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Molecular mechanics calculations of conformational structures, energies and torsional force constants in some bromopropenes and bromobutenes
Journal of Molecular Structure, 160 (1987) 143-157 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
MOLECULAR MECHANICS CALCULATIONS OF CONFORMATIONAL STRUCTURES, ENERGIES AND TORSIONAL FORCE CONSTANTS IN SOME BROMOPROPENES AND BROMOBUTENES
PER J. STAVNEBREKK Department
of Chemistry,
and REIDAR STQLEVIK AVH,
University
of Trondheim,
N-7055 Dragvoll (Norway)
(Received 3 February 1987)
ABSTRACT Gas-phase data on conformational energies and structures of the molecules BrH,CHC=CH,, BrH,C-BrC=CH, , BrH,C-(CH,)C=CH, and BrH,C-CH,-HC=CH, are used to establish parameter values for the nonbonding atom . . . atom interactions Br . . * C(sp’) within the Morse potential formulation. Torsional potentials are calculated for the molecules mentioned above and in addition for cis- and Irans-BrH,C-HC=CHBr, transBrH,C-HC=C(CH,)H, (BrH,C),C=C&, cis-BrH,C-HC=CH-CH,Br and CH,-BrCHHC=CH,. Torsional force constants for the molecules are obtained. A comparison with the corresponding chloro compounds is made. INTRODUCTION
Preliminary parameter values for the nonbonding potential of the atom * - * atom interaction Br * . * C(sp’) were derived in a previous work [l] . The same parameter values were then used for bromo-substituted propenes, biphenyls and 1,3-butadienes. Recently new gas-phase investigations of conformational equilibria in bromopropenes and bromobutenes have become available to us. In this work we have used previously established parameter values [2] for the interactions H - - * H, H . . * C, H - * - Br, Br - - * C(sp3) and Br * - - Br. Parameter values for the interaction C(sp”) * * * C(sp”) were established in a recent work [ 31 on chloropropenes and chlorobutenes. Conformational results for the chloro compounds, being analogues to the bromo compounds studied in this work, are found in ref. 3 and in Table 10. The parameter values used here are those relevant to the Morse potential formulation [ 41. CALCULATIONS
AND RESULTS
Force constants (F) and reference values (Q’) for the energy terms 0.5 F Q”)2 can be found elsewhere [l, 5, 61. However, some new reference values have been introduced according to experience from the work on chloropropenes and chlorobutenes [3], and these are listed in Table 1. (Q -
0022-2860/87/$03.50
o 1987 Elsevier Science Publishers B.V.
144 TABLE 1 Reference values for bond angles in bromopropenes and bromobutenes Bond angle type
Reference value (deg.)
In Cl -c2-c3 Cl=C2-Br C2=Cl-Br C=C-H C=C-C (H at C2) C=C-C (Brat C2) C=C-C (C at C2) C2-C3-Br C2-C3-H, H-C3-Br
119.0 121.0 120.0 123.3 125.0 123.0 111.5 109.5
Bond angle type
Reference value (deg.)
In Cl -C2-C3-C4 C3-C4-Br C3-C4-H, H-C4-Br C2-C3-C4 C2-C3-Br C2-C3-H, H-C3-Br
109.5 109.5 111.5 111.5 109.5
Excess charges on the atoms were computed [7], but reduced by division with 1.3 for the bromo compounds. The parameter values D of the electrostatic energy terms D/R are given in Table 2. An intrinsic torsional potential for rotation around the C-C bonds V = 0.5 V, (1 - cos(39)) was used with V3 = 2.11 kcal mol-’ for C(sp’)-C(sp3) and V3 = 2.65 kcal mol-’ for C(sp3)-C(sp3). Values of the new potential parameters are given in Table 3. These values are more relevant for bromopropenes and bromobutenes than those in ref. 1. The values in Table 3 are those for which the MM calculations reproduced the observations in the best way. Energy minima were obtained by adjusting bond lengths, bond angles and torsion angles simultaneously. For energies not corresponding to minima the torsion angles were held constant. 3-Bromopropene Torsional potential curves for H2C=CH-CHzBr are shown in Fig. 1 together with conformational drawings. S’yn and gauche conformers are possible for TABLE 2 Coulomb parameters D = 332 qq* in kcal a mol-’ bromopropenes and bromobutenes (X = Br) Molecule
H ...H
H,C=CH-CH,X H,C=CX-CH,Xa H,C=C(CH,)-CH,Xb H,C=C(CH,X),C
0.41 1.00 0.30 0.67
C...H -0.14 +0.14 -0.17 -0.03
H...X -1.61 -2.22 -1.43 -1.94
(q and q* are excess charges) for C...X -0.55 -0.31 0.79 0.09
X...X
C...C
4.90 0.09 5.65
Vame values used for cis- and trans-XHC=CH-CH,X. bSame values used for tmns-CH,HC=CH-CH,X, H,C=CH-CH,-CH,X and H,C=CH-CXH-CH,. cSame values used for cis-XH,C-HC=CH-CH,X.
145 TABLE 3 Parameter values of nonbonding atom. formulationa
. - atom interactions in the Morse potential (V)
R, (a)
Rx,, 64)
E (kcal mol-' )
Br . . . C(SP’)
2.90
3.60
1.22
Br
. . . c* (ap’)b C(sp’) * f . C(sp”)C Cl . . * C(sp’)C
3.40 3.00 3.00
4.10 3.43 3.53
1.22 0.083 1.22
Cl . . . C* (sp’)“l”
3.35
4.05
1.22
aThe parameters are related as follows: V(R,) = 0, V(R,) = -E corresponding to minimum of V(R); see ref. 4 for details. bThese values were used for the interactions X . . . C* found only in the molecules H,C=C*H-CH,-CH,X. CValues from ref. 3.
0
30
60
90
120
160
160
0
I
I
30
60
90
120
150
160
Fig. 1. Torsional potential curves E (kcal mol-‘) for 3-bromopropene, H,C=CH-CH,X (X = Br). The torsion angle o(C=C-C-X) is in degrees. The conformer syn (S) possessing C, symmetry has a planar arrangement of the atoms CCCX with o = 0”. The transition form anti (A) also has a planar arrangement of the atoms CCCX with @ = 180”, while gauche (G) has $J = 120”. The dotted curve was obtained without excess charges on the atoms. Fig. 2. Torsional potential curves E (kcal mol-‘) for cis-1,3-dibromopropene, cis-XHC= CH-CH,X (X = Br). The dotted curve was obtained without excess charges on the atoms. The torsion angle o(C=C-C-X) is in degrees. The two transition forms syn (S) and anti (A) have the atoms CCCX in planar arrangements with ~(syn) = 0” and @(anti) = 180”. Gauche (G) is the only stable conformer. Both A and S possess Cs symmetry, while G has C!, symmetry.
this molecule, with gauche the low-energy form. A calculated energy difference equal to 0.8 kcal mol-’ agrees with the gas-phase value of 0.78 kcal mol-’ as determined from low-frequency Raman spectroscopy [8]. From an electron diffraction investigation [9] a value in the range 1.0-2.5 kcal mol-’ was estimated. From liquid-phase NMR spectroscopy [lo] a conformational mixture of 95% gauche was detected. IR and NMR liquid-phase investigations [ 111 revealed 97% of the gauche form.
146 TABLE 4 Results for H,C=CH-CH,Br Parametera
Calc. values gauche
syn Bond lengths (A) C-C c-x
1.508 1.954
Bond angles (degrees) c-c=c C=C-H c-c-x C-C-H X-C-H Torsion angles (degrees) @(c=c-c-X) Torsional force constants
1.503 1.948
1.485(8) 1.961(6)
126.5 119.7 114.1 108.7 108.4
124.0 119.8 110.8 109.7 109.0
126.0(2.6) 122.0(--p 111.5(0.8) 109.5(--p (-)b
0.0
115.6
117.0(5)
(mdyn A rod-l)
F = a’Ela@= ‘X = Br, Cl=C2-C3.
Observed values [ 91
0.030
0.060
C-lb
bNot reported.
Calculated and observed values of the structural parameters are compared in Table 4. cis-1,3-Dibromopropene Torsional potential curves for cis-BrHC=CH-CH,Br and conformational drawings are shown in Fig. 2. The only stable conformation for this molecule is a non-planar gauche form with torsion angle $ = 110.6”. For the torsional force constant the value 0.053 mdyn A Tad-* was obtained. trans-1,3-Dibromopropene Torsional potential curves for trans-BrHC=CH-CH,Br and conformational drawings are shown in Fig. 3. The gauche conformer is 0.3 kcal mol-’ lower in energy than the syn conformer. The values of torsion angles $J(C=C-C- Br) and torsional force constants FQ were calculated and are shown in Table 5. TABLE 5 Torsion angles @(C=C-C-Br) propene
and torsional force constants FQ for trans-1,3-dibromo-
@(degrees)
wn gauche
0.0
115.1
F+ (mdyn A rad-‘) 0.033 0.057
Fig. 3. Torsional potential curves E (kcal mole’) for trans-1,3-dibromopropene, transXHC=CH-CH,X (X = Br). The torsion angle o(C=C-C-X) is in degrees. The conformer syn (S) possessing C, symmetry has a planar arrangement of the atoms CCCX with o = 0”. The transitional form anti (A) also has a planar arrangement of the atoms CCCX with o = 180”, while gauche (G) has @ = 120”. The dotted curve was obtained without excess charges on the atoms. Fig. 4. Torsional potential curves E (kcal mol-‘) for 2,3-dibromopropene, H,C=CX-CH,X (X = Br). The dotted curve was obtained without excess charges on atoms. The torsion angle o(C=C--C-X) is in degrees. The conformer syn (S) and the transition form anti (A) have a planar arrangement of the atoms CCCX with &syn) = 0’ and @(anti) = 180”. Both S and A possess C, symmetry.
2,3_Dibromopropene Conformational drawings and torsional potential curves for H$=CBrCHzBr are shown in Fig. 4. The calculated energy difference AE = E(gauche) E(syn) = 0.8 kcal mol-’ agrees reasonably well with the value 1.0 + 0.2 kcal mol-’ as determined from gas-phase electron diffraction data [ 121. As seen from Fig. 4 the results calculated for this molecule are very sensitive to the magnitude of electrostatic terms. Values of the observed and calculated structural parameters have been compared in Table 6. The barrier height for the transition between enantiometric gauche forms is 6.7 kcal mol-‘. trans-1-Bromo-2-bu tene The torsional potential curve and conformational drawings for trans-CH,CH=CH-CHzBr are shown in Fig. 5. For the energy difference E(syn) E(gauche) the value 0.7 kcal mol-’ was obtained. The torsion angles of the gauche conformer are $J~(C=C-C~-X) = 114.2” and @,(C=C-C4-H) = -O.l”, while for syn the values are $1 = 0” and & = 0”. The values of the torsional force constants obtained are shown in Table 7. Neglecting the electrostatic terms in the energy calculations changed the torsional potential curve only insignificantly.
148 TABLE
6
Results for H,C=CBr-CH,Br Parametera
Observed
Calc. values
gauche
syn
Bond lengths (A) C-C c2-x c3-x
1.506 1.906 1.953
1.507 1.899 1.951
Bond angles (degrees) c=c-C
127.6
C=C-H c=c-x C-C-X C-C-H X-C-H
120.4 118.0 113.6 108.9 108.4
111.9 109.5 108.8
0.0
95.5
Torsion angles (degrees) @J(C=C-C-X) Torsional force constants F = a’E/a@ aX = Br, Cl=C2-C3. TABLE
125.2 120.0 118.7
(mdyn A rad-‘) 0.042
0.073
values [12]
1.480( 14) 1.904( 17) 1.940( 19) 124.2(1.7) 120.5(-)b 120.1(4.4) 113.4(3.5) 106.2(7.0) C-P 112(4)
0.03-0.05
bNot reported.
7
Torsional force constants
(mdyn A rad-‘) for trans-1-bromo-2-butene
F,(C-CH,Br) FJC-CH,)
syn
gauche
0.027 0.059
0.058 0.060
3-Bromo-2-me thyl-1 -propene Conformational drawings and the torsional potential curve calculated for the molecule H&=C(CH3)-CH2Br are shown in Fig. 6. According to a gasphase electron diffraction investigation [13] the compound exists as a mixture of syn and gauche conformers, gauche being the low energy form. Our calculated conformational energy difference of 1.2 kcal mol-’ agrees with the experimentally estimated value of 1.4 + 0.6 kcal mol-‘. From an IR study of the liquid an energy difference of only 0.3 kcal mol-’ between the conformers was reported [14]. When the electrostatic terms in the energy expression were neglected the changes in the potential curve were insignificant. Calculated and observed values of the structural parameters are compared in Table 8.
Fig. 5. Torsional potential curve E (kcal mol-‘) for trans-1-bromo-2-butene, trans-CH,HC=CH-CH,X (X = Br). The torsion angle @(C=C-C-X) is in degrees. The conformer syn (S) and the transitional form anti (A) have a planar arrangement of the atoms C-C= C-C-X with @(syn) = 0” and @(anti) = 180”. Both S and A possess C, symmetry. Fig. 6. Torsional potential curves E (kcal mol-I) for 3-bromo-2-methyl-l-propene, H,C= C(CH,)-C&X (X = Br). The torsion angle @I~(C~=C~--C~--X) and @,, (Cl=C2-C4-H’) are in degrees. The conformer syn (S) has @3 = 0” and o4 = 0”, corresponding to planar syn arrangements of the atoms C=C-C3-X and C=C-C4-H’ simultaneously. The conformer gauche (G) has o4 = +l” and $I$ = + 117’. The energy values of the curve correspond to @a = 0” and 0 = e3 as variable. TABLE 8 Results for H,C=C(CH,)-CH,Br Pammete+
Calc. values syn
Bond lengths (A) c-C3 c-C4 c-x Bond angles (degrees) c=c-c3 c=c-c4 C=C-H C-C-X C-C-H H-C-X Torsion angles (degrees) O3 (C=C-c!S-X) $J,(C=C-C~-H’) Torsional force constants F, = a’E/a@,: F, = a’E/a@: F* = a’Ela@,a@, aX = Br, Cl=C2(C4)-C3X.
1.511 1.506 1.952
gauche
1.509 1.509 1.952
125.6 122.2 120.8 113.8 109.4 108.4
122.8 122.5 120.3 112.7 109.7 108.6
0.0 0.0
+116.9 +l.O
(mdyn A rod-‘) 0.027 0.067 -0.009 bNot reported.
0.103 0.063 -0.026
Observed values [13]
1.484( 6) 1.467(6) 1.965(6) 121.5(0.7) 122.1(0.7) 120.4(-) 112.2(0.5) 109.7(-) C-P +113(2) C-P
150
3-Bromo-2-bromome thyl-1 -propene Conformational drawings and labelling for the molecule H,C=C(CH,Br)2 are shown in Fig. 7(a). Torsional potential curves are shown in Fig. 7(b). From our calculations we expect the existence of four stable conformers for this molecule. The high energy form is SS while the low energy form is GG. The conformers GS and GG” both have energies 1.6 kcal mol-’ higher than GG, and SS has an energy 3.8 kcal mol-’ in excess of GG. The minimum for the GG” conformer has Q& = +69” and I$~ = -109”. This point does not exist on the curves shown in Fig. 7(b). The point @3 = +90” and @4 = -90” has an energy value 0.4 kcal mol-’ above the minimum. Energy values relative to the local minima at @3 = f 69” and $4 = 7109” for various combinations of the torsion angles are shown in Table 9. For torsion angles (@) and torsional force constants (F) the values obtamed are shown in Table 10. The torsional potential remained essentially unchanged when the electrostatic terms were neglected in the energy calculations. cis-1,4-Dibromo-2-
bu tene
Conformational drawings are shown in Fig. 8(a) and torsional potential curves in Fig. 8(b). According to our calculations the low-energy conformer a ss
GS
-_ G-_ G X
X -_
E
b
7-
;i:
X
--X
1 -7
I :
X
-_
I I
I 5-
.
I
.
.
.
.
.
: -5
“AS
-3
“X
GG" Fig. 7. 3-Bromo-2-bromomethyl-1-propene, H,C=C(CH,X), (X = Br). (A) Possible conformations. In SS the fragment Cl=C2-C3-X and Cl=C2-C4-X are both planar (syn), corresponding to torsion angles a3 (C=C-CS-X) = 0” and o4 (C=C-CS-X) = 0”. The form GS has @3 = 120” and o4 = 0”, and GG has 0, = 120” = 04, while GG” has oa = 120” and 9, = -120”. Thus, the symmetries are C,,, C, , C,, and C, for forms SS, GS, GG and GG” respectively. (B) Torsional potential curves E (kcal mol-I). The transition form AS has @3 = 180” and a4 = 0” and thus possesses C, symmetry. The unbroken curve (-) was obtained with the restriction that o3 = @ = @.,, and the broken curve (- - -) with 6, = 6 and d, = -$, while the dotted curve (. . .) had cp, = o and a4 = 0”.
151 TABLE 9 Relative* energy values (kcal mol-‘) of the torsional potential in the region of the GG” conformer of H,C=C(CH,Br), .
@sb
9eb
+70 1.42 0.94 0.45 0.12 0.09 0.29
-70 -80 -90 -100 -110 -120
+80 0.94 0.55 0.39 0.32 0.35 0.75
+lOO
+90 0.45 0.39 0.39 0.58 0.98 1.57
*Minima (E = 0) at @a = +-69” and o4 = rlO9’. e4 (C=C-C4-Br) are in degrees.
+llO
0.12 0.32 0.58 1.16 1.96 2.82
+ 120 0.09 0.35 0.98 1.96 3.17 4.41
0.29 0.75 1.57 2.82 4.41 6.10
bTorsion angles @,(C=C-C3-Br)
and
TABLE 10 Torsion angles and torsional force constants for conformers of 3-bromo-2-bromomethyl1-propene Parametera
SS
&(C=C2-C3-X)
0.0
e4 (C=C2-C4-X)
0.0
F,
=
a2Ela@2,
F,
= a’Ela@: F* = a’Ela$,a@,
0.021 0.021 -0.010
GG
GG”
t 109.9 + 109.9
+ 68.6 -109.2
0.105 0.105 -0.019
0.079 0.101 -0.035
GS 0.0 109.8 0.007 0.113 -0.027
*Angles in degrees, force constants in mdyn I%rade2.
GG”. The point at #1 = +90” and $4 = -90” has an energy 0.6 kcal mol-’ above the minima at $1 = 584” and $e = T112”. Energy values relative to the local minima for various combinations of the torsion angles are shown in Table 11. The GG conformer has an energy only 0.1 kcal mol-’ higher than GG”. Thus, for the gas phase both conformers are expected to exist at room temperature. The point indicated by GS in Fig. 8(b) is a saddle point. Consequently a stable GS form should not exist for this molecule. For the low-energy conformers the values of torsion angles ($) and torsional force constants (3’) shown in Table 12 were calculated. Also when the electrostatic terms were neglected the low energy forms remained GG” and GG, with GG about 0.7 kcal mol-’ higher in energy than is
GG" .
152 A
&
.q$
xp
ii %’
xv
2-
GG”
GG 0
30
60
90
120
150
180
Fig. 8. cis-1,4-Dibromo-2-butene, cis-XH,C-HC=CH-CH,X (X = Br). (A) Possible conformation. In the form SS the fragments X-Cl-C2=C3 and X-C4-C3=C2 are both planar (syn), corresponding to torsion angles o, (X-Cl-C=C) = 0” and o,(X-C4-C=C) = 0”. The form GS has o1 = 90’ and o4 = O”, and for GG o1 = o4 = 90”, while for GG” o1 = 90” and o4 = -90”. The symmetries are C,,, C,, C, and C, for the conformers SS, GS, GG and GG” respectively. (B) Torsional potential curves E (kcal mol-I). The transitional form AS has o1 = 180” and o4 = 0” corresponding to C, symmetry. The unbroken curve (-) was obtained with 0, 5 o4 = 9, and the broken curve (- - -) with o1 = o and o4 = -$,whileforthedottedcurve(...)o, =@ando, =O”. TABLE 11 Relativea energy values (kcal mol-‘) of the torsional potential in the region of the GG” conformer of ci.s-BrH,C-HC=CH-CH,Br ob4
@lb t-70
-70 -80 -90 -100 -110 -120
7.31 4.94 2.75 1.23 0.46 0.41
+80 4.94 3.09 1.51 0.49 0.41 0.12
*Minima (E = 0) at @, = *84’ o,(C=C-C4-Br) are in degrees.
+90 2.75 1.51 0.58 0.12 0.04 0.23
+100 1.23 0.49 0.12 0.09 0.28 0.57
and o4 = r112O. bTorsion
+ 110
+120
0.46 0.41 0.04 0.28 0.62 1.00 angles o 1(Br-Cl-C=C)
0.41 0.12 0.23 0.57 1.00 1.45 and
3-Bronao-1 -butene Results for H&=CH- HCBr-CH3 are shown in Fig. 9. According to our calculations three stable conformations are available to this molecule. The low-energy form with H in the HCBr group eclipsing the C=C bond is denoted GX For the two other conformers GH and SM (see Fig. 9) the energies are 0.8 and 2.2 kcal mol-’ higher than in GX respectively.
153 TABLE 12 Torsion angles and torsional force constants for cis-1,4-dibromo-2-butene Parameters o1 (X-Cl-C2=C3) @,(C2=C3-C4-X)
GG
GG”
+ 90.6 + 90.6
+ 84.4 -111.5
0.065 0.065 + 0.024
F, = a=E/a$; F, = aZEla& F* = aZE/a@, + @4
0.093 0.091 -0.050
aAngles in degrees, force constants in mdyn A rad-* .
E
c
GX
GH
. . --.__GX :* 0
I 30
I 60
I 90
.**
120
160
4
160
Fig. 9. Torsional potential curves E (kcal mol-I) for 3-bromo-1-butene, H,C=CH-X CH-CH, (X = Br, M = CH,). The torsional angles @,(Cl=C2-C3-X) and @,(C2-C3-C4H) are in degrees. The conformers have the following values of 03: + 6” (SM), -123” (GX) and +112” (GH). The values of 9, are approximately 60” for these conformers. Thus, in SM the CH, group eclipses the C=C bond. The fragment C-XCH-CH has a nearly staggered arrangement in each of these conformations. The unbroken curve was calculated with the restriction that & = +@ and 0, = 60”, while the dotted curve corresponds to o, = -0 and @, = 60”. TABLE 13 Torsion angles and torsional force constants for 3-bromo-1-butene Parametera @,(Cl=C2-C3-X) o4 (C2-C3-C4-H’) F, = a’E/a@; F, = aZEta@: F* = aZElao3a@,
GX
GH
SM
-122.7 + 58.9
+ 112.0 + 59.3
+ 5.8 + 58.4
0.065 0.111 -0.003
aAngles in degrees, force constants in mdyn A radm2.
0.048 0.108 -0.003
0.054 0.155 + 0.034
154
The values of torsion angles ($) and torsional force constants (F) shown in Table 13 were obtained. The torsional potential curve remained essentially unchanged when the electrostatic terms were neglected in the calculations. 4-Bromo-1-butene Results for H&=CH-CH2--CHzBr are shown in Fig. 10(b) and in Table 14. Conformational drawings are shown in Fig. 10(a). A conclusion from an investigation of the IR spectra of this molecule [ 151 was that there are two forms coexisting in both the gas and the liquid phases; one with the halogen atom in the anti position and one with the halogen atom in the gauche position. From the three possible conformations with the halogen atom in the gauche position, and the two possibilities for the anti position, a planar carbon skeleton was suggested [15]. However, from an electron diffraction investigation [16] it was shown that the most abundant form in the gas phase is GA with a gauche carbon skeleton and an anti halogen atom. At 23°C the composition (%) was: 38(GA), 50(GG + GG*), 8(5’A) and 4(SG) with error limits of about 10%. Because the C, * * - Br peak of the GA conformer is isolated in the RD curve [16] the percentage of that form was well established in the GED work. Our calculations resulted in the following conformational energies a SA
b
SG E
:
. -7
7/
‘Lx
.
‘X GA
GG
GG*
0
30
60
90
120
150
190
Fig. 10. 4-Bromo-1-butene, H,C=CH-CH,-CH,X (X = Br). (A) Possible conformations. SA and SG have the C atoms in a planar syn (S) arrangement. For GG, GA and GG* the C atoms have a gauche (G) arrangement. The second letter in a conformational name indicates whether X has an anti (A) or gauche (G) arrangement to the C=C bond. The torsional angles are o,(C=C--C--C) and @,(C-C-C-X). Thus the values of the torsion angles (I$~/@~) are: SA (O/180), SG (O/60), GG (120/+60), GA (120/180) and GG* (120/-60). Only SA possesses C!, symmetry. (B) Torsional curves E (kcal mol-‘). The unbroken curve (-) was calculated with the restriction that @ = @,(C=C-C--C) and o,(C-C-C-X) = 120”. The broken curve (- - -) corresponds to the restriction o4 = -@ and o3 = 120”, while for the dotted curve (. . _) 9, = QJand o3 = 0’.
155 TABLE 14 Results for H,C=CH-CH,-CHBr Parametera
Calc. values GA
Bond lengths (a) C2-C3 c3-c4 c-x
1.504 1.517 1.950
GG
1.507 1.521 1.958
Observed values [ 161
1.508(7) 1.528(7) 1.945(8)
Bond angles (degrees) c=c-c C-C-C C=C-H C2-C3-H C3-C4-H H-C-X C-C-X
123.9 112.0 119.9 110.0 109.7 109.4 110.0
123.8 113.7 119.9 110.1 109.6 108.8 111.1
122.9(3.2) 111.5(2.7) 121.5(--p 110.4(--p 111.7(--p 106.3(-)b 111.2(0.7)
Torsion angles (degrees) G3(C=C-c-C) @,(C-C-C-X)
117.2 181.0
112.7 69.4
120(4)c ISOb(
Torsional force constants (mdyn .k rad-‘) F, = a2Ela& 0.061 F, = aZEla@: 0.105 F* = a’Ela@,a@, -0.001 aX = Br, Cl=C2-C3-C4.
0.066 0.138 -0.006
;I$b C-P
bNot reported. CValues for GA form.
(kcal mol-‘) relative to the energy of GA: 0.15 (GG), 0.56 (SA),0.90(GG*) and 0.85 (SG). The calculated composition at 23°C corresponding to these energies is 41% GA, 32% GG, 9% GG*, 10% SG and 8% SA, when conformational differences in vibrational partition functions are ignored. Thus our results agree well with the GED data, but not with the IR data. The results were not significantly changed when the electrostatic energy terms were neglected. Experimental and calculated results are compared in Table 14. CONCLUDING REMARKS
Parameter values presented in this work for the interactions Br . * * C(sp’) correspond to several compromises. Energies as well as structural parameters should be correctly reproduced simultaneously. Thus, mutual concessions had to be made in order to have the best possible fit with experimental values of conformational energies as well as torsion angles, bond angles and bond lengths. For conformational energies the average deviation between observed and calculated values is 0.2 kcal mol-I, while for the chloro compounds [3] the
156
corresponding value was 0.3 kcal mol-‘. No attempts were made to correct for conformational differences in vibrational energies. Uncertainties in the calculated barrier heights are not so easily estimated. However, uncertainties for the bromo compounds are probably about 0.51.0 kcal mol-‘, as estimated for the chloro compounds [3]. Our calculated torsional barrier heights range from 0.5 to greater than 10 kcal mol-‘. One can have this wide range of values even within the same molecule (Fig. 7(b)). However, for molecules possessing a stable syn conformation, the barriers separating syn from other forms have heights between 0.5 and 2 kcal mol-‘. A summary of low energy conformers, and values of conformational energy differences, including bromo and chloro [ 31 compounds, is presented in Table 15. Except for the molecules (X = Cl, Br) cis-XHC=CH-CHzX having only gauche as a stable conformation, the remaining 18 molecules have more than one stable conformation. Thus for molecules with only one XHzC group syn (S) and gauche (G) are stable forms. For molecules possessing two XHzC groups at least three of the four forms SS, GS, GG and GG” are stable. According to our calculations the molecules (X = Cl, Br) H2C= CH-XCH-CH3 have three stable conformations, and the molecules H$= CH-CH2-CH2X have five stable forms. For molecules having a stable syn conformation, calculations and experimental evidence agree that the values of the syn torsion angles (4) are zero degrees corresponding to a planar heavy-atom conformation. Typically the calculated @(gauche) values are about 5” less than the corresponding observed values. However, for H,C=C( CH&CH,Br the calculated value is greater than the observed value. A closer inspection of the structural parameter values for individual molecules reveals some systematic trends. Typically, for syn conformers the values of the bond angles C=C-C and C-C-Br in the fragments C=C- C-Br TABLE 15 Summary of low-energy conformers and conformational Molecule
A,!?’
H,C=CH-CH,X trans-XHC=CH-CH,X trans-H(CH,)C=CH-CH,X H,C=CX-CH,X cis-XHC=CHSH,X H,C=C(CH,)--CH,X H,C=C(CH,X)2 cis-XH,C-HC=CH-CH,X H,C=CH-XCH-CH, H,C=CH-CH,-CH,X Wonformer
S-G S-G S-G G-S gaucheb S-G GS-GG GG - GG” GH-GX GG-GA
energy differences
AE
(kcal mol-‘)
X Br
Cl [13]
0.8 0.3 0.7 1.0
0.6 0.4 0.8 0.7
1.4 1.6 0.1 0.8 0.2
- conformer of lowest energy. bOnly the gauche form is stable.
-
0.7 0.9 0.4 0.7 0.4
157
are 2-2.5” greater than the corresponding values in gauche conformers. The C-C and C-Br bonds of syn conformers are about 0.003-0.004 a longer than those of gauche conformers. Unfortunately such small differences are not easily detected by the experimental methods used in studying these molecules. Calculated values of C-CHzBr torsional force constants (FO) have been obtained in the range 0.02-0.14 mdyn A rad-‘, while the F,(C-CH,) values fall between 0.06 and 0.16 mdyn A rad-*. The effects of neglecting the eIectrostatic terms in the energy expression may be studied in Figs. 1-4. Clearly the effects are small in the molecules H2C=CH-CH,Br, cis-BrHC=CH- CH2Br and truns-BrHC=CH- CH2Br. However, for H,C=CBr-CH,Br the effects are dramatic (Fig. 4). ACKNOWLEDGEMENT
We acknowledge financial forskningsr&d, NAVF.
support
from
Norges
Almenvitenskapelige
REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
R. Stblevik and 8. Thingstad, J. Mol. Struct., 106 (1984) 333. R. StQlevik, J. Mol. Struct., 109 (1984) 397. P. J. Stavnebrekk and R. Stblevik, J. Mol. Struct., 159 (1987) 153. R. J. Abraham and R. Stdlevik, Chem. Phys. Lett., 58 (1978) 622. T. Rydland and R. Stblevik, J. Mol. Struct., 105 (1983) 157. T. Rydland, Thesis, University of Trondheim, AVH, Trondheim, 1981. R. T. Sanderson, Chemical Bonds and Bond Energy, Academic Press, New York, 1976. J. R. Durig and M. R. Jalian, J. Phys. Chem., 84 (1980) 3543. S. H. Schei and Q. Shen, J. Mol. Struct., 81 (1982) 269. A. A. Bothner-By and H. Gunther, Discuss. Faraday Sot., 34 (1962) 127. R. E. Rondeau and L. A. Harrah, J. Mol. Spectrosc., 21 (1966) 332. 0. I. Sdvik, 8. Trongmo, K. Hagen, S. H. Schei and R. StClevik, J. Mol. Struct., 118 (1984) 1. S. H. Schei, J. Mol. Struct., 102 (1983) 305. A. 0. Diallo, Spectrochim. Acta., Part A, 36 (1980) 799. A. Crowder and N. Smyrl, J. Mol. Struct., 8 (1971) 255. S. H. Schei, J. Mol. Struct., 128 (1985) 151.
MOLECULAR MECHANICS CALCULATIONS OF CONFORMATIONAL STRUCTURES, ENERGIES AND TORSIONAL FORCE CONSTANTS IN SOME BROMOPROPENES AND BROMOBUTENES
PER J. STAVNEBREKK Department
of Chemistry,
and REIDAR STQLEVIK AVH,
University
of Trondheim,
N-7055 Dragvoll (Norway)
(Received 3 February 1987)
ABSTRACT Gas-phase data on conformational energies and structures of the molecules BrH,CHC=CH,, BrH,C-BrC=CH, , BrH,C-(CH,)C=CH, and BrH,C-CH,-HC=CH, are used to establish parameter values for the nonbonding atom . . . atom interactions Br . . * C(sp’) within the Morse potential formulation. Torsional potentials are calculated for the molecules mentioned above and in addition for cis- and Irans-BrH,C-HC=CHBr, transBrH,C-HC=C(CH,)H, (BrH,C),C=C&, cis-BrH,C-HC=CH-CH,Br and CH,-BrCHHC=CH,. Torsional force constants for the molecules are obtained. A comparison with the corresponding chloro compounds is made. INTRODUCTION
Preliminary parameter values for the nonbonding potential of the atom * - * atom interaction Br * . * C(sp’) were derived in a previous work [l] . The same parameter values were then used for bromo-substituted propenes, biphenyls and 1,3-butadienes. Recently new gas-phase investigations of conformational equilibria in bromopropenes and bromobutenes have become available to us. In this work we have used previously established parameter values [2] for the interactions H - - * H, H . . * C, H - * - Br, Br - - * C(sp3) and Br * - - Br. Parameter values for the interaction C(sp”) * * * C(sp”) were established in a recent work [ 31 on chloropropenes and chlorobutenes. Conformational results for the chloro compounds, being analogues to the bromo compounds studied in this work, are found in ref. 3 and in Table 10. The parameter values used here are those relevant to the Morse potential formulation [ 41. CALCULATIONS
AND RESULTS
Force constants (F) and reference values (Q’) for the energy terms 0.5 F Q”)2 can be found elsewhere [l, 5, 61. However, some new reference values have been introduced according to experience from the work on chloropropenes and chlorobutenes [3], and these are listed in Table 1. (Q -
0022-2860/87/$03.50
o 1987 Elsevier Science Publishers B.V.
144 TABLE 1 Reference values for bond angles in bromopropenes and bromobutenes Bond angle type
Reference value (deg.)
In Cl -c2-c3 Cl=C2-Br C2=Cl-Br C=C-H C=C-C (H at C2) C=C-C (Brat C2) C=C-C (C at C2) C2-C3-Br C2-C3-H, H-C3-Br
119.0 121.0 120.0 123.3 125.0 123.0 111.5 109.5
Bond angle type
Reference value (deg.)
In Cl -C2-C3-C4 C3-C4-Br C3-C4-H, H-C4-Br C2-C3-C4 C2-C3-Br C2-C3-H, H-C3-Br
109.5 109.5 111.5 111.5 109.5
Excess charges on the atoms were computed [7], but reduced by division with 1.3 for the bromo compounds. The parameter values D of the electrostatic energy terms D/R are given in Table 2. An intrinsic torsional potential for rotation around the C-C bonds V = 0.5 V, (1 - cos(39)) was used with V3 = 2.11 kcal mol-’ for C(sp’)-C(sp3) and V3 = 2.65 kcal mol-’ for C(sp3)-C(sp3). Values of the new potential parameters are given in Table 3. These values are more relevant for bromopropenes and bromobutenes than those in ref. 1. The values in Table 3 are those for which the MM calculations reproduced the observations in the best way. Energy minima were obtained by adjusting bond lengths, bond angles and torsion angles simultaneously. For energies not corresponding to minima the torsion angles were held constant. 3-Bromopropene Torsional potential curves for H2C=CH-CHzBr are shown in Fig. 1 together with conformational drawings. S’yn and gauche conformers are possible for TABLE 2 Coulomb parameters D = 332 qq* in kcal a mol-’ bromopropenes and bromobutenes (X = Br) Molecule
H ...H
H,C=CH-CH,X H,C=CX-CH,Xa H,C=C(CH,)-CH,Xb H,C=C(CH,X),C
0.41 1.00 0.30 0.67
C...H -0.14 +0.14 -0.17 -0.03
H...X -1.61 -2.22 -1.43 -1.94
(q and q* are excess charges) for C...X -0.55 -0.31 0.79 0.09
X...X
C...C
4.90 0.09 5.65
Vame values used for cis- and trans-XHC=CH-CH,X. bSame values used for tmns-CH,HC=CH-CH,X, H,C=CH-CH,-CH,X and H,C=CH-CXH-CH,. cSame values used for cis-XH,C-HC=CH-CH,X.
145 TABLE 3 Parameter values of nonbonding atom. formulationa
. - atom interactions in the Morse potential (V)
R, (a)
Rx,, 64)
E (kcal mol-' )
Br . . . C(SP’)
2.90
3.60
1.22
Br
. . . c* (ap’)b C(sp’) * f . C(sp”)C Cl . . * C(sp’)C
3.40 3.00 3.00
4.10 3.43 3.53
1.22 0.083 1.22
Cl . . . C* (sp’)“l”
3.35
4.05
1.22
aThe parameters are related as follows: V(R,) = 0, V(R,) = -E corresponding to minimum of V(R); see ref. 4 for details. bThese values were used for the interactions X . . . C* found only in the molecules H,C=C*H-CH,-CH,X. CValues from ref. 3.
0
30
60
90
120
160
160
0
I
I
30
60
90
120
150
160
Fig. 1. Torsional potential curves E (kcal mol-‘) for 3-bromopropene, H,C=CH-CH,X (X = Br). The torsion angle o(C=C-C-X) is in degrees. The conformer syn (S) possessing C, symmetry has a planar arrangement of the atoms CCCX with o = 0”. The transition form anti (A) also has a planar arrangement of the atoms CCCX with @ = 180”, while gauche (G) has $J = 120”. The dotted curve was obtained without excess charges on the atoms. Fig. 2. Torsional potential curves E (kcal mol-‘) for cis-1,3-dibromopropene, cis-XHC= CH-CH,X (X = Br). The dotted curve was obtained without excess charges on the atoms. The torsion angle o(C=C-C-X) is in degrees. The two transition forms syn (S) and anti (A) have the atoms CCCX in planar arrangements with ~(syn) = 0” and @(anti) = 180”. Gauche (G) is the only stable conformer. Both A and S possess Cs symmetry, while G has C!, symmetry.
this molecule, with gauche the low-energy form. A calculated energy difference equal to 0.8 kcal mol-’ agrees with the gas-phase value of 0.78 kcal mol-’ as determined from low-frequency Raman spectroscopy [8]. From an electron diffraction investigation [9] a value in the range 1.0-2.5 kcal mol-’ was estimated. From liquid-phase NMR spectroscopy [lo] a conformational mixture of 95% gauche was detected. IR and NMR liquid-phase investigations [ 111 revealed 97% of the gauche form.
146 TABLE 4 Results for H,C=CH-CH,Br Parametera
Calc. values gauche
syn Bond lengths (A) C-C c-x
1.508 1.954
Bond angles (degrees) c-c=c C=C-H c-c-x C-C-H X-C-H Torsion angles (degrees) @(c=c-c-X) Torsional force constants
1.503 1.948
1.485(8) 1.961(6)
126.5 119.7 114.1 108.7 108.4
124.0 119.8 110.8 109.7 109.0
126.0(2.6) 122.0(--p 111.5(0.8) 109.5(--p (-)b
0.0
115.6
117.0(5)
(mdyn A rod-l)
F = a’Ela@= ‘X = Br, Cl=C2-C3.
Observed values [ 91
0.030
0.060
C-lb
bNot reported.
Calculated and observed values of the structural parameters are compared in Table 4. cis-1,3-Dibromopropene Torsional potential curves for cis-BrHC=CH-CH,Br and conformational drawings are shown in Fig. 2. The only stable conformation for this molecule is a non-planar gauche form with torsion angle $ = 110.6”. For the torsional force constant the value 0.053 mdyn A Tad-* was obtained. trans-1,3-Dibromopropene Torsional potential curves for trans-BrHC=CH-CH,Br and conformational drawings are shown in Fig. 3. The gauche conformer is 0.3 kcal mol-’ lower in energy than the syn conformer. The values of torsion angles $J(C=C-C- Br) and torsional force constants FQ were calculated and are shown in Table 5. TABLE 5 Torsion angles @(C=C-C-Br) propene
and torsional force constants FQ for trans-1,3-dibromo-
@(degrees)
wn gauche
0.0
115.1
F+ (mdyn A rad-‘) 0.033 0.057
Fig. 3. Torsional potential curves E (kcal mole’) for trans-1,3-dibromopropene, transXHC=CH-CH,X (X = Br). The torsion angle o(C=C-C-X) is in degrees. The conformer syn (S) possessing C, symmetry has a planar arrangement of the atoms CCCX with o = 0”. The transitional form anti (A) also has a planar arrangement of the atoms CCCX with o = 180”, while gauche (G) has @ = 120”. The dotted curve was obtained without excess charges on the atoms. Fig. 4. Torsional potential curves E (kcal mol-‘) for 2,3-dibromopropene, H,C=CX-CH,X (X = Br). The dotted curve was obtained without excess charges on atoms. The torsion angle o(C=C--C-X) is in degrees. The conformer syn (S) and the transition form anti (A) have a planar arrangement of the atoms CCCX with &syn) = 0’ and @(anti) = 180”. Both S and A possess C, symmetry.
2,3_Dibromopropene Conformational drawings and torsional potential curves for H$=CBrCHzBr are shown in Fig. 4. The calculated energy difference AE = E(gauche) E(syn) = 0.8 kcal mol-’ agrees reasonably well with the value 1.0 + 0.2 kcal mol-’ as determined from gas-phase electron diffraction data [ 121. As seen from Fig. 4 the results calculated for this molecule are very sensitive to the magnitude of electrostatic terms. Values of the observed and calculated structural parameters have been compared in Table 6. The barrier height for the transition between enantiometric gauche forms is 6.7 kcal mol-‘. trans-1-Bromo-2-bu tene The torsional potential curve and conformational drawings for trans-CH,CH=CH-CHzBr are shown in Fig. 5. For the energy difference E(syn) E(gauche) the value 0.7 kcal mol-’ was obtained. The torsion angles of the gauche conformer are $J~(C=C-C~-X) = 114.2” and @,(C=C-C4-H) = -O.l”, while for syn the values are $1 = 0” and & = 0”. The values of the torsional force constants obtained are shown in Table 7. Neglecting the electrostatic terms in the energy calculations changed the torsional potential curve only insignificantly.
148 TABLE
6
Results for H,C=CBr-CH,Br Parametera
Observed
Calc. values
gauche
syn
Bond lengths (A) C-C c2-x c3-x
1.506 1.906 1.953
1.507 1.899 1.951
Bond angles (degrees) c=c-C
127.6
C=C-H c=c-x C-C-X C-C-H X-C-H
120.4 118.0 113.6 108.9 108.4
111.9 109.5 108.8
0.0
95.5
Torsion angles (degrees) @J(C=C-C-X) Torsional force constants F = a’E/a@ aX = Br, Cl=C2-C3. TABLE
125.2 120.0 118.7
(mdyn A rad-‘) 0.042
0.073
values [12]
1.480( 14) 1.904( 17) 1.940( 19) 124.2(1.7) 120.5(-)b 120.1(4.4) 113.4(3.5) 106.2(7.0) C-P 112(4)
0.03-0.05
bNot reported.
7
Torsional force constants
(mdyn A rad-‘) for trans-1-bromo-2-butene
F,(C-CH,Br) FJC-CH,)
syn
gauche
0.027 0.059
0.058 0.060
3-Bromo-2-me thyl-1 -propene Conformational drawings and the torsional potential curve calculated for the molecule H&=C(CH3)-CH2Br are shown in Fig. 6. According to a gasphase electron diffraction investigation [13] the compound exists as a mixture of syn and gauche conformers, gauche being the low energy form. Our calculated conformational energy difference of 1.2 kcal mol-’ agrees with the experimentally estimated value of 1.4 + 0.6 kcal mol-‘. From an IR study of the liquid an energy difference of only 0.3 kcal mol-’ between the conformers was reported [14]. When the electrostatic terms in the energy expression were neglected the changes in the potential curve were insignificant. Calculated and observed values of the structural parameters are compared in Table 8.
Fig. 5. Torsional potential curve E (kcal mol-‘) for trans-1-bromo-2-butene, trans-CH,HC=CH-CH,X (X = Br). The torsion angle @(C=C-C-X) is in degrees. The conformer syn (S) and the transitional form anti (A) have a planar arrangement of the atoms C-C= C-C-X with @(syn) = 0” and @(anti) = 180”. Both S and A possess C, symmetry. Fig. 6. Torsional potential curves E (kcal mol-I) for 3-bromo-2-methyl-l-propene, H,C= C(CH,)-C&X (X = Br). The torsion angle @I~(C~=C~--C~--X) and @,, (Cl=C2-C4-H’) are in degrees. The conformer syn (S) has @3 = 0” and o4 = 0”, corresponding to planar syn arrangements of the atoms C=C-C3-X and C=C-C4-H’ simultaneously. The conformer gauche (G) has o4 = +l” and $I$ = + 117’. The energy values of the curve correspond to @a = 0” and 0 = e3 as variable. TABLE 8 Results for H,C=C(CH,)-CH,Br Pammete+
Calc. values syn
Bond lengths (A) c-C3 c-C4 c-x Bond angles (degrees) c=c-c3 c=c-c4 C=C-H C-C-X C-C-H H-C-X Torsion angles (degrees) O3 (C=C-c!S-X) $J,(C=C-C~-H’) Torsional force constants F, = a’E/a@,: F, = a’E/a@: F* = a’Ela@,a@, aX = Br, Cl=C2(C4)-C3X.
1.511 1.506 1.952
gauche
1.509 1.509 1.952
125.6 122.2 120.8 113.8 109.4 108.4
122.8 122.5 120.3 112.7 109.7 108.6
0.0 0.0
+116.9 +l.O
(mdyn A rod-‘) 0.027 0.067 -0.009 bNot reported.
0.103 0.063 -0.026
Observed values [13]
1.484( 6) 1.467(6) 1.965(6) 121.5(0.7) 122.1(0.7) 120.4(-) 112.2(0.5) 109.7(-) C-P +113(2) C-P
150
3-Bromo-2-bromome thyl-1 -propene Conformational drawings and labelling for the molecule H,C=C(CH,Br)2 are shown in Fig. 7(a). Torsional potential curves are shown in Fig. 7(b). From our calculations we expect the existence of four stable conformers for this molecule. The high energy form is SS while the low energy form is GG. The conformers GS and GG” both have energies 1.6 kcal mol-’ higher than GG, and SS has an energy 3.8 kcal mol-’ in excess of GG. The minimum for the GG” conformer has Q& = +69” and I$~ = -109”. This point does not exist on the curves shown in Fig. 7(b). The point @3 = +90” and @4 = -90” has an energy value 0.4 kcal mol-’ above the minimum. Energy values relative to the local minima at @3 = f 69” and $4 = 7109” for various combinations of the torsion angles are shown in Table 9. For torsion angles (@) and torsional force constants (F) the values obtamed are shown in Table 10. The torsional potential remained essentially unchanged when the electrostatic terms were neglected in the energy calculations. cis-1,4-Dibromo-2-
bu tene
Conformational drawings are shown in Fig. 8(a) and torsional potential curves in Fig. 8(b). According to our calculations the low-energy conformer a ss
GS
-_ G-_ G X
X -_
E
b
7-
;i:
X
--X
1 -7
I :
X
-_
I I
I 5-
.
I
.
.
.
.
.
: -5
“AS
-3
“X
GG" Fig. 7. 3-Bromo-2-bromomethyl-1-propene, H,C=C(CH,X), (X = Br). (A) Possible conformations. In SS the fragment Cl=C2-C3-X and Cl=C2-C4-X are both planar (syn), corresponding to torsion angles a3 (C=C-CS-X) = 0” and o4 (C=C-CS-X) = 0”. The form GS has @3 = 120” and o4 = 0”, and GG has 0, = 120” = 04, while GG” has oa = 120” and 9, = -120”. Thus, the symmetries are C,,, C, , C,, and C, for forms SS, GS, GG and GG” respectively. (B) Torsional potential curves E (kcal mol-I). The transition form AS has @3 = 180” and a4 = 0” and thus possesses C, symmetry. The unbroken curve (-) was obtained with the restriction that o3 = @ = @.,, and the broken curve (- - -) with 6, = 6 and d, = -$, while the dotted curve (. . .) had cp, = o and a4 = 0”.
151 TABLE 9 Relative* energy values (kcal mol-‘) of the torsional potential in the region of the GG” conformer of H,C=C(CH,Br), .
@sb
9eb
+70 1.42 0.94 0.45 0.12 0.09 0.29
-70 -80 -90 -100 -110 -120
+80 0.94 0.55 0.39 0.32 0.35 0.75
+lOO
+90 0.45 0.39 0.39 0.58 0.98 1.57
*Minima (E = 0) at @a = +-69” and o4 = rlO9’. e4 (C=C-C4-Br) are in degrees.
+llO
0.12 0.32 0.58 1.16 1.96 2.82
+ 120 0.09 0.35 0.98 1.96 3.17 4.41
0.29 0.75 1.57 2.82 4.41 6.10
bTorsion angles @,(C=C-C3-Br)
and
TABLE 10 Torsion angles and torsional force constants for conformers of 3-bromo-2-bromomethyl1-propene Parametera
SS
&(C=C2-C3-X)
0.0
e4 (C=C2-C4-X)
0.0
F,
=
a2Ela@2,
F,
= a’Ela@: F* = a’Ela$,a@,
0.021 0.021 -0.010
GG
GG”
t 109.9 + 109.9
+ 68.6 -109.2
0.105 0.105 -0.019
0.079 0.101 -0.035
GS 0.0 109.8 0.007 0.113 -0.027
*Angles in degrees, force constants in mdyn I%rade2.
GG”. The point at #1 = +90” and $4 = -90” has an energy 0.6 kcal mol-’ above the minima at $1 = 584” and $e = T112”. Energy values relative to the local minima for various combinations of the torsion angles are shown in Table 11. The GG conformer has an energy only 0.1 kcal mol-’ higher than GG”. Thus, for the gas phase both conformers are expected to exist at room temperature. The point indicated by GS in Fig. 8(b) is a saddle point. Consequently a stable GS form should not exist for this molecule. For the low-energy conformers the values of torsion angles ($) and torsional force constants (3’) shown in Table 12 were calculated. Also when the electrostatic terms were neglected the low energy forms remained GG” and GG, with GG about 0.7 kcal mol-’ higher in energy than is
GG" .
152 A
&
.q$
xp
ii %’
xv
2-
GG”
GG 0
30
60
90
120
150
180
Fig. 8. cis-1,4-Dibromo-2-butene, cis-XH,C-HC=CH-CH,X (X = Br). (A) Possible conformation. In the form SS the fragments X-Cl-C2=C3 and X-C4-C3=C2 are both planar (syn), corresponding to torsion angles o, (X-Cl-C=C) = 0” and o,(X-C4-C=C) = 0”. The form GS has o1 = 90’ and o4 = O”, and for GG o1 = o4 = 90”, while for GG” o1 = 90” and o4 = -90”. The symmetries are C,,, C,, C, and C, for the conformers SS, GS, GG and GG” respectively. (B) Torsional potential curves E (kcal mol-I). The transitional form AS has o1 = 180” and o4 = 0” corresponding to C, symmetry. The unbroken curve (-) was obtained with 0, 5 o4 = 9, and the broken curve (- - -) with o1 = o and o4 = -$,whileforthedottedcurve(...)o, =@ando, =O”. TABLE 11 Relativea energy values (kcal mol-‘) of the torsional potential in the region of the GG” conformer of ci.s-BrH,C-HC=CH-CH,Br ob4
@lb t-70
-70 -80 -90 -100 -110 -120
7.31 4.94 2.75 1.23 0.46 0.41
+80 4.94 3.09 1.51 0.49 0.41 0.12
*Minima (E = 0) at @, = *84’ o,(C=C-C4-Br) are in degrees.
+90 2.75 1.51 0.58 0.12 0.04 0.23
+100 1.23 0.49 0.12 0.09 0.28 0.57
and o4 = r112O. bTorsion
+ 110
+120
0.46 0.41 0.04 0.28 0.62 1.00 angles o 1(Br-Cl-C=C)
0.41 0.12 0.23 0.57 1.00 1.45 and
3-Bronao-1 -butene Results for H&=CH- HCBr-CH3 are shown in Fig. 9. According to our calculations three stable conformations are available to this molecule. The low-energy form with H in the HCBr group eclipsing the C=C bond is denoted GX For the two other conformers GH and SM (see Fig. 9) the energies are 0.8 and 2.2 kcal mol-’ higher than in GX respectively.
153 TABLE 12 Torsion angles and torsional force constants for cis-1,4-dibromo-2-butene Parameters o1 (X-Cl-C2=C3) @,(C2=C3-C4-X)
GG
GG”
+ 90.6 + 90.6
+ 84.4 -111.5
0.065 0.065 + 0.024
F, = a=E/a$; F, = aZEla& F* = aZE/a@, + @4
0.093 0.091 -0.050
aAngles in degrees, force constants in mdyn A rad-* .
E
c
GX
GH
. . --.__GX :* 0
I 30
I 60
I 90
.**
120
160
4
160
Fig. 9. Torsional potential curves E (kcal mol-I) for 3-bromo-1-butene, H,C=CH-X CH-CH, (X = Br, M = CH,). The torsional angles @,(Cl=C2-C3-X) and @,(C2-C3-C4H) are in degrees. The conformers have the following values of 03: + 6” (SM), -123” (GX) and +112” (GH). The values of 9, are approximately 60” for these conformers. Thus, in SM the CH, group eclipses the C=C bond. The fragment C-XCH-CH has a nearly staggered arrangement in each of these conformations. The unbroken curve was calculated with the restriction that & = +@ and 0, = 60”, while the dotted curve corresponds to o, = -0 and @, = 60”. TABLE 13 Torsion angles and torsional force constants for 3-bromo-1-butene Parametera @,(Cl=C2-C3-X) o4 (C2-C3-C4-H’) F, = a’E/a@; F, = aZEta@: F* = aZElao3a@,
GX
GH
SM
-122.7 + 58.9
+ 112.0 + 59.3
+ 5.8 + 58.4
0.065 0.111 -0.003
aAngles in degrees, force constants in mdyn A radm2.
0.048 0.108 -0.003
0.054 0.155 + 0.034
154
The values of torsion angles ($) and torsional force constants (F) shown in Table 13 were obtained. The torsional potential curve remained essentially unchanged when the electrostatic terms were neglected in the calculations. 4-Bromo-1-butene Results for H&=CH-CH2--CHzBr are shown in Fig. 10(b) and in Table 14. Conformational drawings are shown in Fig. 10(a). A conclusion from an investigation of the IR spectra of this molecule [ 151 was that there are two forms coexisting in both the gas and the liquid phases; one with the halogen atom in the anti position and one with the halogen atom in the gauche position. From the three possible conformations with the halogen atom in the gauche position, and the two possibilities for the anti position, a planar carbon skeleton was suggested [15]. However, from an electron diffraction investigation [16] it was shown that the most abundant form in the gas phase is GA with a gauche carbon skeleton and an anti halogen atom. At 23°C the composition (%) was: 38(GA), 50(GG + GG*), 8(5’A) and 4(SG) with error limits of about 10%. Because the C, * * - Br peak of the GA conformer is isolated in the RD curve [16] the percentage of that form was well established in the GED work. Our calculations resulted in the following conformational energies a SA
b
SG E
:
. -7
7/
‘Lx
.
‘X GA
GG
GG*
0
30
60
90
120
150
190
Fig. 10. 4-Bromo-1-butene, H,C=CH-CH,-CH,X (X = Br). (A) Possible conformations. SA and SG have the C atoms in a planar syn (S) arrangement. For GG, GA and GG* the C atoms have a gauche (G) arrangement. The second letter in a conformational name indicates whether X has an anti (A) or gauche (G) arrangement to the C=C bond. The torsional angles are o,(C=C--C--C) and @,(C-C-C-X). Thus the values of the torsion angles (I$~/@~) are: SA (O/180), SG (O/60), GG (120/+60), GA (120/180) and GG* (120/-60). Only SA possesses C!, symmetry. (B) Torsional curves E (kcal mol-‘). The unbroken curve (-) was calculated with the restriction that @ = @,(C=C-C--C) and o,(C-C-C-X) = 120”. The broken curve (- - -) corresponds to the restriction o4 = -@ and o3 = 120”, while for the dotted curve (. . _) 9, = QJand o3 = 0’.
155 TABLE 14 Results for H,C=CH-CH,-CHBr Parametera
Calc. values GA
Bond lengths (a) C2-C3 c3-c4 c-x
1.504 1.517 1.950
GG
1.507 1.521 1.958
Observed values [ 161
1.508(7) 1.528(7) 1.945(8)
Bond angles (degrees) c=c-c C-C-C C=C-H C2-C3-H C3-C4-H H-C-X C-C-X
123.9 112.0 119.9 110.0 109.7 109.4 110.0
123.8 113.7 119.9 110.1 109.6 108.8 111.1
122.9(3.2) 111.5(2.7) 121.5(--p 110.4(--p 111.7(--p 106.3(-)b 111.2(0.7)
Torsion angles (degrees) G3(C=C-c-C) @,(C-C-C-X)
117.2 181.0
112.7 69.4
120(4)c ISOb(
Torsional force constants (mdyn .k rad-‘) F, = a2Ela& 0.061 F, = aZEla@: 0.105 F* = a’Ela@,a@, -0.001 aX = Br, Cl=C2-C3-C4.
0.066 0.138 -0.006
;I$b C-P
bNot reported. CValues for GA form.
(kcal mol-‘) relative to the energy of GA: 0.15 (GG), 0.56 (SA),0.90(GG*) and 0.85 (SG). The calculated composition at 23°C corresponding to these energies is 41% GA, 32% GG, 9% GG*, 10% SG and 8% SA, when conformational differences in vibrational partition functions are ignored. Thus our results agree well with the GED data, but not with the IR data. The results were not significantly changed when the electrostatic energy terms were neglected. Experimental and calculated results are compared in Table 14. CONCLUDING REMARKS
Parameter values presented in this work for the interactions Br . * * C(sp’) correspond to several compromises. Energies as well as structural parameters should be correctly reproduced simultaneously. Thus, mutual concessions had to be made in order to have the best possible fit with experimental values of conformational energies as well as torsion angles, bond angles and bond lengths. For conformational energies the average deviation between observed and calculated values is 0.2 kcal mol-I, while for the chloro compounds [3] the
156
corresponding value was 0.3 kcal mol-‘. No attempts were made to correct for conformational differences in vibrational energies. Uncertainties in the calculated barrier heights are not so easily estimated. However, uncertainties for the bromo compounds are probably about 0.51.0 kcal mol-‘, as estimated for the chloro compounds [3]. Our calculated torsional barrier heights range from 0.5 to greater than 10 kcal mol-‘. One can have this wide range of values even within the same molecule (Fig. 7(b)). However, for molecules possessing a stable syn conformation, the barriers separating syn from other forms have heights between 0.5 and 2 kcal mol-‘. A summary of low energy conformers, and values of conformational energy differences, including bromo and chloro [ 31 compounds, is presented in Table 15. Except for the molecules (X = Cl, Br) cis-XHC=CH-CHzX having only gauche as a stable conformation, the remaining 18 molecules have more than one stable conformation. Thus for molecules with only one XHzC group syn (S) and gauche (G) are stable forms. For molecules possessing two XHzC groups at least three of the four forms SS, GS, GG and GG” are stable. According to our calculations the molecules (X = Cl, Br) H2C= CH-XCH-CH3 have three stable conformations, and the molecules H$= CH-CH2-CH2X have five stable forms. For molecules having a stable syn conformation, calculations and experimental evidence agree that the values of the syn torsion angles (4) are zero degrees corresponding to a planar heavy-atom conformation. Typically the calculated @(gauche) values are about 5” less than the corresponding observed values. However, for H,C=C( CH&CH,Br the calculated value is greater than the observed value. A closer inspection of the structural parameter values for individual molecules reveals some systematic trends. Typically, for syn conformers the values of the bond angles C=C-C and C-C-Br in the fragments C=C- C-Br TABLE 15 Summary of low-energy conformers and conformational Molecule
A,!?’
H,C=CH-CH,X trans-XHC=CH-CH,X trans-H(CH,)C=CH-CH,X H,C=CX-CH,X cis-XHC=CHSH,X H,C=C(CH,)--CH,X H,C=C(CH,X)2 cis-XH,C-HC=CH-CH,X H,C=CH-XCH-CH, H,C=CH-CH,-CH,X Wonformer
S-G S-G S-G G-S gaucheb S-G GS-GG GG - GG” GH-GX GG-GA
energy differences
AE
(kcal mol-‘)
X Br
Cl [13]
0.8 0.3 0.7 1.0
0.6 0.4 0.8 0.7
1.4 1.6 0.1 0.8 0.2
- conformer of lowest energy. bOnly the gauche form is stable.
-
0.7 0.9 0.4 0.7 0.4
157
are 2-2.5” greater than the corresponding values in gauche conformers. The C-C and C-Br bonds of syn conformers are about 0.003-0.004 a longer than those of gauche conformers. Unfortunately such small differences are not easily detected by the experimental methods used in studying these molecules. Calculated values of C-CHzBr torsional force constants (FO) have been obtained in the range 0.02-0.14 mdyn A rad-‘, while the F,(C-CH,) values fall between 0.06 and 0.16 mdyn A rad-*. The effects of neglecting the eIectrostatic terms in the energy expression may be studied in Figs. 1-4. Clearly the effects are small in the molecules H2C=CH-CH,Br, cis-BrHC=CH- CH2Br and truns-BrHC=CH- CH2Br. However, for H,C=CBr-CH,Br the effects are dramatic (Fig. 4). ACKNOWLEDGEMENT
We acknowledge financial forskningsr&d, NAVF.
support
from
Norges
Almenvitenskapelige
REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
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