Ab Initio Study of the Diels-Alder Reaction of Phosphaethene and Phosphaethyne with Butadiene

Debbie C. Mulhearn and Steven M. Bachrach

Department of Chemistry, Northern Illinois University, DeKalb, IL 60115

Originally published in Proceedings of the First Electronic Computational Chemistry Conference - CD-ROM, S. M. Bachrach, W. Hase, D. B. Boyd, S. K. Gray, H. S. Rzepa, Eds., ARInternet:Landover, MD, 1995, Paper 11. Also available at http://www.ijc.com/articles/library/4/.

Abstract

Continuing in our investigations of the pericyclic reactions of phosphaalkenes and phosphaalkynes, we report an ab initio study of the Diels-Alder reaction of phosphaethene and phosphaethyne with butadiene. Limited experimental studies of these reactions indicate that they are quite facile, however, no determination of activation energies or stereoselection has been reported.

We have optimized the structures of the reactants, transition states, and products for Reactions 1-3 at the HF/6-31G* and MP2/6-31G* levels. Single point energy calculations at MP4SDQ/6-31G*//MP2/6-31G* were performed to correct for the underestimation of activation energies at MP2. ZPE correction were made using the HF/6-31G* analytical frequencies scaled by 0.89.

These reaction are exothermic, ranging from -39.0 kcal/mol for Reaction 1 to -43.1 kcal/mol for Reaction 3. The activation energies for all three reactions are small -- Reaction 1, 19.3 kcal/mol; Reaction 2, 13.0 kcal/mol; Reaction 3, 15.50 kcal/mol -- considerably less than their hydrocarbon analogues. The low activation energies are due to the very reactive P=C bond, as evidenced by its high HOMO and low LUMO.

The reaction of phosphaethene display regioselectivity. The orientation with the phosphorus lone pair exo is favored, both kinetically and thermodynamically. This orientation reduces the lone-pair pi-system interaction. The geometry of the TSs shows a twisting of the phosphaethene fragment to minimize this interaction in both TSs. This regioselectivity is similar to that found for the reaction of butadiene with formaldimine.

Topological electron density analysis was used to gauge the bond orders in the TSs. As we have found for a number of pericyclic reactions involving heteroatoms, the TSs examined here display a remarkable degree of synchronicity. Further, bond order appears to be conserved during the course of the reaction.

Introduction

Of current interest for the use of the Diels-Alder reaction is the incorporation of a heteroatom into either the diene or the dienophile, with the hopes of finding new pathways to synthesize heterocyclic molecules. Many examples of using phosphorus as part of the diene have been observed by Mathey. 2H-Phosphole dimerizes to give the endo product or reacts with various ethynes and ethenes the give the bicyclic cycloadduct.¹ , ² , ³ Theoretical studies have also been done on the reaction of unsubstituted aza- and phospha-1,3-butadienes with acetylene and phospholes with acetylene.⁴ Not many Diels-Alder reactions have been attempes where phosphorus is incorporated into the dienophile, mostly due to the instability of the P=C bond. Märkl and coworkers⁵ have reported Diels-Alder reactions where the P=C is part of a ring system, which then reacts with pyrones to form phosphorins, but without isolating a Diels-Alder adduct.

For the most part, the P-C multiple bond needs to be stabilized with bulky substituents in order to react with either electron-rich or electron-poor dienes. Appel and coworkers ⁶ were one of the first to isolate the primary Diels-Alder adduct derived from open-chain phosphaalkenes with 2,3-dimethylbutadiene, as seen in Scheme 1. They have also reported the Diels-Alder reaction using the same set of dienophiles with cyclopentadiene.⁷

Appel's results show that the configuration of the P=C bond is maintained and suggests a concerted pathway. Rösch and Regitz⁸ isolated the Diels-Alder adduct when the dienophile was a phosphaacetylene, as seen in Scheme 2.

Most of the synthetic interest reported for these reactions is the aromatization of the Diels-Alder adduct to obtain functionalized phosphabenzenes. Not much emphasis has been placed on the initial Diels-Alder reaction, besides noting that it occurs with relative ease. In order to better understand how and why the Diels-Alder step can be a useful tool for making various phosphabenzenes, some physical characteristics of the reaction need to be determined.

We examined the prototype Diels-Alder reaction of butadiene with phosphaacetylene and butadiene with phosphaethylene using ab initio calculations. These reactions will be compared to their carbon analogues since no structural or energetic data are available for the phosphorus system. Electron density analysis was also performed to aid in determining the nature of these reactions.

Computational Methods

Ab initio calculations were done for each species involved in the three reactions shown in Scheme 3 using GAUSSIAN 92.¹⁷ Geometry optimizations were performed for the reactants, transition structures, and products at the HF/3-21G*, HF/6-31G*, and MP2(full)/6-31G* levels. The MP4SDQ(full)/6-31G* energies were also determined using the MP2(full)/6-31G* geometries since it is well documented that HF/6-31G* energies overestimate the activation barrier and MP2/6-31G* energies for Diels-Alder reactions underestimate the activation barrier.⁴ , ⁹, ¹⁰, ¹¹ All three transition structures have only one imaginary frequency at HF/6-31G*. The energies for these reactions have been corrected for ZPE's, which have been scaled by 0.89. The structures reported here are the MP2(full)/6-31G* geometries and the energies used for the discussion of these reactions are at MP4(full)/6-31G*//MP2(full)/6-31G*.

Topological analysis of the transition structures and products were performed using EXTREME,¹⁸ from which the bond critical points were located. The electron density of these critical points is given as (r_c). The (r_c) can be related to bond orders with the use of Equation 1.

Equation 1. n(X-Y) = exp[A[(r_c)] - B]]

where,

X-Y A B

C-P¹⁹ 19.628 0.153

C-C²⁰ 6.458 0.252

X-Y	A	B
C-P¹⁹	19.628	0.153
C-C²⁰	6.458	0.252

Scheme 3

Results

For Diels-Alder reactions where the dienophile is phosphaethylene or phosphaacetylene reacting with various dienes, the primary adduct can easily be converted to a functionalized phosphabenzene.⁶ , ⁷, ⁸, ¹², ¹³, ¹⁴ The apparent interest has been on simply producing the primary Diels-Alder adduct and then focusing in on the functionalized phosphabenzenes. For this purpose, confirmation of the Diels-Alder adduct was the only concern, with little mention of geometries or the energy involved. Since little is known concerning the Diels-Alder reaction of phosphaalkenes or phosphaalkynes, we will be comparing our results of Reactions 1-3, seen in Scheme 3, with the corresponding carbon analogues, i.e. butadiene + acetylene or butadiene + ethylene.

Phosphaacetylene + s-gauche-1,3-butadiene

The first Diels-Alder reaction we looked at was that of phosphaacetylene and butadiene. The MP2(full)/6-31G* optimized geometries for the transition structure TS1 and product 1 are drawn in Figure 1. In TS1, the forming P-C bond length is 2.616 Å and the forming C-C bond length is 2.288 Å. These can be compared with the TS for the reaction of acetylene with butadiene which has the forming C-C bond to be 2.198 Å (at HF/6-31G*).¹⁵ In comparison, the longer C-C bond in TS1 is mostly due to the molecule having to accomodate the larger phosphorus atom. The important angles in the TS are those that will show the relative position of the dienophile with respect to the diene, or the angle that the dienophile is approaching the diene. These angles in TS1 are the C2-C1-P angle which is 100.9° and C3-C4-C5 angle which is 101.7°, in agreement with previously published TS geometries of Diels-Alder reactions.⁴

Figure 1 Geometries of 1 and TS1

TS1

The Diels-Alder product, 1-phospha-1,4-cyclohexadiene 1 turns out to be a planar molecule. The C-C single and double bonds are as anticipated, 1.498 Å and 1.339 Å, respectively, and the P-C single and double bonds are also within expectations, 1.860 Å and 1.675 Å, respectively. The only difference from the carbon system is that the C=C bond in 1 is longer by 0.021 Å then C=C in cyclohexadiene (1.318 Å). Again, this can be rationalized in that the system is simply trying to accomodate the phosphorus into the ring.

Phosphaethylene + s-gauche-1,3-butadiene

For this reaction, two pathways are possible leading to two different products: (a) the phosphorus lone-pair is exo (or H on phosphorus is endo) to the ring, and (b) the phosphorus lone-pair is endo to the ring (and the H exo), as seen in Reactions 2 and 3, respectively. These reactions can be compared with the reaction of ethylene + butadiene and those reported by Houk, et.al. for the cycloaddition of formaldimine with butadiene.¹⁶

We will first look at Reaction 2, where the lone-pair on phosphorus is exo to the ring. For the transition structure TS2 (see Figure 2), the forming C-P bond is 2.552 Å, which is shorter than the corresponding bond in TS1 by 0.064 Å. The forming C-C bond is 2.562 Å<, considerably longer, by 0.274 Å, than in TS1, or the analogous carbon system, where the C-C bond length is 2.2855 Å.⁴ The C2-C1-P and C3-C4-C5 are 98.7° and 100.0°, respectively, following what would be expected for a Diels-Alder reaction.

Figure 2 Geometry of TS2

TS2

For Reaction 3, the lone-pair of electrons on the phosphorus is endo to the ring, and this ha significant affect on the reaction. In TS3 (see Figure 3), the forming C-P bond is 2.638 Å, which is 0.086 Å longer than in TS2, where the lone-pair is exo to the ring, and also longer than TS1. However, the forming C-C bond is 2.439 Å, or 0.123 Å shorter than in TS2, but still longer than TS1. To explain the lengthening and shortening of these two forming bonds, we can look closer at the position of the dienophile relative to the diene. In TS2, the dienophile is positioned so that the P is more turned in torwards the diene than the C. In TS3, the dienophile is positioned exactly opposite, the P is positioned so that it is turned away from the diene. One way to understand this is that in TS3, sterics might play more of a role with the interaction of the H on the P and the H on C1. To avoid collision of these two, the P is slightly pushed out from the diene, in turn lengthening the C-P distance. Besides this, the lone-pair of electrons is endo in TS3 where they will have more of a chance of interacting with the forming pi bond than in TS2. The angles in TS3 of C2-C1-P and C3-C4-C5 are 102.0deg. and 101.6deg., respectively, slightly larger than in TS2. This is another indication that when the phosphorus lone pair of electrons is in an endo position, TS3, the dienophile does not want to be as close to the diene as when the phosphorus lone pair of electrons is in an exo position, in TS2. One last difference that is worth noting is that the breaking C=P is slightly longer here in TS3, by 0.007 Å, than in TS2.

Figure 3 Geometry of TS3

TS3

The same trends observed in TS2 and TS3 are also observed in the Diels-Alder reaction between butadiene and formaldimine studied by Houk and coworkers.¹⁶ As in our reactions, there is the possibility of the nitrogen lone-pair of electrons being either endo or exo to the ring. When the nitrogen lone pair is exo, the N is turned more towards the diene, but to a much greater extent than in TS2. We can also look at the trends in C-C and C-X (X=P or N) bond lengths. Comparing TS2 and TS3, the C-P distance in TS2 (lone-pair exo) is shorter than in TS3 (lone-pair endo) by 0.086 Å. This is analogous to what was found for the nitrogen system, where the exo TS had a shorter C-N bond length than the endo TS by 0.118 Å. The C-C distance in TS2 is 0.123 Å longer than in TS3, while in the nitrogen system, the C-C distance for the TS with the lone-pair exo is longer by 0.163 Å than in the TS with the nitrogen lone-pair endo.

Looking at the products, 2 is a twisted 4-phospha-cyclohexene as seen in Figure 4. This twisted structure is consistent with the carbon system.⁴ The C-P single bonds are nearly equivalent, 1.857 Å and 1.855 Å. The C-C bonds that were originally part of butadiene are 1.502 Å and 1.503 Å, while the C-C bond that is newly formed is 1.525 Å, slightly longer than the other two. This is most likely due to the molecule compensating for the larger size of the phosphorus.

The Diels-Alder product 3 is also a twisted 4-phosphacyclohexene structure, comparable to 2 and cyclohexene. The bond lengths are almost identical to 2, with slight differences in the angles around the phosphorus. The C1-P-C5 angle in 2 is 97.0° whereas in 3 it is 95.0°. The C2-C1-P angle is 115.9deg. in 2 and 109.8° in 3. For 3 (the lone-pair is in the endo position), the ring angles are smaller, placing more strain on the molecule than in 2. This might indicate that the more favorable product is 2, where the lone-pair of electrons are exo to the ring.

Figure 4 Geometries of 2 and 3

Discussion

Table 1 lists the results for the E_a and E_rxn for the three different reactions at various levels of calculation. We will only discuss the MP4SDQ/6-31G*//MP2/6-31G* values that are corrected for ZPE's (in parantheses) since it is known that HF/6-31G* overestimates the activation energies for Diels-Alder reactions, and that MP2/6-31G* underestimates the activation energies.

**Table 1** Activation and Reaction Energies for Reactions 1-3.
	HF/6-31G*^a		MP2(full)/6-31G*		MP4SDQ/6-31G* ^b
Reaction	E_a	E_rxn	E_a	E_rxn	E_a	E_rxn
1	30.82 kcal/mol	-42.29 kcal/mol	7.62 kcal/mol	-42.90 kcal/mol	17.89 kcal/mol	-43.10 kcal/mol
	(32.25 kcal/mol)	(-38.20 kcal/mol)	(9.04 kcal/mol)	(-38.82 kcal/mol)	(19.33 kcal/mol)	(-38.99 kcal/mol)
2	24.01 kcal/mol	-47.94 kcal/mol	1.79 kcal/mol	-53.72 kcal/mol	10.84 kcal/mol	-49.65 kcal/mol
	(26.15 kcal/mol)	(-42.91 kcal/mol)	(4.46 kcal/mol)	(-48.69 kcal/mol)	(12.97 kcal/mol)	(-44.62 kcal/mol)
3	26.40 kcal/mol	-46.32 kcal/mol	4.18 kcal/mol	-52.42 kcal/mol	13.47 kcal/mol	-48.20 kcal/mol
	(28.43 kcal/mol)	(-41.20 kcal/mol)	(6.21 kcal/mol)	(-47.30 kcal/mol)	(15.50 kcal/mol)	(-43.08 kcal/mol)

a) Energies corrected for ZPE listed in parantheses.
b) MP4SDQ(full)6-31G*//MP2(full)/6-31G*

First looking at the Diels-Alder reaction of butadiene with P-acetylene, reaction 1, the E_a is only 19.33 kcal/mol. This activation barrier is much lower than for the reaction of butadiene with acetylene (E_a = 30.63 kcal/mol),¹⁵ indicating that the Diels-Alder reaction with phosphaacetylene is much more likely to occur than the carbon analogue. This is an exothermic reaction having a E_rxn = -38.99 kcal/mol, but not as exothermic as the carbon reaction where E_rxn = -68.75 kcal/mol.¹⁵ Even though the phosphorus system is not as exothermic as the carbon system, it will occur more readily due to its lower activation barrier. This agrees with the known difficulty of reacting butadiene with acetylene¹⁵, and the substantially easier reactions of dienes with substituted phosphaacetylenes.⁸, ¹²

The E_a for reaction 2 is 12.97 kcal/mol, lower than reaction 3 which has E_a = 15.50 kcal/mol. Both of these are quite a bit lower than for Reaction 1, suggesting that the Diels-Alder reaction with phosphaethene may be more likely to occur due to its lower barrier. Compared to the prototype butadiene + ethylene reaction, where the experimental²¹ E_a = 27.5 kcal/mol, the phosphorus system is substantially lower. This is in agreement with the mild reaction conditions for numerous Diels-Alder reactions between dienes and substituted phosphaethylenes. In many cases, these reactions take place at room temperature and usually react within 24 hours.¹²

Reaction 2 forms the more stable product, having a E_rxn = -44.62 kcal/mol and E_rxn(reaction 3) = -43.08 kcal/mol. Even though this difference is only 1.54 kcal/mol, there is a slight preference for Reaction 2, where the lone-pair of electrons are exo to the ring. The E_a for Reaction 2 is lower (by 2.53 kcal/mol) than the activation barrier for Reaction 3. This is also the same trend seen in the reaction of butadiene with formaldimine, where the more favorable pathway is the one going through a TS with the lone pair of electrons exo to the ring.¹⁶ The Diels-Alder reaction between phosphaethene and butadiene is energetically more favorable when the lone-pair is exo (or the substituent H is endo) to the ring.

Topological Analysis.

The discussion of any Diels-Alder reaction would not be complete unless the issue of concertedness is addressed. One way to determine the concertedness of a reaction is to determine the bond orders in the transition structure. Bond orders can be calculated from the results of electron density analysis, using the value of the electron density at the bond critical points r(r_c). The bond orders are listed in Table 2 along with the sum of bond orders for each TS.

**Table 2** Bond Orders in **TS1-TS3**, Determined Using Equation 1
Bond	TS1	TS2 (H endo)	TS3 (H exo)
1-2	1.69	1.67	1.70
2-3	1.53	1.51	1.52
3-4	1.68	1.71	1.69
4-5	0.29	0.27	0.28
5-6	2.63	1.61	1.54
1-6	0.11	0.13	0.12
SUM	7.93	6.90	6.85

The bond orders for the partial double bonds for all thre TSs are remarkably similar, ranging from 1.71 to 1.51. Bonding appears to be made and broken to very similar degrees around the ring in these TSs.

For Reaction 1, there are 2 C=C bonds, 1 C-C, and 1 CP triple bond in the reactant for a total number of 8 bonds. The sum of bond orders for TS1 is 7.93, consistent with a concerted pathway. For Reactions 2 and 3, there are 2 C=C bond, 1 C-C bond, and 1 C=P bond for a total of 7. The sum of bond orders for TS2 and TS3 are 6.85 and 6.90, respectively, once again indicating concertedness.

Conclusion

The Diels-Alder reaction between butadiene and phosphaethyne is determined to have a substantially lower E_a than the carbon system. For the reactions of butadiene with phosphaethene, the energetically favored pathway is when the phosphorus lone-pair is exo ( or the substituent H is endo) to the ring. Activation barriers are substantially lowered by substitution of phosphorus for carbon in the dienophile. This is similar to our⁴ earlier findings the phosphorus substitution inot the butadiene fragment leads to a lower activation berrier in Diels-Alder reactions. Electron density analysis has shown that all three Diels-Alder reactions are concerted. Our results indicate a typical Diels-Alder reaction occurs when phosphorus is part of the dienophile. This perturbation of the molecular symmetry does not alter the course of the reaction.

Acknowledgment

is made to the National Science Foundation and the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research.

References

1 G. De Lauzon, C. Charrier, H. Bonnard and F. Mathey
Tetrahedron Letters 1982, 23, 511-514

2 G. De Lauzon, C. Charrier, H. Bonnard, F. Mathey, J. Fischer and A. Mitschler
Chemical Communications 1982, , 1272-1273

3 F. Mathey, F. Mercier, C. Charrier, J. Fischer and A. Mitschler
Journal of the American Chemical Society 1981, 103, 4595-4597

4 S. M. Bachrach and M. Liu
The Journal of Organic Chemistry 1992, 57, 6736-6744

5 MÄ, G. Rkl, G. Y. Jin and E. Silbereisen
Angewandte Chemie International Edition in English 1982, 21, 370-371

6 R. Appel, F. Knoch and R. Zimmerman
Chemische Berichte 1985, 118, 814824

7 R. Appel, J. Menzel and F. Knoch
Chemische Berichte 1985, 118, 4068-4072

8 W. Rösch and M. Regitz
Zeitschrifft fur Naturforschung B 1986, 41, 931-933

9 R. D. Bach, J. J. W. McDouall, H. B. Schlegel and G. J. Wolber
The Journal of Organic Chemistry 1989, 54, 2931

10 K. N. Houk, R. J. Loncharich, J. F. Blake and W. J. Jorgensen
Journal of the American Chemical Society 1989, 111, 9172-9176

11 W. J. Jorgensen, D. Lim and J. F. Blake
Journal of the American Chemical Society 1993, 115, 2936-2942

12 M. Abbari, P. Cosquer, F. Tonnard, Y. Y. C. Yeung Lam Ko and R. CarriÈ
Tetrahedron 1990, 46, 71-82

13 R. Appel and C. Casser
Chemische Berichte 1985, 118, 3419-3423

14 P. Pellon, Y. Y. C. Yeung Lam Ko, P. Cosquer and J. Hamelin
Tetrahedron Letters 1986, 27, 4299

15 J. M. Coxon, S. T. Grice, R. G. A. R. Maclagan and D. Q. McDonald
The Journal of Organic Chemistry 1990, 55, 3804-3807

16 McCarrick, Y. -D. Wu and K. N. Houk
The Journal of Organic Chemistry 1993, 58, 3330

17 M. J. Frisch, G. W. Trucks, M. Head-Gordon, P. M. W. Gill, M. W. Wong, J. B. Foresman, B. G. Jouhnson, H. B. Schlegel, Robb, E. S. Replonge, R. Gomperts, J. L. Andres, K. Raghavachari, J. S. Binkley, C. Gonzales, R. L. Martin, D. L. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart and J. A. Pople
GAUSSIAN-92
Gaussian, Inc.: Pittsburgh, PA, 1992

18 F. W. Biegler-Konig, R. F. W. Bader and T. H. Tang
Journal of Computational Chemistry 1982, 3, 317-328

19 S. M. Bachrach
Journal of Molecular Structure (THEOCHEM) 1992, 255, 207-219

20 T. S. Slee
In Modern Models of Bonding and Delocalization, J. F. Liebman, A. Greenberg Ed.
VCH Publichers: New York, 1988, 69

21 D. Rowley and H. Steiner
Discussions of the Faraday Society 1951, 10, 198

1	G. De Lauzon, C. Charrier, H. Bonnard and F. Mathey Tetrahedron Letters 1982, 23, 511-514
2	G. De Lauzon, C. Charrier, H. Bonnard, F. Mathey, J. Fischer and A. Mitschler Chemical Communications 1982, , 1272-1273
3	F. Mathey, F. Mercier, C. Charrier, J. Fischer and A. Mitschler Journal of the American Chemical Society 1981, 103, 4595-4597
4	S. M. Bachrach and M. Liu The Journal of Organic Chemistry 1992, 57, 6736-6744
5	MÄ, G. Rkl, G. Y. Jin and E. Silbereisen Angewandte Chemie International Edition in English 1982, 21, 370-371
6	R. Appel, F. Knoch and R. Zimmerman Chemische Berichte 1985, 118, 814824
7	R. Appel, J. Menzel and F. Knoch Chemische Berichte 1985, 118, 4068-4072
8	W. Rösch and M. Regitz Zeitschrifft fur Naturforschung B 1986, 41, 931-933
9	R. D. Bach, J. J. W. McDouall, H. B. Schlegel and G. J. Wolber The Journal of Organic Chemistry 1989, 54, 2931
10	K. N. Houk, R. J. Loncharich, J. F. Blake and W. J. Jorgensen Journal of the American Chemical Society 1989, 111, 9172-9176
11	W. J. Jorgensen, D. Lim and J. F. Blake Journal of the American Chemical Society 1993, 115, 2936-2942
12	M. Abbari, P. Cosquer, F. Tonnard, Y. Y. C. Yeung Lam Ko and R. CarriÈ Tetrahedron 1990, 46, 71-82
13	R. Appel and C. Casser Chemische Berichte 1985, 118, 3419-3423
14	P. Pellon, Y. Y. C. Yeung Lam Ko, P. Cosquer and J. Hamelin Tetrahedron Letters 1986, 27, 4299
15	J. M. Coxon, S. T. Grice, R. G. A. R. Maclagan and D. Q. McDonald The Journal of Organic Chemistry 1990, 55, 3804-3807
16	McCarrick, Y. -D. Wu and K. N. Houk The Journal of Organic Chemistry 1993, 58, 3330
17	M. J. Frisch, G. W. Trucks, M. Head-Gordon, P. M. W. Gill, M. W. Wong, J. B. Foresman, B. G. Jouhnson, H. B. Schlegel, Robb, E. S. Replonge, R. Gomperts, J. L. Andres, K. Raghavachari, J. S. Binkley, C. Gonzales, R. L. Martin, D. L. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart and J. A. Pople GAUSSIAN-92 Gaussian, Inc.: Pittsburgh, PA, 1992
18	F. W. Biegler-Konig, R. F. W. Bader and T. H. Tang Journal of Computational Chemistry 1982, 3, 317-328
19	S. M. Bachrach Journal of Molecular Structure (THEOCHEM) 1992, 255, 207-219
20	T. S. Slee In Modern Models of Bonding and Delocalization, J. F. Liebman, A. Greenberg *Ed.* VCH Publichers: New York, 1988, 69
21	D. Rowley and H. Steiner Discussions of the Faraday Society 1951, 10, 198