Electronic and structural properties of borazine and related molecules

Volume

112, number

2

ELECTRONIC Russell

J

Depmtttenl

CHEhlICAL

AND STRUCTURAL

_BOYD,

30

PHYSICS LETTERS

PROPERTLES

Sai Cheng CHOI and Christopher

OF BORAZINE

AND RELATED

November 1964

MOLECULES

C. HALE

of Cl,etttistry, Dalltousie University. Halifax. h’ova Scotia. Canada B3H 453

Keccived 3 September

1984

Ab initio SCF >I0 calculations are reported for benzene, s-triazine, borazinc and boroxine. The Laplacian of the charge density and the hlullilien population analysis procedure demonstrate that the dclocalization of the ‘ITelectrons decreases

and rhc polariry of the ring bonds increases substantially as the atoms in the ring become more dissimilar. Several other properties, including distortion of the ring angles. puckering of the ring and nuclear quadrupohu coupling constants, emphasize the different chemical properties within the isoelectronic series.

I. introduction Borazine, the inorganic analogue of benzene, is UI physical properties and structure but chenti-

similar

ally much more reactive than the prorotype ofaromatic systems. This is generally attributed [l-3] to the more localized nature of the TTelectrons in borazine, with the evidence coming from molecular orbital (MO) calculations [4-G] and the addition reactions of borazinc vis&vis the clectrophilic substitution reactions of bcnzcnc. In this work the Laplacian of the charge density (71 and ab initio h-10 calculations are used to study the polanty of bonds, the distortion of ring angles dnd d

scrles:

number of electronic propertiesin the isoelectric bewcnc (I), s-triaLine (II), borazinc (III) and

boroxinc

(IV).

I

2.

II

III

IV

Methods

The majority of the computations were performed on a Pcrkin-Elmer 3230 computer using the GAUSSIAN SO series of programs [S] _The electric field gradients were evaluated [9.10] by USCof a modified version 136

of the GAUSSIAN 76 program [ 1 l] on the Dalhousie University CYBER 170-730 computer. All plots of the charge density and its Laplacian were obtained by use of program PLOTDEN [ 1 ‘_I on a Nicolet Zeta 8 plotter attached to the PE-3230.

3. Results and discussion A detailed analysis of the comparison between the theoretical and experimental structures presented in table 1 is hampered by experimental difficulties [ 14]_ In agreement with previous calculations [15-181 all molecules excluding benzene are predicted to have D3,, equilibrium structures_ The 4-31G calculations, which generally give more accurate geometries than the minimal STO-3G basis set [ 19,201, predict an opening of the NCN angle in s-triazine and a closing of the ring angle at boron in III and IV relative to the 120’ angle of benzene_ These results are in reasonable agreement with the experimental data except in boroxine for which little or no ring distortion has been observed. It is also interesting to note that the BN bond in borazine is substantially longer than the CC bond in benzene whereas the CN bond of s-triazine is much shorter; also the BO bond of boroxine is smaller than the BN bond of borazine. Whereas the bond lengths within the rings are readily interpreted in terms of the

degree of delocalization and the sizes of the atomic 0 009-26 14/84/S 03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

Volumi

112, number 2

CHEhlICAL

PHYSICS LETTERS

JO November

1984

Table -1 Equilibrium geometriesa) Molecule

Parameter

benzene (kh)

r(CC) r(CH)

s-triazine (Dsh)

borazine (&h)

STO-3G

4-316

Experiment b,

1.396 + 0.001 1.083 i 0.004

1.387 1.083

1.384 1.072

r(CN) WH) UNCN) L(CNC)

1.354 1.091 126.4 113.6

1.328 1.065 123.6 116.4

1.338 (1.084) 126.8 113.2

r(BN) r(BH) r(NH) L(NBh3 L(BNB)

1.418 1.161 1.019 117.2 122.8

1.430 1.187 0.994 117.5 122.5

1.436 2 0.004 1.258 -c 0.020 1.050 i 0.020 117.7 -c 2.0 121.1 i 2.0

borosine

r@O)

1.362

1.368

1.376

cD3$

r(BW

1.162

1.169

1.19 = 0.02

119.4 120.6

L(OB0) L(BOB)

-c 0.004

120.0 I 0.7 120.0 i 0.7

115-5 124.5

a) Bond lengths in sngstrdm and angles in degrees. b, From ref. 1131.

orbitals, there appears to be no simple explanation for the ring angles. As a check on the 431G results, borazine has been optimized at the 6-31G* level [21]: I = 1.426 a, I = 1.193 a, ~(NII) = 0.996 a Table 2 4-31G charge distributions and quadrupolar hloleculc

Atom

and LNBN = 117.6“. Thus we conclude polarization

functions

that adding

to the basis set of the heavy

atoms has very little effect on the equilibrium structure_ The Mull&en charges [22] listed in table 2 indicate

coupling constants hMliicn

population

Bader

total u electrons

= electrons

total

QCCa) z

benzene

C H

5.189 0.811

1.000

6.189 0.811

5.996 1.002

2.26 0.243

s-triazine

C N HC

4.886 6.362 0.753

0.823 1.177

5.709 7.538 0.753

5.062 8.009 0.922

3.17 5.23 0.244

borazine

B N HB HN

3.822 6.451 7.077 0.650

0.301 1.699

4.123 8.150 1.077 0.650

2.869 8.861 1.603 0.634

7.15 1.90 0.161 O-326

borosine

B 0 HB

3.819 7.149 1.032

0.247 1.753

4.065 8.902 1.032

2.816 9.538 1.659

7.19 5.87 0.170

al The quadrupolar coupling constants, X = e2qzzQ/h, have been calculated using the following quadrupole moments for r”B (Q = 8.5 X 10wz6 cm* [23]), “C (Q = 3.1 X 1O’6 cmZ [23]), *H (Q = 2.860 X lo-” cm* [24]), 14N (Q = 1.93 X 1O-26 cm’ [25]) and t’0
Volume 112. number 2

CHEMICAL PHYSICS LETTERS

taht the polarity of the ring bonds increases with the dissimilarity of the nuclear charges of the atoms. The polarization of u electrons in the ring (0.361. 1.101 and I .I 50e in II, 111and IV, respectively) is augmented by a 0.177 n-electron shift in II and opposed by 0.301 and 0.247 n-electron acceptances by B in III and IV, ___----__._.____--.---____---- -_--- ~“---_:-T--___--

---

/

’

;’

’

‘;

,

. Tr-----------a . _________ __-

Fi;. I. Contour map of the charge density in the molecuix

1984

respectively. Thus, the very large increase in o-electron cloud polarity between s-triazine and borazine is partially offset by differences in the x-electron cloud; each C loses 0.177e to the N atoms whereas the 7reIectron deficient B atoms of III and IV accept ofelectrons from the N and 0 atoms. It should be noted that the larger

. _I

-- _\q. _

30 November

1 it

plane: (a) benzene, @) s-triaziue, (c) borazine, (d) boroxine. The

contour values in au are 0.002.0.004 and 0.008 increasing in powers of 10. The outermost contour in each plot is 0.002 au. The orientation or eachmolecule corresponds to the strucruml formufae given in section 1. 138

Volume 112, number 2 net charge

CHEMICAL

on N in III than on 0 in IV is due to N---H

bond polarity and not to differences within the rings. More insight into the electronic structure of borazine and related compounds is provided by the charge density maps shown in fig. I. In the vicinity of each C-H pair, p(r) in s-triazine remains very similar to benzene,whiIe the electron cloud around each N atom

PHYSICS LETTXRS

30 November

1984

shows a much greater concentration of charge. Further disortion, due to the bonding of a H atom to each N and the replacement of each C by B, is evident in borazine. Note that the BH and NH bonds are more and less polarized, respectively, toward H than the CH bonds. The plot for boroxine shows very similar ring polarity to the borazine plot, while the electron

Fig. 2. Countour map of 7$(r) in the molecular plane: (a) benzene, (b) s-triazine, (c) borazine, (d) bornaine. Positive values of v;(r) are denoted by solid contours, negative vabres by dashed contours. The contour values in ZXIitse -c 0.002, rt 0.004 and 2 0.008 increasing in powers of 10. The orientation of each molecule given in section 1.

139

Volume

112. number 2

CHEMICAL

PHYSICS

distribution around the 0 atom is qualitatively similar to rhe N atoms of s-triazine. An cvcn more sensitive probe of the electronic structure of a molecule is provided by the Laplacian of the charge density, V:(r), which determines the regions of space wherein the electronic charge of a molecule IS locally concentrated anddepleted [26] .This function has been shown to demonstrate the existence of local concentrations of electronic charge in both the bonded and non-bonded regions ofan atom III a molecule 17,261, wItbout recourse to any orbital model or arbitrary rcfercncc state. Interactions resulting from the sharing of charge density between atoms,,as in covalent and polar bonds, are characterized by V&) < 0. A large region between the carbon atoms of benzene in which V:(r) < 0 (see fog. 2) emphasizes the strong covalent bond. The corresponding plot for s-tnazine indicates a small polarization of the covalent CN bond, with the lone pairs [7] on the nitrogen atoms clearly visible. The substantial polarization of the BN bonds in borazine and the BO bonds in boroxine is demonstrated by the V:(r) plots. As expected, the oxygen lone pairs in boroxinc arc less dilTuse than their nitrogen countcrparts in s-triazinc. Here it should be emphasized that non-bonded charge concentrationsare thinner in radial extent than are the bonded ones [7]. Numerical integration of p(r) over regions of space dcllned by the gradient vector field [27-291 of p(r) yields the total elcctromc charge associated with each atom. With the exception of the CH bonds of benzene and s-triazinc. Badcr’s partitioning method [30] leads to greater polarities than the Mulhken population analysts (see table 2). To further characterize the clcctronic structure of borazinc and related molecules we have calculated the cleclric

field gradients,

of the

as described

elsewhere

[9], for

The results are listed in table 2 in rlcc iorm orquadrupolar couplingconstants,~s,which in Iurn arc important for a full understanding of certain nucloJr magnetic resonance spectra. From the ratio of the Iq’N and “B quadrupolar coupling constants in solulion 13 11, the cxperiniental ratio of Lhe clcclric licld gradren ts is 0.73, whereas our 4-3 1G calculations yield 1.17 for r/lZ(N)/rlZZ(B) In view of the fact that rbc calculations ignore the effect of the solvent, and Iiartrec-Fock quality basis sets arc impractical for ~nolcculcs as large as bozarine, the agreement is fairly s3tisfactoIy.

c.rch

nuclei.

30

LETTERS

-12

-6

lzl

6

November 1984

12

rig. 3. Onediniensional cross section of tk conformational energy (in kcai/mole) hypcrsurface for puckering of the sixmembered ring in benzene (upper curve) and bora_&w (lower curve).

X-ray diffraction [32] and spectroscopic [33] studies on (R6 B,N,)Cr(CO), complexes have shown that the borazine ring is puckered with the actual structure intermediate between a true TI complex, as oband a pure u complex in which served in C6HsCr(CO),, the arrangement about the N atoms is nearly tetrahedral. Fig. 3 compares the potentials of benzene and borazine in which alternate atoms of the ring are displaced above and below the plane such that the angle of displacement is the same for all atoms. The much lower potential for borazine further demonstrates that the ‘ITelectrons are substantially less delocalized than in benzene. With a displacement of ISo, corresponding to the crystal structure [32] in which the two parallel planes formed by the three boron atoms and the three nitrogen atoms are separated by 0.07 a, the increase in energy from the planar structure is only 2.1 kcal/mole in borazine and 3.4 kcal/mole in benzene. In borazine complexes this can be provided by the formation of three essentially u bonds LOthe N atoms, whereas a x-type interaction is preferred in the arene metal carbonyls. Apd finally we note that the relative potential for ring puckering in s-triazine is comparable to that of benzene, since the shorter bond length

Volume 112, number 2

CHEMICAL

30 November

PHYSICS LETTERS

I984

largely offsets the effect oflessn delocalization,while the relative potential for boroxine lies about 18% below the borazine curve.

[ 111 J.S. Binklcy, R.A. Whiteside, P.C. Hariharan, R. Seeger, J.A. Pople, W.J. Hehre and h1.D. Newton, QCPE 11 (1978) 368. [ 121 R.F.W. Bader. Department of Chemistry. Mchfaster

Acknowledgement

University, Hamilton, Ontario. Canada L8S 4Ml. [ 131 J.H. Callomon, E. Hirota, K. Kuchitsu. W-J. Lafferty. -4.G. hIaki and C.S. Pote, in: Structure data of free polyatomic molecules_ Landoit-BZimstein, New Series, Group II,Vol. 7, cds. K.H. Hellwge and AX. HeIhvege

We would like to acknowledge many helpful discussions with Professor R.F.W. Bader and the hospitality extended to one of us (SCC) during visits to McMaster University_ The many comments and suggestions ofour colleagues, in particular B.A. Pettitt and R.E. Wasylishen, and the financial support of the Natural Sciences and Engineering Research Council of Canada are gratefully acknowledged.

References J.E. Huhcey. 1norganiccl~e~nistry:principlesofstructure and reactivity,

2nd Ed. (llarper and Row, New York.

1978). F.A. Cotton and C. Wilkinson, Advanced inorganic chemistry, 3rd Ed. (Wiley-Intcrsicience, New York, 1972). [31 K.F. Purcell and J.C. Katz, An introduction to inorP,anic chemistry (Saunders, Philadelphia, 1980). I41 P.hI. Kuznesof and D.F. Shriver, J. Am. Chem. Sot. 90

(1968) 1683. [51 R.J. Uoyd, D.H. Lo and h1.A. Whitehcad, Chern. Phys. Letters 2 (1968) 227. I61 D.R. Armstrong and D-T_ Clark, Chem. Commun. (1970) 99. i71 R.F.W. Badcr, P.J. hlacDougd and C.D.H. Lau, J. Am. Chem_ Sot. 106 (1984) 1594. 181J.S. BinkIey, R.A. Whiteside, R. Krishnan, R. Seeger,

DJ. DeRees.

H.B. Schlegel, S. Topiol, L.R. Kahn and

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1751. Yamashita, J. lIo1. Struct. 265. Sane, J. Mol. Struct.

(THEOCHEM) 104 (1983) 489. [ 181 K. Hirao and H. Kato. Chem. Phys. Letters 98 (1983) 340. [ 191 W-A. Lathan, W-J. Hehre, L.A. Curtiss and J-A. Pople, J. Am. Chcm. Sot. 93 (1971) 6377. 1201 J-A. Pople. in: Modem theorericd chemistry, Vol. 4,

cd. H.F. Schaefer HI (Plenum Press, New York, 1977). 1211 P.C. Hariharan and J.A. PopIe,Theoret. Chim. Acrra 28 (1973) 113. [22] R.S. Mulliien, J. Chem. Phys. 23 (1955) 1833,184l. 1231 G.H. Fuller, J. Phys. Chem. Ref. Data 5 (1976) 835. 1241 D.hI. Bishop and L-11. Cheung, Phys. Rev. A20 (1979) 381. [25] H. Winter and H.J. Andra‘, Phys. Rev_ A21 (1980) 213. [ 261 R.F.W. Bader and Il. Essen, J. Chem. Phys. SO (1984) 1943. [ 271 R-F-W. Bader and G.R. Runtz, hloL Phys. 30 (1975) 117_ 1281 G.R. Runtz, R.F_W. Bader and R.R. &lesser, Can. J. Chem. 55 (1977) 3040. [291 K. Collard and G-G. Hall, Intern. J. Quantum Chem. 12 (1977) 623. 1301 F-W_ Biegler-K6nig, R.P_\V_ Bader and T--H. Tang, J. Comput. Chem. 3 (1982) 317. [31] A. Lotz and J. Voithnder. J. hlagn. Reson. 54 (1983) 427. [32] G. lluttner and B. Krieg. Angew_ Chcm. Intern. Ed. 10 (1971) 512. 1331 J.L_ Adcock and J.J.

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141