An ab Initio Molecular Orbital Study of Small Magnesium Dihalide

Aug 1, 1994 - Kelling J. Donald and Roald Hoffmann. Journal of the American Chemical Society 2006 128 (34), 11236-11249. Abstract | Full Text HTML ...
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J. Phys. Chem. 1994,98, 7823-7831

7823

An ab Initio Molecular Orbital Study of Small Magnesium Dihalide Clusters Jeff Axten, Mendel Trachtman, and Charles W. Bock’ Chemistry Department, Phildelphia College of Textiles and Science, Philadelphia, Pennsylvania 19144 Received: March 22, 1994; In Final Form: May 27, 1994’

The structures, frequencies, and stabilization energies of the magnesium dihalide dimers (MgX2)2 (X = F, C1, Br, and I) and trimers (MgX2)3 (X = F, C1) are investigated using ab initio molecular orbital techniques. Double-bridged (&) and triple-bridged (C3J dimers and bridged (&d) trimers are found to be local minima on the potential energy surfaces for all the magnesium dihalides, with the double-bridged dimers being consistently lower in energy than the corresponding triple-bridged dimers. The exothermicities of the dimerization reactions, 2MgX2 (MgX2)2 (D2h or C30),and the trimerization reactions, 3MgX2 (MgX2)s (&), generally decrease as the size of the halide increases. The computed frequencies of the dimers support the experimental spectral identification of these structures in magnesium dihalide vapors reported by Lesiecki and Nibler ( J . Chem. Phys. 1976, 64, 871).

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Introduction Solids comprising group 2A metal dihalides are well-known to vaporize at sufficiently high temperatures, with the vapors comprising monomers, MX2, dimers, (MX2)2, and higher polymers, (MX2),,.l-’ Standard structural models (VSEPR, ionic, valence-bond,etc.) all predict that gas-phase group 2A monomeric dihalides have linear configurations.8-10 Experimental and computational studies have verified that many of the alkalineearth dihalides, e.g., BeFz(g), MgClz(g), MgBrz(g), and CaC12(g), do indeed have linear structures.8Jl-16 Other studies, however, have revealed that some members of this family, e.g., BaFZ(g), BaClz(g), BaBrz(g), and SrFZ(g), are definitely nonlinear,lI-l7 and it now appears likely that the bonding throughout the group 2A dihalides is not strictly ionic; p orbitals are involved for Be and Mg and d orbitals are involved for Ca, Sr, and Ba.I4 Comparatively little is known about the structures of small clusters of any of the alkaline-earth dihalides. Using Knudseneffusion mass spectrometry, Saha et aLs have shown that calcium(11) iodide vapors contain both monomeric and dimeric units and that the dimerization reaction is approximately 46.1 kcal/mol exothermic, assuming a bridged structure with D2h symmetry for (CaI2)2. Calculations by Ramondo et al.7haveshown that doublebridged structures with DZh symmetry and triple-bridged structures with C3” symmetry are stable for (BeF2)2and (MgF2)z at the RHF/3-21G*//RHF/3-21G* and RHF/6-31G*//RHF/ 6-3 lG* computational levels. The double-bridged forms of (BeF2)2 and (MgF2)Z were found to be lower in energy than the corresponding triple-bridged forms at the RHF/6-3 lG*//RHF/ 6-31G* level by 39.9 and 15.8 kcal/mol, respectively. At the RHF/6-3 lG*//RHF/4-21G* computational level, dissociation of the double-bridged forms of Be2F4 and MgzF4 into two monomers requires 44.8 and 70.3 kcal/mol, respectively. Bridged dimer structures with C2” symmetry were found to be unstable at the RHF/3-21G*//RHF/3-2lGs level for both (BeF2)2 and (MgF2)2. The effects of electron correlation were not included in this study.’ The present paper initiates a comprehensive study of small alkaline-earth dihalide clusters by presenting the results of a6 initio calculations of the structures, stabilization energies, and vibrational frequencies of selected magnesium dihalide dimers and trimers. Energy differences among various forms of the dimers and dissociation energies of the dimers and trimers are reported. Computed vibrational spectra are compared with observed spectral features of magnesium dihalide vapors trapped Abstract published in Aduance ACS Abstracts, July 15, 1994.

0022-3654/94/2098-7823%04.50/0

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in various matrices4 Effects of the basis set and computational level in the evaluation of the geometrical parameters and the stabilization energiesof the dimers are also considered. The results of high-level calculations on monomeric magnesium dihalides are also reported in order to evaluate the relative stabilities of the various dimers and trimers toward dissociation into monomers and to resolve some remaining disputes about the properties of these molecules. Computational Methods A6 initio calculations were performed by using the GAUSSIAN 92 package of programs on a Silicon Graphics IRIS 4D/35 computer.18 Gradient optimizations were employed throughout using split-valence 6-3 lG* basis setslg for the magnesium, fluorine, and chlorine atoms and split-valence Huzinaga and basis sets20 for the bromine and iodine atoms, respectively. For convenience, we shall refer to these basis sets for molecules containing either Br and/or I as HUZSP*.21 Initial optimizations were performed using HartreeFock (HF) theory, but many structures were subsequently reoptimized to include the effects of electron correlation using second-order Maller-Plesset (MP2) perturbation theory with all the orbitals active, Le., MP2(FULL).22 Vibrational frequency analyses were performed for all structures at the R H F level and for selected monomeric dihalides at the MP2 level in order to determine thermal corrections for reaction energies and to verify that the computed structures were indeed local minima on the potential energy surfaces. In many cases, single-point calculations using up to fourth-order Mdler-Plesset perturbation theory with the innershell orbitals frozen, i.e., MP4SDTQ(FC), were employed with avariety of modified basis sets inorder to estimatevarious reaction energies. Results and Discussion Total molecular energies for selected monomeric, dimeric, and trimeric magnesium dihalides at a variety of computational levels are given in Table 1, and the computed geometries are shown in Figures 1-3. In a few instances, experimental bond lengths are available for the monomericunits, and these are included in Figure 1. In all cases, the structures in Figures 1-3 have been verified to be local minima or first-order transition states on their respective potential energy surfaces at the R H F computational level using the 6-31G* or HUZSP* basis sets. Computed vibrational frequencies of the monomers, dimers, and trimers are given in Table 2 and, wherepossible, compared with experiment. It should 0 1994 American Chemical Society

7824

The Journal of Physical Chemistry, Vol. 98, No. 32, I994

U

Axten et al.

Small Magnesium Dihalide Clusters

The Journal of Physical Chemistry, Vol. 98, No. 32, 1994 7825 F r M 9 - F I1.7441 (1.753) (1.763)

CI

2.192 MS-CI 12.1821

Br

2.332 12.3241

Mg

I

2.557 12.5431

Mg

CI

Br

I

-Mg -F 1.720

2.196 12.1861

Br

2.331

Br

2.335

11.7411

Mg

2.193

'I

F

Mg 1.721 F Figure 1. Calculated magnesiumdihalide monomer structures. The bond lengths are given in angstroms and the bond angles in degrees. Computational levels: RHF/6-31G*//RHF/6-31G* or RHF/HUZSP*/ /RHF/HUZSP*, [MP2(FULL)/6-3 1G*// [MP2(FULL)/6-3 1G* or MP2(FULL)/HUZSP*//MP2(FULL)HUZSP*],(MP2(FULL)/631 lG(ZDF)//MPZ(FULL)/6-31 lG(2DF)), and (MP2(FULL)/6-311+G(2D)//MP2(FULL)/6-31 1+G(2D)). Experimentalvalues are given in angle brackets.

I

2.558

be noted that the computed vibrational frequencies are not directly of spectroscopic q ~ a l i t y ; nevertheless, ~3 the computed shifts from monomers to dimers should help in the experimental assignments of the fundamental frequencies. Energy differences between various forms of the dimers are given in Table 3. Dimerization and trimerization reaction enthalpies are summarized in Table 4 at 298 K and at higher temperatures in Table 1 s of the supplementary material. A. Magnesium Dihalide Monomers. At both the RHF/631G*(HUZSP*) and MP2(FULL)/6-31G*(HUZSP1) computational levels, linear forms of all the monomeric magnesium dihalides, MgX2, and mixed dihalides, MgXX', were found to be local minima on their respective potential energy surfaces; see Figure 1. Repeated attempts to locate lower energy bent structures failed, inevitably producing linear structures. For the MgX2 structures (X = F, C1, Br, I), this linearity of the '2, ground state is in agreement with the most recent experimental evidence4.8JC-12 as well as the recent calculations of Kaupp et al.,14 in which all the beryllium and magnesium dihalides were found to be linear. There is apparently no experimental evidence concerning the structures of the mixed magnesium dihalides, but our calculations would suggest they are also linear. As can be seen in Figure 1 and Table 2A, the predicted Mg-X bond lengths and vibrational frequencies computed at the RHF/ 6-31G*(HUZSP*) or MP2/6-31G*(HUZSP*) level of the magnesium dihalide monomers are in reasonable agreement with the experimental data that are currently available. As one might anticipate, however, the greatest discrepanciesbetween experiment and calculation at these computational levels occur for MgF2. For example, at the MP2( FULL) / 6-3 1G*/ / MP2( FULL) / 631G* level, the predicted Mg-F bond length is -0.026 A shorter than the experimental value,Z4 even though the calculated MgC1 bond length in MgCl2 at the same computational level is in excellent agreement with the most recent experimental value;25 see Figure 1. (Unfortunately, the experimental Mg-Br bond length in MgBrz has a large uncertainty associated with it,26and no experimental value is currently available for the Mg-I bond length in Mg12.) Furthermore, at both the RHF/6-31G* and

Axten et al.

7826 The Journal of Physical Chemistry, Vol. 98, No. 32, 1994

2.357

1T.S.l

2R

-I

2.218 12.1'161

2.576

/'\

c'

2E

Figure 2. Calculated magnesium dihalide dimer structures. The bond lengths are given in angstroms and the bond angles in degrees. Computational or RHF/HUZSP*//RHF/HUZSP* and [MP2(FULL)/6-31G*//[MP2(FULL)/6-31GS or MPZ(FULL)/ levels: RHF/6-31GS//RHF/6-31G*

HUZSP*//MP2(FULL)HUZSPt]. MP2(FULL)/6-31G* computational levels, the calculated frequency of the unsymmetrical Mg-F stretching mode is significantly higher than the reported experimental v a l ~ e s ,and 3 ~ the ~~~~ bending frequency differs significantly from the experimental value suggested by Lesiecki and Nibler: although it is in good agreement with the much lower value reported by Baikov;Z7 see Table 3A. Indeed, there was even some early controversy concerning the linearity of MgFz(g), with indications that this molecule may have a bent CZ, structure.28.29 To determine if higher level calculations might alter the linearity of this particular magnesium dihalide, we carried out an optimization and frequency analysis at the MP2(FULL)/6-3 1 lH(2DF)//MP2(FULL)/6311G(2DF) level. The linear form of MgFl remains a local minima on the potential energy surface a t this computational level. However, although the Mg-F bond length increases somewhat, it remains -0.017 A below the most recent experimental value of 1.77(1) A.Z4 A further optimization was also

CI

Figure 3. Calculated magnesium difluoride and dichloride trimer structures. The bond lengths are given in angstroms and the bond

angles in degrees. Computational level: RHF/6-3lG*//RHF/ 6-31GS.

The Journal of Physical Chemistry, Vol. 98, No. 32, 1994 1821

Small Magnesium Dihalide Clusters TABLE 2

Computed Frequencies of Selected Monomeric, Dimeric, and Trimeric Dibalides’

symmetry

A. Computed Monomeric Dihalide Frequencies, cm-1 MgCh MgBr2 MgI2 MgFCl

MgFz

E,, --

962.3 [920.3] [906.6] (879.9) (842,825)b 613.8 [587.2] (576.1) (558.2) (550)e 150.3 [ 150.31 (158.7) (156.7) (249,160)’

E,

TU

625.9 [636.1]

538.9 [549.0]

475.4

(601)‘ 325.7 [329.0]

(497)‘ 201.6 [202.7]

(445)e 143.9

(327)c 118.1 [ 1 1 2.21

(198)c 101.1 [102.3]

(148)‘ 89.2

(93)

(82)

(56)

MgFBr

MgFI

MgClBr

862.2 [837.8]

849.2

840.5

589.5

408.2

319.6

272.8

259.8

133.3

126.3

109.7

[410.71

B. Computed Dimeric Dibridged (&h)

142.4 [138.0]

Magnesium Dihalide Frequencies, cm-1

symmetry FMg(pF2)MgF ClMg(pC12)MgCl BrMg(pBr2)MgBr IMg(pI2)MgI FMg(pCI2)MgF ClMg(pF2)MgCl symmetry ClMg(pFC1)MgF

863.6 523.2 276.0 837.9 490.2 534.6 109.5 468.9 158.3 284.4 53.8 131.7

B1u B2u B3g B3u B2E

552.7 288.5 144.2 528.4 254.3 37 1 .O 62.6 275.4 90.4 166.0 29.3 107.3

405.9 131.3 66.5 384.5 114.5 280.8 32.1 205.2 47.9 118.8 12.1 94.9

468.7 182.2 95.3 443.6 159.8 317.9 42.5 232.7 64.1 138.9 18.5 105.0

828.9 310.4 167.6 816.1 287.0 374.5 96.8 273.3 114.1 181.7 39.6 125.7

664.7 473.7 213.1 639.0 379.7 531.1 68.8 471.2 124.8 273.2 39.2 117.7

A’

839.4 623.2 505.7 453.3 335.6 254.3 201.9 123.1 77.2 228.8 120.6 44.7

A”

B’. Computed Dimeric Tribridged (C3J Magnesium Dihalide Frequencies symmetry AI

E

Mg(pS)MgF

Mg (rCMMgCI

Mg(pBr3)MgBr

Mg(pI3)MgI

819.3 656.6 431.6 353.1 613.6 312.0 28 1.9 133.4

523.7 390.9 246.7 190.2 405.3 165.8 142.2 76.3

448.7 314.5 166.5 124.0 334.5 131.0 97.5 49.7

390.4 265.2 120.9 89.4 294.2 109.7 70.0 36.1

C. Computed Trimeric Magnesium Dihalide Frequencies, cm-1 symmetry AI

B2

E

BI

FMg(pFdMg(pF2)MgF

C1Mg(rClz)Mg(ccClz)MgCl

850.7 514.9 473.6 182.8 846.1 665.5 509.5 343.3 538.5 468.8 264.1 139.0 99.3 31.3 78.2

541.4 283.1 244.9 95.3 538.8 410.1 274.4 180.1 370.3 276.0 149.2 93.0 67.0 18.2 49.0

Computational levels: RHF/6-31GS//RHF/6-31G* or RHF/HUZSP*//RHF/HUZSP*,[MP2(FULL/6-31G*//MP2(FULL)/6-31GS or MP2(FlJLL)/HUZSP*//MP2(FULL)/HUZSP+], (MP2(FULL)/6-31 lG(2DF)//MP2(FULL)/6-311G(2DF)), and (MP2(FULL)/6-311+G(2D)/ /MP2(FULL)/6-311+G(2D)).Experimental values, where available, are given in angle brackets. The first experimental value listed in the angle brackets is from Lesiecki and Niblefi in an argon matrix, and the second value listed is from Baikov.27 e The experimental values are from Lesiecki and Nibler4 in an argon matrix.

performed at the MP2(FULL)/6-3 1 l+G(2D)//MPZ(FULL)/ 6-31 1+G(2D) level, which includes diffuse sp functions. Such functions are likely to be important in this case since the fluorines are expected to carry a high charge density. The Mg-F bond length is now found to be 1.763 A, which is only -0.007 A below the experimental value.24 Considering the different physical interpretations of the experimental and computed results, this is

certainly acceptable agreement. Furthermore, the computed unsymmetrical Mg-F stretching frequency, although still somewhat high, is in much better agreement with the experimental re~ults;4.2~ see Table 2. However, the F-Mg-F bending mode remains 100 cm-1 below the experimental value suggested by Lesiecki and Nibler: 249 cm-1, but in excellent agreement with the value reported by Baikov, 160 f 3 cm-1.27 It is interesting

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7828 The Journal of Physical Chemistry, Vol. 98, No. 32, 1994

should be attributed to an MgF2 dimer or higher polymer and not the monomer (oide infra). In the case of MgI2, separate MP2/HUZSP* optimizations were performed with the core orbitals frozen and with all the orbitals active. If all the orbitals are active, the computed Mg-I bond length is -0.03 Ashorter than with thecoreorbitals frozen, see Figure 1, showing that inner-shell correlation effects have significant geometrical consequences with this rather truncated basis set for iodine. The computed structures of severalmixed magnesium dihalides, XMgX', are also given in Figure 1, and the computed frequencies are given in Table 2A. It is interesting to note that the halide X' has relatively little influence on the computed Mg-X bond length; e.g., the Mg-F bond length in FMgX' changes by only -0.003 A as X' ranges from F to Br. The predicted trends among the dihalide and mixed dihalide frequencies are quite satisfactory and should help in the eventual experimental indentification of these mixed structures. .B. Magnesium Dihalide Dimers. Following Ramondo et a1.2 bridged structures with the forms XMg(p-X2)MgX (&), XMg(p-X,)Mg (Go), and X2Mg(p-X2)Mg (C,) were considered for the magnesium dihalide dimers; see Figure 2. In all cases, the

TABLE 3: Energy Differences (kcal/mol) between Dibridged (&), XMg(p-XdMgX, and Tribridged (C',), XMg(p-Xj)Mg, Magnesium Dihaiide Dimers level

RHF/*//RHF/* MP2/*//RHF/* MP3/*//RHF/* MP4(SDQ)/*//RHF/* MP4(SDTQ)/*//RHF/*

MP2(FULL)/*//MP2(FULL)/* MP2/6-31 1+GS//RHF/6-31G* MP2(FULL)/6-3 1l+G*//RHF/6-31G*

Fa

Cla

BrO

I'

15.8 15.3 14.7 15.4 15.4 13.5 16.7 16.3

16.3 14.0 14.4 14.5 14.1 12.9 13.4 13.2

16.3 12.5 13.4

16.1 8.5

Eidibridged) - E(tribridged). RHF/*//RHF/* designates nonrelativistic all-electron-restricted Hartree-Fockcalculations using 6-3 lG* basis sets for the Mg, F, and C1 atoms and HUZSP* basis sets for the Brand I atoms. Br: (4,3,3,2,1/4,2,1/4,*). I: (4,3,3,3,2,1/4,3,3,2,1/ 4,3,*). MPndenotes Molller-Plesset nth-order perturbation calculations with the core orbitals frozen unless FULL is specified, which indicates that all the orbitals are active.

to note that the computed bending frequency is nearly independent of the level of calculation and the basis set, see Table 2, and in good agreement with other high-levelcalculation~.~~.20.3~ It seems quite likely that the band structure in the spectra at 249 cm-I TABLE 4

Axten et al.

AE and AH(298 K) for the Magnesium Dihalide Dimerization and Trimerization Reactions (kcal/mol) level

-70.2 -71.1 -72.2 -71.2 MP4(SDQ)/6-3lG*//RHF/6-3lG* -71.2 MP4(SDTQ)/6-3lG*//RHF/6-3lG* MP2(FULL)/6-31G*//MP2(FULL)/6-3lG* -72.9 MP2( FC)/6-3 1l+G*//RHF/6-3 1G* -63.5 -64.2 MP2(FULL)/6-3 1 l+G*//RHF/6-3 1G*

-69.5 -70.3 -71.4 -70.4 -70.5 -72.2 -62.8 -63.4

RHF/6-31G*//RHF/6-31G* MP2/6-3 1G*//RHF/6-31GS MP3/6-3 1G*//RHF/6-31GS

2MgC12ClMg(pC12)MgCl

-54.4 -55.8 -57.5 -55.8 -55.8 -59.4 -46.8 -47.8

-53.8 -55.1 -56.8 -55.1 -55.1 -58.8 -46.2 -47.1

2MgC12Mg(pc-CMMgC1

-69.1 -70.2 -71.4 -70.2 -70.1 -72.3 -62.5 -64.2

-68.4 -69.5 -70.7 -69.5 -69.4 -7 1.6 -61.8 -63.5

2MgFC1ClMgb-ClF)MgF

-31.6 -44.1 -43.9 -43.7 -44.3 -46.0 -42.2 -42.6

-37.0 -43.6 -43.3 -43.1 -43.7 -45.4 -41.7 -42.1

-

MgC12 + MgF2 ClMg(pC1F)MgF

level

AE

AH

AE

AH

AE

AH

AE

AH

RHF/6-3 lG*//RHF/6-3 1G* MP2/6-3 lG*//RHF/6-3 lG* MP3/6-31GS//RHF/6-3 1G* MP4(SDQ)/6-3 lG*//RHF/6-3 1G* MP4(SDTQ)/6-3 lG*//RHF/6-31G* MP2(FULL)/6-3 lG*//MP2(FULL)/6-31G* MP2(FC)/6-3 11+G*//RHF/6-3 1G* MP2(FULL)/6-3 1 1+G*//RHF/6-3 1G*

-36.1 -42.9 -42.8 -42.4 -42.9 -44.8 -42.1 -42.5

-35.5 -42.3 -42.2 -41.8 -42.3 -44.2 -41.5 -41.9

-19.8 -28.9 -28.3 -27.9 -28.8 -31.9 -28.7 -29.3

-19.2 -28.4 -27.8 -27.3 -28.3 -31.3 -28.2 -28.7

-54.5 -58.3 -58.7 -58.1 -58.4 -59.7 -54.1 -54.6

-53.9 -57.6 -58.0 -58.4 -57.7 -59.0 -53.4 -53.9

-55.5 -59.2 -59.7 -59.7 -59.1 -60.3 -54.3 -54.8

-54.8 -58.6 59.0 59.0 -58.5 -59.6 -53.6 -54.1

2MgBr2

-

BrMg(p-Br2)MgE

2MgBr2

-

Mg(pBr3)MgBr

level

AE

AH

AE

AH

RHF/HUZSP*//RHF/HUZSP* MPZ/HUZSP*//RHF/HUZSP* MP3/HUZSP*//RHF/HUZSP*

-33.0 -42.0 -40.8

-32.4 -41.4 -40.2

-16.8 -29.5 -27.4

-16.2 -28.9 -26.9

2MgI2 level RHF/HUZSP*//RHF/HUZSP* MP2/HUZSP*//RHF/HUZSP*

AE -26.7 -29.3

+

IMg(pI2)MgI

ZMgI-Mg(p-13)MgI

AH

AE

AH

-26.2 -28.7

-10.6 -20.7

-10.1 -20.2

level

AE

AH

RHF/6-3 lG*//RHF/6-3 1G* MP2/6-3 lG*//RHF/6-31G* MP2(FULL)/6-3 11+G*//RHF/6-3 1G*

-142.1 -143.8 -1 30.2

-1 39.7 -141.5 -127.8

3MgC12

+

ClMg(p-C12)Mg(p-C12)MgCl

level

AE

ryi

RHF/6-31G*//RHF/6-3 1G* MP2/6-31GS//RHF/6-31G* MP2(FULL)/6-3 11+G*//RHF/6-3 1G*

-74.2 -88.3 -88.5

-12.1 -86.2 -86.5

Small Magnesium Dihalide Clusters double-bridged (&) and triple-bridged (Cj,)forms are local mimina on the respective potential energy surfaces at the RHF/ 6-3 lG*(HUZSP*)//RHF/6-3 1G*(HUZSP*) computational level. As expected, the computed values of specific geometrical parameters depend to some extent on whether the optimization was carried out at the R H F or MP2 level. However, in cases where comparisons can be made, differences in the calculated geometricalparameters between the correspondingdouble-bridged and triple-bridged forms, as well as between the corresponding monomers and dimers, are generally consistent at both computational levels. No experimental structural data are currently available for any of the magnesium dihalide dimers. The calculated MgeMg distances are significantly shorter in the triple-bridged forms than in the corresponding double-bridged forms at both the R H F and MP2 levels; see Figure 2A-D. The Mg-X bond lengths in the bridge and the distribution of charge in the triple-bridged configurations suggest significant contributions from ionic valence bond structures of the form MgXs-MgX+. It is also interesting to note that asymmetries of the M-X bonds in the bridge of the triple-bridged forms become more pronounced as the size of the halide increases. The double-bridged (&h) forms for all the magnesium dihalide dimers are lower in energy than the corresponding triple-bridged (C3")forms; see Table 1. Perhaps this is only to be expected since the linear monomeric units need to undergo significantly greater distortion to form the more compact triple-bridged structures than the corresponding double-bridged structures; compare Figures 1 and 2. Calculated energy differences between the double- and triple-bridged forms are given in Table 3 at a variety of computational levels. As long as correlation effects are included, these energy differences do not depend dramatically on the basis set or computational level. As can be seen from this table, the energy difference between the double-bridged and the triple-bridged forms decreases as the size of the halide increases. It will be interesting to see if this trend remains as more sophisticated calculations become possible, particularly on the bromine and iodine dimers. A bridged structure of the magnesium difluoride dimer with &symmetry, Mg(p-Fz)MgFz, proved to be a first-order transition state connecting two equivalent forms of the triple-bridged (C3") configurationat the RHF/6-31G*//RHF/6-3 lG* computational level. At the MP2(FULL)/6-3 1l+G*//RHF/6-31G* level, this transition state is 36.9 kcal/mol higher in energy than the triplebridged structure. The Mg-F bond lengths in the bridge of this transition state are quite asymmetric, see Figure 2A, and the structure resembles a MgF2-eMgF2 adduct. Indeed, at the MP2(FULL)/6-31 l+G*//RHF/6-31G* level, the CZ, structure is only 10.9 kcal/mol below the energy of two separated MgF2 molecules. Attempts at locating similar C , transition states for Mg2C14and MgzBr4 yielded two separated monomeric units. Consequently, no attempt was made to search for the analogous C2, structure for iodine. Optimizations were also performed on two types of mixed double-bridged structures, XMg(pX'2)mgX (&) and XMg(p-XX' )MgX' (Cs),X, X' = F and C1; see Figure 2E. Frequency analyses showed that all of these isomers are indeed stable. The lowest energy structure contains the difluoro bridge, and at the MP2(FULL)/6-3 1l+G*//RHF/6-3 lG* computational level, the structures FMg(p-F,Cl)MgCl and FMg(pCl2)MgF are higher in energy by 9.6 and 21.6 kcal/mol, respectively. The frequencies of the double-bridged and triple-bridged magnesium dihalide dimers calculated at the RHF/6-3 1G*(HUZSP*)//RHF/6-3 lG*(HUZSP*) computational level are given in sections B and B' of Table 2, respectively. As the size of the halide increases, the predicted monotonic trends among the computed frequencies of the double-bridged forms are quite satisfactory, even though the basis set changes somewhat from

-

The Journal of Physical Chemistry, Vol. 98, No. 32, 1994 7829 6-31G* to HUZSP*. Although the fundamental modes of these structures have not yet been assigned experimentally, some observed spectral features have been attributed to the dimers.3.4 Consider first (MgF2)2. Thecomputed frequencies of the doublebridgedformof (MgF2)2inTable2at theRHF/6-31G*//RHF/ 6-31G* level are in fair agreement with those calculated by Ramondo et al.' at the RHF/3-31G*//RHF/3-21G* level. To make a more direct comparison with the observed spectra, however, it will be necessary to make some adjustments to the computed frequencies. For the MgF2 monomer, it is clear that the 2, and 2, stretching frequencies, calculated at the RHF/ 6-31G* level, are too high and require scale factors of approximately 0.875 and 0.896, respectively, where we have used the experimental assignments of Lesiecki and Nibler4 in an argon matrix; see Table 2A. These scale factors are quite close to the standard32 scaling of 0.9.33 Using these scale factors for the corresponding terminal Mg-F stretching modes in the doublebridged form of the dimer yields stretching frequencies of approximately 733 and 774 cm-l, which lends support to the assignments of the observed bands in the range 735-758 cm-1 to dimers and higher polymers of M ~ F zThe . ~ four Mg-F stretching modes involving the bridging fluorine atoms have (unscaled) calculated frequencies of 534,523,490, and 469 cm-l, supporting the suggestions of Lesiecki and Nibler that spectral features in the 450-500-cm-1 range are due to magnesium difluoride dimers! It is also interesting to note that two of the computed dimer frequencies, 276.0 and 284.4 cm-1, would probably occur in the experimental region where Lesiecki and Nibler assigned the ?T, bending mode of the monomer MgF2.4 Next we turn to (MgC12)~. Fortunately, the computed frequencies of the MgC12 monomer are in reasonable agreement with the observed values in an argon matrix with no scaling; see Table 2Ae4The computed stretching frequencies of the terminal Mg-Cl bonds in the double-bridged form of (MgC12)~are 553 and 528 cm-1, supporting the assignment of the observed band at -514 cm-1 to (MgC12)2.4 The computed Mg-Cl stretching modes involvingthe bridging C1 atoms are 37 1,288,275,and 254 cm-1, which correlate well with the band structure observed in the range 260-372 cm-1, also assigned by Lesiecki and Nibler4 to the dimer. For the monomers MgBr2 and MgI2, the computed frequencies are again in reasonable agreement with the observed values. Lesiecki and Nibler4 attribute bands observed at 436 and 387 cm-1 to the dimers (MgBr2)~and (MgI2)2, respectively. The calculated values for the terminal Mg-Br stretching modes of the double-bridged form of (MgBr& are 469 and 444 cm-1, and the correspondingcalculatedvalues for the Mg-I modes in (MgI2)2 are 405 and 385 cm-'. Thus, it seems likely that the monomers and dimers of all the magnesium dihalides have been observed spectroscopicallyin magnesium dihalide vapors trapped in various solid matrices.3~~ Reactions enthalpies for the dimerization reactions 2MgX2

+

XMg(p-X,)MgX

and

are given for X = F, C1, Br, and I in Table 4 at 298 K and at 800 and 1000Kin Table 1 s of the supplementary material. These reactions are exothermic for both forms of all the dimers. Since there are no experimental data for any of these reactions, it is important to establish the sensitivity of the calculated reaction enthalpies to changes in the basis set and/or computational level. Consider first the cases with X = F and C1, where the number of electrons is smaller and, consequently, a broader range of calculations is possible. As can be seen in Table 4, it is apparently adequate to include correlation effects at the MP2 level in the

Axten et al.

7830 The Journal of Physical Chemistry, Vol. 98, No. 32, 1994 description of these dimerization processes, since differences between the reaction enthalpies at the MP4SDTQ(FC)/6-3 1G* and MP2(FC)/6-31G* computational levels are at most a few tenths of a kilocalorie/mole. This is important since MP4SDTQ(FC) level calculations on the analogous bromine and iodine dimers were too large for the current configurationof our computer system. Including diffuse sp functions in the calculations at the MP2(FC)/6-311+G* level decreased the exothermicity of the double-bridgedand triple-bridged dimerization reactions involving fluorine by 7.6 and 8.9 kcal/mol, respectively, compared to calculations at the MP2(FC)/6-3 1G* level, emphasizing again the need to include diffuse functions in calculations that involve magnesium difluoride monomers and dimers. Including similar diffuse functions in the analogous chlorine calculations reduces the corresponding enthalpy changes by only 0.8 and 0.2 kcal/ mol, suggesting that diffuse functions are less important for the larger halides. Comparing the MP2(FULL)/6-311+G* and MP2(FC)/6-311+GS calculations of the enthalpy changes for both the fluorine and chlorine dimerizations shows that keeping the core orbitals fued is also adequate for describing these processes. A crude estimate of basis set superposition errors (BSSE)34in the magnesiumdifluoridedimerizationto the double-bridgedform was obtained by computing the energy difference between an MgF2 monomer at the dimer geometry with and without the basis functions on the second monomeric unit. At the MP2(FULL)/6-3 11+G* computational level, this energy difference amounts to -4.1 kcal/mol. While this suggests that the calculated exothermicities in Table 4 may be somewhat high, it is unlikely to alter the conclusion that the magnesium dihalide dimerization reactions are significantly exothermic. Table 4 clearly predicts that the dimerization enthalpies decrease for both the double-bridged and triple-bridged forms as the size of the halide increases. The exothermicity of the magnesium dichloride dimerization is -20 kcal/mol lower than the difluoride dimerization. The dichloride and dibromide dimerization enthalpies are quite similar, but the iodide dimerization is 10 kcal/mol less exothermic. The enthalpies for the mixed double-bridged dimerization reactions

-

ClMg(pFJMgC1 2MgFCl- ClMg(p-F,Cl)MgF FMg(r-Cl2)MgF

(3) (4) (5)

are quite interesting; see Table 4. The enthalpy changes for reactions 3 and 5 are within a few lengths of a kilocalorie/mole of the enthalpy changes of the dimerization reactions for MgF2 and MgC12, respectively, while the enthalpy change for the formation of the mixed bridged structure in reaction 4 is nearly the average of the enthalpy changes for reactions 3 and 5. This suggeststhat enthalpy changes for the reactions MgXX’ + MgYY’ X’Mg(p-X,Y)MgY’ are determined to a large extent by the atoms in the bridge. This is further supported by noting that the enthalpies for the two reactions

-

2MgFCl- ClMg(pC1,F)MgF MgF2

+ MgCl2

-m

ClMg(M-Cl,F)MgF

(6) (7)

are computed to be the same to within a few tenths of a kilocalorie/ mole; see Table 4. C. Magnesium DihalideTrimers. Only conformers of (MgF2)3 and (MgC12)3 with Dusymmetry were considered; see Figure 3. Beryllium analogues of these structures are well-known.* As can be seen, only a slight asymmetry appears in the bridging Mg-F and Mg-Cl bonds, with one of the bridging bonds being longer

and one being shorter in the trimer than in the corresponding double-bridged dimer. The terminal Mg-X bonds (X = F, Cl) are nearly the same and the M g M g distances are slightlyshorter in thetrimers thanin thecorrespondingDDdimers. Thecomputed positivechargeon the central magnesium atom which isconnected to four fluorine atoms is lower than the positive charge on the outer magnesium atoms which are connected to only three fluorine atoms. The computed frequenciesof the two trimers are given in Table 2C. The two terminal Mg-X (X= F, Cl) stretching frequencies are now separated by less than 5 cm-1 and lie between the two correspondingfrequenciesof the dimers. Comparing the observed spectra of the difluoride and dichloride vapors with the computed frequencies of the trimers, see Table 2C, suggests that lesiecki and Niblel.4 probably trapped trimers as well as dimers in their matrix isolation studies. The calculated enthalpies for the trimerization reactions for (MgF2)s and (MgCl2)3 are given in Table 4 at the MP2(FULL)/ 6-31 1+GS//RHF/6-31G* computational level. The trimerization enthalpy for MgF2 is -40.0 kcal/mol greater than the corresponding trimerization enthalpy for MgC12. Both trimerization reaction enthalpies are reasonably close to twice the dimerization reaction enthalpies, computed at the same level. However, it is worth pointing out that the trimerization reaction enthalpy for MgF2 is -2.0 kcal/mol more exothermic then twice the dimerization reaction enthalpy, whereas for MgClz the trimerization reaction enthalpy is 7.0 kcal/mol less exothermic than twice the dimerization enthalpy. It will be interesting to see if higher level calculations support this finding and whether this trend continues for the larger halides.

-

Concluding Remarks Heating solid magnesium dihalides produces vapors containing a rich mixture of monomers, dimers, and higher polymers. Comparing the computed frequencies of the monomers, dimers, and trimers with the experimental spectra of trapped magnesium dihalide vapors suggests that dimers (and most likely trimers) have already been observed e~perimentally,’.~although they have not yet been fully characterized. The molecular orbital calculations reported above support double-bridged structures with DZh symmetry for all the magnesium dihalide dimers. Triply-bridged structures with C3usymmetry are also stable but higher in energy, although the energy difference decreases as the size of the halide increases. Bridged CZ,structures, however, are apparently not stable for any of these dimers. It will be interesting to see if double-bridged D u forms for other group 2A dihalide dimers are always more stable than triple-bridged (&) forms and whether dimeric CZ,structures are stable species for any alkaline-earth dihalides. One might speculate that if the stable form of a monomer is bent rather than linear, C,, and Cb structures of the dimers may be less strained and, thus, play a more important role in the mix of structures in the vapor phase. Dimerization reactions for all the magnesium dihalides are favorable, but the reaction enthalpies decrease as the size of the halide increases. Trimers of MgF2 and MgClz with Dusymmetry are found to be stable species, and the trimerization enthalpy of MgF2 is calculated to be -40 kcal/mol greater than that of MgC12. Supplementary Material Available: Dimerization and trimerization reaction enthalpies at high temperatures (1 page). Ordering information is given on any masthead page. References and Notes (1) Snelson, A. J . Chem. P h p . 1970, 70, 3208. (2) Snelson, A.; Cyvin, B. N.; Cyvin, S.J. Z . Anorg. Allg. Chem. 1974, 10, 206. ( 3 ) Hauge,R. H.;Margrave.J. L.;Kana’an,A. S . J . Chem.Soc.,Faraday Trans. 2 1975, 71, 1082.

Small Magnesium Dihalide Clusters (4) (5) 1001. (6) (7) 171.

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