On the molecular structure of CdCl2

J~~r~~ of Moie~lar Structure, 318 (1994) 251-255 0022-2860/94/%07.00 0 1994 - Elsevier Science B.V. All rights reserved

251

Short Comm~~cation

On the molecular structure of CdQ S. Gundersen, Department

A. Haaland, K.-G. Martinsen, S. Samdal*

of Chemistry,

University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway

(Received 20 September 1993)

The electron diffraction pattern of gaseous monomeric CdC& has been recorded with a nozzle temperature of 805 f 15 K by Haaland et al. [l]. They have assumed that the molecule is linear, but they refined the shrinkage of the non-bonded Cl.. Cl distance (Sshr = 2r,(Cd-Cl) - r,(Cl . ’ ’ Cl)) as an independent parameter along with the Cd-Cl bond distance, the Cd-Cl and Cl - Cl root-meansquare (r.m.s.) vibrational amplitudes and the asymmetry constant of the Cd-Cl bond. The shrinkage thus obtained, bshr = 7.9( 16) pm, was not significantly different from that calculated from a molecular force field under a harmonic small amplitude motion approximation, 5.4 pm (see footnote b to Table 2), and it was concluded that the data were consistent with a linear equilibrium structure. N. Vogt et al. [2] assumed a bending potential of the form V(q) = 4 k2q2 + k4q4, where q = A - LClCdCl. If k2 < 0, this potential describes a molecule with non-linear equilibrium structure. The motion of Cl atoms during the bending vibration was assumed to be curvilinear. The force constants, kZ, k4, f,, and the Cd-Cl bond distance, denoted rzh, were refined under an harmonic approximation to gas electron diffraction data and the two observed stretching frequencies. The best agreement was obtained for a linear model (k2 > 0), but a quasi-linear model with a bond angle of 165-180” and a low potential barrier to * Corresponding

author.

SSDI 0022-2860(93)07924-L

linearity could not be ruled out. Both these investigations used a static model, i.e. where only one non-linear configuration is used in the analysis. Hargittai and Hargittai [37have discussed different approaches to obtain the equilibrium bond distances for linear three atom molecules. These approaches may give quite different results for the equilibria bond distance, and they concluded therefore that the approach used should be carefully specified. They, and coworkers [4], have determined the molecular structures of CaX2 (X = Cl, Br, I). The derived equilibrium structures for CaX2 (X = Cl, Br, I) have been compared [3] with values obtained from ab initio calculations [5,6]. Their comparison [3] of the equilibrium bond distances derived from electron diffraction and the ab initio calculations indicated that there might be an apparent disagreement between theory and experiment, and they concluded that this might be a challenge for further ab initio calculations. However, this apparent disagreement can be explained by explicitly taking account of the dynamic behaviour of the molecular bending motion [7]. The CaX2 (X = Cl, Br, I) molecules have been analysed using a static model. Such a model will always give a thermal average bend structure. The deviation from a linear structure is compared with the shrinkage effect and on this basis conclusions about a linear or a bend equilibrium structure can be drawn. A much better description would be to take explicitly the bending motion into the electron diffraction analysis, i.e. by

252

S. Gundersen et al.lJ. Mol. Strut.

Table 1 Variationa of the potential bending energy and the Cd-Cl bond distance as a function of the bending angle, as calculated from ab initio using an STO-3C* basis set 4

V(q) 0.0

0.00

10.0 20.0 30.0 40.0 50.0

2.70 10.64 23.41 40.61 62.02

&d-Cl

(4)

220.355 220.463 220.771 221.240 221.820 222.480

&d-Cl

(4 =

0)

-

&d-Cl

(4)

0.000 0.109 0.417 0.886 1.465 2.125

a Rending angle (deg), bending energy (kJ mol-‘) and bond distance (pm).

using a dynamic model which consists of several nuclear configurations. The form of the bending potential would then determine if the equilibrium structure was linear or not. Potential functions [8] have been determined by using the electron diffraction method for a variety of molecular motions such as rotation, puckering and pseudorotation. In order to explain the apparent disagreement [3] between the equilibrium bond distances for the CaX2 (X = Cl, Br, I) molecules derived from electron diffraction and ab initio calculations, the Table 2 Structural parametersa

Cd-Cl Cl. Cl rCd-Cl

ZCI...Ci KCd-Cl

UP 6shr LClCdCl %Q R&

318 (1994) 251-255

variation of the Ca-X bond length with the bending motion explicitly has to be taken into account [‘7].Based on small basis set ab initio calculations it was shown [7] that rather different bond distances might be obtained if a static or a dynamic model is used. For the first time we want to test the theory [7] on experimental data where both static and dynamic models are used, and compare the results from the two models. To be able to include the variation of the Cd-Cl bond length as a function of the bending angle in the electron diffraction analysis we have estimated this variation from some small basis set (STO-3G*) ab initio calculations [9]. The ab initio results are given in Table 1 and also shown in Fig. 1, and the electron diffraction results are given in Table 2. We have used the same photographic plates as recorded previously [1]: four plates obtained with a nozzle-to-plate distance of about 50cm (s from 17.50 to 142Snm-’ with an increment As = 1.25 nm-‘) and six plates with a nozzle-to-plate distance of about 25cm (s from 40.00 to 260.00 nm-’ with an increment As = 2.50 nm-‘). Backgrounds were drawn as ninth (50cm) and tenth (25 cm) degree polynomials to the difference

for Cd-Cl at 805 K

Ref. 1 thermal average

Ref. 2 thermal average

Static thermal average

Dynamic minimum potential

228.2 (4) 448.6 (16) 7.5 (3) 12.2 (14) 68 (20)

228.4 (4) 448.9 (16) 7.5 (3) 12.2 (14)

227.7 (3) 449.1 (13) 7.6 (2) 11.9 (11) 28 (12)

227.1 (3)

7.9 (16) 158.8 0.057 0.131

7.9 (16)

6.4 (13) 160.8 (19) 0.052jO.069 0.123/0.123

7.6 (2) 9.8 (14) 27 (12)C 25.5 (35)

Vibrational force fieldb

7.2 10.2

5.4 0.052/0.069 0.124/O. 123

a Interatomic distances (ra) in pm, r.m.s. vibrational amplitudes (I) in pm, asymmetry constant (n) in pm3, shrinkage (6) in pm and average ClCdCl bond angle in degrees. Error estimates as in ref. 1, i.e. [(2~s,&)’ + (0.1r)2]‘/2 for bond distances and 2ffx,,.d,, for the others. b The force constants are given in ref. 1 and using the normal coordinate program ASYMM [ 19. ’ The same error estimate as for the static model. d V(q) = a,q* and a, is in kJmol_’ radm2. e Goodness of fit; R = ]Cw,A:/C+Z~(obs)] ‘I* where Ai = Z(obs) - Z (theoretical) and wi is a weight function.

S. Gundersen et al./J. Mol. Struct. 318 (1994) 251-255

253

CdCI,

Vlql

Fr ’ q ’

SIO-3G.

kJ/moi

Pm ._.,_Lc-

60

223 V(q)

/

40

20

fx w-“--,_,

-

-e-vI’

0

1

IO

20

30

40

I

/‘II

100

18

‘II

150

/‘I

I”

200

-& 220

q degree Fig. 1. Variation of the Cd-Cl bond distance and the bending potential for CdClz as a function of the bending coordinate 4 which is defined on the Figure. A linear molecular structure is represented by q = 0. (-) Least-squares fitted curves Fc~-cj(q) and V(q) to the ab initio results ( - ) given in Table 1. The functional expressions for &+_~~(q) and V(q) are: Fcd_a(q) = 2.203547 + 0.0359575q’ - 0.0150197q4 + 0.~627265q6 0.000573457q8 and V(q) = 89.0947q’ - 15.8907q4 + 9.54384q6 - 2.47914q’.

between the total and calculated molecular intensities for each side of the photographic plates, and the data from each side have been averaged. Equal weight has been given to the 25 and 5Ocm data in the least squares refinement. The resulting modified molecular intensity curves are displayed in Fig. 2, and the experimental radial distribution curves corresponding to the dynamic model given in Table 2 are shown in Fig. 3. The small differences in the structural parameters between the previous static model [l] and our static model are due to the facts that slightly larger data ranges have been used, and that the relative weights of the data sets are different. The most noticeable differences between the static and dynamic approach are as expected in the Cd-Cl bond distance and in the amplitude

.,-

-

-h

50

or

-7

-_--.,_

I

I

I’

250

1

s, nm(-1)

Fig. 2. Calculated (-) and experimental (...) modified molecular intensity curves for CdCl* with difference curves.

for the non-bonded Cl.. Cl distance. The Cd-Cl bond length from the dynamic approach is 0.54 pm smaller than that from the static approach which corresponds to approximately twice the error estimation. This is as expected from the ab initio

A

~~“~~‘1”1~~““1~‘~~“~“1”“~“~‘1”“‘1~~’1”””’~’ 0

100

200

300

400

500

600 r,

pm

Fig. 3. Calculated (-) and experimental ( - ) radial distribution curves for CdCls with artificial damping constant 3 = 25pm*. Theoretical intensities have been used for s < 17.50nm-‘, equal weight on long camera data for s 17.50-50.00 nm-‘, equal weight on long and short camera data for s 50.00-130.00nm-‘, and equal weight on short camera data for s 130.~-26.~ nm-' .

254

S. Gundersen et al/J.

calculations as shown in Fig. 1. Since the Cd-Cl bond distance increases with the bending angle the thermal average of the bond distance has to be larger than the bond distance corresponding to the minimum of the potential energy function. If the thermal average bond distance is used for a further correction to r,, a systematic error of about 0.54pm might be expected. The difference between the thermal average bond distance derived from the static model and the bond distance corresponding to the minimum of the potential function can be estimated [7] as: ACd-Cl =

l/N

= (Cd-Cl)

J

- Fcd_c,(q = 0)

FCd-Cl('d exP (- V(q)lRT)dq

where Fcd_ct(q) is the variation of the Cd-Cl bond angle, V(q) is the potential energy function as a function of the bending coordinate q, and N is a normalization constant. The integration is from 0 to 50”. If the Fc&ci(q) and V(q) values from the ab initio calculations are used ACd-Cl is calculated [lO,ll] to be 0.25pm, and if Fcd_ct(q) from ab initio and V(q) from electron diffraction are used ACd-Cl is calculated [lO,l l] to be 0.40pm. The semirigid model [2] gives I, x r, - 1.6pm and the centrifugal contribution to the thermal average Cd-Cl distance, &,,, is 0.2pm (see footnote b to Table 2). We believe that the best estimate of the equilibrium Cd-Cl distance at the present time would be to use ra = 227.1 pm from the dynamic model and the results from the semirigid model together with the centrifugal correction to give r,(Cd-Cl) = 225.3pm, which can be compared with re = 232-234pm from ab initio calculations

WI. Thirty different configurations from 0 to 60” in steps of 2” have been used in the dynamic model. This allows the non-bonded Cl.. Cl distance to change from a length of 454.4pm at the linear configuration to a length of 406.3 pm at 60”. The different configurations are populated according to the Boltzmann distribution. The static approach uses only one configuration, and a larger r.m.s. vibrational amplitude, I, has to be applied to

Mol. Struct. 318 (1994) 251-255

simulate the bending motion. Actually, the framework amplitude, l,, should be used in the dynamic model, i.e. the contribution from the bend motion should be excluded. However, for a linear molecule the I and Ir, values should be equal to the first approximation, and as seen from Table 2 the amplitude for the non-bonded Cl.. Cl distance for the dynamic model is in much better agreement with the amplitude calculated from the vibrational force field than if a static model was used. The thermal average Cl-Cd-Cl bond angles from the static models are 158.8 and 160.8”. This thermal average angle can be estimated [7] as: (Cl-Cd-Cl)

=

qexp [-V(q)/RT]

dq

Using V(q) from the ab initio calculation and from electron diffraction, the thermal average values are calculated [lO,l 1] to be 171.O and 163.6” respectively. The potential function derived from electron diffraction gives results which are in good agreement with the observed difference between the Cd-Cl bond found by using a static and a dynamic model, and the thermal average angle as obtained from a static model. The ab initio calculated frequencies are usually about 10% too large, indicating that the bending potentials derived from ab initio calculations are too steep, as is also found from electron diffraction. We have also tried a potential function with two terms, i.e. V(q) = alq2 + a2q4 where al and a2 are refined to 4.0(5.8) kcal mol-’ rad-* and 4.1(12.3) kcalmol-’ rade4 respectively with a correlation of 0.98. These values indicate that the electron diffraction data alone are not accurate enough to reveal finer details about the form of the potential function. However, positive values of aI and a2 do support the molecule being linear. We have also tried to determine the variation of the Cd-Cl bond length as a function of the bending angle by using Fcd_ci(q) = b, q2 and refining b,. Unfortunately, the results were not promising; bi refined to 1.5(9.7)pmrad-* with a correlation to the Cd-Cl bond distance of -0.99. The

S. Gundersen et al.lJ. Mol. Struct. 318 (1994) 251-2SS

corresponding value from ab initio calculations using only one term was 3.0pm rad-*. We have therefore fixed Fed-a(q) to the function determined from ab initio calculations in all leastsquares refinements. It is an open question as to how different ab initio basis sets will alter Fca_cl(q). We will try to explore this further for COZ, but it is quite clear that inclusion of Fcd_cl(q) will be of importance if the aim is to obtain equilibrium distances from an electron diffraction analysis. As seen from Table 2 the average bond angle is about 20” from linearity and is still in full agreement with a linear equilibrium structure. Extreme care should be taken if the results from a static model are to be used to make statements about the equilibrium structure. The difference between the theoretical and experimental curves at about 1.4pm in the radial distribution curve can be traced back to the 25cm data. Different scattering factors, scaling errors and nozzle-to-plate distances have been considered and tested without giving a clear solution to the problem. This problem has to be further explored.

255

References

9

10 11

12

The Norwegian Research Council (NFR) is acknowledged for computer time at the IBM RS6000 cluster at the University of Oslo.

13

A. Haaland, K.-G. Martinsen and J. Tremmel, Acta Chem. Stand., 46 (1992) 589. N. Vogt, A. Haaland, K.-G. Martinsen and J. Vogt, Acta Chem. &and., 47 (1993) 937. M. Hargittai and I. Hargittai, Int. J. Quantum Chem., 44 (1992) 1057. E. Vajda, M. Hargittai, 1. Hargittai, J. Tremmel and J. Brunvoll, Inorg. Chem., 26 (1987) 1171. L. Seijo, Z. Barandiaran and S. Huzinaga, J. Chem. Phys., 94 (1991) 3762. M. Kaupp, P.V.R. Schleyer, H. Stall and H. Preuss, J. Am. Chem. Sot., 113 (1991) 6012. S. Samdal, J. Mol. Struct., 318 (1994) 131. A.H. Lowrey, in I. Hargittai and M. Hargittai (Eds.), Stereochemical Applications of Gas-Phase Electron Diffraction, Part A, The Electron Diffraction Technique, VCH, Weinheim, 1988, Chapter 12, and references therein. M.J. Frisch, G.W. Trucks, M. Head-Gordon, P.M.W. Gill, M.W. Wong, J.B. Foresman, B.G. Johnson, H.B. Schlegel, M.A. Robb, E.S. Replogle, R. Gomperts, J.L. Anders, K. Raghavachari, J.S. Binkley, C. Gonzalez, R.L. Martin, D.J. Fox, D.J. DeFrees, J. Baker, J.J.P. Stewart and J.A. Pople, GAUSSIAN 92, Revision C, Gaussian Inc., Pittsburgh, PA, 1992. S. Wolfram, Mathematics: A System for Doing Mathematics by Computers, Addison-Wesley, 1988. W.H. Press, B.P. Flannery, S.A. Tenkolsky and W.T. Vetterling, Numeri~I Recipes, Cambridge University Press, 1986. D. Stromberg, 0. Gropen and U. Wahlgren, Chem. Phys., 133 (1989) 207. L. Hedberg and I.M. Mills, J. Mol. Spectrosc., 160 (1993) 117.