4778
Ab Initio SCF-MO Calculations of Methyllithium and Related Systems. Absence of Covalent Character in the C-Li Bond1 Andrew Streitwieser, Jr.,* James E. Williams, Jr., Spiro Alexandratos, and John M. McKelvey Contribution from the Department of Chemistry, University of California, Berkeley, California 94720. Received January 10, 1975
Abstract: SCF calculations are reported for CH3Li using several basis sets. The largest basis set used, split shell with d orbitals on carbon (SS+d), gives an optimized geometry of r(C-Li) = 2.021 A, r(C-H) = 1.089A, and LHCH = 1 0 5 . 8 O , with an energy of -47.0206 au. Electron density and projection plots as well as integrated electron populations show that the C-Li bond has essentially no shared-electron covalent character. Monomeric methyllithium is described in terms of largely ionic bonding with about 0.8 e transferred from Li to CH3. Similar calculations are described for ethyllithium, vinyllithium, and ethynyllithium
Organolithium compounds are important reagents, of widespread use in preparative organic chemistry.2 Yet the nature of the carbon-metal bonding in these, the simplest organometallic compounds, does not appear to be well understood. Lithium, a highly electropositive alkali metal, is expected to form highly ionic bonds with less electropositive elements. Organolithiums are often considered as the lithium salts of the corresponding carbon acids, are taken to be good models for the corresponding carbanion^,^ and in many reactions display a high degree of R-Li+ ionic ~ h a r a c t e rThe . ~ high ionicity of methyllithium monomer has been inferred from its ir spectrum.5 Numerous other data, however, appear to indicate a large nonionic component in carbon-lithium bonds. N M R studies indicate that the charge separation in typical organolithiums is substantially less than unity.6 Many organolithium compounds, especially the alkyllithiums, form oligomers whose structures are those of electron-deficient molecules with bridging organic moieties, rather than ionic aggregates or crystal^.^ Cyclohexyllithium forms hexamer crystals for which multicenter bonding has been proposed.8 Methyllithium forms tetramers with extended three-dimensional interactions in the solid state.9 Furthermore, polylithiation of methane, to form CH2Li2,I0 and even CLi4,' and the fact that some alkyllithium reactions have radical mechanisms12 do not seem consistent with highly ionic carbon-lithium bonds. Several theoretical studies of simple organolithium molecules have been reported. Methyllithium monomer, dimer, and tetramer have been studied by minimal-basis a b initio calcul a t i o n ~ ' ~and - ' ~by semiempirical M O methods.16 Ionicity vs. covalency in these molecules was examined using Mulliken population analyses.I3-l6 Electron-deficient bonding in the tetramer was evaluated with the use of electron-density plots.13 V i n y l l i t h i ~ mand ' ~ phenyllithiumIs have also been investigated by the C N D O method. Computations using a minimal Gaussian basis on cy~lopentadienyllithium'~~~~ have also been reported. Ab initio calculations using large extended basis sets have been reported for lithium acetylide.2' Also germane to the discussion of bonding in organolithiums are the calculations of Astier and Millie22 on some methyl Grignard and related molecules. The present study is the introduction to a series of a b initio investigations. In this paper we concentrate first on methyllithium monomer and consider the series methyl-, ethyl-, vinyl-, and ethynyllithium, for comparison with related studies of the corresponding carbanion^.^^ In subsequent papers we shall extend this study to alkyllithium dimers and higher aggregates, polylithiated compounds, and related organometallic compounds. Journal of the American Chemical Society
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Methods of Calculation Calculations were performed with four different basis sets. The simplest of these is the minimal STO-4G basis introduced by Hehre, Stewart, and P ~ p l eOrbital . ~ ~ exponents for carbon and hydrogen are those found optimal for the corresponding h y d r ~ c a r b o n except , ~ ~ for hydrogen on the carbon bound to lithium, for which the standard anion exponent (1.14) is used? This choice gives somewhat lower energy than using the standard anion carbon exponent (1.56) for carbon bonded to lithium or using optimum hydrocarbon exponents throughout. The lithium exponent is 0.83, the optimum value for methyllithium.26 These calculations were performed using a modified version of IBMOL I V . ~ ~ Extended basis calculations were performed using a Gaussian split-shell (SS) basis generated from the 8s4p functions for carbon, the 8s functions for lithium and 4s functions for hydrogen of H ~ z i n a g a , ~and ' a 4p set for lithium optimized for the 2P state of the lithium atom.28These functions are contracted to 4s2p on C, Li, and 2s on H as b e f ~ r e . ~ ~ . ~ ~ T o this basis we added a set of 3d orbitals on carbon, of exponent 0.8 for methyl, ethyl, and vinyl compounds, and 1.O for ethynyl,23 giving the SS+d basis, to which most of our discussions refer. For methyl- and ethynyllithium, SS+d,p calculations, incorporating p orbitals of exponent l .O on hydrogen into the SS+d basis, were also performed, but were found to give results essentially the same as those using the S S f d basis alone. Results and Discussion Geometric Structure. Extensive geometry optimizations were carried out for methyllithium and ethynyllithium with three basis sets. The results are summarized in Table I. The minimal basis gives significantly shorter C-Li bonds than the extended basis sets. However, a basis with 2p orbitals on Li is not really minimal and is undoubtedly overweighted toward Li. Such a basis with first row atoms gives unrealistically high amounts of 7r bonding to LLZsNevertheless, with a large STO basis an essentially Hartree-Fock result of Veillard for ethynyllithium with assumed C C and C H bond distances gives a C-Li distance of 1.880 A,21which is between our minimum basis and extended basis results. Our calculated C-Li bond length for methyllithium is slightly smaller than the value of 2.10 A estimated empirically5 and is expected to be substantially smaller than the C-Li distance of 2.31 A found experimentally for the tetramer.9 Our SS+d computed29force constant for CH3Li in its optimized geometry, 0.99 mdyn A-I, and the dipole moment, 5.90 D, agrees well with Andrews' results for the matrix-isolated monomer, 0.78 mdyn A-I and 6 D, respective1y.j
August 4 , 1976
4779 Table I. Optimized Geometries for Methyl- and Ethynyllithium Molecule ~~
~
Geometry parameter
STO-4G“
C-Li, A C-H, HCH, deg C-Li, A c-c, A C-H, A
1.969 1.122 104.2 1.862 1.213 1.070
Basis set SS
SS+d
2.032 1.092 107.1 1.921 1.219 1.056
2.021 1.089 105.8 1.931 1.208 1.056
~
CH3Li HCECLi
Optimized exponents: CH3Li: C (2s), 1.71; Li (2s, 2p), 0.83; H, 1.12. HC&,Li: Cp (2s, 2p), 1.67; C, (2s, 2p), 1.66; H, 1.29; Li (2s, 2p), 0.74. Inner shell exponents used were not optimized and were taken as C (Is), 5.7, Li (Is), 2.69 for CH3Li and C (Is), 5.67, Li (Is), 2.69 for LiC2H.
Table 11. Computed Total Energies for the Organolithium Molecules” Basis set ~
Molecule Geometrvb STO-4G CH3Li C2HLi C2H3Li C2H5Li
refC opt refd opt refe refC
-46.7767 -83.2352 -83.2395
~
~~
~
SS
SS+d
SS+d.o
-47.0024 -47.0026 -83.6703 -83.6710 -84.8317 -86.0081
-47.0139 -47.0147 -83.6968 -83.6969 -84.8597 -86.0383
-47.0200 -47.0206 -83.6995 -83.6995
Energies in au (1 au = 627.502 kcal mol-’). ref = reference geometry, opt = energy-optimized value (see text). CLi = 2.02 A, optimal for CHjLi. CLi = 1.93 A, optimal for C2HLi. e CLi = 1.98 A, average of optimum values for CH3Li and C2HLi.
The CC and CH bonds in ethynyllithium are essentially the acetylene values. It is known experimentally that the acetylene CC bond length of 1.203 A30 changes insignificantly in the carbide ion, C22- (Na2C2, 1.200 f 0.006 A;31CaC2, 1.19 1 f 0.009 A).32 A minimal basis set optimization of the C-Li length in ethyllithium without concurrent exponent optimization gives a distance of 2.04 essentially the same as the SS and SS+d results for CH3Li. It should also be emphasized that the total energies vary but little with C-Li distance and that the accurate determination of geometric parameters from such broad, flat potential surfaces is difficult if not impossible in any practically reasonable way. These small energy variations are apparent in the total energies summarized in Table 11. The general and expected conclusion to be drawn from the results in Table I is that the carbon moieties in the lithium salts have geometries intermediate between hydrocarbon and carbanion. For convenience in subsequent electron density difference plots, calculations were also made for molecules in their “reference” geometry,23 defined as the experimental geometry of the corresponding neutral hydrocarbon with one hydrogen removed and replaced by lithium a t an appropriate bond distance but with the hydrocarbon bond angle. The Carbon-Lithium Bonding in Methyllithium. In previous a b initio studies of methyllithium monomerI3-l5 the Mulliken atomic and overlap populations were used as criteria for covalent bonding. For example, the SS+d basis set for the reference geometry gives a C-Li overlap population of 0.603, a rather high number. For comparison, the C-C bond in ethane has an overlap population in the same basis of 0.628. This comparison naively suggests that the two bonds have comparable covalency but other considerations indicate that such a conclusion is totally fallacious. Streitwieser et al.
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Figure 1. Total electron density in units of e au-3 plotted as the vertical axis for a LiCH plane, taken as the grid plane, for methyllithium. In the structure superimposed above the electron density plot, the short dotted line refers to C-H bonds of the methyl group above and below the chosen molecular plane; SS+d basis.
The covalent bond requires shared electron density between the atoms.34 Electron density and density-difference contour plots have been used extensively, particularly with respect to diatomic molecules, for detailed descriptions of bond^.^^.^^ Figure 1 shows a perspective plot of the total electron density for methyllithium (SS+d basis) in a plane defined by Li, C, and one H. Especially striking in this plot is the relative absence of a ridge of electron density between C and Li, particularly by comparison with the C-H bonding region. The minimum value of the density along the C-Li internuclear line is 0.038 e au-3 compared with 0.275 e au-3 for C-H. The latter magnitude is typical for highly covalent bonds such as CC and CH. Moreover, even the small ridge observed for C-Li is probably not associated with covalent bonding. Such a ridge is a necessary but not sufficient condition for bonding since overlap of inner shell electrons (as in He-He) can produce such a ridge. The valence electron plot (electron density with the C and Li 1s orbital densities, 1u and 2a, deleted; not shown) shows a much reduced internuclear density; the minimum value of the valence electron density along the C-Li line is now only 2 X 10-5 e a ~ - ~ . This result emphasizes again28,37,38the important limitations of Mulliken populations, particularly when the basis includes diffuse orbitals. The defined “overlap population” measures total overlap of two wave functions everywhere in space and not just in the internuclear region. Similarly, the “atomic population”.with diffuse orbitals takes electron populations close to one atom and “assigns” them to another. In the present case, the Li 2s and 2p orbitals are so diffuse they encompass the entire molecule; hence, any population analysis based on atom-centered basis functions will assign to lithium electrons that are actually in the C-H spatial region. These generalizations are documented by the Mulliken populations summarized in Table 111. Note the changes in assignments given by the three largest basis sets despite the small actual change in electron distribution as shown by the calculated dipole moments. Especially revealing are the atomic charge changes, euen on Li, on adding p functions to H. The electron density criterion leads to the conclusion that the C-Li bond has essentially nil covalent character. The SS+d basis is a reasonably good one and it seems unlikely that this conclusion would differ a t the Hartree-Fock limit. To the next question of whether electron correlation would significantly
A b Initio SCF-MO Calculations of Methyllithium and Related Systems
4780 Table 111. Mulliken Populations for CH3Li‘ Basis ST04G
ss
SS+d SS+d,p
Overlap populations C-Li C-H 0.620 0.572 0.603 0.61 1
0.765 0.710 0.723 0.747
Atomic charges
C
Li
H
-0.066 - I .034 - 1.034 -0.847
+0.191
-0.042 $0.152 +0.158 +0.098
$0.518 +0.560 +0.555
P,
D
4.17 5.80
5.85 5.84
For a methanelike geometry with r(CLi) = 2.02 A.
40.10
i
i
1005
10.05
Figure 2. Difference density plot for C1 electron density and SCF density for CH3Li with the SS basis, p(C1) - p ( S C F ) ; SS basis.
affect this conclusion, we apply a limited C I study. The configuration-interaction calculation included double and single excitation from the g(CLi) MO and the three lowest lying occupied MO’s of the same al symmetry to all of the virtual MO’s of a1 symmetry having significant contributions from lithium AO’s. Because of programming limitations, this calculation was done using the SS basis set, that is, with no polarization functions on carbon. The total number of configurations was 36, and the resulting C I wave function was transformed to natural o r b i t a l ~ The . ~ ~ highest occupied MO is predominantly C whereas the lowest a1 virtual MO is heavily weighted by Li; hence, the C I part of the wave function is heavily dominated by excitation between the highest occupied and lowest vacant MO’s or by charge transfer from C to Li. The energy lowering obtained is 0.01301 au (8.2 kcal mol-’), a rather modest improvement. A plot of the difference between the density given by the CI wave function and that of the SS basis is given in Figure 2. The mixing in of the C-Li antibonding MO’s has moved a small amount of density from the carbon front- and back-lobe regions of the CLi bond pair into lithium and carbon nuclear regions. The resultant bond-pair density also moves closer to carbon. The natural orbital occupation numbers show that the natural orbital having the greatest u(CLi) MO character has lower electron population, from 2.0 electrons in the SCF to 1.96 electrons in the C I function, and 0.03 electrons are in the orbital most like the a*(CLi). The changes are small and do not affect the conclusions derived above concerning the absence of C-Li covalency; a more complete C I is unlikely to modify the conclusions significantly. Electron density functions can be exceedingly useful especially in the comparisons afforded by difference density plots. For example, a criterion for covalency in diatomic molecules in terms of molecular minus atomic density difference plots has been proposed:35c that the molecule should show a charge increase, more or less equally shared by both atoms, in the internuclear region, relative to its constituent atoms. The Journal of the American Chemical Society
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Figure 3. Radical difference density plot for methyllithium, p(CH3Li) p(CH3.) - p(Li-), for a HCLi plane. The p(CH3.1 was obtained from ref 23. The scale of e au-3 is about five times that of Figure 1; SS+d basis.
equivalent difference function for CH$i is the “radical difference” plot shown in Figure 3, a plot of p(CH3Li)p(CH3-)-p(Li-), for a methyl radicalz3 and lithium atom constrained to the same geometry as CHjLi. This plot shows the change in electron density for a HCLi plane when the electrons of an isolated Li atom and pyramidal methyl radical are allowed to relax to form CH3Li. Figure 3 shows a large charge increase in the CLi internuclear region but not shared by both atoms. Indeed, the change is about that expected for the formation of CH3- and Li+ except that the degree of charge transfer appears notably asymmetric; the electron density gain in the carbanion lone pair region appears greater than loss from Li for the plane shown. For considerations of total atomic charges and charge transfer we need to consider the volumes involved and would prefer to have integrated functions over such volumes rather than just electron density changes alone. We have recently proposed4” an electron projection function, P,,, in which, for a given point x,z, the electron density is integrated along the y axis from + a to -a. The resulting function can be displayed in the x z plane in contour or perspective form and has the advantage that apparent volume elements are now directly related to electron populations; that is, the volume of the entire figure gives directly the total number of electrons in the molecule. Figure 4 displays the electron projection function for CH3Li for a plane parallel to a LiCH plane. This figure again shows the absence of electron population between C and Li, especially compared to C-H. In principle, this figure could be used to derive electron populations and atomic charges for each of the atoms but in practice such an assignment is difficult for C and H. The Px, function between these atoms is so continuous and monotonic that the
August 4, 1976
478 1 Table IV.
i
Inteerated Pouulations
0*2/DIV
Svstem CH3Li CH3. Li CH3Li+ CH3CH3. Li+ LiAI‘: CH3Li-0.8(CH3-Li+)0.2(CH3.Li.)
+ +
“Methyl region”
“Lithium region”
9.90 9.39 9.99 9.97 9.08 0.02 0.32 0.03
2.16 2.44 2.08 0.09 0.04 1.99 2.40 0
Total 12.06 11.83 12.07 10.06 9.12 2.01 2.72 0.03
O.O02/OI v Figure 4. Projection function, P x z ,for methyllithium in a HCLi plane; S S basis.
choice of where C ends and H begins is rather a r b i t r a r ~ . ~NO ’ such problem exists for the C-Li bond. The dramatic minimum between these atoms allows clear-cut assignment of electron populations to Li and to the CH3 group. Approximate spatial electron populations were derived by numerical integration of Figure 4 using the grid points as centers of area elements. The result may be referred to as an integrated population, P, (electron population). The Pe of the entire Figure 4 is 12.06 e, in which the excess of 0.06 e is the error associated with this numerical integration using a rather coarse grid of 0.2 au spacing. W e have found such errors to be generally less than 0.1 e. The total P, to be assigned spatially to the methyl group as a unit, up to the minimum between C and Li, is 9.90 e. The corresponding population of Li is 2.16 e; thus, the spatial distribution of electrons in CH3Li corresponds largely to a CH3-Li+ ion pair. For comparison, we have made similar plots for CH3- -tLi+, CH3. Li., as well as for CH3-, CH3-, Li+, and Li, with the atoms placed on the grid exactly a t their positions in CH3Li in Figure 4. The corresponding P,’s summarized in Table IV include dissections into the same CH3 and Li regions derived from Figure 1. Note that CH3-, CH3-, and Li+ are all well behaved in the sense that their P i s lie almost wholly within the grid regions derived from Figure 4. Lithium atom, however, is so diffuse that its electrons overflow beyond the grid limits used, almost 0.3 e lie outside the grid and another 0.3 e lie in the region assigned spatially to methyl. The lithium P, in CH3Li is much more like Lif than Li-. Finally, we have examined several AP,plots in which P,, for various combinations of ionic and radical structures are compared with P,, for CH3Li; that is, eq 1 in which 0 6 x 6
+
1.
AP,; = PX,(CH3Li) - x[Px,(CH3-) + P,,(Li+)] - (1 - x)[Pxz(CH3.)
+ P,,(Li-)]
All such difference plots should have total Ape = 0 and for the plots of interest the total integrated values determined numerically are
