and (X). In either case, the fractionality of the triple bond arises from the contributions of the Dewar structures to the component Lewis structure resonance scheme. A0 hybridization and N-N bond lengths
Increased-valence structure (IX) with a double bond and a fractional triple bond, implies immediately that the N/-N” and NV-N” bond lengths for HNs should be respectively similar to that of
R.D. HarcourtlJ. Mol. Struct. 300 (1993) US-2S6
an N-N double bond (1.24A [l]), but somewhat longer than an N-N triple bond. However there is only N 0.03 A difference in the calculated lengths of N2 and the N”-N”’ bond of HNs. It should be noted that when comparing N-N bond lengths of different molecules, account needs to be taken of the nature of the hybridization of the nitrogen AOs. Comments are restricted here to the lengths of N-N triple bonds. For NZ, the AOs (h = s + Xp) that overlap to form the N-N c bond are largely 2p in character; an estimate of X x l/O.35 has been obtained from VB calculations by Maclagan and Simpson [24] and the present author [25]. This value should also be relevant for the N”’ hybrid A0 that is used for N”‘-N#g bonding in HNs. In contrast, for the latter molecule, X M 1 for the hybrid orbitals of N” that are used to help form the N”-N’ and N”-N”’ u bonds, and X M fi for the N’ hybrid A0 of N/-N”. It is well known that bond lengths shorten as the s-character increases. Therefore the fractionality of the N”-N”’ bond would imply that its length should be rather longer than the triple bond of an N2 valence state that overlap between h” = s + p and involves h”’ = 0.35 s + p AOs in the 0 bond. The latter bond will be shorter than that for ground-state N2 for which both hybrid AOs for the (Tbond are of the form h = 0.35 s + p. Therefore it is perhaps not surprising that the length of the N”-N”’ fractional triple bond should not be appreciably longer than the triple bond of ground-state Nz. The effect of variation of A0 hybridization on the length of the N-N bond of Nz may be demonstrated via the results of the following (STO-6G) ab initio VB calculations for this molecule using Roso’s program [18-231 with (a) X = l/O.35 for each nitrogen atom (see refs. 24 and 25), and (b) X = l/O.35 for one nitrogen atom and X = 1 for the other nitrogen atom. For the latter calculation, the polarity of the u bond was optimized at R = 1.10 A. The nine S = 0 spin canonical structures that differ in the occupations of the four rx and four rY electrons were included in the (see ref. 25), for five bond calculations lengths (1.10, 1.20, 1.30, 1.40 and 1.5OA).
249
R.D. HarcourtlJ. Mol. Strut. 300 (1993) 245-256
With 5-point interpolation, the following results (a) R, = 1.230A, E(RJ = were obtained: (b) & = l.l97A, E(k) = -1088666u; - 108.8038 u. Similar calculations with s-p hybridization for both nitrogen atoms further shorten the N-N bond; the resulting R, value is 1.161 A. Although the calculations for (a) give a bond length which is more than 0.1 A longer than the experimental length, the results of the calculations for both (a) and (b) show the expected effect of hybridization variation on bond length. The results of VB studies of the effect of hybridization on the length of the N-N cr bond of N202 are described in refs. 21 and 22.
For the l-electron A-B bond, the valence, Vob,is equal to one half of the valence for an electron-pair bond when the MO configuration ($Q,)’ is used to describe the electron-pair bond. The latter is equivalent to PonPbb [28], in which P, and Pbb are the charge densities for the a and b AOs in the MO. With tiab = (a + kb)/(l + 2kSd + k2)“.5
(8)
and the Mulliken [29] gross atomic populations Pa, and Pbb of Eq. 9 Pa = 2(1 + k&,)/(1 Pbb = 2k(k + &,)/(
+ 2kS,b + k2) 1 + 2kSd + 2)
(9)
we obtained Eq. (10) for v&.
Atomic valencies for increased-valence structure
V, = 2k( 1 + kS,b)(k + Sd)/(
For any Celectron 3-centre bonding unit, two increased-valence structures may be constructed, namely (10) and (11) of Fig. 1. In either of these structures, the definitions of the A-atom valence (I$), with respect to the formation of a fractional electron-pair bond and a l-electron bond, differ [16,26,27], and this difference permits the A atom to exhibit electronic increased-valence or hypervalence. A greater-than-unity value for V, has been deduced previously on a number of occasions [ 16,26,27] when A0 overlap integrals were omitted from normalization constants. The discussion is extended here via the inclusion of the overlap integrals, and consideration is given to the A-atom valence for one of the two increasedvalence structures, namely (10) of Fig. 1. With $Ob = a + kb, N = l/(k2S22 + 2kS23 + S,,)o.5 and Sij = (Qi]XPj), the (S = 0 spin) wavefunction for increased-valence structure (10) may be expressed as *lo
=
N(IIu"~~%bpII
+
IlyPaa%bbaII)
(5)
= N(lly”da”bi31( + Ily@a’“~baII + klly”aPb”bPII + IIy@a*bpb*II) = (Q3 + kXIQ/(k%,,
+ 2kS23+ &)‘.’
(6) (7)
1 + 2k&, + k2)2 (10)
With respect to the formation of the fractional Y-A electron-pair bond, two definitions for the valence of A were provided in refs. 16, 26 and 27. These are equivalent when A0 overlap integrals are omitted [16,26,27], but as will now be shown, inclusion of the overlap integrals removes the equivalence. (a) V& = A-atom odd-electron charge in the A - k component of increased-valence structure (10). This fractional odd-electron charge spinpairs with a corresponding fraction of the Yatom odd-electron of structure (10); the remainder of the Y-atom odd-electron is spin-paired with the B-atom odd-electron charge of A - 8. In MO parlance, the A. h odd electron occupies the normalized antibonding MO of Eq. (11): & = [(k + %)a - (1 + &@I/[(1 x (1 + 2kSd + kz)]‘.’
- &) (11)
which is orthogonal to the ?j& bonding MO of Eq. (8). The Mulliken definition of odd-electron charge gives Eq. (12): Va,,= k(k + S&)/(1 + 2k&, + kz)
(12)
as the valence Vqy.This definition of Vu,,is indepen-
250
R.D. HarcourtjJ. Mol. Struct. 300 (1993) 245-256
dent of the nature of the Y atom to which A is fractionally bonded, and therefore it is independent of the value of the A0 overlap integral S,. The following definition of V&,is S,, dependent. (b) V&,= weight for VB structure (2) that arises in Eq. (7). Increased-valence structure (10) is equivalent to resonance between Lewis structures (2) and (3), and Lewis structure (2) involves a Y-A electron-pair bond. Therefore the valence Vay is equivalent to the weight of structure (2) in Eq. (7) [16,26,27]. Using the Chirgwin-Coulson definition of structural weight [30], Eq. (13) is obtained: by
=
P2s22
+ ks23Mk2s22
(13)
+ 2kS23 + s33)
as the valence Va,,. Neglecting the small nonneighbour A0 overlap integral Syb, the Sij may be expressed according to Eq. (14): s22 =
20
-
&
s23 =
2&b(1
s33 =
2(1 - & - s& + 2&S&)
-
Table
Valence bond descriptions of the C2 isomer of N6
+ xty,, &
G. and S. [l] have used resonance between the Lewis structures (XI)-(XIV)”
+ SC&,,
(14)
the maximum values for reported for some representative values of the A0 overlap integrals, using methods (a) and (b) to calculate V&,. Method (a) gives VO(max) = 1.125, regardless of the values of In
the A0 overlap integrals. In contrast, the V, values for method (b), which is A0 overlap dependent, are able to exceed the maximum value of 1.125 for method (a). Thus it is seen that V,(max) may exceed unity in an increased-valence structure, but due to the fractionality of the Y-A bond, its value must always be less than 1.5. The latter value would be possible if the Y-A bond of (10) were a nonfractional single bond, and the l-electron A-B bond were homopolar. Consequently, unless the N” atom of increased-valence structure (X) expands its valence shell, so that two distinct rr AOs and two distinct i AOs on this atom are used to help form the N”-N”’ and N’-N”r and 7r’bonds in this structure, the valence of N” must always be less than 5.
1,
V, = V&,+ Vab are
Table 1 A-atom valence in increased-valence
s“a
&lb
KIT
(+) p.p
..q
:NEN-N-N=N=N:
v
(XII)
(+)
c-1 ti
structure (10)
Gb
V,(max)
k
0.375 0.375 0.375 0.375
1.125 1.125 1.125 1.125
J5 1.8349 2.0578 2.3028
0.375 0.418 0.375
1.125 1.167a 1.254
& 2.0 1.4
(a) Eq. (12)forV,, 0.0 _ -
0.0 0.1 0.3 0.5
(b) Eq. (13)
0.75 0.75 0.75 0.75
forv,,
0.0
0.0
0.6 0.6
0.6 0.0
a When
S,,, = S, = 0.1,0.2,. . .0.7, S,, = S, = 0.6 gives
KIMax).
0.75 0.749 0.879
a As in ref. 1, these structures are displayed here as linear. The G. and S. paper does not indicate the l-electron delocalizations that are shown in (XI-(XIV). One, one and three other structures of types (XII-(XIV), (and also XVI-XVIII), may also be constructed. They differ iz the locations of n and n’ bonds in the N---N-N and components of these structures. W& an N= N=Fj &p+ (r&k - @c@ S = 0 spin wavefunction for the four singly-occupied K or ?y’ orbitals in structures (Xv)-(XVIII), spin considerations prohibit the formation of fractional 71or tr’ bonding between the central atoms of these structures.
R.D. HarcourtlJ.
Mol. Strut.
300 (1993) 245-256
to represent the electronic structure of extended Ng, whose most stable isomer is calculated to have a twisted open-chain C, structure [I]. From these structures, increased-valence structures (XV)-(XVIII)
(-I/.?)
(+I/)
.
:NFN&N++NSN: .
l
(XVII) (-l/Z)
(+I!*)
(+lp)
(-l/Z)
:kjFN->-N+NFN:
251
species, it is uncertain as to whether it is possible to prepare NFs. The results of ab initio MO calculations [32-341 suggest that NFs is a vibrationally stable molecule, but severe ligand crowding effects might make its synthesis experimentally difficult [35]. To examine further a possible VB explanation for the difference, the results of some ab initio VB calculations are reported here for the computationally simpler (hypothetical) NH3F2, and for PH3F2 when DJh symmetry is assumed. It is shown that for these compounds the nitrogen atom has a smaller propensity than has phosphorus to form an axial 4-electron 3-centre u bonding unit with the fluorine atoms.
(XVIII)
may then be derived via the l-electron delocalizations that are indicated in (XI)-(XIV). An appeal to the electroneutrality principle would indicate that structure (XV) should be the most stable of the increased-valence structures. Two of its component Lewis structures are the Dewar structures (XIX) and (XX) __-----__ I’
--.*
:~&j++*~-~.=-N: .. (x,x)“%___---’ :N=bj 0.
-$
*._______--’
.’
,*
.---------.
-Y.-N
..
‘:N: -
(XX)
with a zero formal charge on each atom. Although each of the increased-valence structures (XI)-(XIV) will contribute to the VB resonance scheme, the calculated bond lengths for the C, isomer (N/-N” = 1.155 A, N’-N”’ = 1.262 A, N/“-N”” = 1.463 A [l], see also ref. 31 for similar recent estimates) are in accord with those that are implied by increased-valence structure (XV).
Method of calculation
When A-atom (A = N or P) 3dAOs are omitted from the bonding schemes, the axial F-A-F 0 bonding for both NH3F2 and PH3F2 involves four electrons distributed amongst three overlapping pa AOs. In Fig. 2, the Lewis VB structures that correspond to those of Fig. 1 for this type of bonding unit are displayed. The S = 0 spin wavefunctions for the pa-pa electron-pair bonds of structures (12)-(14) are of the form I(. . . a”boll+ 1). . . ba2811.To simplify the S = 0 spin formulations of the wavefunctions when all electrons are included, the six A-H o-bonding electrons (+)
(+) .-.
‘;L F
AH3
F
AH3 F
(12) l.--
F
F
__ ,-* ----““_
AH3
F
C-)
(+a
(6)
‘F’
AH3
‘F’
(15)
xH3
(+)
(+I
F
F
(16)
Pentacoordination:
some valence bond studies
F
:F3 (18)
Attention is now given to the phenomenon of pentacoordination for systems with Dsh symmetry. Whereas PFS is a well-characterized
iiH3
!2
F
(17)
___-----__ .’
F (13)
(14) ‘2
L;’
--.
__--,---____. F
F l-
PF3
F
(1%
Fig. 2. Lewis structures for axial 4-electron 3-centre bonding units of NH3FZ, PH3F2 and Lewis-Dewar structures for NF5 and PF5.
252
R.D. HarcourtjJ. Mol. Strut. 300 (1993) 245-256
have been located in three localized MOs of the general form 0~r.1= spi+klsn. In these MOs, spi is a trigonal hybrid A0 .for the A atom. For a given geometry, the polarity parameter k was assigned various values that sometimes ranged between 0.5 and 9.0. The remaining 18 or 26 electrons were located in nine or 13 AOs. The calculations were performed using Roso’s program [18-231, with STO-SG bases, and “standard” N-H and P-H lengths of 1.91 and 2.68 u. The following sets of orbital exponents were used in several sets of calculations: (i) “best atom” exponents for all AOs; (ii) Slater ion exponents for the pa AOs of A+ and F- with “best atom” exponents for the remaining AOs; (iii) Slater exponents for (A + A+)/2 and (F + F- )/2. The A-F bond lengths were assigned various values, which included 3.31 and 3.2~ for PH3F2; these values correspond to those calculated by Keil and Kutzelnigg [36,37] when d orbitals are respectively excluded and included. The length of 3.2~
also corresponds to the N-F bonds calculated by Keil and Kutzelnigg [36,37] for NHsF1. The 3.02 u length corresponds closely to the calculated lengths of the axial A-F bonds of NF5 and PF5 [32-341. Results and discussion In Tables 2 and 3, the VB energies, the 0Ar.r polarity parameters (k) and the CoulsonChirgwin structural weights are reported. For the A-F bond lengths considered, the optimum values of k are - 0.6 for NH3F2, and N 0.8 for PH3F2. Although the calculations are certainly crude by current standards, they do indicate that a qualitative difference does exist between the nature of the 4-electron 3-centre bonding unit for the two systems when d orbitals are excluded from the bonding schemes. With regard to the structural weights, the following points may be noted. (i) When r(AF) is large, the dominant Lewis structure for the 4-electron 3-centre bonding unit is the Dewar structure (14), which *generates (planar) AH3 + 2F as dissociation products.
Table 2 PH3F2: weights k for Lewis structures (12)-(17), and’energies (-E - 537.0~) for resonance between (12)-(17) Best atom r(PF) = 3.20 u; k (121, (13) (14) (15) WI, (17) -E - 537.0
Best atom + ion” pcz
r(PH) = 2.69 u 0.50 0.75 0.26 0.26 0.25 0.26 0.21 0.20 0.01 0.01 1.651 1.706
1.oo 0.26 0.27 0.19 0.01 1.691
0.50 0.27 0.20 0.24 0.01 1.681
Best atom + iona pa r(PF) = 3.20 U; r(PH) = 2.58 u k 0.50 (W> (13) 0.27 (14) 0.21 (15) 0.24 (la), (17) 0.01 -E - 537.0 1.675 a Slater exponents.
0.75 0.27 0.22 0.22 0.01 1.733
0.75 0.27 0.21 0.23 0.01 1.737
Averagea atom + ion
1.00 0.27 0.22 0.22 0.01 1.723
0.50 0.25 0.29 0.18 0.01 0.796
0.75 0.26 0.28 0.18 0.01 0.879
1.00 0.26 0.28 0.18 0.01 0.916
Best atom + iona po
1.00 0.27 0.22 0.21 0.01 1.723
r(PF) = 3.30 u; 0.50 0.26 0.26 0.20 0.01 1.700
r(PH) = 2.58 u 0.75 0.26 0.27 0.18 0.01 1.755
1.00 0.26 0.28 0.17 0.02 1.743
9.00 0.25 0.32 0.13 0.02 0.966
253
R.D. HarcourtlJ. Mol. Struct. 300 (1993) 245-256 Table 3 NHSF2: weights k for Lewis structures (12)-(17), and energies (-E - 253.0~) for resonance between (12)-(U)
r(NF) = 3.20~ k (1% (13) (14) (15) (1% (17) -E - 253.0
0.50 0.20 0.55 0.04 0.01 0.442
Averagea atom + ion
Best atom + ion po
Best atom
0.75 0.14 0.69 0.02 0.01 0.460
1.00 0.10 0.77 0.01 0.01 0.396
0.75 0.18 0.57 0.07 0.01 0.408
1.00 0.15 0.66 0.04 0.01 0.334
0.50 0.21 0.51 0.05 0.01 0.455
0.75 0.16 0.64 0.03 0.01 0.473
1.00 0.12 0.73 0.01 0.01 0.407
9.00 0.03 0.92 0.00 0.00 -1.084
0.50 0.27 0.36 0.09 0.01 0.413
0.75 0.20 0.54 0.04 0.01 0.453
1.oo 0.15 0.67 a.02 0.01 0.423
Best atom r(M) = 3.02 u k W), (13) (14) (15) (W, (17) -E - 253.0
0.50 0.23 0.44 0.13 0.01 0.402
a Slater exponents.
(ii) As r(AF) is shortened, the weights for the remaining structures - in particular (12), (13) and (15) - increase at the expense of (14). (iii) The values of the weights for the NHsF2 structures show a much greater sensitivity to the choice of the A-H bond parameter k than do those for PH3F2. Indeed when the P-H bonds are strongly polarized towards the hydrogen atoms (e.g. when k = 9 in cAH = spi +kl SH), the structural weights are similar to those for k = 0.75. This is certainly not the case for NH3F2. (iv) With the calculations based on the KeilKutzelnigg [36-381 geometries that were obtained with d orbitals omitted, the weight for the Dewar structure (14) is substantially larger for NH3F2 than it is for PH3F2. This result is obtained for each value of the polarity parameter k, and it suggests that phosphorus is better able to establish the axial 4-electron 3-centre bonding unit than is nitrogen, i.e. phosphorus has a greater ability to participate in both covalent (A+-F) and ionic (A+F- and F-A2+F-) axial bonding. It reflects the existence of larger first and second ionization potentials [39] for nitrogen (14.5 and 29.6 eV) than
for phosphorus (10.5 and 19.7eV). Ionization potential considerations account for the existence of XeF2 and the non-existence of NeF2 [lo]. The calculated greater ability of phosphorus to form the axial 4-electron 3-centre bonding unit is in accord with the greater stability that Keil and Kutzelnigg [36] calculated for PH3F2, when d AOs on the central atom are either included or excluded. When this result is extended to (Dsh symmetry) AFs species, it accounts for the existence of PFS, and for the reported inability to prepare NFS [35]. The latter follows from the considerations below. The three equatorial A-F bonds of NFs and PFs should be polarized towards the equatorial fluorine atoms, i.e. for each of these species, k should be substantially greater than unity in uAF = spi+ khF (with hF = 2pcF + x2SF). For large Values Of k, the weight of structure (18) of Fig. 2 should be larger than that of structure (19) (see Tables 2 and 3 for k = 9). Therefore for relevant axial A-F distances, the propensity for axial A-F bonding to occur should be rather less for NFs than it is for PFs, i.e. nitrogen is less able to establish pentacoordination via the formation of the axial 4-
254
electron 3-centre bonding unit. Ewig and Van Wazer [32] have also determined via MO calculations that there is comparatively little 3-centre bonding in NFS. Kutzelnigg [38] has suggested that the non-existence of pentacoordinate nitrogen compounds is mainly due to steric effects. A similar type of rationalization may be developed to account for the existence of SF4 and ClF3, and the non-existence of OF4 and (T-shaped) FFs. The approach is in accord with the theory of Epiotis [40] for SF4 and OF4, namely that an S+(F,J electronic configuration is much more favourable than an O+(F,)- configuration. Of course 3d AOs are of greater quantitative importance for secondrow systems than they are for the corresponding first-row systems (and therefore these AOs should provide greater strength to the axial bonding for the second-row species considered here). However, when these orbitals are omitted, the present VB studies do suggest that a qualitative difference does exist between the 4-electron 3-centre bonding units for the axial F-A-F u bonding of the firstrow and second-row hypercoordinated systems. Hiberty and co-workers [41-431 have accounted for the existence of SiH; and the non-existence of CHF as stable hypercoordinated species with DJ~ symmetries by the occurrence of appreciable contributions to the resonance scheme of SiHF structures that arise from the transfer of an electron from either of the axial H- orbitals into an equatorial antibonding LT~iH MO. A similar effect is calculated to occur to a lesser extent for CH;. The corresponding calculations for PHsF* have been performed (with k = 0.75 and k* = 1.122 in the orthogonal gpn and & MOs) by including the structures that are derived from: (i) structures (12) and (13) via F(2pa) + C&J delocalizations; (ii) structure (15) via F(2pg) + o&-r delocalizations; and (iii) structures (12) and (13) via F (2pr) +F (2p7r’)+ &j delocalizations. It should be noted that stabilizations of these types reduce the .magnitudes of the formal +ve and -ve charges on the A and F atoms, which are developed when Lewis structures of types (12), (13) and (15) in particular make contri-
R.D. HarcourtlJ.
Mol. Strut.
300 (1993) 245-256
Table 4 PH3F2 energies (E + 538.0~) for resonance between the following sets of Lewis structures. (a) (12)-(17); (b) (a)+(i) of text; (c) (b) + (ii) of text; (d) (a) + (iii) of text. When configurations with four singly-occupied orbitals arise, the o/301IJ+ popa! - c@@ - &o/3 S = 0 spin wavefunction has been used. r(PH) = 2.58 u [36] has been used in these calculations
@‘F)(4 ::;
3.2
3.3
3.6
4.2
-0.8171 -0.7328 -0.8313 _
-0.7568 -0.8336 -0.8438 -0.7654
-0.8605 -0.8066 -0.8638 -0.8119
-0.8843 -0.8936 -0.8849
butions to the 4-electron 3-centre resonance scheme for the 0 electrons. The results of the calculations reported in Tables 2 and 3 suggest that the stabilizations of (i)-(iii) above should be more substantial for pentacoordinate phosphorus than they are for pentacoordinate nitrogen. In Table 4, the PH3F2 energies are reported from calculations that include the additional structures. None of the calculations lead to a stabilization of PH3F2 relative to the F + PHs (planar) + F dissociation products. Whether or not this failure is a consequence of the use of a minimal basis set has yet to be determined. The effect of the inclusion of some phosphorus 3s character in the axial P-F bonds of structures (12) and (13) also needs to be examined. Conclusions The phenomenon of the apparent pentavalence of nitrogen in VB structures of type (I) has interested numerous workers from the mid-19th century [44] up until the present time [1,7,13]. For more than 20 years, the increased-valence approach to it, as indicated by structures (IX) and (XV) for example, has been described regularly by the present author [4-8,15,16] (see also ref. 45 for the initial use of this representation). However, except for Hiberty [46] and Formosinho [47], recent workers have not given consideration to this approach, and have used VB structures of type (I) to represent the apparent pentavalence (see
R.D. HarcourtlJ.
Mol. Struct. 300 (1993) 245-256
for example refs. 1, 13, 48-50, and refs. 61-63 of ref. 7). The disadvantages that are involved in using VB structures of type (I) have been discussed on several occasions [4-81. The paradigm shift that is needed to utilize the increased-valence approach is easy to make, and its consequences have relevance for a large domain of chemistry. It should be noted that it is the substantial contribution of Dewar-type structures to the Lewis structure resonance scheme that is responsible for both the apparent pentavalence in increasedvalence structures, and according to the hypothesis studied in this paper, the reluctance of firstrow elements to form certain classes of stable hypercoordinate molecules. It is also noted that although the preparation of electron-rich pentacoordinate compounds of nitrogen such as NFs has not yet been achieved, electron-deficient cations have been well characterized (see [N(AuPPhs)#’ [51]). Although the electronegativities of the two axial (AuPPhs)+ ligands of 2+ should assist with the develop[N(AuPPhJ 151 ment of an axial 2-electron 3-centre bonding unit, it is also considered necessary [51] to include peripheral metal-metal interactions involving the d” closed shell to account for the bonding. Acknowledgements
I am indebted to and thank (a) Dr. W. Roso for his VB program, (b) Dr. F.L. Skrezenek for installing the program, and (c) the Australian Research Council for financial support. I also offer my congratulations to Professor W.J. Orville-Thomas for his successful editorship of 300 volumes of J. Mol. Struct. References M.N. Glukhovtsev and P. von R. Schleyer, Chem. Phys. Lett., 198 (1992) 547. L. Pauling, The Nature of the Chemical Bond, 3rd edn., Cornell, Ithaca, NV, 1960, p. 272. T.A. Halgren, L.D. Brown, D.A. Kleier and W.N. Lipscomb, J. Am. Chem. Sot., 99 (1977) 6793.
255 4 R.D. Harcourt, J. Mol. Struct., 9 (1971) 221; 12 (1972) 351. 5 R.D. Harcourt, Qualitative Valence Bond Descriptions of the Electronic Structures of Electron-Rich Molecules, Lecture Notes in Chemistry, Vol. 30, Springer, Heidelberg, 1982, Chapter 16. 6 R.D. Harcourt, Chem. Eng. News, 53 (1985) 3, 77. 7 R.D. Harcourt, J. Mol. Struct. (Theochem), 259 (1992) 155, and refs. 3, 4(a)-(e), and 6 cited therein. 8 R.D. Harcourt, New J. Chem., 16 (1992) 667. 9 J.H. Waters and H.B. Gray, J. Am. Chem. Sot., 85 (1963) 825. 10 C.A. Coulson, J. Chem. Sot., (1964) 1442. 11 R.D. Harcourt, Aust. J. Chem., 22 (1969) 271. 12 J. Musher, Angew. Chem. Int. Ed. Engl., 8 (1969) 54. 13 D.L. Cooper, J. Gerratt and M. Raimondi, Chem. Rev., 91 (1991) 929. 14 PC. Hiberty, in D.J. Klein and N. Trinajstic (Eds.), Valence Bond Theory and Chemical Structure, Elsevier, Amsterdam, 1990, p. 221, and ref. 4 cited therein. 15 R.D. Harcourt and J.F. Sillitoe, Aust. J. Chem., 27 (1974) 691. 16 R.D. Harcourt, J. Am. Chem. Sot., 100 (1978) 8060. 17 R.D. Harcourt, ref. 5, p. 140. 18 R.D. Harcourt and W. Roso, Can. J. Chem., 56 (1978) 1093. 19 F.L. Skrezenek and R.D. Harcourt, J. Am. Chem. Sot., 106 (1984) 3934. 20 R.D. Harcourt, J. Mol. Struct. (Theochem), 206 (1990) 253. 21 R.D. Harcourt, J. Chem. Sot. Faraday Trans., 87 (1991) 1089. 22 R.D. Harcourt, Croat. Chem. Acta, 64 (1991) 399. 23 R.D. Harcourt and F.L. Skrezenek, J. Phys. Chem., 94 (1990) 7007. 24 R.G.A.R. Maclagan and R.W. Simpson, Int. J. Quantum Chem., 31 (1987) 463. 25 R.D. Harcourt, J. Chem. Sot. Faraday Trans., 88 (1992) 1119. 26 R.D. Harcourt, J. Am. Chem. Sot., 102 (1980) 5195; corrigendum, 103 (1981) 5623. 27 Ref. 5, p. 166. 28 I. Mayer, J. Mol. Struct. (Theochem), 255 (1992) 1. 29 R.S. Mulliken, J. Chem. Phys., 23 (1955), 1833, 1841, 2338,2343. 30 E. Chirgwin and C.A. Coulson, Proc. R. Sot. London Ser. A, 201 (1950) 196. 31 R. Engelke, J. Phys. Chem., 96 (1992) 10789. 32 C.S. Ewig and J.R. Van Wazer, J. Am. Chem. Sot., 111 (1989) 4172. Jr., J. Chem. 33 H.H. Michels and J.A. Montgomery, Phys., 93 (1990) 1805. 34 N.J.S. Peters and L.C. Allen, in J.F. Liebman, A. Greenberg and W.R. Dobier (Eds.), Fluorine Containing Molecules, VCH, Weinheim, 1988, p. 199.
256
35 36 37 38 39 40
41
R.D. HarcourtjJ. Mol. Struct. 300 (1993) 245-256 J.N. Murrell and C.E.J. Scollary, J. Chem. Sot., Dalton Trans., (1976) 818. K.O. Christe and W.W. Wilson, J. Am. Chem. Sot., 114 (1992) 9934. F. Keil and W. Kutzelnigg, J. Am. Chem. Sot., 97 (1975) 3623. W. Kutzelmgg, J. Chem. Phys., 78 (1981) 2. W. Kutzelnigg, Angew. Chem. Int. Ed. Engl., 23 (1984) 272. J.E. Huheey, Inorganic Chemistry, 3rd edn., Harper and Row, NY, 1983, p. 42. N. Epiotis, Unified Valence Bond Theory of Electronic Structure - Applications, Lecture Notes in Chemistry, Vol. 34, Springer, Heidelberg, 1983, p. 264. G. Sini, P.C. Hiberty and S.S. Shaik, J. Chem. Sot. Chem. Commun., (1989) 772.
42 G. Sini, G. Ohanessian, P.C. Hiberty and S.S. Shaik, J. Am. Chem. Sot., 112 (1990) 1407. 43 J. Maitre, F. Volatron, P.C. Hiberty and S.S. Shaik, Inorg. Chem., 29 (1990) 3047. 44 E. Frankland, Lecture Notes for Chemistry Students, Van Voorst, London, 1866, p. 61. 45 R.D. Harcourt, Theor. Chim. Acta, 6 (1966) 131. 46 P.C. Hiberty, Isr. J. Chem., 20 (1983) 20. 47 S.J. Formosinho, in S.J. Formosinho et al. (Eds.), Theoretical and Computational Models for Organic Chemistry, Kluwer, Dordrecht, 1991, p. 159. 48 D.L. Cooper, M.A. Robb and I.H. Williams, Chem. Br., 26 (1990) 1085. 49 M.T. Nguyen, J. Phys. Chem., 94 (1990) 6923. 50 R. Engelke, J. Phys. Chem., 94 (1990) 6924. 51 A. Grohmann, J. Riede and H. Schmidbaur, Nature, 345 (1990) 140.
On the “pentavalent” pentacoordination
245
nitrogen atom and nitrogen
Richard D. Harcourt School of Chemistry, University of Melbourne, Parkville, Vie. 3052, Australia
(Received 22 March 1993) Abstract Hydrazoic acid (HNs) is an example of a molecule whose bond lengths suggest that the central nitrogen atom is apparently pentavalent, as indicated in the classical valence bond structure (I). H&l&_&:
HGNEN: .
HN-kN: x’ (1)
(In
W)
However, unless the nitrogen atom expands its valence shell, the r bonds of this structure are fractional electronpair bonds. The increased-valence structure (II) with fractional electron-pair ?r and rr’ bonds, and l-electron rr and $ bonds, also involves an apparent pentavalence. Some of the properties of these two VB structures are used to restate the nature of the origin of the apparent electronic pentavalence for nitrogen, namely appreciable contribntions of Dewar-type structures such as (III) to the component Lewis structure resonance scheme. It is shown that although the valence of the central nitrogen atom of structure (II) is able to exceed a value of 4, it can never attain a value of 5. Increased-valence structures for the Cz isomer of N6 are also presented, and the bond lengths that are associated with the most stable of these structures are in accord with those calculated using ab initio techniques. The results of some ab initio VB calculations, with minimal basis sets, are reported for: (a) Nz, to demonstrate the effect of variation in d bond atomic orbital hybridization on the lengths of the N”-N”’ bonds of HN3 (as HN’N”-N”‘) and the N-N bond of Nz; (b) trigonal bipyramidal NH3F2 and PHsFz, to suggest that the unwillingness of nitrogen to form stable pentacoordinate compounds is associated with some reluctance by nitrogen to participate in the formation of axial 4-electron 3-centre D bonding units.
Introduction
When discussing the electronic structures of HNs and Ns, Glukhovtsev and Schleyer [l] (G. and S.) have made the sensible distinction between geometric hypervalence and electronic
aFor
reasons that are discussed here and elsewhere [4-81, thin bond lines are used to represent the two N-N T bonds in structure (I), and other fractional bonds that arise in structures (VI), VIII), (IX) and (XV)-(XVIII). True pentavalence for nitrogen can only arise when the nitrogen atom utilizes five distinct atomic orbitals (AOs), for example, an n = 3 A0 as well as the four n = 2 AOs, for covalent bonding.
hypervalence. Thus, G. and S. have calculated N’-N’ and N”-N” bond lengths of 1.250 and 1.158 A for HNs [l]. These lengths are similar to the G. and S. estimates of 1.265 and 1.13OA for the N-N double and triple bonds of HNNH and N2 respectively [l]. Therefore the presence of double and triple bonds in VB structure I with a pentavalent nitrogen atoma is more immediately in accord with this data than is resonance between the familiar Kekule-type Lewis octet structures (II)(IV) [2]. However, as indicated by G. and S., the calculated valence indices for HNs reported in their paper give no evidence for electronic hypervalence. The latter result is as expected; it is a consequence
246
R.D. HarcourtjJ.
n’
(III)
(IV)
of the use of molecular orbital (MO) definitions of valence for each of the bonds (see ref. 3). On several occasions, aspects of the origin of the phenomenon of (apparent) electronic pentavalence for the nitrogen atom’have been discussed by the author [4-81. One purpose of the present paper is to show the relevance of this discussion to the pentavalence considerations of G. and S. Consideration is given to the apparent pentavalence of the central nitrogen atom (N”) of HN3, via minimal basis sets. (An extension to double zeta basis sets is provided in ref. 7.) Further development of the definition of atomic valence for increasedvalence structures [4-81 is then presented, and consideration is given to types of increasedvalence structures for the C, isomer of Ng, whose geometry has also been calculated by G. and S. [l]. Related to the phenomenon of apparent pentavalence of nitrogen is the non-existence to date of pentacoordinate covalent NF5, as well as 0F4, and FF3, when their second row homologues have been well-characterized. In this paper, consideration is given to a hypothesis that could account for this phenomenon via the results of some ab initio VB calculations for NH3F2 and PH3F2.
bonding unit, for which six S = 0 spin canonical Lewis structures may be constructed, namely (l)(6) of Fig. 1. The wavefunctions for the electron-pair bonds in structures (l)-(3) are of the Heitler-London type - for example Qi = I(ffaabPI( + Ily”yPboa”llfor structure (1). In the “hypervalent” VB structure (7) of Fig. 1, the electrons occupy the localized MOs (LMOs) #& = y + k’a, c& = y + k”a, & = b + l’a and #gU= b + i”a, to give the (S = 0 spin) LMO configuration (cf. refs. 3 and 9-12 with k’ = k” and 1’ = I”) of Eq. (1): Q7MW
II@,4;! +b”, &‘:I1
=
+ II@ 4;; 4; da - II cghg4~~;:ll - It+;<4;: & 4211
(1)
In (7), thin bond lines are used to indicate the fractionality of the bond orders, which is a consequence of the non-orthogonality of the #,,= and &, terms [ll]. The Q7(LMO) may be expressed as a linear combination of the (S = 0 spin) wavefunctions XlX,-Q6for the Lewis structures (l)-(6), according to Eq. (2): a7 = 2(1’ + I”)Q, + 2(k’ + k”)$ + 2(/k’/” + k”I’)$
+ 4Q4
+ 41’1”KlQ + 4k’k’%& .y.
iAB
.A
(2) ‘B’
+--.
Y (1)
(2)
.. YA;
Dewar-type Lewis structures and the origin of apparent nitrogen pentavalence
Y
(4)
---,A ----
b
(3)
FiiB (5)
Y-A-B
HN3 was used to restate and elaborate on aspects of the theory of the origin of apparent pentavalence that have been described elsewhere [4-81. The ground-state of HN3 has four rr electrons distributed amongst three overlapping pr AOs, designated y, a and b. These electrons therefore form a particular example of a 4-electron 3-centre
Mol. Struct. 300 (1993) 24.5-256
..
..
A
B
(6)
Y:A:B 17
.. Y
A
:
B
Y
(8) l -.
Y
Aok (10)
.. B
:A (9)
;
.
A--i (11)
Fig. 1. Valence bond structures for 4-electron 3-centre bonding units.
241
R.D. HarcourtjJ. Mol. Struct. 300 (1993) US-256
As indicated previously in refs. 6-8, the contribution of the Dewar-type structure (3) to the canonical structure resonance scheme is responsible for the apparent hypervalence of atom A in the VB structure (7). This is demonstrated again here. With k’ = k” = 0 and I’ = 1’ = 0 respectively, we obtain
(3)
Qp(LM0) = I14&#f%PII + I#3@fbPII = (k’ + k”)$
+ 2Qd + 2k’k”\E6
(4)
for which the associated VB structures (8) and (9) do not indicate apparent hypervalence. Inspection of Eqs. (3) and (4) shows that resonance between structures (8) and (9) is equivalent to resonance between the Lewis structures (l), (2) and (4)-(6). Consequently, it is the contribution by the Dewartype Lewis structure (3) which is responsible for the (apparent) hypervalence in VB structure (7). For HNs, the Kekule-type Lewis VB structures (II) and (III) have x electron distributions of types (1) and (2) if the x bonds are of the HeitlerLondon type, and (8) and (9) if the rr bonds involve electron occupation of LMOs. The Dewar-type Lewis VB structure is (V):
..--__ . “v-----N-N-N: .. 69
which involves zero formal charge separation. Therefore according to the electroneutrality principle, this structure should make a significant contribution to the canonical structure resonance scheme. As discussed in ref. 7 for example, where a comparison is also made with the conclusions obtained from spin-coupled VB calculations [ 131, the results of VB calculations from a variety of laboratories indicate that for other 1,3-dipolar molecules, analogous Dewar-type canonical Lewis structures, as well as the familiar Kekuletype zwitterionic structures (such as (II)-(I
are important ground-state structures. Thus for the four x electrons of HNs, Hiberty [14] has calculated STO-3G and 4-31G weights of 0.293,0.252 and 0.316, and 0.337,0.211 and 0.304 for structures (II), (III) and (V). Consequently, a VB structure of type (7) which, as shown already, includes both types of structures in the resonance scheme for its component canonical Lewis structures, may be used to represent the R electron distribution of HNs, as is done in the VB structure (I), with an apparent pentavalent nitrogen atom. A second 4-electron 3-centre bonding unit also exists for HN+ It involves the 7r’ electrons of the N’-N” bond, and the lone-pair of electrons on the N’ atom of VB structures (I). Their orbitals overlap (but due to the orientation of the lone-pair hybrid A0 on N’, the y’-d overlap integral is smaller than the y-a overlap integral for the r electrons). As a consequence of some y’-d overlap, the lone-pair electrons are able to delocalize, and this delocalization manifests itself in the familiar VB resonance scheme of (II)+$III)c*(IV). However if the LMO representation of (7) is used to represent the d as well as the r electron distribution, the associated VB structure for HNs is (VI),
(VU
**-___.....-’
(VII)
which is equivalent to resonance between 36 canonical Lewis structures [15], one of which is the Dewar-type structure (VII) with two long bonds. The N” atom of VB structure (VI) is apparently hexavalent, and this is a consequence of using LMOs (as in structure 7) to accommodate the electrons of each of the 4-electron 3-centre bonding units for the rr and i electrons. To retain an apparent pentavalence, and to ensure that both the 7~’and the rr electrons delocalize, resonance between the LMO structures (I) and (VIII) could be used.
248
This resonance scheme is equivalent to resonance between 27 canonical Lewis structures. However the Dewar structure (VII) is not a member of this set of Lewis structures. Increased-valence structures with l-electron bonds
An alternative approach to apparent pentavalence for the nitrogen atom involves the simultaneous formation of l-electron bonds and fractional electron-pair bonds, via l-electron delocalizations of lone-pair electrons in Kekulttype Lewis structures [4-8, 15, 161. For example, one r electron and one sp’ electron that occupy the y and y’ AOs of the N’ in structure (II) may be delocalized into the N’-N” LMOs &,= = y + la and +fd = y’ + l/a’, for which I and 1’ are polarity parameters, as indicated below,
to afford the VB structure (IX) [17]. The latter structure is an example of an “increased-valence” structure [4-8,11,15-221, and it is equivalent to resonance between the canonical Lewis structures (II), (V), (VII) and (X), when the wavefunctions for the N’-N”rr and r’ bonds of structure (II) are formulated using the Heitler-London procedure. When LMOs are used to accommodate the electrons of these bonds, (IX) is equivalent to resonance between 25 canonical Lewis structures [15], which include (II)-(V), (VII) and (X). In either case, the fractionality of the triple bond arises from the contributions of the Dewar structures to the component Lewis structure resonance scheme. A0 hybridization and N-N bond lengths
Increased-valence structure (IX) with a double bond and a fractional triple bond, implies immediately that the N/-N” and NV-N” bond lengths for HNs should be respectively similar to that of
R.D. HarcourtlJ. Mol. Struct. 300 (1993) US-2S6
an N-N double bond (1.24A [l]), but somewhat longer than an N-N triple bond. However there is only N 0.03 A difference in the calculated lengths of N2 and the N”-N”’ bond of HNs. It should be noted that when comparing N-N bond lengths of different molecules, account needs to be taken of the nature of the hybridization of the nitrogen AOs. Comments are restricted here to the lengths of N-N triple bonds. For NZ, the AOs (h = s + Xp) that overlap to form the N-N c bond are largely 2p in character; an estimate of X x l/O.35 has been obtained from VB calculations by Maclagan and Simpson [24] and the present author [25]. This value should also be relevant for the N”’ hybrid A0 that is used for N”‘-N#g bonding in HNs. In contrast, for the latter molecule, X M 1 for the hybrid orbitals of N” that are used to help form the N”-N’ and N”-N”’ u bonds, and X M fi for the N’ hybrid A0 of N/-N”. It is well known that bond lengths shorten as the s-character increases. Therefore the fractionality of the N”-N”’ bond would imply that its length should be rather longer than the triple bond of an N2 valence state that overlap between h” = s + p and involves h”’ = 0.35 s + p AOs in the 0 bond. The latter bond will be shorter than that for ground-state N2 for which both hybrid AOs for the (Tbond are of the form h = 0.35 s + p. Therefore it is perhaps not surprising that the length of the N”-N”’ fractional triple bond should not be appreciably longer than the triple bond of ground-state Nz. The effect of variation of A0 hybridization on the length of the N-N bond of Nz may be demonstrated via the results of the following (STO-6G) ab initio VB calculations for this molecule using Roso’s program [18-231 with (a) X = l/O.35 for each nitrogen atom (see refs. 24 and 25), and (b) X = l/O.35 for one nitrogen atom and X = 1 for the other nitrogen atom. For the latter calculation, the polarity of the u bond was optimized at R = 1.10 A. The nine S = 0 spin canonical structures that differ in the occupations of the four rx and four rY electrons were included in the (see ref. 25), for five bond calculations lengths (1.10, 1.20, 1.30, 1.40 and 1.5OA).
249
R.D. HarcourtlJ. Mol. Strut. 300 (1993) 245-256
With 5-point interpolation, the following results (a) R, = 1.230A, E(RJ = were obtained: (b) & = l.l97A, E(k) = -1088666u; - 108.8038 u. Similar calculations with s-p hybridization for both nitrogen atoms further shorten the N-N bond; the resulting R, value is 1.161 A. Although the calculations for (a) give a bond length which is more than 0.1 A longer than the experimental length, the results of the calculations for both (a) and (b) show the expected effect of hybridization variation on bond length. The results of VB studies of the effect of hybridization on the length of the N-N cr bond of N202 are described in refs. 21 and 22.
For the l-electron A-B bond, the valence, Vob,is equal to one half of the valence for an electron-pair bond when the MO configuration ($Q,)’ is used to describe the electron-pair bond. The latter is equivalent to PonPbb [28], in which P, and Pbb are the charge densities for the a and b AOs in the MO. With tiab = (a + kb)/(l + 2kSd + k2)“.5
(8)
and the Mulliken [29] gross atomic populations Pa, and Pbb of Eq. 9 Pa = 2(1 + k&,)/(1 Pbb = 2k(k + &,)/(
+ 2kS,b + k2) 1 + 2kSd + 2)
(9)
we obtained Eq. (10) for v&.
Atomic valencies for increased-valence structure
V, = 2k( 1 + kS,b)(k + Sd)/(
For any Celectron 3-centre bonding unit, two increased-valence structures may be constructed, namely (10) and (11) of Fig. 1. In either of these structures, the definitions of the A-atom valence (I$), with respect to the formation of a fractional electron-pair bond and a l-electron bond, differ [16,26,27], and this difference permits the A atom to exhibit electronic increased-valence or hypervalence. A greater-than-unity value for V, has been deduced previously on a number of occasions [ 16,26,27] when A0 overlap integrals were omitted from normalization constants. The discussion is extended here via the inclusion of the overlap integrals, and consideration is given to the A-atom valence for one of the two increasedvalence structures, namely (10) of Fig. 1. With $Ob = a + kb, N = l/(k2S22 + 2kS23 + S,,)o.5 and Sij = (Qi]XPj), the (S = 0 spin) wavefunction for increased-valence structure (10) may be expressed as *lo
=
N(IIu"~~%bpII
+
IlyPaa%bbaII)
(5)
= N(lly”da”bi31( + Ily@a’“~baII + klly”aPb”bPII + IIy@a*bpb*II) = (Q3 + kXIQ/(k%,,
+ 2kS23+ &)‘.’
(6) (7)
1 + 2k&, + k2)2 (10)
With respect to the formation of the fractional Y-A electron-pair bond, two definitions for the valence of A were provided in refs. 16, 26 and 27. These are equivalent when A0 overlap integrals are omitted [16,26,27], but as will now be shown, inclusion of the overlap integrals removes the equivalence. (a) V& = A-atom odd-electron charge in the A - k component of increased-valence structure (10). This fractional odd-electron charge spinpairs with a corresponding fraction of the Yatom odd-electron of structure (10); the remainder of the Y-atom odd-electron is spin-paired with the B-atom odd-electron charge of A - 8. In MO parlance, the A. h odd electron occupies the normalized antibonding MO of Eq. (11): & = [(k + %)a - (1 + &@I/[(1 x (1 + 2kSd + kz)]‘.’
- &) (11)
which is orthogonal to the ?j& bonding MO of Eq. (8). The Mulliken definition of odd-electron charge gives Eq. (12): Va,,= k(k + S&)/(1 + 2k&, + kz)
(12)
as the valence Vqy.This definition of Vu,,is indepen-
250
R.D. HarcourtjJ. Mol. Struct. 300 (1993) 245-256
dent of the nature of the Y atom to which A is fractionally bonded, and therefore it is independent of the value of the A0 overlap integral S,. The following definition of V&,is S,, dependent. (b) V&,= weight for VB structure (2) that arises in Eq. (7). Increased-valence structure (10) is equivalent to resonance between Lewis structures (2) and (3), and Lewis structure (2) involves a Y-A electron-pair bond. Therefore the valence Vay is equivalent to the weight of structure (2) in Eq. (7) [16,26,27]. Using the Chirgwin-Coulson definition of structural weight [30], Eq. (13) is obtained: by
=
P2s22
+ ks23Mk2s22
(13)
+ 2kS23 + s33)
as the valence Va,,. Neglecting the small nonneighbour A0 overlap integral Syb, the Sij may be expressed according to Eq. (14): s22 =
20
-
&
s23 =
2&b(1
s33 =
2(1 - & - s& + 2&S&)
-
Table
Valence bond descriptions of the C2 isomer of N6
+ xty,, &
G. and S. [l] have used resonance between the Lewis structures (XI)-(XIV)”
+ SC&,,
(14)
the maximum values for reported for some representative values of the A0 overlap integrals, using methods (a) and (b) to calculate V&,. Method (a) gives VO(max) = 1.125, regardless of the values of In
the A0 overlap integrals. In contrast, the V, values for method (b), which is A0 overlap dependent, are able to exceed the maximum value of 1.125 for method (a). Thus it is seen that V,(max) may exceed unity in an increased-valence structure, but due to the fractionality of the Y-A bond, its value must always be less than 1.5. The latter value would be possible if the Y-A bond of (10) were a nonfractional single bond, and the l-electron A-B bond were homopolar. Consequently, unless the N” atom of increased-valence structure (X) expands its valence shell, so that two distinct rr AOs and two distinct i AOs on this atom are used to help form the N”-N”’ and N’-N”r and 7r’bonds in this structure, the valence of N” must always be less than 5.
1,
V, = V&,+ Vab are
Table 1 A-atom valence in increased-valence
s“a
&lb
KIT
(+) p.p
..q
:NEN-N-N=N=N:
v
(XII)
(+)
c-1 ti
structure (10)
Gb
V,(max)
k
0.375 0.375 0.375 0.375
1.125 1.125 1.125 1.125
J5 1.8349 2.0578 2.3028
0.375 0.418 0.375
1.125 1.167a 1.254
& 2.0 1.4
(a) Eq. (12)forV,, 0.0 _ -
0.0 0.1 0.3 0.5
(b) Eq. (13)
0.75 0.75 0.75 0.75
forv,,
0.0
0.0
0.6 0.6
0.6 0.0
a When
S,,, = S, = 0.1,0.2,. . .0.7, S,, = S, = 0.6 gives
KIMax).
0.75 0.749 0.879
a As in ref. 1, these structures are displayed here as linear. The G. and S. paper does not indicate the l-electron delocalizations that are shown in (XI-(XIV). One, one and three other structures of types (XII-(XIV), (and also XVI-XVIII), may also be constructed. They differ iz the locations of n and n’ bonds in the N---N-N and components of these structures. W& an N= N=Fj &p+ (r&k - @c@ S = 0 spin wavefunction for the four singly-occupied K or ?y’ orbitals in structures (Xv)-(XVIII), spin considerations prohibit the formation of fractional 71or tr’ bonding between the central atoms of these structures.
R.D. HarcourtlJ.
Mol. Strut.
300 (1993) 245-256
to represent the electronic structure of extended Ng, whose most stable isomer is calculated to have a twisted open-chain C, structure [I]. From these structures, increased-valence structures (XV)-(XVIII)
(-I/.?)
(+I/)
.
:NFN&N++NSN: .
l
(XVII) (-l/Z)
(+I!*)
(+lp)
(-l/Z)
:kjFN->-N+NFN:
251
species, it is uncertain as to whether it is possible to prepare NFs. The results of ab initio MO calculations [32-341 suggest that NFs is a vibrationally stable molecule, but severe ligand crowding effects might make its synthesis experimentally difficult [35]. To examine further a possible VB explanation for the difference, the results of some ab initio VB calculations are reported here for the computationally simpler (hypothetical) NH3F2, and for PH3F2 when DJh symmetry is assumed. It is shown that for these compounds the nitrogen atom has a smaller propensity than has phosphorus to form an axial 4-electron 3-centre u bonding unit with the fluorine atoms.
(XVIII)
may then be derived via the l-electron delocalizations that are indicated in (XI)-(XIV). An appeal to the electroneutrality principle would indicate that structure (XV) should be the most stable of the increased-valence structures. Two of its component Lewis structures are the Dewar structures (XIX) and (XX) __-----__ I’
--.*
:~&j++*~-~.=-N: .. (x,x)“%___---’ :N=bj 0.
-$
*._______--’
.’
,*
.---------.
-Y.-N
..
‘:N: -
(XX)
with a zero formal charge on each atom. Although each of the increased-valence structures (XI)-(XIV) will contribute to the VB resonance scheme, the calculated bond lengths for the C, isomer (N/-N” = 1.155 A, N’-N”’ = 1.262 A, N/“-N”” = 1.463 A [l], see also ref. 31 for similar recent estimates) are in accord with those that are implied by increased-valence structure (XV).
Method of calculation
When A-atom (A = N or P) 3dAOs are omitted from the bonding schemes, the axial F-A-F 0 bonding for both NH3F2 and PH3F2 involves four electrons distributed amongst three overlapping pa AOs. In Fig. 2, the Lewis VB structures that correspond to those of Fig. 1 for this type of bonding unit are displayed. The S = 0 spin wavefunctions for the pa-pa electron-pair bonds of structures (12)-(14) are of the form I(. . . a”boll+ 1). . . ba2811.To simplify the S = 0 spin formulations of the wavefunctions when all electrons are included, the six A-H o-bonding electrons (+)
(+) .-.
‘;L F
AH3
F
AH3 F
(12) l.--
F
F
__ ,-* ----““_
AH3
F
C-)
(+a
(6)
‘F’
AH3
‘F’
(15)
xH3
(+)
(+I
F
F
(16)
Pentacoordination:
some valence bond studies
F
:F3 (18)
Attention is now given to the phenomenon of pentacoordination for systems with Dsh symmetry. Whereas PFS is a well-characterized
iiH3
!2
F
(17)
___-----__ .’
F (13)
(14) ‘2
L;’
--.
__--,---____. F
F l-
PF3
F
(1%
Fig. 2. Lewis structures for axial 4-electron 3-centre bonding units of NH3FZ, PH3F2 and Lewis-Dewar structures for NF5 and PF5.
252
R.D. HarcourtjJ. Mol. Strut. 300 (1993) 245-256
have been located in three localized MOs of the general form 0~r.1= spi+klsn. In these MOs, spi is a trigonal hybrid A0 .for the A atom. For a given geometry, the polarity parameter k was assigned various values that sometimes ranged between 0.5 and 9.0. The remaining 18 or 26 electrons were located in nine or 13 AOs. The calculations were performed using Roso’s program [18-231, with STO-SG bases, and “standard” N-H and P-H lengths of 1.91 and 2.68 u. The following sets of orbital exponents were used in several sets of calculations: (i) “best atom” exponents for all AOs; (ii) Slater ion exponents for the pa AOs of A+ and F- with “best atom” exponents for the remaining AOs; (iii) Slater exponents for (A + A+)/2 and (F + F- )/2. The A-F bond lengths were assigned various values, which included 3.31 and 3.2~ for PH3F2; these values correspond to those calculated by Keil and Kutzelnigg [36,37] when d orbitals are respectively excluded and included. The length of 3.2~
also corresponds to the N-F bonds calculated by Keil and Kutzelnigg [36,37] for NHsF1. The 3.02 u length corresponds closely to the calculated lengths of the axial A-F bonds of NF5 and PF5 [32-341. Results and discussion In Tables 2 and 3, the VB energies, the 0Ar.r polarity parameters (k) and the CoulsonChirgwin structural weights are reported. For the A-F bond lengths considered, the optimum values of k are - 0.6 for NH3F2, and N 0.8 for PH3F2. Although the calculations are certainly crude by current standards, they do indicate that a qualitative difference does exist between the nature of the 4-electron 3-centre bonding unit for the two systems when d orbitals are excluded from the bonding schemes. With regard to the structural weights, the following points may be noted. (i) When r(AF) is large, the dominant Lewis structure for the 4-electron 3-centre bonding unit is the Dewar structure (14), which *generates (planar) AH3 + 2F as dissociation products.
Table 2 PH3F2: weights k for Lewis structures (12)-(17), and’energies (-E - 537.0~) for resonance between (12)-(17) Best atom r(PF) = 3.20 u; k (121, (13) (14) (15) WI, (17) -E - 537.0
Best atom + ion” pcz
r(PH) = 2.69 u 0.50 0.75 0.26 0.26 0.25 0.26 0.21 0.20 0.01 0.01 1.651 1.706
1.oo 0.26 0.27 0.19 0.01 1.691
0.50 0.27 0.20 0.24 0.01 1.681
Best atom + iona pa r(PF) = 3.20 U; r(PH) = 2.58 u k 0.50 (W> (13) 0.27 (14) 0.21 (15) 0.24 (la), (17) 0.01 -E - 537.0 1.675 a Slater exponents.
0.75 0.27 0.22 0.22 0.01 1.733
0.75 0.27 0.21 0.23 0.01 1.737
Averagea atom + ion
1.00 0.27 0.22 0.22 0.01 1.723
0.50 0.25 0.29 0.18 0.01 0.796
0.75 0.26 0.28 0.18 0.01 0.879
1.00 0.26 0.28 0.18 0.01 0.916
Best atom + iona po
1.00 0.27 0.22 0.21 0.01 1.723
r(PF) = 3.30 u; 0.50 0.26 0.26 0.20 0.01 1.700
r(PH) = 2.58 u 0.75 0.26 0.27 0.18 0.01 1.755
1.00 0.26 0.28 0.17 0.02 1.743
9.00 0.25 0.32 0.13 0.02 0.966
253
R.D. HarcourtlJ. Mol. Struct. 300 (1993) 245-256 Table 3 NHSF2: weights k for Lewis structures (12)-(17), and energies (-E - 253.0~) for resonance between (12)-(U)
r(NF) = 3.20~ k (1% (13) (14) (15) (1% (17) -E - 253.0
0.50 0.20 0.55 0.04 0.01 0.442
Averagea atom + ion
Best atom + ion po
Best atom
0.75 0.14 0.69 0.02 0.01 0.460
1.00 0.10 0.77 0.01 0.01 0.396
0.75 0.18 0.57 0.07 0.01 0.408
1.00 0.15 0.66 0.04 0.01 0.334
0.50 0.21 0.51 0.05 0.01 0.455
0.75 0.16 0.64 0.03 0.01 0.473
1.00 0.12 0.73 0.01 0.01 0.407
9.00 0.03 0.92 0.00 0.00 -1.084
0.50 0.27 0.36 0.09 0.01 0.413
0.75 0.20 0.54 0.04 0.01 0.453
1.oo 0.15 0.67 a.02 0.01 0.423
Best atom r(M) = 3.02 u k W), (13) (14) (15) (W, (17) -E - 253.0
0.50 0.23 0.44 0.13 0.01 0.402
a Slater exponents.
(ii) As r(AF) is shortened, the weights for the remaining structures - in particular (12), (13) and (15) - increase at the expense of (14). (iii) The values of the weights for the NHsF2 structures show a much greater sensitivity to the choice of the A-H bond parameter k than do those for PH3F2. Indeed when the P-H bonds are strongly polarized towards the hydrogen atoms (e.g. when k = 9 in cAH = spi +kl SH), the structural weights are similar to those for k = 0.75. This is certainly not the case for NH3F2. (iv) With the calculations based on the KeilKutzelnigg [36-381 geometries that were obtained with d orbitals omitted, the weight for the Dewar structure (14) is substantially larger for NH3F2 than it is for PH3F2. This result is obtained for each value of the polarity parameter k, and it suggests that phosphorus is better able to establish the axial 4-electron 3-centre bonding unit than is nitrogen, i.e. phosphorus has a greater ability to participate in both covalent (A+-F) and ionic (A+F- and F-A2+F-) axial bonding. It reflects the existence of larger first and second ionization potentials [39] for nitrogen (14.5 and 29.6 eV) than
for phosphorus (10.5 and 19.7eV). Ionization potential considerations account for the existence of XeF2 and the non-existence of NeF2 [lo]. The calculated greater ability of phosphorus to form the axial 4-electron 3-centre bonding unit is in accord with the greater stability that Keil and Kutzelnigg [36] calculated for PH3F2, when d AOs on the central atom are either included or excluded. When this result is extended to (Dsh symmetry) AFs species, it accounts for the existence of PFS, and for the reported inability to prepare NFS [35]. The latter follows from the considerations below. The three equatorial A-F bonds of NFs and PFs should be polarized towards the equatorial fluorine atoms, i.e. for each of these species, k should be substantially greater than unity in uAF = spi+ khF (with hF = 2pcF + x2SF). For large Values Of k, the weight of structure (18) of Fig. 2 should be larger than that of structure (19) (see Tables 2 and 3 for k = 9). Therefore for relevant axial A-F distances, the propensity for axial A-F bonding to occur should be rather less for NFs than it is for PFs, i.e. nitrogen is less able to establish pentacoordination via the formation of the axial 4-
254
electron 3-centre bonding unit. Ewig and Van Wazer [32] have also determined via MO calculations that there is comparatively little 3-centre bonding in NFS. Kutzelnigg [38] has suggested that the non-existence of pentacoordinate nitrogen compounds is mainly due to steric effects. A similar type of rationalization may be developed to account for the existence of SF4 and ClF3, and the non-existence of OF4 and (T-shaped) FFs. The approach is in accord with the theory of Epiotis [40] for SF4 and OF4, namely that an S+(F,J electronic configuration is much more favourable than an O+(F,)- configuration. Of course 3d AOs are of greater quantitative importance for secondrow systems than they are for the corresponding first-row systems (and therefore these AOs should provide greater strength to the axial bonding for the second-row species considered here). However, when these orbitals are omitted, the present VB studies do suggest that a qualitative difference does exist between the 4-electron 3-centre bonding units for the axial F-A-F u bonding of the firstrow and second-row hypercoordinated systems. Hiberty and co-workers [41-431 have accounted for the existence of SiH; and the non-existence of CHF as stable hypercoordinated species with DJ~ symmetries by the occurrence of appreciable contributions to the resonance scheme of SiHF structures that arise from the transfer of an electron from either of the axial H- orbitals into an equatorial antibonding LT~iH MO. A similar effect is calculated to occur to a lesser extent for CH;. The corresponding calculations for PHsF* have been performed (with k = 0.75 and k* = 1.122 in the orthogonal gpn and & MOs) by including the structures that are derived from: (i) structures (12) and (13) via F(2pa) + C&J delocalizations; (ii) structure (15) via F(2pg) + o&-r delocalizations; and (iii) structures (12) and (13) via F (2pr) +F (2p7r’)+ &j delocalizations. It should be noted that stabilizations of these types reduce the .magnitudes of the formal +ve and -ve charges on the A and F atoms, which are developed when Lewis structures of types (12), (13) and (15) in particular make contri-
R.D. HarcourtlJ.
Mol. Strut.
300 (1993) 245-256
Table 4 PH3F2 energies (E + 538.0~) for resonance between the following sets of Lewis structures. (a) (12)-(17); (b) (a)+(i) of text; (c) (b) + (ii) of text; (d) (a) + (iii) of text. When configurations with four singly-occupied orbitals arise, the o/301IJ+ popa! - c@@ - &o/3 S = 0 spin wavefunction has been used. r(PH) = 2.58 u [36] has been used in these calculations
@‘F)(4 ::;
3.2
3.3
3.6
4.2
-0.8171 -0.7328 -0.8313 _
-0.7568 -0.8336 -0.8438 -0.7654
-0.8605 -0.8066 -0.8638 -0.8119
-0.8843 -0.8936 -0.8849
butions to the 4-electron 3-centre resonance scheme for the 0 electrons. The results of the calculations reported in Tables 2 and 3 suggest that the stabilizations of (i)-(iii) above should be more substantial for pentacoordinate phosphorus than they are for pentacoordinate nitrogen. In Table 4, the PH3F2 energies are reported from calculations that include the additional structures. None of the calculations lead to a stabilization of PH3F2 relative to the F + PHs (planar) + F dissociation products. Whether or not this failure is a consequence of the use of a minimal basis set has yet to be determined. The effect of the inclusion of some phosphorus 3s character in the axial P-F bonds of structures (12) and (13) also needs to be examined. Conclusions The phenomenon of the apparent pentavalence of nitrogen in VB structures of type (I) has interested numerous workers from the mid-19th century [44] up until the present time [1,7,13]. For more than 20 years, the increased-valence approach to it, as indicated by structures (IX) and (XV) for example, has been described regularly by the present author [4-8,15,16] (see also ref. 45 for the initial use of this representation). However, except for Hiberty [46] and Formosinho [47], recent workers have not given consideration to this approach, and have used VB structures of type (I) to represent the apparent pentavalence (see
R.D. HarcourtlJ.
Mol. Struct. 300 (1993) 245-256
for example refs. 1, 13, 48-50, and refs. 61-63 of ref. 7). The disadvantages that are involved in using VB structures of type (I) have been discussed on several occasions [4-81. The paradigm shift that is needed to utilize the increased-valence approach is easy to make, and its consequences have relevance for a large domain of chemistry. It should be noted that it is the substantial contribution of Dewar-type structures to the Lewis structure resonance scheme that is responsible for both the apparent pentavalence in increasedvalence structures, and according to the hypothesis studied in this paper, the reluctance of firstrow elements to form certain classes of stable hypercoordinate molecules. It is also noted that although the preparation of electron-rich pentacoordinate compounds of nitrogen such as NFs has not yet been achieved, electron-deficient cations have been well characterized (see [N(AuPPhs)#’ [51]). Although the electronegativities of the two axial (AuPPhs)+ ligands of 2+ should assist with the develop[N(AuPPhJ 151 ment of an axial 2-electron 3-centre bonding unit, it is also considered necessary [51] to include peripheral metal-metal interactions involving the d” closed shell to account for the bonding. Acknowledgements
I am indebted to and thank (a) Dr. W. Roso for his VB program, (b) Dr. F.L. Skrezenek for installing the program, and (c) the Australian Research Council for financial support. I also offer my congratulations to Professor W.J. Orville-Thomas for his successful editorship of 300 volumes of J. Mol. Struct. References M.N. Glukhovtsev and P. von R. Schleyer, Chem. Phys. Lett., 198 (1992) 547. L. Pauling, The Nature of the Chemical Bond, 3rd edn., Cornell, Ithaca, NV, 1960, p. 272. T.A. Halgren, L.D. Brown, D.A. Kleier and W.N. Lipscomb, J. Am. Chem. Sot., 99 (1977) 6793.
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42 G. Sini, G. Ohanessian, P.C. Hiberty and S.S. Shaik, J. Am. Chem. Sot., 112 (1990) 1407. 43 J. Maitre, F. Volatron, P.C. Hiberty and S.S. Shaik, Inorg. Chem., 29 (1990) 3047. 44 E. Frankland, Lecture Notes for Chemistry Students, Van Voorst, London, 1866, p. 61. 45 R.D. Harcourt, Theor. Chim. Acta, 6 (1966) 131. 46 P.C. Hiberty, Isr. J. Chem., 20 (1983) 20. 47 S.J. Formosinho, in S.J. Formosinho et al. (Eds.), Theoretical and Computational Models for Organic Chemistry, Kluwer, Dordrecht, 1991, p. 159. 48 D.L. Cooper, M.A. Robb and I.H. Williams, Chem. Br., 26 (1990) 1085. 49 M.T. Nguyen, J. Phys. Chem., 94 (1990) 6923. 50 R. Engelke, J. Phys. Chem., 94 (1990) 6924. 51 A. Grohmann, J. Riede and H. Schmidbaur, Nature, 345 (1990) 140.