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Infra-red intensities in CH2F2, CH2Cl2 and CF2Cl2
SpeetrochimieaAcLcta,10Bs,VoL22,pp.1060to1090. PergamonPremLtd. PrJntedinNorthemIrelmd
I&a-red intensities in CH$*, CHJQ ma CF,CI,* J. MORCILLO, L. J. ZAB~ORANO and J. M. V. HEREDIA Institute de Qufmica Ffsica “Rocasolano”, Madrid; and Faoultad de Cienciaa, Univemidad de Madrid (Received 18 Pebmmy 1966)
Abstract-The integrated intensities of the fundamental infrared absorption bands of CHeF,, CH,CI, and CF,Cl, have been measured using the pressure-broadeningtechnique. Experimental results are interpretedin terma of displacement polar tensors, which give the change of the dipole moment of the molecule due to a set of displacementsof the nuclei. The components of theee polar tensors have been calculated for the nuclei of C, H, F and Cl for each of the studied molecules. The results obtained show that the bond moments hypothesis, used by most authors in the interpretation of infrared intensities, is only a rough approximation. Thue, we have found that a bond stretching givee rise to a dipole moment change not directed along the bond but strongly deflected towards the most polarizable atom of the molecule. Similar results have been obtained for the bond bendings. INTRODUCL'ION IN MOST of the papers on i&a-red intensities of gases, the experimental data have been interpreted using the bond moments hypothesis, in which a partial dipole moment is assigned to each bond, and their variations are supposed to be directed along the bond in a bond stretching and perpendicular to it in a bond bending. This hypothesis has the obvious advantage of its simplicity, but the results so far obtained do not confhm its validity. Among other things, the fact that different values are obtained for a bond moment and its derivative (with respect to the bond distance), when calculated from different vibration modes, shows clearly that this model can only be taken as a first approximation. We have put forward elsewhere [l] a more general theory for the interpretation of i&a-red intensities, in which a tensor is associated with each bond, instead of a vector or bond moment, as it is assumed in the bond moments hypothesis. These tensors, which will be called displacement polar tensors, or simply, polar tenmra, give the change of the dipole moment of the molecule, Ap, when the iV atomic nuclei undergo a set of small displacements, r,:
A~.L= ~DJ&x a
= 1, 2, 3, . . . , N)
(1)
where D, is the polar tensor associated with the a atom. In Equation (l), the following assumptions have been made : linear dependence between the displacement of a nucleus and the subsequent change of the dipole moment, and additivity of the effects of simultaneous displacements of several nuclei. * Thiswork ha9 been sponsoredin part by the “Comisi6n para el Foment0 de la Investigaci6n en la Univemidad” through 8 grant for scienti6c research. [l] J. F. BUIWE, J. HERFUNZ and J. MORCILLO, Andes Red Sot. EapdL Fhs. Quh. A 67, 81 (1961). 1060 1
(biadrid)
1970
J. MORCILLO,L. J. ZAWORANO and J. M. V. HEREDIA
The Cartesian expressions with elements
of the polar tensors are of course third-order
(W,h =
2ah (9,h = x,
Y,
matrices
4
It can be easily seen that, for the simplest case of atoms bound to the rest of the molecule by only one bond, the bond moments hypothesis amounts to assuming that the corresponding polar tensor takes a diagonal form. Taking the direction of the bond as the x axis, the Cartesian expression of the polar tensor is D, =
I% 0 ( 0
0 0 pu, 0 0 &.1
where peris the bond moment divided by the bond length, and E, is the bond moment derivative with respect to the bond distance. Expression (3) holds only when the z-axis (directed along the bond) is a n- fold axis of symmetry of the molecule, with n > 3, so that the bond moments hypothesis will be valid just for this particular type of bond. In any other instance, the polar tensors are not diagonal and the bond moments hypothesis is not fulfilled. The general properties of the polar tensors and their relationship with the h&a-red intensities were reported in [l]. This theory is now being applied to the series of halogen derivatives of methane. In this paper, the results obtained for CHsF,, CH,Cl, and CF.&l, are reported. EXPERIMENTAL Measurements have been carried out following the technique and procedure described previously [2-41. Spectra were recorded with a Perkin-Elmer 112 spectrometer, equipped with LiF, NaCl and KBr prisms, and with a Perkin-Elmer 125 grating spectrophotometer. Glass-bodied cells were used, which did not show any noticeable gas adsorption. As broadening gas, we used dry air at 1 atm of pressure, attaining practically a complete broadening. Absolute intensities, P, have been obtained by extrapolation of the apparent intensities to nb -+ 0. Curves showing this extrapolation, as well as plots of the band-area = S log (T,,/T) d log Y vs. nb (mole/cm2), and other experimental details, can be seen in [5]. The values of P are given in Table 1. For non-overlapping bands, the estimated error of the intensity is smaller than 5 per cent. In CH2F2 and CH,Cl,, the overlapping bands y1 and Ye were graphically resolved assuming symmetrical contours. The resolution of the overlapping bands v2 and vs of CH,F, was particularly difficult and was carried out taking into account the contours expected for both bands and the work of STEWART and NIELSEN [6]. [2] J. MORCILLO and J. HERRANZ,Anales RealSoc. Espaft. Fk. Q&m. (Madrid) A 52,207 (1956.) [3] J. HERRANZ,R. DE LA CIERVAand J. MORCILLO,Anales Real Sot. Espafi. Fh. Q&m. (Madrid) A 55, 69 (1959). [4] J. MORCILLO,.J.HERRANZad J. F. BIARUE,Spectrochim.Acta 15, 110 (1959). [6] L. J. ZA?~OR~LNO. Ph.D. Thesis, University of Madrid (1962). [6] H. B. STEWARTand H. H. NIELSEN, PIqa. Rev. 75, 640 (1948).
19’71
Infra-red intensitiesin CHgz, CH&& and CF&l, Table 1. Infra-red intensities, lYk, end moduli, ak, of the vectors (?QJJC$?&,, for CH,F,, CH,Cl, and CF,C1, Gbnpound
Bend (cm-~)
61 98 0 27 82 3 206 12
V7 B, VB B* VP B,
2990 720 1426
~1 AI va A, vs -41
o-11 1.1 0.16
22 33 18
(283) 3065 898 737 1262
~4 -4, ye JA
(6) 0.13 o-13 16.2 2.60
(20) 23 13 131 68
21.2 O-05 1.86
206 6 42
(1) 17.3 o-03
(20) 166 4
33.6 o-03
210 4
629
1096 442 665
CFdA
% (e.s.u.)
3016 1186 1090 1430
1070 (1608)
CJW0
rr x 10-a (cm’/mole) 0.8 6.2 0.00 0.94 1.4 o-003 27-o 0.14
2949
CJ%F0
Assignment
(261) 11.52 476 916 432
VI +‘a VI ~1 VI
4 -41 AI -4, BI
VY B, ~0 J% VP B, Vl
Al
va AI VI 4 ~4 -41 ye BI ~7 BI VII B, vs
B,
The y4 bands of CH,Cl, and CF,Cl,, active in infra-red and with centres at 283 and 261 cm-l, respectively, could not be measured with our spectrometers. Their intensities have been estimated from atomic polarization data following the method reported in a previous paper [7]. The only infra-red intensity measurements on these compounds known to us have been made by STRALEY [8] on the B, and B, species in CH,Cl,. His results, when changed from c/s at N.T.P. to values of l? (cm2/mole), are as follows: Ps = O-12 x 103, r, = O-11 x 10s, I’s = 146 x lo3 and Pe = 2.24 x 105, which are in fair agreement with our results, as can be seen in Table 1. POU
TENSORS
The three studied molecules, of general formula CX,Y,, belong to the C,, symmetry point group. We shall number the nuclei as indicated in Fig. 1, and denote by d and D the bond lengths C-X and C-Y, respectively. We shall use the reference frame III, which is in relation with the symmetry elements of the molecule and defined so that the unit vectors i, j and k have the same directions that the vectors [7] J. HERRANZ, J. F. BIARUE and J. MORCILLO, Anab B 54, 623 (1958). [S] J. W. STRALEY, J. Chem. Phye. i&2183 (1966).
Real Sot. Eepafi. Fh. Q&n. (Madrid)
1972
J. MORCILLO,L. J. ZAXORANO and J. M. V.
HEREDIA
X2,, Y,k, and %, + &a, respectively. Final results will be referred to other orthogonal frames, closely related with the bonds, such as frame I with k directed along &, and j along Y,k,, or frame II with k and j directed along s, and s,, respectively. From the measured intensities rk one can only obtain the moduli a, of the vectors ($~./a~,)~, which are listed in Table 1. The directions of these vectors, as well as that kt(III)”
Fig. 1. Location of the atoms of a C&Y2 type moleoule and orientations of referenceframes I, II and III.
of the dipole moment, can be deduced from the properties of the corresponding symmetry group, only the sign being undetermined. Then we can write
(4 where u,, and u, (k = 1,2, . . . , 3 N-6) are vectors of units length whose directions can be easily deduced from symmetry considerations ; p, is the dipole moment of the molecule, and the c’s are unknown signs that cannot be determined beforehand. The dipole moment of molecules CX2Y, is directed along the symmetry axis (vector k in frame III). Vibrations of A, class affect only to the dipole moment component directed along the axis k, and those of B, and B, classes to the components directed along i and j, respectively, i.e. u,=u,=i;
u, = u, = u, =u3=u4=k;
u,=u,=j
(5)
It is then straightforward to write the matrix A, (A),k = i3,uo/i3Qk, and from it to obtain the matrix P, (P),, = apg/S3,,related to A by the equation p=m-1
(6)
This step implies knowing the L-l matrix, which transforms symmetry co-ordinates into normal co-ordinates (Q = L-IS), and therefore requires a previous knowledge of the potential energy function of the molecule. For the molecules CX,Y,, Equation (6) is reduced to (P,P,PsP,)=(oa b@ ua ba)L Al -1; 1122.3344 (7) (P, P,) = (c&3 W,)LB, -l; (Pa Ps) = (%%l w&3,-*
I&a-red
1973
intensitiesin CX&Fa,CH&~ and CF,Cl,
Once the matrix P is known, one may calaulate the wibrationplar given by the equations {V,} = PB = P@J; S = ;B,‘,
te?zsoT8,V,,
(8)
Here the symbols { } indicate the matrix resulting from juxtaposition of the columns of the matrices enclosed inside the braces (all the matrices having, of course, the same number of rows). The expressions (v,, V2, . . . , V,> and (Br, B2, . . . , BN} are abbreviated to (v,> and (B,}, respectively. The matrix B depends only on the geometrical parameters of the molecule and not on the atomic masses, so that it is independent of the potential energy function and invariant to isotopic substitutions; many of its elements vanish with a suitable choice of the reference frame. The displacement polar tensors, D,, can be expressed as the sum of the vibration polar tensors V, and the rotation polar tensors R,: D, = V, + R,
(9)
Actually, as can be easily deduced from Equations (7) and (8), the vibrational polar tensors are those directly related to the intensities of the i&a-red bands. Nevertheless, the displacement polar tensors are much more useful, since only they are invariant to isotopic substitutions. To calculate the displacement polar tensors by Equation (9), one has to determine previously the rotation polar tensors, which depend only on the geometry of the molecule, atomic masses and dipole moment, and are given by R, =
w-2
~~,UW-%P.)~P
where the m,‘s are the masses of the atoms, 9. their position vectors* with respect to the centre of gravity of the molecule, and I its inertial tensor, which is diagonal in the reference frame III. Using Equations (7-lo), we obtain the polar tensors D, in the reference frame III. In order to check and discuss the obtained results it is very convenient to use the reference frames I and II for the D, and D, tensors, respectively. This is done by applying to tensors D,(III) the transformations corresponding to the appropriate rotation of axes. When all these calculations are carried out, the polar tensors D,, DY and Do in the reference frames I, II and III, respectively, take the form Dx(I)=
(if
;
13:
D,(II)=
(a
iv
g:)
* Given the vector V, the symbol [(v)] will denote the antisymmetric tensor (or pseudo-tensor) whose Cartesianexpression ia -VW [(v)] = -z# “d v, 0 ) ( v, -v. Since only real matrices are involved, the symbol t will be used to denote the transposedmatrix
J. MORCILLO,L. J. ZAMORANOand J. M. V. HEREDIA
1974
Assuming tetrahedric angles throughout the calculations, the components of these tensors are given by the expressions
PX = 2&
P9 +
%ud,-Wc - Omx
eX= +6 [PI- ~4W’~l - @orudv-l : mx 5~
=
-$ [dP)Pl
+ PO1+ ~o&-l
d(2) 5 mx
3
e=$g[pS+J(~)P~+P,]
-~o~dv-l&)(d-~c)mx
TY
=
2di3)D
D + 5~ [--2Pa + 2/W’4 + PO1- docldn-l 7 my
&y=
-
5y=
-
rlY=
-
J(f)@
(11)
+ &)m~
In these Equations c = 3-1’2; 1, and I, are, respectively, the 2 and y components of the moment of inertia; 5 is the z-co-ordinate of the center of gravity of the molecule; and m, and my the masses of the X and Y atoms, respectively. The components of the Dx and D y polar tensors are not independent but are related to the dipole moment by the Equation @o/Jo = - +3[Dr~
--TX + dW7xl=
$prx
- DTY +dwDrlYI
(12)
Also, taking into account that the sum of the polar tensors for all the atoms of the of the polar tensor D, can be expressed by the Equations molecule must be zero, the components
70 = -%[Tx + 3Px + 2&x - 2/(2)(17x + lx)] PC = -%[TY + 3cLy + Z&Y EC= -$[2Tx To calculate,
through
d/(z)(rly
+
ty)l
(131
+ 27~ + EY + 1/(2)(7x + 7~ + tx + 6y)l Equations
(7) and (ll), the components of the polar This matrix can be eliminated, as it is
tensors it is necessary to know the L-l matrix.
Infrared intensitiesin CHp*, CH&l, and CF,C&.
1976
shown in [l], summing the intensities for the bands of the same symmetry species. Assuming also tetrahedric angles, this leads to the following relationships: a,* + aa + a22 + ad2= snzx-’ ([1/(2)7x
+9my-1 {WWy ag2 + a,2 = #mx-l {bx as2 + ag2 = ~my-Yh
+
17x12+ hm)Ex + ~X121 + 542 + MWy + 421 + mc-1g02 (14)
- 2/(2b?x12 + lI2/(2h - M21 +-2mp-1pp2 -
2/Ph12
+ m,-lpc2
- po21g-1
+ m,-lpc2
- po21a-l
+ W/(2bp - Ey121 +2mx-lpx2
These Equations show that the total intensity for each symmetry species is independent of the potential energy function of the molecule, unlike the individual intensities of each band. Equations (14) are very useful to check the calculations of the polar tensors components. RESULTSAND DISCUSSION The L-l matrices have been calculated following WILSON’sF and G;matrix method. The force constants for CH,F, CH,CI, and CF,Cl, were taken from Dowmxa [9], DECIUS[lo] and MESTERand DO~LINQ[ 1I], respectively. As follows from Equation (7) and (ll), the values of the polar tensor components depend on the plus or minus sign choosen for each one of the nine u,. Since there are two possibilities for each sign, the number of possible sets of values for the polar tensor components of each molecule will be 2Q= 612. Most of these sets of values may be obviously neglected taking into account the following physical criteria: (1) The electronegativity of halogens determines the sign u,,, the signs ti, of the stretching vibrations and even those of some bending vibrations. (2) The u, of similar (or just opposite) normal vibrations of analogous molecules, such as CH,F, and CH,CI,, must be alike (or opposite), when the intensities of their corresponding bands are large. If they are small, U, may be different, but this sign has then little influence on the polar tensors components. When substituting hydrogen for a halogen, this criterium holds only for those intense bands corresponding to vibrations where the substituted bond does not play a significant role (its frequency and intensity will be hardly affected). (3) By comparing the values of the polar tensor components obtained for these molecules with values for other related molecules (series of fluorinated and chlorinated methanes), one can let aside some sign choices. Taking into account the similarity of normal co-ordinates and electronegativities of CH,F, and CH,Cl, we may expect the right choice of signs to be the same for both compounds. According to the criteria mentioned above we have chosen the following signs : CT0= fl, . aa = +1, UA= -1, u* = +1 (15) [9] J. M. DO-Q, [lo] [ll]
J. Chem. phy8. 22, 1789 (1954). J. C. DECUIJS, J. Chem. Phya. 16, 214 (1948). A. G. MESTKRand J. M. DOWUNU, J. Chem. Phy8.25,941
(1966).
J. MOROIJ.U&L. J. ZAMORANOand J. M. V. HEREDIA
1976
the partial moments of the C-Y bond have to be negative (Y = F or Cl, and the bond moment is defined to be positive in the sense C- - Y+). In both compounds, u, and ti, (which correspond to the symmetric and antisymmetric C-H stretchings) must show opposite signs. In CH,F,, us does not count for much since the intensity of the ~a band is almost null. In CH,Cl,, u, has been taken as negative, which scarcely affects the results.
since
Table 2. Components of the polar tensors of CH,F, (in D/A) for different combinations of signs Combination ofeigm '01246789
Do(III)
DPm
Da(I)
opos
-1.31 0 -0.05
0 -0.84 0
0.94 0 -4.62
2.33 0 0
0 0 7.78 0 0 3.60
0.12 0 1.07
-1.20 0 0.03
0 -0.98 0
0.91 0 -4.64
0.40 0 0
0 0 7.78 0 2.26 0
0.12 0 1.07
-1.14 0 -0.06
0 -0.98 0
1.02 0 -4G30
0.40 0 0
0 7.66 0
0.68 0 0.03
0 0.07 0.26 0 0 -0.72
-1.26 0 -0.13
0 -0.84 0
1.06 0 -4.18
2.33 0 0
0 0 '7.66 0 0 36.0
0.61 0 -0.01
0 0.07 0.06 0 0 -0.72
-1.31 0 -0.06
0 0.94 -0*'?8 0 -4.62 0
2.18 0 0
0 0 7.78 0 0 3.60
-1.20 0 0.03
0 -0.92 0
0.91 0 -4.64
0.24 0 0
0 0 7.78 0 2.26 0
-1.26 0 -0.13
0 -0.78 0
1.06 0 -4.78
2.18 0 0
0 0 7.66 0 0 3.60
-1.14 0 -0.06
0 -0.92 0
1.02 0 -4.80
0.24 0 0
0 0 7.66 0 0 2.26
+-+-“+-+-
0.68 0
+++-“--+-
0.48 0 0.08
0 0.06 0
+++J--++
0.48 0 0.08
0 0.26 0
0.03
+-+-“+-++ +-+-“+++-
0.61 0 0.06
-I-++-“-++-
0.81 0 -0.01
+-+-‘++++
o-07 0
0
0 0.06 0
0.12 0 1.07
0 0.07 0.26 0 0 -0.72
+++z-+++ 0.61 0 0.06
-0.72
0 0.26 0
0.12 0 1.07
0 0 2.26
The normal co-ordinates of CF,Cl, are very different from those of the other two molecules, since replacements of H by F or Cl alters considerably the mechanical and electrical properties of the molecule. Nevertheless, using similar criteria as above, we could establish for CF,Cl, the following set of signs: u, = -1,
Ul =
-1,
us =
+1,
up =
-1,
us =
+1,
us =
+1 W)
In CF,Cl, we have put F = X and Cl = Y for which some of the signs must be opposite from that for CH,F, or CH,Cl,. With these choices of signs we are left with only eight possible sets for each one of the three molecules. Their corresponding values for the polar tensor components are listed in Tables 2, 3 and 4, where a letter has been assigned to each combination of signs. The combinations V, X, Y, Z of CH,F, (with u, = +l) do not appear in
Infra-red intenktiea in C&F2, CEC,cI, and CF,cI,
1977
Table 3. Components of the polar tensore of CH&l, (in D/A) for different combinations of signs Combination of sip 012346789
+_+-“+_+-
0 -0.72 0
1.36 0 -2.33
la 0 0
0 -0.02 -0.41 0 0 -O*lK
-1.06 0 -0.01
0 -0.72 0
1.34 0 -2.34
1.67 0 0 0 6.88 0 0 0 1.93
0 -0.72 0
1.36 0 -2.32
0.90 0 0 5.88 0 0
0 0 1.00
-0YO8
0.04 0' 0.38
-1.07 0 -0.03
0 -0.02 -0.41 0 -0.08 0
0.07 0 0.40
-1.04 0 0 -0.72 -0.01 0
1.36 0 -2.33
0.90 0 0 6.88 0 0
0 0 1.46
0 0.80 0
0.04 0 0.38
-0.82 0 -0.38
0 -0.72 0
1.88 0 -3.06
0.90 0 0
0 4.44 0
0 0 1.00
0 0.80 0
0.07 0 0.40
-0.79 0 -0.36
0 -0.72 0
1.87 0 -3.07
0.90 0 0
0 0 4.44 0 1.46 0
0 -0.04 0.80 0 0 -0.17
-0.82 0 -0.38
0 -0.72 0
1.87 0 -3.07
1.67 0 0
0 0 4.44 0 1.48 0
0 -0.02 0.80 0 0 -0.16
-0.79 0 -0.37
0 -0.72 0
1.86 0 -3.08
I.67 0 0
0 0 4.44 0 0 1.93
0.24 0 0.10
+++-?--++ T”
0 0 6~68 0 0 1.48
0.24 0 0 -0.41 0.10 0
+++_“I__+_
++++---++
DC(~)
-1.07 0 -0.03
-0.03
5”
0
-0.04 -0.41 0 -0.17 OYlO 0
+-++“-;-+-
++++---+-
DOI
DIdI) 0.23
-0.02 0 -0.08
+-+-“+-++
0.23 0 0.10
-0.03 0 -0.08
+-++“-;-++
Table 4. Components of the polar tensors of CF.&I, (in D/A) for different combinations of signs Combination OfBigM 012346789
Ddn
DoUW
D0ln.u
__++8+_+_
-1.68 0 -0.69
0 -0.77 -1.90 0 -4.39 0
-1.13 0 0.06
0 -0.40 0
1.07 0 -2.43
6.40 0 0
0 0 8.87 0 0 8.61
--++I+-++
-1.68 0 -0.69
-0.77 0 -1.70 0 -4.39 0
-1.08 0 -0.01
0 -0.40 0
1.26 0 -2.89
6.49 0 0
0 0 8.86 0 8.61 0
-1.69 0 -0.62 -1.90 0 0 -4.61 -0.71 0
-1.13 0 0.06
0 -0.20 0
1.07 0 -2.43
6.34 0 0
0 0 8.87 0 0 8.61
-1.90 -0:76
0 -0.77 -1.70 0 0 -4.39
-1.07 0 -O*Ol
0 -0.40 0
1.60 0 -2.44
6.49 0 0
0 0 8.86 0 0 8.46
___+I+_+_
-1.90 0 -0.76
-0.77 0 -1.90 0 -4.39 0
-1.13 0 0.07
0 -0~40 0
1.41 0 -2.19
6.49 0 0
0 8.87 0
__-+f_+++_
-1.81 0 -1.90 0 -0.87 0
-1.13 0 0.07
0 -0.20 0
1.41 0 -2.19
6.34 0 0
0 0 8.87 0 8.46 0
--++g++++
-1.69 0 -0.71
-0.62 0 -1.70 0 -4.61 0
-1.08 0 -0,Ol
0 -0.20 0
1.26 0 -2.69
6.34 0 0
0 0 8.86 0 8.61 0
---+“++++
-1.81 0 -0.87
0 -0.61 -1.70 0 -4.60 0
-1.07 0 -0.01
0 -0.20 0
1.69 0 -2.44
6.34 0 0 8.86 0 0 8.46 0 0
--++c+++__-+!+-++
-0.61 0 -4.60
0 0 8.46
1978
J. MORCILLO, L. J. ZAMORANOand J. M. V. HEREDIA
CH,Cl,. Each one of the other combinations for CH,F, (R, S, T, U) gives rise to two combinations in CH,Cl, according to the choice for 6s. We design with a prime the combination with bs = -1 and with a double prime that with ~a = +l. The combinations of signs for CF,CI, are not comparable with those of CH,F, or CH,Cl, and are accordingly indicated by different letters. The results obtained for each one of these combinations of signs may be interpreted and visualized easily by representing the changes of the molecule dipole moment due to a bond-stretching or a bond-bending of unity displacement. This type of representation has been carried out in Figs. 2, 3 and 4, for CH,F,, CH,Cl, and CFaCl,, respectively. Each figure consists of two diagrams corresponding to the two different bonds of these molecules. The two equivalent bonds considered are in the plane of the figure, while the other two bonds are projected on this plane. Except for carbon, the approximate size of atoms (covalent radii) are indicated by circles. The vectors defining the increment of the molecule dipole moment, due to an unitary displacement of the nucleus considered, are represented by arrows in the local reference frame of the bond. Three unitary displacements are considered; first along the k axis (bond stretching), second along the i axis (bond bending in the plane of the figure) and third along the j axis (bond bending perpendicular to the plane of the figure). Dipole moment increments in bond stretchings make a small angle with the direction of the bond, so that they may be well distinguished in the figures, from those originated by bond bendings which are nearly normal to the direction of the bond. On the top of the Figs. is shown schematically the change of the dipole moment due to a bond bending perpendicular to the plane of the Fig. To make the comparison easier, the direction of vector j is shown as parallel to that of vector i of the main Fig. The letters placed near each vector correspond to the different combinations of signs. Fortunately, for the carbon-halogen bonds, they lead to practically equal results. For the C-H bond stretching and bendings, the changes of the dipole moment are very small, nearly of the same order than their errors. In Figs. 2 and 3, these dipole moment changes have been multiplied by 2 to show them more clearly. As may be seen in the Figs. 2, 3 and 4, the polar tensors of the halogen atoms are left well-defined, independently of the choice of the three signs which remain undetermined. On the contrary, the hydrogen polar tensors are not so well determined, probably because the absolute values of their components, are almost of the same order as their probable errors. The most satisfactory sign choice may be decided after comparison of these results with those obtained for other methane derivatives, which are being now elaborated in our laboratory. For the C-F and C-Cl bonds, as may be seen in the Figs. a bond stretching gives rise to a dipole moment change not directed along the bond, but fairly deflected towards the most polarizable atom of the molecule. The moduli of vectors deflning these increments of the dipole moment are nearly equal for the same bond in analogous molecules. Similar results can be observed for bond bendings in the plane of the Fig. By symmetry considerations, the dipole,moment change due to a bond bending perpendicular to the plane must be normal to the bond direction. Their magnitudes, however, happen to be different from the ones corresponding to the in-plane bending. The change of the dipole moment due to a carbon-halogen bond stretching or
Infra-red intensitiesin C&F,,
ocw -
i IOIl
CYH&l,and CF,CI,
eou
-.toJ.
Fig. 2. Changesof the dipole moment in CH,F, due to C-H (right) and C-F (left) bond stretchingsand bendinga. ( 1) dipole moment change due to a bond bending perpendioularto the plane of the figure.
.wbcl
.Id
rd.
*Id
-
Fig. 3. Changes of the dipole moment in CH,Cl, due to C-H (right) and C--Cl (left) bond stretchingaand bend&e. ( I) dipole moment change due to a bond bending perpendicularto the plane of the figure.
Ud.
-
.
WA
SC*.
-
.,a4
Fig. 4. Changes of the dipole moment in CF,Cl, due to C-Cl (right) and C-F (left) bond stretching8 and bendings. (I) dipole moment change due to a bond bending perpendiculerto the plane of the figure.
1979
1980
J. MOROILLO,L. J. Zmowo
and J. M. V. HXSEDIA
bending may be qualitatively explained as produced by a negative charge associated to the halogen nucleus and moving with it in the presence of other atoms more or less polarizable. The primary dipole moment created by a displacement of this charge becomes modified by the dipole moments induced in other polarizable sites of the molecule. The effect of these induced moments is to reinforce the component of the primary dipole moment directed along the line joining the moving nucleus with the polarizable atom, and to balance the component perpendicular to that direction. This fact accounts for the observed deviation of the dipole moment change, as well as for the larger effect of a bond stretching against a bond bending. On the other hand, the motion of a polarizable atom against a fixed punctual charge does create a dipole moment equivalent to that originated by the movement of a charge of opposite sign (longitudinal displacement) or alike sign (transversal displacement). For this reason, the positive charge on the carbon atom helps to bring about upon the halogen atoms an apparent negative charge much bigger in a bond stretching than in a bond bending, since the effect reported above reinforces and balances, respectively, that produced by the movement of the charge associated with the halogen atoms. For the C-H bonds, it is reasonable to assume that the charge associated with the hydrogen atom is almost null. Therefore the small changes of the dipole moment originated by a G-H stretching or bending are due, to a large extent, to second order effects which cannot be accounted for by a simplified model. After a consideration of the obtained results we must give up any theory trying to reduce the polar behaviour of bonds to their partial bond moments and their derivatives with respect to the bond distance (bond moments hypothesis). The polar behaviour of bonds is not so simple as assumed by this theory, so that, for the interpretation of i&a-red intensities, it is necessary to adopt a further approximation like the polar tensor model, used in this work, or some others that have been recently developed by several authors [12]. [12] L. A. Gmov, Intemiiy Tw Bureau, New York (1904).
for Infrared Spectra of Polyahmic Mol.ecuh.
Conmltmta
I&a-red intensities in CH$*, CHJQ ma CF,CI,* J. MORCILLO, L. J. ZAB~ORANO and J. M. V. HEREDIA Institute de Qufmica Ffsica “Rocasolano”, Madrid; and Faoultad de Cienciaa, Univemidad de Madrid (Received 18 Pebmmy 1966)
Abstract-The integrated intensities of the fundamental infrared absorption bands of CHeF,, CH,CI, and CF,Cl, have been measured using the pressure-broadeningtechnique. Experimental results are interpretedin terma of displacement polar tensors, which give the change of the dipole moment of the molecule due to a set of displacementsof the nuclei. The components of theee polar tensors have been calculated for the nuclei of C, H, F and Cl for each of the studied molecules. The results obtained show that the bond moments hypothesis, used by most authors in the interpretation of infrared intensities, is only a rough approximation. Thue, we have found that a bond stretching givee rise to a dipole moment change not directed along the bond but strongly deflected towards the most polarizable atom of the molecule. Similar results have been obtained for the bond bendings. INTRODUCL'ION IN MOST of the papers on i&a-red intensities of gases, the experimental data have been interpreted using the bond moments hypothesis, in which a partial dipole moment is assigned to each bond, and their variations are supposed to be directed along the bond in a bond stretching and perpendicular to it in a bond bending. This hypothesis has the obvious advantage of its simplicity, but the results so far obtained do not confhm its validity. Among other things, the fact that different values are obtained for a bond moment and its derivative (with respect to the bond distance), when calculated from different vibration modes, shows clearly that this model can only be taken as a first approximation. We have put forward elsewhere [l] a more general theory for the interpretation of i&a-red intensities, in which a tensor is associated with each bond, instead of a vector or bond moment, as it is assumed in the bond moments hypothesis. These tensors, which will be called displacement polar tensors, or simply, polar tenmra, give the change of the dipole moment of the molecule, Ap, when the iV atomic nuclei undergo a set of small displacements, r,:
A~.L= ~DJ&x a
= 1, 2, 3, . . . , N)
(1)
where D, is the polar tensor associated with the a atom. In Equation (l), the following assumptions have been made : linear dependence between the displacement of a nucleus and the subsequent change of the dipole moment, and additivity of the effects of simultaneous displacements of several nuclei. * Thiswork ha9 been sponsoredin part by the “Comisi6n para el Foment0 de la Investigaci6n en la Univemidad” through 8 grant for scienti6c research. [l] J. F. BUIWE, J. HERFUNZ and J. MORCILLO, Andes Red Sot. EapdL Fhs. Quh. A 67, 81 (1961). 1060 1
(biadrid)
1970
J. MORCILLO,L. J. ZAWORANO and J. M. V. HEREDIA
The Cartesian expressions with elements
of the polar tensors are of course third-order
(W,h =
2ah (9,h = x,
Y,
matrices
4
It can be easily seen that, for the simplest case of atoms bound to the rest of the molecule by only one bond, the bond moments hypothesis amounts to assuming that the corresponding polar tensor takes a diagonal form. Taking the direction of the bond as the x axis, the Cartesian expression of the polar tensor is D, =
I% 0 ( 0
0 0 pu, 0 0 &.1
where peris the bond moment divided by the bond length, and E, is the bond moment derivative with respect to the bond distance. Expression (3) holds only when the z-axis (directed along the bond) is a n- fold axis of symmetry of the molecule, with n > 3, so that the bond moments hypothesis will be valid just for this particular type of bond. In any other instance, the polar tensors are not diagonal and the bond moments hypothesis is not fulfilled. The general properties of the polar tensors and their relationship with the h&a-red intensities were reported in [l]. This theory is now being applied to the series of halogen derivatives of methane. In this paper, the results obtained for CHsF,, CH,Cl, and CF.&l, are reported. EXPERIMENTAL Measurements have been carried out following the technique and procedure described previously [2-41. Spectra were recorded with a Perkin-Elmer 112 spectrometer, equipped with LiF, NaCl and KBr prisms, and with a Perkin-Elmer 125 grating spectrophotometer. Glass-bodied cells were used, which did not show any noticeable gas adsorption. As broadening gas, we used dry air at 1 atm of pressure, attaining practically a complete broadening. Absolute intensities, P, have been obtained by extrapolation of the apparent intensities to nb -+ 0. Curves showing this extrapolation, as well as plots of the band-area = S log (T,,/T) d log Y vs. nb (mole/cm2), and other experimental details, can be seen in [5]. The values of P are given in Table 1. For non-overlapping bands, the estimated error of the intensity is smaller than 5 per cent. In CH2F2 and CH,Cl,, the overlapping bands y1 and Ye were graphically resolved assuming symmetrical contours. The resolution of the overlapping bands v2 and vs of CH,F, was particularly difficult and was carried out taking into account the contours expected for both bands and the work of STEWART and NIELSEN [6]. [2] J. MORCILLO and J. HERRANZ,Anales RealSoc. Espaft. Fk. Q&m. (Madrid) A 52,207 (1956.) [3] J. HERRANZ,R. DE LA CIERVAand J. MORCILLO,Anales Real Sot. Espafi. Fh. Q&m. (Madrid) A 55, 69 (1959). [4] J. MORCILLO,.J.HERRANZad J. F. BIARUE,Spectrochim.Acta 15, 110 (1959). [6] L. J. ZA?~OR~LNO. Ph.D. Thesis, University of Madrid (1962). [6] H. B. STEWARTand H. H. NIELSEN, PIqa. Rev. 75, 640 (1948).
19’71
Infra-red intensitiesin CHgz, CH&& and CF&l, Table 1. Infra-red intensities, lYk, end moduli, ak, of the vectors (?QJJC$?&,, for CH,F,, CH,Cl, and CF,C1, Gbnpound
Bend (cm-~)
61 98 0 27 82 3 206 12
V7 B, VB B* VP B,
2990 720 1426
~1 AI va A, vs -41
o-11 1.1 0.16
22 33 18
(283) 3065 898 737 1262
~4 -4, ye JA
(6) 0.13 o-13 16.2 2.60
(20) 23 13 131 68
21.2 O-05 1.86
206 6 42
(1) 17.3 o-03
(20) 166 4
33.6 o-03
210 4
629
1096 442 665
CFdA
% (e.s.u.)
3016 1186 1090 1430
1070 (1608)
CJW0
rr x 10-a (cm’/mole) 0.8 6.2 0.00 0.94 1.4 o-003 27-o 0.14
2949
CJ%F0
Assignment
(261) 11.52 476 916 432
VI +‘a VI ~1 VI
4 -41 AI -4, BI
VY B, ~0 J% VP B, Vl
Al
va AI VI 4 ~4 -41 ye BI ~7 BI VII B, vs
B,
The y4 bands of CH,Cl, and CF,Cl,, active in infra-red and with centres at 283 and 261 cm-l, respectively, could not be measured with our spectrometers. Their intensities have been estimated from atomic polarization data following the method reported in a previous paper [7]. The only infra-red intensity measurements on these compounds known to us have been made by STRALEY [8] on the B, and B, species in CH,Cl,. His results, when changed from c/s at N.T.P. to values of l? (cm2/mole), are as follows: Ps = O-12 x 103, r, = O-11 x 10s, I’s = 146 x lo3 and Pe = 2.24 x 105, which are in fair agreement with our results, as can be seen in Table 1. POU
TENSORS
The three studied molecules, of general formula CX,Y,, belong to the C,, symmetry point group. We shall number the nuclei as indicated in Fig. 1, and denote by d and D the bond lengths C-X and C-Y, respectively. We shall use the reference frame III, which is in relation with the symmetry elements of the molecule and defined so that the unit vectors i, j and k have the same directions that the vectors [7] J. HERRANZ, J. F. BIARUE and J. MORCILLO, Anab B 54, 623 (1958). [S] J. W. STRALEY, J. Chem. Phye. i&2183 (1966).
Real Sot. Eepafi. Fh. Q&n. (Madrid)
1972
J. MORCILLO,L. J. ZAXORANO and J. M. V.
HEREDIA
X2,, Y,k, and %, + &a, respectively. Final results will be referred to other orthogonal frames, closely related with the bonds, such as frame I with k directed along &, and j along Y,k,, or frame II with k and j directed along s, and s,, respectively. From the measured intensities rk one can only obtain the moduli a, of the vectors ($~./a~,)~, which are listed in Table 1. The directions of these vectors, as well as that kt(III)”
Fig. 1. Location of the atoms of a C&Y2 type moleoule and orientations of referenceframes I, II and III.
of the dipole moment, can be deduced from the properties of the corresponding symmetry group, only the sign being undetermined. Then we can write
(4 where u,, and u, (k = 1,2, . . . , 3 N-6) are vectors of units length whose directions can be easily deduced from symmetry considerations ; p, is the dipole moment of the molecule, and the c’s are unknown signs that cannot be determined beforehand. The dipole moment of molecules CX2Y, is directed along the symmetry axis (vector k in frame III). Vibrations of A, class affect only to the dipole moment component directed along the axis k, and those of B, and B, classes to the components directed along i and j, respectively, i.e. u,=u,=i;
u, = u, = u, =u3=u4=k;
u,=u,=j
(5)
It is then straightforward to write the matrix A, (A),k = i3,uo/i3Qk, and from it to obtain the matrix P, (P),, = apg/S3,,related to A by the equation p=m-1
(6)
This step implies knowing the L-l matrix, which transforms symmetry co-ordinates into normal co-ordinates (Q = L-IS), and therefore requires a previous knowledge of the potential energy function of the molecule. For the molecules CX,Y,, Equation (6) is reduced to (P,P,PsP,)=(oa b@ ua ba)L Al -1; 1122.3344 (7) (P, P,) = (c&3 W,)LB, -l; (Pa Ps) = (%%l w&3,-*
I&a-red
1973
intensitiesin CX&Fa,CH&~ and CF,Cl,
Once the matrix P is known, one may calaulate the wibrationplar given by the equations {V,} = PB = P@J; S = ;B,‘,
te?zsoT8,V,,
(8)
Here the symbols { } indicate the matrix resulting from juxtaposition of the columns of the matrices enclosed inside the braces (all the matrices having, of course, the same number of rows). The expressions (v,, V2, . . . , V,> and (Br, B2, . . . , BN} are abbreviated to (v,> and (B,}, respectively. The matrix B depends only on the geometrical parameters of the molecule and not on the atomic masses, so that it is independent of the potential energy function and invariant to isotopic substitutions; many of its elements vanish with a suitable choice of the reference frame. The displacement polar tensors, D,, can be expressed as the sum of the vibration polar tensors V, and the rotation polar tensors R,: D, = V, + R,
(9)
Actually, as can be easily deduced from Equations (7) and (8), the vibrational polar tensors are those directly related to the intensities of the i&a-red bands. Nevertheless, the displacement polar tensors are much more useful, since only they are invariant to isotopic substitutions. To calculate the displacement polar tensors by Equation (9), one has to determine previously the rotation polar tensors, which depend only on the geometry of the molecule, atomic masses and dipole moment, and are given by R, =
w-2
~~,UW-%P.)~P
where the m,‘s are the masses of the atoms, 9. their position vectors* with respect to the centre of gravity of the molecule, and I its inertial tensor, which is diagonal in the reference frame III. Using Equations (7-lo), we obtain the polar tensors D, in the reference frame III. In order to check and discuss the obtained results it is very convenient to use the reference frames I and II for the D, and D, tensors, respectively. This is done by applying to tensors D,(III) the transformations corresponding to the appropriate rotation of axes. When all these calculations are carried out, the polar tensors D,, DY and Do in the reference frames I, II and III, respectively, take the form Dx(I)=
(if
;
13:
D,(II)=
(a
iv
g:)
* Given the vector V, the symbol [(v)] will denote the antisymmetric tensor (or pseudo-tensor) whose Cartesianexpression ia -VW [(v)] = -z# “d v, 0 ) ( v, -v. Since only real matrices are involved, the symbol t will be used to denote the transposedmatrix
J. MORCILLO,L. J. ZAMORANOand J. M. V. HEREDIA
1974
Assuming tetrahedric angles throughout the calculations, the components of these tensors are given by the expressions
PX = 2&
P9 +
%ud,-Wc - Omx
eX= +6 [PI- ~4W’~l - @orudv-l : mx 5~
=
-$ [dP)Pl
+ PO1+ ~o&-l
d(2) 5 mx
3
e=$g[pS+J(~)P~+P,]
-~o~dv-l&)(d-~c)mx
TY
=
2di3)D
D + 5~ [--2Pa + 2/W’4 + PO1- docldn-l 7 my
&y=
-
5y=
-
rlY=
-
J(f)@
(11)
+ &)m~
In these Equations c = 3-1’2; 1, and I, are, respectively, the 2 and y components of the moment of inertia; 5 is the z-co-ordinate of the center of gravity of the molecule; and m, and my the masses of the X and Y atoms, respectively. The components of the Dx and D y polar tensors are not independent but are related to the dipole moment by the Equation @o/Jo = - +3[Dr~
--TX + dW7xl=
$prx
- DTY +dwDrlYI
(12)
Also, taking into account that the sum of the polar tensors for all the atoms of the of the polar tensor D, can be expressed by the Equations molecule must be zero, the components
70 = -%[Tx + 3Px + 2&x - 2/(2)(17x + lx)] PC = -%[TY + 3cLy + Z&Y EC= -$[2Tx To calculate,
through
d/(z)(rly
+
ty)l
(131
+ 27~ + EY + 1/(2)(7x + 7~ + tx + 6y)l Equations
(7) and (ll), the components of the polar This matrix can be eliminated, as it is
tensors it is necessary to know the L-l matrix.
Infrared intensitiesin CHp*, CH&l, and CF,C&.
1976
shown in [l], summing the intensities for the bands of the same symmetry species. Assuming also tetrahedric angles, this leads to the following relationships: a,* + aa + a22 + ad2= snzx-’ ([1/(2)7x
+9my-1 {WWy ag2 + a,2 = #mx-l {bx as2 + ag2 = ~my-Yh
+
17x12+ hm)Ex + ~X121 + 542 + MWy + 421 + mc-1g02 (14)
- 2/(2b?x12 + lI2/(2h - M21 +-2mp-1pp2 -
2/Ph12
+ m,-lpc2
- po21g-1
+ m,-lpc2
- po21a-l
+ W/(2bp - Ey121 +2mx-lpx2
These Equations show that the total intensity for each symmetry species is independent of the potential energy function of the molecule, unlike the individual intensities of each band. Equations (14) are very useful to check the calculations of the polar tensors components. RESULTSAND DISCUSSION The L-l matrices have been calculated following WILSON’sF and G;matrix method. The force constants for CH,F, CH,CI, and CF,Cl, were taken from Dowmxa [9], DECIUS[lo] and MESTERand DO~LINQ[ 1I], respectively. As follows from Equation (7) and (ll), the values of the polar tensor components depend on the plus or minus sign choosen for each one of the nine u,. Since there are two possibilities for each sign, the number of possible sets of values for the polar tensor components of each molecule will be 2Q= 612. Most of these sets of values may be obviously neglected taking into account the following physical criteria: (1) The electronegativity of halogens determines the sign u,,, the signs ti, of the stretching vibrations and even those of some bending vibrations. (2) The u, of similar (or just opposite) normal vibrations of analogous molecules, such as CH,F, and CH,CI,, must be alike (or opposite), when the intensities of their corresponding bands are large. If they are small, U, may be different, but this sign has then little influence on the polar tensors components. When substituting hydrogen for a halogen, this criterium holds only for those intense bands corresponding to vibrations where the substituted bond does not play a significant role (its frequency and intensity will be hardly affected). (3) By comparing the values of the polar tensor components obtained for these molecules with values for other related molecules (series of fluorinated and chlorinated methanes), one can let aside some sign choices. Taking into account the similarity of normal co-ordinates and electronegativities of CH,F, and CH,Cl, we may expect the right choice of signs to be the same for both compounds. According to the criteria mentioned above we have chosen the following signs : CT0= fl, . aa = +1, UA= -1, u* = +1 (15) [9] J. M. DO-Q, [lo] [ll]
J. Chem. phy8. 22, 1789 (1954). J. C. DECUIJS, J. Chem. Phya. 16, 214 (1948). A. G. MESTKRand J. M. DOWUNU, J. Chem. Phy8.25,941
(1966).
J. MOROIJ.U&L. J. ZAMORANOand J. M. V. HEREDIA
1976
the partial moments of the C-Y bond have to be negative (Y = F or Cl, and the bond moment is defined to be positive in the sense C- - Y+). In both compounds, u, and ti, (which correspond to the symmetric and antisymmetric C-H stretchings) must show opposite signs. In CH,F,, us does not count for much since the intensity of the ~a band is almost null. In CH,Cl,, u, has been taken as negative, which scarcely affects the results.
since
Table 2. Components of the polar tensors of CH,F, (in D/A) for different combinations of signs Combination ofeigm '01246789
Do(III)
DPm
Da(I)
opos
-1.31 0 -0.05
0 -0.84 0
0.94 0 -4.62
2.33 0 0
0 0 7.78 0 0 3.60
0.12 0 1.07
-1.20 0 0.03
0 -0.98 0
0.91 0 -4.64
0.40 0 0
0 0 7.78 0 2.26 0
0.12 0 1.07
-1.14 0 -0.06
0 -0.98 0
1.02 0 -4G30
0.40 0 0
0 7.66 0
0.68 0 0.03
0 0.07 0.26 0 0 -0.72
-1.26 0 -0.13
0 -0.84 0
1.06 0 -4.18
2.33 0 0
0 0 '7.66 0 0 36.0
0.61 0 -0.01
0 0.07 0.06 0 0 -0.72
-1.31 0 -0.06
0 0.94 -0*'?8 0 -4.62 0
2.18 0 0
0 0 7.78 0 0 3.60
-1.20 0 0.03
0 -0.92 0
0.91 0 -4.64
0.24 0 0
0 0 7.78 0 2.26 0
-1.26 0 -0.13
0 -0.78 0
1.06 0 -4.78
2.18 0 0
0 0 7.66 0 0 3.60
-1.14 0 -0.06
0 -0.92 0
1.02 0 -4.80
0.24 0 0
0 0 7.66 0 0 2.26
+-+-“+-+-
0.68 0
+++-“--+-
0.48 0 0.08
0 0.06 0
+++J--++
0.48 0 0.08
0 0.26 0
0.03
+-+-“+-++ +-+-“+++-
0.61 0 0.06
-I-++-“-++-
0.81 0 -0.01
+-+-‘++++
o-07 0
0
0 0.06 0
0.12 0 1.07
0 0.07 0.26 0 0 -0.72
+++z-+++ 0.61 0 0.06
-0.72
0 0.26 0
0.12 0 1.07
0 0 2.26
The normal co-ordinates of CF,Cl, are very different from those of the other two molecules, since replacements of H by F or Cl alters considerably the mechanical and electrical properties of the molecule. Nevertheless, using similar criteria as above, we could establish for CF,Cl, the following set of signs: u, = -1,
Ul =
-1,
us =
+1,
up =
-1,
us =
+1,
us =
+1 W)
In CF,Cl, we have put F = X and Cl = Y for which some of the signs must be opposite from that for CH,F, or CH,Cl,. With these choices of signs we are left with only eight possible sets for each one of the three molecules. Their corresponding values for the polar tensor components are listed in Tables 2, 3 and 4, where a letter has been assigned to each combination of signs. The combinations V, X, Y, Z of CH,F, (with u, = +l) do not appear in
Infra-red intenktiea in C&F2, CEC,cI, and CF,cI,
1977
Table 3. Components of the polar tensore of CH&l, (in D/A) for different combinations of signs Combination of sip 012346789
+_+-“+_+-
0 -0.72 0
1.36 0 -2.33
la 0 0
0 -0.02 -0.41 0 0 -O*lK
-1.06 0 -0.01
0 -0.72 0
1.34 0 -2.34
1.67 0 0 0 6.88 0 0 0 1.93
0 -0.72 0
1.36 0 -2.32
0.90 0 0 5.88 0 0
0 0 1.00
-0YO8
0.04 0' 0.38
-1.07 0 -0.03
0 -0.02 -0.41 0 -0.08 0
0.07 0 0.40
-1.04 0 0 -0.72 -0.01 0
1.36 0 -2.33
0.90 0 0 6.88 0 0
0 0 1.46
0 0.80 0
0.04 0 0.38
-0.82 0 -0.38
0 -0.72 0
1.88 0 -3.06
0.90 0 0
0 4.44 0
0 0 1.00
0 0.80 0
0.07 0 0.40
-0.79 0 -0.36
0 -0.72 0
1.87 0 -3.07
0.90 0 0
0 0 4.44 0 1.46 0
0 -0.04 0.80 0 0 -0.17
-0.82 0 -0.38
0 -0.72 0
1.87 0 -3.07
1.67 0 0
0 0 4.44 0 1.48 0
0 -0.02 0.80 0 0 -0.16
-0.79 0 -0.37
0 -0.72 0
1.86 0 -3.08
I.67 0 0
0 0 4.44 0 0 1.93
0.24 0 0.10
+++-?--++ T”
0 0 6~68 0 0 1.48
0.24 0 0 -0.41 0.10 0
+++_“I__+_
++++---++
DC(~)
-1.07 0 -0.03
-0.03
5”
0
-0.04 -0.41 0 -0.17 OYlO 0
+-++“-;-+-
++++---+-
DOI
DIdI) 0.23
-0.02 0 -0.08
+-+-“+-++
0.23 0 0.10
-0.03 0 -0.08
+-++“-;-++
Table 4. Components of the polar tensors of CF.&I, (in D/A) for different combinations of signs Combination OfBigM 012346789
Ddn
DoUW
D0ln.u
__++8+_+_
-1.68 0 -0.69
0 -0.77 -1.90 0 -4.39 0
-1.13 0 0.06
0 -0.40 0
1.07 0 -2.43
6.40 0 0
0 0 8.87 0 0 8.61
--++I+-++
-1.68 0 -0.69
-0.77 0 -1.70 0 -4.39 0
-1.08 0 -0.01
0 -0.40 0
1.26 0 -2.89
6.49 0 0
0 0 8.86 0 8.61 0
-1.69 0 -0.62 -1.90 0 0 -4.61 -0.71 0
-1.13 0 0.06
0 -0.20 0
1.07 0 -2.43
6.34 0 0
0 0 8.87 0 0 8.61
-1.90 -0:76
0 -0.77 -1.70 0 0 -4.39
-1.07 0 -O*Ol
0 -0.40 0
1.60 0 -2.44
6.49 0 0
0 0 8.86 0 0 8.46
___+I+_+_
-1.90 0 -0.76
-0.77 0 -1.90 0 -4.39 0
-1.13 0 0.07
0 -0~40 0
1.41 0 -2.19
6.49 0 0
0 8.87 0
__-+f_+++_
-1.81 0 -1.90 0 -0.87 0
-1.13 0 0.07
0 -0.20 0
1.41 0 -2.19
6.34 0 0
0 0 8.87 0 8.46 0
--++g++++
-1.69 0 -0.71
-0.62 0 -1.70 0 -4.61 0
-1.08 0 -0,Ol
0 -0.20 0
1.26 0 -2.69
6.34 0 0
0 0 8.86 0 8.61 0
---+“++++
-1.81 0 -0.87
0 -0.61 -1.70 0 -4.60 0
-1.07 0 -0.01
0 -0.20 0
1.69 0 -2.44
6.34 0 0 8.86 0 0 8.46 0 0
--++c+++__-+!+-++
-0.61 0 -4.60
0 0 8.46
1978
J. MORCILLO, L. J. ZAMORANOand J. M. V. HEREDIA
CH,Cl,. Each one of the other combinations for CH,F, (R, S, T, U) gives rise to two combinations in CH,Cl, according to the choice for 6s. We design with a prime the combination with bs = -1 and with a double prime that with ~a = +l. The combinations of signs for CF,CI, are not comparable with those of CH,F, or CH,Cl, and are accordingly indicated by different letters. The results obtained for each one of these combinations of signs may be interpreted and visualized easily by representing the changes of the molecule dipole moment due to a bond-stretching or a bond-bending of unity displacement. This type of representation has been carried out in Figs. 2, 3 and 4, for CH,F,, CH,Cl, and CFaCl,, respectively. Each figure consists of two diagrams corresponding to the two different bonds of these molecules. The two equivalent bonds considered are in the plane of the figure, while the other two bonds are projected on this plane. Except for carbon, the approximate size of atoms (covalent radii) are indicated by circles. The vectors defining the increment of the molecule dipole moment, due to an unitary displacement of the nucleus considered, are represented by arrows in the local reference frame of the bond. Three unitary displacements are considered; first along the k axis (bond stretching), second along the i axis (bond bending in the plane of the figure) and third along the j axis (bond bending perpendicular to the plane of the figure). Dipole moment increments in bond stretchings make a small angle with the direction of the bond, so that they may be well distinguished in the figures, from those originated by bond bendings which are nearly normal to the direction of the bond. On the top of the Figs. is shown schematically the change of the dipole moment due to a bond bending perpendicular to the plane of the Fig. To make the comparison easier, the direction of vector j is shown as parallel to that of vector i of the main Fig. The letters placed near each vector correspond to the different combinations of signs. Fortunately, for the carbon-halogen bonds, they lead to practically equal results. For the C-H bond stretching and bendings, the changes of the dipole moment are very small, nearly of the same order than their errors. In Figs. 2 and 3, these dipole moment changes have been multiplied by 2 to show them more clearly. As may be seen in the Figs. 2, 3 and 4, the polar tensors of the halogen atoms are left well-defined, independently of the choice of the three signs which remain undetermined. On the contrary, the hydrogen polar tensors are not so well determined, probably because the absolute values of their components, are almost of the same order as their probable errors. The most satisfactory sign choice may be decided after comparison of these results with those obtained for other methane derivatives, which are being now elaborated in our laboratory. For the C-F and C-Cl bonds, as may be seen in the Figs. a bond stretching gives rise to a dipole moment change not directed along the bond, but fairly deflected towards the most polarizable atom of the molecule. The moduli of vectors deflning these increments of the dipole moment are nearly equal for the same bond in analogous molecules. Similar results can be observed for bond bendings in the plane of the Fig. By symmetry considerations, the dipole,moment change due to a bond bending perpendicular to the plane must be normal to the bond direction. Their magnitudes, however, happen to be different from the ones corresponding to the in-plane bending. The change of the dipole moment due to a carbon-halogen bond stretching or
Infra-red intensitiesin C&F,,
ocw -
i IOIl
CYH&l,and CF,CI,
eou
-.toJ.
Fig. 2. Changesof the dipole moment in CH,F, due to C-H (right) and C-F (left) bond stretchingsand bendinga. ( 1) dipole moment change due to a bond bending perpendioularto the plane of the figure.
.wbcl
.Id
rd.
*Id
-
Fig. 3. Changes of the dipole moment in CH,Cl, due to C-H (right) and C--Cl (left) bond stretchingaand bend&e. ( I) dipole moment change due to a bond bending perpendicularto the plane of the figure.
Ud.
-
.
WA
SC*.
-
.,a4
Fig. 4. Changes of the dipole moment in CF,Cl, due to C-Cl (right) and C-F (left) bond stretching8 and bendings. (I) dipole moment change due to a bond bending perpendiculerto the plane of the figure.
1979
1980
J. MOROILLO,L. J. Zmowo
and J. M. V. HXSEDIA
bending may be qualitatively explained as produced by a negative charge associated to the halogen nucleus and moving with it in the presence of other atoms more or less polarizable. The primary dipole moment created by a displacement of this charge becomes modified by the dipole moments induced in other polarizable sites of the molecule. The effect of these induced moments is to reinforce the component of the primary dipole moment directed along the line joining the moving nucleus with the polarizable atom, and to balance the component perpendicular to that direction. This fact accounts for the observed deviation of the dipole moment change, as well as for the larger effect of a bond stretching against a bond bending. On the other hand, the motion of a polarizable atom against a fixed punctual charge does create a dipole moment equivalent to that originated by the movement of a charge of opposite sign (longitudinal displacement) or alike sign (transversal displacement). For this reason, the positive charge on the carbon atom helps to bring about upon the halogen atoms an apparent negative charge much bigger in a bond stretching than in a bond bending, since the effect reported above reinforces and balances, respectively, that produced by the movement of the charge associated with the halogen atoms. For the C-H bonds, it is reasonable to assume that the charge associated with the hydrogen atom is almost null. Therefore the small changes of the dipole moment originated by a G-H stretching or bending are due, to a large extent, to second order effects which cannot be accounted for by a simplified model. After a consideration of the obtained results we must give up any theory trying to reduce the polar behaviour of bonds to their partial bond moments and their derivatives with respect to the bond distance (bond moments hypothesis). The polar behaviour of bonds is not so simple as assumed by this theory, so that, for the interpretation of i&a-red intensities, it is necessary to adopt a further approximation like the polar tensor model, used in this work, or some others that have been recently developed by several authors [12]. [12] L. A. Gmov, Intemiiy Tw Bureau, New York (1904).
for Infrared Spectra of Polyahmic Mol.ecuh.
Conmltmta