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Theoretical calculation of the geometries of the radical ions of ethylene and the fluoroethylenes
CHEMICAL PHYSICS LETTERS
Volume 82, number 2
THEORETICAL
CALCULATION
OF THE RADICAL
1 September 1981
OF THE GEOMETRIES
IONS OF ETHYLENE
AND THE FLUOROETHYLENES
Stewart MERRY and Colin THOMSON Department of C?zemisrry, University of St. Andrew,
St. Andrews K YI 6 SST, UK
Received 13 Aprd 1981; in final form 1 June 1981
Ab initio UHF calculations of the optimized geometries of the amon and cation of ethylene and perfluoroethylene are reported_ The cations are both predicted to be planar, but both anions are significantly distorted, particularly the CzFi ion, which has Czh symmetry. Further calculations show that all the fluormated ethylene anion radicals should be non-planar
of the internal coordinates forces on these coordinates
1. Introduction
The radical anion of perfluoroethylene C,F, has been prepared by McNeil et al. [ 11, and the isotropic and anisotropic hyperfme coupling constants measured_ The isotropic values of aF = 94.3 G and ac = 48.7 G were consistent with either a planar geometry, as is usually the case in n-electron hydrocarbon radical ions, or a chair structure of Czh symmetry provided that the out-of-plane distortion of the methyl groups is small. It is, of course, well known that the geometries and structures of the fluoro-substituted methyl radicals differ markedly from those of the hydrogen-containing alkyl radicals which are essentially planar [2] _ Symons [3 ] , who has independently prepared C, Fi, has discussed the recent work on fluorinated anion radicals, and concluded that the non-planar structure is the most likely. We report in this note the results of a full geometry optimization study of CzHi and C2 Fy which confirms the non-planar structure of the latter radical anion. However, similar calculations on all the fluoroethylene anion radicals show that they are all non-planar, a result which is rather unexpected.
2. Method of calculation The recent development of geometry optimization methods which minimise the total energy as a function 0 009-26
14/81/0000-0000/S
by minimization of the [4] has made reliable calculations of molecular geometries by ab initio methods much easier. We have used this method of optimization as implemented in the programme GAUSSIAN 80 [S] using the ab initio SCF method to determine the wavefunction. The recently developed 3-21 basis set of Binkley et al. [6] has proved superior to the earlier 4-3 IG basis set for geometry predictions, and we have used this for most of the calculations. For the C,H, ions we also compared the 3-21G geometry with that calculated using the larger 6-3 lG* basis set [7], and for C, Fq ions we have a!so compared the STO-3G and 3-21G basis sets. All the calculations were carried out with the VAX 1 l/780 GAUSSIAN 80 programme package, and we have calculated the structure of the radicals using the unrestricted Hartree-Fock (UHF) method [8] with spin annihilation of any quartet component in the wavefunction. All calculations were run at the University of St. Andrews on the VAX 1 i/780 computer.
3. Results The structures of a large number of free radicals have now been investigated using ab initio methods. It is now well established that the computed s+ctures are somewhat more sensitive to the basis set and (especially to the SCF method used) than for singlet ground
02.50 0 North-Holland Publishing Company
373
CHEMICAL PHYSICS LETTERS
Volume 82, number 2
1 September 1981
Table 1 Calculated energy and geometrical parameters for Ca Hz and Ca G lMolecule
Basis
Energy
R (C-C)
R(C-H)
LCCH
Dl a)
D2 b,
C2Hli
3-21G 6-3IG*
-77.4658 -77.9016
1 442 1.438
1.090 1.093
119.2 118.8
145.1 141.1
-0.0s 0.01
-77.27146 -77.71233
1.405 1.403 -____
1.074 1.076
120.8 120 8
180 0 180.0
0.0 0.0
+ C2H4
3-21G 6-31G” __-______.
a) Dihedral angle for trans hydrogens.
b, Dihedral angle for cis hydrogens
states. We are at present investigatmg the effect of larger basis sets and alternative SCF methods, such as the restricted open shell SCF method (ROHF) [9], on the results. but we do not expect that these will change the conclusion as to the structure of these fluoroethylene anion radicals. We present first the results for the anion and cation radical of ethylene, neither of which have been prepared experimentally, followed by the results for the corresponding ions of perfluoroethylene, and finally the results for the other fhroroethylene anion radicals.
3.1. Ethylene radical ions Table 1 gives the calculated total energies and geometrical parameters for the ethylene anion and cation radicals_ The expectation values of after annihilation were close to 0.75. C2G is predicted to be planar, and the geometrical parameters are very close for the two basis sets. However, the anion radical is predicted to be non-planar. Previous calculations on these ions have assumed a planar structure [lo] and the geometries were only partly optimized. Since it has been shown that geometries calculated using the 3-216: and
(
6-3 1G’ basis sets should be quite reliable [6,11], we do not expect that inclusion of electron correlation will alter the qualitative conclusions_ Calculations on negative ions are known to give larger errors than for neutral species [ 121, and we are currently investigating these various points which will affect the quantitative predictions_ 3.2. Perfluoroethylene
radical ions
T?ble 2 gives the calculated UHF geometries of CZFiand C2F4, for both STO-3G and ST0 3-21G basis sets. The results show clearly that the structures are quite different. C2Fi is planar within the accuracy of the calculations. However, the anion radical is quite definitely non-planar, with essentially C.& symmetry, and fig- 1 depicts the structure of this species. Optimization of C,Fi with the molecule restricted to a planar configuration gave an energy of E = 470.4901 hartree with R(C-C) = 1.387 A, R(C-F) = 1.281 A and LFCC = 121”. The energy barrier to inversion is thus 0.078 hartree = 205 kJ mol-l. There are the expected larger differences between the STO-3G and
3-21G geometries, but as explained above, we expect
Table 2 CalcuIated energy and geometricai parameters for Ca Fz and C,F$ Molecule
Basis
Energy
R (C-C)
R (C-F)
LCCF
Dl al
D2 b,
CaF;
STO-3G 3-21G
-466.7323 -470.8227
1.566 1.483
1.393 1.403
109.8 110.2
146.5 147.8
335 32.2
STOJG 3-21G
-466.6607 -470.4901
1.457 1.281
1.312 1.387
121.1 121.0
179.9 179.9
-0.1 -0.1
* C2Fci
a) Dihedral angle for trans fluorines_
374
b, Dihedral angle for cis fluorines.
Volume 82, number 2
Fig. 1. Structure of CzFi
CHEhlICAL
PHYSICS
LETTJZRS
1 September 1981
sult is even for vinyl fiuoride, the addition of a single electron results in a radical with an essentially planar framework containing the C2H3--fragment hut with the single fluorine appreciably out of plane- The nonplanar structure is more stable than the planar by 44.7 k.I mol-l in the case of C2H3F:. Experimental studies of these molecules would be very interesting.
at optimized geometry.
the 3-21G prediction to be reliable. The hyperfine coupling constants calculated at the optimum 3-21G geometry using the INDO method 1131 are a= = 71.7 G and cq = 104.8 G. Although ozF is not too different from the experimental value, cut is too high.
4. Conciusions Our ab imtio WHF calculations show that the anion radicals derived from all the fluorosubstituted ethylenes are signif?cantly non-planar, and in particular the results for C2Fz show this radical to have C2b symmetry and exclude a planar structure, in agreement with the suggestion of Symons 13 1. A more detaiIed discussion of the dependence of the hyperfme coupling constants on the basis set, and the molecular bonding in these radicals, will be presented at a Iater date 1141.
3.3. The otlzer fluoroethylene union radicals In the light of the results for C!2F& we examined the structure of the other fluoro-substituted ethylene anion radicals. The results are presented in table 3. Each of the anion radicals 1s predicted to be bound, and ail are non-planar. Perhaps the most surprising re-
Table 3 CalcuIated geometrica! parameters for fluoroethyiene anion radicalsa) 7
X5 \
i
/ X6
x3 c2=c{ \
X4
I
Parameter
H \ 4
c2-Cl
H c-c/
\ H
1.399
1.084 1.079
Cl-X3 Cl-X4 c2-X5 C&X6
Dl b) D2 c) D3 d,
1.087 1.492 122.34 120.86 116.96 120.47 168.04 8.19 45.77
energy
-175.80624
LCCX3 LCC& LCCX5 LCa6
a) 3-21G basis Set.
b, Dihedral-e
X4-Cl-C2-X3.
r
\ c-”
F/
H
H
1.422 1.079 1.079 1.424 1.424 115 57 115.57 114.62 114.62 221.25 -49.63 49.70 -274.15873 c)
Dihedral
F \ / H
F \
H c-c’
\
H’
H
/ F
‘F
H C-c/ \
F
1.413 1.452 1.085 1.452 1.085 116.71 11312 116.71 113.12 125.99 163.79 163.82
1.376 1 077 1.473 1.473 1.077 119.34 121.15 121.15 119.34 139.34 -27.88 -28.16
1.406 1.077 1.426 1.405 1.435 124 29 115.73 110.68 122.58 146.73 23.63 45 99
-274.13869
-274.13948
-372.47256
angle X5-C2-Cl-X3.
t) D&dml
angle X6-C2-Cl-X4.
375
Volume 82, number 2
CHEMICAL PHYSICS IE’I-I’ERS
Acknowledgement
The authors thank Professor J.A. Pople for a COPY of the VAX X1/780 version of GAUSSIAN 80, and M. Frkch (Carnegie-Mellon University) for useful discussions. We also thank Professor M.C.R. Symons for useful correspondence, and a referee for helpful comments.
References [I] R-1. McNeiI, M. Shiotani, F. Wiis and M-B. Yim, Chem. Phys. Letters 51 (1977) 433. [2] KS. Chen and J.K. Kochi, Can. J. Chem. 52 (1974) 3529. [3] M C.R. Symons, Ann. Rept. Chem. Sot 75A (1978) 129. [4f P. Pulay, im Modern theoretical chemistry, Vol. 4, ed. H.F. Schaefer III (Plenum Press, New York, 1977) ch. 4.
1 September 1981
[5j J.S. Binkley, R.A. Whiteside,R. Krishnan, R. Seeger, D-J. DeFrees, H-B. Schlegel, S. Topiol, L.R. Kahn and J.A. Pople, GAUSSIAN SO, Carnegie-Mellon University, April 1980 [6] J-S. Binkley, J.A. Pople and W.L Hehre, J_Arn_ Chem. sot. 102 (1980) 939. [7] P-C. Hariharan and J.A_ Pople, Theoret. Chim. Acta 28 (1973) 213. [8] LA. Pople and R.K. Nesbet, J. Chem. Phys. 22 (1954) 571. 191 J.S. Binkley, J.A. Pople and P A. Dobosb, Mol. Phys. 28 (1974) 1423. f 101 J_ AlmWf, A. Lund and K.-ii. Thomas, Chem. Phys. Letters 32 (1975) 190_ [l11 D-J_ DeFrees, B.A. Levi. SK_ PoBack, ‘iV.J_Hehre, J-S. Binkley and J.A. Pople, J_ Am. Chem. Sot. lOl(1979) 4085. [ 121 L. Radom, in. Modern theoretical chemistry, Vol. 4, ed. H-F. Schaefer III (Plenum Press, New York, 1977) ch. 8. 1131 J-A. Pople, D.L. Beveridge and P.A. Dobosh, J. Chem. Phys. 47 (1967) 2026. [ 14 J C. Thomson, to be pubhshed.
Volume 82, number 2
THEORETICAL
CALCULATION
OF THE RADICAL
1 September 1981
OF THE GEOMETRIES
IONS OF ETHYLENE
AND THE FLUOROETHYLENES
Stewart MERRY and Colin THOMSON Department of C?zemisrry, University of St. Andrew,
St. Andrews K YI 6 SST, UK
Received 13 Aprd 1981; in final form 1 June 1981
Ab initio UHF calculations of the optimized geometries of the amon and cation of ethylene and perfluoroethylene are reported_ The cations are both predicted to be planar, but both anions are significantly distorted, particularly the CzFi ion, which has Czh symmetry. Further calculations show that all the fluormated ethylene anion radicals should be non-planar
of the internal coordinates forces on these coordinates
1. Introduction
The radical anion of perfluoroethylene C,F, has been prepared by McNeil et al. [ 11, and the isotropic and anisotropic hyperfme coupling constants measured_ The isotropic values of aF = 94.3 G and ac = 48.7 G were consistent with either a planar geometry, as is usually the case in n-electron hydrocarbon radical ions, or a chair structure of Czh symmetry provided that the out-of-plane distortion of the methyl groups is small. It is, of course, well known that the geometries and structures of the fluoro-substituted methyl radicals differ markedly from those of the hydrogen-containing alkyl radicals which are essentially planar [2] _ Symons [3 ] , who has independently prepared C, Fi, has discussed the recent work on fluorinated anion radicals, and concluded that the non-planar structure is the most likely. We report in this note the results of a full geometry optimization study of CzHi and C2 Fy which confirms the non-planar structure of the latter radical anion. However, similar calculations on all the fluoroethylene anion radicals show that they are all non-planar, a result which is rather unexpected.
2. Method of calculation The recent development of geometry optimization methods which minimise the total energy as a function 0 009-26
14/81/0000-0000/S
by minimization of the [4] has made reliable calculations of molecular geometries by ab initio methods much easier. We have used this method of optimization as implemented in the programme GAUSSIAN 80 [S] using the ab initio SCF method to determine the wavefunction. The recently developed 3-21 basis set of Binkley et al. [6] has proved superior to the earlier 4-3 IG basis set for geometry predictions, and we have used this for most of the calculations. For the C,H, ions we also compared the 3-21G geometry with that calculated using the larger 6-3 lG* basis set [7], and for C, Fq ions we have a!so compared the STO-3G and 3-21G basis sets. All the calculations were carried out with the VAX 1 l/780 GAUSSIAN 80 programme package, and we have calculated the structure of the radicals using the unrestricted Hartree-Fock (UHF) method [8] with spin annihilation of any quartet component in the wavefunction. All calculations were run at the University of St. Andrews on the VAX 1 i/780 computer.
3. Results The structures of a large number of free radicals have now been investigated using ab initio methods. It is now well established that the computed s+ctures are somewhat more sensitive to the basis set and (especially to the SCF method used) than for singlet ground
02.50 0 North-Holland Publishing Company
373
CHEMICAL PHYSICS LETTERS
Volume 82, number 2
1 September 1981
Table 1 Calculated energy and geometrical parameters for Ca Hz and Ca G lMolecule
Basis
Energy
R (C-C)
R(C-H)
LCCH
Dl a)
D2 b,
C2Hli
3-21G 6-3IG*
-77.4658 -77.9016
1 442 1.438
1.090 1.093
119.2 118.8
145.1 141.1
-0.0s 0.01
-77.27146 -77.71233
1.405 1.403 -____
1.074 1.076
120.8 120 8
180 0 180.0
0.0 0.0
+ C2H4
3-21G 6-31G” __-______.
a) Dihedral angle for trans hydrogens.
b, Dihedral angle for cis hydrogens
states. We are at present investigatmg the effect of larger basis sets and alternative SCF methods, such as the restricted open shell SCF method (ROHF) [9], on the results. but we do not expect that these will change the conclusion as to the structure of these fluoroethylene anion radicals. We present first the results for the anion and cation radical of ethylene, neither of which have been prepared experimentally, followed by the results for the corresponding ions of perfluoroethylene, and finally the results for the other fhroroethylene anion radicals.
3.1. Ethylene radical ions Table 1 gives the calculated total energies and geometrical parameters for the ethylene anion and cation radicals_ The expectation values of
(
6-3 1G’ basis sets should be quite reliable [6,11], we do not expect that inclusion of electron correlation will alter the qualitative conclusions_ Calculations on negative ions are known to give larger errors than for neutral species [ 121, and we are currently investigating these various points which will affect the quantitative predictions_ 3.2. Perfluoroethylene
radical ions
T?ble 2 gives the calculated UHF geometries of CZFiand C2F4, for both STO-3G and ST0 3-21G basis sets. The results show clearly that the structures are quite different. C2Fi is planar within the accuracy of the calculations. However, the anion radical is quite definitely non-planar, with essentially C.& symmetry, and fig- 1 depicts the structure of this species. Optimization of C,Fi with the molecule restricted to a planar configuration gave an energy of E = 470.4901 hartree with R(C-C) = 1.387 A, R(C-F) = 1.281 A and LFCC = 121”. The energy barrier to inversion is thus 0.078 hartree = 205 kJ mol-l. There are the expected larger differences between the STO-3G and
3-21G geometries, but as explained above, we expect
Table 2 CalcuIated energy and geometricai parameters for Ca Fz and C,F$ Molecule
Basis
Energy
R (C-C)
R (C-F)
LCCF
Dl al
D2 b,
CaF;
STO-3G 3-21G
-466.7323 -470.8227
1.566 1.483
1.393 1.403
109.8 110.2
146.5 147.8
335 32.2
STOJG 3-21G
-466.6607 -470.4901
1.457 1.281
1.312 1.387
121.1 121.0
179.9 179.9
-0.1 -0.1
* C2Fci
a) Dihedral angle for trans fluorines_
374
b, Dihedral angle for cis fluorines.
Volume 82, number 2
Fig. 1. Structure of CzFi
CHEhlICAL
PHYSICS
LETTJZRS
1 September 1981
sult is even for vinyl fiuoride, the addition of a single electron results in a radical with an essentially planar framework containing the C2H3--fragment hut with the single fluorine appreciably out of plane- The nonplanar structure is more stable than the planar by 44.7 k.I mol-l in the case of C2H3F:. Experimental studies of these molecules would be very interesting.
at optimized geometry.
the 3-21G prediction to be reliable. The hyperfine coupling constants calculated at the optimum 3-21G geometry using the INDO method 1131 are a= = 71.7 G and cq = 104.8 G. Although ozF is not too different from the experimental value, cut is too high.
4. Conciusions Our ab imtio WHF calculations show that the anion radicals derived from all the fluorosubstituted ethylenes are signif?cantly non-planar, and in particular the results for C2Fz show this radical to have C2b symmetry and exclude a planar structure, in agreement with the suggestion of Symons 13 1. A more detaiIed discussion of the dependence of the hyperfme coupling constants on the basis set, and the molecular bonding in these radicals, will be presented at a Iater date 1141.
3.3. The otlzer fluoroethylene union radicals In the light of the results for C!2F& we examined the structure of the other fluoro-substituted ethylene anion radicals. The results are presented in table 3. Each of the anion radicals 1s predicted to be bound, and ail are non-planar. Perhaps the most surprising re-
Table 3 CalcuIated geometrica! parameters for fluoroethyiene anion radicalsa) 7
X5 \
i
/ X6
x3 c2=c{ \
X4
I
Parameter
H \ 4
c2-Cl
H c-c/
\ H
1.399
1.084 1.079
Cl-X3 Cl-X4 c2-X5 C&X6
Dl b) D2 c) D3 d,
1.087 1.492 122.34 120.86 116.96 120.47 168.04 8.19 45.77
energy
-175.80624
LCCX3 LCC& LCCX5 LCa6
a) 3-21G basis Set.
b, Dihedral-e
X4-Cl-C2-X3.
r
\ c-”
F/
H
H
1.422 1.079 1.079 1.424 1.424 115 57 115.57 114.62 114.62 221.25 -49.63 49.70 -274.15873 c)
Dihedral
F \ / H
F \
H c-c’
\
H’
H
/ F
‘F
H C-c/ \
F
1.413 1.452 1.085 1.452 1.085 116.71 11312 116.71 113.12 125.99 163.79 163.82
1.376 1 077 1.473 1.473 1.077 119.34 121.15 121.15 119.34 139.34 -27.88 -28.16
1.406 1.077 1.426 1.405 1.435 124 29 115.73 110.68 122.58 146.73 23.63 45 99
-274.13869
-274.13948
-372.47256
angle X5-C2-Cl-X3.
t) D&dml
angle X6-C2-Cl-X4.
375
Volume 82, number 2
CHEMICAL PHYSICS IE’I-I’ERS
Acknowledgement
The authors thank Professor J.A. Pople for a COPY of the VAX X1/780 version of GAUSSIAN 80, and M. Frkch (Carnegie-Mellon University) for useful discussions. We also thank Professor M.C.R. Symons for useful correspondence, and a referee for helpful comments.
References [I] R-1. McNeiI, M. Shiotani, F. Wiis and M-B. Yim, Chem. Phys. Letters 51 (1977) 433. [2] KS. Chen and J.K. Kochi, Can. J. Chem. 52 (1974) 3529. [3] M C.R. Symons, Ann. Rept. Chem. Sot 75A (1978) 129. [4f P. Pulay, im Modern theoretical chemistry, Vol. 4, ed. H.F. Schaefer III (Plenum Press, New York, 1977) ch. 4.
1 September 1981
[5j J.S. Binkley, R.A. Whiteside,R. Krishnan, R. Seeger, D-J. DeFrees, H-B. Schlegel, S. Topiol, L.R. Kahn and J.A. Pople, GAUSSIAN SO, Carnegie-Mellon University, April 1980 [6] J-S. Binkley, J.A. Pople and W.L Hehre, J_Arn_ Chem. sot. 102 (1980) 939. [7] P-C. Hariharan and J.A_ Pople, Theoret. Chim. Acta 28 (1973) 213. [8] LA. Pople and R.K. Nesbet, J. Chem. Phys. 22 (1954) 571. 191 J.S. Binkley, J.A. Pople and P A. Dobosb, Mol. Phys. 28 (1974) 1423. f 101 J_ AlmWf, A. Lund and K.-ii. Thomas, Chem. Phys. Letters 32 (1975) 190_ [l11 D-J_ DeFrees, B.A. Levi. SK_ PoBack, ‘iV.J_Hehre, J-S. Binkley and J.A. Pople, J_ Am. Chem. Sot. lOl(1979) 4085. [ 121 L. Radom, in. Modern theoretical chemistry, Vol. 4, ed. H-F. Schaefer III (Plenum Press, New York, 1977) ch. 8. 1131 J-A. Pople, D.L. Beveridge and P.A. Dobosh, J. Chem. Phys. 47 (1967) 2026. [ 14 J C. Thomson, to be pubhshed.