Barrier to internal rotation and π-bonding in mercaptoborane, H2BSH, studied by ab initio calculations

289 Journal of Mofecaiar Stractare, 23 (I 974) 289-300 @J Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

BARRIER TO INTERNAL ROTATION AND rc-BONDING. IN MERCAPTOBORANE, H,BSH, STUDIED BY AB INITIO CALCULATIONS

0.

GROPEN*,

E.

WISL0FF

NILSSEN”

AND

H.

M. SEIP

Department of Chemistry, Unicersity of Oslo, Btindern, Oslo 3 (Norway)

(Received 1 February 1974)

ABSTRACT

Ab initio calculations have shown that a partial n-bond is superimposed on the a-bond between B and S in the planar form of mercaptoborane. Including d-orbitals on sulphur in the basis set, the barrier to internal rotation becomes 19-5 kcal mol- 1 if partial geometry optimization is carried out, both in the planar and in the orthogonal form. A sIightly higher value, 21.8 kcal mol-‘, is obtained for rigid rotation with the same basis set. The total energy increases by about 20 kcal mol-’ if the d-orbitals are excluded, but the change in the barrier height is less than 2 kcal mol- ‘_ Approximately half of the barrier is due to the breaking of the partial n-bond when the torsiona angle changes from 0” to 90”. The results are compared with the results of a similar calculation on H2A10H, and those of CNDO/Z calculations on H,BSH and (CH3)ZBS(CH,).

INTRODUCTION

The tendency of boron to form partial double bonds with atoms having one or more lone pairs has been studied by several methods. Considerable n-bond orders have been found for B-N [l-3], B-O [2,4-61, B-F [2, 71 and probably also for B-Cl [S, 91 bonds. Recent electron-diffraction studies have shown that the )B-S’

fragments

are planar

in dimethyl-1,2,4-trithia-3,5-diborolane

dichloro-1,2,4-trithia-3,5diborolane [12], tris(methylthio)-borane (IV) [14-J. _

(II) [13],

(I) [lo],

[ll], methylthio-dimethylborane and bis(dimethylboryl)disulphane‘

(III) (V)

* Present address: Institute of Medical Biology, University of Tromsa, Box 977, N-9001 Tromsnr, Norway

Me\B-*f /

Me

Me

m s-s

/

BMe,

/

H\s-sfH H’

me2

xl

P

These results also seem to be strong evidence for considerable n-bond order in B-S bonds as proposed by Siebert et al. 1151. However, the B-S bond lengths are close to 1.80 A in these compounds (the shortest B-S bond length, 1.779 A, was found in III). Using the vaiues given by Pauling [16] for the atomic radii and the Schomaker-Stevenson rule, the B-S single bond is calculated to be r(B-S)

= 0.81-t 1.04-0.08

x 0.5 = 1.81 A.

The observed shortening is thus very small. It should be noted, however, that a similar calculation of the B-C bond lengths in BMe, gives a bond length of only 1.52 A, while the observed value is 1.58 A [17]. Moreover, Vahrenkamp interpreted the chin [is] and the vibrational spectra [19]. of several thioboranes as evidence for negligible z-bond orders in B-S bonds. A comparison of the n-bond orders in I, 11 and 1,2,4-trithia-3,5-borolane with the corresponding oxygen compounds has been carried out by semi-empirical MO calculations (CNDO/2) [6]. Rather surprisingly similar n-bond orders were found in the B-S and B-O bonds. The best way to clarXy the properties of the B-S bonds seemed to be by ab initio calculations. Unfortunately the computing time prohibits such calculations on the compounds 1-V and mercaptoborane (VI) was chosen, though this compound cannot be studied experimentally by the electron-diffraction method. We have also carried out CNDO/2 calculations on mercaptoborane and methylthio-dimethylborane, and we have tried to analyse the nature of the barrier to internal rotation for the B-S bond.

COMF’UTATIONAL

DETAIL!3

During the past five years a great deal of effort has been spent in the calibration of theoretical methods for prediction of rotational barriers about “pure” single bonds [20,21]. The general conclusion drawn -from these calculations is

291 that the magnitudes of barriers are satisfactorily predicted within the single configuration Hartree-Fock approximation. The rotations about single bonds are accompanied by almost negligibly small changes in the charge distribution, and the correlation energy is therefore expected to be nearly constant during the rotation. Less experience has been accumulated for barriers about partial double bonds [3,22]. In these cases the charge transfer may be greater, leading to a correlation energy contribution to the barrier which should not be neglected. We believe, however, that inclusion of the correlation energy will not change the main conclusion of the calculations in the present case. The calculations were performed with the program REFLECT 1231,which solves the Roothan-Hall equations for a Gaussian type basis. Although some problems, such as the calculation of the inversion barrier in ammonia 1241,require a very large basis set, potential barriers are often calculated quite accurately with a double zeta basis [21]. Polarization functions are important in some calculations, e.g. for hydrogen peroxide 125,261. The accumulated experience indicates that with Gaussian type functions a (9/5/l) set contracted to (4/2/l) is satisfactory for first row atoms. For hydroxyborane [27] the d-orbitals on boron proved to be unimportant for the determination of the barrier. We have therefore used Huzinaga’s (9/5) basis contracted to (412) for boron 1281and a (12/9/l) basis contracted to (6/4/l) for sulphur. The s- andp-functions for sulphur were taken from Veillard [29], and for the d-exponent the value 0.54 proposed by Roos and Siegbahn 1301 was used in most calculations_ However, the exponent was also varied, and we found the best value to be 0.50. The change in total energy was only about 3 kcal mol-‘, and the change in the barrier was negligible. For hydrogen a 4s basis contracted to 3s was applied using Huzinaga’s exponents [28] scaled by the factor 1.25.

RESULTS AND DISCUSSION

(a) Barriers and geometry Calculations were carried out for the planar form (torsional angle + = O”) and for the orthogonal form (4 = 900). In all cases we used 1.20 A for the B-H bond lengths and 120” for the bond angles around boron. The B-S and S-H bond lengths as well as the BSH angle, were varied to find the energy minimum for both the planar and the orthogonal form. These two forms will be denoted by PO (planar optimized) and 00 (orthogonal optimized) respectively. Results are found in’Tablc 1, where we also give total energies obtained in a number of other calculations with the bond lengths and bond angles from the PO form. The result for the ON (orthogonal non-optimized) form was obtained with the complete basis. If the d-orbit& on sulphur were excluded, the energy increased by about 20 kcal mol- ‘. The calculations without the p,-orbital on boron (but with d-

292 TABLE

1 HzBSH

STRUCTURALPARAhfETER~ANDENERGIE.SFOR

B-S

4 Planar forms

OrthogonaZforms

a Parameters

(A)

S-H

(~4)

LBSH

0

Energy

(aa.)

PO without d-orbitals withoutp, on boron

(0”) (0”) (0°)

1.79 (1.79) (I -79)

1.340 (1.340) (I -340)

(Z) (99”)

-423.94430 -423.91072 -423.92575

00 ON without d-orbitals withoutp, on boron

(90’) (905) (90’) (905)

1.88 (1.79) (1.79) (1.79)

1.345 (1.340) (1.340) (I -340)

(& (99”) (99”)

-423.91330 - 423.90950 -423.87872 -423.90937

in parentheses

were not varied.

orbitals on sulphur) were carried out to get a better understanding of the barrier as discussed later. The B-S bond length found for the planar form, 1.79 hi, agrees satisfactoriIy with the value of 1.78 A found in Me,BSMe by electron diffraction [12]. The force constant for stretching of the B-S bond was found to be 3.7 mdyn A-’ in the planar form, somewhat larger than found from the vibrational spectra of MezBSMe [ 121. The barrier to internal rotation about the B-S bond was calculated in several ways as shown in Table 2. Except if the p,-orbital on boron is excluded, we find TABLE

2 (kcalmol-r)

BARRIERSTOINTERNALROTATION

Rigid rotation AE (ON-PO)

with d-orbitals

on S

Geometry variation aIso in orthogonal form, d-orbitats on S AE

OBTAINED

FOR H+BSH

21.8

19.5

(00-PO)

Rigid rotation

without d-orbitals

Rigid rotation

without pz orbital

a barrier caIculated the stable mination.

20.1 on B

10.3

of about 20 kcal mol-l. This barrier is even higher than the barrier for hydroxyborane [27] showing quite clearly that the planar form is one. The d-orbitals on sulphut are not important for the barrier deterIt is interesting that a fairly high barrier is obtained even if thep,-orbital

on boron is excluded, though the drop from 21.8 kcal mol-’ to 10.3 kcal mol-’ demonstrates that the p=-orbital is essential for the determination of the barrier height, and indicates a considerable.n-bond order in the B-S bond in the pIanar form.

293

Barriers to internal rotation are often analysed by splitting the energy into various terms [31]. The differences between the values for 4 = 0’ and C$ = 90” for the one-electron, two-electron and nuclear repulsion energy are presented both for rigid and relaxed rotation in TabIe 3. Even if the barrier is only 2.3 kcal mo1- 1 smaller for a relaxed than for a rigid rotation, the B-S bond lengthening in the 00 form is considerable (0.09 A), and the nature of the barrier appears to be quite different in the two cases as far as the energy analysis is concerned. We will first concentrate on a discussion of the rigid rotation which probabIy gives a better understanding of the origin of the barrier. A short discussion of the relaxed rotation will be given later. TABLE THE

3

DIFFERENCES

INVARIOUS

ENERGY

CONTRIBUTIONS

IN

PLANARAND

ORTHOGONXLFORhf

OF

H2BSH

(a.u.)

Energy (OO)Energy (ON)-

(6)

One-electron

Two-electrorz

Nuclear

Total

coniribulions

contributions

repdsion

energy

- 1.054 j-0.242

- 1.335 -0.01 I

to.3 10 ;0.34g

Energy (PO) Energy (PO)

Population

+ 2.420 -0. I96

analysis

The results from Mulliken’s population analysis [32] are presented inTables 46. Table 4 gives the gross atomic populations found for the three forms, PO, ON, and 00. The electron density on B is higher, and the density on S lower, in the planar than in the orthogonal form-The variations in the charges on the H atoms are small. Table 5 gives the electron populations in the atomic orbitals. The variations with the rotation about the B-S bond occur in the s- and p-orbitals, the populations in the d-orbital are small and nearly equal in the two forms. In the planar form the table shows a charge transfer from boron to sulphur in the a-bonds (0.3 1 Gctrons) and a backdonation in the n-system (0.21 electrons). The total effect is TABLE GROSS

4

ATOMIC

POPULATIONS

IN

H2BSH=

Molecular form

HI

H2

ff3

B

S

PO

ON 00

0.95 0.95 0.95

0.93 0.95 0.95

0.77 0.77 0.77

4.90 4.83 4.83

16.46 16.52 16.51

A(ON-PO)

0.00

to.02

0.00

-0.07

a HI and Hz are bonded to boron; in the planar form H1

to.06

is cis to Ha.

294

TABLE5 ELECTRON

POPULATlONS

IN ATOWC

5

ORBITALS

OF VARIOUS

TYPES=

Pz

PY

P=

dxx

dxy

dx,,

d FF

dF=

dz, -

_-._ PO

ON

B S

2.96 5.85

0.66 3.44

1.07 3.27

0.21 3.78

0.06

0.01

0.01

0.05

0.00 -0.01

B

3.01 5.86

0.70 3.39

1.06 3.23

0.05 3.94

0.06

0.00

0.00

0.05

0.00 -0.01

B

0.05

0.04

0.00 -0.16

S

0.01 -0.05 -0.04

0.00

0.00

0.00

S ACON-~0)

0.15

0.00 -0.01

0.00

il The x-axis is along the ES bond. For B the z-axis is perpendicular to the H2BS plane; for S the z-axis is perpendicular to the BSH pIane and the orientation varies therefore with qk

TABLE

6

DIFFERENCES

S +0.15

IN

NET

B -0.03

AND

OVERLAP

Wl to.05

a(ON-PO)

POPULATIONS,

ffz +0.07

ff3

-0.03

J3rr,

-0.04

BfIz

- 0.03

Sff3

-O.Of

BS -0.09

as expected a charge transfer from boron to the more electronegative sulphur atom (0.10 electrons). In the orthogonal form the population in the p,-orbital on boron is reduced from 0.21 to 0.05 electrons, while the populations in the px and s-orbitals are increased by 0.09 eIectrons compared with the planar form. It seems, therefore,

as if about

0.07 electrons

have been transferred

from the boron

to the suIihur

atom during the rotation from the planar to the orthogonal form. However, the net and overlap populations given in Table 6 indicate that it is a reduction of overlap charge and a weakening of the B-S bond rather than a reduction of the charge on the boron atom. The change in the overlap population in the B-S bond from 0.620 in the planar form to 0.540 in the orthogonal form agrees with the picture that the rotation is accompanied by a destruction of a partial z-bond. The charge transfer from sulphur to the p,-orbital on boron in the orthogonai form can for symmetry reasons not occur from the p,-orbital on sulphur which is in the H,BS plane. If charge is removed from the p,-orbital on sulphur, a weakening of the S-H bond would occur.

The electron density in the p,-orbital on sulphur is high in the orthogonal. form. The resulting repulsion between this lone-pair and the electrons in the B-H bonds may be responsibIe for the barrier of about 10 kcal mol-’ the p,-orbital on boron is excluded from tbe calculation.

obtained when

A A’ A’ A’ A’ A” A’ A’ A’ A’ A’ A”

Valence orbitals Inner orbitals (told) Inner orbitals (S) Inner orbitals (B)

2Ps (S) 3, (a BS BH’ SH BHZ LP (S) II

1sw 25(9 1s(B) 2P,(8)

synmetry

Planar form

-91.993225 - 88974293 - 7.649482 - 6,664662 - 6,663100 - 6.661655 - 0.999756 - 0.696610 - 0.579790 - 0.508630 - 0.454677 --0.407178

,___... -_.-.

A’ A’ A’ A’ A’ A” A’ A’ A’ A” A’ A”

orbirol energy (a,u.) symmetry

.--

-91.966484 - 8.949861 - 7.664042 - 6.640694 - 6.639515 - 6.636702 - 0.991372 - 0.699092 - 0.559284 - 0.538570 - 0.463091 - 0.360229

orbitnl ewgy

Orrhogorrnl form (ON)

HzBSH

-0.204 to,007 i-O,008 -0.001

-0.00068 to,00529 tO.00761 -0,00767 to.08467 to.22203 -0.99806 t1.34174 -1.30350 to.44905

+0.00008 to,00239

orre-elcctrorr lerm

Euergy difererrcrs,

ORBITAL ENERGIES AND ENERGY DIFFERENCE TERMS FOR THE MOLECULAR ORDITALS IN

TABLE 7

mwrs

$0.137 +0.105 to.120 -0.015

-j-O.02670 to,02323 -0,01454 to.02132 to,01978 -t-0,02879 -0.03395 -0,11350 to.51954 -0.70081 to.64333 -0,17758

rwelcctro/r

-0.067 to.112 3-0.128 -0.015

to.02678 to.02562 -0.01522 f0.02661 to,02739 t0.02112 to.05072 1-0.10853 -0.47852 to,64093 -0.66017 1.0,27147

elcctrorr energy fur enclr MO

A(OU-PO) (n,rr.) __.----

296

(c) Energ_v analysis The orbital energies and the differences between various the orbit& found for the two forms are given in Table 7. The (PIi) have recentIy been proposed by Clementi et aI. [33], to be for anaIysing rotational barriers_ The total energy is then given all electrons

energy terms for electron energies convenient terms by the sum over

The meaning of the tentative assignments given for the molecular orbitals in Table 7 shouId not be stressed, as the valence orbitaIs are delocalized to a great extent and change during the rotation. A discussion of the barrier based on the variation in energy terms for the separate moIecular orbitals seems therefore rather doubtfu1. It may be preferabIe to sum a11 terms for the valence shells and a11 for the inner shells as shown in the lower part of Table 7. The numbers seem to imply that a change in the inner shells on the sulphur atom causes the barrier, since the electron energies, or more preciseIy the electron repulsion terms, for these orbitals increase considerably when (b changes from 0” to 90”. However, this picture is rather unsatisfactory since the changes in the inner orbitals with variation of 4 are extremeIy small, the eigenvectors are nearly identical for 4 = 0” and 4 = 90”. The reason for this dilemma may be seen from the definition of the electron energies. The repulsion between an inner electrpn, say in orbital k,and the valence electron in orbital l, is divided equally between qk and Q_ Since the difference in the repuIsion between the inner shell electrons for the ON and PO forms is extremely small (we calculated the difference to be less than 0.0001 a.u.), the difference in the repulsion between valence electrons and inner electrons is responsibie for the inner she11 term (0.105 a.u.). We therefore define a “modified core attraction energy” (MCA), which consists of the one-electron terms (the barrier contribution from this term is -0_196 a.u.) and the repuIsion between the valence shells and the inner shells (barrier contribution 0.210 au.). We then find that both the reduced electron repulsion between valence electrons (0.032 a.u.) and the change in the modified core attraction enera (0.014 a-u.) stabilize the planar form (TabIe 8). It is interesting to compare these results for HzBSH with some preliminary caiculations on H,AIOH [34]. Results for the latter molecule are presented in Tables 8 and 9, and show that according to these calcuiations, the planar form is the stable one also for H,AIOH, though the barrier is only 3.2 kcal mol-‘. We have a charge transfer from oxygen to the formally vacant p=orbital on aIuminium when the dihedral angle changes from 90” to 0”. This should indicate the same type of barrier as in H2BSH. However, the electron energy of the valence orbit& tends to stabilize the planar form of H,AlOH, the electron

297 TABLE ENERGY

8 DIFFERENCES,

A(UN--PO)

(a.u.1 HzBSH

One-electron energy El

HzAIOH

-0.196

0.01 IS

Electron repulsion” VV+&VI 11+*vr 11 VI vv

0.137 0.105 0.000 0.210 0.032

0.0016 - 0.0042 0.000 -0.0085 0.0058

MCA

0.014

0.0033

= El-+-VI

z V = Valence electron, I = inner electron; VV thus denotes the total electron repulsion between electrons in the valence orbit&.

energy of the inner orbitals the orthogonal form; just the opposite of what we found for H,BSH (cf. Tables 8 and 9). The reason for this difference is obviously that in HzAIOH the charge is transferred to the heavier atom and in HzBSH to the lighter atom in the central bond when the torsional angle changes from 90 ’ to 0 O_If, however, the energy is separated into various terms as in Table 8, the similarity of two barriers is evident. In both cases the VV repulsion and the MCA term stabilize the planar form. (ci) Relaxation

of the B-S bomi

Table 3 shows that the rigid rotation is accompanied by an increase in the two-electron energy and a decrease in the one-electron energy. In the discussion in the previous sections we have also pointed out the close connection between the barrier and the weakening of the B-S bond as 4 increases from 0” to 90”. The lengthening of the B-S bond in the 00 form (0.09 A) is therefore reasonable. This lengthening leads only to a small change in the barrier. However, the decrease in the two-eIectron energy and the increase in the one-electron energy are sufficiently large to give opposite signs for the corresponding difference terms for a rigid and a relaxed rotation (Table 3). TABLE 9 ENERGY

DIFFERENCES

(ORTHOGONAL-PLANAR)

One-electron terms IE

Valence orbitals Inner orbitals

FOR

HzAiOH

Two-electron terms

0.0118

- 0.0026

0.0127 -0.0009

0.0016 -0.0042

(a-u.)

Electron energy -0.0092

0.0143

-0.0051

Nuclear repulsion

Total energy

0.004 1

0.005 1

298 (e) Comparison

of results of the ab initio calculations on H,BSH

calculations on HJ3Sfl

As mentioned

and CNDOI2

and Me,BSMe

in the introduction,

Me,BSMe

has been studied by electron

diffraction. Unfortunately the computing time required prevented ab initio calculations on this compound at present, and so the CND0/2 method [35, 361 was used. Calculations were first carried out for H,BSH for comparison with the ab initio results. Previous investigations have shown that if the d-orbitals on sulphur are included as in the standard CND0/2 program, rather unsatisfactory results may be obtained [6]. Table 10 shows the same trend, the barrier obtained without d-orbitals on sulphur is in better agreement with the ab initio results, though the value becomes somewhat too low. The change in the charges on S and B when 4 is varied from 90” to 0” are also similar to the ab initio values. The barrier obtained for Me,BSMe is more than 2/3 of the barrier in HIBSH according to the CNDO/2 resuIt.

TABLE

10

BARRIERS

TO

CND0/2

METHOD

INTERNAL

ROTATION

(kcal mol-*)

With d-orbirals

on S

Wixhout d-orbitals

38.8 26.9

HzBSH MezBSMe

IN HzBSH AND

MezBSMe

OBTAINED

BY THE

on S

14.5 Il.2

Table 11 shows the variation in energy with the torsional angle 4, obtained by CND0/2 (without d-orbitais) for H2BSH. If the potential V(4) is assumed harmonic up to 4 = 20”, a force constant for the torsional oscillation equal to 0.14 mdyn A radm2 is calculated. Assuming the ratio of the energies obtained by CNDO and by ab initio calculations to be the same for all values of 4, the latter method gives 0.19 mdyn A radd2. The force constant used for Me,BSMe [12], 0.20 mdyn A radm2 is therefore reasonable, though perhaps somewhat too iarge.

TABLE ENERGIES

H&f?-)

11 (kCd

IIIOl-‘)

RELATIVE

-0

20 1.2

TO

THE

40 5.1

PLANAR

60 8.8

FORM

FOR

90 14.5

&B!%H

(CNDO/Z)

299 CONCLUSION

In our opinion the present investigation clearly shows HzBSH to be most stable in the planar form. We find the rigid rotation suitable for discussing the origin of the barrier as the changes in the one- and two-electron terms for a relaxed rotation are dominated by the changes caused by the B-S bond lengthening We have proposed a separation of the energy into “modified core attraction”, repulsion between the valence electrons, and nuclear repulsion, as the inner shells are essentially unaffected by the rotation. The charge transfer of 0.21 electrons from sulphur to the nearly empty p-orbital on boron in the planar form leads to a n-bond superimposed on the o-bond between B and S. The breaking of this partial n-bond results in a larger electron repulsion in the valence orbitals in the orthogonal than in the planar form and is the main reason for the substantial barrier to internal rotation. The effects are similar to those found in H2BOH [27]. It is extremely unlikely that improvements in the calculation method will change this conchrsion. On the other hand, the actual numbers obtained must be considered with some caution. Increase in the basis set, optimization of the structural parameters not varied in the present study, and inclusion of the correlation energy may give significant changes. The small effect of the d-orbitals on sulphur, the nearly equal values for the barrier obtained for rigid rotation and with partial geometry optimization of the orthogonal form may perhaps indicate that no large change in the barrier will be obtained within the Hat-tree-Fock approximation. Considering

the value of the barrier in H2BSH,

it is likely that the )B-S’

fragment is also planar in other compounds if the steric effects are not too important*. The CND0/2 results on MezBSMe and the compounds I and II [6] give further evidence for this conclusion, which is in agreement with the electrondiffraction rest&s mentioned in the introduction.

ACKNOWLEDGEMENT

The authors are grateful to cand. real. Harald Jensen for helpful discussions.

REFERENCES 1 K. Niedenzu and J. W. Dawson, in E. L. Mutterties (Ed.), The Ctienzistry of Boron and Its Compounds, Wiley, New York 1967, p_ 377. * The heavy atom skeleton is probably non-planar both in MezBSBMez [iSI and Me2BOBMe2 [37].

300 2 H. N&h and H. Vahrcnkamp, f. Organometal. Clwt17., 12 (1968) 23. 3 D. R. Armstrong, B. J. Duke and P. G. Perkins, J. Chenr. Sot. A, 1969, 2566. 4 C. A. Coulson, Acra Crystallogr., B25 (1969) 807. 5 G. F. Lanthier and W. A. G. Graham, Chem. Comnrun., (1968) 715. 6 O_ Gropen and P. G. Vassbotn, Acta Chem. Stand., 27 (1973) 3079. 7 D. R. Armstrong and P. G- Perkins, T/leer. Chirn. Actu, 15 (1969) 413. 8 M. F. Lappert, M. R. Litzow, J. B. Pedley, P. N. K. Riley and A. Tweedale, J. Clrern. Sot. A, 1968, 3105. 9 D. R. Armstrong and P. G. Perkins, J. Chem. Sec. A, 1967, 1218. 10 H. M. Seip, R. Seip and W. Siebert, Acfa Chem. Scund., 27 (1973) 15. 11 A. Almenningen, H. M. Seip and P. Vassbotn, Acta Chem. Scarrd., 27 (1973) 2112 K. Brendhaugen, E. Wisloff Nilssen and H. M. Seip, Acru Chem. Stand., 27 (1973) 2965. :3 R. Johansen, E. Wisliiff Nilssen, H. M. Seip and W. Siebert, Acfo C%em. Scund., 27 (1973) 3015. 14 R. Johansen, H. M. Seip and W. Siebert, to be published. 15 W. Siebert, E. Gast and M. J. Schmidt, f. Orgononretal. C/rem., 23 (1970) 329. 16 L. Pauling, jVofure o/the Chemical Bond, 3rd Edn., Cornell University Press, lthaca,NewYork, 1960. 17 L. S. Bartell and B. L. Carroll, J. C/renr. Phys., 42 (1965) 3076. 18 H. Vahrenkamp, J. Orgonotnefaf. Chem., 28 (1971) 167. 19 H. Vahrenkamp. J. Orgarronretal_ Chenr_, 28 (1971) 181. 20 J. P. Lowe, Progr. P11y.s. Org. Chem., 6 (1968) I. 21 H. F. Schaefer, III, The Electronic Structures o/Atoms andMolecr:les, Addison-Wesley, Reading, Mass., 1972. 22 P. N. Skancke and J. E. Boggs, J. Mol. Srrucr.. 16 (1973) 179. 23 P. Siegbahn, CXenl. Phys. Left.. 8 (1971) 245. 24 R. M. Stevens, J. Chenr. P&w., 55 (1971) 1725. 25 T. H. Dunning Jr. and N. W. Winter, Chern. Phys. Left., II (1971) 194. 26 J. P. Ranck and H. Johansen, Theor. CIu%l. Acra, 24 (1972) 334. 27 0. Gropen and R. Johansen, J. Mol. Struct., in press. 28 S. Huzinaga, J. Chenr. P/~ys., 42 (1965) 1293. 29 A. Veillard, Theor_ Chim. Acto, 12 (1968) 405. 30 B. Roos and P. Siegbahn, Theor. Chim. Actu, 17 (1970) 199. 31 W. H. Fink and L. C. Allen, J. C%enr.Phys., 46 (1967) 2261. 32 R. S. Mulliken, J. Chem. Phys., 23 (1955) 1833, 1841. 33 E. Clementi and H. Popkie, J. Chem. Phys., 57 (1972) 4870. 34 0. Gr_open and E. Wisldff Nilssen, to be published. 35 J. A. Pople, D. P. Santry and G. A. Segal, J. Chern. Phys., 43 (1965) S129. 36 J. A. Pople and G. A. Segal, 3. Clrem. Phys., 44 (1966) 3289. 37 G. Gundersen, private communication.