LIST OF FIGURES

Figure 1 : Shadow representation of the solid angle of two spheres A and B
Figure 2 : Projection of two atoms onto the plane perpendicular to vector OG:
a - OG defines smallest enveloping cone, used in White et al.[3]
b - OG constructed through region of overlap
Figure 3 :	a - Ellipse projection used by White et al.[3]
		b - Ellipse projection with G in region of overlap
Figure 4 : 	a - CH3 with only C-H overlap
		b - CH3 with all pairs of atoms overlapping
Figure 5 : CH3 with successive addition and subtraction of regions of overlap
Figure 6 : Types of overlap regions:
		a - Overlap enclosed by single atom
		b - Single atom forms more than one segment
		c - Normal overlap region
Figure 7 : Region of triple overlap projected onto the plane perpendicular to G
Figure 8 : White et al.[3] and Multiple overlap solid angles compared to the Tolman cone angle[1]
Figure 9 : Solid angle radial profile of PPh2Me

LIST OF TABLES

Table I : CH3   calculation using double overlap only, for all permutations
Table II : CH3   calculation using double overlap only, for select permutations (White et al.)
Table III : CH3   calculation using all orders of multiple overlap
Table IV : Solid Angles and Cone Angles for 12 selected molecular fragments

Table I : CH3   calculation using double overlap only, for all permutations
19Calculation details		  running total in steradians	
Addition of all two atom solid angles:			
	+  (C‑H1):[1.460833]	= 1.460833	
	+  (C‑H2):[1.460861]	= 2.921694	
	+  (C‑H3):[1.460859]	= 4.382553	
	+  (H1‑H2):[1.919629]	= 6.302182	
	+  (H1‑H3):[1.919634]	= 8.221816	
	+  (H2‑H3):[1.926091]	= 10.147907	
Removal of all extra single atom solid angles:			
	‑ 2* (C): [0.841767]	= 8.464373	
	- 2* (H1): [1.055183]	= 6.354007	
	- 2* (H2): [1.055183]	= 4.243640	
	- 2* (H3): [1.055180]	= 2.133280	
	Total solid angle for CH3 	= 2.133280sr (97.327deg or 17% sphere)	

Table II : CH3   calculation using double overlap only, for select permutations (White et al.)
Calculation details		  running total in steradians	
Addition of all two atom solid angles:			
	+  (C‑H1):[1.460833]	= 1.460833	
	+  (C‑H2):[1.460861]	= 2.921694	
	+  (C‑H3):[1.460859]	= 4.382553	
Removal of extra single atom solid angles:			
	‑ 2* (C): [0.841767]	= 2.699020	
	Total solid angle for CH3	= 2.69902sr (110.44deg or 21% sphere)	

Table III : CH3   calculation using all orders of multiple overlap
Calculation details		  running total in steradians	
Calculation of all single atom solid angles			
	+  (C): [0.841767]	= 0.841767	
	+  (H1): [1.055183]	= 1.896950	
	+  (H2): [1.055183]	= 2.952133	
	+  (H3): [1.055180]	= 4.007313	
Removal of all double overlaps			
	‑  (C‑H1):[0.436117]	= 3.571196	
	‑  (C‑H2):[0.436090]	 = 3.135106	
	‑  (C‑H3):[0.436088]	 = 2.699018	
	‑  (H1‑H2):[0.190737]	= 2.508281	
	‑  (H1‑H3):[0.190729]	= 2.317552	
	‑  (H2‑H3):[0.184272]	= 2.133280	
Addition of all triple overlaps			
	+  (H2‑C‑H1) [0.170066]	= 2.303345	
	+  (H3‑C‑H1) [0.170061]	= 2.473407	
	+  (H3‑C‑H2) [0.166343]	= 2.639749	
	+  (H3‑H1‑H2) [0.039941]	= 2.679690	
Removal of all quadruple overlaps			
	‑  (H3‑H2‑C‑H1) [0.039941]	= 2.639749	
	Total solid angle for CH3	= 2.63975sr (109.12deg or 21% sphere)	

Table IV : Solid Angles and Cone Angles for 12 molecular fragments
19	Cone angle in radians	Solid angles in steradians		
1919Fragment Name	Tolman procedure	White et al.	Multiple Overlap	
Imidazole	1.491077	1.590351	1.415416	
NH2OH	1.742570	1.876093	1.685321	
NH3	1.789398	1.948819	1.859953	
NH2Me	1.982452	2.696721	2.322253	
NH2EtOH	2.002485	2.868522	2.326860	
NH2Me3OH	2.046896	2.853271	2.537361	
NH2Pr(OH)2	2.051723	2.988734	2.184162	
PF3	2.169660	2.609292	2.599425	
PBr3	2.472132	3.156167	3.154727	
PEt3	2.663106	4.122755	3.433989	
PBz3	3.000215	5.088678	4.221555	
P(C6F5)3	3.216643	4.673923	4.017541