8589
J. Phys. Chem. 1995,99, 8589-8598
Formic Anhydride in the Gas Phase, Studied by Electron Diffraction and Microwave and Infrared Spectroscopy, Supplemented with ab-Initio Calculations of Geometries and Force Fields G. Wu, S. ShlykovJ C. Van Alsenoy, and H. J. Geise* Department of Chemistry, University of Antwerpen (UIA), Universiteitsplein I , B-2610 Wilrijk, Belgium
E. Sluyts and B. J. Van der Veken Department of Inorganic Chemistry, University of Antwerpen (RUCA), Groenenborgerlaan 171, B-2020 Antwerpen, Belgium Received: December 8, 1994; In Final Form: March 7, 1995@
The structure of formic anhydride was studied by the joint analysis of gas-phase electron diffraction, microwave, and infrared data. The experimental data are supported with geometrical constraints and force fields from geometry-relaxed ab-initio calculations on the 4-21G and 6-31G** levels. All data agree with the gas phase at room temperature consisting of the planar [sp,ap] conformer, in which the two 0-CH-0 moieties differ significantly in geometrical as well as vibrational parameters. Geometrical least-squares constraints taken from the 4-21G calculations performed slightly better than those from 6-31G** calculations. In contrast, the 6-3 1G**-derived scaled force field performed better in the IR analysis, reproducing the frequencies with a root-mean-square deviation of 6.7 cm-' and a largest discrepancy of 14.1 cm-I. Assisted by 6-31G**-based IR band intensities, a significantly improved assignment of IR frequencies was made. The reported selfconsistent molecular model of formic anhydride is in agreement with all diffraction and spectroscopic data available to date, contains a complete force field of which diagonal and off-diagonal constants allow a physically consistent interpretation, and also points to a rationalization why formic anhydride is thermolabile and acetic anhydride is not.
Introduction
H I
Although anhydrides of carboxylic acids are widely used reagents in synthetic chemistry, the understanding of their conformational and spectroscopic behavior lags behind. This is particularly true for the three most simple members: formic anhydride, formic acetic anhydride, and acetic anhydride (henceforth abbreviated as FA, FAA, and AA, respectively). We will report here on the geometry and force field of FA in the gas phase as well as on the information these data provide about the low thermal stability of FA. The torsion angles pl (03=C2-01-C5) and v)2 ( 0 6 4 3 0 1-C2) characterize the various possible conformations, of which the planar forms are shown in Figure 1. Using the IUPAC nomenclature,' the conformer with = p2 = 0" is called synperiplanar, synperiplanar, [sp,sp], the one with v ) ~= O", p2 = 180" is called synperiplanar, antiplanar, [sp,ap], and the one with v)1 = 9 2 = 180" is called antiplanar, antiplanar, [aP aP1. Earlier electron diffraction (ED)* and microwave ( M W ) spectroscopic ~ t u d i e s are ~ . ~not in complete agreement. Both techniques led to the conclusion that the [sp,ap] form is the only conformer present in the gas phase, but disagreed on its precise geometry. The microwave data indicated the molecule to be planar with C,symmetry, whereas the electron diffraction data seemed to favor a slightly nonplanar geometry, even though the rather high estimated standard deviations could not exclude the planar geometry. Furthermore, an extensive matrix infrared investigation of five isotopic species was performed by Kuhne 9
* Author to whom correspondence should be addressed. On leave from the Department of Physics, Institute of Chemical Technology, U1. Engelsa 7, Ivanovo 153460, Russia. @Abstractpublished in Advance ACS Abstracrs, April 15, 1995. +
'H
?
'
Figure 1. Structural formula and atomic numbering scheme of FA. [sp,ap] rotamer is given with reference to the axes of inertia.
et al.5 This pioneering study suggested the trans-position of a bond and the conformation of a formyl moiety to have a significant influence upon the force constants. Unfortunately, the 76 harmonic force constants could not be unequivocally extracted from the available data set, and hence a number of simplifying and more or less arbitrary assumptions had to be made in the analysis. While our FA work was in progress, Lundell and co-workers published an elegant and penetrating study into FA and its photochemical decomposition.6-8 Therefore, the aim of the present work is 2-fold. With the help of ab-initio calculations we want for FA in the gas phase (i) to extend the vibrational analysis, interpreting the force field whilst checking the validity of Kuhne's et al.5 assumptions, and (ii) to produce a selfconsistent molecular model that is simultaneously consistent with electron diffraction, microwave, and infrared data. The self-consistent molecular model approach provides a view on
0022-365419512099-8589$09.00/0 0 1995 American Chemical Society
8590 J. Phys. Chem., Vol. 99, No. 21, 1995
Wu et al.
5.00 15.00 25,OO 35.0 Figure 2. Experimental leveled intensities,Z(s), with final backgrounds, B(s), for FA.
the molecule that agrees with all gas-phase data available at the present time and has proved useful in a growing number of cases9-I6 in understanding the chemical reactivity. Experimental Section Following a slightly adapted version of the method of Muramatsu et al.,17formic anhydride was synthesized according to eq 1: 2HCOOH
+ C6H, -N=C=N-C,H,
-.
HCO-0-CHO C6H,,-NH-CO-NH-C,H,
+ (1)
A solution of 3 mL (78 "01) of formic acid in 20 mL of dry ether and a solution of 10.3 g (50 "01) of N,Kdicyclohexylcarbodiimide in 38 mL of dry ether were mixed and stirred at -10 "C for 3 h. Note that we used less than the stoichiometric amount of formic acid in order to avoid any excess of acid, because the decomposition of formic anhydride into formic acid and carbon monoxide may be catalyzed by acid.I8 In the beginning some evolution of CO was observed, while later N,N-dicyclohexylurea precipitated. The latter was filtered off, and the ether was removed by pumping the filtrate
Figure 3. Experimental (0) and theoretical (-) sM(s) curve for FA.
at -10 "C. From the residue, pure formic anhydride was obtained by distillation, bp 24 "C/20 " H g . The compound showed in the IH-NMR spectrum (CDCl3 solution, tetramethylsilane as internal standard; room temperature) only one sharp singlet at 6 = 8.75 ppm, proving its p ~ r i t y . ' ~ Electron diffraction data of freshly prepared formic anhydride samples were recorded photographically on the Antwerpen diffraction unit manufactured by Technische Dienst, TPD-TNO, Delft, The Netherlands. Due to the thermal instability of the compound, the small-portion technique20 was used. While keeping the storage vessel at - 10 "C, a small amount of formic anhydride was condensed into a glass tube with the help of liquid nitrogen and sealed. Then the glass tube was warmed to just below room temperature (- 18 "C) and kept at that temperature for less than 7 min, which allowed sufficient formic anhydride to vaporize to make one to two exposures. Then a new portion of anhydride was condensed in, after the previous one had been removed completely. During the experiments the nozzle was kept at 300 K. An accelerating voltage of 60 kV, stabilized within 0.01% during the exposures, was employed. The electron wavelength was calibrated against the known CC bond length of benzene,21 resulting in R = 0.048712(3) A. Four, three, and three plates (Kodak Electron Image) were selected from recordings at the nozzle-to-plate distances of 199.97(2), 350.13(2), and 599.75(2) mm, respectively. Optical densities were measured on a modified, microprocessor-controlled, rotating ELSCAN E-2500 microdensitometer.22 Optical density values were converted to intensities using the one-hit model of Foster.23 Coherent scattering factors were taken from Bonham et al.,24 and incoherent scattering factors from Tavard et al.25 The data were further processed by standard procedures,26 yielding leveled intensities in the following ranges:
60 cm:
3.50 5 s I 12.75 A-'
35 cm:
6.75 I s 5 21.75 k'
20 cm: 13.00 5 s 5 31.25
A-';
all with As = 0.25 A-'
Leveled intensities with final backgrounds and the combined sM(s) curve are shown in Figures 2 and 3, respectively. Gas phase infrared spectra between 3500-400 cm-' were recorded
J. Phys. Chem., Vol. 99, No. 21, 1995 8591
Formic Anhydride in the Gas Phase
TABLE 1: Ab-Initio Optimized Geometries @,-Type)of the Planar Conformations of FA (Bond Distances in Angstroms, Angles in Decimal Degrees) [sp,ap] form; C, symm
[ap,apl form; C L symm
[sp,spl form; CzVsymm
parameter
4-21G
6-31G
6-31G**
4-21G
6-31G
6-31G**
4-21G
6-31G
6-31G**
0(1)-C(2) o(1)-c(5) c(2)-0(3) c(2)-~(4) C(5)-0(6) C(5)-H(7) C(2)-O( 1)-C(5) 0(1)-C(2)-0(3) O( l)-C(2)-H(4) 0(3)-C(2)-H(4) O( 1)-C(5)-0(6) O( l)-C(5)-H(7) 0(6)-C(5)-H(7) 0(3)-C(2)-0( 1)-C(5) H(4)-C(2)-0( l)-C(5) 0(6)-C(5)-0( 1)-C(2) H(7)-C(5)-0(1)-C(2) - E (hartrees) AE (kcaymol) dipole (D) largest residual force (mdyn)
1.372 1.393 1.197 1.074 1.188 1.074 121.42 124.23 109.21 126.56 120.83 112.78 126.39 0.00 180.00 180.00 0.00 300.750 0.00 2.15 0.0001
1.366 1.385 1.200 1.080 1.191 1.082 123.41 124.31 109.78 125.91 120.47 114.03 125.50 0.00 180.00 180.00 0.00 301.322 0.00 2.16 0.0009
1.343 1.363 1.177 1.088 1.171 1.086 120.05 125.56 109.20 125.24 120.37 113.64 125.99 0.00 180.00 180.00 0.00 301.494 0.00 2.04 0.0001
1.383 1.383 1.189 1.075 1.189 1.075 127.51 126.33 107.32 126.35 126.33 107.32 126.35
1.379 1.379 1.193 1.081 1.193 1.081 129.24 126.40 107.92 125.68 126.40 107.92 125.68 0.00 180.00 0.00 180.00 301.319 1.56 4.27 0.0005
1.358 1.358 1.169 1.089 1.169 1.089 124.73 127.26 107.44 125.29 127.26 107.44 125.29 0.00 180.00 0.00 180.00 301.489 3.22 3.92 0.0007
1.377 1.377 1.187 1.080 1.187 1.080 121.93 122.17 113.07 124.76 122.17 113.07 124.76 180.00 0.00 180.00 0.00 300.739 7.43 4.48 0.0003
1.371 1.37 1 1.191 1.087 1.191 1.087 123.08 121.97 114.05 123.97 121.97 114.05 123.97 180.00 0.00 180.00 0.00 301.312 6.41 4.76 0.0004
1.348 1.348 1.170 1.093 1.170 1.093 120.00 122.01 113.81 124.19 122.01 113.81 124.19 180.00 0.00 180.00 0.00 301.486 5.06 3.82 0.0007
at room temperature at a pressure of 5 hPa on a Bruker 113V FTIR spectrometer using a 29 cm gas cell with KBr windows. The comparison with the frequencies observed by Kiihne et al? for the do species in an argon matrix shows a root-mean-square deviation of 5.9 cm-' and a maximum deviation of 10 cm-I. Theoretical Models John and RadomZ7performed ab-initio studies of FA on the STO-3G and 4-31G level. Optimized geometries were calculated by Lundell et alS6at the 6-31G**, MP2/4-31G, and MP2/ 6-31G** level and energies up to the MP4/6-31G**NP2/631G** level. Nevertheless, for our purpose additional calculations on the 4-21G and 6-31G** level are necessary. For example, the 4-21G basis set is still the only one for which the required empirical corrections are available, to convert the ab-initio equilibrium re geometries into rg geometries. Furthermore, scaled force fields, not given in ref 6, are necessary to provide the thermal parameters for the electron diffraction analysis. In this work we used Pulay's gradient meth~d,~*-~O the program BRABO?' and the 4-21G,326-31G, and 6-31G** basis sets33,34to calculate optimized geometries and force fields of the [sp,ap], [sp,sp], and [ap,ap] forms. We also searched for nonplanar energy minimum conformers, but none were found. Thus, in the remainder only planar forms will be considered. The results of the calculations are given in Table 1. Comparison of the 6-31G** data of Table 1 with those of ref 6 shows differences in bond lengths up to 0.006 A, in angles up to 0.2", and in energies up to 0.07 kcal mol-'. They are probably due to differences in the convergence criteria used. In fact, the differences support the belief stated by S ~ h a f e that r~~ when optimization is continued until the largest residual force on any atom is less than mdyn, bond lengths are converged to within 0.005 A and valence angles to within a few tenths of a degree. Concerning the energy difference E(sp,sp) - E(sp,ap), the various basis sets arrive at 0.65 (4-21G), 3.22 (6-31G**), and 2.00 kcal mol-' (MP4/6-31G**/MP2/6-31G**). Below (Constrained Least-Squares Refinements section), we will show that the [sp,sp] form is not detectable in the gas phase at room temperature, and hence [sp,sp] should be at least 1.4 kcal mol-' higher than E(sp,ap). Furthermore, the topomerization from the [sp,ap] form with 91= 0" and 9 2 = 180" to the other with 91 = 180" and 9 2 = 0" via the energetically least demanding
0.00 180.00 0.00 180.00 300.749 0.65 4.05 0.0004
pathway (Le. via the [sp,sp] form) proceeds via a calculated barrier of 4.0 (4-21G), 4.7 (6-31G**), or 4.8 kcal mol-' (MP2/ 6-31G**) (see Figure 4). A dynamic NMR inve~tigation'~ in solution at -180 "C gave an experimental barrier of 4.3(2) kcal/ mol. Turning to geometries, the different basis sets yield, as expected, differences in the numerical values. More important, however, is the great similarity in the geometrical trends. This is even more gratifying, because some parameters (e.g. C(1)O(5) and most valence angles) are strongly conformation dependent. Considering our purposes, there is at this point no compelling preference for a particular basis set. Further inspection of the [sp,ap] geometry shows (i) a large C(2)-O( 1)-C(5) angle, suggesting a high sp2 character of O(l), and (ii) a significant differentiation in the bond lengths of the O=C-0-C=O moiety, indicating the high relative importance of resonance hybrid b over c (see Figure 5). An intramolecular 0(3)...H(7) interaction has been suggested2as one of the causes of the low energy of the [sp,ap] form. The importance of hybrid b supports this view as do the values of some interaction force constants (see below). Nevertheless, the H(7). O(3) distance (2.11 A) is too long and the C(5)-H(7)..O(3) angle (109") too small to consider the interaction as a true hydrogen bond.36 Vibrational Spectroscopy Using the 4-21G and the 6-31G** basis sets, we calculated two harmonic quadratic force fields of the [sp,ap] form of FA by applying a two-sided curvilinear distortion32to each internal coordinate from its equilibrium geometry. Displacements of kO.01 A for bond lengths, k0.05rad for valence angles, and 0.5 rad for torsion angles were used. For each of these distorted geometries the dipole moments and forces on the internal coordinates were determined. Force constants, Fu, follow from F . .= 'I
@j
(si - Ai) - a,(si + Ai) 2Ai
(2)
in which mj denotes the force acting along the internal coordinate % and Ai is the displacement along qi. It is wellknown that, partly due to neglect of electron correlation and partly due to basis set truncation, ab-initio SCF methods systematically overestimate the force constants. Even an MP2/ 6-31G** force field, if unscaled, leads6 to a high root-meansquare deviation, e.g. 95 cm-' between experimental and
Wu et al.
8592 J. Phys. Chem., Vol. 99, No. 21, I995 14
12 10
c
E
$
s
8
g6
a
4
2
0
torsion angle
torsion angle p
-
-
(p
Figure 4. Rotation barriers for some rotation pathways calculated using the 4-21G basis (left) and the 6-31G** basis (right): (0)P I ,0 and ~ 2 0, 180"; (+) v ; ~= 0" and ~ 2 0, 180'; (B) PI = 180" and rp2, 0 180".
-
b
II
-
180°,
C -
Figure 5. Resonance hybrids of the [sp,ap] form of FA.
TABLE 3: Definition of Groups of Symmetry Coordinates
TABLE 2: Definitions of Symmetry Coordinates Si in Terms of Internal coordinate^^^
Si Used in the Scaling of the Force Fields, Together with the Result of the Scaling Procedure
~
specification"
symmetry species
S1 = r(1,2) S2 = r( 1 3 ) S3 = r(2,3) S5 = r(5,6) S4 = r(2,4) S6 = r(5.7) S7 = 28( 1,2,3) - 8( 1,2,4) e(3,2,4) S8 = 0(1,2,4) - 8(3,2,4) S9 = 28(1,5,6) - 8(1,5,7) e(6m s i 0 = e(i,5,7) - e(6,5,7) s i 1 = e(2,is) S12 = ~(4,1,3,2)
A' A' A' A' A' A' A'
S13 = ~(7,1,6,5)
A"
+ +
A" A"
S14 = ~(5,1,2,3) ~(5,1,2,4) S15 = ~(2,1,5,6) ~(2,1,5,7)
scale factors
assignment Y
C(2)-0(1)
v C(5)-O(1) C(2)=0(3) v C(5)=0(6) v C(2)-H(4) v C(5)-H(7) 6 0=C(2)-H bending Y
A' A'
er0=C(2)-H
A' A' A"
er0=C(5)-H
symmetry coordinates Si"
4-21G
6-31G**
1 2 3 4
S1,S2 s3.s S4,S6 S7, S8, S9, S10, S11, S12, S13, S14, S15
0.824 0.886 0.788 0.800
0.691 0.760 0.796 0.809
performanceb
bending 6 0=C(5)-H bending
root-mean-square deviation (cm-I) maximum deviation (cm-I)
bending
6 C(2)-0(1)-C(5) bending n C-H(4) out-of-plane bending n C-H(7) out-of-plane bending t 0(1)-C(2) torsion sO(l)-C(5) torsion
a r(ij), bond distance between atoms i and j ; O(ij,k), valence angle ), deformation of atom between atoms i, j , and k; ~ ( i J , k , l out-of-plane i out of j , k J plane; L(ij,k,l), torsion angle between atoms ij,k,l along bond j , k . See Figure 1 for atomic numbering scheme.
calculated IR frequencies of the [sp,ap] conformer. Force constants may be scaled down using the linear scaling formula Fij(scaled) = FV(unscaled)(aiaj)
group
(3)
where aidenotes a scale factor belonging to internal coordinate qi.37.38 The ai values are enumerated, after defining the local symmetry coordinates Si in terms of the internal coordinates qi (see Table Z), by fitting the calculated vibrational frequencies onto assigned experimental gas-phase IR frequencies. The
4-21G
6-31G**
18.2 44.8
6.7 14.1
a See Table 2 for the definition of the symmetry coordinates. Measured as the root-mean-square and maximum deviation between the experimental frequency set (Table 5 ) and the frequencies calculated after the scaling of ab-initio force fields.
number of scale factors ai and the way the Si are distributed over the scale factors groups should reflect the fact that the ai are called into existence to counteract the systematic errors in the computations. If a basis set would have errors similar in magnitude for all atoms and vibration modes, then one a should be sufficient. In this case, as in most cases, one a is not sufficient. With one optimized a = 0.79, an rms deviation of 38.0 cm-' and a maximum deviation of 90.0 cm-' were found between the experimental and 6-3 1G**-calculated frequencies, the values well outside error limits. In a more realistic view the deficiencies of a basis set for stretching constants may be different from those for bending constants, while modes involving CO may differ from those involving CH. Of the possible divisions based upon this reasoning, the division into four scale factor groups (as given in Table 3 ) is not only physically realistic but also proved statistically realistic because it resulted in root-mean-square (rms) and maximum deviations
J. Phys. Chem., Vol. 99, No. 21, 1995 8593
Formic Anhydride in the Gas Phase
TABLE 4: Scaled 6-31G** Force Constants ( x 100, in mdyn .klor mdyn rad-') Based on Symmetry Coordinates Defined in Table 2 S, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6
I 8 9 10 11
12 13 14 15
491 52 119 16 -16 -10 23 -31 -10 3 39 0 0 0 0
449 -26 -5 119 10 -2 0 28 -29 43 0 0 0 0
1309 30 14 3 26 21 9 -6
6 0 0 0 0
475 3
0 -9 -3 2 0 3 0 0 0 0
1360 25 6 -4 20 26 15 0 0 0 0
484
-1 0
-1 -1 -12 0 0 0 0
122 1 -6 -2 12 0 0 0 0
(Amax)between experimental and 6-3 1G**-calculated frequencies that are close to the rms and Amaxvalues found between the two experimental frequency sets (see the Experimental Section). Although good agreement between the experimental and the 4-21G-calculated frequencies can be found, we were not able to obtain an acceptable agreement using a scale factor group division which we considered physically acceptable in the above sense. Therefore, in the following we will use the 6-31G** basis set as the set of choice to calculate the vibrational properties of FA. The scaled 6-31G** force field is presented in Table 4. Its performance in reproducing the gas-phase vibrational spectrum of FA shows an rms deviation of 6.7 cm-' and a largest discrepancy of 14.1 cm-I. In their force field derivation Kuhne et al.5 used the following assumptions. First, interaction constants are 0 unless the pair of internal coordinates involve at least one common nucleus. Second, the force constants associated with the bending coordinates of the angles around C(2) and C(5) are equal, e.g. F(1,7) = F(2,9), F(7,8) = F(9,10), etc. Inspection of Table 4 reveals the essential validity of the first assumption, except for the small but significant stretch-stretch interaction between C(2)=0(3) and the nonadjoining C(5)-O( 1) (F(2,3) = -0.26 mdyn A-'). Significant exceptions to the second assumption are the bend-bend interaction pair F(7,ll) = 0.12; F(9,ll) = 0 (describing the interaction between the C(2)-O( 1)-C(5) angle bending with the bendings in the O=CH groups) and to a lesser extent the pairs F(1,7) f F(2,9) and F(3,7) f F(5,9), describing the O=C-0 bendings with the adjoining C-0 and C=O stretches. The force field given in Table 4 has the advantage over the previous ones5 in that it is complete and intemally consistent. Inspection shows the following. First, in all cases the longer bond length has the smaller diagonal force constant (C(5)0(1) > C(2)-0(1) and F(2,2) < F(1,l); C(2)=0(3) > C(5)=0(6) and F(3,3) < F(5,5); C(2)-H(4) > C(5)-H(7) and F(4,4) < F(6,6)). Second, the increased double-bond character of 0(1)-C(2) compared to 0(1)-C(5) (see Figure 5) predicts the angular stiffness sequences O( l)-C(2)=0(3) > O(l)-C(5)=0(6), O( 1)-C(2)-H(4) > O( 1)-C(5)-H(7), and 0(3)=C(2)H4 < 0(6)=C(5)-H(7), from which follows F(7,7) > F(9,9), F(8,8) > F(10,10), and F(12,12) < F(13,13). Third, simple resonance arguments, particularly the pulsed vibrations of the C=O group^,^^,^ rationalize most signs and relative magnitudes of interaction force constants. We represent the [sp,ap] form of FA by the combination of resonance hybrids shown in Figure 5. If now, for example, C(2)=0(3) is lengthened, then hybrid b will be strongly favored, leading to great changes in stiffness in the 0(3)=C(2)-0( l)-C(5)=0(6) moiety and much smaller ones in lengths and angles involving C(2)-H(4) and C(5)-
62 -2 1 -6 0 0 0 0
110 2 0 0 0 0 0
61 -4 0 0 0
116 0 0 0
0
0
43 -1 -1 0
46 1 2
3.25 -1
2.34
H(7). It may be seen that 0(1)-C(2) stiffens considerably, and hence F(1,3) must be and is positive and large. In general stretch-stretch constants between bonds sharing a common nucleus are positive and diminish in the order C=O > C-0 > C-H, and thus F(1,3) > F(1,2) > F(3,4) > F(1,4), as is calculated. Similarly, one expects and finds F(2,5) > F(1,2) > F(5,6) > F(2,6) and even F(1,4) > F(2,6), the latter because of the higher stiffness of O( 1)-C(2) compared to O( l)-C(5). The reasoning is easily extended to stretch-stretch constants of bonds without a common nucleus. For example, distortion of C(2)=0(3) softens C(5)-0(1), but stiffens C(5)=0(6) and to a much lesser extent also C(5)-H(7). Hence, F(2,3) should be and is significantly negative, while F(3,5) and F(3,6) are positive. Fourth, stretch-bend interactions are often larger than stretch-stretch interaction constants, because angle stiffnesses are easier to change than bond stiffnesses. Exploiting the same arguments as above, one can see that distortion of C(2)=0(3) gives more double-bond character to O( 1)-C(2), which stiffens the angles 0(1)-C(2)-H(4) and O(l)-C(2)-0(3), and thus F(3,8) and F(3,7) should be large positive. The same distortion of C(2)=0(3) gives more single-bond character to O( l)-C(5), which softens the angle 0(1)-C(5)-H(7) and stiffens O(1)C(5)=0(6) (that is, C(5)=0(6) gains more double-bond character than C(5)-0(1) loses). Thus, F(3,lO) is negative and F(3,9) positive. When 0(1)-C(2) distorts, it acquires more single-bond character, giving C(2)=0(3) as well as O( 1)-C(5) more double-bond character. Consequently, the angles O( 1)C(2)-H(4) and O(l)-C(5)=0(6) soften (C(5)=0(6) loses more than C(5)-0(1) gains), but O( 1)-C(5)-H(7) stiffens. Thus, F(1,8) andF(1,9) are negative with IF(1,8)1 > IF(1,9)1, whereas F( 1,lO) is positive. Fifth, despite the long H(7). * O(3) distance, a significant interaction is found between the C(5)-H(7) stretch and the 0(1)-C(2)=0(3) angle bending (F(6,7) = -0.08, being 6% of F(7,7)). Moreover, it behaves similarly to the C(2)=0(3) stretch/O(l)-C(5)-H(7) rocking interaction (F(3,lO) = -0.06), but differently from the C(2)-H(4)/0( l)-C(5)=0(6) bend interaction (F(4,9) = 0.02). We take this as manifestations of an H(7). * O(3) interaction. We employed the standard Wilson GF method4I to calculate the L-I matrix as well as the derivatives dq$dQi, with Qi representing a vibrational normal coordinate. The latter derivatives can be used to calculate dp/dQi and absolute IR band intensities. These in turn nicely complement the frequency assignments, which we will now discuss (Table 5). The assignments of v(C(5)-H(7)) to V I = 2964 cm-' and v(C(2)H(4)) to v2 = 2948 cm-'-interchanged in ref 5-are strongly supported by the observed and calculated intensity sequence. Note that the interaction force constant F(4,6) = 0. It follows that the relatively small splitting of these CH stretching modes
8594 J. Phys. Chem., Vol. 99, No. 21, 1995
Wu et al.
TABLE 5: Comparison between 6-31G** Calculated and Experimental IR Data and Assignments (See Table 2 for Definition of S;) Vi
1 2 3 4 5
6 7
exp cm-I
calc cm-I
exp int'
calc intd
assignment
assignment
2964 2948 1822 1767 1389 1370 1099
2970 2942 1817 1773 1386 1375 1105 1060 1054 99 1 770 525 255 228 93
m to w m
1.o 3.6 20.9 54.8 0.2 0.1 78.3 0.01 0.8 17.9 0.1 0.7 1.42 2.7 4.0
S6(98) S4(98) S5(75), S3(12) S3(72), S5(12) S8(74), SlO(18) S10(78), S8(20) S1(58), S2(20) S 12(51), S 13(48) S13(53), S12(46) S2(41), S9(33) S7(52), S2(31) S9(56), Sl(22) S11(80), S7(13) S14(85), S15(12) S15(74), S14(22)
C(5)-H(7) stretch C(2)-H4 stretch C(5)=0(6) stretch C(2)=0(3) stretch 0=C(2)-H rocking 0=C(5)-H rocking "C(2)-0(1) stretch' C-H out-of-plane; asym C-H out-of-plane; sym skeletal 0=C(2)-H bending 0=C(5)-H bending C(2)-O( 1)-C(5) bending 0(1)-C(2) torsion O( 1)-C(5) torsion
8 9 10 11 12 13 14
15
998 176 539 260" 230" (85Ib
S
vs W W
vvs
S
W
vw W
m
Taken from ref 5 . Derived by Vaccani et al.4 from microwave spectra; not used in the scaling process. m, medium; s, strong; w, weak; vs, very strong; vvs, very very strong; vw, very weak. lo6 c d m o l .
is entirely due to the different chemical environments of H(4) and H(7) in the [sp,ap] form. The much larger splitting of the C=O stretching modes (Av(obs) = 55 cm-I) is due to coupling (F(3,5) = 0.14), with the in-phase mode absorbing at the higher frequency and the out-of-phase mode at the lower frequency. This situation is unusual in the infrared, but has been noted before.39 Again, the calculated intensity sequence matches the observed one; that is, the low-frequency absorption is the stronger one. In this, formic anhydride contrasts with acetic anhydride and most other open chain anhydrides. The C(5)=0(6) stretching is the highest contributor to the high-frequency C=O mode, and the C(5)=0(6) bond is almost parallel to the a-axis of the inertia frame (see Figure 1). In agreement with this, the band v3 = 1822 cm-' resembles a typical A-band absorption. On the other hand, C(2)=0(3), being the largest contributor to the low-frequency mode, is almost parallel to the b-axis, and the band v4 = 1767 cm-' resembles a B-type absorption. Compared to ref 5, we interchanged the assignments of the strong bands v7 and v10, again in line with the sequence of calculated and observed intensities. Both bands originate as C - 0 modes, but are clearly different from each other. The one at v7 = 1099 cm-I may be described as the 0(1)-C(2) stretch, but is seriously mixed with the 0(1)-C(5) stretch. Consequently, v7 lacks PQR separation, although O( 1)-C(2) is quasi-parallel to the a-axis. The other band at Y I O = 998 cm-' is more appropriately named a skeletal vibration because of its low degree of localization. The origin of the v7, v10 difference is easily traced to the different bond orders of the two C - 0 bonds (Figure 5). Interestingly, ~ 1 calculated 5 at 93 cm-' matches very closely to the value 85(8) cm-' derived by Vaccani et a1.4 from microwave spectra. Finally, the other assignments of Table 5 agree with the previous ones5 Combination of Electron Diffraction and Microwave Data Rotational constants Bo for the [sp,ap] form of FA are available from the microwave data of Vaccani et aL4 The scaled 6-31G** force field was used to calculate B, - Bo corrections, which account for the vibration-rotation interactions. Centrifugal distortions and corrections from electronic contributions were ignored. With these B, - Bo c o r r e c t i ~ n sthe ~ ~Bo values can be converted to B, (close to Ba0 values), needed in the joint microwave-electron diffraction analysis. The results are given in Table 6. Now the microwave data are brought to rao basis; one needs to bring the electron diffraction r, distances to the
TABLE 6: Experimental Bo Values, the Corrections Required for Harmonic Vibration-Rotation Interactions, B, - Bo, and the Resulting B, Values to Be Compared with Ba0 Values Obtained from the Joint Microwave-Electron Diffraction Analysie rot const exp Bo (cm-I) A B C
0.729 817 0.108 263 0.094 378
Bz - Bo (cm-')
B, (cm-I)
Eao(cm-I)
0.003 109(466) 0.732 926(466) 0.733 154 0.108 259(20) 0.108 270 0.094 344(20) 0.094 339
-0.000 004(20) -0.000 034(20)
a Bao values follow from set (iii); see Constrained Least-Squares Refinements section. Estimated errors are given in parentheses.
same basis by eliminating vibrational effects, Le. by applying shrinkage corrections, r, - rao. These corrections are well described in ref 42 and are given by
(4)
I@ represents the vibrational amplitude perpendicular to the internuclear distance. Its value can be calculated either along with vibrational amplitudes U from the harmonic force field41-43 for semirigid distances or from the formula of Tokue et al.44 for distances affected by large torsional amplitudes. A distance is considered affected by large-amplitude motion if the torsional amplitude 6 = (kT/J)"* =- 20°, withfbeing the torsional force c0nstant.4~3~~ Judged by this criterion, distances involving rotation around 0(1)-C(2) (6 = 20.4') as well as those involving the torsion around 0(1)-C(5) (6 = 24.1') may just exhibit large-amplitude motion. Later we found that the leastsquares refinements led to insignificant differences in the geometry and R indices of agreement, irrespective of whether we used shrinkage corrections based on the semirigid model or on the large-amplitude model employing Tokue's'"' formula with Vz = 4.7 kcdmol. Therefore, we show in Table 7 only the 6-31G**-calculated values of U and f?, together with the semirigid shrinkages (eq 4). In order to combine the diffraction intensities with the microwave rotational constants, a proper weighting scheme is needed. Weights for the diffraction data were chosen proportional to s and scaled down at the end of an s intervalsz6 Rotational B, data were given a weight w = k k 2 relative to a diffraction data point; k is commonly chosen as while 6 (the estimated error) is taken as 15% of the B, - Bo correction, or as 20 x for very small B, - Bo correction terms, such as those associated here with B and C rotational constants. These choices led to a weight of 47 for the A , 2.5 x lo4 for the B, and 2.5 x lo4 for the C rotational constant.
J. Phys. Chem., Vol. 99, No. 21, 1995 8595
Formic Anhydride in the Gas Phase TABLE 7: Calculated (6-31G**) Vibrational Amplitudes U, Perpendicular Amplitudes KO, and Shrinkage Corrections, KO - vz/r (A x 1000) atom pair
U
KO
KO - uz/r
0(1)-C(2) 0(1)-C(5) C(2)-0(3) C(5)-0(6) C(2)-H(4) C(5)-H(7) O(l)..O(3) O( 1). * eH(4) 0(1)-O(6) 0(1).**H(7) (32)s. C(5) C(2). * O ( 6 ) C(2). sH(7) 0(3).**H(4) O(3). * C(5) O(3). O ( 6 ) O(3). sH(7) H(4). C(5) H(4) * O(6) H(4) * sH(7) O(6). sH(7)
48 50 37 37 79 78 53 99 54 99 63 61 134 92 90 88 I65 100 107 148 91
4 3 3 9 19 27 2 15 3 19
2 1 2 7 13 21 0 10 1 14 0 0 8 9 -1 -2 8 4 2 8 23
---
2 1 15 13 3 0 20 7 5 14 27
Constrained Least-Squares Refinements The radial distribution function, given in Figure 6, shows C(2).*.0(5), C(2)...0(6), and 0(3).*.0(6) peaks of equal intensity at 2.68, 3.38, and 3.85 A, respectively. This strongly indicates the sole presence of the [sp,ap] form. The absence of the [ap,ap] form follows from the absence of a peak near 4.5 A, while any significant amount of [sp,sp] form would have significantly decreased the intensities of the 3.38 and 3.85 A peaks and increased the one near 2.7-2.8 A. Moreover, the
experimental (11 = 1.813 D3)and calculated dipole moments (Table 1) can only be made to agree, if [sp,ap] is the unique gas-phase conformation. Furthermore, some distances show considerable overlap. In the following least-squares refinements, external constraints must be utilized. The thermal parameters were kept fixed at their calculated values, the accuracy of which surpasses the accuracy that would emerge from a least-squares analysis of the electron diffraction data. Estimated from the agreement between calculated and experimental IR frequencies, the force field (Table 4) has an accuracy of about 1%, and thus, the derived thermal parameters (Table 7) have the same accuracy. Only one overall thermal parameter scale factor, k(U), was refined. The k(U) corrects for the difference (if any) between the actual temperature of the diffracting molecules and the temperature taken in the calculations (300 K). Conversely, when U parameters are fixed to the calculated values, k( U) together with the indices of resolution measures the quality of the ED data set. The closer to unity these indicator parameters are, the better the data set. Furthermore, geometrically constrained models of FA were constructed as defined in Table 8. Five sets of constraints were tested: (i) Those directly taken from the re(6-31G**) values (Table 1). Want of appropriate correction procedures prevents obtaining the 6-31G** constraints at the rao level. (ii) Those directly taken from the re(MP2/6-31G**) values6 Again, want of appropriate correction procedures prevents obtaining MP2/6-31G** constraints at the rao level. (iii) Those after correction of re(4-21G) values to rg values using additive corrections9 and subsequently converting rg to
Figure 6. Experimental radial distribution function of FA at 300 K (upper). A damping factor of exp(-0.0004s2) was used. Important distances are indicated by vertical bars of a length weighted upon nZ,Z,. The difference curve (lower) is given as experimental - theoretical.
Wu et al.
8596 J. Phys. Chem., Vol. 99, No. 21, 1995
TABLE 8: Model Construction with Definition of Refinable Parameters and Values of Constraints A Used in Sets (See Text) O(l)-C(2) 0(1)-C(5) C(2)=0(3) C(5)=0(6) C(2)-H(4) C(5)-H(7)
(4)
A1 A2 (A) A3 (A) A4 (deg) A5 (deg) VI (de@ yl2(deg)
rl rl r2 r2 r3 r3
C(2)-O( 1)-C(5) 0(1)-C(2)=0(3) O( l)-C(2)-H(4) O(l)-C(5)=0(6) O( 1)-C(5)-H(7) 0(3)=C(2)-0(1)-C(5) 0(6)=C(5)-0(1)-C(2)
+ A1 + A2 + A3
01 02 03 02 03 q1
+ A4 + A5
~ ) 2
set (ii)
set (iii)
set (iv)
set (v)
$0.020 -0.006 -0.002 -5.2 $4.4
+0.019 -0.006 -0.002 -6.2 +5.0 0 180
+0.022 -0.014 -0.008 -3.4 +3.6 0 180
+0.020 -0.013 -0.008 -3.4 +3.6 0 180
+0.021 -0.009 0.000 -3.4 +3.6 0 180
0
rao eeom re eeom
rao geom
~
set (i)
180
TABLE 11: Best Fitting Geometry of Formic Anhydride in Angstroms and Degrees" C(2)=0(3) C(5)=0(6) C(2)-0(1) C(5)-0(1) C(2)-H(4) C(5)-H(7)
1.193 1.180 1.374 1.394 1.086 1.078
1.196 1,189 1.378 1.397 1.105 1.105
C(2)-0(1)-C(5) 0(3)=C(2)-0( 1) 0(6)=C(5)-0(1) H(4)-C(2)-0(1) H(7)-C(5)-0(1) H(4)-C(2)=0(3) H(7)-C(5)=0(6) 0(3)=C(2)-0(1)-C(5) 0(6)=C(5)-0(1)-C(2)
118.6 124.2 120.8 112.7 116.3 123.1 122.9 0.0 180.0
For accuracy, see text.
e'= 75 O
V( Pp')= 0,0183
TABLE 9: Results of Least-Squares Refinements of Constrained Models Defined in Table 8 set (i)
set (ii)
set (iii)
set (iv)
set (v)
Geometrical Parameters; ran-Type 1.375(1) 1.376(1) 1.373(1) 1.374(1) 1.373(1) 1.190(1) 1.191(1) 1.194(1) 1.193(1) 1.191(1) 1.087(10) 1.090(10) 1.085(10) 1.086(10) 1.084(10) 117.8(1) 11731) 118.6(1) 118.6(1) 118.5(1) 125.1(1) 125.6(1) 124.2(1) 124.2(1) 124.3(1) 113.3(1) 113.5(1) 112.6(1) 112.7(1) 112.4(1)
rl r2 r3 81 82 e3
1.02(5)
k( v)
kl (20 cm) k2 (35 cm) k3 (60 cm) R(ED) R(MW) R (total) a
Scale Factor on Amplitudes 1.02(5) 1.01(5) 1.01(5)
0.78(6) 0.96(3) 0.97(2)
Indices of Resolution 0.79(6) 0.79(6) 0.95(3) 0.96(3) 0.97(2) 0.97(2)
1.82 0.14 1.04
Disagreement FactoP 1.90 1.73 0.14 0.11 1.08 0.98
Defined as R =
[&(lobs
0.79(6) 0.96(3) 0.97(1)
2.801
-0.40
p= p'= 0.52D
-0.40
e= 1340
#=.ea 0 V( p p')== 0.043
1.01(6) 0.78(6) 0.95(3) 0.97(1)
H
0.11
1.73 0.11 0.98
1.75 0.11 0.99
0.11 0.11
2.341
-0.45
p=O.SSD
- I c a ~ c ) 2 / ~ w l , x~ ~100%. ]~'2
/A'= 0.55D
e-3010 e'=670
TABLE 10: Correlation Coefficients ( x 100) among Parameters Belonging to Set (ivy rl
r2
r3
91
02
03
100 -39 100 -42 -48 100 -47 -8 60 100 -47 -23 32 -18 100 -2 0 03 1 -1 0 100 10 -15 2 -3 3 0 k( v) 44 0 -46 -34 -20 -1 kl 33 -4 -30 -24 -13 -1 k2 0 3 -5 -3 0 0 k3
k(U)
kl
V(pp' p-0.032 k2
k3
0.
rl r2 r3 01 02
a
-0.55
H
0.1 1
100
35 37 60
100 32 100 22 22 100
See Tables 8 and 9 for definition of parameters.
rao values. The conversion of rg to rao uses rao = rg - KO, values taken from Table 7. with (iv) Those after correction of re(4-21G) values to rg using a regression type correction4' and again subsequent conversion of r, to rao values. (v) Those directly taken from the re(4-21G) values (Table 1). Their performance is to be compared with that of set (i). Table 8 summarizes the values used in the sets (i) through (v), while Table 9 shows the least-squares results concerning disagreement factors, geometrical parameters, and other refinables. To discriminate among the sets, we compare the ratio of the R values of two sets with tabulated48values of Seep, n - p , a ) ,
Figure 7. Charges on atoms, partial dipole moments of O=CH-0moieties, and some distances in FA conformers. They, y', and V@$) are in relative units. in which p denotes the number of refinables (degrees of freedom), n the number of data points involved, and a the chosen level of significance. If the R-value ratio is larger than B, then one rejects the hypothesis at the 100a% significance level that the molecular models represented by the two sets are statistically equal. Performing the tests at the 5% level of significance, it was noted that sets (iii)-(v) are equal, but that perhaps surprisingly, sets (i) and (ii) can be rejected. At the 1% level of significance all sets perform equally well. Even though statistically insignificant, we will concentrate on set (iv) because of its performance considering all indicators (indices of resolution, esd's on rotational and geometrical parameters, scale factor k(U)). No large esd's (Table 9) nor large correlation coefficients among parameters (Table 10) were encountered. Nevertheless,
J. Phys. Chem., Vol. 99, No. 21, 1995 8597
Formic Anhydride in the Gas Phase
TrPnsition State
Figure 8. Thermal decomposition of FA with proposed transition state.
to correctly ascertain the accuracy of the obtained geometries poses a problem, because we do not know how possible systematic errors in the re-to-rg corrections or in the vibrational amplitudes are propagated in molecular orbital constrained electron diffraction analyses, such as this. It is believed that an accuracy estimate may be obtained as f01lows.'~~'~ A leastsquares run is made in which the constraints are added to the list of refinable parameters of the converged model. If these refined constraints are not significantly different from their input values, their least-squares esd values multiplied by 3 are taken as a realistic estimate of the accuracy of the individual bond lengths and angles. This led to accuracies of &0.008 and 0.015 8, for individual CO and CH bond lengths, respectively. Individual OCO valence angles are estimated to have an accuracy of &OS0, and individual HCO angles one of &lo. Table 11 summarizes the geometry of gaseous formic anhydride (set (iv)). Self-consistent Molecular Model It has been shown that in the gas phase at room temperature formic anhydride exists in the planar [sp,ap] conformation, thus resolving the discrepancy between the m i c r ~ w a v e ~and .~ a previous electron diffraction study.2 Apart from this, as well as from the improved IR assignments and the complete force field with physically acceptable diagonal as well as off-diagonal constants, the results obtained also corroborate the rationalization proposed by John and RadomZ7 of the energy sequence E(ap,ap) > E(sp,sp) > E(sp,ap) and may be further extended to rationalize some of the thermochemistry. Figure 7 shows for each conformer the calculated charges on the atoms, the partial dipole vectors for the O=CHO moieties, their distances, and the nonbonded distances, which govern the steric hindrance. The [ap,ap] form has a small dipole-dipole repulsion and a large H*..H steric hindrance (actual HH distance of 2.10 8, vs sum of van der Waals radii of 2.4 8,). This apparently makes its energy greater than that of the [sp,sp] form with a larger dipole-dipole repulsion, but no steric hindrance (actual 0. 0 distance of 2.80 8, is equal to the sum of van der Waals radii). The [sp,ap] form shows dipole-dipole attraction together with a small steric hindrance (actual O . * H distance of 2.34 8, vs sum of van der Waals radii of 2.6 A). It follows that only formic anhydride and mixed anhydrides containing the formic moiety can occur in the energetically favorable [sp,ap] conformation. All other acyclic anhydrides including acetic anhydride must occur in another form. We may use this conformational argument together with the formic anhydride force field (Table 4) to rationalize why formic anhydride is thermolabile and acetic anhydride is not. Formic anhydride is k n 0 w n ~ * ~to9 'need ~ little warming to decompose into HCOOH and CO. The molecule has in its reactant state a geometry and electron distribution which strongly resembles resonance hybrid b (Figure 5). That is, H(7) is the most electrophilic H atom, and O(3) the most nucleophilic site (Figure 7). Furthermore, proceeding along the reaction coordinate (see Figure 8) toward the transition state, the bond C(2)=0(3) needs
to acquire more single-bond character and will stretch. The interaction constant F(2,3) = -0.26 mdyd8, (Table 4) shows that this C=O stretch is accompanied by a significant softening of the C(5)-0(1) bond, i.e. the bond that needs to be broken. Furthermore, the transition state (Figure 8) is likely also to resemble resonance hybrid b. Then, Hammonds' principle predicts a small activation energy. Obviously, most of these indicators pointing to a high thermolability of formic anhydride are absent in acetic anhydride. Acknowledgment. C.V.A. acknowledges support as a Senior Research Associate by the Belgian National Science Foundation, N.F.W.O. Financial aid to the laboratory by the Flemish Ministery of Education (Contract Geconcerteerde Actie 8919410) is gratefully acknowledged. This text also presents research results of the Belgian Programme on Interuniversity Attraction Poles initiated by the Belgian State (Prime Minister's Office), Science Policy Programming. Scientific responsibility, however, is assumed by the authors. Supplementary Material Available: Primary electron diffraction data ( 2 pages). Ordering information is given on any current masthead page. References and Notes (1) IUPAC (1974). Rules for the Nomenclature of Organic Chemistry; Pergamon Press: Oxford, 1974; Section E: Stereochemistry, Recommendations. (2) Boogaard, A.; Geise, H. J.; Mijlhoff, F. C. J . Mol. Struct. 1972, 13, 53. (3) Vaccani, S.; Bauder, A.; Giinthard, Hs. H. Chem. Phys. Lett. 1975, 35, 457. (4) Vaccani, S.; Roos, U.; Bauder, A,; Giinthard, Hs. H. Chem. Phys. 1977, 19, 51. (5) Kuhne, H.; Ha, T.-K.; Meyer, R.; Giinthard, Hs. H. J. Mol. Spectrosc. 1979, 77, 251. (6) Lundell, J.; Rasanen, M.; Raaska, T.; Nieminen, J.; Murto, J. J . Phys. Chem. 1993, 97, 4577. (7) Lundell, J.; Rasanen, M.; Latajka, Z. J . Phys. Chem. 1993, 97, 1152. (8) Lundell, J.; Rasanen, M. J . Phys. Chem. 1993, 97, 9657. (9) Geise, H. J.; Pyckhout, W. In Stereochemical Application of Gas Phase Electron Diffraction; Hargittai, I,, Hargittai, M., Eds.; VCH: Deerfield Beach, FL, 1988; Vol. I, Chapter IO. (10) Schafer, L.; Ewbank, J. D.; Siam, K.; Chiu, N. S.; Sellers, H. L. In Stereochemical Application of Gas Phase Electron Diffraction; Hargittai, I., Hargittai, M., Eds.; VCH: Deerfield Beach, FL, 1988; Vol. I, Chapter 9. (11) Pyckhout, W.; Van Alsenoy, C.; Geise, H. J.; Van der Veken, B.; Pieters, G. J. Mol. Struct. 1985, 130, 335. (12) Pyckhout. W.; Van Alsenoy, C.; Geise, H. J.; Van der Veken, B.; Coppens, P.; Tratteberg, M. J . Mol. Struct. 1986, 147, 85. (13) Pyckhout, W.; Horemans, N.; Van Alsenoy, C.; Geise, H. J.; Rankin, D. W. H. J. Mol. Struct. 1987, 156, 315. (14) De Smedt, J.; Vanhouteghem, F.; Van Alsenoy, C.; Geise, H. J.; Van der Veken, B.; Coppens, P. J. Mol. Struct. 1989, 195, 227. (15) Schafer, L. J . Mol. Strucr. (THEOCHEM) 1991, 230, 5. (16) Wang, Y.; De Smedt, J.; Coucke, I.; Van Alsenoy, C.; Geise, H. J. J . Mol. Struct. 1993, 299, 43. (17) Muramatsu, I.; Itoi, M.; Tsuji, M.; Hsgitani, A. Bull. Chem. Soc. Jpn. 1964, 37, 756. (18) Schijf, R.; Scheeren, J. W.; Van Es, A.: Stevens, W. Rec. Trav. Chim. Pays Bas 1965, 84, 594. (19) Noe, E. A.; Raban, M. J . Chem. Soc., Chem. Commun. 1974,479. (20) Haaland, A.; Hammel, A,; Rypdal, K.; Volden, H. V. J. Am. Chem. Soc. 1990, 112, 4547.
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