1880
A. 8. M. S.Bassi and Roy E. Bruns'
Polar Tensors and Effective Charges of Br&O A. B. M. S. Bassi and Roy E. Bruns" lnstituto de Quhlca, Unlversidade Estadual de Campinas, Camplnas, SP, Brazil (Received February 24, 1975) Publication costs assisted by Fundado de Amparo a Pesquisa do Estado de Sio Paul0
Polar tensors and effective charges of BrzCO have been calculated and the recently reported sign ambiguity for the B1 symmetry dipole moment derivatives has been confirmed. Small changes in the values of the dipole moment derivatives of ClZCS, due to a sign ambiguity in earlier treatments, are also reported. The effective charges of BrzCO are compared with those calculated for other X2CY (X = F, C1; Y = 0, S) molecules.
Recently, Prasad and Singhl have pointed out a sign ambiguity in the dipole moment derivatives of the B1 symmetry species of Br&0.2 Using the polar tensor formalism3~* and the effective charges4ysof the XzCY molecules (X = F, C1, Br; Y = 0, S) we have been able to affirm the conclusions of Prasad and Singh for BrzCO and to ascertain that a sign ambiguity also exists in the B1 symmetry species of ClzCS.6 As the polar tensor and effective charge values of the XzCY molecules' are of interest in their own right the previously unreported values for BrzCO are presented in this report. The atomic polar tensor (for atom a) is composed of the derivatives of the molecular dipole moment with respect to the atomic Cartesian coordinates
px',) =
ap,/ax, aPx/aY, ap,/az, apy/ax, apYlay, apy/az, ap,/ax, aPz/aY, ap,/az,
(
)
(1)
The polar tensor for the X2CY molecules is defined as a juxtaposition of its atomic polar tensors
The values of P, are calculated directly using the matrix equation P, = PQL-'UDM1'2 + PP6M"'
( 31
The first term in eq 3 represents purely vibrational contributions to P,. The PQmatrix is of dimension 3(3N - 6) and contains values of ap,/aQ, (rn = x , y, or z; i = 1 , 2 . . , 3N - 6) which are evaluated directly from the infrared int e n ~ i t i e s The . ~ signs of the elements of the PQmatrix are those suggested on the basis of semiempirical CNDO molecular orbital investigations.s The matrices L-l, U, and DM1/2 = B are the standard coordinate transformation matrices involved in the evaluation of the force fields of molecules. The second term in eq 3 expresses the rotational contribution to P, and has been described previously.4 The values of P, are determined in part by the signs of the elements in PQand P, (those of the latter matrix being specified by the sign of the equilibrium dipole moment). Previous analysis of infrared intensity data was hampered by the lack of an analytical expression which clearly indicates the effect of the different sign choices for the equilibrium moment and the ap/aQ, on the values of the dipole moment derivatives with respect to the symmetry coordinates, aplaS,. A knowledge of the polar tensor values leads to a
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The Journalof Physical Chemlstry, Vol. 79, No. 17, 1975
straightforward determination of the effective charge values? tatof atom a
E a 2 = TR[PX'a)(Px((Y))']= (ap/ax,)Z
+
(aP/aY,)' + (ap/az,)' (4) Here, TR[P,(")(P,(a))'] represents the trace of the matrix product of the atomic polar tensor with its transpose. The effective charges are of special interest as they can, in principle, be determined from the intensity sum of all the fundamental bands of a molecule
In this equation m, represents the mass of atom a,n corresponds to a rotational correction which depends on the equilibrium dipole moment and the principal moments of inertia of the molecule, and A h is the experimental infrared intensity of the kth fundamental band. The polar tensor and effective charge values of the X2CY molecules (X = F, C1; Y = 0, S) have been shown' to be related by the empirical equations
P,"y1'(C12CO) - P,(az)(FZCO) = and
where a1 = cy3 = C1 and a2 = a4 = F, a1 = cy2 = 0 and a3 = a 4 = S, or a1 = a2 = a3 = cy4 = C. A knowledge of the atomic polar tensors and effective charges of BrzCO leads to a prediction of the vibrational intensity parameters of Br&S through equations similar to (6) and (7) if they can be extended to the bromine substituents. The polar tensor values for BrZCO, corresponding to the preferred sign choice of Prasad and Singhl are presented in Table I. The atomic Cartesian coordinates are defined in Figure 1. The sign ambiguity can be described as follows. As the two normal coordinates of B1 symmetry, Q4 and Q5, produce dipole moment changes in the x direction a reversal of the signs of ap,/aQd and ap,laQS as well as a sign change for the equilibrium moment results in a change of all the signs for the first row elements of the atomic polar tensors. Elements contained in the other rows are not affected. This corresponds to a change in the ap/aSj values of the B1 symmetry species. As the rotational contributions to P, in eq 3 are large for Br&O (up to 0.10 e) the values of
1881
Polar Tensors and Effective Charges of Br2CO TABLE I: Polar Tensor of BrzCO
*
0 .o -0.37 0.01 0.0 -0.06 i 0.02 0.0 4 . 8 3 i 0.02 0.0 1.58 i 0.04 0.0 0 .o 0,19i 0.01 0.0 0.0 -0.17 f 0.02 0.0 0 .o 0.04 i 0.02 0.0 -1.10 f 0.03 -0.19 -f 0.04 0.0 -0.15 i 0.03 1.40 i 0.10 0.0 0.0 0 .o 0 .o The values of the polar tensor elements are multiples of the electronic charge, e. 1DA-1 = 0.2082 e = 3.335 X 10-20 C. The L - l matrix used in the calculation of these polar tensors is from ref 2. The U matrix and Cartesian coordinate system correspond to those of ref 8. The above polar tensors correspond to a sign choice of ap/aQl > 0 for i = 3, 5 and ap/aQ, < 0 for i = 1, 2, 4, 6. In ref 8 ap/aQa was chosen to be positive and ap/aQa was given a negative sign. The diagonal polar tensor elements for Brz (see Figure 1)are equal to those of Brl. The offdiagonal elements of Brz have the same magnitudes but opposite signs to those of Brl.
TABLE 11: Recalculated Values of the ap/aS, for ClzCS (B1 Symmetry) from the Experimental Intensities of Ref 6a
7.
t
X
Y
Signs
Ref 6 values
aP/aQ, and ap/aQ, aP,/aS4
Recalculated values
of
aP,/aS,
ap,/aS~
aP,/aS,
++
-0.95 +0.15 4.95 +0.08 +0.97 -0.14 +0.95 4.10 +0.02 +-1.05 -0.03 -1.07 +0.04 -+ -0.03 +1.08 +1.07 Units of e. LI Preferred set of signs for the ap/aQt. The ( - - ) sign choice, ap/aQ4 and dp/aQa both negative, was also chosen previously in ref 10. - -b
(1
Figure 1. The Cartesian coordinate system for the X2CY
molecules.
aplaSj which are now preferred (corresponding to the -+ sign combination for apJaQ4 and aprlaQs, respectively) are markedly different from those chosen previously.s As Prasad and Singhl have pointed out, the electronic distortions for the various vibrational displacements deduced from the recalculated values of the ap/aSj are more consistent with those found for FzCO and C12CO. All of the polar tensor elements in Table I with the exception of apJayB, have the same signs as their corresponding elements in the tensors for the latter molecules. This element has values of -0.11, 0.00 and 0.04 e for F, C1, and Br, respectively. These values are expected to become more positive for the heavier atoms. For Cl&S there is only a sign change in the rotational term of eq 3. As the experimental dipole moment (0.28 D) of ClzCS is larger than the recently measured value of 0.08 D9for FzCS the chlorine atoms appear to be situated at the positive end of the dipole (+ClzCS-). This sense of the moment has been predicted by CNDO calculationslO and was used in our calculation of the polar tensor of C ~ Z C STable .~ I1 gives the values of the aplaSj of the B1 symmetry species corresponding to this polar tensor along with the original values.6 Because the rotational contributions are small the differences in magnitudes are less than 0.04 e. The sense of the dipole moment of FzCS is not of importance in the calculation of dipole moment derivatives, as the rotational contributions are smaller than the experimental errors arising in the vibrational analysis. The effective charges of BrzCO evaluated from eq 4 are compared with those for the other X2CY molecules in Table 111. The decrease in the carbon effective charge with substitution of Br for C1 is 0.42 e strikingly similar to the decreases in [c on substitution of C1 for F (0.35, X2CO; 0.41, X2CS). The corresponding increases in [o are 0.23 and 0.12 e. The value of E B ~(0.45 e) is about one-half of the
TABLE 111: Experimental Effectives Charges of FzCO, FzCS, ClzCO, ClzCS, and BrzCO X,CY
5C
SY
Sx
1.04 i 0.03 1.05 i 0.02 2.88 i 0.06 1.16 i 0.04 0.86 i 0.03 2.53 i 0.09 1.39 -f 0.04 0.45 i 0.04 Br,CO 2.11 i 0.10 1.06 i 0.03 0.65 i 0.03 F2CS 2.43 i 0.06 0.78 i 0.04 0.87 i 0.04 c1,cs 2.02 i 0.09 (0.46 i 0.10) Br2CSa (1.66 ~t0.22) (1.00 i 0.10) Values of BrzCS evaluated using an equation analogous to ( 7 ) , and the effective charges of FzCS and FzCO. Effective charge values of BrzCS using the values of ClzCS and ClzCO are very similar (1.60, 1.01, and 0.47 e).
FZCO
c1,co
value of [cl (0.86 e) in ClzCO. As the effective charges of F and C1 are both invariant to substitution of oxygen for sulfur we might tentatively predict a bromine effective charge for Br2CS extremely close to the one found for Br2CO. This is borne out by the estimation of the effective charges of BrzCS, also listed in Table 111, when Br2CO and BrzCS are substituted in eq 7 for ClzCO and C12CS. The effective charge of carbon which is seen to decrease by 0.41 e upon substitution of C1 for F in the thionyl halides is calculated to decrease by a similar amount, 0.36 e, when C1 is replaced by Br. These effective charge values of BrzCO emphasize the previous observation' that this parameter reflects the electronegativities of atoms in molecules. The effective charges of the halogens decrease as does their electronegativities for the heavier atoms. The oxygen effective charges increase and those of carbon decrease with substitution of the less electronegative halogens. It is worth noting that [C in ClzCO and F&S have similar magnitudes as does this parameter in Br2CO and ClzCS. A knowledge of the relaThe Journal of Physical Chemistry, Vol. 79, No. 17, 1975
1882
Douglas R. Caldwell
tionship between the effective charges and the electronegativities (or other atomic or bond properties) awaits the evaluation of more effective charge values for other molecules. Presently we are extending these calculations to aid our understanding of the effective charge parameter.
References and Notes (1) P. L. Prasad and S. Singh, Chem. Phys. Lett., 24, 543 (1974). (2) M. J. Hopper, J. W. Russell, and J. Overend, J. Chem. Phys., 48, 3765 (1968). (3) J. F. Biarge, J. Herranz, and J. Morcillo, An. R. SOC. ESP. Fls. Quim., Ser. A, 57, 81 (1961). (4) W. B. Person and J. H. Newton, J. Chem. Phys., 61, 1040 (1974). (5) W. T. King, G. B. Mast, and P. P. Blanchette, J. Chem. Phys., 56, 4440 (1972). (6) M. J. Hopper, J. W. Russell, and J. Overend, Spectrochim. Acta, Part A, 26, 1215 (1972). (7) A. B. M. S. Bassi and R. E. Bruns. J. Chem. Phys., 62,3235 (1975). (8) R. E. Bruns and R. K. Nair, J. Chem. Phys., 58, 1849 (1973). (9) A. J. Careless, H. W. Kroto, and B. M. Landsborg, Chem. Phys., 1, 371 (1973). (10) R. E. Bruns, J. Chem. Phys., 58, 1855 (1973)
Acknowledgments. Financial support from the FundaGiio de Amparo B Pesquisa do Estado de Siio Paulo (FAPESP) and the Financiadora de Estudos e Projetos (FINEP) is gratefully appreciated.
Soret Coefficient of 1 N Lithium Iodide Douglas R. Caldwell School of Oceanography,Oregon State University, CorvaNls, Oregon 9733 1 (Received January 6, 1975) Publication costs assisted by the National Science Foundation
The thermal diffusion (Soret) coefficient of aqueous 1 N LiI solutions, measured by the thermohaline instability method at atmospheric pressure, is found to be negative a t temperatures below 44O and appears likely to remain negative to the boiling point. A temperature gradient imposed on this solution creates large concentration gradients which are useful for studying convective effects in solutions. By observing the frequency of oscillation a t the onset of convection, as well as the temperature gradient, a second estimate of the Soret coefficient is obtained. Excellent agreement between the two estimates is found.
Introduction The thermal diffusion (Soret) coefficient, ST, of a solution can be positive or negative. In a given solution, it may even change sign with temperature or pressure.l Concentration gradients caused by Soret fluxes can cause convective motions which affect various processes and measurements. Recently much work, both experimental2-“ and theoretical,12-lghas been done on Soret-caused convection, but more interesting results could be obtained if solutions with larger induced density gradients were available, gradients which oppose those directly induced by the temperature field. Such mixtures as ~ a t e r - m e t h a n o l ,CC14-c~~ C,3H12,and H20-C2H50H7 have been used, but large density gradients in this sense cannot be obtained. An index of the separation is a “stability ratio”, y STC( 1 - c)p’/B, c being the mass fraction of solute, fi the thermal expansion, and p’ the solute expansion coefficient p - ’ ( a p / d c ) . Here p is the density of the solution. Large negative values of y are required so a large negative value of ST in a solution with high concentration and low thermal expansion is desired. In their investigation of a number of electrolytes in 0.01 M concentration, Snowden and Turnerz0 found the largest negative value for ST in LiI, -1.44 X deg-l, a t 25.3’. Except for earlier, less accurate measurements,21 this is the only determination of ST for LiI. Longsworth2* showed that for concentrated KC1 solutions, ST increased (became more positive) with molality and temperature. For dilute The Journal of Physical Chemistry, Vol. 79, No. 17, 1975
solutions of KCl, however, ST decreases with concentration, while still increasing with temperature. Apparently then, if the behaviour of KCI is typical of electrolytes, ST can be expected to become more positive as the temperature increases but in varying with concentration seems to have a minimum in the 0.1-1 A4 range. Putting the above considerations together, ST for 1N solutions of LiI might well be negative, a t least a t low temperatures, even for large concentrations. Measurement of ST could not proceed with the methods used in the studies mentioned above because of convective effects. Therefore the “thermohaline instability” methodz3was used, with an improvement in that two independent predictions of the theory were used to derive values of ST,thus giving an estimate of systematic errors. The reader is referred to that previous paper23for an explanation of the method, a drawing of the apparatus, and definitions of some terms. The only change in the apparatus was that a 0.15-cm diameter thermistor probe was positioned in the lower part of the fluid layer for observation of temperature oscillations. It projected into the layer from the side wall, the temperature-sensing bead being located about 3 cm from the wall and about 0.3 cm from the bottom boundary. Procedure As the critical Rayleigh number, R,, for onset of convection in a horizontal layer of the solution (now 1.12
