Comparative ab initic calculations on boron fluorides

INORG. NUCL.

CHEM. LETTERS

Vol. 9, pp. 965,970, 1973.

Persmnoa Press.

Printed in Great Britain.

COMPARATIVE AB INITIC CALCULATIONS ON BORON FLUORIDES Noel J° Fitzpatrick Department of chemistry, university College, Belfield, Dublin 4 (Received 14 May 1973)

Summary and Introduction Geometry optimized ab initio molecular orbital calculations are reported for BF 3, BF 4

and B ~ 4 .

Ab initio calculations

of BF 3 have been published, without geometry optimisation (1) and with it, where optimum B-F bond lengths of 1.306A ~2) and 1.247A (3) were calculated.

Recently the photoelectron

spectrum and anab initio study of B ~ 4 ,

without geometry

optimisation,hsve been published (4).

The calculated bond

lengths in this study agree well with the experimental values and the electronic structures show the similarity of the B-F bonds in BF 3 and B ~ 4

and support the conclusion of Lappert and

coworkers (5) that the sigma charge drift is the dominant factor in deciding the overall bond polarities. to be more stable in the staggered form (D2d).

B~4

is shown

Minimal basis

sets were used where each atomic orbital was represented by three Gaussion functions and the ab initio "Gaussion-70" computer program of Ditchfield, Hehre, Lathan, Newton and pople was used.

965

966

CALCULATIONS ON BORON FLUORIDES

Vol. 9, No. 9

TABLE compound

BF 3

BF 4-

A toms

B-F

B -F

B-F

Bond length (A)

1.31

1.39

1.31

(1.31) a

B2F 4

(1.38)b(1.415c

Stretching force

10.71

const. (md/A5

(7.075 f

(3.725 g

Ionization potential (ev)

13.O3 (15.975 i

2.69

Boron charge Fluorine charge F-F distance, shortest (A) a

f

8.56

B-B 1.72

(1.32)

d

(1.751 e

10.37

3.65

(5-81) h

(3 -05) h

9.47

(12.O75 j

0.66

0.48

0.42

-0.22

-O .37

-O .21

2.27

2.28

2.22

b

electron diffraction (6); X-ray (NH4BF4) not thermally c corrected (7) ; X-ray (NH4BF4) thermally corrected and NMR d e (NaBF 4, KBF4) (7) ; x - r a y (8) ; electron diffraction (9) ; modified Urey-Bradley,

symmetry force constant = 8.8 md/A (i0) ;

g Urey-Bradley (values range from 2.7 to 4.2 md/A, depending on h i force field) (ii) ; Urey-Bradley (12) ; mass spectroscopy (13) ; mass spectroscopy (14).

Discussion The bond lengths in the table show the good agreement of the calculated and experimental results, since the largest difference is O.O2A for the B-F bonds and the difference is 0.O3~ for the B-B bond in B2F 4.

The results also show the

similarity of bond lengths in BF 3 and B2F 4 (1.3088 in the former and 1.3092 in the latter, to four decimals)

and the

appreciably longer bond in the tetrafluoroborate anion.

Wel. 9, No, 9

CALCULA'I'ION$ ON BORON FLUORIDES

In B2F 4 the calculated FBF are at right angles force constant of rotation

angle is 116 ° and the F2B planes

(D2d symmetry).

is 2.07 x io

967

-2

However the torsional

md.A, which

about the B-B bond.

indicates the ease

X-ray determinations

have shown that B2F 4 is planar in the crystal

(8)

(D2h) while

the IR spectrum in an argon matrix and the Raman spectrum have shown that B2F 4 is staggered phases

(12).

in the liquid and gaseous

It has also been reported

(15) that failure to

see the out of plane B-BF 2 mode is consistent with free rotation or almost free rotation.

Thus the calculations

agree with the experimental

in having the D2d structure

results

with lower energy and a very small rotational using semiempirical

and extended H~ckel

force constant.

calculations

planar

B2F 4 was calculated to have lower energy than the staggered molecule

(16), while a consideration

using extended H~ckel rotating,

theory,

of the population

matrix

predicted B2F 4 to be nearly freely

although ~ery slightly more stable in the

staggered form (17).

The stretching ab initio results urey-Bradley

force constants

are larger than the Urey-Bradley

force constants

in all cases.

trend in both cases is the same. constants

from the or modified

However

the

The B-F stretching

force

are larger than the B-B value and for the B-F

stretches the order

is BF 3 ~

Both the experimental potentials

calculated

B2F 4 )

BF 4

and ab initio ionization

of BF 3 are greater than the values for B2F 4,

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CALCULATIONSONBORON FLUORIDES

Vol. 9, No. 9

however the theoretical values are approximately 2~% lower than the experimental values.

In BF 3 the appreciable negative charge on F indicates that the B ~ F

~

bond is of greater importance than the F ~ B

backbonding in agreement with the concept of Lappert and coworkers

(i).

0.22 electrons

The net flow from the fluorine to boron is per

fluorine.

The 2p~ population of B is

0.51, thus O.17 v electrons are donated to the boron from each fluorine and thus the ~ 0.39 electrons.

donation to each fluorine is

In B2F 4 ~ bonding is again important,

the 2pv population of each boron is 0.40.

as

Thus 0.20

electrons are donated from each fluorine and as the fluorine charge is -0.21, the B - ~ F ~

donation is 0.41 electrons.

Thus the B-F bonds in BF 3 and B2F 4 are similar, however the electron donations in B2F 4 are slightly greater than in BF 3. The small increase in stretching force constant and decrease in bond length in changing from B2F 4 to BF 3 is indicative of a stronger bond in the latter due to the larger charge on the boron atom.

In BF 4

multiple bonding does not occur

and the charge of -0.37 indicates the very electronegative nature of fluorine.

In this compound the B-F bond length

is the largest and the B-F stretching force constant is the smallest. One half of the B-B distance the covalent radius of boron,

(O.86A)

may be considered

similar ab initio calculations

on fluorine gave an optimum F-F distance of 1.315~.

Therefore

Vol. 9, No. 9

CALCULATIONS ON BORON FLUORIDES

969

O.66A is considered the covalent radius of fluorine.

Therefore

a B-F covalent distance of 1.52A is expected, without correcting for electronegativity differences. bond in BF 4

The shorter

is thus due to electronegativity differences.

The further decreases in bond length in BF 3 and B2F 4 are due to the multiple bonding in these compounds where O.17 v electrons are donated to each fluorine in BF 3 and 0.20 ~ electrons in B2F 4"

Acknowledgements The author acknowledges an, (Irish) N.S.C.

- C.N.R.S.

Exchange Scholarship, which enabled the calculations to be done on the IBM 370 /165 at Orsay, France. with Professor R. Daudel O n d u l a t o i r e Appliqu~e)

useful discussions

(Director, Centre de M~chanique

and with Dr. W. J. H e h r e

chemistry, u n i v e r s i t y of california, Irvine)

(Dept. of

are also

acknowledged.

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970

CALCULATIONS ON BORON FLUORIDES

Vol. 9, No. 9

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