Structures and stabilities of hydrofullerenes. Completion of crown structures at C60H18 and C60H24

Journal of Molecular Structure (Theochem), 303 (1994) l-9 0166-1280/94/$07.00 c 1994 - Elsevier Science Publishers B.V. All rights reserved

Structures and stabilities of hydrofullerenes. of crown structures at CG0H18and C6*Hz4

Completion

Brian W. Clare, David L. Kepert” Research Centre for Advanced Mineral and Materials W.A. 6009, Australia (Received

11 May 1993; accepted

Processing,

University of Western Australia,

Nedlands,

20 May 1993)

Abstract The calculation of the stabilities of different isomers of C6aHn has been extended from n = 12 to n = 24. Each structure in a first series of molecules was obtained by addition of a pair of hydrogen atoms onto the most stable structure for C60Hn_2. This series culminates in C&Hz4, consisting of a crown composed of 18 linked CH groups plus three CH-CH groups remaining from the original C6aHIZ structure. A second series of structures was similarly obtained based on C6,,H1s, in which all hydrogen atoms are part of the C,sH,s crown. The most stable molecules are C6eH12 (first series) and C6aHz2 (second series)

Introduction The structures and stabilities of products formed by multiple addition to fullerene-60 present a formidable problem. Reduction of C6,, to C6aH2 forms 23 possible structures and the number of isomers rapidly increases until at C6aHs0 approximately lOI isomers are possible. Present indications [l41 are that the hydrogen atoms add onto a double bond common to two hexagonal faces (the hex-hex or 6-6 edges), leading to a substantial reduction in the number of possible isomers to only one for C60HZ and approximately lo7 for C60H30. Addition across a hex-hex edge forms an ethane-type fragment with the hydrogen atoms in the sterically unfavourable eclipsed arrangement and is unfavourable for groups with large steric requirements, such as Cl or Br [2]. An earlier paper [l] considered the compounds formed by successive additions from C6a to C60H12. The C6aHt2 structure is highly symmetrical (Th), * Corresponding

author.

SSDI 0166-1280(93)03411-Y

with the centres of the six CH-CH groups forming an octahedron. There are only three types of carbon atoms: 12 carbon atoms are attached to hydrogen atoms, 24 carbon atoms are attached to these 12, and a second set of 24 are attached to the first set of 24. of hydrogen necessarily Further addition requires a break in the previous structural trends, owing to the necessity of having two or more pairs of hydrogen atoms on the same or adjacent C6 rings. The previous work is extended in this paper, with the object of discerning any underlying structural trends and locating any structures of particular stability. Calculations The numbering system for C6a is shown in Fig. 1 and is the same as used previously [ 11. Calculations were carried out using the AM1 hamiltonian and the program MOPAC 6.0 as before [l]. Geometry optimisation was done with the eigenvector following (EF) option, and the option PRECISE was

B. W. Clue

and D.L. Kept-t/J.

Mol. Struct.

(Theochem)

303 (1994) 1-9

First series

The starting

point

for (&HI4

is to consider

the

highly symmetrical structure of (&H12 (Fig. 2). This is the only structure possible which does not contain two or more CH-CH groups on the same or adjacent C6 faces, which the previous work [I] has shown is a relatively example,

Fig. 1. Numbering system used in this work. Atoms are consecutively numbered around planes perpendicular to a five-fold axis, commencing at a mirror plane.

used throughout. No symmetry was enforced in the calculations; any symmetry observed in the optimised structure is noted in the appropriate table. Diagrams were drawn with SCHAKAL [5].

unstable

arrangement.

the three least stable structures

For

for C&H4

are the 1,6;3,8-, 1,6;2,7- and 1,6;13,14- isomers. An alternative structure of (&HI2 with D3d symmetry has been proposed [6], but our calculations indicate it is very unstable, with a heat of formation compared with 720.47 kcal of 732.47 kcal mol-’ mol-’ for the structure in Fig. 2. All unreduced C=C bonds along the hex-hex edges of C6”H12 are identical and reduction of any one leads to isomer 1 of C60H11. The AWf of 687.09 kcal mol-’ is only 33.4 kcal mol-’ lower than for CmH12, compared with the decrease in AWf of 41.9-42.4 kcal mol-’ for successive members of the series CaHn, where II = 0, 2, 4, 6, 8, 10 or 12,

Results Only a limited number of isomers were able to be considered for each stoichiometry CeOHn. The first series of structures was based on the addition of a pair of hydrogen atoms onto a hex-hex edge of the most stable structure obtained previously for C60Hn_X. An abbreviated nomenclature used in this paper for C,,H, formed from the addition onto the A, B sites of isomer x of C60Hn_2 is [C60Hn_2 : x]A, B. For example, addition of H, onto 1,6;15,16;23,33;28,38;41 ,50;53,58-C6,,H12 forms 1,6;2,7;15,16;23,33;28,38;41,50;53,58-C60H14 or [CeOHIZ : 1]2,7-C6,,H14. A second series of structures was based on the (&H,s crown discovered during the first series of calculations. Many other calculations were carried out which followed various hints of perceived structural trends, but the resulting structures were less stable than those of the first and second series and are reported here in only a few cases.

Fig. 2. Structure of C&HIZ. Six pairs of hydrogen atoms are attached to hex-hex edges, the midpoints forming a regular octahedron. For clarity, the HGCH carbon atoms and bonds are blackened.

B. W. C/are and D.L. Kepert/J. Mol. Struct. (Theochem)

303 (1994)

l-9

Table 1 CG0H14Isomers, series 1: heats of formation

H

No. Isomer

AH”f (kcalmol-‘)

1 [c60%2 : ii &7 2 1,6;5,10;15,16;23,33;41,50;46,47;53,58 3 1,6;15,16;17,18;23,33;41,50;53,58;54,59 4 1,6;5,10;15,16;23,33;41,50;53,58;54,59

687.09 688.93 689.57 689.59

indicating

a sharp change in trend and a relatively

unstable structure. In an extensive search for a more stable structure, calculations were carried out on approximately 50 other isomers, the three most stable being shown in Table 1. All three structures contain five of the six octahedrally arranged CH-CH groups present in &H12, but it should be noted that in the most stable of these three the remaining two CH-CH groups are not part of a second octahedral set. Structures containing only four or three of the octahedral set of CH-CH groups are even less stable than those containing five such groups. A feature of the structure of isomer 1 of &,H14 is that there are two CH groups trans to the C(3)C(8) and C(13)-C(14) double bonds. Lifting these tetrahedral carbon atoms out from the curved surface of CeO leads to greater planarity of these alkene

Fig. 3. Localisation of double bonds containing tram arrangements of CH groups in C60H14. groups with enhanced double bond character. The bond orders of these localised bonds are C(3)C(8) = 1.760 and C(13)-C(14) = 1.770, compared with 1.481-1.540 for the other 21 bonds along the hex-hex edges (Fig. 3).

C6OHl6

The stabilities of all 15 isomers obtained by adding a pair of hydrogen atoms onto a hex-hex edge of isomer 1 of C6,,H14 are shown in Table 2. Three

Table 2 C,,H,, Isomers, series 1: symmetries and heats of formation No. Isomer

Symmetry

AHof (kcalmol-‘)

l LOHI, : 113,8 2 K60H14 : ll4,9 3 [C60H,4 : 1]5,10 4 [C60H,4 : 1]11,12 5 [CGoH,, : 1117, 18 6 [C60H,4 : 1]19,20 7 [C60H,4 : 1]21,31 8 [C,,H,, : 1]26,36 9 [C60H,4 : 1]27,37 10 [C60H,4 : 1]30,40 11 [C60H,4 : 1]44,45 12 [Ce0H14 : 1]46,47 13 [C,,H,, : 1]48,49 14 [C,,H,, : 1]52,57 15 [C,,H,, : 1]54,59

Cl Cl C, (l,6,58,53) C, (23,33,38,28) Cl C, (l-6,53-58) Cl Cl Cl Cl C, (15,16,50,41) C2(15-16,41-50) Cl C2 (23-33,28-38)

650.83 657.34 651.75 667.41 654.54 652.27 654.61 653.30 653.31 652.81 653.71 653.62 654.03 653.40 653.93

ci

B. W. Clue

and D.L. Kepert:‘J. Mol. Struct.

ITheochemI

303

(1994J

I-9

Table 3 (&HIX Isomers, series 1: heats of formation

H H

H

Fig. 4. String of three C6H4 rings linked through CH-CH edges in isomer 1 of C,,H,,.

of these (isomers 3,4 and 11) each retain one of the three mirror plans present in C6eHt2. Similarly, isomers 6, 12 and 14 each retain one of the three twofold axes present in C6aHi2, and isomer 15 retains the inversion centre. The remaining eight structures exist as pairs of optical isomers. Isomer 1 is the most stable, being 1.4 kcal mol-’ more stable than isomer 6. Isomer 4 is substantially less stable than any other isomer, which is associated with the particular instability of structures containing a C6H6 face. Isomers 5 and 10, in which the two additional CH-CH groups not present in (&Hi2 are part of a second octahedral set of such groups, are not particularly stable. As observed for C60H14, the double bonds along the hex-hex edges which have CH groups trans to each other contain strongly localised double bonds. Isomer 1 is unique in containing only one of these localised bonds with a bond order of 1.821, compared with bond orders of 1.477-1.542 for the 21 other hex-hex edges. In all other isomers there are four such strongly localised bonds, with bond orders of 1.743-1.821. The four hydrogen atoms in the most stable isomer (which may be written [C6aHi2 : 1]2,7; 3,8) are grouped together over the same octahedral face formed by the six CH-CH groups in C60H12. This grouping results in the formation of a string of three C,H, rings, linked through common CHCH edges (Fig. 4). The second most stable isomer (isomer 7) has two such linked rings, whereas all other structures have only two isolated C6H4 rings.

No. Isomer

AWf (kcal mol-‘)

1 [C,,H,, : 114.9 2 [C60H,6 : 115;10 3 (C60H,6 : 1111;12 4 [C60H,6 : 1113, 14a 5 [CbOH,6 : 1117. 18 6 [C6,,H,6 : 1119.20 7 [ChOH,6 : 1]21;31 8 [C60H,6 : 1]22,32 9 [ChOHlh : 1]24,34 10 [C6,,Hlh : 1125.35 11 [C60H,6 : 1126.36 12 [C60H,6 : 1]27,37 13 [C60H,6 : 1]29,39 14 [&,H16 : 1]30,40 15 [ChOH,6 : 1]42,43 16 [C60H,6 : 1144.45 17 [C60H,6 : 1]46,47 18 [C6,,H,6 : 1]48,49 19 [ChOHlh : 1151.56 20 [C60H,6 : 1152.57 21 [C6,,H,6 : 1]54,59 22 [C60H,6 : 1]55,60 23 [&Hi2 : 1]2,7; 17,18; 25.35 24 [C&,HIZ : 112.7; 17. i&42,43 25 [CeOHIZ: 11257;17. 18: 54,59 26 [C6,,H,2 : 112.7; 30,40; 42, 43b

636.63 626.00 630.63 626.89 619.34 614.90 618.13 620.91 621.68 621.12 615.32 615.93 616.56 616.38 616.39 618.10 617.00 618.09 617.01 616.79 618.02 617.90 621.10 620.47 620.46 617.47

a C3 Axis through midpoints of 2,3.8,14,13,7 48,49,55,60,59,54. h C3 Axis through midpoints of 11.12,22.32,31,21 26,27.37,47,46,36.

and and

The structures and stabilities were calculated for all 22 isomers of CGOH1s based on the most stable structure of (&HI6 (Table 3). A notable feature of the most stable structure (isomer 6) is that the string of three linked C6H4 rings m C60H16 is extended to four linked C6H4 rings. The second most stable structure of CbOH1s (isomer 11) similarly extends the string of three linked hexagons to four, but now the extension is on the opposite end of the string. Isomers 1, 3 and 4 are substantially less stable than the other structures and it is clear that the presence of a C6H, ring leads to substantial instability.

B.W. Glare and D.L. Kepert/J.

Mol. Strut.

iTheochem)

303 (1994)

Table 4 C&Hz0 Isomers, series 1: heats of formation No. Isomer

AH”r (kcal mall’ )

[C6,,H,s : 6]17,18 [C+,,,H,s : 6]21,31 [&H,s : 6]22,32 [C&,H,s : 6]24,34 [C,,,H,s : 6]25,35 [C&,H,s : 6]26,36 [C6,,H,s : 6]27,37 [&,H,s : 6]29,39 [C6,,H,s : 6130, 40a [C6,,His : 6]42,43 11 [C6,,H,s : 6]44,45 12 [C6,,H,s : 6]46,47 13 [&H,s : 6]48,49 14 [C6sH,s : 6]51,56 15 [&H,s : 6]52,57 16 [&,,H,s : 6]54,59 17 [C6aH,s : 6]55;60

587.10 585.92 585.79 586.01 585.47 578.85 578.78 517.17 571.69 579.99 582.40 580.73 583.06 580.65 580.75 582.09 582.78

1 2 3 4 5 6 7 8 9 10

a C, Axis through midpoints

of 1-6 and 53-58.

Isomers 23-26 are the four structures based on the octahedral arrangement of (&HI2 with the remaining three CH-CH groups forming part of a second octahedral

set. They are all unstable.

c60 H20

All structures of C6aH2s based on isomer 6 of C6sH1s were considered (Table 4) except those four that contain a C6H6 ring. The formation of the most stable structures (isomers 8 and 9) continue the trends noted above, as follows. (a) Complete a set of four hydrogen atoms over a second octahedral face of C60H12. (b) Extend the string of linked C6H4 hexagons, which are now six C6H4 hexagons long. Isomer 9 (with a twofold axis) continues this string in one direction and in the slightly more stable isomer 8 the string bends around in the opposite direction. (c) Minimise the number of localised double bonds arising from a trans arrangement of CH groups. There are two such bonds in isomers 8 and 9, and five in all other isomers. The next most stable structures (isomers 7 and 6) result from hydrogenation of the C(27)-C(37) and C(26)-C(36) edges respectively. These four atoms

5

I-9

Table 5 C&HZ1 Isomers, series 1: heats of formation No. Isomer

AH”r (kcalmoll’)

1 [C6aH,, : 8]17,18 [C6sH,, : 8]21,31 [C6,,H2,, : 8]22,32 [C6sH2s : 8]24,34 [Ch0H2a : 8]25,35 [C6,,H2s : 8]26,36 [C&Hz0 : 8]27,37 [C6,,H2s : 8]42,43 [&Hz,, : 8]44,45 [&Hz0 : 8]46,47 [C6sH2,, : 8]51,56 [C&Hz0 : 8]52,57 [C6,,H2s : 8]54,59 [C6,,H20 : 8]55,60

554.44 548.74 547.80 548.51 548.06 540.56 539.15 542.02 544.90 542.24 542.27 542.68 545.03 547.68

2 3 4 5 6 7 8 9 10 11 12 13 14

lie on a third octahedral face of already noted at this stage that C6sH2s on these four sites would ring of nine C6H4 rings linked edges.

C6sH12. It may be hydrogenation of form a continuous through CH-CH

As anticipated above, further addition of hydrogen continues the linking of C6H4 hexagons to form C6sHz2 (Table 5) and Ce0Hz4 (Table 6) (Fig. 5). The structure can be considered to contain a “crown” formed from a ring of 15 CH groups Table 6 (&Hz4 Isomers, series 1: heats of formation No. Isomer

AH”r (kcalmol-‘)

I [C6aHz2 : 7126, 36a 2 2,5,8,9,11,13,18,20,22,25,26,29,31, 34,37,40,43,45,46,48,51,55,57,59b 3. 3,4,7,10,12,14,17,19,21,24,27,30, 32,35,36,39,42,44,47,49,52,54,56,60

498.56 504.33 840.37

a C, Axis through midpoints of 4,5,10,18,17,9 and 42,43,52,57,56,51. b C, Axes through midpoints of 4,5,10,18,17,9 and 42,43, 52,57,56,51; through 2,3,8,14,13,7 and 48,49,55,60,59,54; through 11,12,22,32,31,21 and 26,27,37,47,46,36; through 19,20,30,40,39,29 and 24,25,35,45,44.34. Cz Axes through midpoints of 1,6 and 53,58; through 15,16 and 41,50; through 23,33 and 28,38. Mirror planes through 1,6,58,53; through 15,16,50,41; through 23,33,38,28.

B. W. Ciare and D.L. KepertlJ.

Mol. Struct.

(Theochrm)

303 (I9941 I-9

CH groups and this is the basis of the second series of calculations. The structure of 1,6;2,7;3,8;15,16;19,20;26,36;27, 37; 28,38;29,39-C&His (isomer 27) has CsV symmetry and is shown in Fig. 6. The calculated heat of formation

of

613.35 kcal molli

is

significantly

lower than the value for the most stable structure in the first series (614.90 kcal mol-‘).

C60H16

Two structures

Fig. 5. Structure of C&Hz4 (isomer 1, first series), containing a C,,H,, crown plus three CH-CH groups. For clarity, the HC-CH carbon atoms and bonds are blackened.

C(l), C(2)> C(3), C(8), C(l5), C(l6L C(26), C(27), C(37), C(38), C(28), C(29), C(19), C(20) and C(6) - with three pendant “thorns” ~ C(7), C(36) and C(39). Three isolated CH-CH groups remain from the original C60H12 structure C(23))C(33), C(41)-C(50) and C(53))C(58). A threefold axis runs between these CH-CH groups and the centre of the crown. Table 6 also lists the two isomers of C60H24 which have been the subject of ab initio calculations [7], with further interest arising from the structure of C60Br24.xBr2(x = O-2) [8].

can be obtained

by removal

of a

pair of hydrogen atoms from the C&His crown structure, depending upon whether the removal is from a hex-hex edge in the continuous string, or one of the three “thorns” isomers 16 and 17 respectively). Both structures (Table 7) are substantially less stable than isomer 1, first series. CsoHro, &oHzz and (IHI4(’ All structures based on the successive addition of pairs of hydrogen atoms to hex-hex edges of C60Hls, eliminating those structures containing C6H6 rings, were calculated as before. Isomer 20 of C6,,HZ0, isomer 18 of C&Hz2 and isomer 6 of &Hz4 are more stable than the corresponding molecules in the first series. The structure of

Second series

The structure of Ce0H14 above has been created from the octahedral structure of CG0H12 by joining three CH-CH groups on a face of the (&Hi: octahedron with intervening C6H, groups, forming a crown consisting of 18 CH groups. The remaining three CH-CH groups of &,Hi2 are not connected to other CH groups. The question then arises as to whether the crown structure is stable in the absence of the three remaining CH-

Fig. 6. Structure of C&HI8 (second series), containing a C,sH,s crown. For clarity, the HC-CH carbon atoms and bonds are blackened.

B. W. Glare and D.L. KepertlJ. Mol. Strut.

(Theochemj 303 (1994) l-9

Table I &OH, Isomers, series 2: heats of formation No. Isomer

AWr (kcal mol-‘)

&Off16

16 [&H,s : 27]-28,38 17 [C6,,H,s : 271-29.39” GOHI 27ahc.d

655.82 655.35 613.35

Go ff20 18 [C6sH,s : 27]23,33 19 [C6,,H,s : 27124, 34a 20 [&,,H,s : 27142, 43b

575.70 581.30 572.11

GOff22

15 16 17 18 19 20

[C60H2020]21r31 [CG0Hz020]22,32 [C6,,Hzo20]41, 50 [C6nHz020]51, 56’ [C6,,H,,20]53, 58 [C6,,Hz,,20]54, 59b

543.15 536.35 536.80 532.61 536.02 539.87

c60H24

4 5 6 7 8 9 10

[C6sHZZ18]21,31C [&Hz2 18]22,32 [C6,,H2218]23,33 [C6aHz218]24,34 [&Hz2 18]44,45 [&,,H,s27]42,43; 51,56; 52, 57a’b.c,d [C60H,827]21, 31; 24,34; 54, 59a,b,c,d

509.29 499.00 495.67 503.40 491.59 504.26 515.98

a Mirror plane through 24,34,29,39. b Mirror plane through 2,7,59,54. ’ Mirror plate through 21,31,36,26. d C, Axis through midpoints of 4,5,10,18,17,9 and 42,43,52, 57,56,51.

C60H22 (Fig. 7) consists of the CisHis crown and C6H4 ring on the opposite side of the molecule. It may be noted that this successive hydrogenation proceeds via the linkage of C6H4 rings as before, but the positioning of these hydrogen atoms precludes the growth into a completed second crown structure at &,Hj6. Table 7 also lists the two isomers of C&Hz4 of Cs., symmetry (isomers 9 and 10) containing the CisHts crown. Discussion Addition

of a pair of hydrogen

atoms to a vacant

Fig. 7. Structure of C60H22 (isomer 18, second series), containing a CbH4 ring and a C,sH,s crown. For clarity, the HC-CH carbon atoms and bonds are blackened.

hex-hex edge of C&Ht2 necessarily leads to the introduction of a C6H4 ring with a heat of formation of 8-9 kcalmol-’ higher than would be expected from the trend from CeO to C,,Ht,. Further successive additions to form C60Hn, without any rearrangement of the CG0HnP2 structure, leads to the first series of structures. This process results in the progressive lengthening of a string of CcH4 rings linked through common CH-CH edges. The formation of such strings minimises the number of strongly localised double bonds along the unreduced hex-hex edges, resulting in less delocalisation in the molecule. The string of C6H4 rings eventually completes a ClsHls crown at C60H24, which also contains the three remaining isolated CH-CH groups present in C6,,Hi2. A second series of molecules was based on this CisH,, crown with the deletion of these three isolated CH-CH groups. A critical question in fullerene chemistry is whether a structure formed in this stepwise addition may rearrange to a more stable structure. The number of possible isomers is very large; for example, there are over 1015 different ways of arranging 24 hydrogen atoms over 60 carbon atoms, and over

8

B. W. Claw and D.L. Kepert,!J. Mol. Struct.

lo6 different

ways of arranging

gen atoms on the 30 hex-hex that a particular energy minimum

12 pairs of hydro-

in this value

edges. Confirmation

series

structure represents a global is not possible with calculations

of calculations.

Extensive

for any C,,H,

can be conveniently

n = 12-24 from this paper and the lowest values obtained to date for n = 26 and 28 [9]. It is clear that many of the C&H, molecules described here

additional

are unstable

searches have been made during the course of this work, but so far no other stable series has been

with

respect

to disproportionation

into lower and higher hydrides, (x + ~&oHn

found. Successive addition of H2 onto CeO leads to a decrease in the heat of formation of approximately 20 kcal mol-’ for each hydrogen atom. Variations

+ ~%oHn-\-

i.e.

+ xC60HntJ,

Between CeO and C60H24, and within the first series of molecules, only C60H12 is stable relative to disproportionation into higher and lower hydrides,

905.0 t

900.0 t

series

First

965.0

960.0

-

series

,,V,> ,,,,(

2

4

Fig. 8. Heats of formation

6

6

10

303 (1994) I-9

visualised by plotting AH”r + 20n against n, as in Fig. 8, which includes data for n = O-12 [l],

of this type. The second series of structures was discovered following clues discovered during the first

(Themhem)

12

14

16

16

20

22

24

26

n of C&H,, plotted as AH”r + 20n (in kcal mol-‘) against n

26

B. W. Claw and D.L. KepertlJ.

Mol. Struct.

with C6eH6 being of marginal second series of molecules, C60H22 are stable. If both interconvert, (first

series),

(Theochem)

stability.

Within

(first

the

&His, C6eH2,, and series are allowed to

the only stable molecules C6,,Ht2

303 (1994)

series)

are C6,,H6 and

of CbO forms predominantly

C6DH12.

On completion of this work we became aware of similar calculations [lo] for a more limited set of isomers of C60H16, CG0H2s and C,,H,,. In all three cases the structures considered are less stable than the most stable isomers reported in this paper.

Acknowledgement This work is funded

Council through programme.

its

Special

Research

Centres

References 1 B.W. Glare and D.L. Kepert, J. Mol. Struct. (Theo2 3 4

5 6 7 8

9 10

by the Australian

9

&,Hz2

(second series). It is not clear how much reliance should be placed on these heats of formation, but the appearance of C6eHt2 as the dominant feature in Fig. 8 suggests that the first stage in the hydrogenation

I-9

Research

them), 281 (1993) 45. D.A. Dixon, N. Matsuzawa, T. Fukunaga and F.N. Tebbe, J. Phys. Chem., 96 (1992) 6107. N. Matsuzawa, D.A. Dixon and T. Fukunaga, J. Phys. Chem., 96 (1992) 7594. A. Hirsch, A. Soi and H.R. Karfunkel, Angew. Chem., Int. Ed. Engl., 31 (1992) 766. E. Keller, J. Appl. Crystallogr., 22 (1989) 19. R. Taylor, J. Chem. Sot., Perkin Trans. 2, (1992) 1667. T. Guo and G.E. Scuseria, Chem. Phys. Lett., 191 (1992) 527. F.N. Tebbe, R.L. Harlow, D.B. Chase, D.L. Thorn, G.C. Campbell, J. Calabrese, N. Herron, R.J. Young and E. Wasserman, Science, 256 (1992) 822. B.W. Clare and D.L. Kepert, unpublished work, 1993. N. Matsuzawa, T. Fukunaga and D.A. Dixon, J. Phys. Chem., 96 (1992) 10747.