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Nuclear spin—spin coupling constants and mutual influence of the ligands
Chemical Physics 18 (1976) 417-430 0 North-Holland Publishing Company
NUCLEAR
SPIN-SPIN
COUPLING
CONSTANTS
AND
MUTUAL
INFLUENCE
V.I. NEFEDOV, V.G. YARZHEMSKY and V.P. TARASOV hstitrrte of GerwraZnrrdImrganic Chemistry. USSR Academy of SLiences. Moscow. Received
10 February
OF THE LIGANDS
USSR
1976
Generalized formulas for the spin-spin coupling constant K
1. Introduction The spin-spin coupling constant J is one of the most convenient properties for studying the mutual influence of ligands in coordination compounds [I]. Some data on the variation of the A-X bond strengths under the effect of the ligand L may be provided by studying the change in J(A-X) in the compounds AX,, when going over from AX,, to AX,,_, L. However, no sufficiently rigorous theory has been developed so Far for descnbmg the variation ofJ(A-X) as 3 function of A and L. Typically, the approximation of the mean excitation energy is used [l] but even the authors of ref. [2] noted that this approximation was not adequate since it could not account for the sign ofJ. In particular, the reduced constant K(13C-1gF) in CFq is negative [3_] _Hence, this study attempts to describe K(A-F) in the compounds AF,,_ll=Tcompared to the compounds AFZalong the lines of the general formulas [2] for the constants R(A-F), taking into account only the contact term, which plays the major r6le [1,2] _ For directly bonded atoms it appears that the contact term is the min one. However, in specific cases the spin-orbital term was found to be important [3] _ Here we develop the following general approach: The sign of K(A-F) in the compound AF,T- is determined from the calculated wave functions and some general considerations_ Then, perturbation theory is used to construct the system of functions and orbital energies for the complex AF,,_, Lx- and the value of K’(A-F) is found for this complex. Replacement of the ligand F and L results in a decrease or increase of K’ compared to K according to the signs of K and 6K, where 6K = K’K. These variations are further analyzed with regard to the change in the A-F bond strengths due to the inductive effect, which is considered in the framework of perturbation theory [4,5] _ Similarly to the inductive effect, the nature of the central atom A has an essential influence on K and 6K [4,5] ;
hence,
transition
and nontransition
atoms
A should be considered
separately.
V.I. Nefedov
418
2. Sign of the reduced constants K(A-F)
et ol.fNuclear
spin-spin
in the compounds
coupling cmu~anr~
AFn of transition and nontransition elements
2.1. Nontransition eleJnerlts The wave functions of the u-levels in the compounds AF, (D3h), AF, (D4,,) and AF, (Oh) may be written down proceeding from the general considerations developed in [2] and taking into account MO LCAO calculations [6-91. For the compounds AF, of nontransition elements the MO LCAO coefficients for the orthogonalized basis may be taken in the form of table I_ ln this table all the coefficients are positive. It should be stressed that the perturbation theory method psed in [2] yields the same MO LCAO node structure as the results of the calculations for E%eFy, BF3. CF$ [6], AlFy, SiF4, PF:, BeFz-, BFT, CF4 [7-q], BeFz-, CFZ- 161, AlFz-, PFZ. and SF, [6,8,9] _ The wave functions are of the same nature and do not depend on symmetry_ The coefficients in the table are related to each other by the conditions of orthonormalization.
Moreover, if we take into account the
weakness of the interaction between the F2s-orbitals and the central atom orbitals we can use perturbation theory for determining the coefficients at the F2s orbitals and finding additional relationships between these coefficients. For instance, the following relationships are valid for the octahedrcn: @=CY4E2--tEt
1
ff#
=
Q4El
*
QlEZ
,
S%p--r-l_
(1)
It should be stressed that eq. (1) obtained by us differ from those in [2] since we consider first the interactions ARS - F2p and Anp - F2p and only then superimpose the perturbing interaction with the F2s orbit&. The authors of [Z] first superimposed the perturbing interaction with the F2s orbitals and only then introduced the interactions Ans - F2p and Anp - FZp. Our procedure has a better substantiation and yields wave functions of a more correct form; for instance, it takes into account the admixture of the F2p orbitals at lower levels which agrees with the MO LCAO calculations. However, this modification is not essential since all the results presented below may be obtained with the function types used in [2]. Since for all the considered complexes AFZ- the functions of the a-levels of a-symmetry are similar, WC may limit ourselves to considering only one point symmetry group, for instance, the octahedral group. In this case the expression for the reduced constant K(A-F) has the following form (to a constant factor): K=--+
&7BE2%
Ela4bE2a1
al -a*
l
2 =(Y
n2-a*
1
:
(
G
* * _~ a2 - 0 al ~ a 1
=
hi;
(a1 --n*p
(1--E:)Kl+I)+-l
I
(2)
where ul, uz, and n-are the orbital energies of the levels lalg, 2atg and 3aqp, Z = (at - =*)/(a2 - 0*) > 1, Ifs is the matrix element between Ans and the group orbital of a tg symmetry from the F2s functions, el is the coefficient if the Ans orbital (see table I). Table 1 The
MO
LC.40
coefficients
Oh MO
for the
AFg-
(Oh)
compounds
Orbit& of central atom
Group
orbitals of
ligands
V.I. Nefedov et oL/hrucleor spin-spin
oxrpling constants
419
Fig. 1. The constant C(A-_F) a~ a function of E:_ Formula (2) has been transformed with the help of formulas of the type (1) and the expressions LCAO coefficients within the framework of perturbation theory, for instance,
q =
for the MO
P2E*ff&z, -a*1 -
(3)
It follows from general considerations and the inequality Ia2 - a* I < loI - a* 1that K is positive for small e: and negative for relatively large e:; the latter case should be expected for the majority of the compounds of AFZ- type. Indeed, the numerical values of the parameters in formula (2) obtained by MO LCAO calculations [6-91 for a large number of compounds (see above) yield K < 0. The general form of the function K =f(et) for I= 2.0 is given in fig. 1. According to this function K is positive in the compounds AFconly if the bond is (see below). Neagtive values of K highly ionic. There is some indirect evidence that this is the case for BeFishould be expected for other AFG- compounds_ The absolute magnitude of K grows steadily in the isoelectronic series of the compounds containing elements belonging to the same pericd, for instance, SiFg- + PF; --f SF, + ClFi since the orbital energy, Ans, increases and e: grows. In principle, For values of e: large enough some decrease in K may be expected since the curves K =f(~f) have minima. However, these minima do not seem to appear in the compounds we considered. Indeed, if we use the experimental values of ut and a2 for SF, [lOa] and CF, [lob] and the estimate a* = 5 eV, we find that I is 1.77 and 1.90, respectively; these values yield rather high values of e:(min) (0.68 and 0.67, respectively) which are higher than the respective values of e: (for the orthogonalized basis). It should also be taken into account that the value of 1 decreases in the isoelectronic series AFiwith increasing atomic number of the element At, that is, wi& increasing t :, which results in a rise of :(min). These theoretical
l
results are in full agreement with the experimental PFS, TeFs, SeF, [ll], SnFz[12], BiF; 1131.
data. Neagtive
values of K(A-F)
have been found
for SiF%,
Some general relationships between the value of K(A-F) and E: are also in fufl agreement with the experimental results. It is convenient to introduce a new parameter, the completely reduced constant C of the spin-spin coupling: C(A-F)
= K(A-F)/S(A)S(F)
,
(4)
where S(A) and S(F) are the densities of the valence s-electrons of the atoms A and F in the vicirutres of their nuclei. The dimension of C is cm3_ It has the same sign as the constant K but, in contrast to K, the constant C takes into account only the variation of the electron density distribution of the s-electrons and is. therefore, more 7 For instance,in the seriesBeFi< ElFi. CF,, if WEuse the experimentalvaluesfor aI and ~1s[lob] and assumeu* = 5 eV. we obtain I= 3.1. 2.2. and 1.9. respectively.
V.I. Nefedov
420
et al./Nuclear spin-spin
coupling cwmtants
C AIIS~VJ
r
I$&
Correlation ; (0)
g&s
of C(A-_F)
the value
of C(A-F)
of the Periodic
convenient
end Ans I”_’ for
AT4
cxphnation The sole
in the tent). (0) The orbital for C is 1 :10m5
(at.
units)3.
Ans energy; (0) the The Roman numerals
value of C(A-F) kw AFt--; denote the numbers ofthc
Table.
for analyzing
chemical
bonding.
It is just the constant
C that makes it possible to analyze
the relation-
ship between the spin-spin coupling and C: and, hence, the orbital energy Ans as a function of the atomic number of the element A. The constant K depends also on the value of S(A)S(F) and, hence, it must characterize the Mriation not only of E: (the influence of the chemical bond) but also of S(A) (the influence of the atomic constant). A similar analysis has been made previously in the papers [14,15] _ The integral D should be calculated to obtain the relativistic
D=j-
value S(A)
[ 161
I
FGdr. 0
where F is the small component, has been calculated. instead general
This E-value
ar.l
G is the lar ge component. In the paper [ 171 the E-value E = F?(O) + G2(0) as well as the value D is proportional to S(A). We have used (fig. 2) the E-values
of the D-values, because the calculated D-values dependence S(A) on 2 and not in the numerical
are not available and we are mainly interested in the values C(A-F). This approach overestimates the S(A)-
values for large Z; this follows, for example, from the comparison of the ratios S(A)/.S’(A) in paper [15] with our S(A)-values. The caiculation of the C(A-F) values (fig. 3) based on semiempirical S(A)-values [ 151 proves however the general trends of C(A-F) along the periods and groups of the Periodic Table as found in fig. 2. The decrease of the C-values on descending along the same group (fig. 3) is however fig. 2. We discuss these trends using fig. 2. Shown
‘3GeF4
in fig. 2 are the values of C(A-F)
in the tetrahedrons
[I l] and the octahedrons “‘SiFz-,
31PFg, 75AsFg,
gBeFi-,
“BF,,
not so well pronounced 13CF4,
77SeF6, 125TeF6, 12%bFg
14NF+ 141, 435 SF,,
[ll],
as in 2gSiF4
[17],
421
Fig. 3. See crption to fg 2. The scale tar C is IO-’ (at. urrits)3. “9SnF;-
[12],
35C1F&1271F;
the data for 49TiFg-
[Zl]
[13],
, 45S~Fz-
discussed below. The values of J(A-F)
“BrF;
[20],
1221, 51VF;
73GeF;-
[21],
1231, 93NbF;,
209 SiFg
1241,
[ 131. This figure represents also
183wF6 and 95MoF6 [I 11 which eu be
are taken from the papers referred to above, the values of the gyromanrtetic
ratio are taken from the Varian reference tables. The virtual values of J(14N-F)
in NF; andJ(l%-F) in CFZhave been estimated by comparing the values of J(Si-F) in SiF, and SiFz- and of J(Ge-F) in GeF4 and CeFzwith the experimental results for NF: and CF,. We have also estimated J(lglTa-19F) in TaF; by analyzing the temperature dependence of the NMR line shape for 19F . The thick dashed lines in figs. 2 and 3 denote the variation of C(A-F) in the period for the isoelectronic compounds of the elements in higher oxidation states, the thin dashed lines denote the variation of this constant in the groups; the numbers of the groups are given in the left-hand side of the figure. The Ans values are taken from calculations [17,25] _ Their variation patterns agree with the experimental data [lot] which are not complete yet. A correlation is found between C(A-F) and Ans which is in full agreement with the considerations discussed above; since the value of : grows with Ans in the period, the~value of C(A-F) also increases [for its absolute
l
magnitude, see formula (2)] _ The only deviation from the steady increase of C(A-F) as a function of Ans in the period has been found for IF:. This deviation is small and it may, probably, be attributed to the fact that the value of E: for C,, in fig. 1 is less than I$ for this compound or to the inaccuracy of the S(A)-values used. From 2- the value of qBe-F) should be negative, otherwise the steady dependence of fig. 2 it may be seen that in BeF%_ _ , BF, , CF4 would be violated. Moreover, in that case Cwould have a maximum Con $0, Ans in the series BeF, in this series which contradicts the general formula (2) ( see fig. 1). since the existence of a maximum would necessitate a rather peculiar dependence of Hs and (a1 - n*) on the central atom in the series of the isoelectronic compounds This result is in agreement with the above conclusion about the positive value of C(A-F) ionic nature of the A-F bond.
for 2 markedly
The correlation between C(A-F) and AJIS is particularly convincing for the compounds of elements belonging to the same group. For the elements 6elonging to the groups III-V the variation of Am in the group is known not to be steady; the value of AJZSdecreases when going over from the second to the third period and increases somewhat or remains constant when passing from the third to the fourth period [lOc] _This nonsteady variation is attributed to the incomplete screening of the 4s electrons by the 3d electron shell in the elements of the Fourth period; it is reflected also by the nonsteady variation of the ionization potentials and by the chemical properties of the isovalent compounds [ lOa,c] _ A similar nonsteady variation is exhibited by C(A-F). Thus, the above discussion shows that C(A-F) is negative in the compounds AFZ- , with the exception of highly ionic compounds of the type BeFz-, and that the variation of C(A-F) in the series of isoelectronic or isovalent compounds is quite similar to the variation of Ans and cbracterizcd by the following: (1) The absolute value of C(A-F) increases in the series of the isoelectronic compounds of the same period with increasing atomic number of A; the larger the period number, the lower the rate of this increase. (2) The change in the absolute value of C(A-F) is not monotonous for the isovalent compounds of the elements belonging to the same group; C(A-F) generally decreases with increasing period number but this is not the case when going over from the compounds of the elements belonging to the third period to those of the fourth period.
2-2. Tmtlsition elements A large volume of MO LCAO calculations has been done for the compounds of the transition elements of the AFZ- type but almost no data have been published on the wave functions [26] _ Moreover, the character of the calculations does not guarantee a sufficient accuracy. It may be assumed that the wave functions will have the same node structure as those of the nontransition elements with respect to the Arzs and F2s levels. The same result follows also from the application of the perturbation theory. Using this assumption the results of the above section may be readily extended to the compounds of transition elements. Hence, our analysis for the compounds of transition elements is somewhat tentative, in contrast to the case of nontransition elements. The ATF bond is significantly more ionic with respect to the Arzs orbitals in the compounds of transition elements compared to nontransition elements compounds, since the Atzs energies vary from 6 to 9 eV for transition elements and from 10 to 30 eV for nontransition elements [IOc] _ If we take into account that the F2p orbital energy is 18 eV, we find that E: should be rather small for the’compounds of transition elements. Hence, C should have a small negative or positive value (see fig. 1) according to formula $2 ); we consider the positive values to be the more probable. Since values of ef are small and lie t in the vicinity of ~~(0) = l/(1 + r) when K = 0 or C=O, absolute magnitude of C(A-F) for transition elements must, apparently, be less than that for nontransition ones; this conclusion is in good agreement with the experimental data (fig. 2). No direct experimental data on the signs of C or K are available at present for the compounds of transition elements discussed here. However, the authors of 1271 report indirect experimental evidence that K(E’-F) is positive in PtFz-. The character of the correlatian between C and Arzs also indicates indirectly that C is positive_ In the series of isoelectronic compounds of the elements belonging to the same period C should tend to a more negative or a less positive value with increasing atomic number of the element A, since Atzs and ET nse in this case [ IOc] _Such correlation is observed if we assume that C is positive (fig. 2). Moreover, just in this case C is observed to decrease systematically with increasing AJZSfor a given value of n (fig_ 2). Finally, evidence for positive values of C is given by the data for BeFg-; the Ans value for this compound is within the range of the Ans values for the transrtronal elements and, according to the above discussion, C is positive. of transItron elements is positive, at least, Thus, there is an indirect evidence that C(A-F) in compounds AF;for the elements at the beginning and in the middle of the period. Note further, that the values of C for the compounds of the 5d elements are small compared to the values for 7 It should
be noted
that, with
increasing
ionicity
OF the bond,
I increases
and e:,
for which
C= 0, decremes.
the isovalen t analogues
of the 3d and 4d elements
(fig. 2). This conclusion
is in good agreement
with the experi-
data [IOc] on the ionization energies (Ins) for the respective elements. For instance, the Ins values in the series V, hb, Ta are 6.48, 6.88, 7.97 eV for the configuration d4s and 7.06, 7.03, 7.62 eV for the configuration d3s2; the hrs values in the series Cr, MO, W are 6.76, 7.07, 8.50 eV for the configuration d5s and 7.28,7.47, 7.95 eV for the configuration d4s’. Thus the variation of the Ins (and, hence, of E:] contri!mtes to our understandNbFg and CrFs, MoF6, WFs (fig. 2). ing of a peculiar variation of C in the series VF;, mental
3. Variation
of C(A-F)
Let us consider K(A-F),
when going over from
the following = C(A-F),
AFZ-
to AF,LX-
variations: [AFSLXP
] -
C(A-F)[AF;P]
and K(A-F)u
= C(A-F),
[AF5 L=- ] -
C(A-F)
[AF;-]
_
using perturbation theory and taking into account the First we calculate the values of C(A--F)& and C(A-F)r, replacement of F with L. We assume that the ligand L is more covaient than F so that the orbital energy Hpp of the operator H’ the valence rrpelectrons (its absolute value) decreases by SH,,,,. i.e., we obtain for the perturbation 1 following relation: (F2pl H’( F2p) = 6Hpp > 0 _
(5)
Taking into account this perturbation operator, we find the variation of the wave functions and the orbital energics for occupied and vacant levels of the complex AF, LX-. For our purpose it is sufficient to consider the variation of the coefficients at the s-orbitals of the atom A; since the orbitals F2s do not take a significant part in chemical bonding we shall not take into considerations the variation of their population ment of F by L. The following formulas are obtained by first order perturbation theory:
SC&=-
@&6b2 +‘o*)F H@*a,)(~,~+,,)A(+,, +‘a*)F H@ra2)(~~, (a, -
af)(u2 - a’)
H(a*~*)(9,~ k,*)&a2 bkti (u2 - .?*)(a* - e*>
(u2 -
n-p
H@*o~)(J/,~ %,)r&~,
-
(ul ~
e*)(u2 -
&*)F~ e*)
resulting
from
replace-
V.I. Nefedov
424
er al/Nuclear
spin-spin
coupling cmsranfs
= =f&:~& 36(al
- a*)(=,
-a*)
6Hpp(u2 - ~*)E~E~X~X~~~P~H#~
+
4
36
+L
nl - =*
(e, - e’)(u’
(e_, - .~~)(e~-a*)~(=~
FHpp+;flH;
- e2)-
4
+
(
6Hpp(=2 -ya*)q
2(4
(el - e*)(n*-
e2)(e2 - =*)2(=2
e*)&
e*)
)I ’
(6)
E’2, - =*)
- e*)2 (uI -e*)
1
- e2)
-
(a, - =3(=2
=1-=2
1
(el -
- e*)(a2 - e*)(=*-
4
- a*)
18
-I-----ul -a*
(e, - e*)(ul
-----+-
a*)@2
e*)2(u1 - e*)
1
1
(
UT,= 36(al-
- e*)(c72-
(el - e*)(u,
E~P~I-QY~P~H&~~
- e-)(=2
- e’) )I
- e*)(a*
4
12
(fl - f)(a’
-
F)(az
-
t’)2(q
-
r+)
(7)
6Cti-6Cti=
-
f3f,,(a,
2 El +7
+6H
al-a
PP
672-
-
2 El
=*)t1e2A1A2S2b2Hs,H,, 12
(
(el - ez)(e2 i=*)z(02-
(el - e*)(=* -
e3-
(e, -
e*)(ol
CZ*)~(U~- e’)
- e*i(=2 - e*)(u’
-
e’) )I
4
=*)q •2~l~2r2~2H&sp 12
e*)(a2 -
(fl -
r’)(a’
-
t-)(a2 - t*)qq
- t*)
(8)
In formulas (h)-(8) the matrix elements H5s, Hsd and Hsp relate to the s, d or p orbit& group F2s orbit& of the appropriate symmetry; Nii is the perturbation matrix element
~a214 = ~~~~ (see [2]), etc. The rest of the notation
t;y19
is explained
of the atom A and the between the orbit& i and
in table 1 or has been used for formula
Formulas (6)-(B) have been derived for the compounds of nontransition elements according to table ever, as discussed above, the node structure of the Ans and F2s orbitals seems to be ratined also for the of transition elements; therefore, these formulas may be used in a somewhat tentative way for analyzing pounds of transition elements. Since the nature of the atom A determines the relationships between the ters of formulas (6)-(B), the compounds of transition and nontransItIon elements should be considered 3.1_ Nontransition
1. Howcompounds the comparameseparately.
elements
In the compounds of nontransition elements the chemical bond involves primarily the s and p electrons of the atom A and, hence, H d may be assumed to be small compared to H,, and Hpp_ According to (6), if we have 1, 1-e.. for the element A at the beginning or in the middle of the period, the following Ef > ET, E;=C~Or&E2 inequality is satisfied: SC,, < 0; and for the element A at the end of the period, where E: > ~22, the inequality SC,, > 0 is satisfied. The sign of SC,, cannot be found for the beginning and the middle of the period but at the. end of the period, where ~22< E:, we obtain 6C,, > 0 (formula (7)). The difrerence 6Ctr - 6Ccis is positive at the beginning and in the middle of the period, since the factor of ET is positive and the first term in brackets in the c$ facts should exceed the second term because, for a markedly ionic character of the A-F bond, we should expect that (a2 - t,) <(a* - t*). At the end of the period, where ? > e$, the value of SC,, - SC,_is is also positive. The above results are summarized in table 2. The following predictions may be made proceeding from these results. the absolute magnitude of C(A-F),i, inWhen a more covalent l&and is introduced into the complex AFg-, creases for A at the beginning and in the middle of the period since the signs of C(A-F) and 6C(A-F),,, are the same. At the end of the period it decreases since C(A-F) and 6C(A-F),, have different signs. Although no definite conclusion can be made about the variation of 6C(A-F),, at the beginning and in the middle of the - 6Ctis is positive suggests that the period (it may be either pos&ve or negative), the fact that the difference 6C,
l
increase
in the value
lute magnitude
1C(A-F),,,I
of C(A-F),,
is always larger than that of decreases
for the elements
I C(A-F)t,l
(if the latter increases
at the end of the period
and this decrease
at all). The absomust be greater
than that of C(A-F)cis_ The experimental data available now are not sufficient for the complete ve&cation of all the results discussed above, but the data for SnF5L2-, PF5Land SeF5 L (table 3) show that our results give a basically correct picture as a function of the position of the atom A in the period. Indeed *, of the variation of C(A-F),, and C(A-F),,, the following
inequalities
IJ(A-F),is[AFSLX-
are satisfied: ]I > IJ(A-F)[AF~-]
I
and
I&--F),,,[AF,LX-]I
> IJ(A-F),,
[AF,LX-]
for A = Sn, P; but
IJ(Se-F),i,[SeFgL]l
< JJ(Se-F)[SeFG]l
and lJ(Se-F),,[SeFSL]I
* In this case J(A-F)
<
IJ(Se--F)tSeFhlI
can be considered instead of C(A-F).
I,
426
V.I. Nefedov
Table 2 ThesignofBCand
AJinAF,L*-
et ol.~Nuclearspin-spin
compounds (AJ=
IJ(AF5L)
coupling cor~~?ams
- lJ(AF,)
I)
Nontransition element A
T_ition
Beginning. middle
End of period
6CCi,
6%
acw-
CO
*0
>o
AJCi.5
AftI
AJtr -
>O
so
co
Table 3 The spin-spin
SC,&
Al&
coupling mnstants J(A-F)
L
F
SnFSL2PFs LSeFsL CF3L SiF,L BFIL
1601 710 1432 257 178 15
IJ(Se-F),I,I
6Ctr
6Ct,--BCC&
6CCiS
6%
6Ctr - 6Cm
>o
>o
10
20
AJcis
AJti
A
AJcis
AJt,
AJtr - AJ&
-co
to
*0
co
< IJ(Se-F),,
Jb -
(Hz) for the compounds AF$-
AJcis
and AFn_lLx?
Br tr
cis
1899 1529 860 725 1258 1352 299 228 34
For L = Cl and OH the following
AU elements
6ccis
Cl cis
inequality
element A
OH tr
2068 1565 _ _ 324 252 56
is satisfied
cis
tr
cis
tr
1776
1278
1320 _ _
1358
830 -
_ 691 _
_
R&S.
CHx
-
WI
129.301 1311 1321 WI 1331
271
_
_
77
instead:
.
This does not agree with our results but for L = OCI, OBr, and 01 the inequality we predicted is satislied: IJ(Se-F)etil > IJ(Se-F)t,l [3 l] _All the above inequalities are also satis_tied for these ligands. Note also that, although the data for TIzF~_~(OH), J(Te-F),,
and J(Te-F&,,
IJ(Te--F),i,
1343 and TeF5L
[3 l] do not provide information
[TeF5 L]
I < IJ(Te-F)
[TeF, ]
I
is usually satisfied. Our results are also indirectly I confirmed by the experimental SiF4(Ox)2-. In this case the inequality which should be expected middle of the period is satisfied: IJ(Si-F)
[SiFz-]
on the relative values of
they show that our inequality
I < lJ(Si-F),,
Thus, the experimental
[SiF,(OX)2-]
I < lJ(Si-F),i,
data [35]
for SiFz-
for the elements
[SiF4(OX)2-
and, for instance,
at the beginning
and in the
]I_
results confirm on the whole the theoretical predictions for octahedrons. Our analysis
does not make clear in which group of the periodic suggests that this takes place for the compounds
table the sign of SC,,
is reversed; the experimental
of the VI group. It is natural, therefore,
* We do not oxwider here the introduction of two mire covaient ligands into the complex AF$-. resulla seam to be feasible.
evidence
that, along with a de-
but Ihe CxttWOhtiOn 0fou.r
VI. Nefedov crease in (J(Te-F)ci,(, TeF,OCl
spin-spin
for the majority of the compounds
as compared to TeF6 [31]
3.2. Thmsition
et al./Nuclear
coupling constantx
427
of Te, a small increase in this value is observed for
_
elements
In the compounds of transition elements the chemical bonding iuvolves mostly the s- and d-electrons of the atom A so that Hsp may be assumed to be small compared to H,, and Hsd_ It should also be taken into account that for the compounds of transition elements, in contrast to those of non-transition elements, the inequality E:
>
sct,
>
6Ct, - 6Cci, < 0
(9)
If this coefficient is assumed to be negative the following system of inequalities is obtained:
sc,j,(0
I
6Ctr ~ 6C,,,>O
6CtrS0,
-
Although the sign of this coefficient can be established only by introducing additional assumptions, some indirect general considerations suggest that the coefficient is positive_ Moreover, the available experimental data suggest the validity of ihe system (9). It should be stressed that each of the systems contains two rigid inequalities so that using the experimental data for selecting the correct system does not guarantee agreement with experiment. Table 2 presents the theoretical results obtained and table 4 summarizes the experimental data available to us [27,36] _As may be seen from the table, replacement of F with Cl or OH in F’tFz- results indeed in a marked decrease of the constant J(Pt-I),, and in a certain decrease in J(pt--F)cis_ Similar results have been obtained for the replacement of F with Cl or OCH, in WFg_ Thus, the experimental data confirm the fairly complex theoretical relationships for J(A-F),i, and J(A-F),, as functions of the atom A (tables 24). The variation of C(A-F), when going from AFg- to AF,LXand from AF;to AF2LZ(table 3) has been considered in [37] _
4. Variation of C(A-F)
when going from AFZ-
to AOFgXX+‘l-
or AOF:-
The replacement of the atom F by the ligand Lr which may form a x-bond (AELI) with the atom A (AFZ- -+ since AF,Lp* )-), may b e considered in first approximation as leading only to a more covalent u-bond A-L,, the existence of the x-interaction A=L, of e-symmetry will not affect directly the former arguments and formulas. Table 4 The spin-spin coupling constan J(A-F)
(Hz)
Compound PtF:F~Fs(OH?PtF&12Ci5FtF4& W6 wa W=s(OCHh
/(A-F)-
/
2003 1936 1931 1882
1049 1115 *44
25 *43
i33
Compound
W6 WF,
J(A-F)cir,
Kefs.
J(A-F)t, +44
o-
*IO 64
WOF4 YFb 'VOF,-
iw
i57
[381 WI WI 1241 [401
88 116
t&F, NbOF; SCF6 SeFsO-
335 410 1432 1190
The prcscncc of the n-bond makes the a-bend
A-L,
[=I
1050
more covalent
and, therefore,
the results obtained
in table 2
should be vahd not only for replacement of F with Cl but, to a greater degree, for the case F + 0. This result is quite similar to the consideration of the inductive effect in these rephtcements [5] _ Indeed,
a comparison
with the experimental data (table 5) shows a complete agreement with the data of table 2. for WOF, is noticeably greater than for WF5(OCH3); the variations AJ,, and AJc, for SeOFF are greater than for SeF5Ct. A comparison of AJ,, and AJcis also yields a correct relationship. An an-alysis of the experimental data presented in table 5 shows that the constant J(A-F)crs always increases in going from WF; to WF,Oor from AFZ- to AF,OX(A=W, V, Nb). Since the data of table 2 show that the value of AJ(A-F),, may both increase and decrease, the experimental relationships indicate that the secondary variations of the parameters of the a-symmetry levels due to the presence of the n-bond of e-symmetry, make such additional contribution to the value of AJ,is so as to render AC,, or Afci, always positwe. The evaluation of these contributions is generally a rather complex problem. It should be stressed that this relationship is valid only for the bond M=O; in the case of WSFT J(W-F),is d ecreases to 33 Hz [41]. Thus, the experimental observations reveal both an increase and a decrease of the constants J(A-F)ci, according to the data of table 2; the variation of the constants is affected not only by the properties of the compound AF;but also by the properties of the &-and L.
For instance, the variation AJ,,
5. Can the constants J(A-F)
characterize
The bond strength is often in the mean excitation 2
K(A-B)
energy 2
--Q’Aog~&~(~)~~1
characterized (AE)
the strength of the A-F through
formula
bond?
(11) (_ree, For instance
[ 11) which has been derived
approximation: r&s(0)12(A@
>
(1
where I& and og are the populations of the ns orbitals of the atoms A and B, II, is the density of the respective ns orbitals in the vicinity of the nuclei of A and B. The increase of the contribution of the Ans orbitals in the compound
AE$-
is assumed to result in an increased strength of the A-B
bond. Thus, an increase in K(A-B)
indicates an increased strength of the A-B bond. The above discussion contains two unproven assumptions which in fact disqualify the conclusions about the correlation betweenJ(A-B) and the strength of the A-B bond. First, formula (11) does not even take into account the possible reversal of the sign ofK(A-B) depending on the structure of the valence levels and, therefore, its apphcation was questioned as early as 1964 [2J_ It is of interest that formtda (11) was used for analysis usually by experimentalists (see, for instance ]l]) while theoreticians (see, for instance [42]) invariably made use of the theory developed in [2] or a more refined theory [43] _The authors of a recent experimental paper [27]
Vf. Nefedov Table 6 Variation of the strengthof the Nontransition
A-F
et ol./Nuclear
bond for the changeAe-
element A
spin--spin
-
AF5
coupling corrStants
429
Lx-
Trransition
clement
A
6m5.5
6mti
6mw - Bm,g
6nkiS
6mtr
6mfi -
SO
10
SO
10
10
have noted though, that there are no grounds infhrence of the ligand on the bond strength.
for using formulas
of the type (11)
Cm,is
when considT.ring
the mutual
Secondly, there is no yet any theoretical or experimental evidence that the increase in the contribution of the Am orbitals is always accompanied by an increase in the strength of the A-B bond, although this seems to be often the case. To verify this conclusion, localized orbitals of the A-B bond should be obtained but this procpdure is used rather rarely. a correlation between SC,_is and SC,, and In this connection, let us find, when going from AFZ- to AF,LX? the parameters 6mcis and 6mt, which characterize, within the Framework of the perturbation theory, the change in the strengths of the bonds A-FciS and A-Ftr [4,5] _ Let us discuss some of the factors which, in principle, make possible a correlation between 8Ci and 6nzi. In tabie 6 values 6mi are given which characterize the strengthening of the bond (+) or its weakening (-) when we go from AFgto AF,LXas obtained from calculations of the inductive effect within the framework of the perturbation theory [4,5]. There is a fairly apparent similarity in signs between the values of SCi (table 2) and 6mi. Taking into account different signs of C in the compounds of transition and nontransition elements, we may expect an increased value of IK(A-F) 1for the compounds of nontransition elements at the beginning and in the rnic!dle of the period as the bond strength decreases; for the compounds of transItIon elements we may expect that IK(A-F) I falls with decreasing bond strength. The similarity between the data of tables 2 and 5 is related to the fact that in calculations of the bond strength and the constants the effect of the valence s- and d-electrons of the atom A (more exactly, of the parameters associated with them) is opposite to that of the pelectrons. It is just these facts that explain why in principle there may be a correlation between 6mj and SCi depending on the ligand to L; for instance, K(Sn-F)cis increases in the series L = Cl, Br, I [28] and the bond strength should be expected decrease in this series [4,5]. However, formulas for 6Ci and 6mi show [4,5] that generally no similar behaviour of 6Ci and 6mi can be expected; this may be seen just from the fact that 6Ci reverses its sign when the nontransition elements A go from the beginning to the end of the period. Thus, the constants K(A-F) cannot be used for predicting the variation of the bond strength. The analysis of the experimental data also leads to this conclusion. As an illustration, note that InKl increases in the series CH, + Cl (PF,L-), CH, + Cl + Br (CF3L), Cl + Br + CH3 (BFzL) (table 5) while only the last series correlates with the variation of the A-F bond. AS an example for the compounds of transition elements, let us consider the changeover WF6 -+ WOFF _As shown in [5] for simila; -compounds, the strength of the W-F bond is decreased both in the cis- and transpositions to the W=O bond, but according to 1361 (table 5) the variations of AK for the cis- and tram-bonds such examples can be given. Thus, the answer to the question heading this section should be negative.
References [l] T-G. Appeleton. H.C. Mark and L.E. Manser, Coord. Chem. Rev. 10 (1973) 353. [Z] J.A. Pople and D.P_ Santry, Mol. Phys. 8 (1964) 1. [3] S. Nagata. T. Yamabe, K. Hirao and K. Fukui, J. Phys. Chem. 79 (1975) 1863.
W-F
have different
signs. More
430 [4] [5] [6] [7] (B]
V.I. V.I. B.F. B.F. E.L. [9] E.L. [lo] Vl.
VI. Ncfedov
et ol./Nuclcar spin--spin coupling constants
Nefedov. Koord. Khimiya (Russ.) 1 (1975) 1299. Nefedov, Chem. Phys. 14 (1976) 241. Shchegolev. Thesis. IONKh AN SSSR (1975). Shchegolev. E-L. Rosenberg. 0-P. Charkin and M-E. Dyatkti. Zh. Strukt. Khimii (Rus.0 14 (1973) 581. Rosenberg and ME. Dyatkina. Zh. Strukt. Khimii(Russ.) ll(lV70) 325. Rosenberg and M.E. Dyatkina. Zh. Strukt. Khimii 12 (1971) 548. Nefedov. The valence electron levels of chemical compounds, set. “Structure of molecules and chemical bonding”, Vol. 3 (VINITI. Moscow, 1975) (a) p_ 152, @) p. 88, (c) p. 63 (in Russian). [ll] W. McFarlane, Quart. Rev. Chem. Sot. 23 (1969) 187. [12] R-J. Gillespie, J. Bacon and J-W. Quail, J. Chem. Phys. 39 (1963) 2555. [I3 j Eiichi Fukusbima. J. Chem. Phys. 55 (1971) 2463. 1141 C.J. Jameson and H.S. Gutowsky. J. Chem. Phvs. 51 (1969) 2790. il5 j DX. Dalliog and H-S. Gutowsk;.j. Chem. Ph& 55 (i971)~4959. 1161 1.1. Sobelman, Introduction in the theory of the atomic spectra (Moscow, 1963) p- 306. [17] 1-M. Band and M-B. Trzhaskovskaya. Tables of Electron Energy Eigenvalues. Densities Near the Origin and the Mean Values in the SelfConsislent Fields of Atoms and Ions, LlYaF AN SSSR (1974) (in Russian). 1181 R-B. Johanncsen, F-E: Brinckmanand T.D. Coyle, J. Phys. Chem. 72 (1968) 660. [lY]_ H. Browostein and H. Selig, Inorg. Chem. 11 (1972) 656. [20] R-J. Gillespieand GE Scluobilgen, Inorg. Chem. 13 (1974) 1230. [21] P-A-W. Dean and D-E. Evans. J. Chem. Sot. (A) 698 (1967). [22] Yu.A. Buslaev, S.P. Petrosyans. V.P. Tarasov and V.I. Chagin, Zh. Neorgan. Khimii 19 (1974) 1790. [23] J-AS. Howelland K-C. Moss. J. Chem. Sot. (A) 2483 (1971). [24] K-J. l%cker and E-L. Muettcrtis, J. Am. Chem. Sot. 85 (1963) 3035. [25] C. FIO~SC. Harttee-Fock Parameters for the atoms helium to radon (Department of Mathematim, University of British Columbia, 1966). [26] ME. Dyatkina anti EL. Rosenberg, Electron Structure of the Compounds of Transition Elements. “Results of Scicncc”, set. “Molecular structure and chemical bonding”, Vol. 2 (VINITI. Moscow, 1974) (in Russian). [27] D-F. Evans and G.K. Turner, J. Chem. Sot. Dalton Trans. 12 (1975) 1238. 1281 PAWDean and D-F. Evans, J. Chem. Sot. (A) 1154 (1968). 129) Yu.A. Buslaev. E.G. Il’in and M.N. Scherbakova, Koord. khimiya 1 (1975) 1179. [30] S.S. Ghan and C.J. Willis, Can. J. Chem. 46 (1968) 1237. (311 K. Scppclt. 2. Anorg. AUg. Chemic 399 (1973) 65. 1321 G. Emsley, G. Feeney and L. Sutcliffe, NMR spectrosmpy of high resolution (hiti, Moscow, 1969) Vol. 2. p. 276 (in Russian). [33] M.J. Bti. DE Hamilton and J.S. Hartman, J. Chem. Sot. Dalton Trans. 1405 (1972). 1341 U. EIgnd and H. Selie. Inoin. Chem. 14 (lR75) 140. i35j P-A-W. Deam and D?. Eva&, J. Chem. sot. (A) 2569 (1970). 1361 W. McFarlane. A. Noble and J. Winfried, Chem Phys. Lett. 6 (1970) 517. f37j V.I. Nefedov, V-G. Yauhemsky and V.P. Tara.sov. Koord. khimiyn 2 (1976) 1443. [38] F.X. Tebbe and E-L. Muerties, Inorg. Chem. 7 (1968) 172. [39] 1-V. Hotton. Y. Saito and W-G. Schneider, Can. J. Chem. 43 (1968) 47. [40] Yu,A. Buslaev, EG. Il’in, V.D. Kopanev and VP. Tamsov. Zh. Strukt. Khimii 13 (1972) 930. [41] Y3.A. Buslacv. Yu.V. Kokunov and Yu.D. Cbubar,Doklady AN SSSR 213 (1973) 1083. [42] A.W. Cowley and W.D. Whte.J. Amer. Chem. Sot. Yl(lV69) 1913. [43] J. Kowalewki, J. Chcm- Communs. Univ. Stockholm 14 (1974) 29.
NUCLEAR
SPIN-SPIN
COUPLING
CONSTANTS
AND
MUTUAL
INFLUENCE
V.I. NEFEDOV, V.G. YARZHEMSKY and V.P. TARASOV hstitrrte of GerwraZnrrdImrganic Chemistry. USSR Academy of SLiences. Moscow. Received
10 February
OF THE LIGANDS
USSR
1976
Generalized formulas for the spin-spin coupling constant K
1. Introduction The spin-spin coupling constant J is one of the most convenient properties for studying the mutual influence of ligands in coordination compounds [I]. Some data on the variation of the A-X bond strengths under the effect of the ligand L may be provided by studying the change in J(A-X) in the compounds AX,, when going over from AX,, to AX,,_, L. However, no sufficiently rigorous theory has been developed so Far for descnbmg the variation ofJ(A-X) as 3 function of A and L. Typically, the approximation of the mean excitation energy is used [l] but even the authors of ref. [2] noted that this approximation was not adequate since it could not account for the sign ofJ. In particular, the reduced constant K(13C-1gF) in CFq is negative [3_] _Hence, this study attempts to describe K(A-F) in the compounds AF,,_ll=Tcompared to the compounds AFZalong the lines of the general formulas [2] for the constants R(A-F), taking into account only the contact term, which plays the major r6le [1,2] _ For directly bonded atoms it appears that the contact term is the min one. However, in specific cases the spin-orbital term was found to be important [3] _ Here we develop the following general approach: The sign of K(A-F) in the compound AF,T- is determined from the calculated wave functions and some general considerations_ Then, perturbation theory is used to construct the system of functions and orbital energies for the complex AF,,_, Lx- and the value of K’(A-F) is found for this complex. Replacement of the ligand F and L results in a decrease or increase of K’ compared to K according to the signs of K and 6K, where 6K = K’K. These variations are further analyzed with regard to the change in the A-F bond strengths due to the inductive effect, which is considered in the framework of perturbation theory [4,5] _ Similarly to the inductive effect, the nature of the central atom A has an essential influence on K and 6K [4,5] ;
hence,
transition
and nontransition
atoms
A should be considered
separately.
V.I. Nefedov
418
2. Sign of the reduced constants K(A-F)
et ol.fNuclear
spin-spin
in the compounds
coupling cmu~anr~
AFn of transition and nontransition elements
2.1. Nontransition eleJnerlts The wave functions of the u-levels in the compounds AF, (D3h), AF, (D4,,) and AF, (Oh) may be written down proceeding from the general considerations developed in [2] and taking into account MO LCAO calculations [6-91. For the compounds AF, of nontransition elements the MO LCAO coefficients for the orthogonalized basis may be taken in the form of table I_ ln this table all the coefficients are positive. It should be stressed that the perturbation theory method psed in [2] yields the same MO LCAO node structure as the results of the calculations for E%eFy, BF3. CF$ [6], AlFy, SiF4, PF:, BeFz-, BFT, CF4 [7-q], BeFz-, CFZ- 161, AlFz-, PFZ. and SF, [6,8,9] _ The wave functions are of the same nature and do not depend on symmetry_ The coefficients in the table are related to each other by the conditions of orthonormalization.
Moreover, if we take into account the
weakness of the interaction between the F2s-orbitals and the central atom orbitals we can use perturbation theory for determining the coefficients at the F2s orbitals and finding additional relationships between these coefficients. For instance, the following relationships are valid for the octahedrcn: @=CY4E2--tEt
1
ff#
=
Q4El
*
QlEZ
,
S%p--r-l_
(1)
It should be stressed that eq. (1) obtained by us differ from those in [2] since we consider first the interactions ARS - F2p and Anp - F2p and only then superimpose the perturbing interaction with the F2s orbit&. The authors of [Z] first superimposed the perturbing interaction with the F2s orbitals and only then introduced the interactions Ans - F2p and Anp - FZp. Our procedure has a better substantiation and yields wave functions of a more correct form; for instance, it takes into account the admixture of the F2p orbitals at lower levels which agrees with the MO LCAO calculations. However, this modification is not essential since all the results presented below may be obtained with the function types used in [2]. Since for all the considered complexes AFZ- the functions of the a-levels of a-symmetry are similar, WC may limit ourselves to considering only one point symmetry group, for instance, the octahedral group. In this case the expression for the reduced constant K(A-F) has the following form (to a constant factor): K=--+
&7BE2%
Ela4bE2a1
al -a*
l
2 =(Y
n2-a*
1
:
(
G
* * _~ a2 - 0 al ~ a 1
=
hi;
(a1 --n*p
(1--E:)Kl+I)+-l
I
(2)
where ul, uz, and n-are the orbital energies of the levels lalg, 2atg and 3aqp, Z = (at - =*)/(a2 - 0*) > 1, Ifs is the matrix element between Ans and the group orbital of a tg symmetry from the F2s functions, el is the coefficient if the Ans orbital (see table I). Table 1 The
MO
LC.40
coefficients
Oh MO
for the
AFg-
(Oh)
compounds
Orbit& of central atom
Group
orbitals of
ligands
V.I. Nefedov et oL/hrucleor spin-spin
oxrpling constants
419
Fig. 1. The constant C(A-_F) a~ a function of E:_ Formula (2) has been transformed with the help of formulas of the type (1) and the expressions LCAO coefficients within the framework of perturbation theory, for instance,
q =
for the MO
P2E*ff&z, -a*1 -
(3)
It follows from general considerations and the inequality Ia2 - a* I < loI - a* 1that K is positive for small e: and negative for relatively large e:; the latter case should be expected for the majority of the compounds of AFZ- type. Indeed, the numerical values of the parameters in formula (2) obtained by MO LCAO calculations [6-91 for a large number of compounds (see above) yield K < 0. The general form of the function K =f(et) for I= 2.0 is given in fig. 1. According to this function K is positive in the compounds AFconly if the bond is (see below). Neagtive values of K highly ionic. There is some indirect evidence that this is the case for BeFishould be expected for other AFG- compounds_ The absolute magnitude of K grows steadily in the isoelectronic series of the compounds containing elements belonging to the same pericd, for instance, SiFg- + PF; --f SF, + ClFi since the orbital energy, Ans, increases and e: grows. In principle, For values of e: large enough some decrease in K may be expected since the curves K =f(~f) have minima. However, these minima do not seem to appear in the compounds we considered. Indeed, if we use the experimental values of ut and a2 for SF, [lOa] and CF, [lob] and the estimate a* = 5 eV, we find that I is 1.77 and 1.90, respectively; these values yield rather high values of e:(min) (0.68 and 0.67, respectively) which are higher than the respective values of e: (for the orthogonalized basis). It should also be taken into account that the value of 1 decreases in the isoelectronic series AFiwith increasing atomic number of the element At, that is, wi& increasing t :, which results in a rise of :(min). These theoretical
l
results are in full agreement with the experimental PFS, TeFs, SeF, [ll], SnFz[12], BiF; 1131.
data. Neagtive
values of K(A-F)
have been found
for SiF%,
Some general relationships between the value of K(A-F) and E: are also in fufl agreement with the experimental results. It is convenient to introduce a new parameter, the completely reduced constant C of the spin-spin coupling: C(A-F)
= K(A-F)/S(A)S(F)
,
(4)
where S(A) and S(F) are the densities of the valence s-electrons of the atoms A and F in the vicirutres of their nuclei. The dimension of C is cm3_ It has the same sign as the constant K but, in contrast to K, the constant C takes into account only the variation of the electron density distribution of the s-electrons and is. therefore, more 7 For instance,in the seriesBeFi< ElFi. CF,, if WEuse the experimentalvaluesfor aI and ~1s[lob] and assumeu* = 5 eV. we obtain I= 3.1. 2.2. and 1.9. respectively.
V.I. Nefedov
420
et al./Nuclear spin-spin
coupling cwmtants
C AIIS~VJ
r
I$&
Correlation ; (0)
g&s
of C(A-_F)
the value
of C(A-F)
of the Periodic
convenient
end Ans I”_’ for
AT4
cxphnation The sole
in the tent). (0) The orbital for C is 1 :10m5
(at.
units)3.
Ans energy; (0) the The Roman numerals
value of C(A-F) kw AFt--; denote the numbers ofthc
Table.
for analyzing
chemical
bonding.
It is just the constant
C that makes it possible to analyze
the relation-
ship between the spin-spin coupling and C: and, hence, the orbital energy Ans as a function of the atomic number of the element A. The constant K depends also on the value of S(A)S(F) and, hence, it must characterize the Mriation not only of E: (the influence of the chemical bond) but also of S(A) (the influence of the atomic constant). A similar analysis has been made previously in the papers [14,15] _ The integral D should be calculated to obtain the relativistic
D=j-
value S(A)
[ 161
I
FGdr. 0
where F is the small component, has been calculated. instead general
This E-value
ar.l
G is the lar ge component. In the paper [ 171 the E-value E = F?(O) + G2(0) as well as the value D is proportional to S(A). We have used (fig. 2) the E-values
of the D-values, because the calculated D-values dependence S(A) on 2 and not in the numerical
are not available and we are mainly interested in the values C(A-F). This approach overestimates the S(A)-
values for large Z; this follows, for example, from the comparison of the ratios S(A)/.S’(A) in paper [15] with our S(A)-values. The caiculation of the C(A-F) values (fig. 3) based on semiempirical S(A)-values [ 151 proves however the general trends of C(A-F) along the periods and groups of the Periodic Table as found in fig. 2. The decrease of the C-values on descending along the same group (fig. 3) is however fig. 2. We discuss these trends using fig. 2. Shown
‘3GeF4
in fig. 2 are the values of C(A-F)
in the tetrahedrons
[I l] and the octahedrons “‘SiFz-,
31PFg, 75AsFg,
gBeFi-,
“BF,,
not so well pronounced 13CF4,
77SeF6, 125TeF6, 12%bFg
14NF+ 141, 435 SF,,
[ll],
as in 2gSiF4
[17],
421
Fig. 3. See crption to fg 2. The scale tar C is IO-’ (at. urrits)3. “9SnF;-
[12],
35C1F&1271F;
the data for 49TiFg-
[Zl]
[13],
, 45S~Fz-
discussed below. The values of J(A-F)
“BrF;
[20],
1221, 51VF;
73GeF;-
[21],
1231, 93NbF;,
209 SiFg
1241,
[ 131. This figure represents also
183wF6 and 95MoF6 [I 11 which eu be
are taken from the papers referred to above, the values of the gyromanrtetic
ratio are taken from the Varian reference tables. The virtual values of J(14N-F)
in NF; andJ(l%-F) in CFZhave been estimated by comparing the values of J(Si-F) in SiF, and SiFz- and of J(Ge-F) in GeF4 and CeFzwith the experimental results for NF: and CF,. We have also estimated J(lglTa-19F) in TaF; by analyzing the temperature dependence of the NMR line shape for 19F . The thick dashed lines in figs. 2 and 3 denote the variation of C(A-F) in the period for the isoelectronic compounds of the elements in higher oxidation states, the thin dashed lines denote the variation of this constant in the groups; the numbers of the groups are given in the left-hand side of the figure. The Ans values are taken from calculations [17,25] _ Their variation patterns agree with the experimental data [lot] which are not complete yet. A correlation is found between C(A-F) and Ans which is in full agreement with the considerations discussed above; since the value of : grows with Ans in the period, the~value of C(A-F) also increases [for its absolute
l
magnitude, see formula (2)] _ The only deviation from the steady increase of C(A-F) as a function of Ans in the period has been found for IF:. This deviation is small and it may, probably, be attributed to the fact that the value of E: for C,, in fig. 1 is less than I$ for this compound or to the inaccuracy of the S(A)-values used. From 2- the value of qBe-F) should be negative, otherwise the steady dependence of fig. 2 it may be seen that in BeF%_ _ , BF, , CF4 would be violated. Moreover, in that case Cwould have a maximum Con $0, Ans in the series BeF, in this series which contradicts the general formula (2) ( see fig. 1). since the existence of a maximum would necessitate a rather peculiar dependence of Hs and (a1 - n*) on the central atom in the series of the isoelectronic compounds This result is in agreement with the above conclusion about the positive value of C(A-F) ionic nature of the A-F bond.
for 2 markedly
The correlation between C(A-F) and AJIS is particularly convincing for the compounds of elements belonging to the same group. For the elements 6elonging to the groups III-V the variation of Am in the group is known not to be steady; the value of AJZSdecreases when going over from the second to the third period and increases somewhat or remains constant when passing from the third to the fourth period [lOc] _This nonsteady variation is attributed to the incomplete screening of the 4s electrons by the 3d electron shell in the elements of the Fourth period; it is reflected also by the nonsteady variation of the ionization potentials and by the chemical properties of the isovalent compounds [ lOa,c] _ A similar nonsteady variation is exhibited by C(A-F). Thus, the above discussion shows that C(A-F) is negative in the compounds AFZ- , with the exception of highly ionic compounds of the type BeFz-, and that the variation of C(A-F) in the series of isoelectronic or isovalent compounds is quite similar to the variation of Ans and cbracterizcd by the following: (1) The absolute value of C(A-F) increases in the series of the isoelectronic compounds of the same period with increasing atomic number of A; the larger the period number, the lower the rate of this increase. (2) The change in the absolute value of C(A-F) is not monotonous for the isovalent compounds of the elements belonging to the same group; C(A-F) generally decreases with increasing period number but this is not the case when going over from the compounds of the elements belonging to the third period to those of the fourth period.
2-2. Tmtlsition elements A large volume of MO LCAO calculations has been done for the compounds of the transition elements of the AFZ- type but almost no data have been published on the wave functions [26] _ Moreover, the character of the calculations does not guarantee a sufficient accuracy. It may be assumed that the wave functions will have the same node structure as those of the nontransition elements with respect to the Arzs and F2s levels. The same result follows also from the application of the perturbation theory. Using this assumption the results of the above section may be readily extended to the compounds of transition elements. Hence, our analysis for the compounds of transition elements is somewhat tentative, in contrast to the case of nontransition elements. The ATF bond is significantly more ionic with respect to the Arzs orbitals in the compounds of transition elements compared to nontransition elements compounds, since the Atzs energies vary from 6 to 9 eV for transition elements and from 10 to 30 eV for nontransition elements [IOc] _ If we take into account that the F2p orbital energy is 18 eV, we find that E: should be rather small for the’compounds of transition elements. Hence, C should have a small negative or positive value (see fig. 1) according to formula $2 ); we consider the positive values to be the more probable. Since values of ef are small and lie t in the vicinity of ~~(0) = l/(1 + r) when K = 0 or C=O, absolute magnitude of C(A-F) for transition elements must, apparently, be less than that for nontransition ones; this conclusion is in good agreement with the experimental data (fig. 2). No direct experimental data on the signs of C or K are available at present for the compounds of transition elements discussed here. However, the authors of 1271 report indirect experimental evidence that K(E’-F) is positive in PtFz-. The character of the correlatian between C and Arzs also indicates indirectly that C is positive_ In the series of isoelectronic compounds of the elements belonging to the same period C should tend to a more negative or a less positive value with increasing atomic number of the element A, since Atzs and ET nse in this case [ IOc] _Such correlation is observed if we assume that C is positive (fig. 2). Moreover, just in this case C is observed to decrease systematically with increasing AJZSfor a given value of n (fig_ 2). Finally, evidence for positive values of C is given by the data for BeFg-; the Ans value for this compound is within the range of the Ans values for the transrtronal elements and, according to the above discussion, C is positive. of transItron elements is positive, at least, Thus, there is an indirect evidence that C(A-F) in compounds AF;for the elements at the beginning and in the middle of the period. Note further, that the values of C for the compounds of the 5d elements are small compared to the values for 7 It should
be noted
that, with
increasing
ionicity
OF the bond,
I increases
and e:,
for which
C= 0, decremes.
the isovalen t analogues
of the 3d and 4d elements
(fig. 2). This conclusion
is in good agreement
with the experi-
data [IOc] on the ionization energies (Ins) for the respective elements. For instance, the Ins values in the series V, hb, Ta are 6.48, 6.88, 7.97 eV for the configuration d4s and 7.06, 7.03, 7.62 eV for the configuration d3s2; the hrs values in the series Cr, MO, W are 6.76, 7.07, 8.50 eV for the configuration d5s and 7.28,7.47, 7.95 eV for the configuration d4s’. Thus the variation of the Ins (and, hence, of E:] contri!mtes to our understandNbFg and CrFs, MoF6, WFs (fig. 2). ing of a peculiar variation of C in the series VF;, mental
3. Variation
of C(A-F)
Let us consider K(A-F),
when going over from
the following = C(A-F),
AFZ-
to AF,LX-
variations: [AFSLXP
] -
C(A-F)[AF;P]
and K(A-F)u
= C(A-F),
[AF5 L=- ] -
C(A-F)
[AF;-]
_
using perturbation theory and taking into account the First we calculate the values of C(A--F)& and C(A-F)r, replacement of F with L. We assume that the ligand L is more covaient than F so that the orbital energy Hpp of the operator H’ the valence rrpelectrons (its absolute value) decreases by SH,,,,. i.e., we obtain for the perturbation 1 following relation: (F2pl H’( F2p) = 6Hpp > 0 _
(5)
Taking into account this perturbation operator, we find the variation of the wave functions and the orbital energics for occupied and vacant levels of the complex AF, LX-. For our purpose it is sufficient to consider the variation of the coefficients at the s-orbitals of the atom A; since the orbitals F2s do not take a significant part in chemical bonding we shall not take into considerations the variation of their population ment of F by L. The following formulas are obtained by first order perturbation theory:
SC&=-
@&6b2 +‘o*)F H@*a,)(~,~+,,)A(+,, +‘a*)F H@ra2)(~~, (a, -
af)(u2 - a’)
H(a*~*)(9,~ k,*)&a2 bkti (u2 - .?*)(a* - e*>
(u2 -
n-p
H@*o~)(J/,~ %,)r&~,
-
(ul ~
e*)(u2 -
&*)F~ e*)
resulting
from
replace-
V.I. Nefedov
424
er al/Nuclear
spin-spin
coupling cmsranfs
= =f&:~& 36(al
- a*)(=,
-a*)
6Hpp(u2 - ~*)E~E~X~X~~~P~H#~
+
4
36
+L
nl - =*
(e, - e’)(u’
(e_, - .~~)(e~-a*)~(=~
FHpp+;flH;
- e2)-
4
+
(
6Hpp(=2 -ya*)q
2(4
(el - e*)(n*-
e2)(e2 - =*)2(=2
e*)&
e*)
)I ’
(6)
E’2, - =*)
- e*)2 (uI -e*)
1
- e2)
-
(a, - =3(=2
=1-=2
1
(el -
- e*)(a2 - e*)(=*-
4
- a*)
18
-I-----ul -a*
(e, - e*)(ul
-----+-
a*)@2
e*)2(u1 - e*)
1
1
(
UT,= 36(al-
- e*)(c72-
(el - e*)(u,
E~P~I-QY~P~H&~~
- e-)(=2
- e’) )I
- e*)(a*
4
12
(fl - f)(a’
-
F)(az
-
t’)2(q
-
r+)
(7)
6Cti-6Cti=
-
f3f,,(a,
2 El +7
+6H
al-a
PP
672-
-
2 El
=*)t1e2A1A2S2b2Hs,H,, 12
(
(el - ez)(e2 i=*)z(02-
(el - e*)(=* -
e3-
(e, -
e*)(ol
CZ*)~(U~- e’)
- e*i(=2 - e*)(u’
-
e’) )I
4
=*)q •2~l~2r2~2H&sp 12
e*)(a2 -
(fl -
r’)(a’
-
t-)(a2 - t*)qq
- t*)
(8)
In formulas (h)-(8) the matrix elements H5s, Hsd and Hsp relate to the s, d or p orbit& group F2s orbit& of the appropriate symmetry; Nii is the perturbation matrix element
~a214 = ~~~~ (see [2]), etc. The rest of the notation
t;y19
is explained
of the atom A and the between the orbit& i and
in table 1 or has been used for formula
Formulas (6)-(B) have been derived for the compounds of nontransition elements according to table ever, as discussed above, the node structure of the Ans and F2s orbitals seems to be ratined also for the of transition elements; therefore, these formulas may be used in a somewhat tentative way for analyzing pounds of transition elements. Since the nature of the atom A determines the relationships between the ters of formulas (6)-(B), the compounds of transition and nontransItIon elements should be considered 3.1_ Nontransition
1. Howcompounds the comparameseparately.
elements
In the compounds of nontransition elements the chemical bond involves primarily the s and p electrons of the atom A and, hence, H d may be assumed to be small compared to H,, and Hpp_ According to (6), if we have 1, 1-e.. for the element A at the beginning or in the middle of the period, the following Ef > ET, E;=C~Or&E2 inequality is satisfied: SC,, < 0; and for the element A at the end of the period, where E: > ~22, the inequality SC,, > 0 is satisfied. The sign of SC,, cannot be found for the beginning and the middle of the period but at the. end of the period, where ~22< E:, we obtain 6C,, > 0 (formula (7)). The difrerence 6Ctr - 6Ccis is positive at the beginning and in the middle of the period, since the factor of ET is positive and the first term in brackets in the c$ facts should exceed the second term because, for a markedly ionic character of the A-F bond, we should expect that (a2 - t,) <(a* - t*). At the end of the period, where ? > e$, the value of SC,, - SC,_is is also positive. The above results are summarized in table 2. The following predictions may be made proceeding from these results. the absolute magnitude of C(A-F),i, inWhen a more covalent l&and is introduced into the complex AFg-, creases for A at the beginning and in the middle of the period since the signs of C(A-F) and 6C(A-F),,, are the same. At the end of the period it decreases since C(A-F) and 6C(A-F),, have different signs. Although no definite conclusion can be made about the variation of 6C(A-F),, at the beginning and in the middle of the - 6Ctis is positive suggests that the period (it may be either pos&ve or negative), the fact that the difference 6C,
l
increase
in the value
lute magnitude
1C(A-F),,,I
of C(A-F),,
is always larger than that of decreases
for the elements
I C(A-F)t,l
(if the latter increases
at the end of the period
and this decrease
at all). The absomust be greater
than that of C(A-F)cis_ The experimental data available now are not sufficient for the complete ve&cation of all the results discussed above, but the data for SnF5L2-, PF5Land SeF5 L (table 3) show that our results give a basically correct picture as a function of the position of the atom A in the period. Indeed *, of the variation of C(A-F),, and C(A-F),,, the following
inequalities
IJ(A-F),is[AFSLX-
are satisfied: ]I > IJ(A-F)[AF~-]
I
and
I&--F),,,[AF,LX-]I
> IJ(A-F),,
[AF,LX-]
for A = Sn, P; but
IJ(Se-F),i,[SeFgL]l
< JJ(Se-F)[SeFG]l
and lJ(Se-F),,[SeFSL]I
* In this case J(A-F)
<
IJ(Se--F)tSeFhlI
can be considered instead of C(A-F).
I,
426
V.I. Nefedov
Table 2 ThesignofBCand
AJinAF,L*-
et ol.~Nuclearspin-spin
compounds (AJ=
IJ(AF5L)
coupling cor~~?ams
- lJ(AF,)
I)
Nontransition element A
T_ition
Beginning. middle
End of period
6CCi,
6%
acw-
CO
*0
>o
AJCi.5
AftI
AJtr -
>O
so
co
Table 3 The spin-spin
SC,&
Al&
coupling mnstants J(A-F)
L
F
SnFSL2PFs LSeFsL CF3L SiF,L BFIL
1601 710 1432 257 178 15
IJ(Se-F),I,I
6Ctr
6Ct,--BCC&
6CCiS
6%
6Ctr - 6Cm
>o
>o
10
20
AJcis
AJti
A
AJcis
AJt,
AJtr - AJ&
-co
to
*0
co
< IJ(Se-F),,
Jb -
(Hz) for the compounds AF$-
AJcis
and AFn_lLx?
Br tr
cis
1899 1529 860 725 1258 1352 299 228 34
For L = Cl and OH the following
AU elements
6ccis
Cl cis
inequality
element A
OH tr
2068 1565 _ _ 324 252 56
is satisfied
cis
tr
cis
tr
1776
1278
1320 _ _
1358
830 -
_ 691 _
_
R&S.
CHx
-
WI
129.301 1311 1321 WI 1331
271
_
_
77
instead:
.
This does not agree with our results but for L = OCI, OBr, and 01 the inequality we predicted is satislied: IJ(Se-F)etil > IJ(Se-F)t,l [3 l] _All the above inequalities are also satis_tied for these ligands. Note also that, although the data for TIzF~_~(OH), J(Te-F),,
and J(Te-F&,,
IJ(Te--F),i,
1343 and TeF5L
[3 l] do not provide information
[TeF5 L]
I < IJ(Te-F)
[TeF, ]
I
is usually satisfied. Our results are also indirectly I confirmed by the experimental SiF4(Ox)2-. In this case the inequality which should be expected middle of the period is satisfied: IJ(Si-F)
[SiFz-]
on the relative values of
they show that our inequality
I < lJ(Si-F),,
Thus, the experimental
[SiF,(OX)2-]
I < lJ(Si-F),i,
data [35]
for SiFz-
for the elements
[SiF4(OX)2-
and, for instance,
at the beginning
and in the
]I_
results confirm on the whole the theoretical predictions for octahedrons. Our analysis
does not make clear in which group of the periodic suggests that this takes place for the compounds
table the sign of SC,,
is reversed; the experimental
of the VI group. It is natural, therefore,
* We do not oxwider here the introduction of two mire covaient ligands into the complex AF$-. resulla seam to be feasible.
evidence
that, along with a de-
but Ihe CxttWOhtiOn 0fou.r
VI. Nefedov crease in (J(Te-F)ci,(, TeF,OCl
spin-spin
for the majority of the compounds
as compared to TeF6 [31]
3.2. Thmsition
et al./Nuclear
coupling constantx
427
of Te, a small increase in this value is observed for
_
elements
In the compounds of transition elements the chemical bonding iuvolves mostly the s- and d-electrons of the atom A so that Hsp may be assumed to be small compared to H,, and Hsd_ It should also be taken into account that for the compounds of transition elements, in contrast to those of non-transition elements, the inequality E:
>
sct,
>
6Ct, - 6Cci, < 0
(9)
If this coefficient is assumed to be negative the following system of inequalities is obtained:
sc,j,(0
I
6Ctr ~ 6C,,,>O
6CtrS0,
-
Although the sign of this coefficient can be established only by introducing additional assumptions, some indirect general considerations suggest that the coefficient is positive_ Moreover, the available experimental data suggest the validity of ihe system (9). It should be stressed that each of the systems contains two rigid inequalities so that using the experimental data for selecting the correct system does not guarantee agreement with experiment. Table 2 presents the theoretical results obtained and table 4 summarizes the experimental data available to us [27,36] _As may be seen from the table, replacement of F with Cl or OH in F’tFz- results indeed in a marked decrease of the constant J(Pt-I),, and in a certain decrease in J(pt--F)cis_ Similar results have been obtained for the replacement of F with Cl or OCH, in WFg_ Thus, the experimental data confirm the fairly complex theoretical relationships for J(A-F),i, and J(A-F),, as functions of the atom A (tables 24). The variation of C(A-F), when going from AFg- to AF,LXand from AF;to AF2LZ(table 3) has been considered in [37] _
4. Variation of C(A-F)
when going from AFZ-
to AOFgXX+‘l-
or AOF:-
The replacement of the atom F by the ligand Lr which may form a x-bond (AELI) with the atom A (AFZ- -+ since AF,Lp* )-), may b e considered in first approximation as leading only to a more covalent u-bond A-L,, the existence of the x-interaction A=L, of e-symmetry will not affect directly the former arguments and formulas. Table 4 The spin-spin coupling constan J(A-F)
(Hz)
Compound PtF:F~Fs(OH?PtF&12Ci5FtF4& W6 wa W=s(OCHh
/(A-F)-
/
2003 1936 1931 1882
1049 1115 *44
25 *43
i33
Compound
W6 WF,
J(A-F)cir,
Kefs.
J(A-F)t, +44
o-
*IO 64
WOF4 YFb 'VOF,-
iw
i57
[381 WI WI 1241 [401
88 116
t&F, NbOF; SCF6 SeFsO-
335 410 1432 1190
The prcscncc of the n-bond makes the a-bend
A-L,
[=I
1050
more covalent
and, therefore,
the results obtained
in table 2
should be vahd not only for replacement of F with Cl but, to a greater degree, for the case F + 0. This result is quite similar to the consideration of the inductive effect in these rephtcements [5] _ Indeed,
a comparison
with the experimental data (table 5) shows a complete agreement with the data of table 2. for WOF, is noticeably greater than for WF5(OCH3); the variations AJ,, and AJc, for SeOFF are greater than for SeF5Ct. A comparison of AJ,, and AJcis also yields a correct relationship. An an-alysis of the experimental data presented in table 5 shows that the constant J(A-F)crs always increases in going from WF; to WF,Oor from AFZ- to AF,OX(A=W, V, Nb). Since the data of table 2 show that the value of AJ(A-F),, may both increase and decrease, the experimental relationships indicate that the secondary variations of the parameters of the a-symmetry levels due to the presence of the n-bond of e-symmetry, make such additional contribution to the value of AJ,is so as to render AC,, or Afci, always positwe. The evaluation of these contributions is generally a rather complex problem. It should be stressed that this relationship is valid only for the bond M=O; in the case of WSFT J(W-F),is d ecreases to 33 Hz [41]. Thus, the experimental observations reveal both an increase and a decrease of the constants J(A-F)ci, according to the data of table 2; the variation of the constants is affected not only by the properties of the compound AF;but also by the properties of the &-and L.
For instance, the variation AJ,,
5. Can the constants J(A-F)
characterize
The bond strength is often in the mean excitation 2
K(A-B)
energy 2
--Q’Aog~&~(~)~~1
characterized (AE)
the strength of the A-F through
formula
bond?
(11) (_ree, For instance
[ 11) which has been derived
approximation: r&s(0)12(A@
>
(1
where I& and og are the populations of the ns orbitals of the atoms A and B, II, is the density of the respective ns orbitals in the vicinity of the nuclei of A and B. The increase of the contribution of the Ans orbitals in the compound
AE$-
is assumed to result in an increased strength of the A-B
bond. Thus, an increase in K(A-B)
indicates an increased strength of the A-B bond. The above discussion contains two unproven assumptions which in fact disqualify the conclusions about the correlation betweenJ(A-B) and the strength of the A-B bond. First, formula (11) does not even take into account the possible reversal of the sign ofK(A-B) depending on the structure of the valence levels and, therefore, its apphcation was questioned as early as 1964 [2J_ It is of interest that formtda (11) was used for analysis usually by experimentalists (see, for instance ]l]) while theoreticians (see, for instance [42]) invariably made use of the theory developed in [2] or a more refined theory [43] _The authors of a recent experimental paper [27]
Vf. Nefedov Table 6 Variation of the strengthof the Nontransition
A-F
et ol./Nuclear
bond for the changeAe-
element A
spin--spin
-
AF5
coupling corrStants
429
Lx-
Trransition
clement
A
6m5.5
6mti
6mw - Bm,g
6nkiS
6mtr
6mfi -
SO
10
SO
10
10
have noted though, that there are no grounds infhrence of the ligand on the bond strength.
for using formulas
of the type (11)
Cm,is
when considT.ring
the mutual
Secondly, there is no yet any theoretical or experimental evidence that the increase in the contribution of the Am orbitals is always accompanied by an increase in the strength of the A-B bond, although this seems to be often the case. To verify this conclusion, localized orbitals of the A-B bond should be obtained but this procpdure is used rather rarely. a correlation between SC,_is and SC,, and In this connection, let us find, when going from AFZ- to AF,LX? the parameters 6mcis and 6mt, which characterize, within the Framework of the perturbation theory, the change in the strengths of the bonds A-FciS and A-Ftr [4,5] _ Let us discuss some of the factors which, in principle, make possible a correlation between 8Ci and 6nzi. In tabie 6 values 6mi are given which characterize the strengthening of the bond (+) or its weakening (-) when we go from AFgto AF,LXas obtained from calculations of the inductive effect within the framework of the perturbation theory [4,5]. There is a fairly apparent similarity in signs between the values of SCi (table 2) and 6mi. Taking into account different signs of C in the compounds of transition and nontransition elements, we may expect an increased value of IK(A-F) 1for the compounds of nontransition elements at the beginning and in the rnic!dle of the period as the bond strength decreases; for the compounds of transItIon elements we may expect that IK(A-F) I falls with decreasing bond strength. The similarity between the data of tables 2 and 5 is related to the fact that in calculations of the bond strength and the constants the effect of the valence s- and d-electrons of the atom A (more exactly, of the parameters associated with them) is opposite to that of the pelectrons. It is just these facts that explain why in principle there may be a correlation between 6mj and SCi depending on the ligand to L; for instance, K(Sn-F)cis increases in the series L = Cl, Br, I [28] and the bond strength should be expected decrease in this series [4,5]. However, formulas for 6Ci and 6mi show [4,5] that generally no similar behaviour of 6Ci and 6mi can be expected; this may be seen just from the fact that 6Ci reverses its sign when the nontransition elements A go from the beginning to the end of the period. Thus, the constants K(A-F) cannot be used for predicting the variation of the bond strength. The analysis of the experimental data also leads to this conclusion. As an illustration, note that InKl increases in the series CH, + Cl (PF,L-), CH, + Cl + Br (CF3L), Cl + Br + CH3 (BFzL) (table 5) while only the last series correlates with the variation of the A-F bond. AS an example for the compounds of transition elements, let us consider the changeover WF6 -+ WOFF _As shown in [5] for simila; -compounds, the strength of the W-F bond is decreased both in the cis- and transpositions to the W=O bond, but according to 1361 (table 5) the variations of AK for the cis- and tram-bonds such examples can be given. Thus, the answer to the question heading this section should be negative.
References [l] T-G. Appeleton. H.C. Mark and L.E. Manser, Coord. Chem. Rev. 10 (1973) 353. [Z] J.A. Pople and D.P_ Santry, Mol. Phys. 8 (1964) 1. [3] S. Nagata. T. Yamabe, K. Hirao and K. Fukui, J. Phys. Chem. 79 (1975) 1863.
W-F
have different
signs. More
430 [4] [5] [6] [7] (B]
V.I. V.I. B.F. B.F. E.L. [9] E.L. [lo] Vl.
VI. Ncfedov
et ol./Nuclcar spin--spin coupling constants
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