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Structures and properties of fluorinated pyridines; assignment of the two homo's of pyridine
Chemical Physics 41 (19791 21--33 0 North-Holland Publishing Company
STRUCTURES AND PROPERTIES OF FLUORINATED
PYRIDINES;
ASSIGNMENT OF THE TWO HOMO’S OF PYRIDINE M.J.S. DEWAR, Y. YAMAGUCHI Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA S. DORAISWAMY,
S.D. SHARhIA
Tate Institute of Fundamental Research. Colaba. Bombaj 400005. India and
S.H. SUCK Department of Physics and Graduate Center for Cloud Physics Research. University of Missouri-Rob, Rolla, Missouri 65401, USA Received 29 November 1978
Structures and properties of fluorinated pyridines have been studied by microwave spectroscopy and theoretically by the MIND0/3 and MNDO methods. While both hllNDO/3 and MNDOreproduce the geometries of fluorinated pyridirres within their experimental limits of accuracy, MlND0/3 does better in predicting the small changes in geometry due to substitution of hydrogen by fluorine in pyridine. Both MlND0/3 and MNDO give rotational constants in quitegood agreement with experiment, but the errors in MlND0/3 are somewhat smaller. Both methods give acceptable estimates of heats of formation of pyridines. MNDO gives better estimates of ionization energies and dipole moments, the results agreeing quite well with experiment. Whereas t4N nuclear quadrupole coupling constants are calculated satisfactorily by both methods, MNDO does b&r in predicting the changes in constants caused by fluorine substitution.
1. Introduction Recent studies of the microwave spectra of 2fluoropyridine (2) [I], 3-fluoropyridie (3) [Z] ,2,6difluoropyridine (4) [3], and perfluoropyridine (5) [4] have seemingly indicated that surprising structural changes take place on replacement of hydrogen atoms in pyridine (1) by fluorine, involving changes in the CC and CN bond lengths and distortion of the ring. These conclusions were based on various assumptions because the measurements referred only to the most abundant Isotopic species and hence led only to the moments of inertia for the four compounds. However, the assumptions made seem very reasonable and the conclusions in one case (4) have been confirmed [5] by a rather detailed microwave-microwave double modulation study. However, we felt that it would be of interest to study this problem theoretically, both
in the hope of confirming our conclusions and as a check on the theoretical procedures used. A further check would also be provided by comparisons of calculated and observed dipole moments and 14N nuclear quadrupole coupling constants, which were obtained as byproducts in microwave studies. If calculations of this kind proved effective and could be carried out at reasonable cost, they could be of considerable value in studies of larger molecules by microwave spectroscopy, in particular for compounds of elements which have only a single isotope (e.g. F)_ The best candidates for the purpose seemed to be the MIND0/3 [6] and MNDO [7] semi-empirical SCF MO methods, which have been shown to reproduce a wide variety of molecular properties with surprising accuracy, including in particular heats of formation [6,7], molecular geometries [6,7], dipole moments [6,7], ionization energies [6,7], molecular vibrational
M.J.S. Dewar et al./Structures and properties of fluorinated pyridine3
22
frequencies (MIND013 [8], MNDO [9]), ESCA chemical shifts (MlND0/3 [lo], MNDO [ 1I I), and nuclear quadrupole coupling constants (MIND0/3 [ 121, MNDO [ 131). The results are generally superior to those from any but rather sophisticated ab initio calculations, which would be expensive in the present connection. We have therefore carried out a systematic study of the fluoropyridines, using both MIND0/3 and MNDO. Here we present our results.
2. Theoretical procedure The calculations were carried out by the standard MlND0/3 [6] and MNDO [7] procedures, using the standard parameters. Geometries were optimized by using the standard Davidon-Fletcher-Powell [14] procedure, no assumptions being made other than that the molecules are planar. Ionization potentials were estimated by using Koopmans’ theorem [ 151. In the LCAO approximation, the electronic contribution to the field gradient at a given nucleus (ol) of atom A is given by
9~,= -e
7 F Pij(Qil(3 COS'e-
lllr31~j),
(1)
where $ and $ are AO’s, Pii is the corresponding element of the bond order matrix, e is the electronic charge, and r, 0 are spherical polar coordinates centered on nucleus 01.The double sum in eq. (1) can be broken down into one-center terms, where $r-and $ are AO’Sof atom A; two-center terms, where & is an A0 of atom A and 3 an A0 of some other atom(B) or where both pi and 4 are AO’s of atom B; and threecenter terms, where pi and oj are AO’s of different atoms B and C (#A). In MIND0/3 and MNDO, the matrix elements in eq. (1) are treated as parameters. This is inevitable in view of the use of the core approximation and consequent neglect of the Stemheimer effect. However, problems still arise because of the neglect of bicentric overlap. Should corresponding matrix elements be likewise neglected, like electron repulsion integrals, or included, like one-electron resonance integrals? And if they are included, should the wavefunction be correspondingly renormahzed? These problems are discussed in detail in a iorthcoming paper [ 131. Previous
work [ 121 has shown that in MIND0/3, it is best to include bicentric overlap and to renormalize the LCAO wavefunction accordingly_ In MNDO the best results for r4N seem to be obtained by including all terms without renormalizing the wavefunction.
3. Results of calculations by MIND013 and MNDO Table 1 lists the geometries calculated by MIND0/3 and MNDO for l-5,4-fluoropyridine (6). 3,5difluoropyridine (7) 2,4,6_trifluoropyridine (8) 3,4&trifluoropyridine (9), and 2,3,5,6-tetrafluoropyridine (10). Values deduced from experiment (see below) are included for reference. Table 2 shows the corresponding values for the rotational constants, together with experimental values, while table 3 gives corresponding results for heats of formation, first ionization potentials, dipole moments, and net charge on nitrogen atom. Table 4 lists the first seven ionization potentials calculated by MNDO. Table 6 shows 14N nuclear quadrupole coupling constants, calculated by MIND0/3 and MNDO for three different models. In the first, only the nonoverlap terms, which are essentially electronic onecenter terms, are included. In the second, both oneand two-center terms are included. in the third, all terms are included. The calculations were carried out in MNDO without renormalization and in MIND0/3 with renormalization of wave functions. The nuclear quadrupole moment of 14N, Q(N), is estimated using coupling constants of I, 4 and 5. Experimental values are included in table 6 when available.
4. Discussion 4.1. Geometries The structure of pyridine (1) has been investigated in detail by microwave spectroscopy [I 71, making practically no assumptions. Nevertheless the resulting structure (“substitution structure”) does not reproduce the observed rotational constants precisely because they are proportional to the inverse of the effective moments of inertia, which are affected by vibronic interactions. The measurements give the reciprocals of the moments of inertia averaged over the ground vi-
M.J.S. Dewar et al. fStructures and properties of fihorinated pyridines
23
Table 1 Structures of fluorinatedpyridinesa&)
MNDO
NIG
BllNDO/3
expt.
1.3533
1.3350
1.3402
1.4114
1.4067
1.3958
1.4047
1.4056
1.3944
1.0950
1.1141
1.0857
1.0889
1.1051
1.0818
118.22 122.79
1.1070 119.95 122.42
1.0811 116.98 123.79
118.79
117.80
118.50
118.63 115.89
119.59 116.46
118.44 116.05
120.87
120.78
121.38
120.68
120.20
120.78
NlC6 c2c3 cSc6 c3c4 c4c5 c2x7 GXll c3xS C5XlO C&9 L216
L321 L561 ~234 ~456 L345 L127 L16,ll L438 L45,lO L349
1.0899
hlND0
MlND0/3
expt.
1.3644 1.3512 1.4230 1.4119 1.4036 1.4047 1.31i4 I .0956 1.0885 1.0888 1.0904 117.36 123.68 123.12 117.62 118.98 119.25 114.19 115.52 121.17 120.81 120.20
1.3112 1.3397 1.4036 I.4040 1.4033 1.4118 1.3618 1.1138 1.1000 1.1029 1so71 117.82 127.27 122.11 114.11 117.99 120.69 111.16 116.34 122.96 120.64 119.32
1.3207 1.3402 1.3732 1.3958 1.3944 1.3944 1.354 1.0857 1.0818 1.0818 1.0811 115.19 127.24 123.79 116.84 118.50 118.44 114.25 116.05 121.38 121.38 120.78
F
hlIND0/3
MNDO N!C2 NlC6 c2c3 %c6 GC4 GCS c2 x7 c6xll c3xs GXlO c4x9
L216 L321 L561 L234 L456 L345 L127 ~16,il L438 i45,lO L349
1.3486 1.3534 1A286 1.4110 1.4198 1A026 1.0949 1.0949 1.3240 1.0896 1.0698 119.00 121.90 122.73 119.05 119.39 117.92 116.22 115.85 120.76 120.39 121.33
.
1.3348 1.3342 1.4004 1A080 1.3982 1.4071 1.1088 1.1115 1.3793 1.1061 1.1024 121.59 118.84 121.95 122.26 118.65 116.71 118.43 116.42 118.30 119.95 121.32
expt. 1.3402 1.3402 1.3828 1.3958 1.3806 1.3944
hlND0
MlNDOJ3
1.3529
1.3355
1A094
1.4086
1A202
1.3981
1.0956
1.1141
1.0888
1.1006
1.3222 118.32 123.31
1.3724 119.71 123.32
121.68 118.81 116.57 116.51
118.13
114.95
118.79 115.83
123.75 116.58
119.82
12150
12195
122.10
120.60
118.13
1.354
117.31 121.84
expt.
M.J.S. Dewar et al./Stmctures and properties of fluorinated pyndines
24 Table 1 (continued)
...---_.--MNDO NlG N1C.s C2CB
W6 c3c4 c4c5 GX7
MlND0/3
expt.
MNDO
MlND0/3
1.3627
1.3148
1.3086
1.3485
1.3327
1.4237
1.4027
1.3760
1.4286
1.4037
1.4035
1A086
1.3944
l-4181
1.3998
1.3169
1.3559
1.354
1.0949
1.1067
1.0886
1.0984
1.084
1.3229
1.3740
1.0909 116.56 123.95
1.1068 116.77 126.16
1.084 115.3 126.21
1.0900 119.17 121.89
1.0991 123.33 118.48
117.84
114.54
11692
119.60
122.66
119.86 113.91
121.83 111.67
118.44 115.21
117.26 116.19
114.39 118.44
121.11
122.80
123.1
120.38
117.92
120.07
119.08
120.1
121.37
172.81
__..-.. expt.
wh G&
Cs&o c4x9
L216 L321 L561 L234 ~456 L345 L127 L16,ll i438 L45,lO L349
F
MNDO
NICZ NIG G?c3
MIND013
expt.
MNDO
M!ND0/3
1.3626
1.3175
1.3482
1.3328
1.4217
1.4036
1A264
1.4048
1.4197
l-4025
1.4341
1.3994
1.3156
1.3523
1.0956
1A078
1.Q889
1.0960
1.3203
1.3763
1.3197 116.69 124-43
1.3642 116.52 126.77
1.3168 119.98 122.36
1.3761 122.52 119.89
117.29
112.52
118.90
120.05
li9.87 113.85
124.90 111.79
117.49 116.14
117.58 118.40
121.64
123.44
120.60
120.63
120.07
117.55
121.26
121.21
cSc6 C3G c4ci c2x7 c6xll c3x8 c5XlO c4x9
L216 f-321 L561 ~234 L456 f345 L127 L16,ll f438 L45,lO L349
expt.
25
M.J.S. Dewar et al.jStructtues and properties of fluorinated pyridines Table 1 (continued)
F/
F
F-
0
MNDO NrCz
F F/
‘F
F
F-0 N’F
expt.
MIND0/3
MNDO
MlNDOi3
. expt.
1.3583
1.3142
1.3582
1.3159
1.3026
1.4409
1.4015
1.4385
1 A024
1.3647
1.4163
1.4035
1A330
1 A038
1.3624
1.3133
1.3595
1.3121
1.3560
1.354
1.3199
1.3771
1.3178
1.3795
4.354
NlC6 c2c3 cSc6 c3c4 c4cs czx7 c5XlL C3Xs GAO
L216
117.91
121.26
1.3144 118.13
1.3686 120.42
1.354 117.98
L321 L561
123.15
121.69
12359
122.89
123.28
L234 L.456
118.70
118.77
118.10
116.71
118-49
IL345
118.40
117.83
118.50
120.37
118.96
L127 L16,ll
114.48
112.65
114.45
112.61
116.55
L438 L45,lO
120.95
119.19
121.09
121.37
121.39
L349
120.80
121.09
120875
119.82
120.77
c4x9
1.09 13
1.1008
-
a) Bond lengths are in A and bond angles are in degree. b, Experimental vslues are calculated using the modified coordinates
brational state, not those corresponding to the equilibrium geometry. In order to study the changes in structure that take place on substitution of hydrogen
by fluorine, we must start with the equilibrium structure for pyridine. We therefore use a slightly modified geometry for pyridine, chosen to reproduce the observed rotational constants of all isotopic species [18]. The bond lengths and bond angles so obtained in fact differ insignificantly from the rs values. They are shown in table 1. It will be seen that both MIND0/3 and MNDO reproduce the geometry of 1 in a very satisfactory manner, the errors in bond lengths and bond angles being much less than the average errors for an extensive range of nitrogen compounds [6,7] _AU the errors in bond lengths are less than 0.03 A and those in angles less than 3”. Turning now to the fluoro derivatives, it will be seen at once that MNDO seems to systematically under-
[18] and CF distance is assumed to be 1.354 A.
estimate CF bond lengths by about 0.03 A while the MIND0/3 values generally agree with experiment to better than 0.02 A. Admittedly, as noted above, the “experimental” values are subject to some uncertainty, but similar errors occur in the case of 4 where the proposed structure, while not unambiguously confirmed, has been supported by independent measurements. The most striking feature of the geometries deduced for 24 is the shortening of the bonds adjacent to the CF unit together with an increase in the bond angle in the ring at the carbon atom adjacent to fluorine, with corresponding decreases in the two adjacent angles in the ring. The net effect is a displacement of the CF group as a whole towards the center of the ring without significant change in the positions of the other atoms; see fig. 1. It will be seen from the results in table 1 that MIND0/3 reproduces these changes quite well whereas MNDO is unsatisfactory. Thus
M.J.S. Dewar et al./Structures arld properties of fluori!mted pvn-ditnes
26
?,-Fluoropyridins
2.6-
Fig. 1. Structural
Difluaopyridina
Psrlluoropyridina
changes in pyridine ring geometry on fluorine substitution
(which are consistent with the observed rotational
constantsand C-F = 1.354 A). changes in the N, C2 and C& bond lengths, on passing from 1 to 2, predicted by MIND0/3, are -0.0238 and -0.0031 A respectively, compared with “experimental” values of -0.0195 and -0.0226 A, whereas the MNDO values are positive (+O.Ol11 and to.0 116 A). Likewise the predicted changes in the NtC2C3 bond angles are tO.89” and +4.85” for MNDO and
MIND0/3 respectively, compared with the “experimental” value of t3.45”. Likewise in 5, MNDO prediets the CC bonds to be longer than in 1 whereas the microwave evidence suggests that they are shorter. It would certainly be surprising if fluorinationlead to an increase in the lengths of adjacent CC bonds and MIND0/3 does predict a decrease on passage from
21
M.J.S. Dewar et aL/Structures and properties of jitcwitzated pyridines
1 to 5. However, MIND0/3 also predicts quite low differences in CF bond length along this series of compounds and between CF bond lengths of different positions in 5 in particular. Mutual conjugation [191 between fluorine and nitrogen would be expected to lead to a decrease in the length of CF bonds in the 2,4,6 positions of pyridine and such changes are indeed predicted by both MIND0/3 and MNDO. In view of the apparent general success of MIND0/3 in predicting changes in this series of compounds, a better estimate of their true geometries could probably be obtained from the microwave data by assuming corresponding changes in the CF bond lengths. The values listed in table I were calculated with the assumption that all the CF bonds have similar lengths (1.354 A). The general conclusion then is that while both MNDO and MIND0/3 reproduce the geometries of l-5 within their experimental limits of accuracy, MIND0/3 does better in predicting the small changes Table 2 Rotational hl0lfXXle
constants of fluorinated Rotational
rN
0/IF
0/‘N
F
F/IF 0
F/ F
F
F‘Clt4’F
pyridines a-c)
constants (MIIz)
observed
01
in geometry due to substitution of hydrogen by fluorine in.pyridine. By combining MIND0/3 data with experimental results for the parent compound, it may thus be possible to deduce good geometries for such derivatives. Turning now to the rotational parameters, here again a similar pattern holds. Both MIND0/3 and MNDO give results in quite good agreement with experiment, but the errors in MIND0/3 are somewhat smaller. For the compounds in table 2 for which experimental data are available, the standard deviations and mean absolute errors are respectively 93.85 and 77.24 MHz for MNDO and 82.17 and 60.27 MHz for MIND0/3. It should, however, be noted that the superiority of MIND0/3 in this particular connection is accidental because the errors in bond lengths and bond angles given by MNDO are usually much less than those given by MIND0/3 [6,7] _MIND0/3 happens to give a somewhat better geometry for pyridine than MNDO
calculated using modified coordinates
using substitution coordinates
MNDO
hf [ND013
A B = 6039.23 5804.90 C = 2959.22
5804.62 (iO.00) 6039.39 (-0.00) 2959.84 (+0.02)
6063.76 (iO.41) 5820.19 (+0.26) 2969.74 (+0.36)
5907.66 (-2.18) 5716.22 (-1.53) 2905.18 (-1.83j
5888.08 5819.16 (-2.50) (+0.25) 2926.71 (-1.10)
A B = 5870.92 2699.94 c = 1849.27
5869.65 2634.26 (-0.02) (-2.43) 1818.25 (-1.68)
5887.67 (-2.17) 2641.35 (+0.29) 1823.35 (-1.40)
5698.41 (-2.24) 2639.45 (-2.94) 1803.90 (-2.453
5761.99 2672.90 (-1.86) (-1.00) 1825.89 (-1.26)
A B = 5829.66 2637.47 C = 1815.65
5859.75 2581.26 (+0.52) (-2.13) 1791.91(-1.31)
5877.40 (+0.82) 2588.41 (-1.86) 1797.01(-1.03)
5693.97 2576.72 (-2.33) (-2.30) 1773.95 (-2.30)
5758.88 2583.46 (-1.21) (-2.05) 1783.41 (-1.78)
A B = 3741.68 1905.82
3677.11 1847.16 (-1.88) (-3.08)
3685.20 1852.24 (-1.67) (-2.81)
3559.09 1880.01 (-5.03) (-1.35)
3540.10 1934.67 (+lSl) (-5.54)
C = 1263.25
1229.52 (-2.67)
1232.68 (-2.42)
1230.19 (-2.62)
1251.00 (-0.97)
A = 1481.54 B = 1075.35 C = 623.10
1438.59 (-2.90) 1047.93 (-2.55) 606.29 (-2.70)
1441.11 (-2.73) 1050.54 (-2.31) 607.61 (-2.49)
1400.22 (-5.49) 1057.11 (-1.70) 602.36 (-3.33)
1380.78 (-6.80) 1058.80 (-1.54) 599.27 (-3.82)
aj CF distance is assumed to be 1.354 A. b) The values in parentheses are % devintion in observed values. ‘j The observed rotational constants can be reproduced by introducing
the distortions
in the pyridine ring (see fig. 1).
M./S. Dewar et al/Structures and properties of fluorinated pyridines
28
and the error in the MNDO value for the CF bond length is unusually large. It should be noted in this connection that the errors for fluorine compounds in MNDO are generally greater than those for other organic species [7] _ Calculations of this kind should nevertheless be useful in helping to assign microwave spectra for larger molecules, particularly if corrections are made using Table 3 Heats cf formation,
AHf (kul/moIe)
for compounds
of known
structure.
MNDO
MNDO MINDOJ3 b)
28.14 34.15 34.55
-2021 -28.03
-16.85 -15.37
-17.41 -18.14
9.850 9.024 (9.131) 9.74
9.807 8.731 (8.996) 9.71
10.119 8.89 1 (9.614)
‘expt. c*d)
9.689 8.465 (9.113) 9.67
dipole moment (debye)
MNDO hlIND0/3 expt.
1.966 1.309 2.26
3.492 3.044 3.40
2.014 1.764 2.09
0.091 0.565
4N (es@
MNDO MIND013
-0.231 -0.166
AHf (kcallmole)
MNDO M!ND0/3 expt.
-61.56 -65.90
1P (eV)
MNDO MIND013
10.012 9.017 (9.169)
expt. dipole moment Ww)
MNDO
0.172
0.652
a) Ref. [23]. c) Ref. [20].
MIND013 MNDO
-0.192 -0.038
10.061 9.300
4.229 3.717 3.9
-0.249 -0.254
-0.212 -0.105
-0.237 -0.203
-0.273 -0.340
-112.57 -141.64
-105.30 -104.81
-153.77 -171.37
-195.98 -211.24
10.347 9.265
10.718 9.656
10.475 9.791
10.397 9.327 (9.546)
10.22
hlIND0/3
-68.10 -90.08
9.87
2.369 1.890
10.27 1.667 2.130
2.413 1.844
expt.
qN (es@
The calcu-
fust ionization potentials, dipole moments and net charge on nitrogen atom
expt. MlN:Y3 IP (eV)
results
lations can also be carried out quite rapidly, even for _ large molecules. The complete geometry optimizations by MIND0/3 and MNDO, for example, for 1 and 5, starting from “experimental geometries” took respectively 125 and 387 s for MIND0/3 and 84 and 879 s for MNDO on a CDC 6400/6600 computer.
-028 1 -0.373
-0.199 -0.078
b, IP values in parentheses are energies of the highest occupied Y orbital. d, Ref. [24].
-0.235 -0.243
0.589 0.378 0.98
-0.285 -0.244
29
M.J.S. Dewaret al./Sfructuresand propertiesof fluotiuaredp_vridines 4.2. Heats of formation, ionization potentials, and dipole moments Both MIND0/3 and MNDO give acceptable estimates of the heat of formation of 1 (table 3) though MIND0/3 is much closer to experiment. This again may be a coincidence since the errors in heats of formation of nitrogen compounds, calcu!ated by MNDO, are on average about half those from MIND0/3 [6,7]. Both methods predict the same order of stability for the monofluoropyridines, i.e., (Y> 7 > 0. This order implies significant stabilization of the a and y isomers by mutual conjugation between nitrogen and fluorine, the effect being greater for the (Yisomer since it leads to a smaller separation of charge [ 19]_ The differences predicted by MIND013 a:e much larger, corresponding to the much larger predicted changes in the CF bond length (table 1). It is unfortunate that no accurate values for the heats of formation of the three monofluoropyridines are available. Table 4 The ionization potentials of fluoropyridines
MNDO
by hlND0 a)
eapt. b,c)
MNDO d) 9.850 10.926 11.389 13.694 13.834 14.695
1
9.689 (~3, a~)
2 3
10.513 (nz. by) 10.926 (n , ai)
4 5
13.155 (U , b2) 13.782 (q, bl)
9.67 see 9.80 1 text 10.50 (~7.. bl) 12-45 (D , b2) 12.6
6 1
14.261 14.732
13.1 (~1, bl) 13.8
MNDOd,
expt. e,
1 3 4 5
9.807 10.831 11282 13.694 13.909
6 7
14.529 15.509
2
(~3,
n2)
(x2, bl) (n , al) (D , bz) (q, bl)
The MNDO values for the lowest ionization energies of the fluoropyridines (table 3) are, as expected, in much better agreement with experiment than those from MIND0/3. In particular MNDO correctly pre,dicts the first ionizations to be of II type (a3, “2) and to show little variation with fluorine substitution (“perfluoro effect” [20]) whereas MIND013 in several cases predicts a u type (n, at) HOMO. This illustrates a known failing of MIND0/3, i.e. a tendency to underestimate the bonding energies of u type MO’s_ In these cases the lowest MIND0/3 n ionization energies are also listed (in parentheses) in table 3. It will be seen that they agree much better with MNDO and with experiment. Hitherto MNDO has been found [7] to reproduce ail MO energies of molecules in the correct order and with approximately correct values, judging by evidence from photoelectron spectroscopy combined with Koopmans’ theorem. Here, however, there seems to be a systematic error of ca. 1 eV in the MNDO values for
9.71
G73, a2)
10.15 (II , al) 10.69 (n2. bl)
expt. e)
(x3, a2) (n2,bl) (n , al) (q,bl) (o , b2)
g-74
15.141
MNDO 10.119 10.488 11.352 13.145 13.930 15.115 15.547
expt. (n3,
z2)
(x2,bl) (n , al) (D , bz) (q, bl)
(773, az)
10.43 (n , aI) 10.86 (~2, bl)
III.J.S. Dewar et al./Stntctures and properties of prtorinared pvridines
36 Table 4 (continued)
UNDO
10.012 bT3,a2)
4 5
14.419 (n , b5)
13.938 (a , bz) 14.0571 Cq,bl)
6 7
14.938 15.196
14.819 15.497
3
9.87
(-3,d
10.061 (q, az) 11.292 (q,tq) 11.912 (n , a,) 13.600 (TQ,bI)
1 2
11.02 (n
, a,)
11.19 (I;p,bl)
MNDO
apt.
e)
11.023 (q,bl)
11.707 (n , ill)
expt.
MNDO
10.475 (x3,a2)
10.22 (n3 , a2)
11.257 (7iZ.bl)
11.12 (rrz,bl)
3 4 5 6
!2.312 (n , al) 13.725 (rl ,bl) 14.383 (o , bz)
11.30 (n
14.974
12.118 (n , al) 13.764 (o , b2) 14.300 (q, bl) 15.734
1
16.324
15.804
1 2
expt.
MNDO
expt. e,
, al)
10.397 @J,
12) 10.939 (ii2, bl)
F
MNDO
2
!0.347 (ir3,B2) 11.756 (x2, by)
3 4 5 6
12.675 (n , aI) 13.909 (TTI,bi) 14.7 14 CD , b2) 15.617
7
16.061
1
expt.
MNDO
apt.
10.718 (7r3, az)
10.27 (n3,
11.655 &.,bl) 13.064 (n ,31) 14.119 (xl, b,)
11.37 (n2, b,) 12.08 (n , a,) 13.62(a,,b,)
14.564 (o , bz) 16.147 16.385
14.38 (o , bz) 15.45 16.27
a) lonizlction potentials are in eV. b, Ref. [20]. ‘) In ref. 1241 the order of the first three levels is given BS7~3> n > x2_ e) Ref. d, Assignments are based on the kymmetry of pyridine (Qv).
the lowest o type ionizations, which correspond to loss of an electron from a MO centered predominantly on nitrogen (i.e. a “nitrogen lone pair” orbital). Similar discrepancies have also been reported for the first (nitrogen lone pair) ionizations of amines, the MNDO
b) a2)
[24].
values for methylamine, dimethylamine, and trimethylamine being, for example, too large by 1.10, 1.I 1, and 1.OS eV respectively [7] _ It would seem that MNDO systematically overestimates such ionization energies by 1.0-I _I eV and that a corresponding correction
M.J.S. Dewar et al./Structwes and properties of jihoriimted pwidines
should be applied when using MNDO calculations to assign photoelectron spectra. In the case of pyridine (1) one of the two lowest ionizations is known to be of rr type and the other lone pair, but no unambiguous assignment has so far been made. Heilbronner et al. [21] have argued on the basis of the shifts in ionization energy produced by methyl or trimethylsilyl substituents that the lower ionization (9.67 eV) is the lone pair one but this conclusion does not seem to follow from the detailed results presented in their second paper [22]. As table 5 shows, these can be interpreted in a satisfactory manner on the assumption that both methyl and trimethylsilyl shift the first two ionization energies by comparable amounts without inverting their order, the effect of trimethylsilyl being greater. Such shifts are consistent with an inductive or rr inductive mechanism for the shifts. There is no reason to invoke d orbital participation by silicon and indeed the results for y-trimethylsilylpyridine and y-tert-butylpyridine, showing similar shifts by both substituents, imply that any effect of d orbital participation by silicon must be small. If this interpretation is admitted to be feasible, it becomes impossible to distinguish between the two ionizations on the basis of the photoelectron data. Our calculations are of course too inaccurate to resolve this ambiguity. However, it is perhaps significant that the errors in the MNDO ionization energies for nitrogen lone pair orbitals do not exceed 1.1 eV in any case so far studied for which unambiguous experimental data are available. This would suggest that the lower ionization of 1 (8.67 eV) is in fact of rr typeThe dipole moments calculated for these com-
31
pounds by both MIND0/3 and MNDO agree quite well with experiment (table 3) but the agreement is, as usual, much better for MNDO. !t will be seen that MNDO predicts much smaller variations in the formal negative charge on nitrogen than does MIND0/3. In particular, it predicts much smaller changes on introduction of fluorine into the 2- or 4-positions. As we have already noted, fluorines in these positions can conjugate mutually with nitrogen. Such mutual conjugation will not only strengthen the CF bond but also transfer negative charge from fluorine to nitrogen. The data in table 3 indicate that this effect is smaller in MNDO than in MIND0/3, in agreement with the corresponding changes in the calculated CF bond length (table 1). The observed dipole moments for 1 and 2 suggest that MNDO is nearer to the truth, but further evidence is definitely needed. This could be provided either (as suggested above) by accurate measurement of CF bond lengths or more easily by measurements of dipole moments. It will be seen that there are quite large differences between the values predicted by MNDO and MIND0/3 for most of the compounds in table 3. Fluorination in the 3,Spositions of pyridine naturally withdraws electrons from nitrogen, by a combination of inductive (field) and R inductive effects.
4.3. Nuclear quadncpolecouplingconstants Each rotational level in a nitrogen compound is spiit because of the coupling between the nitrogen nuclear spin (0 and the rotational angular momentum Q. Analysis of the corresponding hyperfine splittings in the microwave rotational spectrum gives compo-
Table 5 Shifts in ionization energies of pyridine, due to substituents a-c)
ionivtion energies
A B
9.60 9.75
9.20 9.50
8.30 9.30
8.90 9.30
8.50 8.95
9.50 9.60
9.30 9.40
9.30 9.45
8.80 9.25
8.65 8.95
shift due to substitution
A B
-
0.40 0.25
0.70 0.45
0.70 0.45
1 so 0.80
0.10 0.15
0.30 0.35
0.30 0.30
0.80 0.50
0.95 0.80
a) Data from ref. [22]. b, - = methyl; A = trimethylsilyl; ‘) ionization energies are in eV.
-t = t-butyl.
32
JK.I.S. Dewar et aL/Structures and properties of flnorinntedpyriditler
Table 6 t4N nuclear qoadrupole couplineL constants of fluorinated pyridines Coupling constants (MHz)
F’yridinc
observed
calculated hllNDO/3
MNDO :
1
I1
111
I
11
111
-5.136
-5.049
-5.103
-4.918
-4.832
-4.628 -5.099
-4.439 -5.261
-4.413 -5.061
-4.421 -4.919
pyridine a-fluoro
-4.87 -4.63
-4.970 -4.538
3-fluoro-
-5.32
-5.102
-4.623 -5.234
4-fluoro-
2,6difluoro-
-4.870
-5.000
-4.881
-4.597
-4.426
-4.309
-4.24
-4.090
-4.080
-4.172
-4.012
-4.102
-4.210
-4.08
-5.218 -3.958 -5.117 -4.285 -4.153
-5.324 -3906 -5.181 -4.223 -4.035
-5.127 -3.975 -4.95 1 -4.221 -4.003
-5.235 -3.611 -4.802 -4.518 -4.122
-5.009 -3.726 -4.594 -4.536 -4.173
-4.807 -3.800 -4.378 -4.533 -4.142
3,5-difluoro2,4,6-trifluoro3,4,5-trifluoro2,3,5,6-tetrafluoro-
pentanuoro-
mean absolute error standard deviation
0.127 0.137
xbb, X,,) of the qUadrup@leCoUphng tensor glong the three principal axes of inertia of the molecule. In the case of a molecuie such as I where the nitrogen nucleus lies on a C,, axis, the axes of the electric field gradient tensor and the principal axes of inertia coincide. Table 6 shows the experimentally observed maximum component (x,,) of the coupling constant. Ii; the case of 2 and 3, where the x’s should be strictly transformed to the principal axes of inertia, contributions due to off-diagonal terms have been neglected. It will be seen that magnitude of xzz decreases with increasing fluorine substitution, except for 3. The values found in this way have the advantage of not being affected by strong fields due to neighboring molecules as in the case for coupling constants determined by nuclear quadrupole resonance spectroscopy for crystals. As already noted, three values are listed in table 6 for the coupling constants calculated for each molecule by MNDO and MIND0/3. The first (I) was denoted for non-overlap terms alone; the second (It) for a combination of one- and two-center terms; the third (III) includes all terms. It will be seen that the results for all three are similar, and that all six calculations give results in acceptabie agreement with experiment.
nents(x,,.
0.113 0.145
0.109 0.135
0.151 0.172
0.151 0.170
0.148 0.205
In particular, ali reproduce well the observed trends. Note in particular the (apparently correct) prediction that fluorine in the 2,4,6-positions of 1 should lead to a decrease in magnitude of the coupling constant whereas fluorine in the 3 ,Spositions should lead to an increase. These changes correspond to the changes in E electron density at nitrogen. The negative charge at nitrogen increases with substitution by fluorine in the 2,4,6-positions as a result of its electron-reIeasing electromeric (~5) effect, but decreases with substitution by fluorine in the 3,Spositions as a result of field (inductive) and B inductive effects (table 3). A more detailed check on the various procedure is provided by the calculated mean absolute errors and standard deviations, shown in the last two rows of table 6. It will be seen that the best results are given by MNDO, including all terms without renormalizing the wavefunction. The MIND013 results are uniformly less satisfactory, in this case three models give similar results. It is obvious that multi-center terms should be included in the calculation when the wavefunction is not renormalized. The results are in any case very satisfactory and again may prove helpful in assigning the microwave spectra of the other compounds listed in table 6 in particular and of nitrogen compounds in general.
h5 J.S. Dewar et al./Stnmtres
artd properties of fluoriimted p_vridines
Acknowledgement This work was supported by the Ah Force Office of Scientific Research (Grant AFOSR 752749) and the Robert A. Welch Foundation (Grant F-126). S. Doraiswamy and SD. Sharma would like to thank the Robert A. Welch Foundation for fellowships at The University of Texas, Austin and Rice University, Houston, respectively when a part of this work was completed. The calculations were carried out using the CDC 6400/6600 computer at The University of Texas Computation Center.
References [l] S.D. Sharma, S. Doniswamy, H. Legell, H. Mader and D. Sutter, Z. Neturforsch. 26a(1971) !342. [2] S.D. Sharma and S. Doraiswamy, J. Mel. Spectry. 59 (1976) 216. [3] S. Doraiswamy and S.D. Sharma, Chem. Phys. Letters 37 (1976) 527. [4] S. Doraiswamy and SD. Sbarma, Chem. Phys. 6 (1974) 76. [S] O.L. Stiefvater, Z. Naturforsch. 30a (1975) 1765. [6j R.C. Bingham, M.J.S. Dewar and D.H. Lo, J. Am. Chem. Sot. 97 (1975) 1285,1294,1302,1307; M.J.S. Dewar. D.H. Lo and C.A. Ramsden, J. Am. Chem. Sot. 97 (1975) 1311. [7] h1.J.S. Dewar and W. Thiel, J. Am. Chem. Sot. 99 (1977) 4899,4907; hl.J.S. Dcwar and M.L. McKee, J. Am. Chem. Sot. 99 (1977) 5231; M J.S. Dewar and H.S. Rzepa, J. Am. Chem. Sot. 100 (1978) 58,777;
33
M.J.S. Dewar, M.L. McKee and H.S. Rzepa, J. Am. Chem. Sot. 100 (1978) 3607. [S] h1.J.S. Dewar and G.P. Ford, J. Am. Chem. Sot. 99 (1977) 1685. 191 M.J.S. Dewar, G.P. Ford, M.L. McKee, H.S. Rzepa, W.Thiel and Y. Yamsguchi, J. Mol. Struct.43 (1978) 135. [IO] h1.J.S. Dewar and D.H. Lo, Chem. Phys. Letters 33 (1975) 298. [11] M.J.S. Dewar and H.S. Rzepa, unpublished work. 1121 M.J.S. Dewar, H.W. Kollmar and S.H. Suck, J. Am. Chem. Sot. 97 (1975) 5590. [13] L. Chantranupong, h1.J.S. Dewar, Y. Yamaguchi and S.H. Suck, to be submitted for publication. [14] R. Fletcher and h1.J.D. Powell, Comput. J. 6 (1963) 163: R. Fletcher, Comput. J. 8 (1965) 33: W.C. Davidson, Comput. J. 10 (1968).406. [15] T. Koopmans, Physica 1 (1934) 104. 1161 C.H. Townes and B.P. Dailey, J. Chem. Phys. 17 (1949) 782. [17] G.O. Sbrensen, L. h.‘ahler and N-R. Andersen, J. Mol. struct. 20 (1974) 119. [ 181 SD. Sharma and S. Doraiswamy,Chem. Phys. Letters 41(1976) 192. [19] h1.J.S. Dewar, J. Am. Chem. Sot. 74 (1952) 3350. [20] C.R. Brundle, M.B. Robin and N.A. Kuebler. J. Am. Chem. Sot. 94 (1972) 1466. (211 E. Heiibronner, V. Hornung, H. Bock and H. Ah, Angew. Chem. Intern. Ed. 8 (1969) 524. [22] E. Heilbronner, V. Hornung, F.H. Pinkerton and S.F. Thames, Heh. Chim. Acta 55 (1972) 289. [23] J.D. COX and G. Pilcher, Thermochemistry of organic and organometalhc compounds (Academic Press, New York, 1970). [24] G.H. King, J.N. Mureli and R.J. Suffolk, J. Chem. Sot. Dalton (1972) 564.
STRUCTURES AND PROPERTIES OF FLUORINATED
PYRIDINES;
ASSIGNMENT OF THE TWO HOMO’S OF PYRIDINE M.J.S. DEWAR, Y. YAMAGUCHI Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA S. DORAISWAMY,
S.D. SHARhIA
Tate Institute of Fundamental Research. Colaba. Bombaj 400005. India and
S.H. SUCK Department of Physics and Graduate Center for Cloud Physics Research. University of Missouri-Rob, Rolla, Missouri 65401, USA Received 29 November 1978
Structures and properties of fluorinated pyridines have been studied by microwave spectroscopy and theoretically by the MIND0/3 and MNDO methods. While both hllNDO/3 and MNDOreproduce the geometries of fluorinated pyridirres within their experimental limits of accuracy, MlND0/3 does better in predicting the small changes in geometry due to substitution of hydrogen by fluorine in pyridine. Both MlND0/3 and MNDO give rotational constants in quitegood agreement with experiment, but the errors in MlND0/3 are somewhat smaller. Both methods give acceptable estimates of heats of formation of pyridines. MNDO gives better estimates of ionization energies and dipole moments, the results agreeing quite well with experiment. Whereas t4N nuclear quadrupole coupling constants are calculated satisfactorily by both methods, MNDO does b&r in predicting the changes in constants caused by fluorine substitution.
1. Introduction Recent studies of the microwave spectra of 2fluoropyridine (2) [I], 3-fluoropyridie (3) [Z] ,2,6difluoropyridine (4) [3], and perfluoropyridine (5) [4] have seemingly indicated that surprising structural changes take place on replacement of hydrogen atoms in pyridine (1) by fluorine, involving changes in the CC and CN bond lengths and distortion of the ring. These conclusions were based on various assumptions because the measurements referred only to the most abundant Isotopic species and hence led only to the moments of inertia for the four compounds. However, the assumptions made seem very reasonable and the conclusions in one case (4) have been confirmed [5] by a rather detailed microwave-microwave double modulation study. However, we felt that it would be of interest to study this problem theoretically, both
in the hope of confirming our conclusions and as a check on the theoretical procedures used. A further check would also be provided by comparisons of calculated and observed dipole moments and 14N nuclear quadrupole coupling constants, which were obtained as byproducts in microwave studies. If calculations of this kind proved effective and could be carried out at reasonable cost, they could be of considerable value in studies of larger molecules by microwave spectroscopy, in particular for compounds of elements which have only a single isotope (e.g. F)_ The best candidates for the purpose seemed to be the MIND0/3 [6] and MNDO [7] semi-empirical SCF MO methods, which have been shown to reproduce a wide variety of molecular properties with surprising accuracy, including in particular heats of formation [6,7], molecular geometries [6,7], dipole moments [6,7], ionization energies [6,7], molecular vibrational
M.J.S. Dewar et al./Structures and properties of fluorinated pyridine3
22
frequencies (MIND013 [8], MNDO [9]), ESCA chemical shifts (MlND0/3 [lo], MNDO [ 1I I), and nuclear quadrupole coupling constants (MIND0/3 [ 121, MNDO [ 131). The results are generally superior to those from any but rather sophisticated ab initio calculations, which would be expensive in the present connection. We have therefore carried out a systematic study of the fluoropyridines, using both MIND0/3 and MNDO. Here we present our results.
2. Theoretical procedure The calculations were carried out by the standard MlND0/3 [6] and MNDO [7] procedures, using the standard parameters. Geometries were optimized by using the standard Davidon-Fletcher-Powell [14] procedure, no assumptions being made other than that the molecules are planar. Ionization potentials were estimated by using Koopmans’ theorem [ 151. In the LCAO approximation, the electronic contribution to the field gradient at a given nucleus (ol) of atom A is given by
9~,= -e
7 F Pij(Qil(3 COS'e-
lllr31~j),
(1)
where $ and $ are AO’s, Pii is the corresponding element of the bond order matrix, e is the electronic charge, and r, 0 are spherical polar coordinates centered on nucleus 01.The double sum in eq. (1) can be broken down into one-center terms, where $r-and $ are AO’Sof atom A; two-center terms, where & is an A0 of atom A and 3 an A0 of some other atom(B) or where both pi and 4 are AO’s of atom B; and threecenter terms, where pi and oj are AO’s of different atoms B and C (#A). In MIND0/3 and MNDO, the matrix elements in eq. (1) are treated as parameters. This is inevitable in view of the use of the core approximation and consequent neglect of the Stemheimer effect. However, problems still arise because of the neglect of bicentric overlap. Should corresponding matrix elements be likewise neglected, like electron repulsion integrals, or included, like one-electron resonance integrals? And if they are included, should the wavefunction be correspondingly renormahzed? These problems are discussed in detail in a iorthcoming paper [ 131. Previous
work [ 121 has shown that in MIND0/3, it is best to include bicentric overlap and to renormalize the LCAO wavefunction accordingly_ In MNDO the best results for r4N seem to be obtained by including all terms without renormalizing the wavefunction.
3. Results of calculations by MIND013 and MNDO Table 1 lists the geometries calculated by MIND0/3 and MNDO for l-5,4-fluoropyridine (6). 3,5difluoropyridine (7) 2,4,6_trifluoropyridine (8) 3,4&trifluoropyridine (9), and 2,3,5,6-tetrafluoropyridine (10). Values deduced from experiment (see below) are included for reference. Table 2 shows the corresponding values for the rotational constants, together with experimental values, while table 3 gives corresponding results for heats of formation, first ionization potentials, dipole moments, and net charge on nitrogen atom. Table 4 lists the first seven ionization potentials calculated by MNDO. Table 6 shows 14N nuclear quadrupole coupling constants, calculated by MIND0/3 and MNDO for three different models. In the first, only the nonoverlap terms, which are essentially electronic onecenter terms, are included. In the second, both oneand two-center terms are included. in the third, all terms are included. The calculations were carried out in MNDO without renormalization and in MIND0/3 with renormalization of wave functions. The nuclear quadrupole moment of 14N, Q(N), is estimated using coupling constants of I, 4 and 5. Experimental values are included in table 6 when available.
4. Discussion 4.1. Geometries The structure of pyridine (1) has been investigated in detail by microwave spectroscopy [I 71, making practically no assumptions. Nevertheless the resulting structure (“substitution structure”) does not reproduce the observed rotational constants precisely because they are proportional to the inverse of the effective moments of inertia, which are affected by vibronic interactions. The measurements give the reciprocals of the moments of inertia averaged over the ground vi-
M.J.S. Dewar et al. fStructures and properties of fihorinated pyridines
23
Table 1 Structures of fluorinatedpyridinesa&)
MNDO
NIG
BllNDO/3
expt.
1.3533
1.3350
1.3402
1.4114
1.4067
1.3958
1.4047
1.4056
1.3944
1.0950
1.1141
1.0857
1.0889
1.1051
1.0818
118.22 122.79
1.1070 119.95 122.42
1.0811 116.98 123.79
118.79
117.80
118.50
118.63 115.89
119.59 116.46
118.44 116.05
120.87
120.78
121.38
120.68
120.20
120.78
NlC6 c2c3 cSc6 c3c4 c4c5 c2x7 GXll c3xS C5XlO C&9 L216
L321 L561 ~234 ~456 L345 L127 L16,ll L438 L45,lO L349
1.0899
hlND0
MlND0/3
expt.
1.3644 1.3512 1.4230 1.4119 1.4036 1.4047 1.31i4 I .0956 1.0885 1.0888 1.0904 117.36 123.68 123.12 117.62 118.98 119.25 114.19 115.52 121.17 120.81 120.20
1.3112 1.3397 1.4036 I.4040 1.4033 1.4118 1.3618 1.1138 1.1000 1.1029 1so71 117.82 127.27 122.11 114.11 117.99 120.69 111.16 116.34 122.96 120.64 119.32
1.3207 1.3402 1.3732 1.3958 1.3944 1.3944 1.354 1.0857 1.0818 1.0818 1.0811 115.19 127.24 123.79 116.84 118.50 118.44 114.25 116.05 121.38 121.38 120.78
F
hlIND0/3
MNDO N!C2 NlC6 c2c3 %c6 GC4 GCS c2 x7 c6xll c3xs GXlO c4x9
L216 L321 L561 L234 L456 L345 L127 ~16,il L438 i45,lO L349
1.3486 1.3534 1A286 1.4110 1.4198 1A026 1.0949 1.0949 1.3240 1.0896 1.0698 119.00 121.90 122.73 119.05 119.39 117.92 116.22 115.85 120.76 120.39 121.33
.
1.3348 1.3342 1.4004 1A080 1.3982 1.4071 1.1088 1.1115 1.3793 1.1061 1.1024 121.59 118.84 121.95 122.26 118.65 116.71 118.43 116.42 118.30 119.95 121.32
expt. 1.3402 1.3402 1.3828 1.3958 1.3806 1.3944
hlND0
MlNDOJ3
1.3529
1.3355
1A094
1.4086
1A202
1.3981
1.0956
1.1141
1.0888
1.1006
1.3222 118.32 123.31
1.3724 119.71 123.32
121.68 118.81 116.57 116.51
118.13
114.95
118.79 115.83
123.75 116.58
119.82
12150
12195
122.10
120.60
118.13
1.354
117.31 121.84
expt.
M.J.S. Dewar et al./Stmctures and properties of fluorinated pyndines
24 Table 1 (continued)
...---_.--MNDO NlG N1C.s C2CB
W6 c3c4 c4c5 GX7
MlND0/3
expt.
MNDO
MlND0/3
1.3627
1.3148
1.3086
1.3485
1.3327
1.4237
1.4027
1.3760
1.4286
1.4037
1.4035
1A086
1.3944
l-4181
1.3998
1.3169
1.3559
1.354
1.0949
1.1067
1.0886
1.0984
1.084
1.3229
1.3740
1.0909 116.56 123.95
1.1068 116.77 126.16
1.084 115.3 126.21
1.0900 119.17 121.89
1.0991 123.33 118.48
117.84
114.54
11692
119.60
122.66
119.86 113.91
121.83 111.67
118.44 115.21
117.26 116.19
114.39 118.44
121.11
122.80
123.1
120.38
117.92
120.07
119.08
120.1
121.37
172.81
__..-.. expt.
wh G&
Cs&o c4x9
L216 L321 L561 L234 ~456 L345 L127 L16,ll i438 L45,lO L349
F
MNDO
NICZ NIG G?c3
MIND013
expt.
MNDO
M!ND0/3
1.3626
1.3175
1.3482
1.3328
1.4217
1.4036
1A264
1.4048
1.4197
l-4025
1.4341
1.3994
1.3156
1.3523
1.0956
1A078
1.Q889
1.0960
1.3203
1.3763
1.3197 116.69 124-43
1.3642 116.52 126.77
1.3168 119.98 122.36
1.3761 122.52 119.89
117.29
112.52
118.90
120.05
li9.87 113.85
124.90 111.79
117.49 116.14
117.58 118.40
121.64
123.44
120.60
120.63
120.07
117.55
121.26
121.21
cSc6 C3G c4ci c2x7 c6xll c3x8 c5XlO c4x9
L216 f-321 L561 ~234 L456 f345 L127 L16,ll f438 L45,lO L349
expt.
25
M.J.S. Dewar et al.jStructtues and properties of fluorinated pyridines Table 1 (continued)
F/
F
F-
0
MNDO NrCz
F F/
‘F
F
F-0 N’F
expt.
MIND0/3
MNDO
MlNDOi3
. expt.
1.3583
1.3142
1.3582
1.3159
1.3026
1.4409
1.4015
1.4385
1 A024
1.3647
1.4163
1.4035
1A330
1 A038
1.3624
1.3133
1.3595
1.3121
1.3560
1.354
1.3199
1.3771
1.3178
1.3795
4.354
NlC6 c2c3 cSc6 c3c4 c4cs czx7 c5XlL C3Xs GAO
L216
117.91
121.26
1.3144 118.13
1.3686 120.42
1.354 117.98
L321 L561
123.15
121.69
12359
122.89
123.28
L234 L.456
118.70
118.77
118.10
116.71
118-49
IL345
118.40
117.83
118.50
120.37
118.96
L127 L16,ll
114.48
112.65
114.45
112.61
116.55
L438 L45,lO
120.95
119.19
121.09
121.37
121.39
L349
120.80
121.09
120875
119.82
120.77
c4x9
1.09 13
1.1008
-
a) Bond lengths are in A and bond angles are in degree. b, Experimental vslues are calculated using the modified coordinates
brational state, not those corresponding to the equilibrium geometry. In order to study the changes in structure that take place on substitution of hydrogen
by fluorine, we must start with the equilibrium structure for pyridine. We therefore use a slightly modified geometry for pyridine, chosen to reproduce the observed rotational constants of all isotopic species [18]. The bond lengths and bond angles so obtained in fact differ insignificantly from the rs values. They are shown in table 1. It will be seen that both MIND0/3 and MNDO reproduce the geometry of 1 in a very satisfactory manner, the errors in bond lengths and bond angles being much less than the average errors for an extensive range of nitrogen compounds [6,7] _AU the errors in bond lengths are less than 0.03 A and those in angles less than 3”. Turning now to the fluoro derivatives, it will be seen at once that MNDO seems to systematically under-
[18] and CF distance is assumed to be 1.354 A.
estimate CF bond lengths by about 0.03 A while the MIND0/3 values generally agree with experiment to better than 0.02 A. Admittedly, as noted above, the “experimental” values are subject to some uncertainty, but similar errors occur in the case of 4 where the proposed structure, while not unambiguously confirmed, has been supported by independent measurements. The most striking feature of the geometries deduced for 24 is the shortening of the bonds adjacent to the CF unit together with an increase in the bond angle in the ring at the carbon atom adjacent to fluorine, with corresponding decreases in the two adjacent angles in the ring. The net effect is a displacement of the CF group as a whole towards the center of the ring without significant change in the positions of the other atoms; see fig. 1. It will be seen from the results in table 1 that MIND0/3 reproduces these changes quite well whereas MNDO is unsatisfactory. Thus
M.J.S. Dewar et al./Structures arld properties of fluori!mted pvn-ditnes
26
?,-Fluoropyridins
2.6-
Fig. 1. Structural
Difluaopyridina
Psrlluoropyridina
changes in pyridine ring geometry on fluorine substitution
(which are consistent with the observed rotational
constantsand C-F = 1.354 A). changes in the N, C2 and C& bond lengths, on passing from 1 to 2, predicted by MIND0/3, are -0.0238 and -0.0031 A respectively, compared with “experimental” values of -0.0195 and -0.0226 A, whereas the MNDO values are positive (+O.Ol11 and to.0 116 A). Likewise the predicted changes in the NtC2C3 bond angles are tO.89” and +4.85” for MNDO and
MIND0/3 respectively, compared with the “experimental” value of t3.45”. Likewise in 5, MNDO prediets the CC bonds to be longer than in 1 whereas the microwave evidence suggests that they are shorter. It would certainly be surprising if fluorinationlead to an increase in the lengths of adjacent CC bonds and MIND0/3 does predict a decrease on passage from
21
M.J.S. Dewar et aL/Structures and properties of jitcwitzated pyridines
1 to 5. However, MIND0/3 also predicts quite low differences in CF bond length along this series of compounds and between CF bond lengths of different positions in 5 in particular. Mutual conjugation [191 between fluorine and nitrogen would be expected to lead to a decrease in the length of CF bonds in the 2,4,6 positions of pyridine and such changes are indeed predicted by both MIND0/3 and MNDO. In view of the apparent general success of MIND0/3 in predicting changes in this series of compounds, a better estimate of their true geometries could probably be obtained from the microwave data by assuming corresponding changes in the CF bond lengths. The values listed in table I were calculated with the assumption that all the CF bonds have similar lengths (1.354 A). The general conclusion then is that while both MNDO and MIND0/3 reproduce the geometries of l-5 within their experimental limits of accuracy, MIND0/3 does better in predicting the small changes Table 2 Rotational hl0lfXXle
constants of fluorinated Rotational
rN
0/IF
0/‘N
F
F/IF 0
F/ F
F
F‘Clt4’F
pyridines a-c)
constants (MIIz)
observed
01
in geometry due to substitution of hydrogen by fluorine in.pyridine. By combining MIND0/3 data with experimental results for the parent compound, it may thus be possible to deduce good geometries for such derivatives. Turning now to the rotational parameters, here again a similar pattern holds. Both MIND0/3 and MNDO give results in quite good agreement with experiment, but the errors in MIND0/3 are somewhat smaller. For the compounds in table 2 for which experimental data are available, the standard deviations and mean absolute errors are respectively 93.85 and 77.24 MHz for MNDO and 82.17 and 60.27 MHz for MIND0/3. It should, however, be noted that the superiority of MIND0/3 in this particular connection is accidental because the errors in bond lengths and bond angles given by MNDO are usually much less than those given by MIND0/3 [6,7] _MIND0/3 happens to give a somewhat better geometry for pyridine than MNDO
calculated using modified coordinates
using substitution coordinates
MNDO
hf [ND013
A B = 6039.23 5804.90 C = 2959.22
5804.62 (iO.00) 6039.39 (-0.00) 2959.84 (+0.02)
6063.76 (iO.41) 5820.19 (+0.26) 2969.74 (+0.36)
5907.66 (-2.18) 5716.22 (-1.53) 2905.18 (-1.83j
5888.08 5819.16 (-2.50) (+0.25) 2926.71 (-1.10)
A B = 5870.92 2699.94 c = 1849.27
5869.65 2634.26 (-0.02) (-2.43) 1818.25 (-1.68)
5887.67 (-2.17) 2641.35 (+0.29) 1823.35 (-1.40)
5698.41 (-2.24) 2639.45 (-2.94) 1803.90 (-2.453
5761.99 2672.90 (-1.86) (-1.00) 1825.89 (-1.26)
A B = 5829.66 2637.47 C = 1815.65
5859.75 2581.26 (+0.52) (-2.13) 1791.91(-1.31)
5877.40 (+0.82) 2588.41 (-1.86) 1797.01(-1.03)
5693.97 2576.72 (-2.33) (-2.30) 1773.95 (-2.30)
5758.88 2583.46 (-1.21) (-2.05) 1783.41 (-1.78)
A B = 3741.68 1905.82
3677.11 1847.16 (-1.88) (-3.08)
3685.20 1852.24 (-1.67) (-2.81)
3559.09 1880.01 (-5.03) (-1.35)
3540.10 1934.67 (+lSl) (-5.54)
C = 1263.25
1229.52 (-2.67)
1232.68 (-2.42)
1230.19 (-2.62)
1251.00 (-0.97)
A = 1481.54 B = 1075.35 C = 623.10
1438.59 (-2.90) 1047.93 (-2.55) 606.29 (-2.70)
1441.11 (-2.73) 1050.54 (-2.31) 607.61 (-2.49)
1400.22 (-5.49) 1057.11 (-1.70) 602.36 (-3.33)
1380.78 (-6.80) 1058.80 (-1.54) 599.27 (-3.82)
aj CF distance is assumed to be 1.354 A. b) The values in parentheses are % devintion in observed values. ‘j The observed rotational constants can be reproduced by introducing
the distortions
in the pyridine ring (see fig. 1).
M./S. Dewar et al/Structures and properties of fluorinated pyridines
28
and the error in the MNDO value for the CF bond length is unusually large. It should be noted in this connection that the errors for fluorine compounds in MNDO are generally greater than those for other organic species [7] _ Calculations of this kind should nevertheless be useful in helping to assign microwave spectra for larger molecules, particularly if corrections are made using Table 3 Heats cf formation,
AHf (kul/moIe)
for compounds
of known
structure.
MNDO
MNDO MINDOJ3 b)
28.14 34.15 34.55
-2021 -28.03
-16.85 -15.37
-17.41 -18.14
9.850 9.024 (9.131) 9.74
9.807 8.731 (8.996) 9.71
10.119 8.89 1 (9.614)
‘expt. c*d)
9.689 8.465 (9.113) 9.67
dipole moment (debye)
MNDO hlIND0/3 expt.
1.966 1.309 2.26
3.492 3.044 3.40
2.014 1.764 2.09
0.091 0.565
4N (es@
MNDO MIND013
-0.231 -0.166
AHf (kcallmole)
MNDO M!ND0/3 expt.
-61.56 -65.90
1P (eV)
MNDO MIND013
10.012 9.017 (9.169)
expt. dipole moment Ww)
MNDO
0.172
0.652
a) Ref. [23]. c) Ref. [20].
MIND013 MNDO
-0.192 -0.038
10.061 9.300
4.229 3.717 3.9
-0.249 -0.254
-0.212 -0.105
-0.237 -0.203
-0.273 -0.340
-112.57 -141.64
-105.30 -104.81
-153.77 -171.37
-195.98 -211.24
10.347 9.265
10.718 9.656
10.475 9.791
10.397 9.327 (9.546)
10.22
hlIND0/3
-68.10 -90.08
9.87
2.369 1.890
10.27 1.667 2.130
2.413 1.844
expt.
qN (es@
The calcu-
fust ionization potentials, dipole moments and net charge on nitrogen atom
expt. MlN:Y3 IP (eV)
results
lations can also be carried out quite rapidly, even for _ large molecules. The complete geometry optimizations by MIND0/3 and MNDO, for example, for 1 and 5, starting from “experimental geometries” took respectively 125 and 387 s for MIND0/3 and 84 and 879 s for MNDO on a CDC 6400/6600 computer.
-028 1 -0.373
-0.199 -0.078
b, IP values in parentheses are energies of the highest occupied Y orbital. d, Ref. [24].
-0.235 -0.243
0.589 0.378 0.98
-0.285 -0.244
29
M.J.S. Dewaret al./Sfructuresand propertiesof fluotiuaredp_vridines 4.2. Heats of formation, ionization potentials, and dipole moments Both MIND0/3 and MNDO give acceptable estimates of the heat of formation of 1 (table 3) though MIND0/3 is much closer to experiment. This again may be a coincidence since the errors in heats of formation of nitrogen compounds, calcu!ated by MNDO, are on average about half those from MIND0/3 [6,7]. Both methods predict the same order of stability for the monofluoropyridines, i.e., (Y> 7 > 0. This order implies significant stabilization of the a and y isomers by mutual conjugation between nitrogen and fluorine, the effect being greater for the (Yisomer since it leads to a smaller separation of charge [ 19]_ The differences predicted by MIND013 a:e much larger, corresponding to the much larger predicted changes in the CF bond length (table 1). It is unfortunate that no accurate values for the heats of formation of the three monofluoropyridines are available. Table 4 The ionization potentials of fluoropyridines
MNDO
by hlND0 a)
eapt. b,c)
MNDO d) 9.850 10.926 11.389 13.694 13.834 14.695
1
9.689 (~3, a~)
2 3
10.513 (nz. by) 10.926 (n , ai)
4 5
13.155 (U , b2) 13.782 (q, bl)
9.67 see 9.80 1 text 10.50 (~7.. bl) 12-45 (D , b2) 12.6
6 1
14.261 14.732
13.1 (~1, bl) 13.8
MNDOd,
expt. e,
1 3 4 5
9.807 10.831 11282 13.694 13.909
6 7
14.529 15.509
2
(~3,
n2)
(x2, bl) (n , al) (D , bz) (q, bl)
The MNDO values for the lowest ionization energies of the fluoropyridines (table 3) are, as expected, in much better agreement with experiment than those from MIND0/3. In particular MNDO correctly pre,dicts the first ionizations to be of II type (a3, “2) and to show little variation with fluorine substitution (“perfluoro effect” [20]) whereas MIND013 in several cases predicts a u type (n, at) HOMO. This illustrates a known failing of MIND0/3, i.e. a tendency to underestimate the bonding energies of u type MO’s_ In these cases the lowest MIND0/3 n ionization energies are also listed (in parentheses) in table 3. It will be seen that they agree much better with MNDO and with experiment. Hitherto MNDO has been found [7] to reproduce ail MO energies of molecules in the correct order and with approximately correct values, judging by evidence from photoelectron spectroscopy combined with Koopmans’ theorem. Here, however, there seems to be a systematic error of ca. 1 eV in the MNDO values for
9.71
G73, a2)
10.15 (II , al) 10.69 (n2. bl)
expt. e)
(x3, a2) (n2,bl) (n , al) (q,bl) (o , b2)
g-74
15.141
MNDO 10.119 10.488 11.352 13.145 13.930 15.115 15.547
expt. (n3,
z2)
(x2,bl) (n , al) (D , bz) (q, bl)
(773, az)
10.43 (n , aI) 10.86 (~2, bl)
III.J.S. Dewar et al./Stntctures and properties of prtorinared pvridines
36 Table 4 (continued)
UNDO
10.012 bT3,a2)
4 5
14.419 (n , b5)
13.938 (a , bz) 14.0571 Cq,bl)
6 7
14.938 15.196
14.819 15.497
3
9.87
(-3,d
10.061 (q, az) 11.292 (q,tq) 11.912 (n , a,) 13.600 (TQ,bI)
1 2
11.02 (n
, a,)
11.19 (I;p,bl)
MNDO
apt.
e)
11.023 (q,bl)
11.707 (n , ill)
expt.
MNDO
10.475 (x3,a2)
10.22 (n3 , a2)
11.257 (7iZ.bl)
11.12 (rrz,bl)
3 4 5 6
!2.312 (n , al) 13.725 (rl ,bl) 14.383 (o , bz)
11.30 (n
14.974
12.118 (n , al) 13.764 (o , b2) 14.300 (q, bl) 15.734
1
16.324
15.804
1 2
expt.
MNDO
expt. e,
, al)
10.397 @J,
12) 10.939 (ii2, bl)
F
MNDO
2
!0.347 (ir3,B2) 11.756 (x2, by)
3 4 5 6
12.675 (n , aI) 13.909 (TTI,bi) 14.7 14 CD , b2) 15.617
7
16.061
1
expt.
MNDO
apt.
10.718 (7r3, az)
10.27 (n3,
11.655 &.,bl) 13.064 (n ,31) 14.119 (xl, b,)
11.37 (n2, b,) 12.08 (n , a,) 13.62(a,,b,)
14.564 (o , bz) 16.147 16.385
14.38 (o , bz) 15.45 16.27
a) lonizlction potentials are in eV. b, Ref. [20]. ‘) In ref. 1241 the order of the first three levels is given BS7~3> n > x2_ e) Ref. d, Assignments are based on the kymmetry of pyridine (Qv).
the lowest o type ionizations, which correspond to loss of an electron from a MO centered predominantly on nitrogen (i.e. a “nitrogen lone pair” orbital). Similar discrepancies have also been reported for the first (nitrogen lone pair) ionizations of amines, the MNDO
b) a2)
[24].
values for methylamine, dimethylamine, and trimethylamine being, for example, too large by 1.10, 1.I 1, and 1.OS eV respectively [7] _ It would seem that MNDO systematically overestimates such ionization energies by 1.0-I _I eV and that a corresponding correction
M.J.S. Dewar et al./Structwes and properties of jihoriimted pwidines
should be applied when using MNDO calculations to assign photoelectron spectra. In the case of pyridine (1) one of the two lowest ionizations is known to be of rr type and the other lone pair, but no unambiguous assignment has so far been made. Heilbronner et al. [21] have argued on the basis of the shifts in ionization energy produced by methyl or trimethylsilyl substituents that the lower ionization (9.67 eV) is the lone pair one but this conclusion does not seem to follow from the detailed results presented in their second paper [22]. As table 5 shows, these can be interpreted in a satisfactory manner on the assumption that both methyl and trimethylsilyl shift the first two ionization energies by comparable amounts without inverting their order, the effect of trimethylsilyl being greater. Such shifts are consistent with an inductive or rr inductive mechanism for the shifts. There is no reason to invoke d orbital participation by silicon and indeed the results for y-trimethylsilylpyridine and y-tert-butylpyridine, showing similar shifts by both substituents, imply that any effect of d orbital participation by silicon must be small. If this interpretation is admitted to be feasible, it becomes impossible to distinguish between the two ionizations on the basis of the photoelectron data. Our calculations are of course too inaccurate to resolve this ambiguity. However, it is perhaps significant that the errors in the MNDO ionization energies for nitrogen lone pair orbitals do not exceed 1.1 eV in any case so far studied for which unambiguous experimental data are available. This would suggest that the lower ionization of 1 (8.67 eV) is in fact of rr typeThe dipole moments calculated for these com-
31
pounds by both MIND0/3 and MNDO agree quite well with experiment (table 3) but the agreement is, as usual, much better for MNDO. !t will be seen that MNDO predicts much smaller variations in the formal negative charge on nitrogen than does MIND0/3. In particular, it predicts much smaller changes on introduction of fluorine into the 2- or 4-positions. As we have already noted, fluorines in these positions can conjugate mutually with nitrogen. Such mutual conjugation will not only strengthen the CF bond but also transfer negative charge from fluorine to nitrogen. The data in table 3 indicate that this effect is smaller in MNDO than in MIND0/3, in agreement with the corresponding changes in the calculated CF bond length (table 1). The observed dipole moments for 1 and 2 suggest that MNDO is nearer to the truth, but further evidence is definitely needed. This could be provided either (as suggested above) by accurate measurement of CF bond lengths or more easily by measurements of dipole moments. It will be seen that there are quite large differences between the values predicted by MNDO and MIND0/3 for most of the compounds in table 3. Fluorination in the 3,Spositions of pyridine naturally withdraws electrons from nitrogen, by a combination of inductive (field) and R inductive effects.
4.3. Nuclear quadncpolecouplingconstants Each rotational level in a nitrogen compound is spiit because of the coupling between the nitrogen nuclear spin (0 and the rotational angular momentum Q. Analysis of the corresponding hyperfine splittings in the microwave rotational spectrum gives compo-
Table 5 Shifts in ionization energies of pyridine, due to substituents a-c)
ionivtion energies
A B
9.60 9.75
9.20 9.50
8.30 9.30
8.90 9.30
8.50 8.95
9.50 9.60
9.30 9.40
9.30 9.45
8.80 9.25
8.65 8.95
shift due to substitution
A B
-
0.40 0.25
0.70 0.45
0.70 0.45
1 so 0.80
0.10 0.15
0.30 0.35
0.30 0.30
0.80 0.50
0.95 0.80
a) Data from ref. [22]. b, - = methyl; A = trimethylsilyl; ‘) ionization energies are in eV.
-t = t-butyl.
32
JK.I.S. Dewar et aL/Structures and properties of flnorinntedpyriditler
Table 6 t4N nuclear qoadrupole couplineL constants of fluorinated pyridines Coupling constants (MHz)
F’yridinc
observed
calculated hllNDO/3
MNDO :
1
I1
111
I
11
111
-5.136
-5.049
-5.103
-4.918
-4.832
-4.628 -5.099
-4.439 -5.261
-4.413 -5.061
-4.421 -4.919
pyridine a-fluoro
-4.87 -4.63
-4.970 -4.538
3-fluoro-
-5.32
-5.102
-4.623 -5.234
4-fluoro-
2,6difluoro-
-4.870
-5.000
-4.881
-4.597
-4.426
-4.309
-4.24
-4.090
-4.080
-4.172
-4.012
-4.102
-4.210
-4.08
-5.218 -3.958 -5.117 -4.285 -4.153
-5.324 -3906 -5.181 -4.223 -4.035
-5.127 -3.975 -4.95 1 -4.221 -4.003
-5.235 -3.611 -4.802 -4.518 -4.122
-5.009 -3.726 -4.594 -4.536 -4.173
-4.807 -3.800 -4.378 -4.533 -4.142
3,5-difluoro2,4,6-trifluoro3,4,5-trifluoro2,3,5,6-tetrafluoro-
pentanuoro-
mean absolute error standard deviation
0.127 0.137
xbb, X,,) of the qUadrup@leCoUphng tensor glong the three principal axes of inertia of the molecule. In the case of a molecuie such as I where the nitrogen nucleus lies on a C,, axis, the axes of the electric field gradient tensor and the principal axes of inertia coincide. Table 6 shows the experimentally observed maximum component (x,,) of the coupling constant. Ii; the case of 2 and 3, where the x’s should be strictly transformed to the principal axes of inertia, contributions due to off-diagonal terms have been neglected. It will be seen that magnitude of xzz decreases with increasing fluorine substitution, except for 3. The values found in this way have the advantage of not being affected by strong fields due to neighboring molecules as in the case for coupling constants determined by nuclear quadrupole resonance spectroscopy for crystals. As already noted, three values are listed in table 6 for the coupling constants calculated for each molecule by MNDO and MIND0/3. The first (I) was denoted for non-overlap terms alone; the second (It) for a combination of one- and two-center terms; the third (III) includes all terms. It will be seen that the results for all three are similar, and that all six calculations give results in acceptabie agreement with experiment.
nents(x,,.
0.113 0.145
0.109 0.135
0.151 0.172
0.151 0.170
0.148 0.205
In particular, ali reproduce well the observed trends. Note in particular the (apparently correct) prediction that fluorine in the 2,4,6-positions of 1 should lead to a decrease in magnitude of the coupling constant whereas fluorine in the 3 ,Spositions should lead to an increase. These changes correspond to the changes in E electron density at nitrogen. The negative charge at nitrogen increases with substitution by fluorine in the 2,4,6-positions as a result of its electron-reIeasing electromeric (~5) effect, but decreases with substitution by fluorine in the 3,Spositions as a result of field (inductive) and B inductive effects (table 3). A more detailed check on the various procedure is provided by the calculated mean absolute errors and standard deviations, shown in the last two rows of table 6. It will be seen that the best results are given by MNDO, including all terms without renormalizing the wavefunction. The MIND013 results are uniformly less satisfactory, in this case three models give similar results. It is obvious that multi-center terms should be included in the calculation when the wavefunction is not renormalized. The results are in any case very satisfactory and again may prove helpful in assigning the microwave spectra of the other compounds listed in table 6 in particular and of nitrogen compounds in general.
h5 J.S. Dewar et al./Stnmtres
artd properties of fluoriimted p_vridines
Acknowledgement This work was supported by the Ah Force Office of Scientific Research (Grant AFOSR 752749) and the Robert A. Welch Foundation (Grant F-126). S. Doraiswamy and SD. Sharma would like to thank the Robert A. Welch Foundation for fellowships at The University of Texas, Austin and Rice University, Houston, respectively when a part of this work was completed. The calculations were carried out using the CDC 6400/6600 computer at The University of Texas Computation Center.
References [l] S.D. Sharma, S. Doniswamy, H. Legell, H. Mader and D. Sutter, Z. Neturforsch. 26a(1971) !342. [2] S.D. Sharma and S. Doraiswamy, J. Mel. Spectry. 59 (1976) 216. [3] S. Doraiswamy and S.D. Sharma, Chem. Phys. Letters 37 (1976) 527. [4] S. Doraiswamy and SD. Sbarma, Chem. Phys. 6 (1974) 76. [S] O.L. Stiefvater, Z. Naturforsch. 30a (1975) 1765. [6j R.C. Bingham, M.J.S. Dewar and D.H. Lo, J. Am. Chem. Sot. 97 (1975) 1285,1294,1302,1307; M.J.S. Dewar. D.H. Lo and C.A. Ramsden, J. Am. Chem. Sot. 97 (1975) 1311. [7] h1.J.S. Dewar and W. Thiel, J. Am. Chem. Sot. 99 (1977) 4899,4907; hl.J.S. Dcwar and M.L. McKee, J. Am. Chem. Sot. 99 (1977) 5231; M J.S. Dewar and H.S. Rzepa, J. Am. Chem. Sot. 100 (1978) 58,777;
33
M.J.S. Dewar, M.L. McKee and H.S. Rzepa, J. Am. Chem. Sot. 100 (1978) 3607. [S] h1.J.S. Dewar and G.P. Ford, J. Am. Chem. Sot. 99 (1977) 1685. 191 M.J.S. Dewar, G.P. Ford, M.L. McKee, H.S. Rzepa, W.Thiel and Y. Yamsguchi, J. Mol. Struct.43 (1978) 135. [IO] h1.J.S. Dewar and D.H. Lo, Chem. Phys. Letters 33 (1975) 298. [11] M.J.S. Dewar and H.S. Rzepa, unpublished work. 1121 M.J.S. Dewar, H.W. Kollmar and S.H. Suck, J. Am. Chem. Sot. 97 (1975) 5590. [13] L. Chantranupong, h1.J.S. Dewar, Y. Yamaguchi and S.H. Suck, to be submitted for publication. [14] R. Fletcher and h1.J.D. Powell, Comput. J. 6 (1963) 163: R. Fletcher, Comput. J. 8 (1965) 33: W.C. Davidson, Comput. J. 10 (1968).406. [15] T. Koopmans, Physica 1 (1934) 104. 1161 C.H. Townes and B.P. Dailey, J. Chem. Phys. 17 (1949) 782. [17] G.O. Sbrensen, L. h.‘ahler and N-R. Andersen, J. Mol. struct. 20 (1974) 119. [ 181 SD. Sharma and S. Doraiswamy,Chem. Phys. Letters 41(1976) 192. [19] h1.J.S. Dewar, J. Am. Chem. Sot. 74 (1952) 3350. [20] C.R. Brundle, M.B. Robin and N.A. Kuebler. J. Am. Chem. Sot. 94 (1972) 1466. (211 E. Heiibronner, V. Hornung, H. Bock and H. Ah, Angew. Chem. Intern. Ed. 8 (1969) 524. [22] E. Heilbronner, V. Hornung, F.H. Pinkerton and S.F. Thames, Heh. Chim. Acta 55 (1972) 289. [23] J.D. COX and G. Pilcher, Thermochemistry of organic and organometalhc compounds (Academic Press, New York, 1970). [24] G.H. King, J.N. Mureli and R.J. Suffolk, J. Chem. Sot. Dalton (1972) 564.