660
J. Phys. Chem. 1991, 95,660-663
to the examination, in the present study, of a large number of solutions in the three alternative cells. Only two other reliable experimental determinations of both the magnitude and the sign of the quadrupole moment of benzene have been reported. In the first of these, Battaglia, Buckingham, and Williamsa used the vapor-phase electric field gradient induced birefringence of benzene, measured over limited ranges of temperature and pressure, to establish that the contribution of the field gradient hyperpolarizability to the effect is negligibly small, and to derive the free-molecule quadrupole moment. Of course, their conclusion in relation to the hyperpolarizability provides justification for our neglect of this contribution. Furthermore, the excellent agreement between their quadrupole moment (-29.0 f 1.7) and ours (-28.3 f 1.2) is confirmatory evidence for the adequacy of our treatment of the local field gradient and the reaction field gradient in a nonquadrupolar, isotropically polarizable solvent such as carbon tetrachloride. The other relevant study, reported by Stolze, Stolze, Hubner, and S ~ t t e rexploits ,~ an ingenious approach, originally developed by Shoemaker and Flygare," that enables the quadrupole moment of benzene to be derived from measurements of the rotational Zeeman effect in fluorobenzene. Although certain assumptions underlie this procedure, the revised quadrupole moment that emerges (-28.4 f 4.7) clearly is concordant with the vapor-phase and dilute-solution results discussed above. In addition, several reliable ab initio molecular-orbital calculations have been reported, so that the quadrupole moment of benzene can now be considered very well defined.I2 It remains to note that the value of the quadrupole moment of benzene derived in the present work with cyclohexane as solvent (-27.0 f 1 .I) is well within the range spanned by the uncertainties given for the preferred dilute-solution value (-28.3 f 1.2), the vapor-phase field gradient birefringence value (-29.0 f 1.7), and the spectroscopic value (-28.4 f 4.7). A plausible inference could therefore be that carbon tetrachloride, a nonquadrupolar, isotropically polarizable solvent, can be replaced by cyclohexane, a weakly quadrupolar, anisotropically polarizable solvent, without significant effect on the apparent quadrupole moment of the solute. However, it has already been noted that the theory is not rigorously applicable to the latter case; and we believe that even a weakly quadrupolar solvent may indeed yield a slight underestimate of (11) Shoemaker, R. L.; Flygare, W. H. J . Chem. Phys. 1969, 51, 2988-2991. ( I 2) See relevant literature summarized in refs 3a and 4d,and also: Ha, T.-K. Chem. Phys. Lea. 1981, 79, 313-316.
the true quadrupole moment of the solute. In support of this view, it may be noted that use of l,edioxane, a solvent whose molecules are much more strongly quadrupolar but roughly as anisotropically polarizable as those of cyclohexane, results in an apparent quadrupole moment for benzene that is about 40% smaller, rather than perhaps 5% smaller, than the value obtained with carbon tetrachloride as solvent. Clearly, the difficulty 'parallels the much older problem of the extraction of reliable molecular dipole moments from the relative permittivities of dilute solutions of solutes in dipolar solvents, most notably water, and relevant theory is under consideration. In the meantime, however, we will, where necessary, continue to use cyclohexane as an alternative solvent for our measurements, in the knowledge that the quadrupole moments so obtained may be slightly underestimated.
Summary The present investigation of dilute-solution field gradient induced birefringence has resulted in a significant advance in the technology of this important method for the determination of molecular quadrupole moments. In particular, a novel four-pole field gradient birefringence cell characterized by simplicity of design and use, greatly reduced internal volume, enhanced optical stability and applicability to reactive compounds under inertatmosphere conditions, has been constructed and tested. A comparative study of the field gradient birefringence of benzene in the three available cells (four-pole, monopole, and two-wire) and in two solvents (carbon tetrachloride and cyclohexane) has yielded an improved value of the dilute-solution quadrupole moment of benzene that agrees with other reliable experimental and theoretical results. The question of whether or not carbon tetrachloride (a nonquadrupolar, isotropically polarizable, and sometimes reactive solvent) can be replaced by cyclohexane (a weakly quadrupolar, anisotropically polarizable, and generally unreactive solvent) without significant effect on the apparent quadrupole moment of the solute was also considered. Insofar as the infinite-dilution quadrupole moments of benzene in carbon tetrachloride and cyclohexane, respectively, were found to be virtually the same, it was inferred that, where for reasons of reactivity or solubility an alternative is required, the latter solvent is also suitable for such measurements. Acknowledgment. Technical assistance from Mr. R. Koch and Mr. J. Zylmans (University of Sydney), and financial support from the Australian Research Council (to G.L.D.R.) are gratefully acknowledged.
Hydrogen Bond Energy of CH&N-HCI by FTIR Photometry Lance Ballard and Ciles Henderson* Department of Chemistry, Eastern Illinois University, Charleston, Illinois 61920 (Received: May 29, 1990)
The temperature dependence of an IR absorption band of CH,CN-HCI is characterized by FTIR photometry. The heat of dimer formation at 41 OC obtained from this data, MD= -13.8 1.2 kl/mol, is used to calculate the equilibrium hydrogen bond dissociation energy, De = 21.8 & 1.7 kJ/mol. These results are compared with recent ab initio theoretical calculations and empirical estimates based on centrifugal distortion parameters.
*
Introduction Although extensive efforts have been expended to theoretically and experimentally characterize weakly bound complexes, surprisingjy, no expeimental measuremenis of gas-phase hydrogen bond energies for any of the nitrile complexes of hydrogen chloride have been remrted. Room-temperature IR spectra of gas-phase mixtures of CH$N and HCI kxhibit a weik dimer band near 2725 cm-' (Figure 1) originally reported and assigned to the HCI
stretching mode of the hydrogen-bonded hetercdimer by Thomas and Thompson:' CH-.CN + HCI F? CHiCN-HC1 (1) ., The Observed A' = cm-' red shift Of this mode from the corresponding monomer frequency may be qualitatively correlated ( 1 ) Thomas, R. K.; Thompson, H.Proc. R. Soc. London A 1970,316,303.
0022-3654/9 1/2095-0660%02.50/0 0 199 1 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 661
Hydrogen Bond Energy of CH3CN-HCl 0
3486
2457
F ( cm-')
1429
400
N N
2833
.. 2860
28'02
2743
2685
;(cm-' ) Figure 1. (a) Fr'IR absorption spectrum of a room-temperature mixture of CH3CN (76 mmHg) and HCI (301 mmHg) with a IO-cm path length, 0.5 cm-l resolution. (b) Expansion of the HCI stretching mode of the hydrogen-bonded CH,CN-HCI heterodimcr.
2791
2748
2706
G ( cm-' Figure 2. Temperature dependence of the CH3CN-HCI dimer band. These spectra were measured with p(CH3CN) = 79.2 mmHg, p(HCI) = 254.8 mmHg. The curves from top to bottom correspond to T = 28.0, 38.0, 43.0, 48.0, and 53.0 OC, respectively. The reproducible sharp features observed from approximately 27 10-2730 cm-I have been interpreted as P-branch band-heads of hot bands involving the out-of-phase bending mode and have been used in ref 1 to estimate the ue bending frequency.
with the srrengrh of the hydrogen bond.2 However, in this study we wish to employ FI'IR photometry to measure the temperature dependence of the dimer band in order to obtain quantitative values of AHD,the heat of dimer formation. Appropriate partition functions and heat capacities may then be used to calculate the equilibrium dissociation energy De, which will be compared with recent ab initio theoretical calculation^^*^ and empirical estimates based on centrifugal distortion parameters obtained from FTmicrowave rotational ~ p e c t r a . ~
of CH3CN-HCI in the gas mixtures was obtained by summing the integrals of the corresponding H-CI stretching mode over the following integration limits: 2706.5-2722.7; 2733.1-2742.8; 2760.0-2768.5; 278 1.8-2790.1; 2805.6-2813.0; 2829.1-2832.3 cm-l. These limits were selected to exclude contributions from the vibrational-rotational lines of the HCI monomer. Spectra of pure HCI and CH3CN at similar conditions revealed no detectable absorption due to the (HCl)* or (CH3CN), homodimers in the frequency regions integrated.
Experimental Section The measurements reported in this study were carried out with hydrogen chloride (Matheson) and spectro grade acetonitrile vapor (Kodak) thermostated in a IO-cm gas cell equipped with KCI windows. The sample composition and pressure were controlled with a conventional vacuum line and mercury manometer. Gas mixtures were initially prepared at temperature T I ,the sample cell was closed, and 100 interferograms were scanned with a resolution of 0.5 cm-', averaged, Fourier transformed, and ratioed to the background of the empty cell with a Nicolet 20 DXB FTIR spectrometer. Measurements were then taken at other temperatures, T2,ranging from 298 to 326 K. The cell was then pumped out and the above procedure repeated with different gas mixtures. Clague and Bernsteid have used IR photometry to determine heats of dimerization for several vapor-phase carboxylic acids. They found that values obtained from dimer peak heights were in discrepancy with values obtained from dimer band areas by as much as 4 kJ/mol. This observation can be explained in terms of the temperature dependence of the absorption coefficients at a single wavelength. As the temperature changes the Boltzman populations of the dimer eigenstates change, resulting in a temperature-dependent band shape. However, the vibrational-rotational wave functions and corresponding transition moment integrals are not temperature dependent and the integrated absorption value of a resolved dimer band remains a reliable measure of the dimer concentration. Accordingly, the relative concentration
Results The thermodynamic equilibrium constant for eq 1 may be expressed in terms of the partial pressures of the components: P(CH3CN-HCI) K= (2) P(CH,CN)P( HCI)
( 2 ) See, for example: (a) Pimentel, G. C.; McClellan, A. L. The Hydrogen Bond; Freeman: San Francisco, 1960. (b) Legon, A. C.; Millen, D. J.; Schrems, 0. J. Chem. Soc., Faraday Trans. 2 1979, 75, 592. (3) Boyd, R. J.; Choi, S.C. Chem. Phys. Lett. 1986, 129, 62. (4) Hinchliffe, A. Ado. Mol. Relax. Interact. Processes 1981, 19, 221. ( 5 ) Legon, A. C.; Millen, D. J.; North, H. M. J . Phys. Chem. 1987, 91, 5210. ( 6 ) Claguc, A.; Bernstein, H. Spectrochfm. Acta 1967, 2 5 4 593.
Since heat is evolved in dimer formation, the equilibrium is expected to shift to the left, favoring higher monomer concentrations and lower dimer concentrations at elevated temperatures. This trend is clearly evident in Figure 2. If we assume the partial pressure of the dimer is ideal and that the integrated absorption of the dimer band is described by Beers law:
K=
(D)RTI (%)IP(CH$N)P(HCl)
( D )R TIZ
- ( t ~ ) l P ( c H ~ c N ) P ( H T2c l ) N
(3) where ( D ) is the integrated absorption of the dimer, (eD) is the integrated absorption coefficient of the dimer, I is the optical path length, R is the gas constant, T I and T2 are the initial and final temperatures of the gas mixture, and P(i)is the initial pressure of the ith component. Since plots of (D) vs P(CH3CN)P(HCl) exhibited negligible curvature in the range 50.0 IP ( C H 3 C N ) I80.0 and 100.0 IP(HC1) I300.0 mmHg, we assume the concentration of the dimer to be small compared to the concentration of the monomers and approximate the P(monomers) as P(monomers) in the right-hand side of eq 3. Finally, if the temperature of the sample is changed at constant volume, the equilibrium pressure of each component is changed by the factor 7 - 2 1 TI * The shift in equilibrium with temperature is dependent on AHD: AGOD = -RT In K = A H O D - T A S O D (4) where AGOD, AHOD, and ASoDare the usual standard free energy,
662 The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 v)
Ballard and Henderson TABLE I: CH3CN-HCI Diwr Modes (v,), V h t i u a a l Heat (zpe,) Camcities (Cdvib]) rt 314 K, and Zero-Point -ea
7
////
u.
97 f 3 350 100’ 40 f 2oC
**
0.984 0.001 0.58 & 0.02 1.62 0.1 4.21 1.2 1.994 f 0.002 0.48 f 0.2
#Reference5. Note that Thomas and Thompson1estimate vu = 100 cm-l from the (u, = vu) difference band. bEstimated from infrared measurements of CH,CN-HF, ref 10. CReferenceI .
/
N I
hydrogen bond stretch
ug in phase bend uB out of phase bend
TABLE 11: CH3CN-HCI Hydrogen Bond Dbo~htiwEnergy De (kJ/mol) source
*
3.8
3.6
1/RT
X
lo4
4.0
Figure 3. Representativeplot of eq 5 for a single data set in which Q = [ (D)RTl*/lp(CH3CN)P”(HCI)T2]and AHD = -slope.
enthalpy, and entropy of dimerization. Replacing K with eq 3 we obtain:
In
[
1-
( D )R TI IPo(CH3CN)Po(HCl)T2
If we neglect any temperature dependence of AH over the small range of T2values employed in this study, we expect plots of the left-hand side of eq 5 vs l/RT2 to give straight lines with slopes equal to -AHoD. This method of data analysis precludes the determination of the entropy of dimerization from the intercepts of these plots since we do not have any reliable estimate of the dimer’s integrated absorption coefficient. Moreover, we found that at P(HC1) 2 200.0 mmHg, Benesi-Hildebrand’s plots exhibit significant deviation from linearity suggesting that at these pressures, trimers or higher order9 complexes may contribute to the absorption near 2725 cm-I. This behavior prevents us from experimentally determining accurate values of (eD) or numerical values of the dimer equilibrium constant with our current apparatus. Approximately 1500 spectra were measured with initial mole fractions of HCI ranging from 0.4 to 0.8 and temperatures ranging from 300 to 326 K. A representative plot of eq 5 for a single data set is presented in Figure 3. The average least-squares slope of all of our measurements gives AH3I4D = -13.8 f 1.2 kJ/mol. The heat capacities of the components of the gas mixture may be used along with the zero-point energies of the dimer vibrational modes to calculate the equilibrium hydrogen bond dissociation energy:
De =
+ Azpe + AC,T + AnRT
(6)
where zpq is the zero point energy of the ith vibrational mode, Azpe = Zzpef(products) - Zzpef(reactants) of eq 1, AC, = C,(dimer) -ZC,(monomers), and AnRT is the PAVexternal energy associated with eq 1. The translational and rotational contributions to the heat capacities may be obtained classically from the equipartition theorem. The CH3CN and HCl monomers have 12 and 1 vibrational modes, respectively. In contrast, the CH3CN-HCl dimer has 3 N - 6 = 18 vibrational modes. We assume that the frequency of the monomer modes are essentially unaffected upon dimer formation and effectively cancel in the Azpe Benesi, H. A.; Hildebrand, J. H. J. Am. Chem. Soc. 1949,71,2703. R. K. Proc. R.Soc. London A 1971, 322, 137. (9) Schriver, L.; Schrivcr, A.; Perchard, J. P. J. Chem. Soc., Faraday (7)
( 8 ) Thomas,
Trans. 2 1985, 81, 1407. (IO) Thomas, R. K. Proc. R. Soc. London A 1971, 325, 133.
FTlR photometry pseudodiatomic approximation
22.0 1.7 18.6 f 0.6 22.15 18.85
6-31G** GAUSSIAN
80’
large scale SCF-MOC
‘This study. ’Reference 2. CReference3.
and AC” terms in eq 6. The 18 - 13 = 5 new vibrational modes of the dimer consist of low frequency doubly degenerate in phase (ve) and out of phase (vs) bending modes in which the semirigid monomer subunits effectively librate about respective center-ofactions and a hydrogen bond stretching mode (v,) in which the semirigid subunits translate in opposite directions. The contribution of each of these dimer modes to the vibrational heat capacity and zero-point energies was calculated from the vibrational freq~enciesl-~ and partition functions and are presented in Table I. These results were used with eq 6 to obtain a well depth for the CH3CN-HCl hydrogen bond:
De = 22.0 f 1.7 kJ/mol
Discussion Although there have been no previous measurements of gasphase dissociation energies of this complex, an estimate can be made from the observed hydrogen-bonding stretching frequency. If we employ a pseudodiatomic model” in which we regard the two subunits as point masses located at their respective mass centers, separated by a distance rand bound by a Lennard-Jones 6-12 potential of the form
it is easily shown from the coefficient of the quadratic term of a Taylor series expansion about r = re that m(HCl)m(CH$N) (*cIfe)2 De = m(HC1) + m(CH3CN) 18
(8)
where m ( i ) is the mass of the ith subunit, c is the speed of light, 8 is the hydrogen bond stretching wave number if given in cm-I, and re is the equilibrium distance between the subunit mass centers. Using a value of re = 4.569 X 10” cm, calculated from structural parameters obtained from microwave st~dies?JZ’~ and I = 97 cm-’, as reported by LRgon et al.?, in the pseudodiatomic approximation described above, we estimate the Lennard-Jones well depth as De = 18.6 f 0.6 kJ/mol. Several theoretical a b initio studies of this complex have been reported. Boyd and Cho? used a fully optimized structure a t the 6-31G** level with GAUSSIAN 80 programs to obtain De = 22.15 kJ/mol. Hinchliffe4has employed a larger, Gaussian orbital, basis set in a SCF-MO calculation to obtain a lower value, De = 18.85 kJ/mol. These various results are compared in Table 11. The ( I I ) Balle. T. J.; Campbell, E. J.; Keenan, M.R.;Flygare, W. H. J. Chem.
Phys. 1980. 72, 922.
(12) Thomas, L. F.; Sherrard, E. 1.; Sheridan, J. Trans. Faraday Soc.
London 1955, 51, 619.
(13) Costain, C. C. J. Chem. Phys. 1958, 29, 864.
663
J. Phys. Chem. 1991,95,663-665 uncertainties in our result reflects contributions from our experimental precision in UfD,the uncertainty in the dimer mode frequencies and the corresponding uncertainties in the zero-point energy, vibrational partition function, and heat capacity. The uncertainty assigned to the pseudodiatomic approximation contains only the experimental uncertainty in Y, and the dimer structure and has no contribution from any model-dependent error. Accordingly, this precision limit should be regarded as a lower limit. Boyd and ChoP have previously noted that the empirical procedure
based on the pseudodiatomic approximation underestimates bond energies by as much as 25%. Refinements in experimental values of De obtained by photometric equilibrium methods will require longer optical path lengths, higher sensitivity, and more precise values of the dimer mode frequencies. It is evident from Table I1 that in spite of the sensitivity to small differences between large numbers, modern a b initio theoretical methods are capable of calculating reliable hydrogen bond energies in gas-phase complexes.
Extrapolation of the Born Model to Solvated Point Charges in Ammonia and Water Manfred Bucher Department of Physics, California State University, Fresno, California 93740-0037 (Received: July 24, 1990)
An extrapolation of the Born model of ion solvation predicts ammoniation energies A G ( F ) = -4.57 eV and AG(H+) = -12.54 eV, provides insight into the different nature of short-range interaction of ammoniated and hydrated anions with solvent molecules, and indicates the different reactions of alkali metal with ammonia and water.
Introduction The Born model of ion solvation' approximates the Gibbs' free energy of solvation, AG, through the change of the electrostatic energy of an ion of charge Ze in vacuum and in a solvent of permittivity c
TABLE I: Experimental Solvation Energies AG (in eV) of Univalent Ions in Ammonia [am]and Water [aJ Corresponding Born Radii rB (in A), and Pauling Ionic Radii rp (in A). ion -AGIam]* r,Jam] rp -AG[aqlc rBlaql cs+ 2.26 3.05 1.69 3.08 2.3 I
Rb+ K+ Na+
3.30 3.64 4.58 5.79 12.54* 3.33 3.66 3.75 4.57* 12.54;
2.09 1.90 1.51 1.19 0.55; 2.07 1.88 1.84 1.51; 0.55;
1.48 1.33 0.95 0.60 0.00 2.16 1.95 1.81 1.36 0.00
3.32 3.50 4.26 5.36 11.30 2.66 3.14 3.29 4.50 -23.69'
2.14 2.03 1.67 1.33 0.63 2.61 2.26 2.16 1.58 430*
Li+ The empirical Born radius rBdepends on the ion species and on H+ the solvent. Values of rB for alkali-metal and halide ions, cal1Brculated from experimental solvation energies2" AG in ammonia CI[am] and in water [aq] and with permitti~ities~ t[am] = 23.9and F e[aq] = 78.39,are listed in Table I. A plot of Born radii rBvs nPauling ionic radii rp in Figure 1 shows linear relations for the groups of solvated cations and anions in ammonia and in ~ a t e r . 2 ~ ~ Values with an asterisk are theoretical estimates extrapolated from While the data for the cations in both solvents fall along two close, Figure 1 with an uncertainty of 110%. *Reference 2. CReference3. parallel straight lines, a remarkable difference exists for the lines connecting the anion data. The difference concerns the considrepulsive contributions in the short-range interaction between erably flatter and steeper slopes of the lines for halide ions in solvated p6-shell (or ls2-shell) ions and the surrounding solvent molecules. This behavior is well reflected in Figure 1 by the ammonia, X-[am], and in water, X-[aq], respectively. Employing the linear relation between f B and rp,we show that extrapolations straight lines through the data of the solvated alkali metal ions of the simple Born model to small and vanishing Pauling radii in ammonia and water, A+[am] and A+[aq], with slopes, s = drB/drbof values close to s = 1. Our interpretation of A+ solvation yield estimates of (1) ammoniation energies of F and H+, for which no experimental values have been reported, and of (2)the in terms of negligible short-range interaction, AG,, = 0, is supamount of short-range interaction in the solvation of anions. ported by its extension to the hydration of a proton where, due Furthermore, the extrapolations (3) provide insights into the kind to the lack of an electron shell, AG,,(H+) = 0 and rp(H+)= 0. of short-range interaction involved and (4) indicate, from a unified Figure 1 shows that the Born radius of a hydrated proton, rBpoint of view, the different behavior of ammonia and water when (H+[aq]), obtained from the experimental value of the hydration alkali metal is added to these polar solvents. energy AG(H+[aq]), falls on the extended line of the A+[aq] data. By analogy we extrapolate the close parallel line of A+[am] data Extrapolations to obtain estimates for rB(H+[am])and AG(H+[am]) of an ammoniated proton, listed in Table I, for which no experimental value In a previous analysis of the Born model7 we have shown that is known. the sucxcss of the approximation in eq 1 for the solvation of alkali In our analysis of the Born model7 we have pointed out that metal ions is a consequence of nearly cancelling attractive and the differences (re - rp) should not be interpreted in terms of the structural configuration of solvent molecules around a solvated (1) Born, M.2.Phys. 1920, I , 45. ion, e.g., molecular voids or solvation numbers. Such a structural (2) Senozen, N. M. J. Inorg. Nucl. Chem. 1973.35, 721. interpretation of ( f B - rp) must be ruled out because of another (3) Friedman. H.L.; Krishnan. C. V. In Wuter, Franks, F., Ed.; Plenum: New York, 1973; Vol. 3, p 55. approximation underlying eq 1, namely the use of the bulk per(4) Marcus, Y.IonSoloution: Wiley: Chicharter, U.K., 1985; pp 136-137. mittivity of the solvent, t, in the immediate vicinity of a solvated (5) Voet, A. Trans. Furuduy Soc. 1936.32, 1301. ion instead of a distancedependent permittivity, t(r). Rather than (6) Latimer. W. M.;Pitzer, K. S.;Slansky, C. L. J. Chem. Phys. 1939, revealing the molecular configuration around a solvated ion, the 7. 108. (7) Bucher, M.;Porter, T. L. J. Phys. Chem. 1986, 90, 3406. Born radii provide information about the associated short-range (I
0022-3654/91/2095-0663$02.50/0
0 1991 American Chemical Society
