Coordination number of carbon in methyllithium tetramer

Question

According to J. D. Lee's Concise Inorganic Chemistry, the coordination number of carbon in $\ce{Li4(CH3)4}$ is $7$. But the structure of the tetramer is

Doesn't carbon have coordination number $6$ here? Am I missing something?

Answer 1

TL; DR: coordination number of carbon atom in methyllithium tetramer is indeed 7, arising from 6 intramolecular interactions, as you suggested, and an extra bond with the lithium atom of the next tetramer.

---

The key point is that you need to look beyond the tetramer. I'm sorry to inform you that the image from Wikipedia of the standalone cubane $\ce{Li4(CH3)4}$ is useless for the determination of C.N. of carbon. In fact, there is a 3D network of interlinked clusters, and the description given in J. D. Lee's Concise Inorganic Chemistry is in fact very precise [1, pp 304]:

The structure of the $\ce{(LiCH3)4}$ cluster is unusual. The four $\ce{Li}$ atoms occupy the corners of a tetrahedron. Each methyl $\ce{C}$ atom is above a face of the tetrahedron, and forms a triple bridge to the three $\ce{Li}$ atoms that make up the face of the tetrahedron. The intramolecular $\ce{Li-C}$ distance is $2.31~\mathrm{Å}$. The $\ce{C}$ is bonded to the three $\ce{H}$ atoms in the methyl group. The $\ce{C}$ is also bonded to a $\ce{Li}$ atom in another tetrahedron (with an intermolecular $\ce{Li-C}$ distance of $2.36~\mathrm{Å}$). The coordination number for the $\ce{C}$ atom is therefore $7$.

The problem I stumbled upon is that I didn't find any ready-to-use CIFs for methyl lithium with 3D coordinates (there are plenty for the derivatives and some powder XRD of questionable quality). I ended up creating my own CIF based on data published by Weiss et al. [2] with VESTA program and visualized the content of the unit cell with OLEX2:

Figure 1. Unit cell of the methyl lithium tetramer with the central cubane core $\ce{Li4(CH3)4}$ linked via four crystallographically equivalent $\ce{C}$ atoms with 4 neighboring cubanes displayed as tetrahedra $\ce{Li4}$ for clarity. Color code: $\color{#EEEEEE}{\Large\bullet}~\ce{H}$; $\color{#CC80FF}{\Large\bullet}~\ce{Li}$; $\color{#909090}{\Large\bullet}~\ce{C}$.

Figure 2. Coordination environment of the carbon atom and interatomic distances (Å).

In addition, I run the test for C.N. with Dirichlet subroutine of the ToposPro, which also suggests the C.N. 7:

Central atom:C1 0.320 0.320 0.320 Rsd:0.900
 D(CP):0.624  ( 0.3698 0.3698 0.3698 )
 D(VDP):0.364  ( 0.3490 0.3490 0.3490 )
Atom:0.980 < r < 2.370  <r>=1.747   Top: 1.229 < R < 1.556  <R>=1.357
CN=7:0:0 NV=10 V=3.052/6.126 S=13.376 Cpac=0.161 Ccov=5.175
G3=0.114818789
Face distribution: {3/1 4/3 5/3 }
Vertex distribution: {3/10 }

  N  Atom   x      y      z     Dist.   D1      D2     SAng. 
  1  H_1  0.3510  0.1920  0.3510  0.97957  0.89982  0.07975  27.31224
  2  H_1  0.1920  0.3510  0.3510  0.97957  0.89982  0.07975  27.31224
  3  H_1  0.3510  0.3510  0.1920  0.97957  0.89982  0.07975  27.31224
  4  Li1  0.3690  0.3690  0.6310  2.30686  0.89982  1.40704   5.76860
  5  Li1  0.3690  0.6310  0.3690  2.30686  0.89982  1.40704   5.76860
  6  Li1  0.6310  0.3690  0.3690  2.30686  0.89982  1.40704   5.76860
  7  Li1  0.1310  0.1310  0.1310  2.37007  0.89982  1.47025   0.75748

Figure 3. Voronoi-Dirichlet coordination polyhedron for the carbon atom.

Content of the CIF file:

#======================================================================

# CRYSTAL DATA

#----------------------------------------------------------------------

data_VESTA_phase_1


_chemical_name_common                  'Methyl lithium tetramer'
_cell_length_a                         7.24000
_cell_length_b                         7.24000
_cell_length_c                         7.24000
_cell_angle_alpha                      90
_cell_angle_beta                       90
_cell_angle_gamma                      90
_space_group_name_H-M_alt              'I -4 3 m'
_space_group_IT_number                 217

loop_
_space_group_symop_operation_xyz
   'x, y, z'
   '-x, -y, z'
   '-x, y, -z'
   'x, -y, -z'
   'z, x, y'
   'z, -x, -y'
   '-z, -x, y'
   '-z, x, -y'
   'y, z, x'
   '-y, z, -x'
   'y, -z, -x'
   '-y, -z, x'
   'y, x, z'
   '-y, -x, z'
   'y, -x, -z'
   '-y, x, -z'
   'x, z, y'
   '-x, z, -y'
   '-x, -z, y'
   'x, -z, -y'
   'z, y, x'
   'z, -y, -x'
   '-z, y, -x'
   '-z, -y, x'
   'x+1/2, y+1/2, z+1/2'
   '-x+1/2, -y+1/2, z+1/2'
   '-x+1/2, y+1/2, -z+1/2'
   'x+1/2, -y+1/2, -z+1/2'
   'z+1/2, x+1/2, y+1/2'
   'z+1/2, -x+1/2, -y+1/2'
   '-z+1/2, -x+1/2, y+1/2'
   '-z+1/2, x+1/2, -y+1/2'
   'y+1/2, z+1/2, x+1/2'
   '-y+1/2, z+1/2, -x+1/2'
   'y+1/2, -z+1/2, -x+1/2'
   '-y+1/2, -z+1/2, x+1/2'
   'y+1/2, x+1/2, z+1/2'
   '-y+1/2, -x+1/2, z+1/2'
   'y+1/2, -x+1/2, -z+1/2'
   '-y+1/2, x+1/2, -z+1/2'
   'x+1/2, z+1/2, y+1/2'
   '-x+1/2, z+1/2, -y+1/2'
   '-x+1/2, -z+1/2, y+1/2'
   'x+1/2, -z+1/2, -y+1/2'
   'z+1/2, y+1/2, x+1/2'
   'z+1/2, -y+1/2, -x+1/2'
   '-z+1/2, y+1/2, -x+1/2'
   '-z+1/2, -y+1/2, x+1/2'

loop_
   _atom_site_label
   _atom_site_occupancy
   _atom_site_fract_x
   _atom_site_fract_y
   _atom_site_fract_z
   _atom_site_adp_type
   _atom_site_B_iso_or_equiv
   _atom_site_type_symbol
   Li1        1.0     0.131000      0.131000      0.131000     Biso  1.000000 Li
   C1         1.0     0.320000      0.320000      0.320000     Biso  1.000000 C
   H1         1.0     0.351000      0.351000      0.192000     Biso  1.000000 H

References

1. Lee, J. D. Concise Inorganic Chemistry, 4th ed.; Chapman & Hall: London ; New York, 1991. ISBN 978-0-412-40290-6.
2. Weiss, E.; Hencken, G. Über Metall-Alkyl-Verbindungen: XII. Verfeinerung der Kristallstruktur des Methyllithiums. Journal of Organometallic Chemistry 1970, 21 (2), 265–268. https://doi.org/10.1016/S0022-328X(00)83621-9. (In German)