Dipole Moment of Cyclotriborazane (28) J. Pa&. Theor. Chim. Acta. 29. 21 11973). (29) N. Bodor,'M. J. S. Dewar, A. Harget,'and E. Haselbach, J. Am. Chem. SOC., 92, 3854 (1970). (30) M. J. S. Dewar and N. TrinajstiE, Chem. Commun., 646 (1970). (31) F. 0.Ellison and F. M. Matheu, Chem. Phvs. Lett.. 10.322 (1971). (32j J. Pan&, Collect. Czech. Chem. Comhun., 40, 2726 (1975). (33) J. W. McIver and A. Kornornicki, J . Am. Chem. Soc., 94, 2625 (1972). (34) B. E. Wilson, J. C. Decius, and P. C. Cross, "Molecular Vibratlons", McGraw-Hi!, New York, N.Y., 1925. (35) R. Zahradnik, 2. Slanina, and P. CBrsky, Collect. Czech. Chem. Commun., 39, 63 (1974). (36) 2. Slanina, Collect. Czech. Chem. Commun., 40, 1997 (1975). (37) R. J. Gillespie, "Molecular Geometry", Van Nostrand-Reinhold, London, 1972. (38) H. Eyring, J . Chem. Phys., 3, 107 (1935). (39) G. Herzberg, "Molecular Spectra and Molecular Structure. 111. Electronic Spectra and Electronic Structure of Polyatornic Molecules",
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Van Nostrand-Reinhold,New York, N.Y., 1966. (40) D. H. Liskow, C. F. Bender, and H. F. Schaefer, 111, J. Chem. Phys., 56, 5075 (1972). (41) 2. Slanlna, Thesis,Czechoslovak Academy of Sciences,Prague, 1974. (42) N. C. Baird and M. J. S. Dewar, J . Chem. Phys., 50,1262 (1969). (43) L. L. Combs and M. Hollornan, Spectrosc. Lett., 5, 319 (1972). (44)L. L. Combs and M. Hollornan, Spectrosc. Lett., 6, 257 (1973). (45) A. K. 0.Siu and E. F. Hayes, Chem. Phys. Lett., 21,573 (1973). (48) R. J. Thorn and G. H. Winslow, J . Chem. Phys., 26, 186 (1957). (47) L. S. Bartell and B. Andersen, Chem. Commun., 786 (1973). (48) 2. Slanina, P. Berlk, and R. Zahraddk, Collect. Czech. Chem. Commun., 42, l(1977). (49) R. C. Bingharn, M. J. S.,Dewar, and D. H. Lo, J. Am. Chem. Soc., 97, 1285 (1975). (50) 2. Slanina and R. Zahraddk. Collect. Czech. Chem. Commun.. 39. 729 (1974). (51) C. F.'Hansen, 8. J. Henderson,and W. E. Pearson, J. Chem. Phys., 60, 754 (1974).
Dipole Moment of Cyclotriborazane Donald R. Leavers Behrend College, Pennsylvania State University, Erle, Pennsylvania 165 10
and William J. Taylor" Department of Chemistty, Ohio State University, Columbus, Ohio 432 10 (Received September 22, 1975; Revised Manuscript Received September 12, 1977) Publication costs assisted by the Department of Chemistry of the Ohlo State Univers/ty
Cyclotriborazane (CTB),B3N3H12,has the chair conformation of cyclohexane, CsH12, but with symmetry Csv rather than D3d; CTB, unlike cyclohexane, may therefore possess a permanent dipole moment. From measurements of the dielectric constants and specific volumes of four solutions of CTB in p-dioxane we obtain 170.4 f 6.3 mL mol-l for the partial molar polarization of CTB at infinite dilution. With a correction of 30 f 5 mL mol-1 for distortion polarization, the apparent dipole moment of CTB in solution is calculated to be 2.69 f 0.11 D; a further correction for the solvent effect yields an estimate of 2.42 f 0.16 D for the dipole moment of the isolated CTB molecule. This value is consistent (within their respective uncertainties) with the value of the dipole moment calculated from atomic charges estimated from x-ray intensities by Corfield and Shore. On the other hand, an unpublished ab initio SCF molecular orbital calculation by Ermler, Corliss, and Kern yields a much larger value, 5.58 D, for the dipole moment of CTB. It is concluded that the latter value is probably in error because of the use of a minimal basis set of Slater type orbitals, and the sensitivity of the result to small errors in the charges on the axial hydrogen atoms. Introduction Cyclotriborazane, B3N3HI2(designated hereafter as CTB), is the analogue of cyclohexane, C&12, in the boron-nitrogen system;lI2the two molecules are isoelectronic, and the x-ray diffraction study of crystalline CTB3shows that the molecule has the chair conformation of cyclohexane. The site group of the CTB molecule in the crystal is C, but the molecule is only moderately distorted from CSusymmetry; it seems safe to assume that the isolated molecule (e.g., in the gas phase) has strict C3" symmetry, with the dipole moment along the threefold axis. The fact that relatively large dipole moments are observed for the amine-borane~~ suggests that CTB may also have a sizable moment. Although a great many methods for the measurement of molecular dipole moments now exist,5 the low sublimation pressure of CTB6 eliminates gas-phase methods, and we have therefore resorted to measurement of dielectric constants of solutions of CTB. Since CTB is slightly soluble in p-dioxane, the latter was selected as solvent and all measurements made at 41.1 "C; further details on the experimental methods may be found in the dissertation of Leavers.' The previously reported value of 3.2 D for the dipole moment of CTB6is significantly too
large because of an error in the value of the parameter ,@ defined in the following section, and the omission of a correction for distortion polarization. In addition to rectifying these two deficiencies we have applied a correction for the solvent effect: in order to obtain an estimate of the dipole moment of the isolated CTB molecule. Following the presentation of our results we discuss a previously unpublished ab initio molecular orbital calculation of the dipole moment of CTB by another group in the laboratory, as well as the information on atomic charges obtainable from the x-ray dataa3 Rigorous Form of the Halverstadt-Kumler Equation In the dielectric-constant-of-solutions method_ one calculates first the apparent molar polarizations, P2,, of the polar solute in a sequence of s_olutionsof decreasing concentration, and extrapolates Pzato zero_solute concentration (or "infinite dilution") to obtain P2,. A direct extrapolation of Pza is inaccurate, however? and the dielectric constant, E, and specific volume, v (or density) of the solution are commonly extrapolated separately, followed by calculation of P2, from the Halverstadt-Kumler'O (or Hedestrandll) equation. The significance of values of The Journal of Physical Chemistty, Voi. 81, No. 24, 1977
2258
D. R.
TABLE I: Dielectric Constants and Specific Volumes of Solutions of Cyclotriborazanein p-Dioxane at 41.1 C O
N2
E
0.003047 0.003798 0.005364 0.006888 0.006888
2.2122 2.2215 2.2340 2.2523
- Ec&d
v,mL g-'
-0.0003 t 0.0014
0.98964 0.98965 0.98919 0.98871 0.98909
E
-0.0020 +0.0009
- vcalcp
mL g-
-0.00007
+ 0,00010 -0.00003 -0.00019 t 0.00019
p2)zm obtained in this way has been questioned by Smith;12J3 the problem has been reexamined by one of us on the basis of the theory of partial molar properties, and the following rigorous form of the Halverstadt-Kumler equation derived:14
Here P,O = (aP/an2),,,0 is the partial molar polarization of the solute in its standard state of infinite dilution, which is exactly iefined, and replaces the somewhat ambiguous quantity, Pz,. The dielectric constant of pure solvent is denoted by elo, while (YO = (dt/dN2)0 is the derivative of the solution dielectric constant, e, with respect to solute mole fraction, N2, evaluated at N2 = 0. The molar volume of pure solvent is represented by V t , and V,O = (aV/an2)n: is the partial molar volume of solute in its standard state. The latter may be computed from the relation where Ml and M2 are the molecular weights of solvent and solute, respectively, ul0 = V*/Ml is the specific volume of pure solvent, and Po = (du/dN2)0is the derivative of the specific volume of the solution, u, with respect to N2, evaluated at N2 = 0. The present investigation will serve also as an example of the application of eq 1 and 2. Dielectric Constant Measurements The preparation and purification of CTB, and purification of the sample of p-dioxane used, as well as the experimental procedures for measurement of the dielectric constants of the solutions, have been described previously.6J Table I gives, in the second column, the measured dielectric constants, E , of four solutions having the mole fractions, Nz, of CTB shown in the first column; the uncertainties are estimated to be f 5 X in the mole fractions, and fO.0008 in e. A linear relation, E = el0' + a0N2,was fitted by the method of least squares to the values of e in Table I, with equal weight assigned to each. The constants obtained were elo' = 2.1817 f 0.0021 and (YO = 10.12 f 0.42, with probable errors calculated from the equations of Birge.15 The deviations of the observed values of e from the linear relation are shown in the third column of Table I; the rms deviation is f0.0013. The least-squares value of E?, or extrapolated value of e at N2 = 0, is in excellent agreement with the value €10 = 2.182 f 0.003 for pure p-dioxane selected for the calibration of the ce11.16 In the subsequent calculations we have used the values
Leavers and W. J. Taylor
a second measurement on the solution of highest concentration using another pycnometer of volume 24.898 mL. These data were fitted by least squares to the linear relation u = ul0' + @ON2,yielding the following values for the constants and probable vIo' = (0.99035 +- 0.00018) m L g-' (44 Po = -(0.211 i: 0.033) m L g-' (4b) The deviations of the observed values of u from this relation are given in the final column of Table I; the rms deviation is f0.00013 mL 8-l. We have taken for the specific volume of the solvent, ul0, the intercept, ul"', of the least-squares line, as given by eq 4a.18 The molar volume of the pure solvent at 41.1 "C, as obtained from eq 4a and Ml = 88.107, is VIo= (87.26 ir 0.02) m L mol-' (5a) Substitution of M1,M2 = 86.546, and eq 4 into eq 2, yields for the partial molar volume of CTB, at infinite dilution in p-dioxane and 41.1 0C:20 V2' = (67.1 i: 2.9) m L mol-' (5b) Apparent Dipole Moment of Cyclotriborazane at Infinite Dilution The partial molar polarization of CTB at infinite dilution, as obtained by substitution of eq 3 and 5 into eq 1, iszoP20 = (170.4 f 6.3) mL mol-'. It is necessary to estimate the distortion polarization21of the CTB molecule. The electronic polarization of the isoelectronic cyclohexane molecule, as calculated from the refractive index and molar volume of the liquid at 20 OC, is 27.73 mL mol-l; increasing this by the usual 5-15% to allow for atomic polarization yields 30.5 f 1.4 mL mol-l for the distortion polarization of the cyclohexane molecule. Since no refractive kdex data are available for CTB, we adopt an estimate of P2d = (30 f 5) mL mol-l for the distortion polyization of CTB. Substitution of these values of P2 and P2d (and T = 314.3 K) into eq 17 of ref 14 yields for the apparent dipole moment of the CTB molecule at infinite dilution in pdioxane solution:22 pSo = (2.69 ir 0.11) D (6) Correction for Solvent Effect The dipole moment, p, of a polar solute molecule (at infinite dilution) has associated with it a field which may be expected to induce dipoles in the surrounding solvent molecules. If the mean vector sum of the induced dipoles is colinear with the dipole of the solute molecule, we need consider only its scalar value, pi, and the apparent dipole moment of the solute molecule at infinite dilution will be p: = p pi. The problem of calculating pi has been treated by H i g a ~ ifor ; ~ the ~ case of a point dipole, p , at the center of a solute molecule having the form of an oblate spheroid immersed in a solvent of dielectric constant elo, pi = A p , where
+
el0 = 2.182 rt 0.003 (YO
=
( k 2 - 1)-1'2 arcsin (1- k-2)1'2]- 1
10.12 ir 0.42
Volumetric Data The specific volumes of the four solutions of CTB in p-dioxane used for the dielectric constant measurements were measured, using a calibrated pycnometer of volume 24.600 mL (at 20 "C), and are given in the fourth column of Table I. The final value in this column is the result of The Journal of Physical Chemistry, Vol. 81, No. 24, 1977
(7)
with Ft the ratio of the major to the minor semiaxis for the spheroid. Finally
(8) (1 + A)-'p: The atomic coordinates for crystalline CTB? combined with an approximate van der Waals radius of 1 A for the
p =
Dipole Moment of Cyclotriborazane
2259
TABLE 11: Gross Atomic Charges and Dipole Moment for Cyclotriborazane from a Molecular Orbital Calculation Orbital exponents
Coordinatesa
Atom triad Ha(B)
2, a P,a 1s 2s 2P -1.420 1.500 1.080 B -0.234 1.537 4.683 1.428 1.449 -0.125 2.420 1.246 He(N) N + 0.234 1.462 6.672 2.019 2.061 He(B) + 0.260 2.640 1.080 Hri(N) t 1.240 1.550 1.246 = 0,120, 240" for B, H,(B), and H,(B); e = 60,180, 300" for N, H,(N), and H,(N).
0
H atom, indicate that the isolated molecule (of symmetry C3J may be approximated as an oblate spheroid of minor semiaxis 2.2 A (parallel to the threefold axis) and major semiaxis 3.5 A.7 Substitution of k = 1.6 f 0.2 and elo = 2.182, in eq 7 yields A = 0.11 f 0.03; combining this result with eq 6 and 8, we obtain as our estimate of the dipole moment of the isolated CTB molecule22 1.1 = ( 2 . 4 2 f 0 . 1 6 ) D ( 91 Dipole Moment and Atomic Charges from Other Sources An unpublished self-consistent field (SCF) molecular orbital (MO) calculation for the CTB molecule by Ermler, Corliss, and Kern has been referred to briefly in ref 3, p 1487. We are indebted to Dr. Ermler for supplying the more detailed information given in Table 11. The atomic coordinates used were the best estimates of Corfield and Shore3for the isolated molecule having CSusymmetry, with the corrections described in footnote 36 of ref 3. They are tabulated as cylindrical polar coordinates, in columns 2 and 3 of Table 11. The cylinder axis, z , coincides with the threefold rotation axis, p is the perpendicular distance from this axis, and 8 the angle of rotation about this axis (the plane midway between the planes of the B and N atoms is arbitrarily assigned the value z = 0). Each row of Table I1 refers to a triad of atoms which are equivalent under the operations of the point group C3". The triads are indicated by the symbols in the first column of Table 11, where the subscripts a and e distinguish axial and equatorial H atoms, respectively, while the atom to which a H atom is bonded is indicated in parentheses. The values of the orbital exponents, S; in the minimal basis set of Slater-type orbitals (STO) are given in columns 4-6 of Table 11;they are identical with a set of optimized orbital exponents obtained by Palke in a similar calculation for BH3NH3 (ref 24, Table 11). The expectation value of the dipole moment operator is given by
where the first sum extends over the nuclei and the second sum over the n doubly occupied MO's, cpi; 2, is the atomic number of the sth nucleus, z, is its coordinate, and z is the coordinate of a typical electron. In the SCF MO procedure, in the LCAO approximation, each MO is determined as a h e a r combination of atomic orbitals (AO), Xk:25
vi=
2CkiXk k
(i = 1,.. ., n)
Substitution of eq 11 into 10 yields ( p ) = zzsz, - 22Pkl(Xt I z / x k ) s
wherez6 PkZ
=
rCkicli i
kl
(11) (12)
The value of is
(p)
Gross atomic charge
-0.1674 t 0.1664 t0.1894 -0.1351 -0,2049 +0.1517
A4D)
= 4.803.
(3v) -t 3.43
-0.56 -0.34 -0.46 -0.77 + 2.71
calculated for CTB from eq 12 and 13
( p )= 2.194 au = 5.58 D
(14)
The preceding value of ( p ) is more than twice as large as the experimental value (corrected for solvent effect) given in eq 9. Some insight into possible causes of this disagreement is provided by an approximate analysis of the contribution of individual atomic charges to the dipole moment. The total number of electrons can be analyzed as follows:
where ski= Slk = ( X k l X L ) is the overlap integral between X k and x ~ On . the basis of eq 15, one may adopt the view that 2Pkk electrons are to be assigned to the A 0 X k , and 4PklSlk to an overlap population shared by X k and xLaZ6 Alternatively, following M~lliken,~' one may allot half of the overlap population to X k (and the other half to xl), and define the gross number of electrons in the Ftth A 0 as
The gross charge (in atomic units) on the sth atom is then
q s = zs- 2 qk kCs
(17)
where the first term on the right-hand side represents the nuclear charge, and the sum extends over those AO's centered on the sth nucleus. The gross atomic charges calculated from eq 17 for a typical atom of each triad in CTB are given in column 7 of Table 11; a negative value of q, (there denoted by q ) corresponds to an excess, and a positive value of q, to a deficiency, of electrons. Finally, the total dipole moment of CTB may be approximated as
where the sum extends over all atoms. The final column of Table I1 gives the contribution of each triad of equivalent atoms to the sum in eq 18.28 The dipole moment calculated from eq 18 for CTB is 4.01 D. Information on the atomic charges having a partly experimental and partly theoretical basis has been obtained by analysis of the x-ray diffraction intensities from a single crystal of CTB by Corfield and Shore.3 A sequence of nine such adjustments is presented in Table I of ref 3, differing in the values assigned to several parameters; the average atomic charges, and rms deviations from these averages, are given in the third column of Table I11 of the present paper. The fourth column of Table I11 lists the contribution of each triad of atoms to the dipole moment, and its rms deviation, as calculated from the preceding charges and z coordinates. The sum of these contributions (with an uncertainty estimated from the propagationThe Journal of Physical Chemlstry, Vol. 8 1. No. 24, 1977
2260
D. R. Leavers and W. J. Taylor
TABLE 111: A t o m i c Charges a n d D i p o l e M o m e n t for Cyclotriborazane from X - R a y D i f f r a c t i o n Intensities Atom triad
z, A
H,(B) B $(N)
-1.420 -0.234 -0.125 +0.234 t0.260 +1.240
H,(B) H,(N)
44D) 4.803(3qz) t5.9 t 2.9 -2.3 k 0.5 -0.16 i 0.07 -1.0 i 0.3 -1.1 i 0.5 t1.6 f 0.7
A t o m i c charge and r m s deviation =
-0.29 t t0.69 t +0.09 i -0.29 i -0.29 i t0.09 i
0.14 0.16 0.04 0.10 0.14 0.04
of-error equation) is 2.9 f 3.1 D.
Discussion The error estimate of *7% for our experimental value of p, as given in eq 9, is based on the precision of the data (with allowance, also, for uncertainties in the corrections for distortion polarization and solvent effect). An estimate of the probable error inclusive of systematic errors may be arrived at by comparison of experimental results obtained by the present method with those obtained for the same molecules in the gas phase;29on this basis, it seems justified to conclude that the overall error in our experimental value, p = 2.42 D, is unlikely to exceed *15%, and is almost certainly less than f25%. We discuss next possible reasons for the marked lack of agreement of the SCF MO value, ( p ) = 5.58 D, with our experimental value. Experience has shown that Hartree-Fock (HF) values of the dipole moment have a reliability of only about 1D (see ref 30, p 241); the error in the HF values is due to neglect of electron correlation. A minimal basis set, such as that used in the SCF MO calculation of Ermler et al., cannot be counted upon to yield dipole moments which are close to the HF limit (ref 30, pp 78-81); in fact, errors of 2 or 3 D in calculated dipoles are not exceptional. Examination of the final column of Table I1 shows that, in the approximation in which the dipole moment is estimated from the gross atomic charges (see eq 18), the H atoms of the CTB molecule contribute 5.0 D (primarily because of the large separation and opposite charge of the axial H atoms bonded to B and N atoms), while the contribution of the B and N atoms, -1.0 D, is not only much smaller but of opposite sign. Thus, in this minimal-basis calculation the dipole moment is dominated by the charges on the H atoms, and is sensitive to errors in these charges, while the charges on the B and N atoms play a subsidiary role. Another factor disposing the minimal-basis calculation for CTB to error is the unbalanced character of the basis, in the sense defined by Mulliken;3l the result is a tendency to put too many electrons on the B atoms, and too few on the N atoms.32 The x-ray diffraction results in Table I11 support this view, as they yield charges of 0.69 f 0.16 and -0.29 f 0.10 atomic units for the B and N atoms, respectively, compared with 0.166 and -0.135 from the SCF calculation of Table 11. Correspondingly, the x-ray data yields -3.3 f 0.6 D, rather than the SCF MO value of -1.0 D, for the contribution of the B3N3ring to the dipole moment of CTB. An increase in the magnitude of this
The Journal of Physical Chemistry, Vol. 81, No. 24, 1977
contribution, which is directed oppositely to the larger contribution of the H atoms, would yield a smaller overall dipole moment for the CTB molecule, bringing the SCF value into better agreement with our experimental value of 2.42 D. Acknowledgment. The authors are grateful to Professor Sheldon G. Shore for making his laboratory facilities available, and for helpful advice during the synthesis of the CTB sample used in this investigation. We also express our appreciation to Professor C. William Kern and Dr. Walter C. Ermler for permission to publish the portions of their SCF MO calculation relevant to the dipole moment of CTB. However, the authors are solely responsible for the discussion of this calculation in the present paper.
References and Notes (1) G. H. Dah1 and R. Schaeffer, J. Am. Chem. Soc., 83, 3032 (1961). (2) S. G. Shore and C. W. Hickam, Inorg. Chem., 2, 638 (1963). (3) P. W. R. Corfleld and S.G. Shore, J . Am. Chem. Soc., 95,1480 (1973). (4) J. R. Weaver and R. W. Parry, Inorg. Chem., 5, 713 (1966). (5) A. L. McClellan, "Tables of Experimental Dipole Moments", Vol. 1, W. H. Freeman, San Francisco, Calif., 1963; Vol. 2, Rahara Enterprises, El Cerrito, Calif., 1974. (6) D. R. Leavers, J. R. Long, S.G. Shore, and W. J. Taylor, J . Chem. SOC. A , 1580 (1969). (7) 0. R. Leavers, W.D. Dissertation, Ohio State Universky, 1971, Chapter 3. (8) C. P. Smyth, "Dielectric Behavior and Structure", McGraw-Hill, New York, N.Y., 1955, pp 39-51. (9) J. W. Smith, "Electric Dipole Moments", Butterworths, London, 1955, pp 52-55. (10) I. F. Halverstadt and W. D. Kumler, J . Am. Chem. Soc., 64, 2968 (1942), eq 5. (1 1) G. Hedestrand, Z. Phys. Chem. B , 2, 428 (1929), eq 8. (12) J. W. Smith, Sci. Prog., 36, 483 (1948). (13) J. W. Smith, Trans. Faraday Soc., 48, 802 (1952). (14) W. J. Taylor, J . Phys. Chem., 79, 1817 (1975). (15) R. T. Birge, Phys. Rev., 40, 207 (1932). (16) A. A. Maryott and E. R. Smith, Natl. Bur. Stand. Circ. No. 514, 12 (195 1). (17) The erroneous value of bo inadvertently used in ref 6 was based on a single preliminary measurement of specific volume. (16) The extrapohted value is in relatively g o d agreement with the value 0.9900 mL g-' for pure pdioxane at 41 "C calculated from the data of Herz and Lorentz." (19) W. Herz and E. Lorentz, Z. Phys. Chem. A , 140, 406 (1929). ' have been estlmated on the (20) The probable errors of V; and F2 assumptions that the errors of u1 , Po, el0, and 01' are dlstrlbuted normally and are uncorrelated. (21) R. J. W. LeFkre, "Dipole Moments", 2nd ed,Methuen, London, 1948, pp 10-13. (22) In estimating the error in eq 6 from those in P ; and and also the error in eq 9 from those in eq 6 and A , we have assumed the least favorable combination of errors. (23) K. Higasi, Sci. Pap. Inst. Phys. Chem. Res. (Jpn.), 28,284(1936), eq 18. (24) W. E. Palke, J . Chem. Phys., 56, 5308 (1972). (25) C. C. J. Roothaan, Rev. Mod. Phys., 23, 69 (1951). (26) W. J. Taylor, Phys. Rev., 87,214 (1952). (27) R. S.Mulllken, J . Chem. Phys., 23, 1833 (1955). (28) If zsin eq 18 is in A, as in Table 11, one must multiply the right-hand side by 4.803 to obtain I.L In debyes. (29) See Table 18.1, p 48 of ref 8, and Table 12, p 129 of ref 9. (30) H. F. Schaefer, 111, "Electronic Structure of Atoms and Molecules: A Survey of Rigorous Quantum Mechanical Resutts", Addison-Wesley, Reading, Mass., 1972. (31) R. S. Mulliken, J. Chem. Phys., 36, 3428 (1962). (32) C.W. Kern, R. M. Pitzer, and 0. J. Sovers, J . Chem. phys., 60,3583 (1974).
B2,,,
