Bond angles around tetrahedrally bonded carbon, and distortion of the tetrahedron in CH3-X structures

THEO CHEM ELSEVIER

Journal

of Molrcular

Structure

(Theochem)

33X (I 995) 15S- 173

Bond angles around tetrahedrally bonded carbon, and distortion of the tetrahedron in CH3-X structures Philip George”, Jenny P. Glusker”,*,

and Charles W. Bockb

Abstract

To investigatethe extent to which individual bond anglesarounda tetrahedrally bondedcarbonatom deviatefrom the regular tetrahedral angleof 109.47. and the sumof the six anglesfrom the maximum value of 656.83”,we have used resultsderived from neutron diffraction studieson moleculescontaining the XPCH1-Y grouping, and corresponding resultsfor CH3-X. XPCHzPY and HPCXYZ structurescalculatedusingab initio molecularorbital methods.In both setsof data the individual valuesvary between105’ and I I7 ‘. Yet. provided there is no stericconstraint such asthe bondingof the carbonin a four- or three-membered ring. the summationof the anglesislessthan the maximumby only a few tenthsof a degree.An inherenttendencyfor the summationto attain this maximumvalueis further substantiatedby the data for CCC and COC rings. Eventhough the CCC and CC0 ring anglesare about 60”. compensatoryincreasesin the remainingfive anglesare sufficiently large to reducethe deficit in the summationto approximately 14’. The distorsionof the tetrahedrais discussed in termsof the interplay betweenbond anglerelationshipsand the bond lengths.In the CHjPX structuresin which C X is a trigonal axis of symmetry. the tetrahedraare elongatedalong this axis. In other CH3- X structures,wheretwo of the hydrogen atoms, Hb and H,, are located symmetricallyabout the planecontainingC, X. and the other hydrogenatom. H,. the tetrahedraare alsoelongatedbut tilted a little toward, or away from, the H,-H, sideof the H,HbH, triangle at the base of the tetrahedron.

1. Introduction

The proposal that the four atoms attached to a saturated carbon atom are arranged at the corners of a tetrahedron with the carbon atom in the center was made independently by Jacobus Hendricus van? Hoff and Joseph Achille Le Be1 in 1874 (see Refs. [l-4]. For English translations of Refs. [lb] and [2], seeRef. [3]). Their concept has had a profound effect on our understanding of the * Corresponding author. Tel: .- I71 728-3574;

internet:

gluskerwz

5-7X-2220.

Fax:

+ 12 15-

fccccdu

0166-1280/95/$09.50 sc 1995 Elsewer SSDI 0166-1280(94)04056-7

Suence

B.V.

All rights

three-dimensional structures of organic molecules. It is indeed an honor to commemorate their work, and we have chosen to do so by describing studies of the bond anglesaround saturated carbon atoms, and the shape of the tetrahedron. When four identical unsubstituted atoms (ligands) are bonded in a tetrahedral manner to a carbon atom, as in CH4 or CF4, symmetry requires the tetrahedron to be a regular tetrahedron so that each bond angle is 109.4712.. .‘, and the sum of the six bond angles is therefore 656.8272.. .O.If, however, one or more of the atoms is chemically different from the others, the angles between the bonds reserved

will no longer be 109.47 ; some will be larger, some smaller. The question arises as to whether the sum of the angles is still close to this maximum value of 656.83”. or whether significant deviations occur, and, if so, under what structural constraints. The first part of our paper addresses this issue, by the use of bond angles derived from neutron diffraction studies on molecules containing the X-CH2-Y group and from geometries obtained from ab initio molecular orbital calculations on CH,-X. X-CH2-Y and H-CXYZ structures. The neutron diffraction data give nuclear positions and hence do not contain the small distortions seen by X-ray diffraction in which electron density is measured. They also provide more precise hydrogen atom positions. In addition we have classified various bond angle relationships to see if there is any correlation with the nature of the atoms directly bonded to the tetrahedral carbon. With one or more different atoms (ligands) attached to the carbon atom the tetrahedron will no longer be regular’. but distorted in some way. The bond angles, and also the bond lengths, determine its actual shape. Taking the bond angles first, their role is illustrated in Fig. 1 for the simple case of CH3-X structures with a trigonal axis of symmetry. C-X. For the regular tetrahedron, X = H, see Fig. l(a). Elongation of the tetrahedron is characterized by the C-X group moving away from the HHH plane along the C-X axis, so that HCH < HCX (see Fig. l(b)). In the geometrical limit each angle HCH would be zero and the angles HCX would be 180”. giving 540’ for the sum of the bond angles. Flattening of the tetrahedron is characterized by the C-X group moving toward the HHH plane along the C-X axis, so that HCH > HCX (see Fig. l(c)). A special case arises when the carbon atom lies in the ’ can’t Hoff used perspective draalngs and cardboard model tetrahedra to illustrate his proposal. representing the carbon carbon single bond, in one method. by the (now very familiar) touching of the corners of two tetrahedra. None of the models were constructed as regular tetrahedra: and he argued that a regular tetrahedron would be expected only if the four groups attached to the carbon atom were identical (see Ref. [5]. especially p. 77 and Figs. 1 and 2). Many of these models can still be seen in the Rijksmuseun voor de Geschiedenis der Natuurwetenschappen. Leyden [4]. and in the Deutsches Muscum, Munich [5].

plane of the three H-atoms

a

b

C

Fig. I. Bond angle relationships in the CH3-X structures in which C-X is a trigonal axis of symmetry. and their role in determining the shape of the tetrahedron. (a) X = H, regular tetrahedron, each bond angle is 109.4712” and the sum of the six angles is therefore 656.8272”. (b) Elongation of the tetrahedron with respect to the C-X axis: angle HCH < angle HCX. (c) Flattening of the tetrahedron with respect to the C-X axis: angle HCH > angle HCX.

HHH plane, i.e. the angles HCH and HCX are 120” and 90” respectively, giving 630” for the sum of the bond angles. Thus, in principle, significant deviations from 656.83” are possible for the summation of the six angles. Since X-C bonds are much longer than H-C bonds, the tetrahedron in these structures could still be elongated even though the bond angle relationship is indicative of flattening. We note, in passing. that were the carbon atom to move through the HHH plane in Fig. l(c) an unusual three-dimensional structure would result, with all four attached groups in the same hemisphere [6.7]. In the second part of the paper we show, in practice, that the tetrahedra are, in fact, elongated in the CH?-X structures with a trigonal axis of symmetry, and also in the CH3-X structures which lack this symmetry element, but still have a plane of symmetry defined by H,, C, and X with Hb and H, located symmetrically on either side of this plane (see Fig. 2(i)). We also show that elongation of the tetrahedron in these structures, however, is not necessarily accompanied by a significant deviation of the sum of the bond angles from the maximum value of 656.83” found for the regular tetrahedron. These terms, elongation or flattening, have been used specifically to describe the distortion in CH3-X structures. The more complex distortion present in X-CH2-Y and H-CXYZ structures will be dealt with in a future paper.

157 X

Ha

Ha

\ -x *O-C ,...+ Hb “”

( ,$

\

/

X

HC

Hb ...’...

/

H a --c,..,,

/‘\

“.....,. Y \

Y

(iii)

(ii)

(9

i!

’\ ::i:--1 C’

C’ \

/

\

P

69

(iv)

% ::‘Ha H c .. ,,..”.D .‘...‘G, ,/ “I‘,,,,,,,d@

+l!w

+39O

04

/

I

+131°

+3O -

\

0

0

/ AH -H

f 1270I

f ‘No

in-plane H,- C

(vii) Fig. 2. Structures: (i) CH-(-X, (ii) X-W-Y. (vi) cyclooctatriene, (vii) the ketene resulting bonds, and (viii) toluene [22].

(iii) from

HPCXYZ. a I,5 H-atom

orthogonal H,- C

(viii)

(iv) cyclohexadiene, (v) bicyclo[5,l,O]octa-2,4-diene [21], BCOD, shift m eZ:Ee-hexadiendial. with torsion angles about the C/C

Table 1 Computational levels, in the order cited with the lettering the Tables that follow”

used in

RHF/6-31G* MP2(FC)/6-3 1 G* h MP2(FULL):6-3 I G* ’ RHFiHUZSP(3)** MP2(FC)!HUZSP(3)** h MP2(FC)!‘6-3 lG** ’ MP2(FC):6-31++G** h RHF:6-31G**(5D) RHF/6-31G*(5D) RHF/6-31+-G**

[I2 141 [13 151 [13~ 151 [12.16- 181 [15-IS] [I3315 [13- 15,19] [I2 141 [12 141 [1214.19]

a The GAUSSIAN series of programs were [IO,1 I]. b FC indicates the core orbitals wre frozen. ’ FULL indicates all orbitals were active.

by use of the computer

program

2.2. Computational

Refs. A. B. C. D. E. F. G. H. I. J.

then calculated ICRVIEW [9].

used

All

calculations were carried out with the series of programs using gradient optimization techniques [lo,1 11. A variety of basis sets, i.e. 6-31G*, 6-31G**, 6-31++G**, and HUZSP(3)**, and computational levels, i.e. restricted Hartree-Fock (RHF) and second-order Moller-Plesset perturbation theory (MP2), were used in these studies (see the listing in Table 1) [ 12- 191. In many cases vibrational frequencies of the structures were obtained from analytic second derivatives in order to determine if the computed structures were stable states or first-order transition states. For comparison, the bond angles for several of the structures are reported for more than one basis set and/or computational level. GAUSSIAN

throughout

2. Methods 2.1. Esperimentai

3. Results Results from the neutron diffraction studies reported in the scientific literature were obtained from the Cambridge Structural Database (CSD) [8]. Atomic positions were extracted from this database for molecules containing the X-CH,-Y grouping, and the geometry of each molecule was

The bond angles obtained from the diffraction studies on selected molecules ing the X-CH2-Y grouping are listed in Bond angles calculated from a variety of molecular orbital studies for a selection of

neutron containTable 2. ab initio CHs -X

Table 2 Neutron diffraction data in the Cambridge Structural Database [8]. Bond angles. in degrees, about the tetrahedrally bonded carbon atom in typical X-CH2-Y structures, and their summation, C L calculated using IRCYIEW [9]. The two hydrogen atoms are designated H, and Hi,. Values of estimated standard deviations (c.s.d.) for these neutron diffraction results are about 0.2” (individual e.s.d. range from 0.1 to 0.7’) Molecule

REFC”

Bonding (XCY)

H,CHh

H,CX

HbCX

H,CY

H,,CY

XCY

CL

L-Arginine dihydrate Cyclodecane-1.6~rrans-dial Succinic acid Tripotassium citrate monohydrate Triethylenediamine L-Arginine dihydrate Monofluoroacetamide N-Acetyl-L-cysteine Glycine

ARGIND I1 CDECOLI 1 SUCACBOZ ZZZHV102 TETDAM03 ARGINDI 1 FACETAOI NALCYS02 GLYCIN16

C4CC4h C4CC4 C4CC3h c4cc3 C4CN C4CN C4CF c4cs C3CN

105.2 105.7 105.6 109.9 107.3 104.7 109.4 109.4 108.9

107.2 108.1 I1 I.0 106.0 112.0 106.4 109.1 109.0 108.4

107.1 106.8 112.0 107.9 112.4 112.4 109.8 108.8 111.2

111.6 111.9 107.1 108.1 107.2 108.5 108.8 106.3 108.6

110.5 110.5 107.8 108.7 107.2 112.2 108.7 109.4 107.9

114.8 113.4 113.0 116.2 110.5 112.1 111.1 113.9 111.7

656.3 656.4 656.4 656.8 656.6 656.3 656.8 656.8 656.7

a Reference listing (REFCODE) in CSD. ’ C4 and C3 denote a carbon atom with a connectivity

POI.

of four and three. respectively.

i.e. tetrahedrally

and trigonally

bonded

carbon

Table 3 Bond angles. in degrees. m CHIPX structures m which C-X is a trigonal axis of symmetry. Data are from the results of ab initio molecular orbital calculations. The number below each angle in the angle columns gives the deviation from the regular tetrahedral angle of 109.47”, and the number below the summation of the angles, CL. gives the deviation from the regular tetrahedral sum of 656.83’ Molecule

Computattonal IeveV

HCH

HCX

1

CH,-Li

B

CHs-BeH

B

CH,-F

B

107.0~ 2 45 IO6 97 -2 50 109.x.’ tO.38 I1074 tl.3 I ox 80 --0.67 I Oh.89 -2.5X 107 00 -1.38 I IO.99 T I.52 I 10.04 t 0.57 107.67 ~ I .x0 107.66 -1.x1 107 71 -I 76

I 11 .x2 +2.35 1 1 1.x7 1-2.40 109.09 -0.38 10x.17 -1.30 I 10.13 -0.66 111.94 t2.47 I 11.76 +1.19 107.90 ~ I .57 IOX. -0.57 1 I I.22 -I 75 III 22 + 1.75 III.18 $1 71 lll.l? + 1.65 I I I .02

656.52 -031 656.51 -0.31 656.82 -0.01 656.73 -0 IO 656 79 -0.04 656.49 -0.34 656.55 -0.28 656 67 -0.16 656.82 -0.01 656.67 -0.16 656.64 -0. I9 656.67 -0.16 656.70 -0.13 656.70

G CH,-Na

B

CH, -MgH

B

CHs-MgF

A

CH,-Mg+

A

CH, -CL

B

CH, -CH?

H

B CH, -SiH3 B

107.78 -1.69 107.X8 I.59

a See Table

+ I .55

-0

13

angles obtained from ab initio studies for the bonding around tetrahedral carbon atoms in toluene. ally1 alcohol, norcaradiene and cycloheptatriene, oxirane, fluorooxirane, and benzene oxide, their oxonium ions, the para-quinoid benzene carbocation, and four conformers of 2-formyl-2Hpyran, are listed in Tables 6 to 12. In Tables 2. 4 and 5 the carbon atoms bonded to the tetrahedral carbon in the CH3-X and X-CH:-Y structures are denoted by their connectivity, i.e. C4 for a carbon atom connected to four atoms and C3 for a carbon atom connected to three atoms [20]. In Tables 6, 8, 11, and 12 the designation C(r) is used to indicate a carbon atom in the ring. and in Table 12, C(f) is used to indicate the carbon atom of a formyl group. To further facilitate identification of the various tetrahedrally bonded carbon atoms, the more complex structures are depicted in Figs. 2(iv)-2(viii), 3(i)-3(v) and 4(i) and 4(ii). When the atoms bonded to the tetrahedral carbon atom in the CH,-X, X-CHZ-Y, and H-CXYZ structures have different electronegativities, the angles are listed with HCX preceding HCY, HCY preceding XCY, etc. according to increasing electronegativity in going from X to Y to Z. The number below each angle in the Tables gives the deviation from the regular tetrahedral angle of 109.47’, while the number below the summation of the angles gives the deviation from 656.83”. In the majority of cases where the angles have been obtained using two different basis sets or computational levels, the relative values are unaltered.

1

4. Discussion structures in which CX is a trigonal axis of symmetry are listed in Table 3. Table 4 lists a further selection of optimized CH3-X structures which lack this symmetry element but which still have a plane of symmetry defined by H,. C. and X with Hb and H, located symmetrically on either side of this plane (see Fig. 2(i)). Table 5 lists the angles calculated for X-CH2-Y structures (X, Y # H) in which H, and Ht, lie equidistant on either side of the X-CY plane (see Fig. 2(n)). Data for several structures which lack these symmetry properties have also been included for comparison. Additional

4. I. Deviation of individual bond angles from 109.47 I and their summation from 656.83” In typical X-CH1_-Y structures obtained by neutron diffraction studies the individual bond angles around tetrahedral carbon atoms are found to vary from approximately 105” to 116”, see Table 2. where the estimated standard deviations of the individual experimentally determined bond angles are of the order of a few tenths of a degree in each case. In spite of this variation,

160

sulfur. For several of the molecules in Table 2, as well as for many other X-CH2-Y structures listed in the CSD. the HCH angle is the smallest and the XCY angle (X, Y # H) is the largest, showing the importance of the size of X, Y, and H, or some allied property.

the summations of these angles differ from the maximum value of 656.83” by only a few tenths of a degree, as shown in the last column of Table 2. The near constancy of the sum holds true despite the different nature of the atoms bonded to the -CH2group, i.e. carbon, nitrogen. fluorine. or Table Bond either from regular

4 angles, in degrees. in CH1-X structures, with the plane through H,. C, and X as a reference. Hydrogen atoms H, and H, lie on side (see Figure 2i). Data are from ab initio calculations. The number below each angle, in the angle columns, gives the deviation the regular tetrahedral angle of 109.47‘, and the number below the summation of the angles, C i, gives the deviation from the tetrahedral sum of 656.83

Molecule

Computational level”

CHj-CQ CH?-CH?CH,

CHJ-CH2NHZ

CHI-CH20H

CH;-CH?F

CH,-CH2PHI CH3-CH:CHzCH3 CH3-CH2CHzNLHj CHI-CH2CHzSCHI rrcms-CH?-CH?ONO,

CH, - C3 CH?CHCH,

(CHj

),CCH:

CH? -CHO CH,-CO?H CH,-CO,Na

A

H,CH,

H,CH,

HcCH-I,

H,CX

107.64 -1.83 107.70 -1.77 107.71 -1.76 107.79 - 1.68 108.30 -1.17 108.51 -0.96 10X.40 -1.07 108.59 -0.88 107.79 -1.68 107.63 -1.84 108.45 -I .02 107.83 -1.64 108.70 -0.77

107.74 -1.73 107.89 -1.58 108.48 -0.99 108.72 -0.75 IOU.65 -0.82 108.81 -0.66 108.54 -0.93 10X.6X -0 79 107.83 -1.64 -1.76 107.82 -I 65 107.74 -1.73 IOX 55 -0.92

107.74 -1.73 107.89 -1.58 108.48 -0.99 108.72 -0.75 108.65 -0.82 108.81 -0.66 108.54 -0.93 108.68 -0.79 107.83 -1.64 107.71 -1.76 107.85 -1.62 107.74 -1.73 108.55 -0.92

111.38 +I.91 111.55 +2.08 115.15 -1.68 111.33 +1.86 110.68 +I.21 110.77 +1.30 110.34 +0.87 110.45 to.98 110.80 f1.33 111.30 +I.83 109.81 to.34 110.86 f1.39 109.10 -0.37

107.06 -2.41 107.06 --2.41 106.89 -2.58 107.x -3.21 10x.04 - 1.43 107.18

10x.20 - 1.27 108.22 -1.3 108.23 -1.24 109.85 +0.3x 109.39 -0 ox 109 91

108.20 -1.27 108.22 - 1.25 108.23 -1.24 109.85 t0.38 109.38 -0.09 109.91

11 I.40 +1.93 110.95 +I.48 111.78 +2.3 1 110.23 ‘0.76 109.34 -0.13 111.27

IO?.71

H,,CX

H,CX

CL

111.08 +I.61 110.82 +1.35 110.46 +0.99 110.10 +0.63 110.25 +0.78 109.95 f0.48 110.47 +1.00 110.20 LO.73 111.22 +1.75 111.16 +I.69 111.39 t1.92 111.26 f1.79 110.94 +1.47

111.08 +I.61 1 IO.82 f1.35 110.46 +0.99 110.10 f0.63 110.25 +0.78 109.95 ~0.48 110.47 f1.00 110.20 +0.73 I1 1.22 +1.75 111.16 +1.69 111.39 +1.92 111.26 +I.79 110.94 +1.47

656.66 -0.17 656.67 -0.16 656.74 -0.09 656.76 -0.07 656.78 -0.05 656.80 -0.03 656.76 -0.07 656.80 -0.03 656.69 -0.14 656.67 -0.16 656.71 -0.12 656.69 -0.14 656.78 -0.05

110.91 +1.44 111.12 +I.65 110.77

110.91 +1.44 111.12 +I.65 110.77 +1.30 109.83 +0.36 110.32 +035 109.24

656.68 -0.15 656.69 -0.14 656.67 -0.16 656.19 -0.04 656.8 1 -0.02 656.75

A.30 109.83 +0.36 110.34 f0.87 109.24

Table

4 contmued

Molecule

Computational level”

HhCH,

H,CHh

H,CH,

H,CX

CH3+Z02Mg+

A

I 1 I .67 +7.70 107.57 PI.90

108.57 -0.90 I IO.32 -0.85

108.56 -0.91 I 10.40 to.93

107.64 -1.83 110.76 +I.29

109.96 +0.49 107.50 -1.97 106.02 -3.45 107.54 PI.93 :w43 - 1.04 108.80 PO.67 109 88 f0.41 IO9 49 +0.02 109.40 -0.07 107.53 ~ 1.94 106.70 -2.77 109.79 +0.32 109.77 +0.30 109.46 PO.01 108.56 p0.91 107.18 -1.29

106.31 -3.16 I ox .o 1 ~ 1.36 107.71 -1.76 108.71 -0.76 109.43 PO.04 108.52 -0.95 108.46 - 1 .01 108.71 -0.76 110.77 1.30 10x.51 --0.96 108.31 -1.16 1 IO.18 -0.71 I IO.09 -0.62 108.69 -0 78 IIO.hX -1 21 107.60 -I .x7

106.30 -3.17 108.01 ~ I .46 107.71 -1.76 10x.71 -0.76 109.43 PO.04 108.52 -0.95 108.46 pl.Ol 108.71 -0.76 110.77 11.30 108.51 -0.96 108.31 -1.16 111.20 +1.73 110.93 +I.46 108.69 PO.78 1 IO.10 +0.63 107.60 PI.87

104.99 -4.48 115.39 +5.92 113.16 +3.69 113.71 +4.24 112.16 +2.69 106.25 -3.22 106.65 -2.82 107.50 - 1.97 110.45 10.98 112.61 t3.14 112.98 t3.51 I 11.80 +2.33 112.73 +3.26 107.51 PI.96 107.81 -1.66 112.34 +2.87

CH- 1-CO

A

2Al’*

CH,-hrtrromm CH?-BH2

B

CH, -NH,

B

CH?-AlH2

B

CH,-PHI

B

CH,-ASH?

D

CHlpOH

B

CHl+H

B

CH3-SCHI

A

CH3++(CHj)2

A

CH~-P(CH!I~

A

CH,-Ga(CH3)2

E

CHjpN(NO,)lh

A F A Ah A

a See Table I. h Unsymmetrical

H,CX

H,CX

CL

110.15 to.68 108.81 PO.66

110.14 +0.67 108.89 -0.58

656.73 -0.10 656.75 -0.08

114.26 t4.79 108.82 -0.65 110.95 + 1.48 108.99 -0.48 108.66 ~0.81 112.31 t2.84 111.62 +2.15 111.17 -1.70 107.68 -1.79 109.77 +0.30 110.16 +0.69 106.85 -2.62 106.58 -2.89 I II.20 +1.73 108.69 -0.78 110.94 +1.47

114.26 +4.7t? 108.82 -0.65 110.95 + I .48 108.99 -0.48 108.66 -0.81 112.31 +2.84 Ill.62 +2.15 Ill.17 +1.70 107.68 -1.79 109.77 +0.30 110.16 +0.69 106.88 -2.59 106.60 -2.87 111.20 +1.73 110.98 +1.51 110.94 +1.47

656.07 -0.76 656.55 -0.28 656.50 -0.33 656.65 -0.18 656.77 -0.06 656.7 1 -0.12 656.69 -0.14 656.75 -0.08 656.75 -0.08 656.70 -0.13 656.62 -0.21 656.70 -0.13 656.70 -0.13 656.75 -0.08 656.82 -0.01 656.60 -0.23

structure.

Leaving aside for the moment structures in which the tetrahedral carbon atom is part of a four- or three-membered ring, the bond angles obtained from the ab initio molecular orbital calculations substantiate these neutron diffraction results, and extend them to include bonding of the carbon to an even wider range of heavy atoms: Li, Be, B, 0. Na, Mg, Al, Si, P, Cl, As, and Ga. A survey of the data shows that individual bond angles in the

CH3-X structures with the trigonal axis vary from about 107’ to 112” (Table 3); in the CHs-X structures in which Hb and H, are located symmetri-tally on either side of the H,CX plane from approximately 106“ to 113’ (Table 4); and in the X-CH2-Y structures from 105’ to 117’ (Table 5). Yet again, the summation of the angles about the tetrahedrally bonded carbon rarely differs from the maximum of 656.83’ by more than a few tenths of a degree.

162 Table 5 Bond angles, in degrees. in XPCH:-Y structures. H,-C and HhPC lit at the same distance on either side of the XPCPY plane. Structures of the larger molecules are depicted m Fig. ?(iv)-?(viii) and 3(i)-3(iv). Data are from ab initio calculations. The number below each angle, in the angle columns. gives the deviation from the regular tetrahedral angle of 109.47”. and the number below the summation of the angles. 1 . gives the deviation from the regular tetrahedral sum of 656.83 Molecule

C4&CH,-C4 CH1-CH:CH,

Computational levela

H
‘4

I06 26 -3.21 106.30 -3.17 106.24 -3.23 106.65 -2.82 Il4.21 13.73 117.83 +x 36 107 35 -2.12 106.74 -2.73

lO9.4l PO.06 109 48 10.01 109.40 PO.07 107.92 PI.55 I17 57 +X.10 95.51 -13.96 109.65 fO.lX 109.67 +0.x1

10X.64 -0.83 105.45 -4 02 106.38 -3 09

B A Cycloheptadtene

A

ciwid-BCOD. 3-ring [2l] cisoi&BCOD, TS: 1.5 H-shift [21] CH1-CH2+I?H2N+H3

A“ A” A 4

C4-CH,-C3 Cyclobutene

4

Cycloheptadiene

.4h

ci.wid-BCOD. 7-ring [2 I]

Ah

C3-CH,-C3 Cyclooctatriene Keteneb from eZ:Ee-hexadiendtal rrclnsoid-BCOD, TS: Cope rearrangement C4-CH:-heteroatom CH,-CH,pNH,

CH,-CH:-OH

CH,-CH2pF

Ah A Ah

H,CX

HhCX

H,CY

HbCY

XCY

c:

’ 109.41 -0.06 109.48 +0.01 109.40 -0.07 107.92 -1.55 Il9.00 t9.53 8X.60 -20.87 109.65 f0.18 109.67 +0.20

109.38 -0.09 109.48 f0.01 109.25 -0.22 109.26 -0.21 117.89 +8.42 115.41 -5.94 109.62 to.15 109.32 -0.15

109.38 -0.09 109.48 fO.0 1 109.25 PO.22 109.26 -0.21 117.94 +8.47 114.79 -5.32 109.60 -0.13 109.32 PO.15

112.79 +3.32 112.43 +2.96 113.08 +3.61 115.46 +5.99 59.69 -49.78 119.95 +10.4x 110.91 f1.44 1 I 1.98 +2.51

656.63 -0.20 656.65 -0.18 656.62 -0.21 656.47 PO.36 646.30 -10.53 652.09 -4.74 656.78 -0.05 656.70 -0.13

114.89 -5.42 10X.16 PI.31 108.97 -0 50

114.89 -5.42 109.68 f0.21 109.43 -0.04

I1 5.X3 +6.36 107.75 -1.72 108.30 -1.17

115.83 +6.36 109.15 PO.32 110.31 +0.84

X5.46 -24.01 116.09 +6.62 113.20 +3.73

655.54 - 1.29 656.28 -0.55 656.59 -0.24

IO6 12 ~ 3 35 IOX.OX - 1.39 lOY.21 -0.26

107.x8 -1 5’) 110.68 +I.21 112.77 +3.!0

108.45 -1.02 111.83 f2.36 112.70 f3.23

108.00 - 1.47 107.26 -2.21 117.15 -7.68

108.95 -0.52 107.85 -I .62 109.15 -0.32

116.92 +7.45 110.97 +1.50 95.36 -14.11

656.32 -0.51 656.67 -0.16 656.34 -0.49

106.10 -3.37 106.13 -3.34 107.53 ~ I .94 107.61 -I 86 108 73

109.32 -0 I5 109.45 -0.02 I 10.07 to.60 110.17 f0.76 I1 1.53 +2.06 III.63 tl. I6

109.32 PO.15 109.45 -0.02 110.07 +0.60 110.17 +0.70 III.53 f2.06 111.63 +2. I6

110.32 +o.s5 110.58 +1.1 I 110.58 +1.11 110.91 fl.44 107.67 - 1.80 107.78 -1.69

110.32 +0.85 110.58 +1.1 I 110.58 +I.11 110.91 +1.44 107.67 -1.80 107.78 -1.69

111.30 Al.83 110.55 +1.08 108.00 -1.47 107.07 -2.40 109.55 f0.08 109.19 -0.28

656.68 -0.15 656.74 -0.09 656.83 0.00 656.84 +0.01 656.68 -0.15 656.70 -0.13

-

-0.74

108.69 -0.78

Molecule

Compurational level“

H,CHh

H,C)<

HhCX

H,CY

H,,CY

XCY

Cl

CH3-CH>-PHz

A

105.X? -3.64 109.10 -0.37 109.11 -0.36 107.84 - I .63

I IO.21 co.74 112.44 -2.Y7 1 12.34 +2.X1 1 IO.14 +0.67

1 IO.21 -0.74 112.46 -2.99 112.34 t2.87 110.14 t 0.67

106.68 -2.19 106.02 -3.45 108.76 -0.71 108.94 -0.53

106.68 -2.79 106.03 -3.44 108.76 -0.71 108.94 -0 53

116.63 +7.16 110.40 f0.93 105.36 -4. I I I IO.78 f1.31

656.24 -0.59 656.45 -0.38 656.67 -0.16 656.78 -0.05

107.36 -2. I I 107.51 -1.96 107.33 -2.14 106.45 -3.02 I I 1.90 -2 43

109.72 to.25 110.11 +0.64 I IO 22 +0.75 107.96 -1.51 105.63 -3.84

109.72 hO.25 110.1 I +O 64 110.22 to.75 108.17 -1.30 105.63 -3.84

108.13 -1.34 110.60 +I I3 111.00 +1.53 105 33 -4.14 114.73 +5.26

108.13 -1.34 110.60 +I.13 I II.00 +I.53 108.67 -0 80 114.73 1-5.26

113.59 +4.12 107.91 -1.56 107.10 -2.37 119.54 t10.07 102.89 -6.58

656.65 -0.18 656.84 +0.01 656.87 f0.04 656.12 -0.71 655.51 -1.32

109.52 fO.05 10X.30 -1.17 109.01 -0.46 113.47 +3 95 114.40 t 4.93

107.Yl -1.56 10X.54 -0.93 106.52 -2.95 108.76 -0.71 10X.47 -1.00

107.91 -1.56 108.54 -0.93 III.29 +I.82 I OX 76 -0.71 108.47 -1.00

107.95 - 1.52 110.23 -0.76 III.46 +1.99 108.76 -0.71 108.47 -1.00

107.95 -1.52 I IO.21 -0.74 109.86 f0.39 108.76 -0.71 IO8 47 -1.00

115.51 +6.04 110.95 +1.48 108.66 -0.81 108.25 -1.22 108.42 -2.05

656.75 -0.08 656.77 -0.06 656.80 -0.03 656.71 -0. I2 656.70 -0.13

CH3CH2-CH,-N

‘HI

A

wznx-CH,-CH,-ONO,

A

CH3CH,-CH,-SCHq

A

C3-CH~~hrrerocrtor,1 sw-CH?CH-CH2-OH

A

anti-CH,CH-CH?-OH

A B

-OJ-CH,-SCH,

Ah

H,C-

-CH2-OH

A

hrterocrtonl-CH~-k~rrroatonl Li-CH,-Li

B

H>N-W-OH

.A

HO-CH,

-OH

F-CH,-F

Bh .I (;

BCOD. bicyclo[5, I .O]octa-2.4.dlenc a See Table I. h Unsymmetrical structure.

The computed bond angles around the tetrahedral carbons in four- and three-membered rings reveal a strong tendency to attain the maximum value - despite the small ring angles - by particularly large compensatory increases in the remaining angles. For example. in cyclobutene. see Table 5. the CCC ring angle is 24.0 less than 109..5’, but the summation of the angles falls short of 656.8’ by only 1.3. as a result of compensatory increases of 5.4’ and 6.4 in the HCC angles. In the three-membered CCC rings in c&id-BCOD. Fig. 2(v) and Table 5. and norcaradiene. Fig. 3(ii) and Table 8, the ring angles are 49.8 and 48.3.’

respectively less than 109.S’, but compensatory increases in the HCC angles of &9”, and also an increase in the HCH angles of about 5’, reduces the deficit in the summation of the angles to about 10.5&. The data for -CH2in the three-membered COC rings in oxirane, fluorooxirane, and the corresponding oxonium ions, see Table 9, show very similar features. There are likewise compensatory increases in the bond angles around H-C in the three-membered COC rings in benzene oxide, fluorooxirane, and their oxonium ions which offset the adverse contribution of the small ring angles (see Table 10).

Table 6 Bond angles, rn degrees. m CH?groups m toluene. (i) in whtch H,-C lies in the plane of the phenyl ring, (ii) in which H,-C is orthogonal to the nominal ring plane [22] (see Fig. 2viii). Data are from ab initio calculations. The number below each angle, in the angle columns. gives the deviation from the regular tetrahedral angle of 109.47.. and the number below the summation of the angles, C L, gives the deviation from the regular tetrahedral sum of 656.X3 Structure

Computational level”

HhCHc

H,CH,

H,CH,

H,CC(r)

&CC(r)

(9

A

(ii)

A

107.43 -2.04 107.92 -1.55

107.81 ~ 1.66 107.54 -I .93

107.81 -1.66 107.54 -1.93

I II.26 +1.79 I I I .09 ~1.62

111.18 fl.71 III.29 +I.82

” See Table

KXC(r)

1 I I.18 +1.71 I II.29 +I.82

CL

656.67 -0. I6 656.67 -0.16

I

Table 7 Bond angles, in degrees. in the -CH2 - groups in ally1 alcohol, ayn, in which the H-atom of the H-O group is coplanar with 0-C-C=C and lies toward the C=C bond. and anti, in which the H-atom lies away from the C=C bond (see Fig. 3i). Data are from ab initio calculations. The number below each angle, in the angle columns, gives the deviation from the regular tetrahedral angle of lO9.47”, and the number below the summation of the angles, C I, gives the deviation from the regular tetrahedral sum of 656.83 Structure

Computational level”

H,CHh

H,CC3

HhCC3

H,CO

&Co

c3co

CL

syn

A

anti

.4

107.36 -2. I I 107.51 ~ I .Y6 107.33 -2.14

109.72 -0.25 110.11 -0.64 I IO.22 +0.75

109.72 +0.25 110.1 I +0.64 110.27 +0.75

108.13 -1.34 110.60 +I.13 I I I .oo -1.53

108.13 -1.34 110.60 +I.13 111.00 +I.53

113.59 +4.12 107.91 -1.56 107.10 -2.31

656.65 -0.18 656.84 +O.Ol 656.87 +0.04

B

’ See Table

1.

Table 8 Bond angles. in degrees. in the -CH,groups m norcaradtene (NCD) and cycloheptatriene (CHT) [23], see Figs. 3(ii) and 3(iii), the transition state for the valence tautomerism. NCD ++ CHT, and the transttion state for the inversion of the ring in CHT. Data are from ab initio calculations. The number below each angle. in the angle columns, gives the deviation from the regular tetrahedral angle of lO9.47”, and the number below the summation of the angles, C : . gives the deviation from the regular tetrahedral sum of 656.83 Structure

Computational level”

H,CI-Ih

H,CCI

NCD

.4

114.95 +5.48 112.57 +3.10 107.14 -2.33 104.12 -5.35

117.26 +7.79 114.63 +5.16 109.29 -0.18 107.87 ~ I .60

TS: NCD

-

CHT

CHT TS: CHT

A A

Inversion

a See Table

I

r)

YICC(r)

&CC(r)

H&C(r)

C(r)CC(r)

C i

117.26 +7.79 114.63 f5.16 109.29 -0.18 107.87 -1.60

117.86 -8.39 I 15.25 +5.78 110.29 +0.82 107.87 -1.60

117.86 -8.39 115.25 +5.78 110.29 +o.s2 107.87 -1.60

61.20 -48.27 81.14 -28.33 110.46 to.99 120.44 f10.97

646.39 -10.44 653.47 -3.26 656.76 -0.07 656.04 -0.79

Table 9 Bond angles, in degrees. about the KHZgroups in oxirane. fluorooxirane. and the corresponding oxonium ions (see Fig. 3iv) [24]. Data are from ab initio calculations. The number below each angle, m the angle columns, gives the deviation from the regular tetrahedral angle of 109.47”. and the number below the summation of the angles. C ‘_ gives the deviation from the regular tetrahedral sum of656.83 Structure

Computational level”

H.,CH,

H,CC

&CC

Oxirane

A

1 15.22 -5.75 I 17.42 t7.95 116.45 f6.98 1 IX.42 +8.95 118.47 t 9.00

119.88 +10.41 119.90’ t 10.43 118.5X’ t9.1 1 119.17” 19.70 118.33” -8.86

119.88 -10.41 120.46” + IO.99 121.01’ +I 1.54 120.02“’ +10.55 120.83”’ +I 1.36

Oxonium

ionh

‘4

Fluorooxirane’ anti-F

A

oxonium

ion’

A

sq’n-F oxonium protonation

ion’

A

HhCO

H,,CO

cc0

115.23 -5.76 112.68’ +3.21 114.40’ +4.93 108.69” -0.78 112.66” t3.19

115.23 +5.76 109.15” -0.32 115.10’ -5.63 113.11”’ +3.64 109.22”’ -0.25

58.78 -50.69 61.13 -48.34 56.63 -52.84 61.01 -48.46 60.98 -48.49

a See Table I. b s and a denote the structures where the H-atom of the H-O groups IS respectively in the syn and anti position H/X atom: c and I denote the structures where the H-atoms of the H,C group are respectively, cis and tram in relation Fig. 2iv).

To characterize the interplay between the increase in some angles and the decrease in others, the interrelationships have been classified according to the schemes set out in Table 13(A) and 13(B) for the optimized CHj-X structures in Tables 3 and 4. and in Table 13(C) for the computed X-CH?-k structures in Table 5. The

644.22 -12.61 640.74 -16.09 642.17 - 14.66 640.42 -16.41 640.49 -16.34

in relation to the to the F-atom (see

breakdown of the CHs-X structures among the various classes is given in Table 14. If nuclear repulsion between bonded hydrogen atoms in the methyl group is a significant factor, it might be expected that the smaller angle(s) would be subtended by the longer bond(s), and vice-versa. This possibility is tested by classifying the H-C

Table 10 Bond angles, in degrees, about the H C group in benzene oxide [25]. Auorooxirane and the corresponding oxonium ions [24] (see Figs. 3iv and 3~). Data are from ab nutio calculations. The number below each angle. in the angle columns, gives the deviation from the regular tetrahedral angle of 109.47 and the number below the summation of the angles, 1 ,I, gives the deviation from the regular tetrahedral sum of 656.83 Structure

Benzene

oxide

Benzene

oxonium

ion

Fluorooxirane

Computattonal level”

H,,(‘C4

H,c‘CZ

H,CO

c4cc3

A

119.49 + IO.02 11921 t 9 74

1 17.23 h7.76 11X.91 +L).44

113.50 +4.03 109.09 -0.38

117.73 +8.26 119.04 +9.57

l-1,a(‘c4

H,*CF

H,CO

124. I? 714.70 111.73 --cl3 26 123 26 -14.79

110.86 Al .39 114.92 c5.45 115.41 e5.94

117.26 +7 79 112.64 t3.17 110 13 tO.66

A

A

anti-F

oxonium

ionb

A

syn-F

oxonium

ionb

A

a See Table 1. b See footnote to Table

8. and Fig. 3(iv).

c3co

c4co

c-’

116.92 +7.45 112.91 +3.44

58.31 -51.16 61.85 -47.62

643.18 -13.65 641.01 -15.82

C4CF

OCF

c4co

118.95 +9.4x 119.95 +10.48 I 18.26 +8.79

115.61 f6.14 110.46 f0.99 111.86 +2.39

61.04 -48.43 61.67 -47.80 61.76 -47.71

647.89 -8.94 642.37 -14.46 641.68 -15.15

Table 11 Bond angles. in degrees, about the H,* -C group in the cis. gauche, and tram conformers of thepara-quinonoid benzene carbocation [25] (see Fig. 4i). Data are from ab mitio calculations. The number below each angle, in the angle columns, gives the deviation from the regular tetrahedral angle of 109.47 and the number below the summation of the angles, C i, gives the deviation from the regular tetrahedral sum of 656.83 Structure

Computational level”

H,CC(r)

H,CC(r)

H,CO

C(r)CO

C(r)CO

CWCC(r)

C L

cis

A

gaucheh

-4

trans

.4

102.08 -7.39 102.45’ -7.95 IO1 02 -8.45

102.08 -7.39 lOIS?! -7.02 101.02 -8.45

112.33 --2.16 112.08 t 2.61 105.63 -3.84

112.50 f3.03 110.66 +1.19 115.60 t6.13

112.50 f3.03 114.54 +5.07 115.60 -6.13

114.48 +5.01 114.54 +5.07 I 15.00 f5.53

655.87 -0.96 655.79 -1.04 653.87 -2.96

’ See Table I b s and I indicate the H,CC(rj group and the H-atoms bonded

angles associated with the shorter and longer to the adlacent C(r) atoms m the ring.

distances.

respectively,

between

the H-atom

of the H-O

Table I2 Bond angles, in degrees. about the H,-C group in the pyran ring in the anti-axial (a-a), anti-equatorial (a-e), syn-axial (s-a), and syn-equatorial (s-e) conformers of 2-formyl-2H-pyran [26] (see Fig. 4ii). The data are from ab initio calculations. The number below each angle. in the angle columns, gives the deviatton from the regular tetrahedral angle of 109.47”, and the number below the summation of the angles, c gives the deviation from the regular tetrahedral sum of 656.83 Structure

Computational level”

H,CC(f

a-a

A

a--c

4

s-a

.4

s-e

.4

IO6 74 -7.73 106.97 -2.55 107 48 -1.99 106.22 -3.25

d See Table Table 13 Classification

I

H,CC(r!

H,CO

C(fYXr)

C(f)CO

C(r)CO

C i

I IO.19 -0.72 110.08 -0.61 1 IO.45 +0.9x 109.44 -0.03

106.56 -2.91 108.57 -0.90 106.00 --3.47 108.62 -0.85

110.31 f0.84 112.20 +2.?3 109.57 -0.10 I IO.85 +I.38

108.60 -0.87 106.20 -3.27 110.57 f1.10 108.57 -0.90

114.10 f4.63 112.62 +3.15 112.63 +3.16 112.89 +3.42

656.50 -0.33 656.59 -0.24 656.70 -0.13 656.59 -0.24

1. of the bond angle relationships

about

the tetrahedral

carbon

atom Class

A.

B.

C.

CH?-X. HCH HCH CH,-X, H,CH, Ht,CH, H,CH, H,CH,

trigonal < HCX > HCX Fig. < < > >

axis

2(i) (H,CH,=H,CH,) (H,CH,,=H,CH,) (H,CH,=H,CH,) (H,CH,=H,CH,)

X-CH,-Y. Fig. ‘Iii) (H,CX=HbCX; = (H,CY=HhCYI H,CX=HhCX) < (H,%CY=H,CY (H,CX=H,,CX) > !H,CY=H,CY)

I II

and and and and

H,CX H,CX H,CX H,CX

I

> i > <

(H,CX=H,CX) (Ht,CX=H,CXI (H~CX=H,CXI (H,CX=H,CX)

I II III IV

I II III

167

(iii)

(ii)

Fig. 3. Structures: (i) ally1 alcohol. (ii) norcaradicne and (v) benzene oxonium ion [25].

(NCD)

(iii) cycloheptatriene

(CHT)

[23]. (iv) oxonium

and fluoroxonium

ions [24],

gauche

CiS

anti-axial

Fig. 3. Structures:

(i) pwo-quinonoid

tram

mti-quatorial

benzene

carbocatton

[20], and (ii) 2-formyl-2H-pyran

[26].

Table 14 Classification of the bond angle relationshlps abou( the tetrahedral carbon axis of symmetry, and 13(B) with Hh and H, lymg either side of the H,CX distances, see Table 15, according to whether (i) H,%-C > H,-C=H,-C. Molecule A. CH,-X CH3-Li CH3-BeH CH3-F CHI-Na CH,-MgH

(trigonul

a Unsymmetrical

Class

Molecule

Class

I I II I I

CH, MgF CH,-Mg‘ (‘Hx --Cl CH>-CHI CHi-SiHl

I II II 1 1

I(10 I(i) I(i) Ill) II(i) I(ii) IV(ii) IV(ii) IV(l)

(‘Hi-ffl~rernutont C‘H;-BH2 W-NH, CH,-AIH: CH,-PH, CH, -ASH, W-OH CH?-SH CHJ-SCH; CH~-S’ICH,J~

IV(i) VI I(ii) I(ii) I(ii) IV(ii) IV(i) IV(ii) I(ii)

CH;-P(CHI)2 CH?-GalCH: J: (‘H?-N(N02)2 CH, -SCH,(‘H2CH, CH,-SCH,CQ CHI-CIAICI~AICICH;

I(i) I(ii) a IV(il) a I(ii)

13(A). with the trigonal between the H-C bond

0.1.i.y,

B. CH, - X i Hh urrd H, cithrr CH, - C4 CH, -CHJH, CH, -CH2NH2 CHI-CH,OH CH,-CH,F CH;-CH,PH2 CHx-CH2CH2CHJ CHJ-CH2CH2N+H1 CH3-CH2CH,SCHJ rrans-CH,-CH,ONO, CH, - C3 CH? -CHCH, (CH~)KCHz CH,-C,H, (H,-C CH3-C6Hc (Hz,-C CH? -CHO CHq-C02H CH? -CO?% CHj-CO:Mg’ CH, -CO,AI’+

atom m CH?-X. as set out in Tables plane. together with the relationship or (il) H,-C < H,-C=H,-C

sit/c, (I/ ff,;C.l’

m ring plane) orthogonal)

plutw I

II(U) I(ii) I(111 fV(I) I(11) II I(ii) IV(i) I(ii)

structure.

bond lengths. as listed in Table 15, and linking the bond length relationships to the bond angle relationships as shown in Table 14, e.g. I(i), I(ii), II(i). etc. Of the 31 examples the majority are thus in accord with expectations. Nevertheless there are important exceptions. There are five examples in category I(i), among which. for example, X has the adjacent C4 atom bonded to the electronegative atoms N, 0. and F, and there are four examples in category IV(ii), two of which have -OH and -SCH, bonded to the carbon of the CH3 group. Clearly no simple generalization is evident. In the X-CH?-Y structures. HCH is the smallest angle and XCY the largest in 13 of the 25 examples. as in several of the neutron diffraction structures in Table 2. in keeping with the

supposition that nuclear repulsion (minimal with HCH but maximal with XCY) is a significant factor. The HCH angles range from about 105 to 108’, and the XCY from about 111 to 117”. But in eight examples neither angle meets these criteria; in three, XCY is the largest angle but HCH is not the smallest, and in one case HCH is the smallest but XCY is not the largest. The classification of the HCX and HCY angles in Table 16, according to the scheme in Table 13(C), shows further inconsistencies. Only two of the six C4-CH2-C4 structures and one of the C3-CH,-C3 structures come into Class I, even though the atoms bonded to CH2 are identical. Li-CH:-Li and F-CH2-F do, however, meet this criterion. With two different heavy atoms

Table I5 Hz,-C. Hh-C and H,-C bond lengths (Al in CH:-X. Fig. I(it. The computational higher level arc given for those cases where two levels have been employed Molecule

KC

HhC

H,C

CH, - C4 CHJpCHLCHI CH,-CH:NH: CH, -CH?OH CH-CH,F CH,+?HZPH2 CH,-CH2CH,CHj CH,-CH,CHIN-H, CH,+EH,CH2SCH> trarzs-CH,pCH,ONO,

I .09? I .0950 I .OY32 I .0934 I .0865 I 0857 I.0821 I .0x2 I .0846

I ,094 I I .0924 I.0917 1.0916 3.0851 I .(I864 I .0843 I .086l 1 .083 I

I 0941 I .0924 I.0917 I.0916 I .08S I I .(I864 I .(I843 I .08hl I .0x3 I

CH,-C3 CHI-CHCH, (CH,),CCH, CHIpC,H,. CH,-C,H,. CH?-CHO CHs-C02H CH,-CO?Na CH1+JOZMg+ CH--CO,AI?+ 1

1.OY3 I I .0x22 I 0835 I 0870 I OX16 I 0794 I ox IO I 0860 IO795

I .0949 I .0X65 1.0861 I .0843 I .0866 1.0839 I 0848 I .0799 I 0839

I .(I949 I .0X65 I.0861 I .(I843 I .0X66 I.0839 I .0848 I .0799 I .(I836

in plane orthogonal

Table 16 Classification

of the bond angle rclattonships Class

Molecule C4-CH:-C4 CH,-CH,pCH, CH3-CH2pCH:CHr Cycloheptadiene Norcaradiene (NCD) choid-BCOD, 3-rmg BCOD. TS: 1.5-H Shift CH:-CH2-CHzN+H3 CH,-CH:-CH,SCH, C4-CH?-C3 Cyclobutene Cycloheptadiene cisoid-BCOD.

III

II a a

7-rmg

C3-CH:-CJ Cycloheptatriene (CHT) TS: NCD ++ CHT CHT. TS: inversion Cyclooctatriene “1.5” ketene from CZzEe-hexadiendial BCOD. T’s: Cope rearrangement

a Unsymmetrical

I III II II a a

structure

about

the tetrahedral

levels are listed

Molecule

carbon

atom

in X-CH2-Y.

Molecule

Class

(‘46 CH: ~hrrc~rouron~ CH:-CHzpNH2 CH;pCH-OH CII:pCH:-F CH:-CH~PPH? CH;--CHpW-N’H, rrcrrr\-CH-CH:-ONO, CH; -(‘I~, CH,pSCHI Oxtranc Oxomum ion Fluorooxiranc unri-Fluoroosonium ion .st,,r-Fluorooxonium ion

II II III III III 111 111 III a a a a

III II ;I

I II a I

in Tables

3 and 4. Values

at the

N-C

Hb-C

H,-C

I.1025 1.1002 I .0929 1.0908 I .0806 I .0899 I .0906 I .0822 I .0807 I .0864 I .0885 I .0852 I .086X

1.0921 I .0924 I.0961 I .0922 I .0828 1.0971 I .0904 I .0x30 I .0809 1.0853 1.0913 I.0861 I .0874

1.0921 I .0924 I .096l I .0922 1.0828 1.0971 I .0904 1.0830 I .0809 1.0853 1.0913 1.0861 1.0874

as set out in Table

13(C)

Table 17 CX bond lengths. m .& units. for the CH1-X structures m Tables those structures with the trigonal axis of symmetry The computational given for those cases where two levels have been employed Bond

Length

CH3-Li CH;-Be CH3-F CH3-Na CHI-Mg CH3 -Cl CH3-C4 CH3-Si

2.01 I 1.687 1.405 1.340 1.100 1.779 1.526 I.883

( 1.097) (I ,096) ( 1.087) (I ,094) (1.095) (I ,088) (1.093) (1.093)

14(A) and 14(B). and, in parentheses. the H-C bond lengths, for levels are listed in Tables 3 and 4. Values at the higher level are

Bond

Length

C‘HIpC3 (olefinic) CH>-C? (carbonyl) W-B CHIPN (‘Hi -rZI CH;pP C‘Hi-A\ CH;+J (‘H; -S CH : PGa

I 49X 1.496- 1.516 I.563 I 465- 1.468 I 946 I X53-1.860 I .97x I .-I74 1.803-1.816 I .Y75

bonded to CH2 it might be expected that HCX < HCY. i.e. Class II, since the angles are listed such that X is less electronegative than Y. Nevertheless the majority of the structures come into Class III. i.e. HCX > HCY. the most notable case being CH3-CH2-F for which angle HCC = 111.6’, whereas angle HCF = 107.8 The changes in the bond angles which accompany various intramolecular processes (rotation and ring inversion), and the protonation of the oxirane ring, can be calculated from the data in Tables 6- 12. As a further demonstration of the compensatory increases and decreases in the angles. it may be noted that the changes can amount to several degrees, even though the summation of the angles for the initial and final structures is still very close to 6.5683~ (Tables 7. 11 and 12).

The tetrahedra are all elongated with respect to the CX axis in the CH3-X structures in which this is a trigonal axis of symmetry. For the seven structures in Class I. Table 13, HCH < HCX, which is characteristic of elongation (see Fig. 1b). Moreover the C-X bonds are longer than the CH bonds by at least 0.3 A, see Table 17. thus accentuating the elongation. Although the bond angle relationships for the other three structures puts them in Class II. i.e. HCH > HCX, which is characteristic of flattening, see Fig. l(c). the tetrahedra are nevertheless elongated. The HCX angles in

these structures range from 107.9 to 108.9” (see Table 3). But even in the geometrical limit with HCX = 90”. where the carbon atom is in the HHH plane, the longer CX bond would still result in elongation along the CX axis since the three CH bonds in the plane are all much shorter. There is some indication that electronegativity may play some role in determining the bond angle relationships. CH-, - Li is in Class I, whereas CHs -F and CHI-Cl are in Class II. but CHj-CH, and CHJ-SiH3 are both in Class I. The effect of electronegativity is being investigated further. Even though the H,CHt,, HbCH,. and H,CH, angles are not all the same in the CHs-X structures with Hb and H, located symmetrically on either side of the H,CX plane, the individual values are systematically less than the H,CX, H,CX. and H,CX angles in the majority of these structures (see Table 4). Hence the tetrahedra in these structures are clearly elongated both on account of this bond angle relationship and the greater length of the C-X bonds (compare Tables 15 and 17). The tetrahedra in the CH,-C3 group in the two rotamers of toluene are also elongated according to these criteria (see Table 6 for the bond angle relationships). The difference between the HCH bond angles, however, shows there to be a minor distortion, with the C-X axis (no longer a trigonal axis) tilted somewhat either toward, or away from, the H,-H, side of the H,H,,H, triangle at the base of the tetrahedron. The summation of the bond angles in these CH3-X structures is on average only 0.2” less

than the maximum value for a regular tetrahedron. Hence elongation is not necessarily accompanied by a significant deviation. even though, as shown in the Introduction, it is theoretically possible. The tetrahedra in the X-CH?-Y structures in Table 5 are undoubtedly even more distorted. The problem of characterizing this distortion is necessarily more complicated because there are two heavy atoms instead of one to take into account.

5. Concluding remarks Differences in the bond angles around a saturated carbon atom are implicit in van’t Hoffs use of irregular tetrahedral models to illustrate the bonding of the carbon to one or more different groups’. Yet, as we have shown using bond angles derived from neutron diffraction studies and from ab initio calculations, even though individual values vary from about 105 to 117’, the summation, in most cases, is only a few tenths of a degree less than the maximum of 656.83’ for a regular tetrahedron. This is still the more remarkable in view of the wide range of X atoms bonded to the carbon in the CH3-X structures: Li, Be, B, C4, C3. N. 0, F, Na. Mg, Al, Si. P, S, Cl, As. and Ga. An inherent tendency for the summation of the angles to attain this maximum value is further substantiated by the data for CCC and COC rings. Although the CCC and CC0 angles in these three-membered rings are approximately 60.. i.e. about 50’ less than the value for a regular tetrahedron, compensatory increases in the remaining five angles are sufficiently large to reduce the deficit in the summation to about 14-. To characterize the distortion of the tetrahedra in the X-CH?-Y, H-CXYZ and other unsymmetrical structures, we plan to compare the internuclear distances between the atoms situated at the corners. i.e. the lengths of the sides’. These ’ To represent the enantiomers of CR,RzRIR4. van’t Hoff constructed irregular tetrahedral models. the sides of which were unequal in length, varymg from about 2.2. to 28cm. In the model representing three identical groups bonded to the carbon. three of the sides had the same length. about 2cm. while the fourth was larger. about 2.5cm (see Ref. [5]. especially p. 77 and Figs. 1 and 2).

distances are, of course, composite geometrical properties whose magnitudes are determined by each pair of bond lengths and the included angle.

Acknowledgments We thank the Advanced Scientific Computing Laboratory, NCI-FCRF, for providing time on the CRAY YMP supercomputer. This work was also supported by grants CA-10925 and CA-06927 from the National Institutes of Health, by Grant CN-10 from the American Cancer Society. and by an appropriation from the Commonwealth of Pennsylvania.

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