792
Journul o f the American Chemical Society
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101:4
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February 14, 1979
Perturbation Theory and the Effects of Substitution in Square and Bipyramidal a-Bonded Compounds Evgeny Shustorovich’ Contribution f r o m the Department of Chemistry, Cornell Unioersity, Ithaca, New York 14853. Recrioed April 10, 1978
Abstract: The effects of substitution of L by L’ in square EL.4 and bipyramidal [trigonal (TB) ELs, tetragonal (octahedral) ELh, and pentagonal (PB) EL..II a-bonded complexes, for E a transition metal M or main group element A, have been considered in the framework of the perturbation theory of canonical MOs. The difference in ligand u orbital energies, 6a‘ = a(L’) - a ( L ) ,where 6n‘ > 0 ( < O ) correspond t o a better donor (acceptor) substituent I-’, was taken as a perturbation and all changes in overlap populations of different E--L bonds, GN(E-L)/ha’, were obtained in terms o f the ns, np, and ( n - I)d contributions. It was found that in all transition metal complexes ML,,, the s and d contributions to I L V ( M - - I . . , ~ ~ ~ are ~ , ) always / ~ ~ ’ negative and bigger in absolute value than the p one, which is always positive. The s and d contributions to 6N(M-LCi,)/6tu’ are always of opposite sign, typically the s one positive and the d one negative, so that 6 N ( M ~ ~ L Cwill J be smaller in absolute value than AN(M-L,,) and may be of any sign. The effects of substitution in main group element coinplexcs AL,,, strongly depend on the oxidation state of the central atom. The role of a-bonding effects was also briefly discussed. The results obtained agree with experiment and permit the fundamental regularities of substitution, particularly the !ram and cis influence, in EL,,,-h Lk’ complexes, to be explained and predicted.
Introduction Recently we have developed the general analytical LCAO MO for treating the effects of substitution of L by L’ in any chemical compound EL,,,; E is a transition metal M or main group element A. In the preceding paper? we have considered these effects in linear EL2 Dmh,trigonal AL3 D3h, and tetrahedral AL4 Td compounds where all the ligands L are geometrically equivalent with respect to the substituent I.’ i n the EL,,,-] L’ complex. The purpose of the present work is to consider the effects of substitution in complexes where not all the ligands L are equivalent with respect to L’, namely, in square EL4 D4h, octahedral EL6 oh, trigonal EL5 D31T,and pentagonal EL, D5t, bipyramidal compounds. As we choose the overlap population N(E-L) as a criterion of the E-L bond strength. Further, we adopt the difference in ligand u orbital energies, Le., diagonal matrix elements (Coulomb integrals) (uL,lHln,)
- (ULIHlUl.)
= 6a’
effects of substitution of the ligand L , I ) on the x axis. The relevant orbitals of the metal M and ligands L may be found in any textbook on quantum ~ h e m i s t r y I. f~we use the proper orthogonalized sd,z hybrids, namely
If
$1
= p~ t ud;z
(5)
$2
= US - pd:z
(6)
(a,t u2
t
u3
i
t u4) = 0
the relevant occupied MOs of ML4 will be 1 $1 = US - pd:Z) t b - ( u I t ~2 2
+ +
$2
1 = gd,2-,.2 t h - (uI - uz t 2
~3
(7)
~3
~ 4 )
(8)
-~
4 )
(9)
(1)
as a perturbation, so that, to first order, all changes in N(E-L) for a given ligand L will be (the closed-shell case)
The vacant MOs obtained according to (3) and (4) correspond to $ I * = $5, $2* = $4, and $3* = $6 with the typical energy order5 c($I)
< €($2) < 4$3) < €($4) < t ( $ S ) < €($6)
( 1 1)
Further, we can write Here the LCAO M O coefficients c and energies t are designated by the indexes where x refers to AOs of the central atom E (x = s, p, d), i and j to the occupied and vacant canonical MOs, respectively, and S x =~ (XIU! ) . Finally, for every bonding canonical M O $ = C E X E + CLOl. we shall use as its antibonding counterpart
(3)
f - e2 > b2 - a2 2 h 2 - g2 > 0 ef < ab 5 gh El, > EzJ > E3J, j = 4, 5 , 6
(12) (13) (14) To the first order, changes in the M-L,, overlap population will be
$* = C L X E - C t O L (4) where X E is an A 0 of the central atom E and 6’~is a symmetry-adapted group orbital formed from the UL orbitals, ct2 c ~ =. I ~. All the interrelations between the coefficients CE, CL., the energies e ( $ ) , e($*), and other necessary formulas may be found in ref 2 and 3.
+
Results and Discussion Square Complexes EL4 D4h. 16e d* ML4. Let us begin with transition metal complexes d8 ML4 where we will consider the 0002-7863/79/1501-0792$01 .OO/O
0 1979 American Chemical Society
Shustorovich
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Taking into account (12) and (l4), we obtain
Jz - -e2 >-f - e 2 > ( h 2 - g 2 ) + ( b 2 - a 2 ) _ E35
E16
E35
2E35
>-h 2 - g-’ 2E25
In the very last step of this chain of inequalities we also used N- E25. From (16) we immediately conclude that the s contribution to 6N(M-Ltr)/6a’ ( 1 5 ) is always negative. Quite similarly we find that the d, contributions are also negative but the po one is positive. I f we add the relationship E14
we come to the strict conclusion that the negative s and du contributions are always bigger in absolute value than the positive pa contribution. Thus, for a better donor substituent L’ (when 6a‘ > 0) we can predict a trans weakening. Similarly, for the M-L,,, bond we have
h2 16
The principal difference of (1 5) from (1 8) is that the latter does not contain the p contribution, Le., not only the S,, terms but also the terms with the coefficientsfand e. From (12)-(14) we can anticipate that the s and d co’ntributions will be of opposite sign, the s one typically positive and the d one negative. Thus, 6N(M-LC,,)/6a’ will be smaller in absolute value than 6N(M-Ltr)/6a’ and may be, in principle, of any sign. The experimental data agree perfectly with our model conclusions. It is well-known that such strong donor ligands as H, CH2R, or SiR? cause a significant lengthening of the M-L,, bonds, by 0.1 1-0.14 A, though changing very slightly the M-L,,, bond lengths.6-8 Referring the reader to the relevant reviews6-* we would like to stress that in d8 ML4 complexes the main changes under substitution always occur along the linear L’-M-L fragment, the trans lengthening for a better donor substituent L’. The cis changes are relatively smaller so that the steric factors can play the decisive role. We shall see below that exactly the same picture is valid for octahedral MLh complexes. AL4. Main group element complexes AL4 can have square geometry only if A is not of the highest oxidation state, namely, in 12e complexes of the XelVF4or [Te’1C14]2-type.9-’0If we adopt the hypervalent scheme for their structure,I1 Le., neglect the nd orbitals, we reduce (1 5 ) and (1 8) to
6N(A-Ltr)
793
Perturbation Theory in a-Bonded Compounds
abe’
6a’
This result represents an explicit proof of the general statement made earlierI3 for the AL,,,-kLk‘ complexes with the 30-4e bonding, a result confirmed by all the available experimental data.lo.I4For instance, in the relevant square Tell complexes, when a phenyl group is one of the ligands, the position opposite to the phenyl group is virtually vacantt0,l4but the cis bond lengths are strikingly insensitive to substitution. Bipyramidal Complexes EL,. Considering octahedral complexes EL6 as the special case of tetragonal bipyramidal ones, one can treat all the bipyramidal complexes, EL5 D 3 h (TB), EL6 oh, and EL7 D 5 h (PB), along similar lines. Such an approach proved to be rather fruitful in considering relative bond strengths in these polyhedra3 and we shall follow it in the present work. I n both ML5 and ML7 complexes there exists the problem of sd-2 mixing within the A ) ’ representation. Our previous analysis has shown3 that the resulting bond strengths in ML,+2, ML5 and ML7, are changed only slightly depending on which orthonormalized linear combinations of uax = ( I / d ) ( u l + a z ) a n d ~ , ~ = ( I / ~ ) ( u 3 + ~ 4.+ar+2), +.. orthogonal to s or dz2, we use as the basis one. Therefore for our further consideration we choose the linear combinations 8 , =-
1
r+2
l
r
(“I
+ (72 + . + ar+2) * *
.
(u3 + u4 + . . . + u r + 2 ) -vr(r+2) L
(22)
where 82 (22) is orthogonal to s. Such a choice makes all the relationships easier to obtain, in particular, by reducing the transition metal cases to the main group element ones where owing to the hypervalent structure we neglect the d orbital contribution to bonding completely. Axial Substitution. (2r 4je-18e ML,+2. We shall consider the effects of substitution of the ligand L(1) on the z axis. The relevant orbitals can be found in ref 3 and 4. The occupied MOs of do ML,+2 will be
+
+ $3
= epz
1
+f,/Z (‘51 - 02)
(25)
and their vacant counterparts $ I * = $5, $2* = $4, and $3* = $6 are obtained according to (3) and (4). The inequalities (1 2) and (13) which are typical for any transition metal complex ML, remain valid. To first order, we obtain for the M-L,, bond hN(M-L,r) = ab 2 r 1 f I 6a‘ [:(E35 2(r 2)
i16)
In main group element complexes AL,, the differencef - e2
