9062
J. Phys. Chem. 1995, 99, 9062-9071
Molecular Structures and Force Fields of Monomeric and Dimeric Magnesium Dichloride from Electron Diffraction and Quantum Chemical Calculations Judit Molntir,+ Colin J. Marsden,**$and Magdolna Hargittai*9+ Structural Chemistry Research Group of the Hungarian Academy of Sciences, Eotvos University, PJ: 117, H-1431 Budapest, Hungary, and IRSAMC, Laboratoire de Physique Quantique CNRS URA.505, Universitk Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France Received: February 13, 1995@
Monomeric and dimeric MgClz have been investigated by high-temperature electron diffraction and ab initio calculation at the SCF and MP2 levels of theory. The effect of the size of the basis set, and particularly the number of polarization functions and their exponents, has been carefully investigated. The basis set size was increased until a convergence in the monomer bond length was reached at the TZ5P2f(+)/MP2 level. The highest level of calculation for the dimer was of DZP(+)/MP2 quality. Harmonic vibrational frequencies were calculated and normal-coordinate analyses were performed for both monomeric and dimeric molecules. For the electron diffraction determination of the dimer geometry, constraints based on the quantum chemical calculation, such as the differences of the Mg-C1 bond lengths, were incorporated into the analysis, as the dimer was present only as a minor component of the vapor (12.8 f 1.3 mol %). Monomeric MgCl2 is linear with a bond length of r,(Mg-Cl) = 2.179 f 0.005 A. The converged calculated bond length, r,(Mg-Cl) = 2.169 A, is consistent with the value estimated from electron diffraction applying vibrational corrections, f(Mg-Cl) = 2.163 f 0.011 A. This agreement, however, can only be obtained with large basis sets; standard bases of DZP quality and standard exponents give much larger bond lengths than the experimental value. The calculated equilibrium structure of the dimer has a four-membered planar ring with two bridging chlorines (D2h symmetry). At the high temperatures used, the dimer appears strongly puckered if a standard electron diffraction analysis is used, but the best fit to the experimental data was obtained by adopting a dynamic model, in which the calculated rather anharmonic ring-puckering potential, together with the associated changes in the other geometrical parameters, was used as an additional constraint. Only a very minor increase in bond length with bending was found for the monomer, whose bending potential is close to harmonic.
Introduction Magnesium dichloride is a simple fundamental molecule. Yet the determination of the molecular structure even for the monomeric form has posed intriguing problems. Of the experimental techniques, only gas-phase electron diffraction (ED) is applicable to this work. However, it is hampered by the necessary high-temperature conditions and by the lowfrequency bending vibrations. Magnesium dichloride has been investigated by ED twice before.' The first investigation'" used the visual ED technique which had inherent limitations in determining structural details. In a later work by Kasparov et al.Ib data in a rather limited range of the scattering variable were collected as only a single camera range was used in the experiment instead of the customary two ranges. In both studies the vapor was supposed to contain only monomeric molecules. According to mass spectrometric studies, however, there is a relatively large amount of dimers present in the vapor.2 If the presence of these dimers is not taken into account, the geometry determined for the monomeric molecules can be erroneous. Each percent of ignored dimer increases the determined monomer bond length by about 0.1% compared to the actual value of the ~ a r a m e t e r . ~ The above-mentioned deficiencies warranted a reinvestigation of this important molecule with current ED technique. Quantum chemical calculations of MgCl2 and its dimer were undertaken concurrently with the experimental ED study, both Hungarian Academy of Sciences. = UniversitC Paul Sabatier. Abstract published in Advance ACS Absrrucrs, May 1, 1995.
for their own sake and also to reduce the uncertainties associated with the ED analysis. In view of the recent interest in the shape of C ~ F Z ? -which ~ is best described as "quasi-linear", a thorough theoretical analysis of monomeric MgC12, which is of course valence-shell-isoelectronic with CaF2, seemed worthwhile in itself. Although there have been a few earlier theoretical studies of monomeric MgC12?g-' there is little information available at present on how the size of the Mg basis might influence the results obtained. The dimer has been only incompletely characterized to date, by vibrational spectroscopy.5 Its structural parameters are unknown and its force field mostly unknown. Even its symmetry is not known with certainty. We are not aware of any previous theoretical analysis of the dimer. Studies by microwave spectroscopy do not seem feasible, as we predict the molecule to be nonpolar (see below), besides the formidable difficulties posed by its low volatility, and the presence of four chlorines in the molecule causing quadrupolar splitting in the spectrum. As the dimer makes up only a minor component of the vapor, a complete structural study by ED is very difficult. It therefore appears as though computational chemistry offers the best means to study the dimer at present. The difficulties experienced in the ED experiment are largely associated with the dimer, which is present in appreciable concentrations even at the high temperatures needed to obtain sufficient vapor pressure. Since the two distinct bond lengths in the dimer are presumably different, both from each other and from that in the monomer, the ED analysis would have great difficulty in reliably determining all three. Therefore, an indication from ab initio calculations of the magnitudes of these bond length differences would increase the reliability of the ED
0022-365419512099-9062$09.00/0 0 1995 American Chemical Society
Monomeric and Dimeric Magnesium Chloride TABLE 1: Experimental Conditions camera ranges (cm) 50 nozzle temperature (K) 1171 no. of plates used in analysis 7 2.625 9.25 Smin (A-') 14.000 25.75 Smax (A-9
J. Phys. Chem., Vol. 99, No. 22, 1995 9063 19 1171 7 9.25 27.25
investigation. Although the physical meaning of bond lengths determined by ED and quantum chemical calculation is not the same, this can be ignored to a good approximation in considerations of differences of bond lengths. Several low-frequency bending motions can be envisaged for the dimer, but most of these have not yet been measured; shrinkage effects will therefore be very important at the high temperatures needed to volatize MgClz. If an approximate harmonic force field for the dimer were available from quantum chemical calculations, it would yield estimates of vibrational amplitudes and shrinkage corrections which would be most useful for the ED analysis. These considerations show how a joint application of both experimentaland theoretical techniques can yield more reliable structural data than can either when used separately. Experimental Section The sample of magnesium dichloride was an Aldrich product (purity 98%). A combination of electron diffraction and quadrupole mass spectrometric experiments was employed.6The mass spectra showed the presence of relatively large amount of dimeric species that was subsequently confirmed by the eIectron diffraction analysis. The ED pattems were recorded in our modified EG-lOOA apparatus. A so-called radiation-type nozzle system was used7 with a molybdenum nozzle. The diffraction patterns were recorded on Kodak photoplates. Due to the high experimental temperature, there was some light radiation from the glowing nozzle resulting a detectable unevenness of the diffraction pictures in the short camera range experiments. Therefore, the data from the two sides of the photographic plates were averaged separately in the data reduction process. Thus eventually three sets of data were used in the analysis. The two sets of 19 cm data were both assigned 0.5 weights. Some of the experimental conditions are listed in Table 1. The electron scattering factors were taken from the usual sources.* The molecular intensity and radial distribution curves of magnesium dichloride are given in Figures 1 and 2. Listings of total electron diffraction intensities are available from the authors upon request. Quantum Chemical Calculations Monomeric and dimeric magnesium dichloride were studied at both SCF and MP2 levels of theory, using the program Gaussian 92.9 Geometrical parameters were optimized by 8, or gradient methods, and converged to better than 2 x 0.02", respectively. Harmonic vibrational frequencies were calculated from analytical second derivatives. A large range of basis sets was used, since results already obtained for the closely related compound CaF2 show that careful attention is needed to the quality of the basis, particularly concerning the polarization functions on the group 2 metal, if properly converged parameters are to be obtained, even at the SCF level.4b.dl'0 A detailed study of MgFz has shown that correlation effects are of relatively minor importance in that moleculei0 and that the differences between MP2 and QCISD results are very small, so it was not felt necessary in this work to go beyond the MP2 level of theory. Five spherical-harmonic components
of d-type functions were used throughout, except for the 3-21G* and 6-31G* bases, for which the six Cartesian functions are standard. The lowest 11 occupied MO were constrained to be doubly occupied in the correlated calculations, and excitations into the corresponding high-energy virtual orbitals were excluded. This choice of active space excludes MO corresponding to the Is, 2s, and 2p A 0 on C1, and 1s on Mg; however, the 2s and 2p A 0 on Mg are included, as we wished to investigate the possible influence of polarization of these "near-core" orbitals in the field created by the chlorine atoms. 3-21G* and 6-31G* basis sets are internal to the Gaussian series of programs. A "DZP' (double-zeta plus polarization) basis was constructed as follows: a double-zeta s, p basis was obtained from the (1 1s 7p) primitives obtained by Huzinaga," with the [6s, 4p] contraction developed by Dunning and HayI2 adopted for C1, while a slightly more flexible [7s, 5p] contraction, of the form 5, 6*1 for the s space and 3, 4*1 for the p space, was employed for Mg. Exponents for a single set of d-type polarization functions on both Mg and C1 were varied, with simultaneous geometry optimization at the SCF level. Optimum values were found to be 0.25 for Mg and 0.34 for C1. These are rather different from the "standard" values of 0.175 and 0.75 which are used in the 3-21G* and 6-31G* bases for Mg and C1, respectively. Calculations were also undertaken with a D Z P set in which the exponents of the polarization functions were the same as those in the 6-31G* basis. As the chlorine atoms in MgC12 bear a substantial net negative charge (a natural charge of -0.869 e has been determined by Schleyer and co-workers at the SCF level4h), we investigated the effects of adding diffuse s and p functions to the C1 basis; exponents of 0.06 were chosen for both s and p functions by downward extrapolation, to give the DZP(+) basis. Two sets of d-type functions were added to both Mg and C1 in the DZ2P(+) basis; exponent values of 0.45 and 0.15 for Mg, and 0.6 and 0.2 for C1, were adopted. We also used a flexible valence triple-zeta (TZ) basis, due to McLean and Chandler;I3 this set contains 12s and 9p primitives, contracted to [6s, 5pl. In view of the anionic character of C1 in MgC12, the basis optimized for C1- was adopted. The TZP, TZP(+), and TZ2P(+) bases are exact analogues of their DZ counterparts, but exponents for the diffuse functions added to the TZP basis were chosen to be 0.06 (s) and 0.035 (p). We systematically expanded the polarization space for both Mg and C1, until addition of extra functions made no significant difference to the properties of interest to us. In the TZ3P(+) basis, the d-type exponents were 1.0, 0.33, and 0.1 on Mg, combined with 1.4, 0.45, and 0.15 on C1. A single set of f-type functions was added (exponent values 0.3 for Mg and 0.4 for C1) to obtain the TZ3Pf(+) basis. When four sets of d-type functions were employed, their exponents were 3.0, 1.0, 0.33, and 0.1 for Mg, and 3.5, 1.1,0.35, and 0.1 for C1. Two sets of f-type functions were included on both atoms in the TZ4P2f(+) basis; their exponents were 0.8 and 0.2 for Mg, and 1.0 and 0.25 for C1. The TZ4P2f(+) basis is fairly large for correlated studies (173 contracted functions for MgC12). However, the Mg-Cl bond length has not quite converged with this basis, so further basis extensions were tested. A fifth set of d functions (exponent 10.0) was added to the Mg basis only; this set is denoted TZ5(4)P2f(+). Then a fifth d set (exponent 11.0) was also added to C1, to give the TZ5P2f(+) basis. Finally, as this fifth d-type set on C1 produced little effect on either the energy or geometry of MgC12, it was deleted and a sixth d-type set (exponent 35.0) added to Mg, to give the TZ6(4)P2f(+) basis. Ab initio results for monomeric MgCl2 are reported in Table
Molnk et al.
9064 J. Phys. Chem., Vol. 99, No. 22, 1995
"
I
I
I
0
,
I
I
a
4
I
I
12
I
s,
I
v-
I
20
16
--
v
-v
A
I
I
24
28
I
A-I
Figure 1. Electron diffraction molecular intensities for 50 and 19 cm camera ranges. The two sides of the 19 cm plates were averaged separately, E = experimental, T = theoretical, A = difference curves.
4 / I
I
I
I
I
I
I
0
1
2
3
4
5
6
r,
I
7
8
A
Figure 2. Radial distribution obtained from the electron diffraction intensities combined from the two camera ranges. E = experimental, T = theoretical, A = difference curves. The heights of vertical bars are roughly proportional to the relative weights of contributions of internuclear distances r to the electron scattering. Contributions from the monomer molecule are underlined. Because of their small weight, contributions of the dimer nonbonded distances are multiplied by a factor of 5.
2. Data obtained by earlier workers are included, for purposes of comparison. Linearity was initially assumed, and confirmed by the subsequent calculation of vibrational frequencies, all of which are real. D2h symmetry was assumed for the dimer, with a four-membered ring, as shown in Figure 3; this geometry was
found to be a true minimum, as all vibrational frequencies are real. Other possible geometries were not investigated, as this is the optimum arrangement for a completely ionic system, and this structural type has been shown to be adopted by several other x2Y4 metal halides.3b Equilibrium structural parameters
J. Phys. Chem., Vol. 99, No. 22, 1995 9065
Monomeric and Dimeric Magnesium Chloride TABLE 2: Ab Initio Equilibrium Bond Length (A), Vibrational Wavenumbers (cm-l), Absolute Energies (hartrees), and Experimental Vibrational Wavenumbers (cm-l) for Monomeric MgC12 basidmethod
-Ea
v2
v3
3-2 1G*/SCF 6-31G*/SCF DZP'/S CF DZP/SCF DZP(+)/SCF DZ2P( +)/SCF TZP/SCF TZP(+)/SCF TZ2P(+)/SCF TZ3P(+)/SCF TZ3Pf(+)/SCF TZ4Pf(+)/SCF
Present Study 2.194 324 123 2.192 326 118 2.182 331 125 2.176 336 119 2.185 328 119 2.180 328 115 2.182 329 117 2.182 330 119 2.176 329 117 2.176 329 112 2.174 331 113 2.173 331 112
632 626 642 648 633 626 633 633 628 628 63 1 63 1
3.47272 8.727 18 8.70845 8.71482 8.7227 1 8.72606 8.79567 8.79674 8.80034 8.801 13 8.80508 8.80570
DZP( +)/MP2 TZP( +)/MP2 TZ2P(+)/MP2 TZ3P(+)/MP2 TZ3Pf(+)/MP2 TZ4Pf(+)/MP2 TZ4P2f( +)/MP2 TZ5(4)P2f(+)/MP2b TZ5P2f(+)/MP2 TZ6(4)P2f(+)/MP2b
2.197 2.193 2.182 2.176 2.164 2.171 2.170 2.169 2.169 2.169
117 116 111 104 109 109
624 628 622 625 643 630
8.97722 9.07463 9.14618 9.18476 9.23841 9.32420 9.34719 9.38839 9.38936 9.38878
HF/model potential HF/all-el pseudopot HF/2-ve pseudopot 6-3 1G*/MP2
Literature Data 2.206 292 105 2.183 328 123 2.17 1 324 122 2.182 330 112
577 63 1 625 639
gas phase gas phase MI IR,' Kr MI IR,' Ar MI IR,' Ar MI IR Ra,d Ar calculated scalede
+
re
VI
321 325 323 326 323 327
Experimental Wavenumbers 597 588 87.7 590 585 603 326.5 93.0 600.8 306 112 594
TABLE 3: Ab INtio Equilibrium Structural Parameters (Bond Lengths in A, Angles in deg) and Binding Energies (kJ/mol) for Dimeric MgC12'I ref
basidmethod
r(15)
r(12)
L(214)
AEb
3-2 1G*/SCF 6-3 1G*/SCF DZP/SCF DZP( +)/SCF DZ2P(+)/SCF TZP/SCF TZP(+)/SCF DZP( +)/MP2
2.201 2.198 2.186 2.196 2.189 2.190 2.190 2.206
2.383 2.388 2.378 2.381 2.372 2.372 2.372 2.384
92.4 91.3 92.1 91.8 92.2 91.7 91.8 92.2
184 151 167 153 157 149 151 168
a For atom numbering, see Figure 3. Electronic binding energy of 1 mol of dimer.
4g 4h 4h 4i 14a 14b 14c 14d 14d 5
a Absolute energies, below - 1 1 10. See text for explanation of these bases. Matrix isolation infrared spectroscopy. Matrix isolation infrared and Raman spectroscopy. e For 19the average of experimental values, 594 cm-I was taken and the other two computed (DZP(+)/ MP2 basis, see text for details) frequencies were scaled accordingly.
assuming it is reasonably small, but it would affect the apparent bond length obtained. These calculations also provide information about anharmonicity in the bending vibration. As the molecule bends, the bond length increases slightly as shown in Table 5. Although the changes are small, they are "significant" as the optimizations were converged to better than 2 x A. However, their physical significance is slight, given the experimental uncertainties associated with the ED analysis. The increases in energy resulting from the bending (at the relaxed bond lengths) are also given in Table 5. Bending anharmonicity is thus detectable but not large, as the energy increase for a 50" bend is 107 times larger than that for a 5" bend, instead of 100 times which it would be in the absence of bending anharmonicity. The puckering of the four-membered ring in dimeric MgC12 was investigated at the DZP(+)/SCF level of theory. Results are presented in Table 6. If X denotes the midpoint of the line joining the bridging C1 atoms 2 and 4, the puckering of the ring is indicated by the angle 6, which is the deviation of the angle Mgl-X-Mg3 from 180". Puckering lowers the symmetry of the dimer from D2h to C2". The energy of dimeric MgC12 was calculated for 5" increments of 6, ranging up to 50°, with the other geometrical parameters maintained at their equilibrium values. Increases in energy due to this "rigid" puckering are denoted AE' in Table 6. On a coarser grid of 10" increments for 6, the four other independent geometrical parameters were optimized. Increases in energy due to this "relaxed" puckering are denoted AE. As the ring puckers, the terminal bonds decrease in length very slowly but the bridge bonds extend at a moderate rate. The angle at Mg decreases notably, and the terminal bonds bend so that the conformation of the molecule, as viewed from the side, resembles a shallow
bbw'.
i
C14
i
Figure 3. Numbering of atoms in the MgC12 dimer molecule. and the binding energy for the dimer appear in Table 3 and the harmonic vibrational wavenumbers for the dimer are presented in Table 4. All vibrational wavenumbers are calculated for 24Mg and 35Clisotopic species. In view of the substantial thermal energy available to the molecules in the ED study, the potential surfaces of both monomer and dimer were probed away from the equilibrium geometries. For the monomer, the optimum bond length was studied as a function of bond angle, at the TZ4Pf(+)/MP2 level of theory; any such variation could not be detected by ED,
Anharmonicity in the puckering motion is appreciable, as the rigid energy change for a 50" pucker is 129 times greater than that for 5". The effects of relaxing the other geometrical parameters are not negligible; they amount to nearly 4kJ/mol, or nearly 12% of A,?,for a puckering of 50". It is intriguing to notice the similarity in energy changes calculated for bending the monomer by 50" (36 kJ/mol) and puckering the dimer by 50" (35 kJ/mol if relaxation is neglected). Normal Coordinate Analysis A normal coordinate analysis was carried out for both monomeric and dimeric magnesium dichloride using a new version of the program ASYM20.15 Magnesium dichloride has been investigated repeatedly by gas-phase infrared and matrix isolation infrared and Raman spectro~copy.~.'~ In one of these studies5 several of the dimer bands have also been assigned. The vibrational wavenumbers of the monomer were calculated by ab initio calculation prior to this in~estigation.~g-' The
Molniir et al.
9066 J. Phys. Chem., Vol. 99, No. 22, 1995 TABLE 4: Vibrational Wavenumbers for Dimeric MgClz (cm-l) basislmethod frequency typea 3-21G*/SCF 6-31G*/SCF DZPISCF DZP(+)lSCF DZ2P(+)/SCF TZPISCF TZP( +)lSCF DZP(+)/MP2 experimentalb NCA 1Dd NCA2D‘
4
Bb
RS 293 289 294 290 290 294 293 284 286 285 283
TS 559 553 566 553 55 1 557 556 550 548 544
RB 139 144 150 148 149 148 148 143
RS 294 276 282 279 280 284 283 285
IPB 90 90 95 92 96 94 94 84
B2g OPB 109 107 109 109 111 110 110 107
143 142
286 284
84 84
109 108
B1U OPB 164 166 169 168 167 169 169 161 14OC 164 162
B2u RP 30 29 29 30 31 30 30 28 28 28
RS 388 37 1 379 373 375 374 374 372 372 377 374
B3u IPB 63 63 66 63 66 65 65 60 61 60
TS 534 529 540 528 526 533 532 526 5 14 524 520
RS 258 254 260 257 256 260 259 253 260 250 248
TS: terminal stretching, RS: ring stretching, RB: ring bending, IPB: terminal in-plane bending, OPB: terminal out-of-plane bending, RP: ring puckering. Experimental values, where available, from ref 5. This frequency was disregarded at the scaling. Calculated by the normalcoordinate analysis from the DZP(+)/MP2 wavenumbers for the experimental geometry. e Calculated by the normal-coordinate analysis for the experimental geometry and with scaling to experimental wavenumbers (through force constants).
TABLE 5: Ab Initio Bending Potential for Monomeric MgClf Ob (deg)
Ar(Mg-Cl)c
0
(A)
0.0 0.0 0.0001 0.0008 0.0018 0.0034 0.0058
5 10 20 30 40 50
AEd (M/mol)
0.0 0.336 1.347 5.417 12.340 22.402 36.025
TZ4Pf(+)/MP2 level of theory. Deviation from linearity. Bond length increase compared to the linear molecule. Energy change during bending.
TABLE 6: Ab Initio Ring Puckering Potential for Dimeric MgC12 (Distances in A, Angles in deg, Energy in kJ/mol)l @‘
r(15)
r(12)
L(214)
L(X15)
0 5 10 15 20 25 30 35 40 45 50
2.196
2.382
91.8
180.0
0.0
2.196
2.382
91.7
179.3
1.083
2.196
2.383
91.2
178.5
4.410
2.195
2.386
90.5
177.6
10.236
2.194
2.390
89.5
176.4
19.011
2.193
2.396
88.2
174.9
31.447
AEc
0.0 0.273 1.100 2.507 4.538 7.256 10.747 15.119 20.510 27.094 35.086
For atom numbering see Figure 3, DZP(+)lSCF level of theory. See text for description of puckering angle. Energy change due to puckering, when other geometrical parameters allowed to relax. dEnergy change due to puckering with no relaxation of other parameters.
present work is the first report, however, on the vibrational spectrum of the dimer. Monomer. All spectroscopic studies agree that the monomer molecule is linear with D,h symmetry. The treatment of a triatomic linear molecule is a textbook example on normal coordinate analysis as given, e.g., in ref 16. The vibrational wavenumbers of MgC12 calculated in this study are given in Table 2 together with the results of earlier calculations as well as with the experimental wavenumbers. There is disagreement at all levels among the different sets of wavenumbers; between gas-phase and matrix measurements, between different gas-phase as well as different matrix results, between different level calculations, and, finally, between experimental and calculated wavenumbers. There can be different origins for these discrepancies. When comparing the gas-phase and matrix wavenumbers “matrix effects” may be an obvious reason for discrepancy. For highly polar molecules
(see, e.g., ref 17) the stretching modes have been observed to decrease considerably in the matrix. Interestingly, Fe2C16 also shows similarly rather large matrix shifts for the stretching modes in argon matrix as compared to the gas-phase value although this molecule is nonpolar.’* On the other hand, as shown in ref 18, FeC12 and Fe2C4 display very small matrix shifts at going from gas-phase to argon matrix while they have rather large shifts between the Ar and N2 matrix measurements. According to data from ref 5 , the situation is similar for the monomeric and dimeric magnesium dichloride molecules. The Ar and N2 matrix values differ considerably, while the difference between the gas-phase and Ar matrix values is less obvious, especially because there is already a discrepancy between the two gas-phase values of the asymmetric stretching mode. When comparing the experimental (gas and matrix) and calculated wavenumbers, it is to be remembered that the calculated wavenumbers are harmonic wavenumbers while the experimental ones are anharmonic. It is difficult to judge the amount of shift caused by this difference and whether it manifests itself the same way for the stretching and the bending vibrations. The following scheme was followed in our analysis: From among the calculated wavenumber sets of Table 2 the DZP(+)/ MP2 set was chosen to be consistent with our highest level calculation of the dimer. First we assumed that this computed set of wavenumbers corresponds to the gas-phase values and camed out the normal-coordinate analysis accordingly. Then, we took the average of all measured asymmetric stretching wavenumbers, 594 cm-’, and used it as the estimated gas-phase value. With scaling the force constants, the other calculated wavenumbers were adjusted. This wavenumber set is also given in Table 2. The electron diffraction experimental bond length and temperature were used in all these calculations. The force constants and the mean amplitudes of vibration corresponding to the two wavenumber sets are given in Table 7. Dimer. The dimers of metal dihalides have a four-membered halogen-bridged structure (Figure 3) with D2h symmetry, according to different experimental and theoretical evidences (see, e.g., refs 3 and 4i). The molecule has 12 normal modes and they belong to the following irreducible representations:
rvib = 3 A, + 2 B , , + 1 B,,
+ 2 B , , + 2 B,, + 2 B,,
The following internal coordinates were used as bases for the representations to build up the symmetry coordinates (the numbering of atoms is given in Figure 3): terminal Mg-C1 stretch (Ar-1,~and Ar3.6). bridging Mg-C1 stretch (Ar1,2,Ar2.3, Ar3.4, and Ari,4), terminal in-plane bend (a2.1.5,a4.3,6, a4,1,5,
J. Phys. Chem., Vol. 99, No. 22, 1995 9067
Monomeric and Dimeric Magnesium Chloride TABLE 7: Force Field Parameters (mdynldi for Stretching and mdyn.dilrad3for Bending), Mean Amplitudes of Vibration (A), and Shrinkage (A) for Monomeric MgC12 from the Normal Coordinate Analysis
TABLE 9: Elements of the F-Matrix for the Dimer (Stretching Force Constants in mdyddi, Stretch-Bend Interactions in mdydrad, and Bending Force Constants in mdyn&rad2P ~~~
parameter
NCA 1Ma
NCA2Mb
2.123 0.171 2.049 2.086 0.037 0.089 0.124 0.103
1.924 0.067 1.856 1.890 0.034 0.094 0.130 0.112
FI1 F22
F33
fr frr
l(Mg-Cl) l(C1. * C1) d(C1. * C1)
a Corresponds to the DZP(+)/MP2 set of wavenumbers. Corresponds to the “calculated scaled” set of wavenumbers of Table 2 (see text for details).
TABLE 8: Symmetry Coordinates for MgzCL SdA,) = (l~d‘%Arl,s+ A r d &(Ag) = I/2(Ar1,2 Ar2.3 + Ar3.4 + b1,4) S3(Ag)= 1/2(a2.1.4 a 2 ,~ a1.2.3 - a1.4.3) S4(Blg) = l/~(-Ar1,2 h 2 , 3 - Ar3.4 + Ar1.4)
+ +
+
= V2(a2,1.5 + a 4 . 3 . 6 - a2.3.6 - a 4 . 1 ~ )
= (1/&)@1,2,4,5 - p3.4.2.6) S7(Blu) = ( l / f i ) @ l , ~ , 4 , 5 + p3.4,2,6) S ~ B I=J y2.3.4.1 &(B2u) = ’/2(-Ar1.2 - Ar2.3 Ar3.4 Ar1.4) SIO(B~J = ‘ / 2 ( - a ~ , 1 , 5 a4.3.6 - a2,3,6 + a4.1.5) S I I ( B=~ (l/fi)(Arl,5 - A n d S12(B3u) = I/2(Arl,2 - A m - Ar3.4 Ar1.4) S6(B2g)
+
+
+
+
a2,3.6), ring bend ( a ~ 2 . 3 ,a1,4,3,a2,1,4,a d out-of-plane bend @1,2.4,5, p3,4,2,6), and torsion (y2,3,4,1)+The symmetry coordinates are given in Table 8. Only 5 of the 12 wavenumbers of the Mg2C4 molecule were assigned e~perimentally.~ They are given in Table 4 together with the computed ab initio wavenumbers. Here we followed a strategy similar to the one used with the monomeric molecule and thus two sets of calculations were carried out. First, we supposed that the best set (DZP(+)/MP2) of the computed wavenumbers corresponds to the gas-phase values. Second, supposing that the gas-phase values are close to the ones measured in the matrix (cf. the experience with the iron dichloride monomer and dimer’*), the computed wavenumbers were scaled to the measured wavenumbers in the normalcoordinate analysis. For both calculations the experimental geometrical parameters and temperature were used. The refinement of the force constants was carried out on the main isotopes (24Mg and 35Cl) but the root-mean-square amplitudes were calculated with the use of average masses (Mg, 24.312; C1, 35.435) to correspond to the electron diffraction experimental conditions. The corresponding force field, for the computed normal-mode set (NCAlD, see Table 4), is given in Table 9. The calculated mean amplitudes of vibration are given in Table 10 for both sets of calculations. Electron Diffraction Analysis According to the radial distribution curve (Figure 2) the basic component of the vapor is the monomeric MgC12 molecule. There are only two major contributions, the Mg-C1 bond distance and the Cl-Cl nonbonded distance of the monomer. There are, however, smaller peaks as well, indicating the presence of dimeric molecules. The relative abundance of the dimeric species in the vapor is small; therefore, the determination of their molecular geometry is not possible on the basis of electron diffraction data alone.
Ag
BI,
1 2 3
1 2.017 0.026 -0.019
4 5
4 0.737 -0.089
2
3
BI, 1.097 0.071
6
~
7 8
7 0.144 -0.018
8
9 1.037 -0.002
10
9 10
11 1.992 0.091
12
11 12
0.219
0.482
5
Bzu
0.120
0.090
6 Big
~
B3u
0.129
1.003
Corresponds to frequency set NCAlD of Table 4. Numbering of colums and rows corresponds to the symmetry coordinates. a
Calculated Mean Amplitudes of Vibration for
Mgl -C15 Mgl -C12 Mg 1-*.Mg3 C 12. * C 14 C 12. * C 15 Mgl.. C16 C 15. * C 16
lb
‘I
0.091 0.135 0.188 0.166 0.293 0.206 0.223
0.092 0.136 0.189 0.167 0.295 0.208 0.225
a For numbering of atoms see Figure 3. Amplitudes calculated from the wavenumber set NCAlD of Table 4. Amplitudes calculated from the scaled wavenumbers (NCA2D of Table 4).
Moreover, the strong correlation between the parameters of the monomer bond and the two different dimer bonds hinders the unambiguous determination of the monomer geometry. In addition, the dimer molecule is floppy, performing largeamplitude vibrations. To alleviate these difficulties some constraints have been introduced into the analysis. Constraints. First of all, the difference between the monomer bond length and the dimer terminal bond lengths and the difference between the two different dimer bond lengths were adopted from the ab initio calculations (later the latter constraint could be removed). When combining actual geometrical data originating from different sources, it is important to scrutinize the choice of data to minimize the introduction of systematic errors as these data, as a rule, have different physical meaning. The electron diffraction bond lengths are thermal average bond lengths, while the calculated ones are the equilibrium bond lengths corresponding to the potential energy minimum. The introduction of constraints in terms of differences rather than absolute values of parameters greatly diminishes the systematic errors caused by the application of constraints. The equilibrium geometry of the dimer has a planar ring (D2h symmetry). Under the ED experimental conditions, however, a thermal average structure is determined, characterized by a puckered ring with tilted bonds to the terminal chlorine ligands (C2” symmetry). In order to approximate the experimental situation, the dimer geometry was also calculated at different puckering angles by ab initio method (vide supra). From the energies of these structures the distribution of these different dimer “conformers” was estimated using the expression V = exp(-AE/RT‘). The ED pattern was then approximated by a set of such dimers of different geometry (again, only differences of parameters were used in the ED analysis from the ab initio calculations) with weights corresponding to their calculated distribution. The mean amplitudes of vibration for the dimeric molecule, calculated by the normal-coordinate analysis, were assumed in
Molnir et al.
9068 J. Phys. Chem., Vol. 99, No. 22, 1995 TABLE 11: Geometrical Parameters of Magnesium Dichloridd rg (A), 1,("1
1(4
K
(A3)
Monomer Mg-Cl C1. * c 1 qc1. * C1) 6, (dyn)
2.179 f 0.005 4.259 & 0.009 0.099 f 0.007 0.101 f 0.007
Mg-Cl,b Mg-Clbb A(D,-Mon)d A(Db-Dty
2.188 & 0.007 2.362 & 0.010 0.009' 0.174 f 0.006 94.3 f 0.7 12.8 f 1.3 5.5 1
0.087 f 0.002 0.137 f 0.004
2.31 x
f 8.8 x
0.089 f 0.002 0.132 f 0.003
2.52 10-5' 1.23 x 10-4"
Dimer
LClb-Mg-Clb' dimer content (%) R (%)8
a Estimated total uncertainties,22indicated as error limits, include 4 2 times the least-squares standard deviation, a systematic error of 0.2% for distances and 2% for vibrational amplitudes, and a third term reflecting the influence of constraints. Cl,, terminal dimer chlorine atom; clb, bridging dimer chlorine atom. Adjusted after K(Mg-C1),,,, see text. Difference between dimer terminal bond length and monomer bond length. e From DZP(+)/MP2 quantum chemical calculation. Difference between dimer bridging and terminal bond lengths. 8 Goodness of fit.
'
the analysis without change. The same set of amplitudes were used for all dimer "conformers". Since the experimental vibrational amplitude of the monomer bond agrees well with the calculated value for the computed wavenumber set (NCAlM set of Table 7), and not for the one scaled to the experimental wavenumbers (NCA2M of Table 7), we decided to use the corresponding set of amplitudes for the dimer as well. However, for the dimer the difference between the two sets is so small that either set could be used with the same result. Due to the considerable anharmonicity of the vibrations of these types of molecules, the asymmetry parameter ( K ) is an important parameter in the electron diffraction analysis. It could be refined for the monomer bond but not for the two dimer bonds. Therefore, we estimated the Morse constant (a) from the amplitude ( I ) and K values of the monomer from the relation~hipl~
Then, using this Morse constant and the vibrational amplitudes of the dimer bonds, we calculated their asymmetry parameter. These values were gradually adjusted as the monomer K changed. It has recently been suggested20that the bond length of metal dihalides changes during their large-amplitude bending. Although this effect has been shown to be very small,2' we looked into the possible variation of the electron diffraction r, distances during bending. To probe this supposition for MgC12, the monomer geometry was calculated for different bending angles at the TZ4Pf(+)/MP2 level (see Table 5). It was found that the Mg-Cl bond length changes less than the uncertainty of the electron diffraction r, parameter during the bending of the molecule. When we attempted to include the change of monomer geometry into our dynamical analysis, the system proved insensitive to it. Accordingly, only one geometry was refined for the monomer. This seems to be justified also by the dimeric molecule being much more floppy than the monomer and by the calculated change of the monomer bond length during bending being smaller than the experimental error of this parameter. Table 11 gives the results of the electron diffraction analysis. In calculating the total uncertainties of geometrical parameters, the effects of all constraints have been taken into account in addition to the least-squares standard deviation and an estimated systematic experimental error of 0.2% for distances and 2% for vibrational amplitudes.
TABLE 12: Bond Length of MgClz from Different Experimental Sources and Different ADDrOXimatiODS ~
tvDe 8'
r, r, '8 g'
'8
I$" r:
~
Mg-Cl
2.179 f 0.005" 2.1856 f 0.0114 2.18 f 0.02 2.203 f 0.005b 2.190 f 0.005' 2.185 f 0.005d 2.163 f 0.011' 2.162 f 0.005'
ref
this work lb
la this work this work
this work this work this work
a Preferred rg value as result of present study; refinement with inclusion of dimer and refining K (see Table 11) R factor = 5.5%. Result of refinement for monomer only (excluding the dimer), R = 8.6%. Refinement for monomer only, with ignoring K (Le., K = 0), R = 11.5%. Refinement as in c except that the range of intensity data corresponds to that of ref lb. e Estimated from electron diffraction with Morse-type anharmonic corrections; see ref. 23. /Result of the combined electron diffraction and vibrational spectroscopic analysis, using the DZP(+)/MP2 wavenumbers as input parameters.
Discussion Monomer Bond Length. Table 12 compares experimental bond lengths of different origin for MgC12. When comparing the Mg-Cl bond lengths determined in three ED studies, the two latest results fall within the rather large error limits of the first investigation. The value published by Kasparov et al., r, = 2.1856 f 0.0114 A, also agrees with our result, r, = 2.179 f 0.005 A, within the experimental uncertainties. However, it is worthwhile to further scrutinize these two parameters. The presence of dimers was ignored in the study by Kasparov et al., so what they actually determined was a kind of weighted average Mg-C1 distance. If we refine the structure with the assumption that only monomeric molecules are present in the vapor, the Mg-C1 distance refines to 2.203 f 0.005 8,with an asymmetry parameter about 4 times larger than expected. The increase of these two parameters compensates for the missing dimer contribution in this model. If, further, we assume that there is no anharmonicity present and the asymmetry parameter is ignored (as was done by Kasparov et al.), the bond length gets shorter, 2.190 f 0.005 A, and the R factor increases. Finally, using the same range of data sets as by Kasparov et al.,Ib the monomer bond length decreases further to 2.185 f 0.005 A, thus reproducing their value. The dependence of the bond length on the range of intensity data used for the analysis is not surprising since the effect of the asymmetry parameter increases at larger s values. Thus, in Kasparov et al's study
Monomeric and Dimeric Magnesium Chloride the effect of ignoring the dimer presence was fortuitously compensated by neglecting the asymmetry parameter and by the relatively small range of data used in the analysis. Experimental and calculated bond lengths can only be compared after bringing the two parameters to a common d e n ~ m i n a t o r .The ~ ~ results of the electron diffraction analysis, the r, parameters, do not have a well-defined physical meaning; therefore they are usually transformed into r, parameters that are thermal average bond lengths. Due to the high experimental temperature and the floppy nature of these types of molecules, the rg parameter is expected to be considerably larger than the equilibrium bond length. With simple Morse-type anharmonic correction^^^,^^ the re parameter can be estimated on the basis of ED data. This, so-called rf parameter, is also given in Table 12. We have also carried out a combined electron diffraction and vibrational spectroscopic analysis in the anharmonic a p p r o ~ i m a t i o n . ’ Its ~ ~ ~result, ~ the so-called r: parameter, is effectively the same as the rf parameter. They agree well, within experimental uncertainties, with the results of the TZ3Pf(+)NP2 and higher bases calculations (see Table 2). All smaller bases provided larger Mg-C1 equilibrium bond lengths. There is a large number of calculated bond lengths for magnesium dichloride. The total range of variation in the computed bond length for MgClz is 0.028 A, or 1.3%. While there is a trend toward a contraction of the bond at the SCF level as the basis is improved, as is to be expected, the trend is not perfectly regular. For example, the addition of diffuse functions to the C1 DZP basis produces an appreciable increase in bond length of 0.009 8,, presumably due to the reduction in BSSE.27 The reduction in energy of nearly 8 mH due to these diffuse functions is certainly not negligible. Similarly, the extension from DZP to TZP also leads to an increased Mg-Cl bond length, of 0.006 8,; however, the addition of diffuse functions to the TZP basis produces only a very minor change in the bond length of 0.0001 A, and an energy improvement of only 1 mH, indicating that the larger, more flexible s, p basis is almost adequate at the SCF level. It is noticeable that the 6-31G* basis predicts appreciably longer bonds than are found with the DZP set. Only part of this difference is due to the variationally nonoptimum polarization exponents in the 6-3 lG* basis, as comparison of the DZP’ and DZP results shows a contraction of 0.006 when optimum exponents are used. More contracted d functions lead to shorter bonds; in the range of values studied here, the bond length is far more sensitive to the Mg exponent than to that on C1. At the SCF level, the bond length is effectively converged when a TZ4Pf(f) basis is used; the addition of the f function makes only a modest change, even though 4 mH are gained, while the fourth set of d functions produces very minor structural and energetic changes. It was not thought sensible to use smaller bases than the DZP(+) set for post-HF calculations. Correlation effects lengthen the bonds by a nontrivial amount of 0.012 8, with this basis; while this is a typical change,28 it leads to poorer agreement with experiment, as the DZP(+)/SCF result is already too long. Most of the correlated calculations were performed with the TZ s, p basis augmented with diffuse functions. As the size of the polarization space is increased, the predicted bond length decreases rather quickly, so that with the TZ3Pf(+) basis it is 0.01 8, shorter than found at the SCF level. The influence of the single set o f f functions is appreciable; they decrease the bond length by 0.008 A at the MP2 level, and lower the energy by no less than 4 4 mH, over 10 times greater than their effect at the SCF level. It is not necessary to comment in detail on every entry in Table 2. We note merely that effective saturation of the basis was attained by our largest sets, given the choice
. I . Phys. Chem., Vol. 99, No. 22, 1995 9069
of active space and properties of interest, as the influences of the sixth d-set on Mg, and the fifth on C1, were insignificant on both energy and bond length. Several important points emerge from these results. Firstly, the use of standard bases on DZP quality leads to bond lengths which are appreciably larger than the experimental value, even at the SCF level of theory, with correlated methods giving worse agreement. Secondly, careful attention needs to be paid to the choice of polarization exponents, as casual adoption of “standard” values can produce poor results. Thirdly, in order to obtain converged results with respect to basis extension for the bond length in MgClz, much larger basis sets must be used than those which are in common use. There seems no reason to suppose that MgCl2 is special in this regard. Converged results were obtained here only with five sets of d functions and two sets of f functions. It is possible that the polarization exponents used in this work could have been chosen so as to span the space needed in a more economical fashion, but such a choice could only be possible with the benefits of hindsight. Fourthly, once sufficiently large bases are used, the predicted bond length is indistinguishable from the estimated experimental equilibrium value, within the experimental uncertainties. Quite tight d functions on Mg (exponents in the range 3-10) produce a substantial shrinking of the bond length at the MP2 level of theory; these functions cannot possibly be important for the description of valence electrons, given their radial extent, so it is clear that polarization of the “core” 2s and 2p electrons on Mg has significant structural effects, which cannot be ignored if quantitatively accurate results are sought. The prediction of slightly shorter bonds using correlated methods than those obtained at the SCF level is most unusual for main-group compounds.28 We believe it to be a consequence of polarization by the highly negative C1 atoms, which will make the Mg core nonspherical; the resulting spheroid will be compressed along the Mg-Cl bonds and elongated perpendicular to that direction, leading to a shrinking of the effective size of the Mg atom, and hence a decrease in the bond length. We cannot exclude the possibility that correlation of the 2s and 2p core electrons on C1 would also have a significant influence on the bond length, but we did not investigate such effects in this work, because the core-valence separation is much more complete for atoms in group 7 than those in group 2, and because the correlation of 16 extra electrons would have greatly increased the computational effort required. The good agreement between the equilibrium bond length estimated from the ED data (see Table 12) and the value computed at the MP2 level with our largest bases (Table 2) is gratifying, but we should acknowledge that our correlation treatment is far from complete. Judging by experience already gained for MgF2 (but admittedly with a smaller basis),I0 the bond length would be shorter by a few thousandths of an angstrom at the CCSD level compared to our MP2 result. However, since the influence of triple substitutions, which we have neglected here, would surely lengthen the bonds slightly, it is quite conceivable that our final result is indeed fairly accurate, albeit fortuitously, to within a few thousandths of an angstrom. Morse Constant. There are two ways to estimate the Morse constant from electron diffraction data. One is from the asymmetry parameter, K , by using eq l . I 9 The other is from the cubic force constant through the equationz9
The cubic force constant can be determined by the anharmonic approximation of the combined electron diffraction and vibrational spectroscopic analysis. The Morse constant estimated
9070 J. Phys. Chem., Vol. 99, No. 22, 1995 in the above ways is 0.84 f 0.28 and 0.92 f 0.37 from the asymmetry parameter and the cubic force constant, respectively. The Morse constant calculated ab initio at the T24Pf(+)/ MP2 level of theory is 1.36 in reasonable agreement with the estimated values. Shrinkage. The shrinkage, d,, determined on the basis of the electron diffraction thermal average parameters, is 0.099 f 0.007 8,. If we take into account the possible relaxation of the Mg-Cl bond length during bending (see Table 5), the corrected shrinkage, d,(dyn), is 0.101 & 0.007 8,. The “calculated” value for this parameter, obtained from the normal coordinate analysis using the ab initio wavenumbers, is 0.103 8, (see Table 7); in perfect agreement with the above values. Structural and Energetic Features of the Dimer. Our aims in studying the dimer were more modest than for the monomer. We had no hope of approaching the basis-set limit closely at any correlated level. We were most interested in the changes in bond length from monomer to dimer, as these are the structural features which are most difficult to determine in the ED experiment. While the predicted structural parameters for dimeric MgCl2 in Table 3 naturally show some variation with basis size and theoretical method, these changes are fortunately very similar at all levels of theory used here. The terminal bond length is consistently some 0.009 A larger than that of the monomer, while the bridge bonds are about 0.18 8, longer than the terminal ones; our best estimate for this difference, obtained by adding the correlation effect found with the DZP(+) basis to the TZP(+)/SCF result, is 0.175 A, to which it is prudent to attach an uncertainty of some 0.005 8,. The four-membered ring halogen-bridged structure agrees with our experimental data. The terminal bond of the dimer was supposed to have a bond length 0.009 8, longer than the monomer bond according.to the results of the quantum chemical calculations. The difference of the two dimer bond lengths from quantum chemical calculation was first used as a constraint in the electron diffraction analysis. Later on, however, it seemed to be possible to refine this difference as well. The result, 0.174 & 0.006 A, agrees excellently with the computed difference, 0.175(5) A. This good agreement between calculation and experiment supports the notion that differences of geometrical parameters from different sources can better be compared than actual parameters. The bond angle, Clb-Mg-Clb, from the calculation also varies over only a narrow range, with our best estimate being 92.2”, with an apparent uncertainty of perhaps 0.5”. This angle is somewhat larger from electron diffraction, 94.3 f 0.7”. The purely electronic binding energy for dimeric MgC12 is substantial. The values in Table 3 show the importance of adding diffuse functions to a DZ-style basis, to reduce BSSE, as these extra functions on C1 lower the binding energy of Mg2C4 compared to 2 mol of MgCl2 by 14 kJ/mol. Correlation effects increase the binding energy modestly, by some 15 kJ/mol at the MP2 level. Our best estimate of the electronic binding energy is 165 kJ/mol; it is not easy to give a realistic uncertainty for this result, since we were not able to use very sophisticated levels of theory for the dimer, but the following discussion suggests that our value is reasonably accurate. As the binding energy is large, should not the proportion of the dimer in the vapor also be large? In fact, entropy factors greatly favor the monomer at high temperatures and low pressures. We may estimate AG at 1171 K (the temperature of the nozzle in the ED experiment) for the equilibrium involving 2 mol of the monomer and one of the dimer: to AE (-165 kJ/mol), we add the change in zero-point vibrational
Molnfir et al. energies (+3.0 kJ/mol), the change due to population of excited vibrational states (f6.8 kJ/mol), and the APV term (-9.7 kJ/ mol), to obtain AH(1171) = -164.9 kJ/mol. Here we have used the unscaled DZP(+)/MP2 vibrational frequencies. However, the TAS term is estimated to be f163.7 kJ/mol; the translational, rotational, and vibrational components are 261.7, 22.5, and -120.5 kJ/mol, respectively, where a pressure of 0.01 a m was assumed. The final estimate is therefore AG = - 1.2 kJ/mol. It is remarkable how the enthalpy and entropy terms almost cancel. It need scarcely be stressed that there are many uncertainties in the conversion of AE to AG; in view of the large vibrational entropy contribution, the inevitable assumption of purely harmonic vibrations in both monomer and dimer is probably the largest, numerically. Since the relationship between the equilibrium constant and AG is exponential, it is clearly impossible to predict the overall composition of the vapor with any accuracy. Our estimated value of AG implies an equilibrium dimer concentration of 1.1 mol %, at 1171 K and 0.01 atm; while this is not really close to the experimentalvalue of 12.8 f 1.3 mol %, it is close to be within 1 order of magnitude. We feel this agreement is reasonable, in view of all the possible uncertainties; in addition to those already mentioned, we must consider whether the ED sample is at equilibrium, and what its effective temperature and pressure might be. So this reasonable agreement implies either a fortuitous cancellation of errors or that the estimate of the electronic dimer binding energy is reasonably accurate; it seems unlikely that the error could exceed say 20 kJ/mol. Monomer Vibrational Frequencies and Force Field. Most of the harmonic vibrational frequencies calculated for monomeric MgC12 in Table 2 vary over a rather narrow range. The lack of flexibility in the DZ basis is clearly seen by the perceptible decrease in the stretching frequencies caused by the addition of diffuse functions; this parallels the increase in bond length. Extension of the polarization space tends to decrease the bending frequency but has little effect on the stretching frequencies. It is noticeable that the influence of correlation is small, as the largest change from SCF to MP2 values with the largest basis for which calculation of the frequencies was feasible is only 4 cm-I, for VI. Agreement with the experimental frequencies is mixed; for V I it is relatively good, while the calculated v2 and v3 values are consistently higher than the experimental ones. Of course, in making these comparisons, the reader should remember that the experimental values for V I and v2 are obtained from matrix isolation experiments, and there may well be significant differences between gas-phase and matrix f r e q u e n c i e ~ .For ~ ~ v3 already the reported experimental matrix isolation values are scattered within a 18 cm-’ range. We call attention to the dramatic shift in the bending frequency for monomeric MgF2, from 249 cm-I in an “inert” argon matrix5 to only 160 cm-I in the gas phase.31 In contrast to this it is interesting to note that the ED data agree better with the calculated value of 117 cm-I for the bending frequency than with the experimental matrix isolation value of 88 or 93 cm-I. Dimer Vibrational Frequencies and Force Field. The size of the dimer prevented us from using large basis sets in the calculation of its vibrational frequencies, but the evidence in Table 3 suggests that the dimer’s frequencies are not sensitive to the theoretical method employed. Five bands have been assigned to the dimer, four of these match our calculated values astonishingly well, and the deviation for the fifth is only 20 cm-I. Considering the paucity of their data and the lack of precedents, we feel that the experimentalists displayed remarkable perception in making their partial assignment. It is interesting to note from Table 9 that the calculated force
Monomeric and Dimeric Magnesium Chloride constant for the stretching of the bridge bonds of the dimer is almost exactly half that of the terminal bond. It appears that this almost too simple behavior is found fairly generally in compounds which contain planar four-membered rings with terminal bonds, as a similar pattem is found in B2H6, Al2Cl6, and Fe2C14.18 We note the striking succZss of another simple model. Pauling’s bond order-bond length relation~hip~~ predicts that a half-bond should be 0.21 8, longer than a single bond, while we have determined the difference between the bridge and terminal bonds in dimeric MgC12 to be 0.175(5) 8, from ab initio computation or 0.174(&0.006) 8, from the ED experiment. Conclusion Magnesium dichloride has been studied in the gas phase by electron diffraction at 1171 K. At that temperature, the vapor is found to consist mostly of monomer, but an appreciable portion of dimer is also present (12.8 f 1.3 mol %). The monomer is linear and the rg bond length is 2.179 & 0.005 A. The structure of the dimer appears to be based on a puckered ring with two bridging chlorine atoms (C2” symmetry) if the ED data are analyzed assuming a rigid molecular model. Ab initio electronic structure calculations have also been performed on both monomeric and dimeric MgClz, using both SCF and MP2 levels of theory and a graded series of basis sets. Large basis sets containing as many as five sets of d-type functions and two sets of f-type functions are necessary to obtain converged predictions for the bond length at the MP2 level, though three d sets and one f set are sufficient for SCF calculations. The converged bond length at the SCF level of 2.173 8, is slightly larger than that found at the MP2 level (2.169 A), which is rather unusual. The MP2 value agrees well with the estimated equilibrium bond length of 2.163 zt 0.011 8, obtained in the ED analysis. We believe that the correlationinduced “shrinkage” of the Mg-Cl bond length is associated with polarization of the Mg 2p-like electrons in the field provided by the chlorine atoms. To describe this polarization correctly, tight d functions are needed in the Mg basis. Sophisticated analyses were undertaken of the ED data, using information obtained from the ab initio calculations about the potential energy surfaces of both monomeric and dimeric forms of MgCl2. The dimer has a planar ring at both SCF and MP2 levels of theory, though it is quite floppy as the lowest vibrational frequency, which is mainly the ring-puckering motion, is at only about 30 cm-’. This large-amplitude rather anharmonic motion for the dimer was modeled by a series of conformers, whose weights were determined by their relative energies. Relaxation of the other geometricalparameters during the ring puckering was found to be nonnegligible, but the bending motion of the monomer appears almost purely harmonic. This dynamic description of the dimer with a planar equilibrium structure gives an excellent fit to the ED data, showing that the puckered structure obtained in the standard analysis is an artifact of the large-amplitude vibrational motion. The bridge bonds in the dimer are 0.174 f 0.006 8, longer than the terminal bonds, while the latter are computed to be some 0.009 8, longer than those in the monomer. Normal coordinate analyses were undertaken for both the monomer and the dimer, and harmonic force fields are reported. This investigation amply demonstrated the great utility of a concerted application of precise electron diffraction data and high-level computational results for an accurate determination of molecular structure in which geometry and motion interweave in a high degree of complexity.
J. Phys. Chem., Vol. 99, No. 22, 1995 9071 Acknowledgment. We are grateful to Ms. Maria Kolonits for performing the electron diffraction experiment. We are indebted to Dr. Lise Hedberg for her gracious help and useful comments in applying the ASYM20 program. We thank Professors Istvfin Hargittai and Ken Hedberg for their comments and suggestions. The experimental part of this work was supported by the Hungarian Scientific Research Fund (OTKA T 014073). References and Notes (1) (a) Akishin, P. A.; Spiridonov, V. P. Kristallogr. 1957, 2, 475. (b) Kasparov, V. V.; Ezhov, Ju. S.; Rambidi, N. G. Zh. Srrukt. Khim. 1979, 20, 260. (2) Berkowitz, J; Marquart, J. R. J. Chem. Phys. 1962, 37, 1853. (3) (a) Hargittai, I.; Hargittai, M., Eds. Stereochemical Applications of Gus-PhaseElectron Dzfluction; VCH Publishers: New York, 1988; Vol. B; Chapter 9. (b) Hargittai, M. Coord. Chem. Rev. 1988, 91, 35. (4) (a) von Szentpaly, L.; Schwerdtfeger, P. Chem. Phys. Lett. 1990, 170,555. (b) Hassett, D. M.; Marsden, C. J. J . Chem. SOC.,Chem. Commun. 1990, 667. (c) DeKock, R. L.; Peterson, M. A.; T i m e r , L. K.; Baerends, E. J.; Vernooijs, P. Polyhedron 1990, 9, 1919. (d) Salzner, U.; Schleyer, P. v. R. Chem. Phys. Lett. 1990, 172, 461. (e) Dyke, J. M.; Wright, T. G. Chem. Phys. Lett. 1990, 169, 138. (f) Wright, T. G.; Lee, E. P. F.; Dyke, J. M. Mol. Phys. 1991, 73,941. (g) Seijo, L.; Baraandiaran, 2.;Huzinaga, S. J . Chem. Phys. 1991, 94, 3762. (h) Kaupp, M.; Schleyer, P. v. R.; Stoll, H.; Preuss, H. J . Am. Chem. SOC. 1991, 113, 6012. (i) Ramondo, F.; Bencivenni, L.; Spoliti, M. J . Mol. Struct. (THEOCHEM) 1992, 277, 171. ( 5 ) Lesiecki, M. L.; Nibler, J. W. J . Chem. Phys. 1976, 64, 871. (6) (a) Hargittai, I.; Tremmel, J.; Kolonits, M. HSI Hung. Sci. Instrum. 1980, 50, 31. (b) Hargittai, I.; Bohatka, S.; Tremmel, J.; Berecz, I. Ibid. 1980, 50, 51. (7) Tremmel, J.; Hargittai, I. J . Phys. E 1985, 18, 148. (8) Bonham, R. A.; Schafer, L. lntemational Tables for X-Ray Crystallography; Kynoch: Birmingham, England, 1974; Vol. 4, p 176 (coherent scattering factors). Tavard, C.; Nicolas, D.; Rouault, M. J . Chim. Phys., Phys.-Chim. Biol. 1967, 64, 540 (incoherent scattering factors). (9) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomberts, R.; Andres, J. L.; Raghawachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; DeFrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92; Gaussian Inc.: Pittsburgh, PA 15213, 1992. (10) Hassett, D. M.; Marsden, C. J. J . Mol. Struct. 1995, 346, 249. ‘(11) Huzinaga, S. Approximate Atomic Wavefunctions; Chemistry Department, University of Alberta, 1971. (12) Dunning, T. H.; Hay, P. J. Modem Theoretical Chemistry; Schaefer, H. F., Ed., Plenum Press: New York, 1977; Vol. 3, Chapter 1. (13) McLean, A. D.; Chandler, G. S., J . Chem. Phys. 1980, 73, 5639. (14) (a) Buchler, A,; Klemperer, W. J . Chem. Phys. 1958, 29, 121. (b) Randall, S. P.; Greene, F. T.; Margrave, J. L. J . Phys. Chem. 1959, 63, 758. (c) White, D.; Calder, G. V.; Hemple, S.; Mann, D. E. J . Chem. Phys. 1973, 59, 6645. (d) Cocke, D. L.; Chang, C. A,; Gingench, K. A. Appl. Spectrosc. 1973, 27, 260. (15) Hedberg, L.; Mills, I. M. J . Mol. Spectrosc. 1993, 160, 117. (16) Cyvin, S. J. Molecular Vibrations and Mean Square Amplitudes; Elsevier: Amsterdam, 1968. (17) Weltner, W. Jr. Adv. High Temp. Chem. 1969, 2, 85. (18) Frey, R. A.; Werder, R. D.; Gunthard, Hs. H, J. Mol. Spectrosc. 1970, 35, 260. (19) Hargittai, M.; Subbotina, N. Yu.; Kolonits, M.; Gershikov, A. G. J . Chem. Phys. 1991, 94, 7278. (20) Samdal, S. J . Mol. Struct. 1994, 318, 133. (21) Hargittai, M.; Veszprtmi, T.; Pasinszki, T. J . Mol. Struct. 1994, 326, 213. (22) Hargittai, M.; Hargittai, I. J . Chem. Phys. 1973, 59, 2513. (23) Hargittai, M.; Hargittai, I. Inr. J Quantum Chem. 1992, 44, 1057. (24) Hargittai, M.; Kolonits, M.; Knausz, D.; Hargittai, I. J. Chem. Phys. 1992, 96, 8980. (25) Bartell, L. S. J. Chem. Phys. 1979, 70, 4581. (26) Gershikov, A. G. Khim. Fiz. 1982, 1, 587. (27) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (28) See, for example, Hehre W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (29) Kuchitsu, K.; Morino, Y. Bull. Chem. SOC. Jpn. 1965, 38, 805. (30) See, for example, Jacox, M. E. J . Mol. Spectrosc. 1985, 113, 286. (31) Baikov, V. I. Opt. Spectrosc. 1967, 194. (32) Pauling, L. The Nature of the Chemical Bond; Come11 University Press: Ithaca, NY, 1960; p 239. JP9504027
