Dipole moment derivatives for trihalogenomethanes, CHX3 (XF Cl, Br)

Spectrochimica Acta,Vol 33A, pp.499to 505.Pergamon

Dipole

moment

derivatives

Press

1977. Printed

in Northern

Ireland

for trihalogenomethanes, R. AROCA and E. A.

CHX, (X = F, Cl, Br)

ROBINSON

Erindale College, University of Toronto, Mississauga, Ontario LSL lC6 Canada. and T. A. Department

FORD

of Chemistry, University of Witwatersrand, Johannesburg

2001 (South Africa).

(Receioed 1 June, 1976) Abstract-Dipole moment derivatives of the molecules CHX, (X = F, Cl, Br) have been obtained using the polar tensor approach and the procedure of Mayants and Averbukh. It is shown that these two methods are closely related. Effective atomic charges are used to eliminate several sign combinations for the experimentally determined dipole moment derivatives.

INTRODUmON The calculation of dipole moment derivatives, (ap/aQ,), where p is the molecular dipole moment and Q, is a normal coordinate, from the experimentally determined i.r. band intensities of polyatomic molecules is a standard procedure [I]. Neglecting electrical and mechanical anharmonicity, the relation between the i.r. band intensity, A,, and the dipole moment derivative, (dp/aQi), may be written [l]

where v, is the observed absorption frequency, wi is the harmonic frequency, N is Avogadro’s number and c is the velocity of light. Due to the presence of the squared term in this equation, a sign ambiguity is introduced in the calculation. Normal coordinates are related to vibrational (or Cartesian) coordinates by means of the normal coordinate transformation matrix, L, with a subscript for the appropriate coordinate system. Thus, for internal coordinates, R, the relationship is given by R=LRQ The L matrix is obtained from vibrational matrix equation

(2) the corresponding

GRFRLR = LR A

(3)

Knowledge of the force constant matrix, F, and of the inverse kinetic energy matrix, G, of the molecule is therefore required for the analysis.

In view of the fact that molecular translation does not change the dipole moment, its expansion up to the first partial derivative may be written [l]

+3E3 (z)oQi

p = ,.,,,

i=l

where CL,,is the equilibrium molecular dipole moment and N is the number of atoms in the molecule. Consequently, either the L matrix is complete (of order 3N- 3), or the problem is separated into two parts, a vibrational part and a “rotational correction.” A number of methods have been proposed for calculating dipole moment derivatives with respect to vibrational (or Cartesian) coordinates: (i) methods based on the “valence optical” scheme [2]; (ii) the polar tensor approach developed by MORCILLO et al [3] (this method has recently been revived by PERSON et al. [4,5]), and the scheme proposed by Mayants and Averbukh [6] (the fundamental principles of these two methods are quite similar and they may be discussed together); (iii) the effective atomic charge model of KING et al. [7,8], and of DECIUS [9]; (iv) the formulism recently developed by SA&KI et al. [lo] for calculating the derivatives of molecular dipole moment with respect to bond length or bond angle. It may be shown that the polar tensor approach [4,5] and the Mayants-Averbukh scheme [6], together with the effective charge model [7,8], present a number of advantages when analysing i.r. 499

R. AROCA. E. A. ROBINSONand T. A. FORD

500

intensities. We shall summarize some of the relationships and common features of the two approaches. The main difference between the two methods is that, while in the polar tensor approach the vibrational and rotational tensors, PR and P,,, are calculated separately and the total atomic polar tensor P, then obtained using the relation [4],

The “own” set of Cartesian coordinates X,” is related to the main axes Cartesian coordinate set X, (a column vector of dimension 3N - 3) by an orthogonal matrix A, i.e., X, = AX,’

(8)

P, = P,B + PJ3

D = ADoA+

(9)

and correspondingly

(5)

in the Mayants-Averbukh method a complete L matrix is obtained, introducing an appropriate system of coordinates that allows the calculation of a tensor DF related to Pxi by a simple orthogonal matrix. In the Mayants-Averbukh procedure the changes of the (N- 1) independent bond vectors R’ are used to introduce a tensor Di = (ap/dR’). Therefore a matrix termed Do, of order 3N - 3, may be obtained, whose elements are the derivatives of the dipole moment with respect to the projections X,” of the vectors R’ on the axes of the coordinate system, i.e., the vector’s “own” coordinate system (see Fig. 1). The complete set of these coordinates is Xso, having dimension 3N - 3. The advantages of this Do matrix have been pointed out [ 111, the chief advantage being the very simple structure of the blocks Die for each bond vector R’. Symmetry coordinates X,” could also be introduced, that would allow the treatment of the problem separately for each symmetry species, and for which the number of parameters is equal to the number of the equations. These two coordinate sets are connected by the equation

The dipole moment derivatives in matrix notation, by [ll]

where matrix

where

Ct is the transpose

PO = llp’i. . . fp3N-3j), pi

(7)

of C.

the

column

E, = IIWS &II, E3 is the three-dimensional unit matrix and Ls is the normal coordinate transformation matrix of dimension 3N- 3 (including the three rotations) in the X6 coordinate system. Summarizing, it could be said that the D matrix in the Mayants-Averbukh approach is the same as the atomic polar tensor of the Morcillo method without the atomic polar tensor for the “first atom” of the bond vector coordinates. This may be easily calculated since the sum of these tensors must be zero, i.e., $, Do matrix

PC=0

in the

Mayants-Averbukh

(11) ap-

orthogonal matrix A of Equation 8. It should be noted that in some cases a treatment of the problem in symmetry coordinates, such as in the Mayants-Averbukh formulation, is desirable. It allows a reduction in the number of parameters and the investigation of the symmetry blocks separately (see, e.g., ALEKSANYAN et al. [ 121).

RESULTS

Fig. 1. Reference coordinates for the CHX, where x, y, and z refer to the main axes system, and x’, y’ and z’ refer to the “own” system, with the I’ axis along the C-X bond axis in the HCX plane.

is

(10)

(6) proach is related to the polar tensor D through the

and consequently Do = CDSC+

are given,

PO = E,ACDSC+A+L8

The x,” = cxas

(ap/aQ,)

molecules, coordinate coordinate and the x’

AND

DISCUSSION

The normal coordinate transformation matrices L used in the calculations for the CHX, molecules have been reported previously [13]. The dipole moments for these molecules were taken from the compilation of WEAST [14]. The reference coordinates used in the calculations are shown in Fig. 1. studies of the A number of i.r. intensity trihalogenomethanes have been published. For chloroform and deuterochloroform three different

Dipole moment derivatives for trihalogenomethanes,

501

CHX, (X = F, Cl, Br)

Table 1. Dipole moment derivatives (+/aQiI” of the trihalogenomethanes Symmetry species

iq~m-

pcJaQlb

CDCI,

CHCIx

CDF3 L~CII-’

(acL/aQr

lap/aQY

larJaQ/=

ikm-’

CHBr,

IalJaQi’

IadaQI”

IacJaQI’

IacJaQl

i&x-’

‘4,

2261

0.768

3033

0.090

0.087

0.326

2265

0.051

0.038

0.207

3050

0.549

AI

1111 695

1.422 0.541

676 367

0.346 0.083

0.323 0.109

0.335 0.048

658 364

0.332 0.102

0.351 0.084

0.435 0.112

543 223

0.162 0.024

1213

2.508

1220

0.751

0.610

0.600

915

0.907

I.017

1.053

1149

0.692

975 502

0.719 0.244

774 260

1.784 0.039

1.635 0.024

1.682 1.104

747 259

1.576 0.043

1.363 0.024

1.397 0.124

669 155

1.244 0.015

A, E E E

’ units of lap/aQI are Dk’

(an~~*‘~

b Ref. [lo]


d Ref. [16]

[IS]

’ Ref. [17]

sets of experimental intensities are available [15171, from which three sets of dipole moment derivatives, aF/aQi, may be obtained. These quantities are reproduced in Table 1, having been first converted to units of DA-’ (amu)-“z.* A dipole moment derivative calculation has been carried out for each set of experimental intensities in order to determine the sensitivity of the calculated polar tensor elements to the observed intensities. For fluoroform and deuterofluoroform the intensity results are incomplete due to the inability to measure the intensities of the v2 and v5 bands of fluoroform separately [lo]. However, separate values for the intensities of all six fundamentals of deuterofluoroform were reported [lo], and our dipole moment derivatives were calculated using the data for this molecule only. Similarly, the intensities of the vg and v6 bands od deuterobromoform were not available [17], so all six dipole moment derivatives could be determined for bromoform only, using the intensities of Ratajczak et al. [17]. The results for deuterofluoroform and bromoform are included in Table 1. In the absence of full intensity data for both CHF, and CDF3, and for CHBr, and CDBr,, we have assumed that the best sign combinations for chloroform were also the best for fluoroform and bromoform.

The most important criterion is that the atomic polar tensor P,” does not change on isotopic substitution, since it is related to the electronic structure of the molecule only. The criterion that the diagonal elements of the polar tensor P,” must be negative and those of Pxc positive has also been adopted. At this point we would like to discuss the concept of “effective atomic charges” introduced by KING, MAST and BLANCHETTE [7,8] as an additional criterion in determining the appropriate sign combination. PERSON and NEWTON [4] have shown that this effective atomic charge 50 may be expressed in terms of the polar tensor [PIX“ as follows:

Chloroform

which allows one to use the magnitude of the vector dipole gradients lap/ar,l= 5, as further criteria to eliminate some of the sign combinations, since there exist in general 23N-3 different combinations of 5, which fulfil the intensity sum rule (one for each sign set of the ap/aQi values). Most of the effective charge sets (and correspondingly the sets of signs for the experimental dipole moment derivatives) may be eliminated using the relation

and deuterochloroform

Assuming positive values for the dipole moments of these molecules, there exist two possibilities for the sign of each derivative aj.@Q,, i.e., 26= 64 different sign combinations, and an equal number of different polar tensors. Morcillo et al. [15] have pointed out a number of physical criteria that allow most of these sign combinations to be neglected. *The units of CL and Q, are, res ectively, D (i.e., lo-” g”’ cm “*s-‘) and ,& (wIu)~’ (i.e., 1.2888~ 10e2” cm g”‘)‘.

&’ = Tr[P,“(P:)+]

= (a~/ax,)‘+(a~/ayJ2 + (ap/az,)’ (12)

Therefore & may be calculated together with the polar tensor. Since the trace of a matrix is invariant under a similarity transformation, it is evident that these quantities may be calculated equally from P,, D or Do. Furthermore, the intensity sum rule is just [ll] 3N-3 ,z,

(WaQY=

C (l/~J(5pY LI

CL=0

(13)

(14)

502

R. AROCA, E. A. Table

“1

v2

+

_.

+ + _ + + + _ + + _ + + _ +

+ + + + + + _ _ _ _ _ _ _

-. _. _. _. _. _. +; +; _. -; +; +; _. -; +; +; _. _.

FORD

2. Effective atomic charges” for chloroform for different sign combinations

Sign combination v3 v4

+

ROBINSON and T. A.

+

_ + + + + + + + + + + + + + +

vs

V6

+

+

+ _ + _ + _ _ _ _ _ -

+ + _ + _ _* _* _* _* _ _ _ _ _

5H 0.32 0.12 0.11 0.65 0.32 0.11 0.32 0.11 0.11 0.11 0.11 0.08 0.07 0.07 0.08 0.10 0.08 0.08 0.11

5CI 0.87 0.79 0.79 0.77 0.84 0.82 0.81 0.75 0.75 0.73 0.73 0.70 0.70 0.67 0.67 0.67 0.68 0.66 0.66

5C

A

1.42 1.78 1.79 0.62 1.42 1.77 1.44 1.81 1.81 1.82 1.81 1.63 1.64 1.64 1.64 1.69 1.70 1.71 1.69

1.51 0.71 0.69 2.34 1.42 0.80 1.31 0.55 0.55 0.48 0.49 0.55 0.53 0.44 0.45 0.42 0.42 0.35 0.40

Reference 15

15 15 15 15 15 15 15 15 15 15 16 16 16 16 17 17 17 17

a in units of electron charge * selected sign combinations; see text. in which .& has been given the sign of the atom charge (determined, for example, from calculations of atomic populations or by any chemical method). For instance for the CHX, molecules a positive charge on the carbon atom and negative charges on the hydrogen and halogen atoms are expected. Therefore & = & + 35,. These simple relations permit us to neglect several sign combinations in a very straightforward manner, as illustrated in Table 2. In this table A is the absolute value of the difference & - (5” + 35,). Table 2 also permits the comparison, in a very compact form, of the results calculated for the same molecule using different sets of experimental intensities. The differences in the results would give an indication of the experimental errors involved. In this way the last four results, those obtained from the intensities of RATAJCZAK et al. [17], which are considered to give the best solutions according to the criteria outlined above, may be compared with those obtained using the same sign combinations, but different experimental data. From sixty four different sets of signs for acL/aQi, only those for which the signs for the E species are (+ - -) give a low A value (eight sets). From these eight sets, only four yield an atomic polar tensor P,” with positive diagonal elements. (These sets are shown with asterisks in Table 2). Of these four remaining sets we selected the sign choice which produced the lowest A value, i.e. (- - -, + - -). The results obtained with this sign combination are listed in Table 3. The atomic polar tensors and effective atomic

charges calculated for deuterofluoroform and bromoform using the same sign combination are presented in Table 4. It should be noted that the atomic polar tensors P,” and P,” (X = F, Cl, Br) shown in Tables 3 and 4 are open to a different interpretation. These atomic polar tensors have been computed in a frame of reference in which the C-H or the C-X bond is the z axis and the x axis is in the HCX plane directed inside the angle HCX, i.e., they represent the derivatives of the dipole moment with respect to the projection of the bond vectors on the axes of their “own” coordinate system. Hence the and P,” polar tensors are the threeP,” dimensional blocks of the Do matrix in the Mayants-Averbukh formulation [6]. Since the transformation is a similarity transformation, the effective charges are the same. The effective charges so obtained may be described as “bond properties” rather than as “atomic properties,” as was pointed out by KING, MAST and BLANCHETTE [7,81. Effective charges $ evaluated from the experimentally measured intensity values are obtained independently of the normal coordinate transformation, i.e.. independently of the force field of the molecule. The effective charge &, has the important property that it is independent of the masses of the atoms as can be seen from Equation 13. It is, however, a function of the elements of the atomic polar tensor P,” as it is shown by Equation 12. Hence a different value of .&, can be obtained for

Dipole moment derivatives for trihalogenomethanes, Table 3. Atomic polar tenso& Molecule CHCI,

CDCls

CHCI,

CDCI,

CHCI,

CDC&

and effective atomic chargesb of CHCl, and CDC& for the (- - -; combination of ]+/aQ]

0 -0.36 0 0 0.16 0 0 -0.25 0 0 -0.13 0 0 -0.23 0 0 -0.13 0

0 0

0.01 0 0 0.11 0 0 0.01 0 0 0.13 0 0 -0.23 0 0 -0.04

-0.31 0 -0.31 -0.26 0 -0.09 -0.33 0 -0.28 -0.29 0 -0.24 -0.22 0 -0.21 -0.31 0 -0.12

0

-0.49 0 0 -0.51 0 0 -0.41 0 0 -0.41 0 0 -0.70 0 0 -0.77 0

+ - -) sign

Ref-

P xc’

RxH(RxD) -0.36 0 0 0.16 0 0 -0.25 0 0 -0.13 0 0 -0.23 0 0 -0.13 0 0

503

CHX, (X = F, Cl, Br)

PxC

-0.47 0 -3.41 -0.55 0 -3.55 -0.50 0 -3.15 -0.36 0 -3.22 -0.29 0 -3.08 -0.16 0 -3.08

6.12 0 0 5.74 0 0 5.53 0 0 5.42 0 0 5.73 0 0 5.65 0 0

6.:2 0 0 5.74 0 0 5.53 0 0 5.42 0 0 5.73 0 0 5.65 0

Mb)

0 0 1.11 0 0 1.02 0 0 1.09 0 0 1.01 0 0 1.25 0 0 1.49

-5-1

5~

erence

0.11

0.73

1.82

15

0.05

0.76

1.70

15

0.07

0.67

1.64

16

0.05

0.68

1.61

16

0.08

0.66

1.71

17

0.04

0.67

1.69

17

a in units of Dk’ b in units of electron charge each atomic polar tensor calculated from a given sign set of the PO elements in Equation 5 (where PR = P&L,-‘) as well as from an approximated normal coordinate transformation. Therefore when effective charges, evaluated from the experimentally measured intensity values for isotopic molecules, are available, they can be used to compare the reliability of the results derived for different force fields, and to eliminate certain sign combinations. For example, using the procedure given by KING et al. [7,8] and the intensities of both chloroform and deuterochloroform, the 5” values of chloroform were found to be 0.14 (Ref. [17]), 0.16 (Ref. [16]) and 0.28 electron charges (Ref. [15]). The lack of agreement among the results obtained using different sets of experimental intensities for chloroform and deuterochloroform stresses the fact that uncertainty in the experimental

values of infrared band intensities is perhaps the main obstacle to obtaining consistent results for the dipole moment derivatives of similar structural groups in series of related molecules. The effective charges for all the molecules studied are summarized in Table 5 (for the sake of comparison our unpublished results on CH,X, molecules have been included in Table 5). An increase in the effective charge on the C-X bond is observed from bromine to chlorine to fluorine, reflecting the increase in halogen electronegativity in the same order. We believe that the differences observed in the magnitudes of & are mainly due to experimental errors. From the values of A shown in Table 5, it may be concluded that the dipole moment derivatives of deuterofluoroform are highly inaccurate in comparison with those of chloroform and bromoform. Considering that the reliability of

Table 4. Atomic polar tensorsa and effective atomic chargesb of CDF, and CHBr, for the (- - - ; + - -) sign combination of (+/dQI Molecule

CDF3 CHBr,

PxF(PxB’)

PxD(PxH) 0.04 0 0 -0.38 0 0

0 0.04 0 0 -0.38 0

a in units of DA-’ b in units of electron charge

0 0 -0.09 0 0 -0.48

-1.28 0 -0.37 -0.20 0 -0.36

0 -0.03 0 0 -0.22 0

pxc 0.03 0 -5.45 -0.45 0 -2.58

7.60 0 0 4.59 0 0

0 7.60 0 0 4.59 0

tD(&,)

0 0 5.08 0 0 1.04

&(&d

&

Reference

0.02

1.17

2.48

10

0.15

0.55

1.37

17

R. AROCA, E. A. ROBINSONand T. A. FORD

504

Table 5. Effective atomic charges” for some di- and trihalogenomethanes

(X=&1,

Molecule

&

CH2Fzb CH& CH,Br, CDF,” CHC& CHBr,

0.15 0.07 0.12 0.02 0.08 0.15

Br)

1.18 0.63 0.48 1.17 0.66 0.55

&

A

1.84 1.21 0.93 2.48 1.71 1.37

0.82 0.19 0.27 1.05 0.35 0.43

associated mainly with the intensity of the C-H (or C-D) bond stretching vibration of these molecules. In Table 7 the Mayants-Averbukh d parameters are presented. These parameters are built up from the elements of the D,” matrix blocks, namely

and

a in units of electron charge. bSign set (---+; -+; +-) ‘Signset (---; +--) the force field of fluoroform has been confirmed by the calculation of a number of molecular vibrational constants therefrom, [13] the source of inaccuracy must be considered to lie mainly in the experimental band intensity values. Using the polar tensors of chloroform, bromoform and deuterofluoroform listed in Table 3 and the Mayants-Averbukh method, [6] the dipole nfoment derivatives of the isotopic variants fluoroform, deuterochloroform and deuterobromoform were caldulated and are reported in Table 6. For deuterochloroform the best agreement was obtained with the experimental data reported

As was shown above, the numerical values DF elements are those given in Table 3. CONCLUSION

The calculation of the polar tensors of a molecule may be carried out using either the original proposed by MORCILLO et al. [3] or the approach developed

by MAYANTS

and AVERBUKH [6].

The

second method allows the treatment of the different symmetry species independently, and a reduction in the number of parameters within each symmetry

by TANABE and SA~~KI[16]. It should also be noted that the uncertainty in the experimental

of the

data is

Table 6. Observed and calculated dipole moment derivatives“ of some trihalogenomethanes Symmetry species F/cm-’ A, 3034 Al 1141 ‘4, 700 E 1371 E 1152

E

508

D in units of DA-’

CHFS lalL/aQI @rs/aQ) obsb 0.766 0.559

talc -0.555 -1.527 -0.519

1.017 0.275

0.916 -2.443 -0.246

CDCll lad/aQI @/L/aQ) IatiaQI (+IaQ) 2265 658 364

ohs’ 0.051 0.332 0.102

talc -0.131 -0.332 -0.087

obsd 0.038 0.351 0.084

talc -0.127 -0.308 -0.112

ohs’ 0.207 0.435 0.112

talc -0.299 -0.321 -0.052

915 747 259

0.907 1.576 0.043

1.267 -1.442 -0.039

1.017 1.363 0.024

1.107 -1.338 -0.024

1.053 1.397 0.124

1.222 -1.380 -0.104

ihI-’

(am~)-~‘*, b Ref. [lo], = Ref. [15], ’ Ref. [16],

Table 7. Mayants-Averbukh Symmetry species

d parameter

Al

Cbd,Y-d~X

Al Al

CdsX - dix

E E E E

dy@’ 0.04 CdbX + d,X CdyX + dcX d2”

@‘o’

n in units of DA-’ b C = lsin p(cos pi where 6 LHCX

CDBr,

IacJaQl (acL/aQ)

l

MCIV

2256 517 222 848 634 155

IWQI

(afi/aQ)

ohs’ 0.327 0.242 0.972 1.062 -

talc -0.434 -0.153 -0.024 0.943 -1.033 -0.015

Ref. [17].

d parameters”

for some trihalogenomethanes

CDF, (Ref. [lo])

(Ref. [15])

CHCI, (Ref. [16])

(Ref. [17])

CHBr, (Ref. [17])

-3.12 5.53 -0.09 0.04 -2.29 14.84 -0.03

-0.67 1.93 0.01 -0.36 -1.29 -11.22 -0.49

-0.76 1.57 0.01 -0.25 -1.21 -10.43 -0.41

-0.48 2.17 -0.23 -0.23 -0.88 -10.00 -0.70

-0.25 1.20 -0.48 -0.38 -1.30 -8.33 -0.22

Dipole moment derivatives for trihalogenomethanes,

The concept of the effective atomic charge [7-Y] appears to be a very useful tool in selecting the best sign combination for the experimental dipole moment derivatives. species.

REFERENCES

[l] J. OVEREND,in Infrared Spectroscopy and Molecular Structure, (ed. M. Davies.) Elsevier Scientific Publishing Company (Amsterdam), 1963, pp. 345-376. [2] L. A. GRIBOV,Intensity Theory of Infrared Spectra of Polyatomic Molecules. Consultants Bureau (New York), 1964. [3] J. F. BIARGE, J. HERRANZand J. MORCILLO,Anales Real Sot. Espafi. Fix Quim. A57, 81 (1961). [4]. W. B. PERSONand J. H. NEWTON,J. Chem. Phys., 61, 1040 (1974). [5] W. B. PERSONand D. STEELE,in Chemical Society (London) Specialist Periodical Reports. Mol. Spectrosc. 2 (1074), pp. 357-483. [h] L. S. MAYANTSand B. S. AVERBUKH,J. Mol. Spectrosc., 22, lY7 (1067).

CHX, (X = F, Cl, Br)

505

171W. T. KING, G. B. MAST and P. P. BLANCHES, J. Chem. Phys., 56,444O (1972). @I W. T. KING, G. B. MAST and P. P. BLANCHETTE,J. Chem. Phvs.. 58. 1272 (1973). J.‘Mol. Siectrosc., 57, 348 (1975). PI J. C. DE&, [lOI S. SAQKI, M. MIZUNO and S. KONDO, Spectrochim. Acta, 32A, 403 (1976). [ill L. S. MAYANT~and B. S. AVERBUKH, Theory and Calculations of Intensities in Vibrational Spectra of Molecules. Nauka Publishing House (Moscow), 1971. [121S. K. SAMVELYAN,V. T. ALEKSANYANand B. V. LOKSHIN,J. Mol. Spectrosc. 48, 47 (1973). [I31 R. AROCA, E,. A. ROBINSONand T. A. FORD, J. Mol. Structure, 31, 177 (1976). [I41 R. C. WEAST (ed.). Handbook of Chemistry and Phvsics, 52nd edition. Chemical Rubber Companv (Cleveland, Ohio), 1971, pp. ESl-52. . . J. MORCILLO.J. F. BIARGE. J. M. V. HEREDIA and A. ME~INA, j. Mol. Structure, 3 77 (1969) K. TANABE and S. SABKI, Spectrochim. Acta, 2, A, 14, Y (1970). H. RATAJCZAK,T. A. FORD and W. J. ORVILLETHOMAS,J. Mol. Structure, 14, 281 (1972).