LCP theory

In chemistry, ligand close packing theory (LCP theory), sometimes called the ligand close packing model describes how ligand – ligand repulsions affect the geometry around a central atom.[1] It has been developed by R. J. Gillespie and others from 1997 onwards [2] and is said to sit alongside VSEPR[1] which was originally developed by R. J. Gillespie and R Nyholm.[3] The inter-ligand distances in a wide range of molecules have been determined. The example below shows a series of related molecules:[4]

F-F distance (pm) O-F distance (pm) C-F bond length (pm) C=O bond length (pm)
CF4 216 132
O=CF3− 216 223 139 123
O=CF2 216 222 132 117

The consistency of the interligand distances (F-F and O-F) in the above molecules is striking and this phenomenon is repeated across a wide range of molecules and forms the basis for LCP theory.

Ligand radius

From a study of known structural data a series of inter-ligand distances has been determined[1] and it has been found that there is a constant inter-ligand radius for a given central atom. The table below shows the inter-ligand radius (pm) for some of the period 2 elements:

Ligand Beryllium Boron Carbon Nitrogen
H 110 90 82
C 137 125 120
N 144 124 119
O 133 119 114
F 128 113 108 106
Cl 168 151 144 142

The ligand radius should not be confused with the ionic radius.

Treatment of lone pairs

In LCP theory a lone pair is treated as a ligand. Gillespie terms the lone pair a lone pair domain and states that these lone pair domains push the ligands together until they reach the interligand distance predicted by the relevant inter-ligand radii.[1] An example demonstrating this is shown below, where the F-F distance is the same in the AF3 and AF4+ species :

F-F distance (pm) A-F bond length (pm) F-A-F angle (degrees)
NF3 212 136.5 102.3
NF4+ 212 130 109.5
PF3 237 157 97.8
PF4+ 238 145.7 109.5

LCP and VSEPR

LCP and VSEPR make very similar predictions as to geometry but LCP theory has the advantage that predictions are more quantitative particularly for the second period elements, Be, B, C, N, O, F. Ligand -ligand repulsions are important when[1]

  • the central atom is small e.g. period 2, (Be, B, C, N, O)
  • the ligands are only weakly electronegative compared to the central atom
  • the ligands are large compared to the central atom
  • there are 5 or more ligands around the central atom
gollark: Just that they hadn't yet fused.
gollark: I did not mean that the two things were separated, to clarify.
gollark: Flour, and because those need to be baked properly to work, which isn't a concern in this scenario.
gollark: Why does that matter? What if they're in some environment a millimeter apart through some contrived method, such that they probably will soon?
gollark: But the two separate things *could be used* to do that.

References
  1. Teaching the VSEPR model and electron densities R. J. Gillespie and C. F. Matta, Chem. Educ. Res. Pract. Eur.: 2001, 2, 73-90
  2. Reinterpretation of the Lengths of Bonds to Fluorine in Terms of an Almost Ionic Model E A. Robinson , S A. Johnson, Ting-Hua Tang, and R J. Gillespie Inorg. Chem., 36 (14), 3022 -3030, 1997. ic961315b S0020-1669(96)01315-8
  3. Inorganic stereochemistry Gillespie, R.J. & Nyholm, R.S. (1957). Quarterly Reviews of the Chemical Society, 11, 339-380 doi:10.1039/QR9571100339
  4. Bonding and Geometry of OCF3−, ONF3, and Related Molecules in Terms of the Ligand Close Packing Model Gillespie RJ, Robinson EA, Heard GL. Inorg Chem. 1998 Dec 28;37(26):6884-6889 doi:10.1021/ic981037b
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