1908
Roy E. Bruns
The Journal of Physical Chemistry, Vol. 82, No. 17, 1978
The Signs of the Dipole Moment Derivatives of Br2C0 and Predicted Derivatives for Br2CS Roy E. Bruns Instituto de QGmica, Universidade Estadual de Campinas, C.P.1170, Campinas, SP, Brasii (Received February 21, 1978) Publication costs assisted by Universidade Estadual de Campinas
Preferred signs for the ap/aQi of Br2C0 have been determined using semiempirical CNDO theory. The corresponding experimental values of the ap/aS, for this molecule have been compared with previously reported preferred values for F2C0 and Cl2CO. The CNDO calculated values are analyzed in terms of the various contributive terms to the dipole moment derivatives and compared with the corresponding terms for F2C0 and Cl2CO. The preferred experimental set of ap/aS, for Br2C0 is used to predict values of the dipole moment derivatives and atomic polar tensors of BrzCS using known empirical equations.
Introduction The signs of the dipole moment derivatives with respect to the normal coordinates, the ap/aQ,, of several X2CY (X = F, C1; Y = 0, S ) molecules have been determined by approximate semiempirical CNDO the0ry.l Signs for H,CO have also been determined by CNDO calculations2 and by ab initio calculations employing Gaussian orbital basis sets.3 Comparisons of the CNDO results with the results of the more exact theory and with the limited experimental information available on the relative signs for H2C0 have helped establish credibility in the semiempirical values of the dipole moment derivatives for these molecules. Also the selection of the preferred experimental signs for F,CO, Cl2CO, F2CS, and C12CShas permitted a quantitative correlation of the individual fundamental infrared intensities of these molecules.ld Since CNDO results have proven to be very useful in the interpretation of the infrared intensities of the above-mentioned and other molecules containing first and second row atoms it is of interest to see if this technique can be extended to molecules containing heavier atoms. Approximate quantum mechanical results for the dipole moment derivatives of polyatomic molecules containing atoms in the third row of the periodic table (K Br) have only been reported for the CH3Br molecule.4 Although the CNDO calculated and experimental results are in reasonably good agreement there exists one inconsistency in sign for these theoretical results and those determined by the use of vibrational intensity data for isotopically related CH,Br molecules. However it is not clear if this inconsistency is due to the general approximations involved in CNDO theory or if it results from the extension of these approximations to molecules including third row atoms. As such further investigation of the accuracy of the CNDO procedure applied to the derivatives of these molecules is necessary. Here this is done by determining the preferred values of the dipole moment derivatives with respect to the symmetry coordinates, the ap/aSj, for Br2C0 based on CNDO calculations. These values are then compared with those values expected to be the correct ones based on the preferred experimental sets of values for FZCOlband Cl2C0.lC The preferred set of values for the derivatives of Br2C0 is then used to obtain predicted values for the dipole moment derivatives of Br2CS.
-
Calculations The CNDO parameterization scheme proposed by Hase and Schweig5 is used in the CNDO calculations. The experimental equilibrium geometry determined by Dornte6 0022-3654/78/2082-1908$01.00/0
TABLE I: Comparison of the Experimental and CNDO Calculated Dipole Moment Derivativesa A1
wz/as,
-- -& --t
-1.10
-tt --
t 1.44
(e a) -0.22 -0.02 -0.03 -0.18 -0.04
(e) t 0.15 t 0.35 -0.34 t 0.15 t 0.15
-1.42
CNDO -1.79 B,
apz/as,
apz/as2
(elC -1.08
apXlas, (e)
aPxlaS5 le A ,
--
+ 0.20
-0.11
t 1.01
t-t
-0.40 t0.49 t 0.44
-0.63 t0.85 -0.48 -0.51
t+
CNDO
t 0.25
t
+ 0.09
-
CNDO -0.21 a Units of electrons, e. 1 D A-l = 0.2082 e. The signs of the aplaQj. For example (- t -) indicates that apzlaQ, and apzlaQ,< 0 and apz/aQ,> 0. The symmetry coordinates distortions used to calculate these derivatives are: AS, = Arco, AS, = 2 - 1 1 2 ( ~( 3r) ~ ~ r ArCBr(4)), AaBr(,)CO),
= 6-1/2(2A(YBr(3)CBr(4)- A“Br(,)CO -
AS, = 2-’”(ArCBr(,) - ArCBr(4)),A S S =
2 - ” 2 ( A o r g r ( 3 )-~ A(YB~(,)co), ~ and A S , = A?, where y is
the angle between the equilibrium molecular plane and the bisector of the Br(3)CBr(4)angle.
(rco = 1.13 A, rCBr= 2.05 A, and @BfiBr = 110’) is assumed to calculate the equilibrium dipole moment. Bond and angle distortions of 0.02 A and 2 O were used for the internal coordinate distortions. The symmetry coordinate definitions in terms of the internal coordinates are given in a footnote of Table I. The Cartesian coordinate system and atom numbering scheme are shown in Figure 1. This figure also includes the values of the rotational corrections and their corresponding distortions for the B1 and B2 symmetry coordinates. These are the values necessary to correct the ap/aSj’s from the condition of zero angular momentum, i.e. (ap,/ as,)= C (ap,/aQi) (aQi/ aSj) i
to a set of conditions such that the symmetry coordinates can be described using the space-fixed Cartesian coordinate representations given in this figure. These distortions can 0 1978 American Chemical Society
The Journal of Physical Chemistry, Vol. 82, No. 17, 1978
Signs of the Dipole Moment Derivatives *Z
9
0
v& = - 0.91
v;,=-0.22
vo', =
- 0.80
Figure 1. Definitions of the symmetry coordinate distortions and their relationship to the space-fixed right-handed Cartesian coordinate system. The directions of the rotations and the magnitudes of the rotational corrections, voir,required to correct the experimental ap /asivalues in Table I to the states of zero angular momentum are also indicated.
TABLE 11: Preferred Experimental and CNDO Calculated Dipole Moment Derivatives of F,CO, Cl,CO, and Br,COa
A, apz/as, (e) F,CO -0.86 (-1.13) c1, co -0.98 (-1.46) BGCO -1.10 (-1.79) B, F,CO c1,co Br2C0
ci,co Br,CO
ap,laS, (e) +0.81 ( t 0 . 9 6 ) 10.50 ( t 0 . 3 1 ) +0.35 ( t 0 . 1 5 )
apxlaS, (e) t 1 . 0 9 (+1.06) t 1.08 ( t0.54) t 0.49 ( t0.44)
ap,laS, (e a) -0.38 (-0.40) -0.14 (-0.26) -0.02 (-0.04)
apxlaS5 (e a) -0.26 (-0.49) -0.31 (-0.52) -0.48 (-0.51)
+o.oi (-0.33j
t 0.09 (-0.21)
a Units of electrons. The preferred experimental values are followed by the CNDO calculated values given in parentheses.
be interpreted as being purely vibrational.
Results Hopper, Russell, and Overend' have measured the infrared fundamental intensities of Br,CO and have calculated its normal coordinates. The experimental alternative values of the ap/aSj as a function of the possible signs of the ap/aQi, presented in Table I, have been obtained using their value^.^^^ In the AI symmetry species the CNDO results show opposite relative signs for ap,/aS, and ap,/aSz. Since the (-+-) and (+--I sign choices contain identical experimental signs for these derivatives each of these sets can be eliminated from further consideration as being the correct one. The relative signs of the ap/aSj for the (---) and (--+) combinations are in agreement with the CNDO calculated signs for all three derivatives. The CNDO magnitude of ap,/aS, favors selection of the (---) set although its predicted magnitude for ap,/aS, points to the (-- +) combination. Clearly the theoretical values are not sufficiently accurate to allow a choice to be made between these two sets. In Table I1 the preferred experimental values of the dipole moment derivatives of FzCO and ClzCO are presented. If the changes in the electronic configurations for the Br2C0 distortions follow the trends indicated by the results for F2C0 and ClzCO the (--+) set of derivatives is to be preferred. Acceptance of the (---) set would lead to values of ap,/aS, which have an ordering of absolute magnitudes FzCO > BrzCO > C1,CO. This seems unlikely in view of the systematic behaviors found for the values of the derivatives of the XzCY (X = F, C1; Y = 0, S) molecules.lc,d In the B1 symmetry species the CNDO values are in excellent agreement with the (- +) set. Upon comparison with the preferred experimental values of the ap/aSj for FzCO and C1,CO this set seems more reasonable than the (--) set which also contains signs in agreement with those
1909
calculated by the theory. For example, the value of ap,/aS, in the (-+) set is about 112 the values of this derivative for F2C0 and C1,CO whereas the value for the (--) set is less than 115 of these values. It should be noted that the experimental magnitudes of both ap,/aS, and ap,/aS, are relatively invariant upon substitution of chlorine for fluorine in contrast to the differing values found for the derivatives of the AI species. An inspection of all the possible experimental magnitudes of the ap/aSj in the B1 species of Br,CO shows that, independent of the sign selection for the ap/aQ,, these derivatives have values which are quite different from those found for FzCO and
c12co.
The out-of-plane experimental values of ap,/aS6 are necessarily of positive sign although the CNDO result has a relatively large magnitude and is of negative sign. For the other XzCY molecules CNDO values of this derivative have been consistently calculated to be much too negative (see Table 11). However the theory does appear to be reflecting the correct trend in the experimental values. The value of +0.09 e rather than the experimental alternative of +0.25 e can be tentatively selected for ap,/aS6 in view of its closer proximities t o the CNDO calculated value for BrzCO and to the preferred experimental values for FzCO and Cl2CO. The negative sign of ap,/aSl and the positive ones for ap,/aS2 and ap,/aS, indicate dipole moment changes of the sense +C-Br- and +C-0- for the stretching of these bonds. This is in agreement with the sense of the stretching distortions for the other XzCY molecules.lw Indeed dipole moment changes for which the stretched terminal atom (s) becomes more negative have been found for almost all molecules that have been tested thus far by ab initio and semiempirical molecular orbital technique^.^ The preferred experimental and calculated signs of ap,/aS3 and apz/aSs,when interpreted using the bond moment model, indicate bond dipoles of the sense +C-Brfor these in-plane bending distortions. The experimental values of apJaS,, should ap,/aQ, be chosen to be positive or negative, indicate an opposite sense for the CBr bond dipole. Opposite senses for the CH and CC1 bond dipoles for the in-plane and out-of-plane distortions of H2C0 and Cl2C0 have also been found.1c,2 For formaldehyde this change in sign for the C-H bond dipole has been verified experimentally and by ab initio Gaussian orbital basis set calculations.
Discussion One of the aims of this report is to establish the degree of credibility of the CNDO method for molecules containing atoms of the third row. The application of this theory to molecules containing only first row atoms has been judged to be quite successful based on comparison with experimental and ab initio calculated r e ~ u l t s . ~ J ~ CNDO calculations for molecules with second row atoms, although somewhat less accurate than those for the first row atoms, have also been extremely useful in the interpretation of infrared vibrational intensities. The results for BrzCO presented here are encouraging as the predicted senses of the charge distortions for each of the symmetry coordinate displacements are the same as those found for ClZCO. Certainly one would intuitively expect that they might be identical. It is also of interest to see if the different contributions to the CNDO calculated derivatives of BrzCO are also consistent in sign and relative magnitude with those found for Cl2C0 and F2C0. Such consistency, which one might anticipate, would indicate that the method is functioning in the same way for all these molecules. As has been
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Roy E. Bruns
The Journal of Physical Chemistty, Vol. 82, No. 17, 1978
TABLE 111: Analysis of the Different Contributions t o the CNDO Calculated Dipole Moment Derivatives of Br,COa APq,IASi
-0.117 t 0.078
-0.133 t0.112 -0.160 -0.395
AP,,lASi
-1.293 t0.136 -0.042 +0.629 -0.432 0,000
AP,/
AS?
-0.069 -0.046 -0.204 -0.368 -0.220 -0.650
APpdIASi’
-0.314 -0.017 t0.341 t0.070 +0.301 +0.830
Units of electrons, e and e A . apV,laSiand Ap,d/ASi are the polarization contributions where a
A P p d A S i = AP,/ASi
t APpdIASi.
pointed out frequently, the dipole moment derivative contains contributions from (1) the movement of equilibrium net charge ap,,/aS,, ( 2 ) intramolecular charge transfer due to changes in the molecular geometry, ap ,/as,, and (3) changes in sp and pd polarizations, ap,,l/a81. In Table I11 the values of these contributions to the Br2C0 derivatives are presented. These values can be compared with those previously published for F2COlband C12C0.1c The CNDO calculated equilibrium dipole moment for Br2C0 (-0.409 D) is almost identical with the calculated value of 4 . 4 0 6 D for Cl2CO. (The estimated experimental value is f1.38 D). If the experimental signs of the dipole moment derivatives are all of the sense +X2C0-, as calculated by the theory one expects an ordering of values IpF2c0I < lpclzcol< lpBrzc~I.The above mentioned CNDO values along with the value of -0.95 D calculated for F2C0 indicate a basic failure of the theory. Although the largest contributions to the dipole moments of C12C0 and Br2C0 are from sp and pd polarizations part of the error in the calculated moments can be traced to the contribution due to the equilibrium charges. The equilibrium net CNDO charge on bromine, qB:, is calculated to be almost twice as negative as the one on chlorine (qB: = -0.096 e, qc? = -0.057 e). Based on electronegativity values and other chemical information, the charge on chlorine should be more negative than the one on bromine. Fortunately, as far as the dipole moment derivatives are concerned, ap,,/aS,! which depends only on the magnitude of the equilibrium net charges and the form of the symmetry coordinate distortion, is not the predominant contribution for any of the derivatives of Br2C0 or C12C0 (see Table I11 and Table VI1 of ref IC). For the stretching derivatives of these molecules the intramolecular charge transfer contribution is easily the most important, its value always being much larger than the sum of the other contributions. Furthermore the signs of the contributions from ap,,/aS, and apqz/aS,,for each value of j , are the same for these two molecules. As such these contributions always combine constructively producing relatively large absolute magnitudes of the theoretical derivatives due to effects (1)and ( 2 ) listed above. The polarization contributions, on the other hand, are small for the stretching derivatives. Only ap,,/aS4 of all these contributions is more than 50% of its corresponding value for ap,,/aS,. This value may be considered suspect as the corresponding polarization contribution for ClZCO is of opposite sign. Indeed all of the contributions in Table I11 have the same sign as their corresponding contributions for C12C0 except for ap,,/aS4 (and ap, /as2,which is calculated to be close to zero for both C1260 and Br2CO). For the bending distortions the polarization contributions are found to be relatively large. For S3 and s6,the symmetric in-plane and the out-of-plane coordinates, ap,,/aS, and apd/aS,, have absolute magnitudes which are much higher than the corresponding ones for ap,,/aS, or
,TABLE IV: Predicted Values €or the Dipole Moment Derivatives of Br,CS (e and e A ) -0.89 t 0 . 6 2 -0.03 t 0 . 3 8 -0.31 t o . 1 9 -0.88 t 0 . 5 5 -0.02 t 0 . 4 0 -0.34 1-0.20 a Evaluated using eq 1 with the di ole moment derivaEvaluated using eq 1 tives of Br,CO, Cl,CO, and C1,CS. with the dipole moment derivatives of Br,CO, F,CS, and F,CO. ap/asja ap/asib
ap,,/aSj. For the asymmetric in-plane CBr bend all contributions are important with ap,,/aS5 having the largest absolute magnitude. These situations are identical with the ones found in C12C0 for the corresponding derivatives. For both molecules ap,,/aSj is always negative whereas the corresponding value of apPd/aSjis positive. This “polarization-back polarization” effect in CNDO calculated equilibrium dipole r n ~ m e n t s ~and ~~’ derivativeslc,d has been noted previously. For ap/aS3the sum of the polarization contributions is positive and slightly smaller than the sum of apql/aS3and ap,,/aS,. This results in the negative sign and small calculated magnitude (-0.04 e) for ap,/aS3 Such a delicate balance between the charge and polarization contributions does not lead to much confidence in the calculated sign of ap,/aS3. However all the experimental alternatives for this derivative in Table I have negative signs. The selection of a positive sign for ap/aS3 would necessitate changing the signs of the preferred values for the Al stretching derivatives. This possibility has already been eliminated. For ap,/aS5 the sum of the polarization contributions is small and positive. The contribution from the charge transfer term determines the negative sign of this derivative. As stated earlier the sign of ap,/aS6 is experimentally determined to be positive. The erroneous negative sign calculated by the theory is seen to arise from values which are a cancellation of ap,,/aS6 and apPd/aS6 large and of opposite signs. The sum of the polarization contributions is +0.180 e which is easily outweighed by the contribution of -0.398 e from ap,,/aS6. This latter value is known to be much too large as it arises from the unrealistically large net negative charge assigned by the CNDO theory to the bromine atom. A zero value of apq2/aS6 for Br2C0 is consistent with the results found previously for the other X2CY molecules.
Applications to BrzCS Recently two articles have appeared in which the infrared vibrational intensities of molecules have been predicted based on intensity data for related molecule^.^^^^^ Here predicted values of the dipole moment derivatives of Br2CS calculated using the derivatives of other XzCY molecules (X = F, C1, Br; Y = 0, S) are presented. Use is made of the reported empirical equationld involving rotationally corrected dipole moment derivatives (ap/aSj)cizcs- (ap/aSj)FPCS = (aP/asj)c12co (ap/ aSj)F,co (1) where j = 1, 2, ..., 6. If this equation can be extended to the bromine containing molecules of this family the data reported here for BrzCO can be combined with the results for ClzCSldand Cl2COlcor F2CSldand FZCOlbto obtain accurate estimates of the dipole moment derivatives of Br2CS. In Table IV the estimates for the derivatives of Br2CS are presented. The first row contains values estimated using the derivatives of the chlorine containing molecules, the second those obtained from the data of BrzCO, F,CO, and F2CS. The estimated derivatives based on the fluoro compounds are in close agreement with those obtained from the chlorine containing molecules as should
Signs of the Dipole Moment Derivatives
The Journal of Physical Chemistry, Vol. 82,No. 17, 1978
be expected. The stretching derivatives for the CS and CBr bonds have the largest absolute magnitudes. This is consistent with the two strong infrared absorption bands reported14 in the matrix isolated spectra of Br2CS, these bands having frequencies which can be assigned to CS and CBr stretching vibrations. It should be added that the signs of the Br2CS derivatives are consistent with those for Br2C0 as one would intuitively expect. It is of interest to examine the data in Table IV transformed into polar tensor values15as infrared intensity predictions are currently being made based on the transferability of atomic polar tensors from one molecule to another.l2$l3In Table V the polar tensor values for Br2CS predicted using
TABLE V: Predicted Values of t h e Polar Tensor Elements for Br,CS (e)"
cP a
p =0
(3)
Le., the sum of the atomic polar tensors for a molecule must give the null matrix. The Br2CS polar tensor predicted using the C12C0 and C12CS values lead to a maximum absolute value of 0.02 e for the expected null matrix elements whereas a value of 0.14 e is encountered using the data on the fluoro compounds. It should be noted here that the predicted polar tensor elements in the first two columns of Table V can be transformed into ap/aS, values. This allows a comparison of predicted ap/aSj values derived from eq 1 and 2. The discrepancies between corresponding ap/aS, values are less than 0.1 e except for ap/aS, for which a maximum difference of 0.15 e is encountered. This is not surprising as eq 1 for X = F, C1 and Y = 0, S is valid within the propagated experimental errors for all the derivatives except for ap/aSs.16For this derivative eq 1 would also be valid if the propagated experimental error of 0.09 was increased to 0.17 e. In any case the values of the ap/aS;s calculated from the polar tensors and those given in Table IV have the same signs and similar magnitudes. As such predicted intensities for Br2CS using eq 1 or 2 will lead to essentially the same results. The final column of Table V contains values for the bromine and sulfur atomic polar tensors of Br2C0 and C12CS. These are the ones most likely to be chosen in attempts to predict infrared intensities using transferred values of polar tensor elements. The elements for the carbon atom were calculated using eq 3. The largest deviation between the Br2CS polar tensor elements obtained by transferring atomic polar tensors and those calculated by means of eq 2 is 0.34 e ( p z zfor the C atom). Because all of the signs for the polar tensor elements
X = Fb
X = Clc
-0.28 i-0.11
-0.25 t 0.10 -0.26 -0.08 -0.35
transferredd
px(BS 1 ) ) Pxx PY y' Pzz Pxz Pzx
-0.21 -0.07 -0.29
-0.37
+ 0.04 -0.15 -0.06 -0.19
PX(S)
Px(a4)(Br2CS)= PX(*2)(Br2CO)+ PX("3)(X2CS)P,("1)(X,CO) (2) are given. This equation, applied to Br&O and Br2CS with X = F or C1, is a generalization of a previously reported empirical equation16 valid for the fluorine and chlorine containing molecules. The symbols, a;,refer to the appropriate halogen, group 6, or carbon atoms. As can be seen, the polar tensor values calculated on the basis of the fluorine or chlorine containing molecules are in very good agreement, the largest difference occurring for prxof the carbon atomic polar tensor (0.17 e). The predicted infrared spectrum of Br,CS using either set of values would be in very close agreement considering possible experimental errors. However one might choose the best set of values based on the criterion
1911
Pxx PYY PZZ
+0.10
-0.45
PX(C) Pxx PYY Pzz
+ 1.04 -0.31 + 1.31
-0.87
-0.36 +0.07 -0.89
t0.04
t 0.87 -0.25
+ 0.86 -0.12 + 1.07
+ 1.41
-0.12 -0.77
U n i t s of electrons, e. Values calculated using e q 2 and t h e p o l a r tensor values of F,CO, F,CS, a n d Br,CO. Values calculated using e q 2 a n d t h e polar tensor values of Cl,CO, Cl,CS, a n d Br,CO. Transferred values of t h e p o l a r tensors. T h e values for P ( B r l ) were transferred from Br C O a n d those for Px(srfrom C1,CS. T h e values for P x ( ~ were obtained by means of e q 3. a
predicted in Table V are in agreement and their magnitudes are reasonably consistent, quantitative estimates of the infrared fundamental intensities of the unstable Br2CS molecule can be made if reasonable estimates of the normal coordinates of this molecule can be obtained.
Acknowledgment. The author is very grateful to Dr. Ulf Schuchardt for pointing out ref 14 and to Mr. Francisco B. T. Pessine for loaning his copy of the CNDO program (QCPE No. 261). Acknowledgment is also due to FINEP (Financiadora de Estudos e Projetos) for partial financial support. References and Notes (a) G. A. Segal, R. E. Bruns, and W. B. Person, J . Chem. Phys., 50, 381 1 (1969); (b) D. C. McKean, R. E. Bruns, W. B. Person, and G. A. Segal, ibid., 55, 2890 (1971); (c) R. K. Nair and R. E. Bruns, bid., 58, 1849 (1973); (d) R. E. Bruns, ibid., 58, 1855 (1973). R. E. Bruns and W. B. Person, J. Chem. Phys., 58, 2585 (1973). G. Jalsovsky and P. Pulay, J. Mol. Sfrucf., 26, 277 (1975). A. J. van Straten and W. M. A. Smit, J. Chem. Phys., 67, 970 (1977). H. L. Hase and A. Schweig, Theor. Chim. Acta, 31, 215 (1973). R. W. Dornte, J . Am. Chem. SOC.,55, 4126 (1933). M. J. Hopper, J. W. Russell, and J. Overend, J . Chem. Phys., 48, 3765 (1968). P. L. Prasad and S. Singh, Chem. Phys. Left., 24, 543 (1974). CNDO calculations for the CH stretching coordinates of HCN (R. E. Brhs and W. B. Person, J. Chem. Phys.,53, 1413 (1970)) and CzHz (ref 3) and the carbon-halogen stretches of CH,CI (J. H. Newton and W. B. Person, J . Chem. Phys., 64, 3036 (1976)) and CH3Br (A. J. van Straten and W. M. A. Smit, ibid.. 67, 970 (1977)) predict senses of the dipole moment change which indicatethat the sbetched terminal atom becomes more positive. For the methyl halides, experimental results and CNDO calculated derivatives for the other displacement coordinates indicate that the CNDO sign for these stretching coordinates is incorrect. For HCN and CzHzab initio and CNDO results give identical signs for the dipole moment changes. W. B. Person and D. Steele in "Molecular Spectroscopy", R. F. Barrow, D. A. Long, and D. J. Millen, Ed., The Chemical Society, London, 1974, p 357. D. P. Santry and G. A. Segal, J . Chem. Phys., 47, 158 (1967). W. B. Person and J. Overend, J . Chem. Phys., 66, 1443 (1977). B. J. Krohn, W. B. Person, and J. Overend, J . Chem. Phys., 65, 969 (1976). R. Steudel, Angew Chem., Int. Edit. Engl., 6, 635 (1967). W. B. Person and J. H. Newton, J . Chem. Phys., 61, 1040 (1974); J. F. Biarge, J. Herranz, and J. Morcillo, An. R. Soc. ESP. Fls. a i m . , Ser. A , 57, 81 (1961). A. B. M. S.Bassi and R. E. Bruns, J. Chem. Phys., 62, 3235 (1975); J . Phys. Chem., 79, 1880 (1975).
