J . Phys. Chem. 1990, 94, 8762-8766
8762
momentum could be conserved for each pair of internal levels (E! + Et, ET + g )but also to calculate cos x using (AIII.2). Thus, at each triplet of Ea, Eb,E,, the calculation provided not only a number proportional to the density of states, but also a distribution of cos x. The continuous range of E,, Eb, and E, between the energies of 0 and E,, = 15 386 cm-l was discretized into 30 bins. After all pairs conserving energy were counted, the distribution Q(Ea,Eb,EC)was normalized. The angular distribution in the bottom panel of Figure 6 was calculated by summing each of the above determined cos x dis), Ptributions weighted by P ( E a , E b , E c ) / Q ( E a , E b , E cwhere (Ea,Eb.EC)is the distribution whose projections agree with the data and which is otherwise of maximum entropy. B . Acetone. The calculation of Q(Ea,Eb,Ec)for acetone proceeded in a manner similar to that for C , 0 2 . The internal-state densities for CO and CH3 were calculated separately up to a total energy of 20 000 cm-' and stored in arrays of dimension 200. For each triplet of internal levels (E: Et, E: Et, E; E t ) , subject to E: E: IEa,E: Eb < Eb, and E; Et IE,, a degeneracy corresponding to q:q:q!~&qt was added to Q(Ea,Eb,EC),where were used as and 9; = (25, q; = 2J, 1, 9: = ( 2 J b the degeneracies of the rotational levels and 4:. qt, and qF are the
+
+
+
+
+
+
+
+
+
degeneracies of the vibrational levels. The square of 25 + 1 was used as the methyl rotational degeneracy to account implicitly for K values. The available energy was taken as E,, = 18 540 cm-I, and the final results were again discretized into 30 bins. C. Symmetric Tetrazine. The calculation of Q(E:,EF,G) for symmetric tetrazine proceeded somewhat differently since the distribution function ranges over a pyramid rather than a triangle. With the use of the rigid rotor, harmonic oscillator approximation, the internal-state densities for N2 and HCN were calculated separately up to a total energy of 40000 cm-I and stored in arrays of dimension 1000. For each triad (E: + Et, E: + Et, E; E;) the product of the three densities was added to each element of Q(E:,EF,EF) that satisfied
+
E: IE,, - E; - E:,
E! 5 E,, - E,b - E:, E: IE,, - E; - E;, and E: 4- E! + Et = E,, - E: - Et - E! - E t - E: - E:
based on a grid of translational energies of dimension 30 between E , = 0 and E, = E,, = 39033 cm-I. Q was then normalized. Registry No. C , 0 2 , 504-64-3; (CH3)*CO,67-64-1 ; tetrazine, 29096-0.
ARTICLES Conformation In 2,3-Difluorobutanes G. Angelhi,*-+E. Gavuzzo,f A. L. Segre,f and M. Speranzas Istituto di Chimica Nucleare del C N R , Area della Ricerca di Roma, C.P. I O , 00016 Monterotondo Stazione, Roma, Italy; Istituto di Strutturistica Chimica del C N R , Area della Ricerca di Roma, C.P. 10, 00016 Monterontodo Stazione, Roma, Italy; and Universitd degli Studi della Tuscia, Viterbo, Italy (Received: January 22, 1990; In Final Form: May 30, 1990)
A conformational analysis for m e m and d,l-2,3-difluorobutanes has been carried out, employing 'Hand "F N M R and theoretical calculations. The real configurations of the two isomers were assigned by specific optical rotation measurements of the products coming from an optically active precursor. Gauche conformations were predominant for meso (E) isomer, while the d.1 (T) isomer showed all possible staggered rotamers almost equally populated. Finally remarks for NMR peak assignment of homoand copolymers partially fluorinated by using gauche additive effects are given.
Introduction
Conformational analysis of haloalkanes was the subject of considerable interest in the past decades.Is2 Most of the studies were carried out by ' H NMR spectroscopy,3-iialthough other techniques, such as IR,I2 microwaves,i2 and electron diffraction s p e c t r o ~ c o p yoften . ~ ~ supported by conformational analysis,I4 and a b initio calculation^^^ were employed. N o difficulties were met with the rationalization of experimental N M R data concerning haloalkanes containing CI, Br, and 1, whereas with those containing fluorine atoms some uncertainty is still present. This is partly due to the spin of I9F, a nucleus that complicates N M R spectra of F alkanes. A further complication arises from the so-called "gauche effect",16 which seems to play an important rolc only in F alkanes and not in the CI, Br, and I homologues.
' lstituto di Chimica Nucleare.
' lstituto di Strutturistica Chimica
9 Universitj.
degli Studi Tuscia
0022-3654/90/2094-8762$02.50/0
Semiempirical potential energy calculations have often been employed on model compounds to predict the configurational ( I ) Mizushima, S. The Structure of Molecules and Internal Rotation; Academic Press: New York, 1954. (2) Lister, D. G.; MacDonald, J . N.; Owen, N.L. Internal Rotation and Incersion; Academic Press: London, 1978. ( 3 ) Emsley, J. W.; Feeney, J.; Sutcliffe, L. H. High Resolution N.M.R. Specfroscopy; Pergamon Press: Oxford, 1967; Vol. 1. ( 4 ) Abraham, R. J.; Pachler, K. G. R. Mol. Phys. 1963, 7 , 165. (5) Kingsbury, C. A.; Best, D. C. J . Org. Chem. 1966, 32, 6. (6) Abraham, R . J.; Cavalli, L.; Pachler, K. G.R. Mol. Phys. 1966, / I , 471. (7) Abraham, R. J. J . Chem. Phys. 1969, 73, 1192. (8) Abraham, R. J.; Gatti, G. J . Chem. Soc., Perkin Trans. 2 1970, 961. (9) Abraham, R. J.; Kemp, R. H. J . Chem. Soc., Perkin Trans. 2 1971, 1240. ( I O ) Phillips, L.; Wray, V. J . Chem. Soc., Perkin Trans. 2 1972, 536. ( I I ) Anderson, J. E.; Doecke, C. W.; Pearson, H. J . Chem. Soc., Perkin Trans. 2 1976, 336. (12) Wilson, E. 8. Chem. SOC.Rec. 1972, I , 293. ( I 3) Clark, A. H.Electron Diffraction Studies and Rotational Isomerism. I n Internal Rotation in Molecules: Orville-Thomas, W. J., Ed.; Wiley: Chichester. 1974: Chapter IO.
0 1990 American Chemical Society
Conformation in 2,3-Difluorobutanes sequences in fluorinated homo- and copolymer^.'^-^^ However, no experimental support has been provided to these calculations till now. We, therefore, decided to undertake a detailed N M R and theorctical study aimed at assessing the conformation of two model F-alkane compounds, namely, meso- (E) and d,l- (T) 2,3-difluorobutanes suitable for application in the conformational analysis of fluorinated polymers.
Experimental Section Materials. Preparation of isomeric 2,3-Bis(p-toluenesulfonyloxy)butanes.21*22Pyridine (70 g, 0.888 mol) was slowly added, in 2 h, to a mechanically stirred mixture of 10 g (0.11 1 mol) of isomcric 2,3-butanediol and 47 g (0.247 mol) of ptoluenesulfonyl chloride at 0 OC. The suspension was allowed to warm to room temperature and stirred for 3 h. Then the reaction mixture was poured into 300 mL of ice water. The suspension was shaken for 5 min and, after neutralization of the residual pyridine with dilute sulfuric acid, extracted with 100 mL of ether. The organic solution was washed with ice-cold 2 N sulfuric acid, icewater, ice-cold 2 N potassium hydroxide, and finally additional portions of ice water. The ethereal solution was dried over anhydrous sodium carbonate, and the solvent was evaporated under vacuum. A white solid product was isolated (27 g, yield 61%) which was dried under vacuum at 40 OC for 12 h. The isomeric 2,3-bis(p-toluenesulfonyloxy)butanes produced were identified by IR and N M R analysis (CDCI,, TMS; 6 1.2 (6 H, m), 2.5 (6 H, s), 4.60 (2 H, m), 7.60 (8 H, m)). Preparation of meso- ( E ) and d,l- ( r ) 2,3-Difluorobutanes. A two-necked round-bottomed flask, throughly dried before use, was provided with a magnetic stirrer and a 25-cm Vigreaux column, fitted with glass pellets. An isomeric mixture (8.7 g, 0.022 mol) of 2,3-bis(p-toluenesulfony1oxy)butanes was placed into the flask together with 17.7 g (0.305 mol) of anhydrous potassium fluoride and 45 mL of diethylene glycol. The pressure was adjusted to 15 mmHg, and the flask was slowly heated at 120 OC. Development of a gas was observed at 50 OC, which was promptly collected in a "U"trap, cooled with liquid nitrogen. Then the condensed product was transferred in a cooled vial kept at -30 OC. GLC analysis of the product, using a 4-m stainless steel column containing 15% didodecyl phthalate on 60 mesh Chromosorb Q at 40 OC, showed three main components, which were isolated by preparative GLC, yield I . 1 g (53%). The first component (1, retention time 30 min, relative yield 30%) was identified by N M R analysis as 2-butyne. The second (2) and third (3) components (retention time 38 and 60 min, relative yield 30% and 40%, respectively) were identified by N MR analysis as isomeric 2,3-difluorobutanes, but the complex nature of these N M R spectra did not allow us to assign any configuration. To discriminate between the isomeric 2,3-difluorobutanes, the synthesis was repeated using optically active (R,R)-(-)-2,3-bu= -18.1' (CHCI,, 0.015 g/mL), as starting comtanediol, [a]20 pound. In this way, formation of the optically active d or I isomer of 2,3-difluorobutane (T) and of the inherently inactive meso form (E) is expected, whose corresponding retention times in the GLC analysis can be directly assessed by simple optical activity measurements. Thus, IO g of (R,R)-(-)-2,3-butanediolwas converted in a 2,3-difluorobutane isomeric mixture, whose optically active fraction was isolated by preparative GLC analysis under the above-described conditions. I n this way, the optically active (14) Scott, R. A.; Scheraga, H. A. J . Chem. Phys. 1966, 45, 2091. (IS) Veillard A. Ab Initio Calculations of Barrier Heights. In Internal Rofafionin Molecules: Orville-Thomas, W. J.. Ed.; Wiley: Chichester, 1974: Chapter 1 I . (16) Truax, D. R.; Wieser. H.; Lewis, P. N.; Roche, R. S . J . Am. Chem. Soc. 1914, 96. 2327. (17) Poplc, J . A.; Gordan, M. J . Am. Chem. SOC.1975, 89, 4253. (18) Klaboe. P.; Nielsen, J. R. J . Chem. Phys. 1960, 33, 1764. (19) Tonelli. A. P. Macromolecules 1980, 13, 734. (20) Tonelli, A. P. Macromolecules 1982, I S , 849. (21) Edgell, W. F.; Parts, C. J . A m . Chem. Soc. 1955, 77, 4899. (22) Kym, K . C.; Cooks, R. G.J . Org. Chem. 1975, 40, SI 1 .
The Journal of Physical Chemistry, Vol. 94, No. 25, I990 8763 SCHEME I CH~CHCHCHJ
TsCWPyr
H d AH (optically active) slim
reten
CH3CHCHCH3 TsL dTs 1X)'C
I
KF
I
invers
CHjC ECCH3
retention time (min): 30 peak no.1
F
I
CH~CH~HCH~
L
CH3CHCHCH3 I
I
k # optically active
optically inacliive
60
38
peak no. 3 (=T)
peak no. 2 (=E)
product T, [a]20 = + 5 S 0 (CHCI,, 0.128 g / ~ n L ) , ~showed , same retention time (60 min) of peak 3, whereas the optically inactive product (E) matched that of peak 2 (Scheme I). As a consequence, it was possible to directly identify product 3 as the d,l form (T) of 2,3-difluorobutane and product 2 as its meso isomer (E).
Methods 'H and 19F N M R spectra were run on a Bruker W P 200 spectrometer, operating on protons at 200 MHz. Solutions in CDCI, and CD,COCD3 were obtained by condensing the gas (2 mg) into a 5-mm N M R tube connected to a greaseless vacuum line and containing 0.5 cm3 of the degassed solvent. The N M R test tubes were then sealed off without any additional reference compound. 'Hchemical shifts are given in ppm from TMS, with the appropriate frequency of the residual 'Hsignal of the solvent as a reference. 19Fchemical shifts are given only as a difference between meso (E) and d,l (T) derivatives. All M N R spectral analysis were performed on a Bruker Aspect 2000 computer. Two different methods were used for the conformational analysis: an a b initio total energy method24and semiempirical potential energy f ~ n c t i 0 n s . lIt~ is then possible to compare the two sets of calculations both to gain confidence in the obtained results, once they are similar to each other, and to compare experimental and theoretical results. The total energies, within the quantum mechanical framework, have been computed by the HFR-MO-LCAO-SCF method (Hartree-Fock-Roothaan molecular orbital linear combination of atomic orbitals self-consistent field).24 The basis set used is a minimal one: the STO-3G (Slater type orbitals).25 The coefficients of the van der Waals potential energy functions were taken from ref 14 except for those concerning the F-F potential, which were taken from ref 26. Coulombic interacions were calculated from Ve(ru)= q,q,/DrI,where qi and q are partial charges from the Mullikan population analysis24of the HFRMO-LCAO-SCF wave functions, centered at the atoms i and j (Table II), rl, is the interatomic distance expressed in angstroms and D is the dielectric constant taken as unity. Results and Discussion N M R Analysis. All N M R spectra are AA'B3B,'XX'. They all show a very large number of lines. For each analysis, 300 lines were used. The spectral analysis was performed with PANIC,27 a modified version of LAOCOON type programs,28able to include magnetic equivalence. (23) This value is relative not only to the d enantiomer but probably also to a mixture between d and l enantiomers in different proportions (d > 1 ) . (24) Czismadia, 1. G. Theory and Practice of MO Calculations on Organic Molecules. In Progress in Theoretical Organic Chemistry; Elsevier: Amsterdam, 1979; Vol. 1, p. 1. (25) Hehre, W. J.; Stewart, R. F.; Pople, J . A. J . Chem. Phys. 1969, 51, 2657. (26) Scott, R. A.; Scheraga, H. A. J . Chem. Phys. 1965, 42, 2209. (27) PANIC: A least-squares program in the Bruker library. (28) Castellano, S.;*Bothner-By,A. A. J . Chem. Phys. 1964, 41, 3863.
8764
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The Journal of Physical Chemistry, Vol. 94, No. 25, 1990
TABLE I: 2,3-Difluorobutanes J Coupling Constant Values F
F
I (5) I (6)
(3) H 3 C - - C 4 4 H 3 ( 4 1
I
411
RT."CDCIj 1-2
6.5 0. I 48.0 17.8 24.0 1.1 -13.4 0.05
0.0
1-4 1-5
47.8 15.6 24.2
1-6 3-5 3-6 5-6 rmsb error
T -40
OC,CD3COCD3
2.9
3.6 6.5
1-3
a
E RT,CDJCOCDj
1
He)
1.3
- I 3.8 0.1
2.5 6.5 0.1 48.0 19.1 24.1
I .o -13.8 0.1
RT,CD3COCD3
4.5 6.5 0.0 47.9 18.2 24.0 0.9 - 1 1.6 0.1
4.4
6.5 0.0 48.2 19.6 23.9 0.9
-11.1 0.05
RT = room temperature. Rms = root-mean-square deviations. H
TABLE II: Partial Charge" Values on the Atoms of T and E HI H, H3
c,
HS F,
C, a
RT,CDCIj
T
E
0.07 0.07 0.07 -0.20 0.06 -0.16 0.09
0.07 0.07 0.07
-0.20 0.06 -0.16 0.09
HE FP Clo
c,, HI2
HI3 HI,
T
E
0.06 -0.16 0.09 -0.20 0.07 0.07 0.07
0.06 -0.16 0.09 -0.20 0.07 0.07 0.07
Partial charges expressed as fraction of electrons.
Coupling constants for all analyzed spectra are reported in Table I; root-mean-square deviations are always less than 0.1 Hz. It is interesting to point out that some information can be obtained from the temperature dependence of the line width of NMR spectra of E and T even without any spectral analysis. The I9F spectrum of T broadens at 20 OC, and this broadening increases continuously by lowering the temperature. The proton spectrum of T is slightly broadened (ca. 3-Hz line width) at -40 OC, and this effect is clearly observable only at -80 OC. Both the 19Fand 'H spectra of E are sharp and well resolved even at -80 "C. The spectrum pattern of E changes from room temperature to -40 "C, but spectra run in CD3COCD3at -40 OC or at -80 OC do not show any variation. The spectrum at room temperature of T is well resolved in all its parts, but by lowering the temperature the I9F spectrum progressively broadens. At -80 OC the line width of the I9F spectrum broad band decoupled from IH is ca. 70 Hz. This broadening can be interpreted as due to the presence of rotational isomers. In E, either only one isomer is present at low temperature or the rotational barrier between isomers is so low that it does not produce observable effects on the N M R time scale. In T, the barrier is high enough so that rotational isomers interconvert in a time comparable with the NMR time scale. This fact is observable only on I9F due to chemical shift differences, which are very large in I9F spectrum29but small in IH spectrum, while all coupling constants are still averaged by the rotational process. More information can be drawn from the actual value of coupling constants (Table I ) for both E and T, mainly from the 35H-H coupling constants, Well related to dihedral angles by a reliable Karplus type e q ~ a t i o n . ~ The " lack of a reliable Karplus - F their intrinsic dependence type equation for )JH+and 3 J ~ and on solvent polarity, even if the molecule is conformationally rigid.31 force their interpretation to be only qualitative. For obvious energetic reasons, only the possible staggered rotational isomers of E (1-111 E) and T (1-111 T) are taken into (29) Weigert, F. J . J . Org. Chem. 1980, 45, 3476. (30) Haasnoot. C. A. G.:de Leeuw. F. A . A . M.;Altona. C. Tetrahedron 1980. 36. 2783. ( 3 1 ) Watanabe. S . : Ando. I . J . Mol. Struct. 1983. 104. 1 5 5 .
H
H
CKJ
H
F
I E
II E
111 E
Figure 1 Staggered rotamers of meso-2.3-difluorobutane. I
H
H
H
H
CKJ
F
I T
II T
111 T
Figure 2. Staggered rotamers of d,l-2,3-difluorobutane.
account in the discussion (see Figures 1 and 2). The 3 J ~data - ~of Table I can be summarized as follows: for E, Jl-2(CDCI3, RT) > J1_2(CD3COCD3,RT) > J1_2(CD$OCD3, -40 "C); for T, Jl-2(CDC13,RT) N Jl-2(CD3COCD3,RT) [RT = room temperature]. Irrespective of the population of the rotamers of each derivative, one should expect a solvent-polarity effect on the 35H-H data, in agreement with the observed trend. In fact for E, only rotamer I1 E has no dipole moment for symmetry reasons and a rather large value for 'JH+vicinal Coupling. On the contrary, all possible rotamers of T are polar, even if rotamer I1 T must be less polar than I T and 111 T. As a consequence, whatever is the most stable isomer for E and T, the dependence of JH-H vicinal coupling as a function of the solvent polarity is in agreement with the above consideration and with data previously reported on substituted ethanes and butane^.'^,^^ I f I 1 E were the most stable isomer of E, one should expect a 3J1-2value of ca. 8 Hz, while if I E E 111 E were the most stable ~ the isomer, a 3Jl-2value of ca. I Hz should be ~ b t a i n e d .Thus, small value observed in both solvents indicates that, for E derivative, I E (111 E) is the most stable conformation. These findings are in agreement with the results observed in solution for 1,2-difl~oroethane?~~* which is in a gauche (F-F) conformation in organic solvents as well as in the gas phase. In the T derivative, the Value of 'JH-H is 4.5 Hz, and this value does not appreciably change with solvent polarity. Both isomers I I T and 111 T have a y-gauche methyl affecting the F chemical shift, while this effect is not present in isomer I T. Thus, the presence of a large chemical shift difference in the I9F spectra at low temperature (at -40 "C the line width of I9F{'H)peak is 50 Hz) shows that isomer I T and one or both the isomers I1 T (32) Abraham, R. J. J . Phys. Chem. 1969, 73, 1192. (33) Gambaretto, G . : Napoli. M . Ann. Chim. 1973, 63, 235.
The Journal of Physical Chemistry, Vol. 94, No. 25, 1990 8765
Conformation in 2,3-Difluorobutanes H12
F9
F6
(F6)
(H 5 )
Figure 3. Atomic numbering and internal rotational angles of the molecules T (labeled with H5 and F, in brackets) and E. Bond lengths (angstroms) are H-C = 1.08, C-C = 1.54, and C-F = 1.36. Bond angles (degrees) are all tetrahedral, except C4-C7-Cl0 = C7-Clo-Cll = 114.00 and HS-C7-F6 = H8-Clo-F9 = 104.53.
0.0
p Ill T
0
IT 120 Qi,
and 111 T are present in the solution. Two alternative interpretations may be considered for fitting experimental data of T, but both of them must be considered as limiting cases. The first one is based on the fact that calculated energies all lie within 1 kcal (see Figures 4-7). I f one admits that all three T isomers are present in solution with comparable populations, even at low temperature, one would expect that by increasing the polarity of the solvent the population of I1 T should decrease, favoring isomers I T and 111 T, which have a larger dipole moment. However, if, due to a fluorine gauche effect, isomers 111 T and 1 T are more favored than isomer 11 T, no observable effect on J H - H would be found. Anyhow '/3(JiT JllT JI!IT) = 4.2, well comparable with Jexpll = 4.5. The geminal 'JH-F changes slightly with the solvent polarity, while the vicinal j J H - F shows a larger variation (Table I). Therefore, by changing the solvent polarity, some variation in the rotamers population may be present. Additive parameters for calculating I9F chemical shifts have been recently developed by Weigert.29 By using Weigert's ygauche parameters and experimental chemical shift difference, it is possible to check whether the set of conformations so far obtained is reasonable. To this purpose, we used the chemical shift difference obtained at -40 OC in which T is downfield with respect to E by 2.03 ppm. In the hypothesis that E has only the I E ( I l l E) rotamer, while T has the three rotamers equally populated, a chemical shift difference of 2.0 ppm with E upfield is obtained. In spite of the large number of approximations involved, the agreement between the experimental and the calculated values is extremely good, corroborating the proposed rotamer populations. An alternative explanation (we thank a referee for this inter-H T is that only isomers esting suggestion) of the observed ~ J Hin with strong fluorine gauche effects are present in solution, namely, isomers I and 111 T. This would give a calculated coupling 1/2(JIT + JIIIT)= 3.7 Hz, slightly lower than the experimental value. This alternative explanation is corroborated by its consistency with the small solvent effect on all couplings and well consistent with the Value [ ~ J H F19 HZ '/2(Jgauche Jlrans)]. However with this hypothesis it is difficult to explain the observed 19F chemical shift difference between E and T since the same number of Weigert's y-gauche effects are present in both E and T. Thus the first hypothesis gives a better agreement between the 3JH-H observed and calculated and the I9F chemical shift values, while the second one gives a better agreement with the gauche from effect as observed in E and with the independence of 3JH-H solvent polarity. Conformational Analysis. To better understand all the possible conformations that the molecules (T and E) can assume and to approximately know the relevant potential energy profiles, we have undertaken a theoretical study of the conformation of 2,3-difluorobutanes. The conformation is described by three internal rotation angles p l , cp2, and cps (Figure 3), which represent the dihedral angles H(I)-C(4)-C(7)-C( IO), C(4)-C(7)-C( lO)-C( I I ) , and C(7)-C( 10)-C( I I)-H( 12), respectively.
+
It T
240
360
("1
Figure 4. Ab initio calculation of total energy (b) and dipole moment (a) for T isomer as a function of p2 angle (when p1= p3 = 60').
i
6.0
+
+
0
120
240 92
io
("I
Figure 5. Semiempirical calculations of van der Waals together with Coulombic potential energy contribution for T isomer as a function of p2 angles (when p1 = p3 = 60').
The analyses were computed as a function of the three internal rotation angles cp,, cpz, and cp3, giving angular increments of loo and subsequently of 5 O . The assumed geometry is shown in Figure 3. The two torsion angles cpl and cpj are considered zero when the atoms H(I), C( 10) and, respectively, the H(12), C(7) atoms are in the "cis" conformation. In both E and T molecules, the torsion angle cpz is Oo when the two hydrogens H(5) and H(8) are eclipsed. A counterclockwise rotation is considered positive looking from C(4) toward C(7) for cpI, from C(7) toward C( 10) for cpz, and from C ( 10) toward C ( 1 1 ) for cp3. The two torsion angles cp, and cp3 do not influence the conformation of the molecule, which is a minimum always about cp, = cp3 = 60° for all the allowed values of cp2, namely, when the two methyl groups are distant enough. In all the diagrams the energies are expressed as AE = E - E O , where Eo is the energy of the most stable conformation, set equal to zero. The results of a b initio LCAO calculations are shown for T in Figure 4b where the energy in kcal mol-' is a function of cp2 and where curve a represent the dipole moment of the molecule expressed in debyes at different values of 9 2 . This diagram clearly shows that when the fluorine atoms are in a gauche position (cp2 = 5 5 O or cp2 = 17S0), the dipole moment is quite high (around 2 D), whereas when they are in a trans position (cp2 = 310°), the dipole moment is almost zero. The energy differences among the three minima are the following: AE(1T-IIIT) N 0.9 kcal mol-', AE(IIT-IIIT) = 0.8 kcal mol-', and AE( IT-IIT) N 0.1 kcal mol-'. Similar results are obtained if we apply semiempirical potential energy functions as can be seen from Figure 5. In fact the agreement of the position of the minima is rather good, being with ab initio calculations cp, N 5 5 O ,
8166
The Journal of Physical Chemistry, Vol. 94, No. 25, I990
Angelini et al.
-
60-
? -
I
m
I
Y
Lb
40.
a 20-
00-
1
0
I
120
240
360
F2 !Om
v2
io)
Figure 6. Semiempirical calculations of van der Waals together with Coulombic potential energy contribution for E isomer as a function of p2angle (when pI = p3 = 60').
Figure 7. Ab initio calculation of total energy (b) and dipole moment (a) for E isomer as a function of p2angle (when ql = p3 = 60O).
p2 =
rotamers, which show a higher dipole moment (see Figure 7), may significantly increase, while that of the apolar trans rotamer decreases. Furthermore, analysis of the temperature effect on the 3JH-y of E in acetone indicates that gauche rotamers become predominant over the trans one, in this solvent. The fact that, in acetone, 35H-H decreases from 2.9 to 2.5 Hz as the temperature is lowered from rmm temperature to -80 'C shows the increased predominance of the gauche conformations under these conditions. Thus, independently from solvent effects, only F-F gauche effects can be invoked to explain the observed coupling constants.
172', and 9, = 310°, versus 9,= 65', cpz = 165', and cp3 = 3 IO' with semiempirical potential energy functions.
Moreover the agreement of energy differences among the three minima is quite good in the two diagrams. In fact with semiempirical potential energy calculations we have the following differences: AE(1T-IIIT) 0.6 kcal mol-', AE (IIT-IIIT) 0.5 kcal mol-', and hE(IT-IIT) = 0.1 kcal mol-'. Therefore there is no doubt that the minimum with the two methyl groups nearly trans and the two fluorine atoms nearly gauche represents the most stable conformation for the isolated molecule, while the other two conformations show about the same energy. Taking the values from ab initio calculations, an energy barrier value of at most about 3.8 kcal mol-' is obtained. 3JH-H values have been calculated30for I, 11, and I11 T rotamers with dihedral angles corresponding to the minima obtained with ab initio calculations. The relevant values are 7.31, 5.04, and 0.00, respectively. Allowing a Boltzmann distribution with energies corresponding to the minima shown in Figure 4, it is possible to calculate 3JH-H = 1.9 Hz, a value that is quite far away from the experimental one of 4.5 Hz. On the contrary a much better agreement is found for 35F-F. In fact allowing Jgaeche = -14.0 Hz and J,,,,, = 0.0 Hz,29331an averaged value is calculated as )JF-! = -1 1.5 Hz, almost equal to the experimental one, although a suitable functional dependence of F-F coupling constants on the dihedral angle is to our knowledge not available to date. Now if exactly the same calculations are repeated for the meso compound (E), the diagram of Figure 6 with semiempirical energy functions and the diagram of Figure 7 with a b initio calculations are obtained. In both diagrams, the deepest minimum is the one with the two methyl groups, the two hydrogens HSand H8and the two fluorine atoms in a trans position (cpz = 180') and with an energy difference of 0.6 kcal mol-' compared to the two gauche conformations (p2 = 75' and 285'). For these angular values the Haasnoot equationz7 provides the following 3JH-H coupling constants: 0.78, 7.89, and 0.78 for 75', 180'. and 285', respectively. Now, if these results are compared with those found experimentally by NMR, the agreement, as for the threo compound, seems to be not good. In fact, coupling constants of 3.63 Hz at room temperature in CDCI, solvent for HS-Hs and 2.91 Hz in CD3COCD, solvent are measured against the 5.0 Hz calculated. This discrepancy points to a substantial solvent effect on the relative stability of the rotamers, supporting the view of a weighted average conformation for E, in polar solvents, shifted toward gauche conformations. A rationale for this shift arises from the fact that, in polar solvents, the relative weight of the gauche
Conclusions N M R experiments clearly show that in solution isomer E is predominantly in a gauche conformation, while isomer T has all possible staggered rotamers almost equally populated or only the two conformers with fluorine atoms in the gauche position are populated. Assuming the validity of the Haasnoot equation30 and the position of energy minima given by conformational analysis in the isolated stare, it is possible to calculate the 3 J ~ coupling - ~ for each rotamer. For E derivative the gauche conformer (cpz = 75' or 285') gives the calculated 3 J ~ =- 1~Hz vs an experimental value of 2.5 Hz. The value for T can be calculated by using dihedral angles taken from conformational analysis. The calculated 35H-H = 3.7-4.2 Hz well compares vs an experimental value of 4.5 Hz. Thus the Haasnoot equation, which has no theoretical reason for not holding in fluorinated substituted ethanes, does indeed show a reasonable agreement. The value of torsion angles obtained by theoretical calculations seems to account well for the experimental NMR values. However energy absolute minima in solution do not necessarily correspond to those calculated on isolated molecules. Polymer sequence determination is one of the major applications of N M R . A fundamental requirement for this type of analysis is a precise assignment of experimental peaks to particular sequences, steric for homopolymers, chemical in copolymers. The task is not trivial, and in most cases a heavy use of model compounds is required. In the case of homo- and copolymers partially fluorinated, peak assignments were made by considering gauche additive effects on chemical shifts and performing conformational analysis on polymer fragments to obtain the most stable rotational isomer and to evaluate gauche contribution^.'^,^^ In light of our results on 2,3-difluorobutanes this method does not appear reliable since it would predict chemical shifts reversed with respect to the ones experimentally found. In this respect, 2,3-difluorobutanes give a clear warning.
