conformational preferences of 34 valence electron a2x4 molecules: an ab initio study of b2f4, b2cl4,...

20

Conformational Preferences of 34 Valence Electron A2X4 Molecules: An Ab Initio Study of B2F4,

Timothy Clark and Paul von Ragu6 Schleyer Institut fur Organische Chemie der Friedrich-Alexander- Universitat Erlangen-Nurnberg, 0-8520 Erlangen, Federal Republic of Germany Received 19 May 1980; accepted 11 August 1980

Ab irzitio molecular orbital structures and energies of B2F4, B2C14, N204, and C20:- have been calculated for both perpendicular D2d and planar D2h rotamers. The experimental trend toward greater preference for the D2d forms in going from B2F4 to BzCl4 is reproduced. N204 favors the planar conformation, although the rotation barrier is overestimated at the theoretical levels used. The oxalate dianion is calculated to be more stable in the D2d conformation; the experimental planar arrangement in the solid may be due to crystal packing forces. The preferences for one conformation over another are small; analysis indicates that different effects may predominate in each case: x stabilization for B2F4, hyperconjugation for B2Cl4, lone-pair interactions for N204, and electrostatic repulsions for CzOi-.

INTRODUCTION

Isoelectronic molecules generally prefer similar geometries. X2AAX2 systems with 34 valence electrons are exceptional in this respect. Such molecules have formal A-A single bonds and the barriers to rotation are not very large. However, some examples are found to be planar while others favor perpendicular conformations. We now report a detailed examination of B2F4, B2C14, N2O4, and C20i- by means of ab initio molecular orbital calculations.

B2Cl4, first prepared by Stock in 1925,l is one of the few molecules known to adopt basically different conformations in the crystal (planar)2 and in the gas phase (perpendi~ular) .~ The available theoretical calculations4 are not definitive. The closely related compound, B2F4, is planar in both the solid5 and the gas phases,6 but has a rotation barrier (via the D2d form) of only 0.42 kcal m ~ l e - l . ~ ~ > ~ * Both ~ e m i e m p i r i c a l ~ ~ , ~ ~ . ~ and ab ini-

* The trend along the halogen series continues: BZBr4 prefers Dzd symmetry with a rotational barrier of 3.07 kcal mole-1.7

tio9-ll studies of B2F4 are available. Unfortu- nately, one ab initio investigationg reported calculations only for the D2d rotamer and the others used fixedlo or partially optimized1' geometries. N2O4, known to be planar in the gas phase and to have a rotation barrier of 2-3 kcal mole-l,12 has been the subject of many semiempirical and ab initio molecular orbital s t u d i e ~ . ~ J l J ~ In crystals, oxalate dianions are either or may be twisted up to 26°.14d In solution, CzO2- is sus- pected to be perpendi~u1ar.l~ Radornl6 optimized the structure of D2h C20:- a t the minimal and split-valence basis set levels, but did not consider the D2d form as his study was primarily concerned with assessing the reliability of Hartree-Fock calculations in reproducing known geometries of anions. Yoshioka and Jordan17 have also optimized only the D2h rotamer of (220:- using a modified 6-31G basis set.

We have examined all four species in planar (D2h and perpendicular (&d) conformations with full geometry optimization. This not only allows an evaluation of the performance of Hartree-Fock

Journal of Computational Chemistry, Vol. 2, No. 1, 20-29 (1981) 0 1981 by John Wiley & Sons, Inc. CCC 0192-8651/81/010020-10$02.00

Ab Znitio Study of B2F4, B2C14, N204, and C20:- 21

Table I. ride.

Calculated and experimental structures and energies for diboron tetrafluoride and boron trifluo-

Rotamer Paramter STO-3G//STO-3G 4-31G//4-31G 6-31G//4-31G X-ray" Electmn Diffract ionf

!J2Fb(A> D2h) B - B ~ 1.722 1.705 1.67+.05 1.719+.004 B - f a 1.308 1.339 1.322.04 1. 314f.CJ31

-

<BB+ 122.1 121.6 121. 4:O. 1 Total Energy' -441.12252 -446.80414 -447.22457

Rel-ative Energy 0.0 0.0 0.0 0.0

"F4'f ' D2d' B - B ~ 1.719 1.694

B - f a 1.309 1.341 -

~ B B P 122.1 121.8

Total Energy' -441.12378 -446. 80422 -447.22547 Relative Energyd -0.79 -0.05 -0.54

BF3' 331-, B-Ed 1.30ggYh 1.322h

Total Energy' -218.661gh -322. 7863h -323.08531

+0.42

1.31'

* In angstroms. In degrees. In hartrees (= 627.49 kcal mole-l). In kilocalories per mole. Reference 5.

calculations with relatively modest basis sets, but also permits interpretation of the results a t a uniform level.

QUANTUM MECHANICAL METHODS

All calculations used standard, single-determi- nant Hartree-Fock theory and used the GAUSS- IAN 7018 and GAUSSIAN 7619 series of programs. Initial geometry optimizations used the minimal STO-3GZo basis set. B2F4, N2O4, and C20:- were also optimized a t the split-valence 4-31G21 level; single-point calculations were then carried out with the larger ti-31G basis set21 (6-31G//4-31G). Similarly, the STO-3G optimum geometries for B2C14 were used for 4-31G//STo-3G and STO- 3G*//STO-3G single-point calculations. The STO-3G* basis includes a set of d functions for second-row atorns.22

RESULTS

Diboron Tetrafluoride

The STO-3G and the 4-31G optimized geometries for planar ( 1) and perpendicular (2) confor-

Reference 6b. g Reference 9.

Reference 23. Reference 34.

mations of B2F4 are shown in Table I, as are the total and relative energies and a summary of the experimental results. Data for BF3 are included for comparison.23

Surprisingly, the STO-3G geometry for 1 is in better agreement with the experimental structure. The larger 4-31G basis overestimates the length of the B-F bonds and underestimates the B-B distance. Both basis sets predict a slight shortening of the B-B bond on rotation from 1 to 2. All three basis sets (STO-3G, 4-31G, and 6-31G//4-31G) indicate the D2d rotamer, 2, to be the more stable, contrary to the experimental results.6b However, the magnitude of the error is small a t all levels (0.5-1.2 kcal mole-'), even though the sign is not given correctly.

(1)

The experimental heat of fluorination of &,F4 [eq.

BZF4 + F2 + 2BF3

22 Clark and Schleyer

Table 11.

R e a c t i o n A HoR (kca l rr01-l)

Heats of halogenation and hydrogenation.

STO-3G/ / STO- 3G STC-3G*/ /STO-3G 4- 3 1 G 6- 3 1G/ /4- 31G E x p e r i m e n t

B2F4 (2) + F2 - 2 BF3 -137.0 - - 1 9 4.5" -187.4 -200.6'

C2F6 + Fp - 2 CF4 125.3'

B2C14 ( 9 ) t C12 * 2 El3 -74.4 80.4 -73.2b - -68:. pe

C2C16 t C12 * 2 CC14 -15. gd

C2042- ( p ) t H2 - 2 HC02- -111.6 -95.7 -94.8

C2H6 + H2 - 2 CH4 -18.8 - -23. la -15. gd

a 4-31G geometry. Reference 25. sTo-3G geometry. e Reference 27. Reference 23.

(l)], calculated from the heats of formation of B2F4 (ref. 24) and BF3 (ref. 25), is -200.6 kcal mole-'. The STO-3G value for this reaction is too low (-137.0 kcal mole-l) but the 4-31G value (-194.5 kcal mole-l) is in better agreement. This data is summarized in Table 11. The fluorination energy of C2F6 is -125.3 kcal mole-l (ref. 25) (Table 11). The difference in magnitude between carbon and

boron species reflects the differences in bond energies CC > BB and BF > CF.25

Diboron Tetrachloride

The STO-3G geometries of the D2h (3) and D2d (4) rotamers of B&14 are compared with experimental results in Table 111.

Table 111. chloride.

Calculated and experimental structures and energies for diboron tetrachloride and for boron tri-

Ro tamer P a r a m e t e r STO-3G//STO-3G 4-31G//SM-3G STO-3G*/ /STO- 3G E x p e r i m e n t

B 2 C l 4 ( 2 , g2h) B-Ba 1 . 7 1 2 1. 752+.048e

B-Cla 1.796 1 . 7 2 8 t . 0 2 0 e -_

tBBClb 120 .6

T o t a l Energy' -1867.22016 -1885.39468

R e l a t i v e Ene rgyd 3.49 2.75

-1867.31509

2 . 9 1

B2C14(Y, I l l ) B-Ba 1 . 6 9 0

B-Cla 1 . 7 7 1

tBBClb 1 2 0 . 1

T o t a l Energy' -1867.22572 -1885.39906 -1867.31927

R e l a t i v e Energy' 0.0 0.0 0.0

E 1 3 ' E33h B-Cla 1 . 7 6 8 - T o t a l Energy' -1388.22976 -1401 .72481 -1388.30357

1 2 0 . 5 ? l . l e

1 . 8 5 ,f 1. 7g

1 .702:.06Sf 1. 750:.011f

120.7:. 033f

0.0

1 . 7 4 2 2 . W h

a-d Units same as for Table I. Reference 2. Reference 3.

g Reference 35. Reference 26.

A b Initio Study of B2F4, B2C14, N204, and (220:- 23

Table IV. Calculated and experimental structures and energies for dinitrogen tetroxide.

6-31G//4-31G Exper k n t e Rotmer P a r a m e t e r STO-3G//SM-3G 4-31G//4-31G

5 , :I N - N a 1 .622 1 .631 - -2k. N-Oa 1.257 1 .188

-

<"Ob 113.8

T o t a l Energy' -402.52433

R e l a t i v e Energyd 0.0

113.4

407.35909 -407.11135

0.0 0.0

5 , :j N-Na 1.619 1 .563 - -2d N-Oa 1.261 1 .135

-

<"Ob 114.6 113.9

rota1 Energy' -402.51714 -407.34843 -407.76803

2 e l a t i v e Energyd t 4 . 5 6 . 7 t 5 . 8

1 . 7 5 , 1.782

l . l E

113..

0.0

+2 .9

a-d IJnits same as for Table I. Reference 12.

The B-B bond lengths and BBCl angles are reproduced within experimental error, but the B-C1 bond lengths a re overestimated. The relatively large error limits for the experimental structures of B2C4 and the possible effects of crystal packing forces on the geometry of the planar form make it difficult to ascertain the changes in corresponding geometrical parameters of 3 to 4 reliably. STO-3G, however, confirms the apparent shortening of the B-B bond on going from the planar to the perpendicular conformation.

All three basis sets correctly predict 4 to be the more stable rotamer, although the calculated barriers to rotation are 1 kcal mole-' or so higher than the experimental values. The STO-3G barrier (3.5 kcal mole-') is reduced to 2.9 kcal mole-' by the inclusion of d functions (STO-3G*). The slightly lower 4-31G barrier is closest to experiment. As for B;:F4 the theoretical methods used artificially favor the D 2 d rotamer over its planar counterpart but. the errors are not large.

I n order to compare B-C1 bond lengths and thermochemical stabilities we have also optimized BC1:3 at the STO-~G level. The results (Table 111) show the same overestimation of the B-C1 bond

lengths as for BzC14, but the STO-3G geometries are consistent in that they give almost identical B-Cl bond lengths for BCl3 and BZCll, as observed e~perimentally.3,6~?~~ The calculated heats of chlorination [eq. (2)] are somewhat more exo- thermic than the experimental value27 (see Table 11).

(2) B2Cl4 + C12 - 2BC13

Dinitrogen Tetroxide

The calculated structures and energies for DZh ( 5 ) and D 2 d (6) forms of N204 are compared in Table IV with the available experimental data.

0 00 / \N N.-*--O

-0 \ 0 /N-N\ 5 00 / 6

In accordance with previous ab initio calcula- tionsl1J3 and with experiment,I2 the planar D2h

rotamer 5 is found to be the most stable at all levels of theory, although the rotation barrier is consistently overestimated. The STO-3G and 4-31G N-N bond lengths are both far too short. This was found earlierll with other basis sets. It has been suggested28 that a strong contribution from the electronic state in which the a*" orbital is occupied may be responsible for the long NN


Table V. Calculated and experimental structures and energies for the oxalate dianion. Rotamer Parameter STC-3G//STO-3G 4-31G//4-316 6-31G//U-31G Experiment'

2 9 D2h c-ca 1.660f 1. 58Zf 1.57

1.25 f c-oa 1. 280f 1 . 2 6 1 - <CCOb 117. Sf 117. 4f 116.9

Total Energy' -369.61402 -374.52022 -374.90626

Relative Energyd +2.0 + 2 . 8 +3.8

!- 22d c-ca 1.654 1.531

c-oa 1.281 1.266 -

<CCOb 117.4 1 1 7 . 1 Total Energy' -369.61715 -374.52464 -374.91232

Relative Energy 0.0 0.0 0.0

a-d Units same as for Table I. e Reference 14. Reference 17.

bond; therefore, Hartree-Fock calculations should consistently underestimate the N-N distance. An examination of the effects of electron correlation is needed to clarify this matter. The experimental N=O bond length is well reproduced at 4-31G, but is too long at STO-3G. Both basis sets reproduce the NNO angle well. The most noteworthy feature of the 4-31G geometries is the extraordinary difference in the N-N bond lengths (1.631 8, in 5 versus 1.563 8, in 6) but this is not found at the STO-3G level. Either value is abnormally long for a single N-N bond; this is consistent with the low bond energy.

The Oxalate Dianion

RadomlG has discussed the performance of the STO-3G and 4-31G basis in reproducing the x-ray geometry14 of the planar oxalate dianion, 7, but did not consider the perpendicular form, 8.

0 0 0 2- \ 2- / \ 0 /c-c\o/c- 7 8 -0

However, the D2d form, 8, is consistently predicted to be 2-3 kcal molew1 more stable than the D2h rotamer, 7. The geometries and energies of 7 and 8 are shown in Table V. As the calculated C20i-

rotation barrier, 2-3 kcal mole-l, is larger than the likely errors (compare N204, B2F4, and B2C141, we conclude that the Dz,-J rotamer should be the more stable in the gas phase: experiments suggest this to be the case in s01ution.l~ The rather long C-C central bond in planar 7 (1.582 A, 4-31G) is . reduced to a more normal value (1.531 8,) in perpendicular 8. The high heat of hydrogenation [eq. (3)] of C202- (Table 11) indicates that the CC bond is approximately 70 kcal mole-' weaker than that in ethane, but this also reflects the energy gained by separating the two negative charges.

(3) C2Of + He - 2HCO;

DISCUSSION

The rotational barriers and conformational preferences in A2X4 molecules have been analyzed many times in the literature. Earlier work, cited in detail by Howell and Van Wazer,l' concentrated mostly on the T stabilization in the D2h conformation. Later interpretations, notably by Howell and Van Wazer,l' Epiotis et a1.,28 and Gimarc et al.,29 emphasize the effects of the lone pairs on the X atoms. No consistent qualitative treatment has, however, been able to predict satisfactorily the preferred conformation of all the A2X4 molecules. Qualitative molecular orbital (MO) theory is often successful in rationalizing known results, in indi-

Table VI. Summary of geometry and overlap changes on rotati0n.a

STO-3G Overlap Populations Bond Rotational lengthening, barrier,

AAb Axc In plane l,4d In plane 1,3e g2h - kcal ml-I

STO-3G 4-31G Expt. C a l ~ . ~ : I ?h D2d D Z h D2d D2h D2d D2h D2d

132F,l .OO!> .om . I39 .009 .a31 .ooo -.012 .ooo .003 .002 t . 2 -.8

r i o 4 f - ,012 .005 .202 .202 .CQ1 .000 -.026 -.025 .006 .051 -2.0

H + ' l , , .017 .014 .lo9 .lo5 .CQO .COO -.028 - . O X .022 - 1 . 8 5 ~ -3.5 t 2 . 9 ' t4.S N?O,< .OO!, .001 .184 .183 .004 .001 -.024 -.025 .003 .068

a All values are STO-SG unless otherwise stated. The overlap between p orbitals on the A atoms perpendicular to the AX2 plane(s): in the Dad rotamer this is

The overlap between p orbitals on adjacent A and X atoms. The overlap between XI and X2 p orbitals parallel to the A-A axis. The total overlap between X1 and XI' involving both sets of p orbitals in the AXX' plane. The difference in AA bond lengths (A) between Dad and D2h forms. The bond is always longer in the planar

the hyperconjugative overlap.

form. g A negative barrier indicates the D2d rotamer to be more stable.

Reference 6. Reference 3.

j Reference 1.2.

cating trends, and in making predictions for cases in which one dominant orbital effect is involved. However, when several smaller effects oppose each other, as in the present case, conclusions based on qualitative arguments are unconvincing. I t is, perhaps, too much to expect that a qualitative treatment should be able to predict the conformation of B2F4 when the best available ab initio calculation (4-31G//4-31G) still favors the wrong rotamer. We shall now consider the electronic effects operating in planar and perpendicular A2X4 molecules. These will be assessed in terms of Mulliken overlap populations a t a uniform level (STO-SG, Table VI).

?r Conjugation

7r Effects can be analyzed in terms of simple Huckel MO theory, using the isoelectronic, planar dianion 9a as a model.30 $3 and $4 in Figure 1(A) are nonbonding MOS with nodes a t the central atoms and can be ignored. The key occupied orbitals $ 1 and $2 are bonding and antibonding, re- spectively, across the central AA bond. Due to mixing with +s and $6, the central atom coeffi-

cients in 9a are larger in $1 than in $2; a central ir bond order of 0.333 results. However, the same mixing reduces the TAX bond orders (from 0.707 in allyl to 0.667 in 9a). The net stabilization of 9a is -0.343p relative to the perpendicular rotamer 9b (equivalent to two allyl anions). However, the magnitude of this stabilization is dependent on the relative electronegativities of A and X. As shown in Figure 1(B), the coefficients on X in occupied orbitals and on A in unoccupied orbitals ($5 and $6) will become larger with greater electronegativity differences; this will result in diminished A-A 7r bonding. The bonding T A A populations for planar B2F4 (0.005) and for planar B2C14 (0.012) (Table VI) show this clearly.

In isolated AX2 fragments, an increase in the electronegativity difference will result in a de- crease in AX 7r bonding. This is shown by the AX populations in the D z ~ forms; the value for B2F4 (0.009) is much less than that for B2C14 (0.105). In the D2h conformation of B2F4, however, idhe AX ir overlap population (0.139) has increased greatly, much more so than that in B2C14 (0.109) or in the other A2X4 systems. Because of the large B coefficients and B-B bonding character, $5 in planar


9 b

i 4 i 8-c

- \

- $5 \ tt

Figure 1. degenerate set); (B) the changes on going from 9a to B2F4.

The orbitals of A2X4 systems: (A) the changes upon rotation from 9b to 9a (only one orbital is shown for each

B2F4 is decreased in energy and mixes with $1 'more effectively. As a result of this mixing, the coefficients on A and X tend to become more nearly equal; increased A-A and A--X bonding results. Conversely, $6 mixes less with $2 as a consequence of the larger A-X electronegativity difference. The AA antibonding and AX bonding character of $2 therefore is increased somewhat. The net result when $1 and $2 are taken together is a large increase in AX bonding in planar B2F4, but little net AA bonding.

K Effects thus favor planar over perpendicular conformations, but B2F4 is the only molecule among the four in which this influence dominates. Paradoxically, it is not the XBB but rather the KBF

bonding which is strongly favored in planar B2F4. Attention is called to the detailed PMO analysis of interactions in related systems by Devaquet,

Townshend, and Hehre.32 Included in their study are 34 additional valence electron species, such as oxalyl fluoride and 2,3-difluoroethylene.

1,4 and 1,3 Interactions

Previous analyses have emphasized the impor- tance of the X lone-pair orbitals in determining the most stable conformation of A2X4 molecule^.^^,^^^^^ However, with the possible exception of N204, the in-plane 1,4 populations (Table VI) do not provide support; these effects seem to be insignificant. G i m a r ~ ~ ~ has argued convincingly that the small NO2 association energy and the preference of N2O4 for the perpendicular conformation are both con- sequences of large p z contribution from oxygen and relatively small pure p z contribution of ni- trogen as exemplified by the 4al, orbital.

Ab Znitio Study of B2F4, B2C14, Nz04, and CzOi- 27

& 0 n - 4 h

\ / x

D2d

Figure 2. Hyperconjugative orbital interactions in A2X4 molecules.

Electrostatic factors, it should be emphasized, favor the perpendicular conformations where the electronegative X atoms are farther apart. The electron-electron repulsion energy is higher for the planar form of all four compounds. Electrostatic repulsion should be particularly important for the oxalate dianion, which has calculated charges of -0.5 to -0.6 on the oxygen atoms.

1,3 Interactions between X atoms are seen from Table VI to be antibonding. Overlap populations for B2C14, N&4, i3nd (22042- are all negative and are essentially conformation independent. B2F4, with the largest AX electronegativity difference, shows decreased 1,3 repulsion in the perpendicular form. Gimarc has described some of the factors which may be responsi ble.29

Hypercon jugation

In D2d conformations, double hyperconjugation across the A-A bond can take place (Fig. 2). Each AX2 group acts simultaneously as a donor (A-X bonds) and, in the perpendicular plane, as an acceptor (x orbital on A). The hyperconjugative preference for perpendicular conformations can

be appreciable; e.g., B2H4 is calculated to be 12.7 kcal mole-' (STO-3G) more stable in the D2d than in the D2h form.31

The nature of A and X strongly influences such hyperconjugation. As BF3 is a weaker Lewis acid than BC13,33 a BF2 group should be a poorer hyperconjugative acceptor than BC12. Because of the greater electronegativity of F than C1, BFl should likewise be a poorer hyperconjugative donor than BC12. Thus, hyperconjugative stabilization of perpendicular B2C14 should be greater than B2F4; this is shown by the TAA (&d) overlap populations in Table VI. N2O4, which prefers the planar form, has a negligible D2d T A A population and this is not much larger in CzO;, which prefers the L)2d conformation. Hyperconjugation appears to be sig- nificant only with B2C14.

CONCLUSIONS

(1) Thirty-four valence electron A2X4 systems show low rotational barriers, 4 kcal mole-' or less, which are reproduced within 1-2 kcal mole-' a t the minimal and split-valence basis set ab initio levels. The 4-31G heats of halogenation of B2F4 and B2Cl4 are given accurately.


(2) The experimental geometries are reproduced well except for the long N-N bond in N2O4 which is calculated to be too short by over 0.1 A. In general, the AA bond lengths are shorter in perpendicular than in planar geometries.

(3) In agreement with experiment, N204 is calculated to prefer the planar and B2C14 the perpendicular conformations. The theoretical rotation barrier of B2F4 is near zero, even though the experimental preference for the planar form is not reproduced. A major finding of this study is the indicated perpendicular preference of C20i- in the gas phase; the planarity of oxylate dianions observed in some x-ray studies may be due to crystal packing forces.

(4) Different effects seem to dominate in determining the conformational preferences of all four species. For B2F4, greater A delocalization (chiefly in the BF bonds) favors the planar form. For B2Cl4, hyperconjugation in the perpendicular conformation is important. Planar N204 is stabi- lized by 1,4 lone-pair interactions. Finally, electrostatic repulsions may be responsible for the preferred perpendicular conformation of the oxylate dianion, C202-.

The authors thank N. D. Epiotis and Y. Apeloig for discussions and the Regionales Rechenzentrum for assis- tance. The Fonds der Chemischen Industrie provided support.

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conformational preferences of 34 valence electron a2x4 molecules: an ab initio study of b2f4, b2cl4,...

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