A density functional treatment of methylmagnesium halides

THEO CHEM Journal of Molecular Structure (Theochem) 333 (1995) 147-152

A density functional

treatment

Lawrence Department

qf Chemistry,

M. Pratt*, Clark Atlanta

of methylmagnesium

halides

Ishrat M. Khan* Universify. Atlanta,

GA 30314, USA

Received 18 February 1994;accepted 30 June 1994

Abstract Density functional calculations were performed on the unsolvated methylmagnesium fluoride, chloride, and bromide. The calculations show that each of these species exists as halide bridging dimer. The fluoride Grignard has the largest dimerization energy of the three, which is consistent with experimental studies of solvated systems. Other structural isomers of the methylmagnesium chloride and bromide dimers were shown to be thermally accessible at 300 K, and may exist as reactive intermediates.

1. Introduction Grignard reagents and the corresponding organolithium reagents are among the most important synthetic reagents for carbonPcarbon bond formation in organic synthesis. Although the solution structures of many alkyllithium compounds have been determined by lithium and carbon NMR coupling, this technique is not useful for determination of the Grignard solution structure due to the large magnesium quadrupole moment. As a result, indirect methods have been used to determine the molecular structure of alkylmagnesium compounds in solution. These techniques, such as colligative property measurements, proton NMR, and vibrational spectroscopy, have shown that simple alkylmagnesium chlorides and bromides exist in a monomeric form in THF [l] and triethylamine [2], as either a monomer or dimer in ethyl ether [3-51, and as a dimer in less polar solvents [6]. In contrast, the simple alkylmagnesium fluorides exist only as * Corresponding authors.

dimers in ethereal solvents [7,8]. The Schlenk equilibrium between the alkylmagnesium halide and the dialkylmagnesium-magnesium dihalide mixture is also very solvent dependent, with the less basic solvents favoring the alkylmagnesium halide form [9,10]. Although the Schlenk equilibrium and aggregation state can be measured fairly accurately in solution, the molecular geometry of the dimeric forms remains largely unknown in solution, and is usually assumed to resemble the solid state structure. Solid state geometries have been determined by X-ray diffraction of solvated Grignard reagents. Methylmagnesium bromide crystallizes as trisolvated monomer from THF [ll], while the ethylmagnesium bromide bis(diisopropy1 ether) solvate crystallizes as a bromide bridged dimer (1) [l]. Studies by Ashby, Voorbergen, and co-workers [2,6] have shown that ethylmagnesium bromide exists as a monomer in triethylamine and as a dimer in diisopropyl ether. Clearly, the nature of the solvent is an important factor in determining the aggregation state, with aggregation being favored by weakly

0166-1280/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI

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148

L.M. Pratt and I.M. Khan/Journal

of’kfolecular

,Br\ .,a

‘Mg

Et’

‘B{

S = solvent

Mg

‘s

1 Three possible geometries of the methylmagnesium halide dimers were examined. The first isomer is bridged by the methyl groups (2a), in analogy to the corresponding alkyllithium dimers. The second isomer is bridged by the halide atoms (2b), as in the X-ray crystal structures. The third isomer is bridged by one methyl group and one halide (2~). This structure has been proposed as a possible intermediate in some alkyl exchange reactions [5,12].

h

(Theochem)

CH3

,x\

H,C' 'U-I3 \/ Mg

333 (199.5) 147-152

orbitals, which are expressed as a linear combination of atomic orbitals as in the other LCAO methods. The local density approximation, used to calculate the exchange-correlation energy, states that the charge density changes slowly on an atomic scale, and is based on the model of a uniform electron gas. A major advantage of density functional methods is that correlation energies are included in the calculation without the need for configuration interaction (CI) calculations. Furthermore, the cost of the density functional calculations is considerably less than comparable HartreeeFock calculations. In theory, the computational expense increases as N3, where N is the number of basis functions, as opposed to N4 for HartreeeFock calculations, and up to N’ for CI calculations, although the exact savings in cost may depend on the problem and hardware. Thus, density functional optmizations can be performed on reasonably large systems with much greater computational economy, compared to other ab initio methods. Several density functional programs have been used for calculations involving transition metal complexes and small organic molecules. Generally, such calculations were far more accurate than Hartree-Fock methods for transition metal compounds due to the importance of electronic correlation in these systems

coordinating solvents. Unfortunately, the solution and solid state structures of the unsolvated Grignard reagents remain unknown due to the difficulty in preparing the reagent without residual coordinating solvent molecules. Attempts to remove the residual ether or THF usually result in decomposition of the Grignard reagent. This paper will examine the molecular structure of unsolvated methylmagnesium halides in order to evaluate the role of bridging atoms in the aggregation state in the absence of coordinating solvent molecules.

SI,,

Structure

W-Mg,

j'k

a3

X

H3C--M( ;Mg-X X

X 2a

2c

2b

The detailed theory of the density functional method has been reviewed elsewhere [13-171. In contrast to Hartree-Fock methods, the density functional operator expresses the total molecular energy as a function of charge density. This energy consists of kinetic, electrostatic, and exchange and correlation energies.

[16]. The local density approximation underestimates many single bond lengths by about O.OllO.O2A, which is comparable to HartreeFock calculations, while bond angles generally agree with experimental values within 1” [ 131.

G[Pl= %I + VP1+ -%[PI

2. Computational

The change

density

is summed

over the molecular

Density

methods

functional

calculations

were performed

L.M. Pratt and I.M. Khan/Journal Table 1 Geometries X

CpMg

F Cl Br

2.011 2.004 2.006

of methylmagnesium (min)

C-Mg

(DNP)

2.037 2.024 2.020

of Molecular Structure (Theochem)

Table 2 Effective atomic charges

halide monomers Mg-X 1.869 2.317 2.477

(min)

Mg-X

(DNP)

1.751 2.208 2.363

with the DMOI program and the INSIGHT II graphical interface, both produced by Biosym [ 181 on a Silicon Graphics Indigo 2 workstation. Calculations were performed using a minimal numerical basis set and a double numeric with polarization functions (DNP) basis set on each molecule with full geometry optimization. The minimal basis set calculations utilized frozen inner core orbitals, while the DNP calculations did not use any frozen core orbitals. Since DMOI uses a numerical basis set, the resonance and overlap integrals are approximated by finite sums. This is done by way of a numerical mesh of integration points. An increase in the number of mesh points increases the accuracy of the integrations but also increases the computational cost. In each calculation the fine numerical mesh was used, since fewer mesh points frequently result in a failure of the SCF cycle to converge. Convergence was achieved when either the energy changed by less than 0.00001 kcalmoll’, or when the gradient changed by less than 1.Okcalmoll’ A-‘. The calculations were based on the local density approximation without nonlocal corrections. Vibrational calculations were performed using the DNP basis set and a fine numerical mesh. All such calculations were performed on the DNP geometry. The results were compared with published literature values.

3. Results and discussion 3. I. Structure

and bonding

Each of the methylmagnesium halide monomers optimized to a linear geometry. With both the minimal and DNP basis sets, the calculated carbon magnesium (C-Mg) bond length was longer in methylmagnesium fluoride than in the chloride or bromide. The C-Mg and Mg-Cl bond lengths are

149

333 (1995) 147-152

in methylmagnesium

halide monomers

X

C

H

Mg

X

F Cl Br

-1.765 ~ 1.727 -1.757

0.355 0.374 0.371

1.438 1.134 1.129

-0.738 -0.528 -0.485

in reasonable agreement with the calculated ab initio values of 2.090 and 2.2 17 A, respectively, using the 631G* basis set, reported by Sakai and Jordan [19]. The difference between the ab initio and DFT calculated C-Mg bond lengths is similar to the values that we recently reported for alkyllithium compounds. The geometries are summarized in Table 1. The effective atomic charges were calculated from the Mulliken population analysis for each of the Grignard monomers, and the results are given in Table 2. The halogen atom is seen to have little effect on effective charge on the carbon atom, although the charge on magnesium increases with the electronegativity of the halogen atom, resulting in a more polar metal-carbon bond. The methyl bridging dimers (2a), analogous to alkyllithium dimers, show a larger basis set dependence on the C-Mg bond length than do the monomers, while the magnesium-halide (Mg-X) bond length shows roughly the same basis set dependence in both the monomeric and dimeric form. As with the monomer, the C-Mg bond length was weakened by the stronger Mg-F bond. The bond angles were nearly identical in the three methylmagnesium halides, but were basis set dependent, with the MggC-Mg angle decreasing from about 82 to 75” in each of the three methylmagnesium halide dimers. The results, summarized in Table 3, show the inadequacy of the minimal basis set in describing the methyl bridging dimer geometry. Table 3 Geometries of the methyl dimers (2a) X

CpMg

F Cl Br

2.187 2.188 2.194

(min)

CpMg 2.164 2.155 2.152

bridging

(DNP)

methylmagnesium

Mg-X 1.859 2.303 2.464

(min)

Mg-X 1.748 2.191 2.341

halide

(DNP)

L.M. Pratt and I.M. Khan/Journal

150

Table 4 Geometries of the halide dimers (2b) X

F Cl Br

bridging

of Molecular

methylmagnesium

halide

C-Mg (min)

C-Mg (DNP)

Mg-X (min)

Mg-X (DNP)

X-M&X (min)

(DNP)

2.000 1.999 1.990

2.050 2.032 2.028

1.959 2.483 2.656

1.886 2.380 2.538

79.0 84.9 89.3

83.1 91.8 94.6

in the mixed

bridging

(Theochem)

Table 6 Bond angles dimer (2~)

333 11995) 147-152

in the mixed

bridging

methylmagnesium

methylmagnesium

halide

.I

X

a

b

c

e

e

f

F (min) F(DNP) Cl (min) Cl (DNP) Br (min) Br (DNP)

2.200 2.237 2.222 2.227 2.198 2.226

2.002 2.044 2.004 2.040 2.006 2.036

1.952 1.889 2.498 2.418 2.676 2.560

1.922 1.865 2.438 2.318 2.610 2.480

2.216 2.132 2.179 2.109 2.198 2.112

1.851 1.749 2.304 2.193 2.466 2.341

halide

CL P

X-Mg-X

The pattern of increasing C-Mg bond lengths with more electronegative halogens is repeated in the halide bridging dimer (2b), although the effect is quite small with the minimal basis set. The DNP basis set calculation shows a 0.018 A increase in the C-Mg bond length between the chloride and fluoride bridging atoms. The minimal basis set underestimates the X-Mg-X bond angle by about 4-6” in each dimer. This angle increases by about 11” in going from the fluoride to the bromide bridge. The results are summarized in Table 4. The mixed bridging dimer (2~) showed a signiticant effect of the basis set on the molecular geometry for each of the methylmagnesium halides. The C-Mg bond lengths varied relatively little from the fluoride to the bromide, while the MgX distance increased with the size of the halide. The bond angles were also basis set dependent. The X-Mg-X bond angle decreases with increasing size of the halide, apparently as a result of increased steric interaction between the bridging methyl group and the non-bridging halide. The bond lengths and angles are summarized in Tables 5 and 6, respectively. Table 5 Bond lengths dimer (2~)

Structure

Y X

a

B

7

6

c

F (min) F (DNP) Cl (min) Cl (DNP) Br (min) Br (DNP)

87.7 91.8 91.3 97.3 93.3 99.3

100.0 94.2 81.1 75.2 76.0 70.9

87.9 95.9 93.9 103.3 99.6 105.1

84.4 80.0 93.6 83.6 95.0 84.7

149.7 141.4 144.4 137.4 140.7 132.9

A Mulliken population analysis showed different effective atomic charges on the carbon and halogen atoms, depending on whether the atom was in a bridging or terminal position (2a or 2b). For example, the bridging carbon atom had a more negative effective atomic charge than a carbon in the terminal position. In structure 2c, with one bridging and one terminal atom of each type, the effective atomic charges were similar to those of the same atom type in structures 2a and 2b. The results are summarized in Table 7. As in the case of the methylmagnesium halide monomer, the charge on the carbon atom showed relative little change with different halogens, while the metal-carbon polarity increased with halogen electronegativity due to a greater positive charge on the magnesium atom. The dimerization process of each of the methylmagnesium halides was exothermic, with the fluoride having the largest dimerization energy. Of Table 7 Effective atomic charges on the carbon, magnesium, gen atoms of methylmagnesium halide dimers X

F Cl Br

Bridging

C

Terminal

(2a)

(W

- 1.999 -1.961 -1.988

-1.641 -1.701 -1.722

C

Mg

1.440 1.177 1.160

Terminal

X

and halo-

Bridging

@a)

(2h)

-0.722 -0.543 -0.489

-0.759 -0.583 -0.536

X

L.M. Pratt and I.M. Khan/Journal of Molecular Structure (Theochem) Table 8 Dimerization

energies of methylmagnesium

halides (kcal mol-‘)

(2)

333 (1995) 147-152

151

Table 9 Relative internal energies of the methylmagnesium (kcal mol-‘) (2)

X

E (min)

E (DNP)

X

2a

2b

2c

F Cl Br

-64.98 -42.15 -36.10

-64.61 -40.71 -36.71

F (min) F (DNP) Cl (min) Cl (DNP) Br (min) Br (DNP)

49.38 34.51 28.64 11.35 22.81 8.00

0.0 0.0 0.0 0.0 0.0 0.0

23.34 19.13 15.96 7.35 12.98 5.47

the three possible structures, the halide bridging dimer (2b) was the most stable. The results are consistent with the fact that alkylmagnesium fluorides exist only in the dimeric form even in highly coordinating solvents such as THF, while such solvents break up the aggregates of alkylmagnesium chlorides and bromides [S]. The basis set dependence on the dimerization energy was relatively small, with the largest energy difference less than 2 kcal mol-‘. The results are summarized in Table 8. The calculated relative energies of the three isomerit dimers are given in Table 9. For each methylmagnesium halide, the order of stability of the isomers is 2b > 2c > 2a. The energy difference between 2b and 2c is 23.34 kcal mol-’ in methylmagnesium fluoride, compared to 7.35 and 5.47 kcal mol-‘, respectively, for the chloride and bromide. Zero point energy (ZPE) calculations showed a negligible ZPE difference of less than 0.5 kcal mol-’ between the three isomeric dimers of each Grignard reagent. Thus, the mixed bridging form or the chloride and bromide are thermally accessible at about 300 K, and may, in fact, be reactive intermediates as suggested by Ashby and co-workers [5,12]. The methyl bridging dimer (2a) isomer of methylmagnesium bromide is also thermally accessible with an energy only 8 kcalmol-’ higher than the bromide bridging form, and could also be the reactive form in some reactions. Calculations were also performed on the monomer (3a) and dimer (3b) of dimethylmagnesium, which, like alkyllithiums [20], can only from bridges via the methyl group. The minimal basis set optimized to a slightly unsymmetrical structure with ring C-Mg bond lengths of 2.157 and 2.236 A, and terminal C-Mg bond lengths of 2.002A. The larger DNP basis set generated a symmetrical structure with ring bond

halide dimers

lengths of 2.202A and Mg-terminal carbon lengths of 2.051 A. The DNP basis set calculations showed a much more exothermal dimerization energy of -27.35 kcalmol-‘, compared to only -17.56kcalmol-’ with the minimal basis set. We conclude that although magnesium can form alkyllithium-like bonds via bridging alkyl groups, halide bridging is much more energetically favorable. Several examples of analogous lithium-halogen bridges have been reported, as mixed aggregates between lithium amides and lithium halides [21,22]. QI3

H,C-Mg-CH,

H;C--Mg

;M,-CH3 a3

3.2. Vibrational

analysis

Relatively few vibrational studies on alkylmagnesium halides were found in the literature. Kress and Novak [4,23] investigated the vibrational frequencies of the disolvated ethylmagnesium bromide monomer. The experimental C-Mg stretching frequency was between 485 and 506 cm-’ compared to a calculated value of 633.7 cm” in the unsolvated methylmagnesium bromide monomer. This frequency increased to 642.8 and 770.5cm-t, respectively, in the methylmagnesium chloride and fluoride. The Mg-Br stretching frequency was reported between 238 and 248 cm-‘, compared to the calculated value of 288.2cm-‘. The corresponding Mg-Cl and Mg-F frequencies were 366.0 and 494.0cm-‘,

152

L.M. Pratt and I.M. Khan/Journal of Molecular Structure (Theochem)

respectively. In order to check for solvent perturbations on the vibrational frequencies, a calculation was performed on the dimethyl ether monosolvate of methylmagnesium chloride. Salvation increased the Mg-Cl stretching frequency from 366 to 372cm-‘, while the C-Mg frequency was reduced from 642.8 to 605.8cm-‘. We therefore conclude that the coordinated solvent molecules cause a weak perturbation in the calculated vibrational frequencies. The ratio of the experimental to calculated vibrational frequencies yields a scaling factor of approximately 0.8 for the monomeric Grignard reagents. The lack of experimental data precludes a more accurate evaluation of the vibrational frequencies at this time. Kress and Novak [4] also investigated the vibrational frequencies of the disolvated ethylmagnesium chloride dime, and reported an Mg-C stretching frequency of 479-498 cm-‘. Our calculations revealed three vibrations containing substantial Mg-C stretching at 565.0, 603.3, and These calculated frequencies also 610.3 cm-‘. yield a scaling factor of about 0.8. The corresponding calculated vibrations occur at 595.9, 604.8, and 628.2cm-I in methylmagnesium bromide, and at 564.4, 601.9, and 624.4cm-’ in methylmagnesium fluoride.

4. Conclusions Density functional calculations have shown that unsolvated methylmagnesium halides exist exclusively as dimers. The dimerization energy of the fluoride is the most exothermic due to the bridging ability of the fluorine atom. This fact explains the existence of the methylmagnesium fluoride in good donor solvents such as THF, while the corresponding chloride and bromide exist as monomers in the same solvent. Of the three possible dimer isomers, the halide bridging isomer is the most stable, although the other isomers of the chloride and bromide are thermally accessible at about 300K, and may exist as reactive intermediates. Methyl bridging as-clearly demonstrated in the dimethylmagnesium dimer, which cannot form halide bridges.

333 11995) 147-152

Acknowledgments The authors gratefully acknowledge the support of this work by NSF Grant #RII-9005 196 and NIH Grant #GM 08247-06. Purchase of the Silicon Graphics Indigo 2 workstation and the Biosym computational program by NASA Grant #NAGW2939 is also acknowledged.

References [l] W.E. Lindsell, in G. Wilkinson (Ed.), Comprehensive Organometallic Chemistry, Vol. I, Pergamon. Oxford, 1982, pp. 181-254, and references cited within. [2] E.C. Ashby and F.W. Walker, J. Org. Chem., 33 (1968) 3821. [3] J. Kress and A. Novak, J. Organomet. Chem., 99 (1975) 199. [4] J. Kress and A. Novak, J. Organomet. Chem., 99 (1975) 23. [5] E.C. Ashby and M.B. Smith. J. Am. Chem. Sot.. 86 (1964) 4363. [6] P. Voorbergen, C. Blomberg, F. Bickelhaupf, J. Organomet. Chem., 40 (1972) 225. [7] E.C. Ashby and S. Yu, J. Organomet. Chem., 29 (1971) 339. [8] E.C. Ashby, Bull. Sot. Chim. Fr., (1972) 2133. [9] T. Holm, Acta Chem. Stand., 23 (1969) 579. [lo] R.M. Salinger and H.S. Mosher, J. Am. Chem. Sot., 86 (1964) 1782. [ll] M. Vallino, J. Organomet. Chem., 20 (1969) 1. [12] G.E. Parris and E.C. Ashby, J. Am. Chem. Sot., 93 (1971) 1206. [13] J. Andzelm and E. Wimmer, J. Chem. Phys., 96 (1992) 1280. [14] B. Delly, J. Chem. Phys., 92 (1990) 508. [15] T. Ziegler, Chem. Rev., 91 (1991) 651. [16] I. Papai and J. Mink, J. Phys. Chem., 97 (1993) 9986, and references cited within. [17] DMOI User Guide, BIOSYM Technologies, San Diego, CA, (1993). [18] Computational results obtained using software program from Biosym Technologies of San Diego, CA. [19] S. Sakai and K.D. Jordan, J. Am. Chem. Sot., 104 (1982) 4019. [20] L.M. Pratt and I.M. Khan, A Density Functional Treatment of Organolithium Compounds, J. Comp. Chem.. (in press). [21] P. Hall, J.H. Gillchrist, A.T. Harrison, D.J. Fuller and D.B. Collum, J. Am. Chem. Sot., 113 (1991) 9575. [22] P.L. Hall, J.H. Gilchrist and D.B. Collum, J. Am. Chem. sot., 113 (1991) 9571. [23] J. Kress and A. Novak, J. Organomet. Chem., 86 (1975) 281.