J. Phys. Chem. 1993,97, 8403-8409
8403
Molecular Quadrupole Moments, Magnetic Anisotropies, and Charge Distributions of Borazine, BTrichloroborazine, N-Trimethylborazine, and BTrichloro-N-trimethylborazine. Comparison with Benzene and Its Derivatives Gary R. Dennis1*and Geoffrey L. D. Ritchie'Jb School of Science and Technology, University of Western Sydney, Nepean, New South Wales 2750, Australia, and Department of Chemistry, University of New England, Armidale, New South Wales 2351, Australia Received: April 6, 1993
Measurements of the dilute-solution molar Kerr constants, field-gradient birefringence constants, and CottonMouton constants of borazine and three substituted borazines as solutes in cyclohexane or carbon tetrachloride at 25 OC are reported. The observations yield the first direct experimental values of the effective polarizability anisotropies, electric quadrupole moments, and magnetic anisotropies, which are important descriptors of the molecular charge distributions. A comparison of the results for borazine with literature data for benzene shows that all three properties have the same signs in the two species but that all are considerably smaller in magnitude in borazine than in benzene. An analysis of themagnetizabilities indicates that the extent of electron delocalization in borazine is only about one-third of that in benzene, a conclusion which is consistent with a range of other evidence.
Introduction Over the last 60 years, the physical and chemical properties of borazine ("inorganic benzene"), in particular the extent of electron delocalization and the aromatic character, if any, have attracted great interest, and an enormous amount of literature now exists.2 Although electric and magnetic properties are well recognized as important descriptors of molecular charge distributions, some of the simplest such properties (for example, the polarizability anisotropy, quadrupole moment, and magnetic anisotropy) of borazine have not previously been measured, at least partly because of the difficulties associated with species that are as reactive and generally difficult to manipulate as borazine. Proced~res3-~ developed in these laboratories, involving observations of field-induced birefringence in dilute solutions, are well established as useful routes to the properties mentioned above, specially for involatile and nondipolar species that cannot easily be examined by other methods. In this paper, further improvements in relation to studies of reactive compounds under inert-atmosphere conditions are described, the dilute-solution molar Kerr, field-gradient birefringence, and Cotton-Mouton constantsof borazine,B-trichloroborazine,N-trimethylborazine, and B-trichloro-N-trimethylborazine are reported, and the derived polarizability anisotropies, quadrupole moments, and magnetic anisotropies are analyzed to elucidate the molecular charge distributions. "ry
conclusive evidence from a variety of experimentaland theoretical techniques (X-ray diffraction? vibrational spectra,lo dipole moments,I1 microwave absorption,12 and, especially, ab initio molecular orbital c a l c ~ l a t i o n s ~ ~ that J ~ )the ring is planar. In consequence,the molecules of interest in this study are nondipolar and possess a 3-fold rotation axis (labeled with subscript z) perpendicular to the plane of the ring. For such species, the theoretical expressions, in terms of molecular properties, for the three quantities mentioned above are, in SI units,
,K = (NA/405t0kl*)( A a O / A a )kc)' (
(1)
,Q = (2NA/45cok7")A a f e
(2)
,c
= (NAp;/405q,kT)AaAx
(3)
in which Pao (= aozz - aoxx) and Aha!(= azz- ax*)are the effective anisotropies in the static and optical-frequency molecular polarizabilities; f is the reaction field gradient factor; 6 (= 8, = -26,) is the molecular quadrupole moment; and Ax (= xzzxxx) is the anisotropyin the molecular magnetizability. The Kerr constant therefore defines, through eq 1, the polarizability anisotropy, knowledge of which enables the field gradient birefringence and Cotton-Mouton constants to be analyzed, through eq 2 and 3, to yield the quadrupole moment and magnetic anisotropy, respectively. The molecular quadrupolemoment is defined by the equation15
In this study the objective was to obtain values of the molecular quadrupole moments, magnetic anisotropies, and related properties of the borazines from the measured dilute-solution molar Kerr, field-gradient birefringence, and Cotton-Mouton constants of these molecules. Relevant theory has been given elsewhere; symbols and other details not explicitly mentioned here are as in earlier reports.3-7 The question of the precise geometry, in particular the planarity or otherwise, of the boron-nitrogen ring in borazine and simple symmetrically substituted borazineshas generated much interest and, until recently, some controversy.* However, there is now
in which the summationis over all nuclear and electronic charges, e/, located by position vectors, rja. It is of interest to separate the nuclear (subscript n) and electronic (subscript i ) contributions to Club, and for an axially symmetric molecule the quadrupole moment, 6,can be expressed as
* Please address correspondenceto ProfessorG. L. D. Ritchie, Department
where e is the elementary charge, Z,is the atomic number of the nth nucleus, and e { ( z * )- ( ~ 2 ) ) is the anisotropy in the second moment of the electronic charge distribution. From perturbation
of Chemistry, The University of New England, Armidale, New South Wales 2351, Australia.
(4)
0022-3654/93/2097-8403$04.00/00 1993 American Chemical Society
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Dennis and Ritchie
The Journal of Physical Chemistry, Vol. 97, No. 32, 1993
theory,16J7the magnetizability of a diamagnetic molecule is
(6) in which xd,,g and xpd are theoppositely signed diamagnetizability and temperature-independent paramagnetizability, respectively. The magnetic anisotropy of an axially symmetric molecule is therefore expressible in the form
+
Ax = Axd Axp (7) and since Axd can be written in terms of the molecular geometry and the quadrupole moment as
e2 = - { ( z 2 ) - (x2)) 4% the separation of these two terms is readily effected. In addition, the anisotropy, g,, - l/gxx, in the molecular g value, which relates the rotational angular momentum to the rotational magnetic moment, is accessible;'* for a planar, axially symmetric molecule this quantity is given by the equation 1
g,, - /2gxx -(mp/eZ,,){(4me/e)A~ + e) (9) whereZ,,is themoment of inertia for rotation about the symmetry axis. Experimental Section Solutes, Solvents, and Solutions. The species under consideration here presented difficulties well beyond those generally encountered in such studies. Borazines react vigorously with water and are slowly oxidized, and it was therefore necessary to employ standard inert-atmosphere procedures for all preparations and manipulations. A sample of B-trichloroborazine (Borax Chemicals, mp 84 O C , lit.19 83.9-84.5 "C) was purified by vacuum sublimation before use; it is an extremely hygroscopic compound and slowly decomposes with evolution of hydrogen chloride. Borazine was prepared by a modification of a reported method? B-trichloroborazine (34.5g) was ground under nitrogen in a drybox and then suspended in dry di-n-butyl ether (50.0 mL); lithium borohydride (20.0g) in di-n-butyl ether (200mL) was added to the slurry over 2 h; and crude borazine was distilled into a dry-ice condenser and purified by several line transfers. The compound was further purified by fractional distillation, and its identity was confirmed by its IR10,21 and lHNMRZ1spectra and its boiling point (54-55 OC, litz255 "C). Borazine is extremely sensitive to the presence of water and polymerizes and/or decomposes over time. The symmetrically hexasubstituted compound Btrichloro-N-trimethylborazinewas synthesized by the reaction of boron trichloride with a solutionof methylammonium chloride in chl~robenzene.~~ The mixture was refluxed for 40h, the solvent was removed, and the product was purified by sublimation; authentication was by its IR spectrumz4and melting point (160161 O C , lit.23 162-164 "C). Finally, N-trimethylborazine was obtained by reducing B-trichloro-N-trimethylborazine(26.0g) with sodium borohydride (17.9g) in triethylene glycol-dimethyl ether.23 The crude product was distilled from the mixture and purified by fractional distillation; the purity of the compound was confirmed by its boiling point (130-131 "C, lit.25 132 "C) and its IR,24 lH NMR,*l and mass spectra.
I
I
&
E F Figure 1. Inert-atmosphere filling system: A, solvent; B, solution; C, Teflon membrane filter; D, graduated cylinder; E, birefringence cell; F, waste container; G, gas bubbler.
All four compounds were repurified immediately prior to the measurements by inert-atmosphere (argon or nitrogen) fractional distillation or, alternatively, vacuum sublimation with a specially designed inert-atmosphere sublimator.26 The solvents, Merck analytical-grade cyclohexane and carbon tetrachloride, were refluxed over phosphorus pentoxide for 1 h and fractionally distilled under nitrogen; great care was taken to remove water and oxygen in order to prevent decomposition of the solutes. Solutions were prepared under dry nitrogen using Schlenk techniques and transferred by means of an inert-atmospherefilling system (Figure l), as follows. The system was purged by four evacuation and flush cycles, and the solution, B, was pressurized with nitrogen and filtered through a Sartorius membrane filter (Teflon, pore size 0.45 Fm), C, into a graduated cylinder, D. A small portion of the filtered solution was transferred to the birefringence cell, E, as a rinse, and then blown through to the waste container, F; the cell was then filled and the Luer-Lok fittings were capped with Teflon plugs. Finally, the system was rinsed with solvent,A, and dried under vacuum; the solvent could be removed from the waste container which was protected from water and oxygen by a gas bubbler, G, and the solute was easily recovered and repurified. Apparatus, Procedures,and Results. Apparatus and procedures used to obtain the infinite-dilution molar Kerr constants, -(,,,&), field-gradient birefringence constants, m(mQ2),and CottonMouton constants, m(mC2), of the borazines as solutes in cyclohexaneor carbon tetrachloridewere as previously described,s7 except that the birefringence cells used in all three experiments were significantly improved to permit the manipulation of airor water-sensitive compounds under inert-atmosphere conditions. Details of the Kerr and Cotton-Mouton cells are given here; those of a novel four-pole field-gradient birefringence cell were included in a recent report on the dilute solution molecular quadrupole moment of b e n ~ e n e . ~ The body of the Kerr cell (Figure 2) was fashioned from a cylinder (diameter = 72 mm) of 25% glass-reinforced Teflon, a material characterized by high mechanical stability, easy machinability, and chemical inertness. Two circular 3 16-grade stainless-steel electrodes with highly polished faces are screwed into the cell body so as to achieve a constant gap (3.0 mm) and, by means of an adjustable DC voltage, a variable uniform electric field (20-30 kV cm-I). Quartz windows (Heraeus Suprasil 11, 20 X 2mm) are mounted in stainless-steelcarriers between Teflon washers and Viton O-rings and pressure-sealed with Teflon endplugs; the carriers are then screwed into and pressure-sealed against the cell body. Any strain birefringence in the windows is easily minimized by rotation of the window carriers. The cell is fitted with two filling ports designed for Luer-Lok attachments; it is filled by Luer-Lok syringe or, alternatively, with the inertatmosphere filling system described above (Figure 1). Obvious advantagesof this Kerr cell over earlier designsinclude the absence
Electric and Magnetic Properties of Borazines
The Journal of Physical Chemistry, Vol. 97, No. 32, 1993 8405
TABLE I: Solvent Constants for Cyclohexane and Carbon Tetrachloride at 298 K and 632.8 w property F J
L
loLsKl/(m V-2) V-2 k g l )
10lsQl/(m
V-l)
lQl/(ms V-Lkg-I)
loLsCI/(m A-2)
,Cl/(ms A-2 mol-')
CsHiz 1.01 1 1 0.4975 0.1230 0.555 1.481 -1 -05 -35.4 -0.174 -0.834
cc4 1.0575
0.4731 0.1035 0.857 0.986 -0.24 -3.8 -0.084 -0.192
See refs 3-7 for definitions of symbols. A
I
-0. -c
D
I
E
T F
in which the subscripts 1 and 2 refer to the solvent and the solute, respectively; &I,sQ1, and sC1are the specificKerr, field-gradient birefringence and Cotton-Mouton constants of the solvent; F = (3nlZ-2)/(nI2 + 2), J = 2/(q + 2), and L = 2/(3e12 2 4 are constants characteristic of the solvent; 6 = (AK/w2)/K1, 5 = (AQ/w2)/Q1, and 6' = (AC/wz)/C1 measure the dependence of the bulk birefringence constants K, Q, and C on the weightfraction concentration, WZ;and M Zis the molar weight of the solute. Solventconstants for cyclohexaneand carbon tetrachloride are given in Table I. The quantities 0, y,and a q , obtained from the incremental densities, refractive indices, and relative permittivitiesofsolutionsor, alternatively,estimated from appropriate data for the s o l u t e ~ , ~ usually ~ ~ 2 2 ~make ~ ~ only small contributions in eqs 10-12; these are included in Table 11, together with the parameters 6, 5, and 6' and the derived molar birefringence constants. The analysis of the experimental results in terms of the molecular properties of interest is summarized in Table I11 and discussed below. SI units are used throughout; relevant conversion factors have been given elsewhere.%-' For simplicity, numerical values of polarizabilities, quadrupole moments, magnetizabilities, etc., are quoted in the text as l W a / ( C m2 V-'), lO%/(C m2), 1029x/(JT-2), etc.
+
iG B
Discussion
Figure2. Kerr cell: A, glass-reinforcedTeflon cell body; B, Viton O-rings; C, circular stainless-steelelectrodes;D, stainless-steelwindow carrier; E, Teflon washer; F, quartz window; G,Teflon end-plug.
of electrode movement and the constancy of the interelectrode gap, its high optical stability, the ease with which it can be dismantled, cleaned, and reproducibly reassembled, its small internal volume, and the fact that it is gas-tight and therefore suitable for studies of reactive compounds under inert-atmosphere conditions. The Cotton-Mouton cell is of particularly simple construction: the body of the cell comprises a brass block (length 215 mm, rectangular cross section 20 X 9 mm) through which a central hole (diameter 7.0 mm) was bored to accommodate the sample and to which Luer-Lok filling ports were soldered. Microscope cover slips cemented to the ends of the cell body with Dow Corning 730 RTV fluorosiliconesealant enclose the sample; this adhesive has proved much superior to water glass (sodium silicate), in that the cell can be filled under nitrogen, window drift is greatly reduced, and the possibility of reaction between the solute and the sealant is eliminated. Both cells gave results consistent with published data for the dilute-solution Kerr and Cotton-Mouton effects of benzene in the relevant solvents. The definitions of m(mKz), &,Q2), and m(mC2) in terms of experimental observables are
Polarizabilities. Analysis of the experimental Kerr constants of the borazines through eq 1 yields, in each case, the magnitude but not the sign of the molecular polarizability anisotropy. However, the magnetic anisotropy, Ax, of B-trichloroborazine is known, from direct measurementsZ8on the crystalline solid, to be negative in sign, and, since the Cotton-Mouton constant (Table 11) is positive, it is obvious from eq 3 that the polarizability anisotropy, P a , of this species is also negative in sign, like that of 1,3,5-trichlorobenzene.29 It follows, by simple arguments of analogy with benzene and its derivatives, that ha is negative for all four borazinesconsidered here. The borazine ring is, therefore, more polarizable in the x and y (in-plane) directions than in the z (out-of-plane) direction, as expected. In order to use eq 1 to determine ALYit is also necessary to estimate the ratio Aao/Aa of the static to the optical-frequency anisotropy. The difference between Aao and Pa originates in the frequency dependence of the dominant electronic polarizability and in the anisotropy in the vibrational polarizability, which contributes to the former but not the latter. Reliable values of AaO/Aa are available for only a few simple molecules of which benzene, 1,3,5-trifluorobenzene, and hexafluorobenzene30most closely resemble the borazines. Although the ratio for benzene (0.88 f 0.05) is less than unity, those for 1,3,5-trifluorobenzene (1.16 f 0.05) and hexafluorobenzene (1.18 f 0.06) are significantly greater than unity; for the present purposes, Aao/Aa has been taken as 1.00 f 0.10. It must also be emphasized, once again, that polarizability anisotropies derived by application of eq 1 to solutes are apparent values that reflect the inadequacy of the theoretical model in
8406 The Journal of Physical Chemistry, Vol. 97, No. 32, 1993
Dennis and Ritchie
-(,a),
TABLE Ik InfiiteDilution Molar Kerr Constants, -(.IC.), Field-Gradient Birefringence Constants, and Cotton-Mouton Constants, &,CS),from Birefringences of Solutions of Borazines' in Cyclohexane or Carbon Tetrachloride at 298 K and 632.8 nm property BsHsNiHi B3ClsN3Ho BIH~N~M~~ B3ClaN3Me3 solvent C6Hl2 C6H12 cct C6H12 solutionsb 2.3-17.8, 5 3.1-6.9,6 1.9-8.9, 5 3.1-5.1, 3 0.88 0.42 -0.84 0.56 d -0.03 -0.12 1.04 0.08 1.88 f 0.15 3.44 0.21 10.4 1.0 -9.9 1.0 2.54 i 0.28 2.25 i 0.12 -12.9 0.7 8.05 0.48
Y' aqC
*
( ~ O ~ ~ A K / W ~m) V-2) /( 6d
1027,(,K2)/(m5 V-2 mol-') (1Ol5AQ/w2)/(mV-l)
**
.Ed
10zs-(mQ2)/(mSV-' mol-') ( 1015AC/w2)/(mAJ) 6' d
*
0.01 0.26 2.99 0.36 5.38 0.65 15.8 i 1.8 -3.6 2.7 3.5 2.6 -2.6* 1.7 1.60 0.41 -9.2 i 2.4 13.2 3.6
*
*
-0.01 -0.06 5.63 f 0.15 6.57 & 0.18 10.2 f 0.2 11.3 0.8 -47.1 3.2 2.11 0.15 3.58 0.11 -42.6 f 1.3 9.59 0.30
0.08 0.37 4.18 0.52 7.5 i 0.9 25.8 & 3.1 -7.2 0.8 6.8 0.7 -5.7 0.6
**
* *
1027&C2)/(m5 A-2 mol-') BJH~N~ =H borazine; ~ BjCljNpHj = E-trichloroborazine;BsHsN3Mes = N-trimethylborazine; B3Cl3NsMe3 = B-trichloro-N-trimethylborazine. Entries show the approximate weight-fraction concentration range (expressed as 102~2)and the number of solutions from which the concentration dependences of the bulk birefringence constants (K,Q, and Q were determined. Calculated from data in refs 11,22, and 27. d 6 = ( M / w * ) / K l , = (AQ/wz)/Ql, 6' = (AC/W~)/CI; see refs 3-7 for definitions of other symbols.
TABLE IIk Analysis of the Kerr Constants, Field-Gradient Birefringence Constants, and Cotton-Mouton Constants of the Borazines property BIHIN~H~ B3C13N3H3 B3H3N3Me3 B3CIaN3Me3 1Oz7,,,K/(m5 V-2 mol-') 3.44 f 0.21 15.8 f 1.8 10.2 i 0.2 25.8 f 3.1 AaQ/Ad
1.00 0.10 -2.90 0.17 9.846 7.9 10.8 2.54 i 0.28 1.12 -10.6 1.3 -911.3 900.6 8.05 i 0.48 -43.0 3.6 -82.4 -111 -68 -396.0 353.0
*
1040Aa/(C m2V-I)
10%/(C m2 V-1) 1040a,/(C m2 V-1) 1040a,/(C m2 V-1) iO25,,Q/(ms V-1 mol-') f d
*
10% (Cm2) 1040e Zn(Z,'- xn2)/(Cm2) -1040e((z2) - (xz)]/(C m2) lOZ7,C/(mS A-2 mol-') 1OZ9Ax/(JT-2) 1029x/(~T - ~ c ) i029~,,/(~T-2) 1 0 2 9 ~ ~T-2) ~/(~ 1029 ~ ~ (J T-2) d / 1OZ9AxP/(JT-2)
f
1.00 0.10 -6.23 f 0.47 16.28' 12.1 18.4 -2.6 1.7 1.12 5.1 3.3 -4851.3 4856.4 13.2 & 3.6 -33 9 -180.3 -202 -1 69 -2135.4 2102.5
*
*
1.00 0.10 -5.00 f 0.26 16.766 13.4 18.4 2.11 & 0.15 1.15 -5.0 i 0.4 -2688.9 2683.9 9.59 0.30 -29.8 f 1.8 -130.5 -150 -121 -1 180.1 1150.3
1.00 0.10 -7.95 0.63 22.41' 17.1 25.1 -5.7 i0.6 1.12 8.7 1.1 -6638.1 6646.9
*
*
(-20 i 10) (-228)
a Assumed value (see text). Reference 22. Reference 27. Reaction field gradient factor,f = (3fl + 2)(2c2 + 3)/5(3cl + 2 4 . e References 42 and 43. relation to the polarizability of an anisometric molecule in a dense TABLE rV: Effect of Substituents on the Mean medium.,' However, it is now well established that reliablevalues Polarizabilities, a,and Apparent Dilute-Solution Polarizability of the quadrupole moment and magnetic anisotropy are obtained Anisotropies, Aa, of Boraziw and Benzene at 632.8 I& when the dilute-solution field-gradient birefringence constant and property C3X3C3Y3c Cotton-Mouton constant, respectively, are analyzed in conjunca (X = H, Y = H) 9.84 11.6 tion with the apparent polarizability anisotropy deduced from 6a (X = CI, Y = H)d 6.4 7.2 the dilute-solution Kerr constant of the solute in the same 6a (X = H, Y = CH3) 6.9 6.5 solvent .34,7,3* 6a (X = C1, Y = CH3) 12.6 13.4 The experimental mean polari~abilities,2~.*'a (= a, + 2a,/ A a (X = H, Y = H) -2.90 0.17 -4.70 0.1 1f 3), and polarizability anisotropies, Aa (= azz - axJ, of the 6Aa (X = C1, Y = H)e -3.3 0.5 -4.7 0.4 6Aa (X = H, Y CH3) borazines are summarized in Table 111. It is of interest to examine -2.1 0.3 -1.1 i0.4 6Aa (X = C1, Y = CH3) -5.0 A 0.6 -5.5 0.6 the reliability of a simple group-additivity model of these properties. For this sequence of molecules, the appropriate a Mean polarizabilities and apparent dilute-solution polarizability additivity relationships can be expressed as anisotropies expressad as lWa, C m2 V-' and 1046 Aa, C m2 V-', respectively. Data for B3X3N3Y3from Table 111. Data for C3X3C3Y3 a(B,Cl,N,Me,) = a(B,Cl,N,H,) + cr(B,H,N,Me,) analogues from refs 3 and 29. d6a (X,Y) = a(B3X3N3Y3) a(B,H3N3H3), etc. 6Aa (X,Y) = Aa(B3X3N3Y3) - A ~ ( B ~ H I N ~ H ~ ) , a(B,H,N,H,) (1 3) etc. 1Solvent cyclohexane and the effect of the substituents on these properties in the two cases. Aa(B,Cl,N,Me,) = Aa(B,Cl,N,H,) Aa(B,H,N,Me,) The comparison is summarized in Table IV, from which two inferences can be drawn: first, in relation to the mean polarizA"(B,H,N,H,) (14) ability, the value for borazine is only slightly (= 15%) smaller from which it is easily confirmed that for both a(B3C13N3Me3) than that of benzene, and the substituents havevery similar effects and Aa(B3C13N3Me3) the predicted and actual experimental on the two ring systems; and second, in relation to the anisotropies, values differ by
