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Accurate structures of simple dicyanides
Journal
of
MOLECULAR STRUCTURE ELSEVIER
Journal of Molecular Structure 376 (1996) 399-411
Accurate
structures
of simple dicyanides’
J. DemaisonaT*, G. Wlodarczak”, H. Riickb, K.H. Wiedenmannb, H.D. Rudolphb ‘Laboratoire
de Spectroscopic Hertzienne, URA CNRS 249. Bbt. PS. Vniversit~ de Lille I. 59655 Villeneuve D’Ascq Cedex. France ‘Department of Chemistry, University of Urn. D-89069 L’lm, German) Received
6 July 1995; accepted
21 August
1995
Abstract Accurate structures have been determined for dicyanomethane, HzC(CN)z, vinyl dicyanide, HzC=C(CN)z, cyanide. O=C(CN)z. and sulfur dicyanide, S(CN)z, by combining the results of electron diffraction, microwave
carbonyl
spectroscopy and ab initio calculations. The different methods are compared. The influence of the correlations between the fits (rr,, and r0 rotational constants when calculating the rk structure and the weighting scheme in the least-squares methods) are analyzed. The possibility of obtaining the true equilibrium C=O distance from ab initio calculations is also discussed.
1. Introduction The structures of simple dicyanides have already been determined in the gas phase either by electron diffraction or by microwave spectroscopy or by combining the two techniques [l]. Their ab initio structures have also been calculated using various basis sets and methods. However, there seem to be some inconsistencies in these structures, making a meaningful comparison difficult. In particular, there has been some debate concerning the linearity of the X-C-N bond and incompatible results have been published. In the attempt to clear up this situation, we have redetermined the structures of dicyanomethane, H2C(CN)2, vinyl dicyanide, H&=C(CN)2, carbony1 cyanide, O=C(CN)*, and sulfur dicyanide, S(CN)2, using all the data available and calculating * Corresponding
’Dedicated 75th birthday.
author. to Professor James E. Roggs on the occasion
of his
a new set of consistent ab is in direct continuation of the structures of methyl vinyl cyanide, H,C=CHCN CH,CH=CHCN [4].
initio structures. This our previous work on cyanide, CHICN [2], [3], and crotononitrile,
2. Methods To determine structures possible to the equilibrium ferent methods, as follows.
which are as near as structure, we used dif-
2.1 Ab initio calculations The structure obtained from an ab initio calculation is generally significantly different from the equilibrium structure. However, if the basis set used is large enough, and if the electron correlation is taken into account at least at the MP2 level, the ab initio angles are generally in very good agreement with the equilibrium values and the error in
0022-2860/96/$15.00 cQ 1996 Elsevier Science B.V. All rights reserved SSDI 0022-2860(95)09087-8
400
J. Demaison
et al./Journal
qf.Molecuiar
the ab initio bond lengths is largely systematic and can be corrected using offsets derived empirically [5 71. These offsets have been used for a long time [7-l l] but they have been derived to mainly calculate ra structures (or in some cases r0 structures). We have recently derived new offsets to determine the equilibrium CH, CC, CN and CF bond lengths [3,4,12-141. It is noteworthy that these offsets are often significantly different from zero. In some cases, it was found necessary to take into account the electron correlation [3,4,14-161, so all calculations were carried out at the MP2 level using GAUSSIAii 92 [17].
2.2. Relationship between ri (and rpj structure und re structure In the following discussion, the conclusions reached for the rz bond lengths are also valid for the rg bond lengths. The r, (or rJ structures have been determined for many molecules. The most reliable parameters have been obtained by combining the electron diffraction and microwave data. The rz angles are generally a good approximation to the equilibrium values. However, the rr bond lengths are different from the r, values. To derive the rC structure from the r, values, a knowledge of the anharmonic force field is necessary [ 181, which is rarely the case. However, for some particular bonds, it has sometimes been suggested that the difference rz - r, is constant [19-211. In fact, the difference r, - r, should increase with the bond length because anharmonic effects are larger for softer bonds. Nevertheless, a plot of rz as a function of r’, should give a nearly straight line. This was indeed found for CH [13], C-C [3,12], C-N [2] and C-F [14] bonds. Hence, if a few accurate rz and corresponding re values are known, and if their range is large enough, it is possible to predict by interpolation (or by extrapolation) new r, values knowing the corresponding r, values. In fact, the r, ~ r, difference may depend on the environment if higher order interactions between bond stretching and angle bending vibrations have a significant effect on I’, distances. However, their effect seems to bc very small [18].
Structure
376 (19961 399-411
2.3. r$ structure The substitution structure (rS) calculated from the dill‘erences in moments of inertia [22] is sometimes far from the equilibrium structure. The estimated mean error is about 0.003 A for distances between heavy atoms and 0.005 A for C-H distances, but differences as large as 0.009 A have been found [23]. Moreover, it is empirical, making comparisons with other molecules difficult. However? following the work of Watson [24], who demonstrated that Ze = 2zs - I0
(1)
Harmony and co-workers [25-311 proposed a new procedure for obtaining near-equilibrium structures using only ground-state data. The groundstate moments of inertia I” are first scaled by a factor 2p - 1: Z&(i)
= (2~~ ~ l)Zi(i)
g = u, b, c; i = all isotopomers
(2)
where PX = P,(l)
w = ZO(l) R
i = 1 = parent
(3)
The “substitution moments” of the parent molecule Z:(l). g = a, b, c, are calculated from the substitution coordinates which must have been derived by the application of the full Kraitchman equations, where formally zero-valued squares of coordinates for substitutions on a principal plane or axis may happen to come out negative. To obtain the Zi, negative contributions must also be included in the sums over coordinate squares. Then Harmony advocates correcting the data for the deuterated isotopic species to account for overscaling. This “Laurie” correction is equivalent to an elongation of the C-D bond by an amount 6r = 0.0028 A. For instance, for the a-axis: KX,,
= (Z&)u
+ 2mp j-(biGb; I
+ qSc,)
(4)
and analogously for the b- and c-axes by cyclic permutation of U, b and c. The (I,~bi and ci are the Cartesian coordinates of the D atoms and 6ai, Sbi are SC, the components of 6r. After the subsequent
J. Demaison
et al.iJournai
of Molecular Structure376 (1996) 399-41 I
rs-type least-squares fit to the scaled moments as prescribed by Harmony’s rules, the correction, Eq. (4), leads to a structure where the C-D bond is longer by approximately 0.0028 A and the respective C-H bond by 0.0056 A compared with the results obtained without this correction. Furthermore, this correction has been shown [32] to remain restricted to the resulting C-H bond length, hardly affecting the rest of the bonds. The results reported in Tables 4 and 6 do not take this correction into account. If desired, the C-H bond lengths in Tables 4 and 6 could be directly adjusted to conform to what is expected if Laurie corrections were introduced (i.e. an elongation of the C-H bond of 0.0056 A). The structural parameters of the molecule derived from the fit have been designated as the r& structure. This method has already been applied to several molecules containing hydrogen atoms [2,12,27-331. It seems to give fairly accurate results, except for the C-H bonds. However, there is another way to obtain reliable C-H bond lengths. It has been shown that there is a linear and accurate relationship between isolated C-H stretching frequencies and C-H bond lengths [34]. This relationship has been reviewed recently [13] and applied successfully to many molecules [2,3,12,35]. To date, the rf, method has apparently been mostly applied assuming that the scaling coefficients are error free and that the Z& are uncorrelated. In fact, the three Z:(l), g = a,b, c. are functions of all Z:(i) (but of no other variables), and the same is true for the Z&,,(i). The errors of the Zi( 1) (Eq. (3)) are almost invariably much larger than those of the Z:(l), in particular when the molecule has atoms with small coordinates. Therefore, the errors of the py and hence those of the scaling factors 2p, - 1 (Eq. (2)) are large enough to make the errors of the inertial moments IL,,(i) i larger by orders of magnitude for all isotopomers than those of the Z:(i). Even more important is the fact that the scaling factors which dominate the errors of the Z&,,(i) are independent of the isotopomer. That means that the same factor, e.g. 2p, - 1, multiplies the moments Z:(i) of all isotopomers when the moments Z$,(i) are calculated. Consequently, these moments are extremely highly correlated, separately for each g = a, b: c. In
401
contrast, the correlations between moments of different g are only moderate and directly reflect those of the corresponding components pg. For the rotype fit as prescribed by Harmony’s work, the variance-covariance matrix of the data fitted (i.e. the errors and correlations of the moments Z&(i) affect also the numerical values of the internal coordinates obtained from the fit, and not only their errors. In particular, when the very high correlations between the Z&,,(i) with the same g but different i = 1, N are neglected, the numerical results may be distinctly different from those when these correlations are retained. The differences in the numerical structures when produced with or without the neglect of these correlations were conspicuous in the very stable cases of cyclopropylgermane [32] and cyclopropylsilane [36].
3. Carbonyl cyanide The rg and r, structures of carbonyl cyanide, O=C(CN),, have been determined by combined use of the rotational constants and the electron diffraction intensities [37]. The C-CeN chain appears to be nearly linear, the deviation from linearity being -0.2(6)“. A small inward bend was found by ab initio calculations at the RHF level [38,39], but contradicted by calculations at the MP2 level where the C-C=N is bent outwards by 1.2” [16]. First the ab initio structure was calculated using 6-3 1G*, 6-3 1 lG(d), 6-3 11+G(d) and 6-311+G(2d) basis sets at the RHF and MP2 levels. Only the MP2 calculations are reported in Table 1. Next the C-H, C-C and C-N bond lengths were corrected with the previously estimated offsets [3]. The derived equilibrium structure is also shown in Table 1. To determine the equilibrium C=O bond length, we calculated ab initio structures for molecules containing the C=O bond and for which an r, structure is known. The experimentally known r,(C=O) values are collected in Table 2 together with the ab initio results. As expected, at the MP2 level, there is a good correlation between the experimental and ab initio values. As for the C-C bond [3], the offset Y,,~ - r,,ic, does not seem to be constant for a given basis set. Nevertheless, in
402
J. Demaison
a al./Journal
of Molecular
Structure
376 11996) 399-411
Table 1 MP2 ab initio structures (distances in A and angles in degrees)
Molecule
HK(W2
Bond
cc
6-3 IG’
6-31 lG**
6-31 l+G**
6-3 I1 +G(2d,
2p)
Tea
CH CN ccc HCH CCN
1.4686 1.0955 1.1802 111.84 107.45 178.71
1.4679 1.0945 1.1734 111.96 107.79 179.06
1 4684 1 0946 1.1741 112.01 107.86 178.81
1.4668 1.088 1.1693 111.98 107.82 178.76
1.464 1.091 1.155 111.98 107.82 178.88
H&=C(CN)I
c-c C-H c-c CN HCC c=cc CCN
1.3479 1.0844 1.4394 1.1831 120.67 121.60 179.56
1.3484 1.084 1.4389 1.1764 120.37 121.60 179.78
1.3496 1.0844 1.4393 1.177 120.35 121.65 179.62
1.3437 1.0784 1.4378 1.1724 120.31 121.51 179.87
1.342 1.080 1.437 1.158 120.36 121.63 179.70
@WN2
co cc CN cc0 CCN
1.2231 1.4642 1.1843 122.56 179.05
1.2122 1.466 1.1776 122.81 179.21
1.2137 1.4657 1.1783 122.71 179.25
1.2131 1.4649 1.1735 122.55 179.54
1.204 1.461 1.159 122.63 179.23
S(CN)z
cs CN csc CCN
I .7069 1.1849 98.03 175.40
1.7039 1.1785 97.72 175.90
I .7037 1.1795 9190 175.25
1.7117 1.1748 97 55 175 22
1.160 97.55 175.22
a Estimated
value, see text.
the particular case of O=C(CN)2, either a constant offset or a linear fit gives the same result: r=(C=O) = 1.204(3) A. It may be noted that the error is rather large. As a check of this result, it is interesting to verify that there is a linear relationship between rz(C=O) and re(C=O). The known rZ values are also listed in Table 2. Clearly, the difference rz - re is not constant. However, a linear regression of r, as a function of r, gives an extremely good fit (detcrmination coefficient: R* = 0.9994) and allows us to = 1.204(11) A using r,(C=O) = predict r,(C=O) 1.209 A [37]. Although this result is not very accurate, it is in good agreement with the ab initio equilibrium structu:e. Likewise, it was found that rg - r, = 0.01 l(2) A f?r the C-C single bond [2]. rg(C-C) = 1.469(l) A in carbonyl cyanide gives re = 1.458(3) A, in reasonable agreement with the ab initio corrected value, 1.461(2) A. For the C-N bond, the experimental value is rg = l.lPl(2) A: an offset correction of rg - r, = 0.005 A [2] gives r, = 1.1_56(2), in fair agreement with the ab initio
corrected value, 1.1 B(2) A. Groups more electronegative than carbon stabilize the carbonyl group and lead to a short C=O bond (see Table 2). However, in CO(CN)*, the C=O bond is long, 1.204 A. In fact. the carbon of CN bears a positive charge and, as a result, the interaction with the positively charged carbonyl carbon is repulsive [40]. It is difficult to confirm whether the C-C=N bond bends away from the C=O bond because the zero-point average angle is not significantly different from 180", i.e. 1X0.2(6)“. Moreover, the ab initio calculation at the MP2 level gives a very small bend (0.5-l “), which decreases as the size of the basis set increases (see Table 1). However, for molecules with two highly electronegative elements (i.e. C=O and C-N), it is necessary to take into account the electron correlation and it seems that the Msller-Plesset perturbation calculation is not accurate enough [4]. A calculation using the QCISD method with the 6-3 1 lG(d) basis set also gives a very small bend, 0.37’. The deviation from linearity is too small to be considered significant.
J. Demaison Table 2 Equilibrium,
ab initio
(MP2) and rz C=O
rc @P.)
HzCO HCOOH HCOF HCOCl Cl&O F2CO OCFCl H,C=C=O co: ocs
1.203 1.201 1.183 1.182 1.176 1.170 1.170 1.161 1.160 1.156
co HCO+
1.128 1.106
Mean’ Medianb v (fit)’ Ranged
et al./Journal
bond lengths
of Molecular
Structure
376 (1996)
403
399-41 I
(in A)
11+G(Zd,
Ref.
6-31G*
6-31 lG**
6-311+G**
6-311+G** (full)
6-3
[571
1.221 1.214 1.195 1.200 1.195 1.187 1.190 1.181 1.180 1.180
1.211 1.203 1.184 1.188 1.183 1.176 1.179 1.168 1.169 1.169
1.213 1.205 1.185 1.191 1.186 1.177 1.181 1.168 1.170 1.170
1.212 1.205 1.184 1.191 1.186 1.176 1.181 1.168 1.169 1.170
1.213 1.205 1.184 1.188 1.183 1.177 1.180 1.168 1 170 1 169
1.186 1.185 1.179 1.172 1.173 1.163 _ _
1.151 1.132
1.139 1.120
1.140 1.120
1.139 1.119
1.138 1.118
_
0.015(13) 0.020 0.004 0.051
0.008(4) 0.008 0.004 0.013
0.009(4) 0.010 0.004 0.013
0.009(4) 0.009 0.004 0.013
O.OOS(3) 0.009 0.003 0.012
1581 [591 [6Ol [611 [621 163,641
[651
WI
b71
WI [691
’ Mean value of exp - talc. Standard deviation b Median of exp. - talc. ’ Standard deviation of linear regression. d Range of exp. - talc.
2p)
r,
I .207 1.205
in parentheses
4. Sulfur dicyanide The r, structure of S(CN)2 was first determined by Pierce et al. [41] and was calculated ab initio at the RHF level by Palmer [39]. The results of the new ab initio calculations are given in Table 1. It is not possible to determine a complete equilibrium structure because the equilibrium value of the C-S bond length is not yet known for enough molecules, so it is not possible to “correct” the ab initio result. To calculate the experimental structures, we first redetermined the rotational constants of the different isotopomers using the literature data [41-431. The centrifugal distortion constants of the parent species with three times their standard errors were assumed for all isotopomers. After the elimination of a few outliers, the rotational constants in Table 3 were obtained. The relative r,,, fit [44] standard deviation of a preliminary with the experimental errors and correlations was 5.1. This is larger than unity and shows that even the Y,,I method, one of the more advanced methods of structure determination, is not able to take full advantage of the experimental precision of the
rotational constants owing to the still existing model error (i.e. the inadequate treatment of the rovibrational contributions). For the rO fit, the errors of the internal coordinates were excessive, they were highly correlated and the relative standard deviation of the fit was very large, 625. To avoid different weighting of any two rotational constants of different precision when both are more precise than can be effectively utilized, the experimental errors of the rotational constants should be appropriately corrected towards a more balanced weighting. i.e. by assuming larger but more equal errors for all isotopomcrs. This can be done by increasing the variance of all experimental inertial moments, adding terms on the diagonal of their variance-covariance matrix in such a way that the relative standard deviation of the resulting least-squares fit, which eventually determines the molecular structure, is near unity (see remark on p. 39 of Ref. [45]). We have applied the same procedure that was previously used for the determination of the structures of 2-chloropropane [46] and cyclopropylgermane [32]. A preliminary rr,I fit [44] with unity weight for all inertial moments and no
404
J. Demauon
Table 3 Rotational
constants
(MHz),
errors and correlation
coefficients A
C
Inertml
AC
Pk
(u
34S(CN)z SI’CNCN SC”NCN H,C=C(CN;12 H!‘C=C(CN), ‘ D:C=C(CN)2 H:C=“C(CN)> H2C=C’kNCN II+CC’SNCN
2835 509(3) 0 66Y4 2835.506(13) 0.1589 2809.663(18) -0.5428 2759.640(30) PO.0446 2882 0342( I X) 0 7425 2882 OY21(26) 0.4637 2853.0595(13) 0.6464 2882.1631(82) -0.3214 2857.7338(26) 0.1933 2804 0X33(100) 00116
22 I9 262(4) 0 6310 2203.506(14) 0.4384 2203.033(1 I) 0.6664 2165.682(23) 0.8163 2000.9270( 17) 0 8478 1975.7195(26) 0.6363 1905.9711(13) 0.7880 1999.3514(81) 0.9504 1988.5464(32) 0.3720 1957 3832(83) 0.9246
dcfcct”
A2)
0.49025(27) 0.4915(13) 0.48920(94) 0.49621(84) 0.40368( 12) 0.40921(27) 0.40981(12) 0.40538(64) 0.40199(40) 0 40878(60)
505 379 u A2 MHz.
correlations between any of the inertial moments had an absolute standard deviation of vu = 0.0016 u A*. The terms to be added on the diagonal were chosen as
@i(i)]
376 11996) 399 411
,‘ab
10313.536(11) 0.7432 9981X146(41) 0.3702 10305.326(30) PO.6568 10162.560(43) -0.2651 6579.2729(46) 0.8848 6314.5314(66) 0.8575 5768.5060(28) 0.8571 6561.7455(116) -0.2178 6572.1647(73) 0.6058 6516.5881(118) 0.1599 factor:
Structure
A
WW2
* Conversmn
et al.~Journai of Molecular
Wi)l*
= mu x
[ml2
for g = a, b, c; all
z
g’=a,b,c
(5) In a crude form, this additional variance takes account of the different magnitude of the inertial moments for g = a. b. c. The additional variance was in all cases much larger than the corresponding experimental variance. Since the covariances were not changed, the additional terms on the diagonal resulted in a substantial reduction of the correlations between the inertial moments. The experimental structures are given in Table 4. In the first column, 12 inertial moments were fitted to obtain four independent internal coordinates. Although the errors of the rotational constants had been adjusted (made larger, as discussed
above),
the relative
standard deviation of the r. unity (117) because this error correction was aimed at letting the re,l fit, not the r0 fit, attain a standard deviation near unity. In column 2 is reported the ro-type fit to the eight planar moments with g = a, b of the four isotopomers and excluding the four planar moments with g = c. It indicates that here it is seemingly easier to obtain an r. fit with a low standard deviation (1.9) and small parameters errors for a small planar molecule with a sizable inertial defect. However, the lack of balance (third moment absent) may make the numerical values obtained for the structure unreliable, despite their apparent precision. In column 3 (Y,,~ structure), 12 inertial moments were fitted to obtain four internal coordinates and three rovibrational contributions Ed. The standard deviation is indeed near unity (1.4), as intended by the correction discussed above. Although the (isotopomer-independent) Q, could not be determined at a significant level (Ed = -0.033(28), q, = O.Ol(l4) and t, = 0.47( 14) u A’), the precision of the structure is not affected, because this structure is strictly identical with that
fit is much larger than
J Demaison Table 4 Structures
of S(CN)Z and H2C=C(CN)?
Column Method
et d.iJournd
(distances
of Molecdar
Structure
in A and angles in degrees)
I
2
3
4
5
6
QI
ro (a, b)
re.1
rs
rC
re a
Sf CNIz ub s-c C=N i(CSC) [(SCN)
117 l-707(61) 1.146(89) 98.6(43) 175.4(64)
19 1.697(2) 1.164(2) 98.6(l) 175.5(2)
1.4 1_6Y8(1) 1.159(l) 98.46(6) 175.14(8)
&C=C(CN)2 ISh C-HE c=c c-c C-N [(HCH) /(C=C-C) /(C-C-C) I(C-CEN
624 1.085(35) 1.346(66) 1.438(64) 1.156(67) 120.0(29) 121.4(39) 117.2(77) 179.7(79)
1.3 1.087(l) 1.342(3) 1.439(3) 1.159(3) 120.20(8) 121.6(2) 116.8(3) 179.6(3)
1.0 1.087(l) 1.349(2) I .436(2) 1.157(l) 120.10(5) 121.25(8) 117.5(2) 179.q 1)
a See Table
’Standard ’ Without
405
376 (1996) 3Y9-411
_ 1.700(4) 1.159(3) 98.3(3) 175.0(3) _ 1.087(l) 1.348(3) 1.435(5) 1.158(3) 120.11(9) 121.3(3) I17.3(6) 179X(5)
1.2 1.699(l) 1.159(l) 98.38(6) 175.14(7)
1.4 1 085(2) 1.344(2) 1.436(2) 1.156(2) 120.14(8) 121.43(9) 117.1(2) 179.7(2)
1.160 97.55 175.22 _ 1.080 1.342 1.437 1.158 119.28 121.63 116.74 179.70
1. deviation of the fit. Laurie correction.
obtained by fitting only the isotopic differences of inertial moments (Ye,) or planar moments (YQ), if proper account is taken also of the inertial to planar transformation of errors and correlations. When isotopic differences of inertial moments are fitted, isotopomer-independent eg are clearly irrelevant. Column 4 gathers the substitution (r,) structure calculated using Chutjian’s equations to substitutions on a principal plane or axis [47]. The process is no longer a fit but a direct calculation, propagating only the errors assumed for the moments of the parent and all substituted isotopomers. The Y, and the rc,, structure are usually of comparable precision. This is true also in the present case for the Cartesian coordinates, but with the exception of the small substitution h-coordinate of the carbon atom with its necessarily larger than average error, which induces in turn larger errors of all internal coordinates. Column 5 contains the r& structure obtained by Harmony’s method, as described previously. Two different calculations have been made: the first one uses the errors calculated from Eq. (5) as for the other structures and the second uses the original experimental errors and correlations of the rotational
constants, because the “scaled” rotational constants to which the subsequent r. fit is applied have very uniform errors over all isotopomers owing to the dominant influence of the errors of pa. In the particular case of S(CN)2, the differences between the parameters of the two fits arc very small but the errors are about twice as small with the first weighting scheme, so only the results of the first fit are given. The reason for the smaller errors of the structural parameter is that the first weighting scheme of Eq. (5) produces inertial moments of the parent with higher errors which are, however, also more balanced in the sense of Eq. (5), i.e. the relative magnitude of the moments for g = a, h, c is still reflected by the errors and overcompensates the higher error level in the subsequent least-squares fit of the r$, method. The experimental structures are in good agreement with each other. Furthermore, sulfur dicyanide is a heavy molecule without hydrogen. One may be fairly confident that the true equilibrium value is not far from 1.700 A for the C-S bond length. The derived r,(C=N) bond length is rather long, 1.160 A. In fact, all conjugated 57 systems should
J. Demaison
406 Table 5 Centrifugal
distortion
constants
H2C=C(CN)I H:SC=C(CN)2 D2C=C(CN)z H2C-“C(CN)2 H2C=C”CNCN H 2C=CCi5NCN
et al.~Journal of Molecular
Structure
376 (1996)
399-411
(kHz) of dicyanoethene
A,
AJK
AK
61
6K
ma
“b
1.2655(52) 1.271(13) 1.2130(39) 1.033(76) 1.229(16) 1.158( 102)
-8.564(28) -7.990(80) -6.899(25) -9.44(14) -8.518(82) -7.80(28)
32.324(55) 29.48(12) 22.928(25) 32.02(63) 31.79(11) 30.00(99)
0 5540(22) 0.5651(74) 0.5330(24) 0.5151(81) 0.5330(81) 0.552( 19)
1.452(37) 1.184(107) 1.243(33) 2.55(15) 1.49(13) 0.91(34)
SO 71 4s 55 88 54
51 41 62 15 44 17
a Standard deviation of the fit (kHz). b Number of transitions in the fit.
show an increase in the length of the CGN bond, and correspondingly the adjacent CX bond should be shortened. This is in good agreement with the fact that the C-S bond is much shorter in sulfur dicyanide than in dimethyl sulfide. the corresponding values being 1.701 and 1.802 A, respectively (rs value for dimethyl sulfide [48]). On the other hand, the CSC angles are very similar: 98.8” in (CH3)ZS and 97.6” in S(CN)2. All structures calculated show a significant outward tilt of the C-N bond with respect to the S-C bond which can be given as 4.9(3)“.
5. l,l’-Dicyanoethene The microwave spectra of H2C=C(CN)2 and D2C=C(CN)2 have already been measured [49,50], but these data are not sufficient to determine a complete structure. The rotational spectra of the 13C and “N isotopomers were measured as part of this work. The frequencies of all transitions measured are deposited with the Sektion fur Spektren- und Strukturdokumentation, University of Ulm. In all cases, three rotational constants and five quartic centrifugal distortion constants could be fitted, although with different precision depending on the number and character of the lines measured. The rotational constants are also gathered in Table 3 and the centrifugal distortion constants in Table 5. The equilibrium structure is also estimated from the ab initio results in Table 1 using the method discussed previously and the offsets of Ref. [3]. The experimental structures are reported in Table 4. They were calculated using
the procedure previously used for S(CN)2 (see above) and the above discussion also applies here. For the t$, method, the same two different weighting schemes as for S(CN)2 were used and gave nearly identical results. Laurie correction was not applied to compensate for the shorter CD bond length compared with the C-H bond length. If it is applied, the agreement with the equilibrium (i.e. ab initio corrected) structure is worse. The agreement of the different structures in Table 4 and the r, structure in Table 1 is generally good, except for the C-H bond length, for which the experimental values are probably not reliable as usual (see discussion below). Moreover, the ro, rc,I and Y, bond lengths are significantly too long. r,(C=C) = 1.3420 A, which is longer Othan in ethylene, 1.331 A [51],_ propene, 1.333 A [4], or vinyl cyanide, 1.337 A [3], but it is near the values found for cis-crotononitrile: 1.341 A, trurzs-crotononitrile, 1.339 A, and methacrylonitrile, 1.339 A [4]. This is in agreement with the Stoicheff rule, which states that the bond length increases with the number of bonds adjacent to it [52]. The CC bond length, 1.437 A, is longer than in vinyl cyanide, 1.432 A [3], or cis- and transcrotononitrile, 1.43 1 and 1.430 A, respectively [4], but it is similar to that in methacrylonitrile, 1.438 A [4]. It was established that the substitution of a vinyl group by oxygen increases the C-C bond length by about 0.02 A [52]. This effect is conIirmed in the case 1,I-dicyanoethene and carbonyl cyanide, where the difference is 0.024(3) A. the C=C-C bond angle, 121.6”, is similar to the values found for vinyl cyanide, 122. l”, and
J. Demaison
er al./Journal
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Srrucrure 376 (1996)
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407
Table 6 Structures
of H>C(CN),
C0lUnUl Method “d C-He C-C CZN /(HCH) i(CCC) i(C-CEN)
(distances
in A and angles in degrees)
1
2
3
ro
‘?./
rs
I .o I .099(3) I .467(N)
19 1.086(2)
1.466(9) 1.152(13) 103 7(4) 112.6(7) 17X.7(8)
I. 150(8) 106.8(6) 112.7(5) 17X.7(6)
4 rg
_ 1.100(10) 1.452( 13) 1.159(9) 106.9(1 I) 112.9(11) 17Y.l(8)
12 1.080(S) 1.463(6) 1.147(5) 105.9(2) 113.09(9) 178.50(Y)
5 !Jb ‘“3 0.35 I .089(4)
1.45X(4) l-157(4) 106.4(6) 112.8(2) 178.4(2)
6 rcc
I 091 1.464 1.155 107.82 111 98 178 88
a Weighting with experimental errors. b Weighting with adjusted errors (see text). ’ See Table 1. d Standard deviation of the fit. e Without Laurie correction.
cis- and trans-crotononitrile, 122.4” and 122.1”, respectively, but it is slightly larger than that of methacrylonitrile, 119.2”. The HCH angle is very near 120”. All structures show a very slight outward tilt of the C=N bond with respect to the C-C bond which, however, could not be determined at a significant level. Both sulfur dicyanide and dicyanoethene are planar molecules with sizeable inertial defects (Table 3). The scaled inertial moments of the rg method are proposedly nearer to the unknown inertial moments of the Y, structure. Therefore, the inertial defects calculated with the scaled moments should be smaller than the experimental ground-state values. This is indeed the case, although to different extents for the two molecules. For sulfur dicyanide, the rg inertial defects are approximately one quarter of the ground-state values for all isotopomers. For dicyanoethene, the reduction goes down to one twentieth, again for all isotopomers. Owing to the large errors of the moments Ig,g z mentioned above, the rk inertial defects are all within the error range of a zero mertlal defect: ‘)
6. Dicyanomethane The species
microwave spectra of dicyanomethane,
of
several isotopic H&(CN)*, have
recently been measured and the rs, rz and r”, structures have been determined [53]. The CN group was found bent away from the X-CN internuclear axis. This result is confirmed by ab initio calculations [38,39]. However, the rk C-H bond length, 1.103(3) A, seems to be too large, the empirical correlation between the isolated stretching frequencies and r, giving 1.088 A [131. Moreover, the r& CEN bond length, 1.152(3) A, seems to be too short when compared with the values found for other cyanides, whose median is 1.157 A [31. First the equilibrium structure was estimated from the new ab initio results in Table 1 using the method previously discussed and the offsets of Ref. [3]. Then the experimental structures were redetermined using the rotational constants of Ref. [53] (seven isotopomers) and the procedure previously outlined. When treated by any Kraitchman-type method, the problem is complicated by the very small b-coordinate of the atom Ccyan. Therefore, rO-derived methods should, in principle, locate the atomic positions more reliably, at least for atoms with small coordinates. The experimental structures are gathered in Table 6. In column 1 (ro), 21 inertial moments were fitted to obtain six independant internal coordinates. The fact that after the adjustment of the errors (to make the standard deviation of the Y,,[ fit unity) the r. fit has a standard deviation of only 2 indicates that the expected improvement of the r,,, fit over the r0 fit will not
408
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of‘Molecular Srructure 376 (1996) 399-411
Table 7 Equilibrium structures of CHzXz derivatives (distances in A and angles in degrees)”
CHJ
CH& CHzClz CH2BI, CHz(CH,h CHz(CNh HZC=CHZ H:C=C=CH? H:C-C-O cycle-C,Ho
r&C H)
i(HCH)
1.086 1.084 1.084
109.5 112.8 112.1 112.4 106.1 107.8 117.1 118.3 121.8 114.5
1083 1.091 1.088 1081 1.081 1.076 1.082
* Data from Ref. [13].
nearly be as conspicuous as with the former molecules S(CNh and H2C=C(CN)1. Since dicyanomethane is not planar, there is no column corresponding to column 2 for the former two molecules. In column 2 (v,,,), 21 inertial moments were fitted to obtain six independent internal coordinates plus three isotopomer-independent rovibrational contributions. The number of isotopomers is obviously again much too small for a significant determination of these rovibrational contributions. The C-H bond length differs conspicuously from that of the r0 structure. As expected, the errors of the structural parameters are hardly less than for column 1, but they are perhaps slightly more balanced. This failure could be evidence for the fact that, for this molecule, the assumption of isotopomer-independent rovibrational contributions is inadequate. This happens, e.g., when the individual contributions of the normal vibrations to E have different signs and add up to an almost zero E. Then the variation of E from isotopomer to isotopomer may appear erratic, and E can no longer be approximated by a constant. Here again, the r& structure was calculated using two different weighting schemes (see discussion on S(CNk). As they give parameters which are significantly different, the results of both fits are given. When comparing the different structures, it appears that the range of the parameters is large: 0.015 A for C-C, 0.012 A for C-N and 0.020 _.&for the C-H bond length. The standard deviations of
the bond lengths are high, the mean yalue for r(C-C) and r(C=N) being about 0.01 A. Owing to these high standard deviations, a Student’s t-test indicates that only the C-H bond length and /(HCH) angle are incompatible with the corresponding equilibrium values. The Y& structure in column 5 (with adjusted errors) is the nearest to the Y, structure, but the 0& (HCH) angle is far from the corresponding equilibrium value. Taking the Laurie correction into account does not improve the results. The r. structure is also not too bad but the B0 (HCH) is also much too low (by 4.1”). On the other hand, both the Y, and Y, , structures show large deviations from the equilibrium values. The poor behaviour of the experimental structures is due to the ill-conditioning of the system of normal equations. This is a general phenomenon. In that case the C-H distance is not reliably determined as expected, but the HCH angle is also not reliable. A similar behavior has already been found for several molecules, particularly vinyl alcohol and vinyl fluoride [54]. On the other hand, all methods are in good agreement for the C-C-N angle, which shows a small bend away from the symmetry axis. As expected, the C-C bond length is longer ia CH,(CN)2 than in CH3CN: 1.464 and 1.457 A [2], respectively. CN is a x acceptor and pairing it with a c acceptor such as CN is unfavorable energetically and leads to bond lengthening. On the other hand, the CN bond, 1.155 & is rather short, which is in good agreement with a long C-C bond. This point has already been discussed [4]. The CCC angle, 112”, is nearly identical with the value found in propane, 112.2” [30].
7. Discussion One of the main dificulties is the determination of accurate r,(C-H) bond lengths and i(HCH) bond angles in CH,(CN), and H&=C(CN)2. For CH2(CN)2, it has already been found that the ab initio corrected value, r,(C-H) = 1.091 A, is compatible with the value given by the isolated stretching frequency, 1.088 A. There is another way to check the accuracy of the ab initio results
J. Drmaison et ai./Journol
qf Molecular Slruclurr
376 (1996) 399-411
409
because it has been shown that there is an empirical relationship between the i(HCH) angle and the C H bond length [55]. this correlation gives extremely good results in the particular case of methyl derivatives, except for methyl fluoride [12]. In Table 7 are collected the rc (C-H) bond lengths and I(HCH) bond angles for a few CHzXz molecules. In Fig. 1 is plotted the :(HCH) angle as a function of the r(C-H) length. This correlation is fairly good, except for allene and, to a lesser dcgrcc, for CHzFz (as for CH3F). This confirms that our structures for CH2(CN)2 and H2C=C(CN)2 are likely to be reliable. Furthermore, it allows us to improve the accuracy of the r,(C-H) value in CHzClz. There are two recent independent determinations of the equilibrium structure of CH2C12. Berry and Harmony [28] determined the rL structure pf that molecule and found r&(C-H) : 1.087(4) A. Duncan [56] estimated the equilibrium structure and found re(C-H) = 1.080(3) A. The correlation shows that the former value is slightly too high whereas the latter is slightly too low, a more accurate value being 1.084 .& This last value was obtained from the isolated stretching frequency and was confirmed by ab initio calculations (see Table 7). We have seen that the two more advanced methods of calculating the molecular structure from inertial moments, the Y, , and the r$ methods, show different success for different molecules: (1) The T~,I method hardly improved the standard deviation of the fit for dicyanomethane (factor 2 with respect to the basic r,, method), whereas the improvement was one to two orders of magnitude better for sulfur dicyanide and dicyanoethene, with a corresponding improvement in the error level of the structural parameters determined. (2) The inertial defects calculated with the scaled moments of the t$, method approximated the expected zero value much better for dicyanoethene than for sulfur dicyanide. The true isotopomer-dependent rovibrational contributions to the ground-state inertial moments, i.e. the differcnccs between the ground-state moments and the equilibrium moments, are .$
where g = a, h, c and i is the individual isotopomer. The models by which the two methods try to account for these elusive parameters are different. The r,,, method introduces them as only three isotopomer-independent constants cg whose values are to be determined as three additional variables in the least-squares fit to the groundstate inertial moments. the rg, method scales the ground-state moments first by three isotopomerindependent factors 2p,, - 1 whose values follow from the substitution structure of the parent, the r$, structure is then determined by the subsequent ro-type fit to the scaled moments. From Eq. (2) it follows that the rf,, method models the rovibrational contributions E:, here the differences IiJi) - Z:(i). as 2(p, - 1) Ii(i). That means that they do depend on the individual isotopomer, but they are rigidly proportional to the ground-state inertial moment I:(i). Clearly, the success that can be expected depends on the extent to which either model conforms to the reality of the specific problem being treated.
References [l] Landolt-Bernstein, New Series. Vols. II/7 and H/15, Strutture Data of Free Polyatomic Molcculcs, Springer, Berlin, 1Y76 and IYX7. [2] M. Le Guennec, G. Wlodarczak, J. Burie and J. Demaison, J. Mol. Spectrosc., 154 (1992) 305. [3] J. Demaison, J. Coslbou. R. Bocquet and A.G. Lesarri, J. Mol. Spectrosc., 167 (1994) 400. [4] A.G Lesarri, J. CoslPou, X. Li, G Wlodarczak and J. Demaison, J. Mol. Spectrosc.. 172 (19Y5) 520. [5] J.E. Boggs. in A. Domenicano and I. Hargittai (Eds.), Accurate Molecular Structures, Oxford University Press, Oxford, 1992, p. 322. [6] W J. Bouma and L Radom, J. Mol. Struct., 43 (197X) 267 [7] P. Pulay, G. Fogarasi, F. Pang and J.E Boggs, J. Am Chem. Sot., 101 (1979) 2550. [S] L. SchBfer, C. Van Alsenoy and J.N. Scarsdale, J. Mol. Struct. (Theochem.), 86 (1982) 349. [9] L. Schiifer, J. Mol. Struct. (Thcochem.). 100 (1983) 51. [lo] J De Smedt, F. Vanhouteghem, C. VanAlsenoy, II J. Geese and L. Schiifer, J. Mol. Struct. (Theochem.), 259 (1992) 289. [11] G. HBfelinger, CU. Regelmann, T.M. Krygowski and K. Wozniak, J. Comput. Chem. 10 (1989) 329. [12] M. Le Guennec, J. Demaison, G. Wlodarczak and C.J. Marsdcn, J. Mol. Spectrosc., 160 (1993) 471. [131J. Demaison and G Wlodarczak, Struct. Chem.. 5 (1994) 57.
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[43] H.M. Jemson and M.C.L. Gerry, J. Mol. Spectrosc., 124 (1987) 481. [44] H.D. Rudolph, Struct. Chem., 2 (1991) 581. [45] D.L. Albtitton, A.L. Schmeltekopf and R.N. Zare. An introduction to the least-squares fitting of spectroscopic data, in K. Narahari Rao (Ed.), Molecular Spectroscopy: Modem Research, Academic Press, New York. 1976. [46] M. Mayer, J.-U Grabow, H. Dreizler and H.D. Rudolph, J. Mol. Spectrosc., 151 (1992) 217. [47] H.D. Rudolph, J. Mol. Spectrosc., 89 (1981) 460. [48] M. Hayashi, M. Nakata and S. Miyazaki, J. Mol. Spectrosc., I35 (1989) 270. [49] B.T. Tan, J. Demaison and H.D. Rudolph. J. Mol. Spectrosc., 71 (1978)471. [50] B.T. Tan, J. Demaison and H.D. Rudolph, J Mol Spectrosc., 76 (1979) 104. [51] P. Botschwina, personal communication. [52] K. Kuchitsu, in G. Allen (Ed.), MTP International Review of Science, Vol. 2, p. 203, Butterworth, London. 1972. [53] J. Randell, A.P. Cox, I. Merke and H. Dreizler, J. Chem. Sot., Faraday Trans., 86 (1990) 1981. [54] B.J. Smith, D. Coffey and L. Radom, J. Chem. Phys., 97 (1992) 6113. [55] I.Y. Schapin and VS. Mastryukov, J. Mol. Struct., 268 (1992) 307. [56] J.L. Duncan, J. Mol. Struct., 158 (1987) 169. [57] J.L. Duncan, Mol. Phys., 28 (1974) 1177. [58] B.P. Van Eijck, in A. Domenicano and I. Hargittai (Eds.), Accurate Molecular Structures, Oxford IJniversity Press, Oxford, 1992, p. 47. [59] P.A.G. Huisman, K.J. Klebe, F.C. MijlhotI and G.H. Renes, J. Mol. Struct., 57 (1979) 71. [60] R.W. Davis and M.C.L. Gerry, J. Mol. Spectrosc., 97 (1983) 117. [61] M. Nakata, T. Fukuyama, K. Kuchitsu, H. Takeo and C. Matsumura, J. Mol. Spectrosc, 83 (1980) 118. [62] M Nakata, K. Kohata, T. Fukuyama and K Kuchitsu, J Mol. Struct., 68 (1980) 271. [63] H. Oberhammer, J. Chem. Phys., 73 (1980) 4310. [64] W.D. Anderson, M.C.L. Gerry and C.J. Marsden, J. Mol. Spectrosc., 114 (1985) 70. [65] J.L. Duncan and B. Munro, J. Mol. Struct., 161 (1987) 311. [66] G. Graner, C. Rossetti and D. Badly, Mol Phys., 58 (1986) 627. [67] J.G. Lahaye, R. Vandenhaute and A. Fayt. J. Mol. Spectrosc., 123 (1987) 48. [68] E. Tiemann, H. Artist, W.U. Stieda, T. Tiirring and J. Hoeft, Chem. Phys., 67 (1982) 133. [69] P. Botschwina, S. Seeger, M. Horn, T. Fltigge, M. Oswald, M. Mladenowic, U. Hoper, R. Oswald and E. Schick, in 1 Nenner (Ed.), AIP Conference Proceedings 312, Molecules and Grams in Space, Mont Sainte-Odile, France, September 1993, American Institute of Physics, New York, 1994.
of
MOLECULAR STRUCTURE ELSEVIER
Journal of Molecular Structure 376 (1996) 399-411
Accurate
structures
of simple dicyanides’
J. DemaisonaT*, G. Wlodarczak”, H. Riickb, K.H. Wiedenmannb, H.D. Rudolphb ‘Laboratoire
de Spectroscopic Hertzienne, URA CNRS 249. Bbt. PS. Vniversit~ de Lille I. 59655 Villeneuve D’Ascq Cedex. France ‘Department of Chemistry, University of Urn. D-89069 L’lm, German) Received
6 July 1995; accepted
21 August
1995
Abstract Accurate structures have been determined for dicyanomethane, HzC(CN)z, vinyl dicyanide, HzC=C(CN)z, cyanide. O=C(CN)z. and sulfur dicyanide, S(CN)z, by combining the results of electron diffraction, microwave
carbonyl
spectroscopy and ab initio calculations. The different methods are compared. The influence of the correlations between the fits (rr,, and r0 rotational constants when calculating the rk structure and the weighting scheme in the least-squares methods) are analyzed. The possibility of obtaining the true equilibrium C=O distance from ab initio calculations is also discussed.
1. Introduction The structures of simple dicyanides have already been determined in the gas phase either by electron diffraction or by microwave spectroscopy or by combining the two techniques [l]. Their ab initio structures have also been calculated using various basis sets and methods. However, there seem to be some inconsistencies in these structures, making a meaningful comparison difficult. In particular, there has been some debate concerning the linearity of the X-C-N bond and incompatible results have been published. In the attempt to clear up this situation, we have redetermined the structures of dicyanomethane, H2C(CN)2, vinyl dicyanide, H&=C(CN)2, carbony1 cyanide, O=C(CN)*, and sulfur dicyanide, S(CN)2, using all the data available and calculating * Corresponding
’Dedicated 75th birthday.
author. to Professor James E. Roggs on the occasion
of his
a new set of consistent ab is in direct continuation of the structures of methyl vinyl cyanide, H,C=CHCN CH,CH=CHCN [4].
initio structures. This our previous work on cyanide, CHICN [2], [3], and crotononitrile,
2. Methods To determine structures possible to the equilibrium ferent methods, as follows.
which are as near as structure, we used dif-
2.1 Ab initio calculations The structure obtained from an ab initio calculation is generally significantly different from the equilibrium structure. However, if the basis set used is large enough, and if the electron correlation is taken into account at least at the MP2 level, the ab initio angles are generally in very good agreement with the equilibrium values and the error in
0022-2860/96/$15.00 cQ 1996 Elsevier Science B.V. All rights reserved SSDI 0022-2860(95)09087-8
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qf.Molecuiar
the ab initio bond lengths is largely systematic and can be corrected using offsets derived empirically [5 71. These offsets have been used for a long time [7-l l] but they have been derived to mainly calculate ra structures (or in some cases r0 structures). We have recently derived new offsets to determine the equilibrium CH, CC, CN and CF bond lengths [3,4,12-141. It is noteworthy that these offsets are often significantly different from zero. In some cases, it was found necessary to take into account the electron correlation [3,4,14-161, so all calculations were carried out at the MP2 level using GAUSSIAii 92 [17].
2.2. Relationship between ri (and rpj structure und re structure In the following discussion, the conclusions reached for the rz bond lengths are also valid for the rg bond lengths. The r, (or rJ structures have been determined for many molecules. The most reliable parameters have been obtained by combining the electron diffraction and microwave data. The rz angles are generally a good approximation to the equilibrium values. However, the rr bond lengths are different from the r, values. To derive the rC structure from the r, values, a knowledge of the anharmonic force field is necessary [ 181, which is rarely the case. However, for some particular bonds, it has sometimes been suggested that the difference rz - r, is constant [19-211. In fact, the difference r, - r, should increase with the bond length because anharmonic effects are larger for softer bonds. Nevertheless, a plot of rz as a function of r’, should give a nearly straight line. This was indeed found for CH [13], C-C [3,12], C-N [2] and C-F [14] bonds. Hence, if a few accurate rz and corresponding re values are known, and if their range is large enough, it is possible to predict by interpolation (or by extrapolation) new r, values knowing the corresponding r, values. In fact, the r, ~ r, difference may depend on the environment if higher order interactions between bond stretching and angle bending vibrations have a significant effect on I’, distances. However, their effect seems to bc very small [18].
Structure
376 (19961 399-411
2.3. r$ structure The substitution structure (rS) calculated from the dill‘erences in moments of inertia [22] is sometimes far from the equilibrium structure. The estimated mean error is about 0.003 A for distances between heavy atoms and 0.005 A for C-H distances, but differences as large as 0.009 A have been found [23]. Moreover, it is empirical, making comparisons with other molecules difficult. However? following the work of Watson [24], who demonstrated that Ze = 2zs - I0
(1)
Harmony and co-workers [25-311 proposed a new procedure for obtaining near-equilibrium structures using only ground-state data. The groundstate moments of inertia I” are first scaled by a factor 2p - 1: Z&(i)
= (2~~ ~ l)Zi(i)
g = u, b, c; i = all isotopomers
(2)
where PX = P,(l)
w = ZO(l) R
i = 1 = parent
(3)
The “substitution moments” of the parent molecule Z:(l). g = a, b, c, are calculated from the substitution coordinates which must have been derived by the application of the full Kraitchman equations, where formally zero-valued squares of coordinates for substitutions on a principal plane or axis may happen to come out negative. To obtain the Zi, negative contributions must also be included in the sums over coordinate squares. Then Harmony advocates correcting the data for the deuterated isotopic species to account for overscaling. This “Laurie” correction is equivalent to an elongation of the C-D bond by an amount 6r = 0.0028 A. For instance, for the a-axis: KX,,
= (Z&)u
+ 2mp j-(biGb; I
+ qSc,)
(4)
and analogously for the b- and c-axes by cyclic permutation of U, b and c. The (I,~bi and ci are the Cartesian coordinates of the D atoms and 6ai, Sbi are SC, the components of 6r. After the subsequent
J. Demaison
et al.iJournai
of Molecular Structure376 (1996) 399-41 I
rs-type least-squares fit to the scaled moments as prescribed by Harmony’s rules, the correction, Eq. (4), leads to a structure where the C-D bond is longer by approximately 0.0028 A and the respective C-H bond by 0.0056 A compared with the results obtained without this correction. Furthermore, this correction has been shown [32] to remain restricted to the resulting C-H bond length, hardly affecting the rest of the bonds. The results reported in Tables 4 and 6 do not take this correction into account. If desired, the C-H bond lengths in Tables 4 and 6 could be directly adjusted to conform to what is expected if Laurie corrections were introduced (i.e. an elongation of the C-H bond of 0.0056 A). The structural parameters of the molecule derived from the fit have been designated as the r& structure. This method has already been applied to several molecules containing hydrogen atoms [2,12,27-331. It seems to give fairly accurate results, except for the C-H bonds. However, there is another way to obtain reliable C-H bond lengths. It has been shown that there is a linear and accurate relationship between isolated C-H stretching frequencies and C-H bond lengths [34]. This relationship has been reviewed recently [13] and applied successfully to many molecules [2,3,12,35]. To date, the rf, method has apparently been mostly applied assuming that the scaling coefficients are error free and that the Z& are uncorrelated. In fact, the three Z:(l), g = a,b, c. are functions of all Z:(i) (but of no other variables), and the same is true for the Z&,,(i). The errors of the Zi( 1) (Eq. (3)) are almost invariably much larger than those of the Z:(l), in particular when the molecule has atoms with small coordinates. Therefore, the errors of the py and hence those of the scaling factors 2p, - 1 (Eq. (2)) are large enough to make the errors of the inertial moments IL,,(i) i larger by orders of magnitude for all isotopomers than those of the Z:(i). Even more important is the fact that the scaling factors which dominate the errors of the Z&,,(i) are independent of the isotopomer. That means that the same factor, e.g. 2p, - 1, multiplies the moments Z:(i) of all isotopomers when the moments Z$,(i) are calculated. Consequently, these moments are extremely highly correlated, separately for each g = a, b: c. In
401
contrast, the correlations between moments of different g are only moderate and directly reflect those of the corresponding components pg. For the rotype fit as prescribed by Harmony’s work, the variance-covariance matrix of the data fitted (i.e. the errors and correlations of the moments Z&(i) affect also the numerical values of the internal coordinates obtained from the fit, and not only their errors. In particular, when the very high correlations between the Z&,,(i) with the same g but different i = 1, N are neglected, the numerical results may be distinctly different from those when these correlations are retained. The differences in the numerical structures when produced with or without the neglect of these correlations were conspicuous in the very stable cases of cyclopropylgermane [32] and cyclopropylsilane [36].
3. Carbonyl cyanide The rg and r, structures of carbonyl cyanide, O=C(CN),, have been determined by combined use of the rotational constants and the electron diffraction intensities [37]. The C-CeN chain appears to be nearly linear, the deviation from linearity being -0.2(6)“. A small inward bend was found by ab initio calculations at the RHF level [38,39], but contradicted by calculations at the MP2 level where the C-C=N is bent outwards by 1.2” [16]. First the ab initio structure was calculated using 6-3 1G*, 6-3 1 lG(d), 6-3 11+G(d) and 6-311+G(2d) basis sets at the RHF and MP2 levels. Only the MP2 calculations are reported in Table 1. Next the C-H, C-C and C-N bond lengths were corrected with the previously estimated offsets [3]. The derived equilibrium structure is also shown in Table 1. To determine the equilibrium C=O bond length, we calculated ab initio structures for molecules containing the C=O bond and for which an r, structure is known. The experimentally known r,(C=O) values are collected in Table 2 together with the ab initio results. As expected, at the MP2 level, there is a good correlation between the experimental and ab initio values. As for the C-C bond [3], the offset Y,,~ - r,,ic, does not seem to be constant for a given basis set. Nevertheless, in
402
J. Demaison
a al./Journal
of Molecular
Structure
376 11996) 399-411
Table 1 MP2 ab initio structures (distances in A and angles in degrees)
Molecule
HK(W2
Bond
cc
6-3 IG’
6-31 lG**
6-31 l+G**
6-3 I1 +G(2d,
2p)
Tea
CH CN ccc HCH CCN
1.4686 1.0955 1.1802 111.84 107.45 178.71
1.4679 1.0945 1.1734 111.96 107.79 179.06
1 4684 1 0946 1.1741 112.01 107.86 178.81
1.4668 1.088 1.1693 111.98 107.82 178.76
1.464 1.091 1.155 111.98 107.82 178.88
H&=C(CN)I
c-c C-H c-c CN HCC c=cc CCN
1.3479 1.0844 1.4394 1.1831 120.67 121.60 179.56
1.3484 1.084 1.4389 1.1764 120.37 121.60 179.78
1.3496 1.0844 1.4393 1.177 120.35 121.65 179.62
1.3437 1.0784 1.4378 1.1724 120.31 121.51 179.87
1.342 1.080 1.437 1.158 120.36 121.63 179.70
@WN2
co cc CN cc0 CCN
1.2231 1.4642 1.1843 122.56 179.05
1.2122 1.466 1.1776 122.81 179.21
1.2137 1.4657 1.1783 122.71 179.25
1.2131 1.4649 1.1735 122.55 179.54
1.204 1.461 1.159 122.63 179.23
S(CN)z
cs CN csc CCN
I .7069 1.1849 98.03 175.40
1.7039 1.1785 97.72 175.90
I .7037 1.1795 9190 175.25
1.7117 1.1748 97 55 175 22
1.160 97.55 175.22
a Estimated
value, see text.
the particular case of O=C(CN)2, either a constant offset or a linear fit gives the same result: r=(C=O) = 1.204(3) A. It may be noted that the error is rather large. As a check of this result, it is interesting to verify that there is a linear relationship between rz(C=O) and re(C=O). The known rZ values are also listed in Table 2. Clearly, the difference rz - re is not constant. However, a linear regression of r, as a function of r, gives an extremely good fit (detcrmination coefficient: R* = 0.9994) and allows us to = 1.204(11) A using r,(C=O) = predict r,(C=O) 1.209 A [37]. Although this result is not very accurate, it is in good agreement with the ab initio equilibrium structu:e. Likewise, it was found that rg - r, = 0.01 l(2) A f?r the C-C single bond [2]. rg(C-C) = 1.469(l) A in carbonyl cyanide gives re = 1.458(3) A, in reasonable agreement with the ab initio corrected value, 1.461(2) A. For the C-N bond, the experimental value is rg = l.lPl(2) A: an offset correction of rg - r, = 0.005 A [2] gives r, = 1.1_56(2), in fair agreement with the ab initio
corrected value, 1.1 B(2) A. Groups more electronegative than carbon stabilize the carbonyl group and lead to a short C=O bond (see Table 2). However, in CO(CN)*, the C=O bond is long, 1.204 A. In fact. the carbon of CN bears a positive charge and, as a result, the interaction with the positively charged carbonyl carbon is repulsive [40]. It is difficult to confirm whether the C-C=N bond bends away from the C=O bond because the zero-point average angle is not significantly different from 180", i.e. 1X0.2(6)“. Moreover, the ab initio calculation at the MP2 level gives a very small bend (0.5-l “), which decreases as the size of the basis set increases (see Table 1). However, for molecules with two highly electronegative elements (i.e. C=O and C-N), it is necessary to take into account the electron correlation and it seems that the Msller-Plesset perturbation calculation is not accurate enough [4]. A calculation using the QCISD method with the 6-3 1 lG(d) basis set also gives a very small bend, 0.37’. The deviation from linearity is too small to be considered significant.
J. Demaison Table 2 Equilibrium,
ab initio
(MP2) and rz C=O
rc @P.)
HzCO HCOOH HCOF HCOCl Cl&O F2CO OCFCl H,C=C=O co: ocs
1.203 1.201 1.183 1.182 1.176 1.170 1.170 1.161 1.160 1.156
co HCO+
1.128 1.106
Mean’ Medianb v (fit)’ Ranged
et al./Journal
bond lengths
of Molecular
Structure
376 (1996)
403
399-41 I
(in A)
11+G(Zd,
Ref.
6-31G*
6-31 lG**
6-311+G**
6-311+G** (full)
6-3
[571
1.221 1.214 1.195 1.200 1.195 1.187 1.190 1.181 1.180 1.180
1.211 1.203 1.184 1.188 1.183 1.176 1.179 1.168 1.169 1.169
1.213 1.205 1.185 1.191 1.186 1.177 1.181 1.168 1.170 1.170
1.212 1.205 1.184 1.191 1.186 1.176 1.181 1.168 1.169 1.170
1.213 1.205 1.184 1.188 1.183 1.177 1.180 1.168 1 170 1 169
1.186 1.185 1.179 1.172 1.173 1.163 _ _
1.151 1.132
1.139 1.120
1.140 1.120
1.139 1.119
1.138 1.118
_
0.015(13) 0.020 0.004 0.051
0.008(4) 0.008 0.004 0.013
0.009(4) 0.010 0.004 0.013
0.009(4) 0.009 0.004 0.013
O.OOS(3) 0.009 0.003 0.012
1581 [591 [6Ol [611 [621 163,641
[651
WI
b71
WI [691
’ Mean value of exp - talc. Standard deviation b Median of exp. - talc. ’ Standard deviation of linear regression. d Range of exp. - talc.
2p)
r,
I .207 1.205
in parentheses
4. Sulfur dicyanide The r, structure of S(CN)2 was first determined by Pierce et al. [41] and was calculated ab initio at the RHF level by Palmer [39]. The results of the new ab initio calculations are given in Table 1. It is not possible to determine a complete equilibrium structure because the equilibrium value of the C-S bond length is not yet known for enough molecules, so it is not possible to “correct” the ab initio result. To calculate the experimental structures, we first redetermined the rotational constants of the different isotopomers using the literature data [41-431. The centrifugal distortion constants of the parent species with three times their standard errors were assumed for all isotopomers. After the elimination of a few outliers, the rotational constants in Table 3 were obtained. The relative r,,, fit [44] standard deviation of a preliminary with the experimental errors and correlations was 5.1. This is larger than unity and shows that even the Y,,I method, one of the more advanced methods of structure determination, is not able to take full advantage of the experimental precision of the
rotational constants owing to the still existing model error (i.e. the inadequate treatment of the rovibrational contributions). For the rO fit, the errors of the internal coordinates were excessive, they were highly correlated and the relative standard deviation of the fit was very large, 625. To avoid different weighting of any two rotational constants of different precision when both are more precise than can be effectively utilized, the experimental errors of the rotational constants should be appropriately corrected towards a more balanced weighting. i.e. by assuming larger but more equal errors for all isotopomcrs. This can be done by increasing the variance of all experimental inertial moments, adding terms on the diagonal of their variance-covariance matrix in such a way that the relative standard deviation of the resulting least-squares fit, which eventually determines the molecular structure, is near unity (see remark on p. 39 of Ref. [45]). We have applied the same procedure that was previously used for the determination of the structures of 2-chloropropane [46] and cyclopropylgermane [32]. A preliminary rr,I fit [44] with unity weight for all inertial moments and no
404
J. Demauon
Table 3 Rotational
constants
(MHz),
errors and correlation
coefficients A
C
Inertml
AC
Pk
(u
34S(CN)z SI’CNCN SC”NCN H,C=C(CN;12 H!‘C=C(CN), ‘ D:C=C(CN)2 H:C=“C(CN)> H2C=C’kNCN II+CC’SNCN
2835 509(3) 0 66Y4 2835.506(13) 0.1589 2809.663(18) -0.5428 2759.640(30) PO.0446 2882 0342( I X) 0 7425 2882 OY21(26) 0.4637 2853.0595(13) 0.6464 2882.1631(82) -0.3214 2857.7338(26) 0.1933 2804 0X33(100) 00116
22 I9 262(4) 0 6310 2203.506(14) 0.4384 2203.033(1 I) 0.6664 2165.682(23) 0.8163 2000.9270( 17) 0 8478 1975.7195(26) 0.6363 1905.9711(13) 0.7880 1999.3514(81) 0.9504 1988.5464(32) 0.3720 1957 3832(83) 0.9246
dcfcct”
A2)
0.49025(27) 0.4915(13) 0.48920(94) 0.49621(84) 0.40368( 12) 0.40921(27) 0.40981(12) 0.40538(64) 0.40199(40) 0 40878(60)
505 379 u A2 MHz.
correlations between any of the inertial moments had an absolute standard deviation of vu = 0.0016 u A*. The terms to be added on the diagonal were chosen as
@i(i)]
376 11996) 399 411
,‘ab
10313.536(11) 0.7432 9981X146(41) 0.3702 10305.326(30) PO.6568 10162.560(43) -0.2651 6579.2729(46) 0.8848 6314.5314(66) 0.8575 5768.5060(28) 0.8571 6561.7455(116) -0.2178 6572.1647(73) 0.6058 6516.5881(118) 0.1599 factor:
Structure
A
WW2
* Conversmn
et al.~Journai of Molecular
Wi)l*
= mu x
[ml2
for g = a, b, c; all
z
g’=a,b,c
(5) In a crude form, this additional variance takes account of the different magnitude of the inertial moments for g = a. b. c. The additional variance was in all cases much larger than the corresponding experimental variance. Since the covariances were not changed, the additional terms on the diagonal resulted in a substantial reduction of the correlations between the inertial moments. The experimental structures are given in Table 4. In the first column, 12 inertial moments were fitted to obtain four independent internal coordinates. Although the errors of the rotational constants had been adjusted (made larger, as discussed
above),
the relative
standard deviation of the r. unity (117) because this error correction was aimed at letting the re,l fit, not the r0 fit, attain a standard deviation near unity. In column 2 is reported the ro-type fit to the eight planar moments with g = a, b of the four isotopomers and excluding the four planar moments with g = c. It indicates that here it is seemingly easier to obtain an r. fit with a low standard deviation (1.9) and small parameters errors for a small planar molecule with a sizable inertial defect. However, the lack of balance (third moment absent) may make the numerical values obtained for the structure unreliable, despite their apparent precision. In column 3 (Y,,~ structure), 12 inertial moments were fitted to obtain four internal coordinates and three rovibrational contributions Ed. The standard deviation is indeed near unity (1.4), as intended by the correction discussed above. Although the (isotopomer-independent) Q, could not be determined at a significant level (Ed = -0.033(28), q, = O.Ol(l4) and t, = 0.47( 14) u A’), the precision of the structure is not affected, because this structure is strictly identical with that
fit is much larger than
J Demaison Table 4 Structures
of S(CN)Z and H2C=C(CN)?
Column Method
et d.iJournd
(distances
of Molecdar
Structure
in A and angles in degrees)
I
2
3
4
5
6
QI
ro (a, b)
re.1
rs
rC
re a
Sf CNIz ub s-c C=N i(CSC) [(SCN)
117 l-707(61) 1.146(89) 98.6(43) 175.4(64)
19 1.697(2) 1.164(2) 98.6(l) 175.5(2)
1.4 1_6Y8(1) 1.159(l) 98.46(6) 175.14(8)
&C=C(CN)2 ISh C-HE c=c c-c C-N [(HCH) /(C=C-C) /(C-C-C) I(C-CEN
624 1.085(35) 1.346(66) 1.438(64) 1.156(67) 120.0(29) 121.4(39) 117.2(77) 179.7(79)
1.3 1.087(l) 1.342(3) 1.439(3) 1.159(3) 120.20(8) 121.6(2) 116.8(3) 179.6(3)
1.0 1.087(l) 1.349(2) I .436(2) 1.157(l) 120.10(5) 121.25(8) 117.5(2) 179.q 1)
a See Table
’Standard ’ Without
405
376 (1996) 3Y9-411
_ 1.700(4) 1.159(3) 98.3(3) 175.0(3) _ 1.087(l) 1.348(3) 1.435(5) 1.158(3) 120.11(9) 121.3(3) I17.3(6) 179X(5)
1.2 1.699(l) 1.159(l) 98.38(6) 175.14(7)
1.4 1 085(2) 1.344(2) 1.436(2) 1.156(2) 120.14(8) 121.43(9) 117.1(2) 179.7(2)
1.160 97.55 175.22 _ 1.080 1.342 1.437 1.158 119.28 121.63 116.74 179.70
1. deviation of the fit. Laurie correction.
obtained by fitting only the isotopic differences of inertial moments (Ye,) or planar moments (YQ), if proper account is taken also of the inertial to planar transformation of errors and correlations. When isotopic differences of inertial moments are fitted, isotopomer-independent eg are clearly irrelevant. Column 4 gathers the substitution (r,) structure calculated using Chutjian’s equations to substitutions on a principal plane or axis [47]. The process is no longer a fit but a direct calculation, propagating only the errors assumed for the moments of the parent and all substituted isotopomers. The Y, and the rc,, structure are usually of comparable precision. This is true also in the present case for the Cartesian coordinates, but with the exception of the small substitution h-coordinate of the carbon atom with its necessarily larger than average error, which induces in turn larger errors of all internal coordinates. Column 5 contains the r& structure obtained by Harmony’s method, as described previously. Two different calculations have been made: the first one uses the errors calculated from Eq. (5) as for the other structures and the second uses the original experimental errors and correlations of the rotational
constants, because the “scaled” rotational constants to which the subsequent r. fit is applied have very uniform errors over all isotopomers owing to the dominant influence of the errors of pa. In the particular case of S(CN)2, the differences between the parameters of the two fits arc very small but the errors are about twice as small with the first weighting scheme, so only the results of the first fit are given. The reason for the smaller errors of the structural parameter is that the first weighting scheme of Eq. (5) produces inertial moments of the parent with higher errors which are, however, also more balanced in the sense of Eq. (5), i.e. the relative magnitude of the moments for g = a, h, c is still reflected by the errors and overcompensates the higher error level in the subsequent least-squares fit of the r$, method. The experimental structures are in good agreement with each other. Furthermore, sulfur dicyanide is a heavy molecule without hydrogen. One may be fairly confident that the true equilibrium value is not far from 1.700 A for the C-S bond length. The derived r,(C=N) bond length is rather long, 1.160 A. In fact, all conjugated 57 systems should
J. Demaison
406 Table 5 Centrifugal
distortion
constants
H2C=C(CN)I H:SC=C(CN)2 D2C=C(CN)z H2C-“C(CN)2 H2C=C”CNCN H 2C=CCi5NCN
et al.~Journal of Molecular
Structure
376 (1996)
399-411
(kHz) of dicyanoethene
A,
AJK
AK
61
6K
ma
“b
1.2655(52) 1.271(13) 1.2130(39) 1.033(76) 1.229(16) 1.158( 102)
-8.564(28) -7.990(80) -6.899(25) -9.44(14) -8.518(82) -7.80(28)
32.324(55) 29.48(12) 22.928(25) 32.02(63) 31.79(11) 30.00(99)
0 5540(22) 0.5651(74) 0.5330(24) 0.5151(81) 0.5330(81) 0.552( 19)
1.452(37) 1.184(107) 1.243(33) 2.55(15) 1.49(13) 0.91(34)
SO 71 4s 55 88 54
51 41 62 15 44 17
a Standard deviation of the fit (kHz). b Number of transitions in the fit.
show an increase in the length of the CGN bond, and correspondingly the adjacent CX bond should be shortened. This is in good agreement with the fact that the C-S bond is much shorter in sulfur dicyanide than in dimethyl sulfide. the corresponding values being 1.701 and 1.802 A, respectively (rs value for dimethyl sulfide [48]). On the other hand, the CSC angles are very similar: 98.8” in (CH3)ZS and 97.6” in S(CN)2. All structures calculated show a significant outward tilt of the C-N bond with respect to the S-C bond which can be given as 4.9(3)“.
5. l,l’-Dicyanoethene The microwave spectra of H2C=C(CN)2 and D2C=C(CN)2 have already been measured [49,50], but these data are not sufficient to determine a complete structure. The rotational spectra of the 13C and “N isotopomers were measured as part of this work. The frequencies of all transitions measured are deposited with the Sektion fur Spektren- und Strukturdokumentation, University of Ulm. In all cases, three rotational constants and five quartic centrifugal distortion constants could be fitted, although with different precision depending on the number and character of the lines measured. The rotational constants are also gathered in Table 3 and the centrifugal distortion constants in Table 5. The equilibrium structure is also estimated from the ab initio results in Table 1 using the method discussed previously and the offsets of Ref. [3]. The experimental structures are reported in Table 4. They were calculated using
the procedure previously used for S(CN)2 (see above) and the above discussion also applies here. For the t$, method, the same two different weighting schemes as for S(CN)2 were used and gave nearly identical results. Laurie correction was not applied to compensate for the shorter CD bond length compared with the C-H bond length. If it is applied, the agreement with the equilibrium (i.e. ab initio corrected) structure is worse. The agreement of the different structures in Table 4 and the r, structure in Table 1 is generally good, except for the C-H bond length, for which the experimental values are probably not reliable as usual (see discussion below). Moreover, the ro, rc,I and Y, bond lengths are significantly too long. r,(C=C) = 1.3420 A, which is longer Othan in ethylene, 1.331 A [51],_ propene, 1.333 A [4], or vinyl cyanide, 1.337 A [3], but it is near the values found for cis-crotononitrile: 1.341 A, trurzs-crotononitrile, 1.339 A, and methacrylonitrile, 1.339 A [4]. This is in agreement with the Stoicheff rule, which states that the bond length increases with the number of bonds adjacent to it [52]. The CC bond length, 1.437 A, is longer than in vinyl cyanide, 1.432 A [3], or cis- and transcrotononitrile, 1.43 1 and 1.430 A, respectively [4], but it is similar to that in methacrylonitrile, 1.438 A [4]. It was established that the substitution of a vinyl group by oxygen increases the C-C bond length by about 0.02 A [52]. This effect is conIirmed in the case 1,I-dicyanoethene and carbonyl cyanide, where the difference is 0.024(3) A. the C=C-C bond angle, 121.6”, is similar to the values found for vinyl cyanide, 122. l”, and
J. Demaison
er al./Journal
of
Molecular
Srrucrure 376 (1996)
399-41 I
407
Table 6 Structures
of H>C(CN),
C0lUnUl Method “d C-He C-C CZN /(HCH) i(CCC) i(C-CEN)
(distances
in A and angles in degrees)
1
2
3
ro
‘?./
rs
I .o I .099(3) I .467(N)
19 1.086(2)
1.466(9) 1.152(13) 103 7(4) 112.6(7) 17X.7(8)
I. 150(8) 106.8(6) 112.7(5) 17X.7(6)
4 rg
_ 1.100(10) 1.452( 13) 1.159(9) 106.9(1 I) 112.9(11) 17Y.l(8)
12 1.080(S) 1.463(6) 1.147(5) 105.9(2) 113.09(9) 178.50(Y)
5 !Jb ‘“3 0.35 I .089(4)
1.45X(4) l-157(4) 106.4(6) 112.8(2) 178.4(2)
6 rcc
I 091 1.464 1.155 107.82 111 98 178 88
a Weighting with experimental errors. b Weighting with adjusted errors (see text). ’ See Table 1. d Standard deviation of the fit. e Without Laurie correction.
cis- and trans-crotononitrile, 122.4” and 122.1”, respectively, but it is slightly larger than that of methacrylonitrile, 119.2”. The HCH angle is very near 120”. All structures show a very slight outward tilt of the C=N bond with respect to the C-C bond which, however, could not be determined at a significant level. Both sulfur dicyanide and dicyanoethene are planar molecules with sizeable inertial defects (Table 3). The scaled inertial moments of the rg method are proposedly nearer to the unknown inertial moments of the Y, structure. Therefore, the inertial defects calculated with the scaled moments should be smaller than the experimental ground-state values. This is indeed the case, although to different extents for the two molecules. For sulfur dicyanide, the rg inertial defects are approximately one quarter of the ground-state values for all isotopomers. For dicyanoethene, the reduction goes down to one twentieth, again for all isotopomers. Owing to the large errors of the moments Ig,g z mentioned above, the rk inertial defects are all within the error range of a zero mertlal defect: ‘)
6. Dicyanomethane The species
microwave spectra of dicyanomethane,
of
several isotopic H&(CN)*, have
recently been measured and the rs, rz and r”, structures have been determined [53]. The CN group was found bent away from the X-CN internuclear axis. This result is confirmed by ab initio calculations [38,39]. However, the rk C-H bond length, 1.103(3) A, seems to be too large, the empirical correlation between the isolated stretching frequencies and r, giving 1.088 A [131. Moreover, the r& CEN bond length, 1.152(3) A, seems to be too short when compared with the values found for other cyanides, whose median is 1.157 A [31. First the equilibrium structure was estimated from the new ab initio results in Table 1 using the method previously discussed and the offsets of Ref. [3]. Then the experimental structures were redetermined using the rotational constants of Ref. [53] (seven isotopomers) and the procedure previously outlined. When treated by any Kraitchman-type method, the problem is complicated by the very small b-coordinate of the atom Ccyan. Therefore, rO-derived methods should, in principle, locate the atomic positions more reliably, at least for atoms with small coordinates. The experimental structures are gathered in Table 6. In column 1 (ro), 21 inertial moments were fitted to obtain six independant internal coordinates. The fact that after the adjustment of the errors (to make the standard deviation of the Y,,[ fit unity) the r. fit has a standard deviation of only 2 indicates that the expected improvement of the r,,, fit over the r0 fit will not
408
J. Demaison et al./Journal
of‘Molecular Srructure 376 (1996) 399-411
Table 7 Equilibrium structures of CHzXz derivatives (distances in A and angles in degrees)”
CHJ
CH& CHzClz CH2BI, CHz(CH,h CHz(CNh HZC=CHZ H:C=C=CH? H:C-C-O cycle-C,Ho
r&C H)
i(HCH)
1.086 1.084 1.084
109.5 112.8 112.1 112.4 106.1 107.8 117.1 118.3 121.8 114.5
1083 1.091 1.088 1081 1.081 1.076 1.082
* Data from Ref. [13].
nearly be as conspicuous as with the former molecules S(CNh and H2C=C(CN)1. Since dicyanomethane is not planar, there is no column corresponding to column 2 for the former two molecules. In column 2 (v,,,), 21 inertial moments were fitted to obtain six independent internal coordinates plus three isotopomer-independent rovibrational contributions. The number of isotopomers is obviously again much too small for a significant determination of these rovibrational contributions. The C-H bond length differs conspicuously from that of the r0 structure. As expected, the errors of the structural parameters are hardly less than for column 1, but they are perhaps slightly more balanced. This failure could be evidence for the fact that, for this molecule, the assumption of isotopomer-independent rovibrational contributions is inadequate. This happens, e.g., when the individual contributions of the normal vibrations to E have different signs and add up to an almost zero E. Then the variation of E from isotopomer to isotopomer may appear erratic, and E can no longer be approximated by a constant. Here again, the r& structure was calculated using two different weighting schemes (see discussion on S(CNk). As they give parameters which are significantly different, the results of both fits are given. When comparing the different structures, it appears that the range of the parameters is large: 0.015 A for C-C, 0.012 A for C-N and 0.020 _.&for the C-H bond length. The standard deviations of
the bond lengths are high, the mean yalue for r(C-C) and r(C=N) being about 0.01 A. Owing to these high standard deviations, a Student’s t-test indicates that only the C-H bond length and /(HCH) angle are incompatible with the corresponding equilibrium values. The Y& structure in column 5 (with adjusted errors) is the nearest to the Y, structure, but the 0& (HCH) angle is far from the corresponding equilibrium value. Taking the Laurie correction into account does not improve the results. The r. structure is also not too bad but the B0 (HCH) is also much too low (by 4.1”). On the other hand, both the Y, and Y, , structures show large deviations from the equilibrium values. The poor behaviour of the experimental structures is due to the ill-conditioning of the system of normal equations. This is a general phenomenon. In that case the C-H distance is not reliably determined as expected, but the HCH angle is also not reliable. A similar behavior has already been found for several molecules, particularly vinyl alcohol and vinyl fluoride [54]. On the other hand, all methods are in good agreement for the C-C-N angle, which shows a small bend away from the symmetry axis. As expected, the C-C bond length is longer ia CH,(CN)2 than in CH3CN: 1.464 and 1.457 A [2], respectively. CN is a x acceptor and pairing it with a c acceptor such as CN is unfavorable energetically and leads to bond lengthening. On the other hand, the CN bond, 1.155 & is rather short, which is in good agreement with a long C-C bond. This point has already been discussed [4]. The CCC angle, 112”, is nearly identical with the value found in propane, 112.2” [30].
7. Discussion One of the main dificulties is the determination of accurate r,(C-H) bond lengths and i(HCH) bond angles in CH,(CN), and H&=C(CN)2. For CH2(CN)2, it has already been found that the ab initio corrected value, r,(C-H) = 1.091 A, is compatible with the value given by the isolated stretching frequency, 1.088 A. There is another way to check the accuracy of the ab initio results
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because it has been shown that there is an empirical relationship between the i(HCH) angle and the C H bond length [55]. this correlation gives extremely good results in the particular case of methyl derivatives, except for methyl fluoride [12]. In Table 7 are collected the rc (C-H) bond lengths and I(HCH) bond angles for a few CHzXz molecules. In Fig. 1 is plotted the :(HCH) angle as a function of the r(C-H) length. This correlation is fairly good, except for allene and, to a lesser dcgrcc, for CHzFz (as for CH3F). This confirms that our structures for CH2(CN)2 and H2C=C(CN)2 are likely to be reliable. Furthermore, it allows us to improve the accuracy of the r,(C-H) value in CHzClz. There are two recent independent determinations of the equilibrium structure of CH2C12. Berry and Harmony [28] determined the rL structure pf that molecule and found r&(C-H) : 1.087(4) A. Duncan [56] estimated the equilibrium structure and found re(C-H) = 1.080(3) A. The correlation shows that the former value is slightly too high whereas the latter is slightly too low, a more accurate value being 1.084 .& This last value was obtained from the isolated stretching frequency and was confirmed by ab initio calculations (see Table 7). We have seen that the two more advanced methods of calculating the molecular structure from inertial moments, the Y, , and the r$ methods, show different success for different molecules: (1) The T~,I method hardly improved the standard deviation of the fit for dicyanomethane (factor 2 with respect to the basic r,, method), whereas the improvement was one to two orders of magnitude better for sulfur dicyanide and dicyanoethene, with a corresponding improvement in the error level of the structural parameters determined. (2) The inertial defects calculated with the scaled moments of the t$, method approximated the expected zero value much better for dicyanoethene than for sulfur dicyanide. The true isotopomer-dependent rovibrational contributions to the ground-state inertial moments, i.e. the differcnccs between the ground-state moments and the equilibrium moments, are .$
where g = a, h, c and i is the individual isotopomer. The models by which the two methods try to account for these elusive parameters are different. The r,,, method introduces them as only three isotopomer-independent constants cg whose values are to be determined as three additional variables in the least-squares fit to the groundstate inertial moments. the rg, method scales the ground-state moments first by three isotopomerindependent factors 2p,, - 1 whose values follow from the substitution structure of the parent, the r$, structure is then determined by the subsequent ro-type fit to the scaled moments. From Eq. (2) it follows that the rf,, method models the rovibrational contributions E:, here the differences IiJi) - Z:(i). as 2(p, - 1) Ii(i). That means that they do depend on the individual isotopomer, but they are rigidly proportional to the ground-state inertial moment I:(i). Clearly, the success that can be expected depends on the extent to which either model conforms to the reality of the specific problem being treated.
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