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On the sign of the dipole moment derivatives in CH3X (X = F, Cl, Br, I)
Chemical Physics 40 (1979) 385-395 0 North-Holland Publishing Company
ON THE SIGN OF THE DIPOLE MOMENT DERIVATIVES IN CH3X (X= F, Cl, Br, I)
S. ABBATE and M. GUSSONI Centro CNR di Chimicae C’himica-Fisica dei Materiali di Geneva, Nucleo di Spettroscopia. c/o Istituto di Chimica Imiusttiale de1Politecnico, Milano. Italy Received 5 January 1979; in final form 28 February 1979
It is shown in this paper that the principal methods for reducing the indeterminacy of the sign of (6,4f/SQ$ (isotropic inmechanicalcalculations,determination of (6M/6Qi) via high resolution data or the Stark effect) lead. in the case of CHSX (X=F, Cl, Br, I) molecules, to contradictory conclusions. The discrepancies are illustrated and discussed. It is also pointed out that either a Ievision of the previous results or a calculation of electro+ptical parameters on a set of chemically similar molecules including CH3X oould pwiily lead to a unique determination of the signvaliance of M, quantum
1. Introduction
Let us briefly outline the most often used methods for determination of the sign.
The intensity Ai of an absorption band due to the ith normal mode Qi in a given molecule is essentiaUy determined [l] by the square of the derivative of the dipole moment M: NOT vi
6~
At = 3~2 “i I SQi I
2
cm/mole
(N= Avogadro’s number; c = light speed in vacuum; vi = observed frequency of the ith mode; Wi= harmonic frequency of the same mode). iMf/6QJ may be then regarded as an observed quantity and may be used ’ for two main purposes [2] : (a) to derive information on the electrical behaviour of the molecule during the motion; (b) to compute electro-optical parameters useful to predict the intensities of similar molecules. Unluckily only the absolute value of SM/SQ, is known; its sign cannot be determined by eq. (1). Therefore for a molecule showing n infrared active modes, 2” different choices of signs of 16M/6Qi\.can be made when the corresponding Als are measured. A number of investigations have been carried out by several authors [3-101 on various methods intended to restrict the indetermination of the sign of SM/liQi. We wish to present in this paper a case (CH3X molecules, X = F, Cl, Br, I) where the various criteria for the choice of the sign are somewhat in contrast.
I. I. Use of infrared intensitydata under the assumption of isotopic invariance of M
In the Born-Oppenheimer approximation [ 1 I] the dipole moment of a molecule is not altered by isotopic substitution. Therefore the quantities &V/S& and SM/Sx,, defmed by:
SM!SQj= C (SM}SX,)L~~, n
are isotopic invariants provided that the quantities S, (symmetry internal displacements [12]) or xn (Cartesian displacements [12]) represent the same motion of atoms in the parent molecule (a) tid in its isotopic derivative (b) -Crawford [3] has shown that this is always the case for SM/Sx, while some complications arise for SM/SS,: even when the same St’s are chosen for (a) and @), they correspond to different displacements of the atoms due to the different Eckart conditions in (a) and in (b), respectively. Therefore:
S Abbate. M. GursonilDipole
386
where vt(b,a) = ,@ x A@a)
_
(4)
fl is the dipole moment of the molecule at equilibrium and Aopal is the rotation that would be induced in (b) if the displacements re resenting the vibration S, in (a) were applied to (b). V,Pbsa) is completely determined when i@ is known because ~~~~~~~can be easily computed [2,3] when the dynamical behaviour of (a) and (b) is known. When all the intensities of molecules (a) and (b) have been measured * one may derive SM/Sx, of (SMi S,St)(a) in all possible sign choices for (~M/I~Q$~); these quantities (the &V/X?, may need to be corrected by V,‘“,“)) are used to compute (SM/SQi)@) by the eigenvectors (Lf)@) as in eq. (2); the best sign choice is then that which provides the closest values to ]SM/SQ&~_ Because of the unavoidable uncertaintiesboth inAp) and Ajb) this criterion:: not an absolute one; yet, such as: when some quantities N
I(SMlSQi)F& - (SM/SQi)scI
z =C i
,
(5)
moment derivatives in CH3 X
.
molecule has been examined. We refer to those papers for a detailed discussion on the subject; let us only recall that the minimum indeterminacy which can be reached within a symmetry species is 2(*op) except for symmetry species containing a rotation in polar molecules; in the latter case, provided that the versds of M” is known, the indeterminacy is completely removed. 1.2. Use of other independent experimental data Another way to obtain some information on the signes of 6M/6Qj from experimental data is provided by high resolution infrared spectra. From the shape of the spectrum of two interacting rovibrational bands one can derive the sign of the intensity perturbation between the two associated normal modes Qi, Qi and therefore the relative sign of 6M/SQi with respect to SM/SQ,. (see, for instance, ref. [7]). It has also been shown that the measurement of the average dipole moment in vibrationally excited states by Stark effect may provide useful information on the signs of the 6M/6Q;s (see, for instance, ref. [16]).
or
1.3. Use of quantum mechanics calculations
or any other
Quantum mechanics provides the way of computing, in a more or less sophisticated way, several observables of a molecular system, inclu$ng M for any relative position of the atoms. Therefore
uantity which represents the deviations of iSM/SQil@ s c from ISM/SQJ$$ turn out to be higher for a sign choice up than for all others, then up should be rejected. Let us stress that the use of this method for the determination of signs does not require any other hypothesis except that of the isotopic invariance; the choice comes only from experimental data. Some authors [ 13-1.51 have already discussed the minimum indeterminacy which can be attained by this method, neglecting experimental uncertainties; also the possible use of isotopic derivatives with symmetry lower than that of the parent * Far the application of the isotopic invticx aiterion in the particular way we suggesthere, it may be not necessary that all the intensities of the two moleculesbe known; for the semnd molecule the knowledge of the sum of the intensities of overlapping bands may be suftkient. ** Nis the number of experimental data; degenerate modes are counted once.
SM/SS, = Asho {[M(Q)
-
iMol/AS,l,
(7)
tcan be computed and the signs Of 6M/6Qi can be predicted. The CNDO is the method most widely used for this purpose, after the fast paper on the subject by Segal tid Klein [17], but also other more sophisticated methods have been applied on a number of molecules (see, for instance, refs. [l&19]). While applying this method, two points should be kept in mind: (i) A& must be performed in such a way that no rotational component appears in it [20]; (ii) it may happen that the values of intensities predicted by quantum mechanical calculations are very far from the observed ones; in this case one must be cautious in relying on the prediction of signs from the same calcula’tions [9].
S Abbatc, M. QmonilDipok
I.4 Useofthe intensities of similar molecdes as a constraint
Normal coordinate calculations on large sets of molecules have shown that often the same force constants explain the vibrational behaviour of the same group of atoms in different molecules; a classical example is the force field for n-paraffms [21]. We believe that, also in the case of intensities, a set of parameters can be found which simultaneously explains the features of the spectra of several molecules containing the same groups of atoms. For this purpose quantities such as 6M/&St or &M/6x,, seem to be not completely appropriate because they give the variation of the total dipole moment; it seems more advisable to look for parameters referring to local quantities. If we write M as a sum of bond dipole moments
(& is the unit vector giving the instantaneous direction of the kth bond) one has:
moment derivatives itz CHJX
387
rigorously proven [2] starting from the isotopic invariance ofM, was used as a probe for the choice of signs. While a study only on methanes indicated +(t-) as the best sign choice, a study only on ethanes indicated ?(+ -) (- + -) and + (+ -) (- + t) as equally likely; only the overlay calculations were able to indicate +(t -)(-+-) as the best choice for ethane together with +(+ -) for methane. The + corresponds to a complete reversal of the signs of all electro-optical parameters and could be resolved neither by isotopic invariance [ 151 nor by “overlay” calculations. However, a good agreement between the values of the (SM/SS,) corresponding to our electro-optical parameters and the values of (SM/GS,) calculated by “ab initio” methods [18,19] is found if the sign ‘It” is retained for both molecules: (+ -) for CH4 and (+ -) (- + -) for C&He. In this study, therefore, no contradiction appeared between the results of different criteria for the determination of the sign; it must be noticed, however, that the experimental information came only from infrared intensities: no data from Coriolis coupling are, to our knowledge, yet available.
2. The case of CH3X molecules where the R,‘s are the vibrational coordinates. The quantities +‘, (&.rk/&~r) are usually called electro-optical parameters [22,23] and seem more appropriate for transferability [24]. A simultaneous refinement of electro-optical parameters on the intensities of a series of similar molecules (“overlay” refinement *), if correctly carried out considering all the possible sign combinations for the 6M/6Qi of all the molecules included, can drastically reduce the indeterminacy in the sign. Following this criterion we have already completed the study of a small series of molecules; the infrared intensities of nine molecules (CH4 and four deuterated derivatives, C2H6 and three deuterated derivatives) provided a set of electro-optical parameters [IO] which successfully predicted the infrared intensities of polyethylene and perdeuteropolyethylene [24]. The isotopic invariance of the electro-optical parameters, which was * The “overlay” techniqueis largelyused in force constant caIculations [21,25] and may be well appliedto intensity parameters calculations[lo]: a set of parameters the largestpart of which are common to all moleculesincluded in the calculation, is refried simultaneously on all the experimental intensities of all molecules
We have recently undertaken a similar study on the halogenated methanes starting from CH3X and CD3X (X= F, Cl, Br, I). In this case, however, we are faced with an initial difficulty: the available information on the signs (infrared intensities [26], Coriolis data [7], Stark effect [ 161, CNDO calculations [8,9]) do not lead to a common solution of the problem. We believe it is worthwhile to discuss in detail this discrepancy in hope that new investigations may give a reason for it and may lead to the “true” solution. The intensity data were taken from a paper of Russell et al. [26] and are reported in table 1. The geometries of the four molecules are reported in table 2; the internal and symmetry ccordinates and the Cartesian system are reported in fig. 1 and table 3. The force fields for CH,X and CD,X (X= Cl, Br, I) were taken from Duncan et al. [27]; that one for CH,F and CD3F from a later paper of the same school [28]. Applying the isotopic invariance criterion we have calculated the ISM/SQiI’Sof CDxX by transferring the SM/SS,lscomputed from CH3X for all the possible sign choices of SM/SQiin CHsX. The results are reported in table 4 (A, species) and table 5 (E species). As expected, a complete reversal of aB signs
S Abbate. M_ GussonilDipoIe monfent derivatives in CHgX
388
Table 1 Calculated [27,28] ww numbers (cm-‘). observed [261 intensities r&cm2jmole) and “observed” 16M/&Ql (D/Aam@*) fur methyl halides
Molecule
E
AI w
r
16iW6Ql
w --
ISMl6Ql
I-
CH3F
3024 850 0.782 1488 61 0.147 1063 9056 1.512
3131 2030 0.868 1493 591 0.323 1207 221 0.178
CD3F
2178 1020 0.121 1137 3653 0.994 1009 7393 1.332
2323 1699 0.685 1086 442 0.239 924 39 0.066
CHsCl
3075 726 0.729 1383 502 0.406 738 3167 0.746
3164 1481 1039
318 0.346 846 0.386 396 0.221
CDJCI
2201 686 0.599 1041 1046 0.509 706 2210 0.609
2349 1072 780
224 0.250 653 0.289 143 0.115
CH3Br
3084 621 0.675 1331 1069 0.582 617 1414 0.455
3184 1471 974
150 0.238 828 0.380
753 0.295
2204 503 0.512 1004 1137 0.520 582 1167 0.401
2362 1068 725
94 0.163 670 0.292 281 0.156
CH3I
3081 427 0.559 1277 1651 0.708 539 362 0.215
70 0.163 3187 1465 736 0.358 902 1012 0.329
CD31
2200 963 506
2363 1064 668
CD3 Br
345 0.425 483 0.333 196 0.154
30 0.091 596 0.275 483 0.196
in At species gives the same results; therefore only four cases instead of eight are reported_ On the contrary, all the eight possible sign choices for E species are -reported; the SMjSS,‘s transferred for each molecule ,bave obviously been corrected by the appropriate VH,D
Fig- 1. Deftition of internal coordinates and cartesian axes for methyl halides.
terms reported in table 6. Notice that, just because of the existence of nonvanishing VjHPD) in this species, up and -up are not equivalent in this case. The eigenvectors are reported in table 7; let us stress that in a discussion of sign choices the knowledge of ah details of the calculations is essential: a possible different choice of the Cartesian system, of the symmetry coordinates or even of the phase of the eigenvectors (which fLvesthe phase of the normal modes Q) from author
Table 3 Deftiition of symmetry
coordinates for CHaXand CD3X [4,26~.(k=-3sin~“cos~o/sin~o) Sl
Table 2 E@ibrium geometries (27,281 and equilibrium dipole moments [29] for methyl halides
s2
-a+
E
C&F
1.095
1.382
llOO30’
1.79
cH3cl CH3Br CH3I
1.095 1.095 1.095
1.780 1.938 2.139
lloeso’ 111020’ 111040’
1.869 1.797 1.65
3-112(rl + r2 + ra) (3k2 i- 3)-ln [kq+ P2 ;
kq+
P3)l
s3
R
4 SY S? Ss:
6-ln(2r1 - ra - ?a) 2-q?* - ?a) 6-“*(2a, - P’L - ~3) 2-q,, - a3)
Ss”
6-‘“(21%
SX
2-932
-
02 -
- P3)
03)
kol3
S Abbate, M. Gussoni/Dipole moment derivatives in CHJX
389
Table 4
Calculated16Mz/6Qil(D/A amu”*) of deuterated methyl halides for all the possible sign choices of the correspcnding hydrogenated molecule. Al species Sign choice for CH3X: CD3F
CD&l
CDsBr
I aMZlaQil~c
1 2 3 signs p!edicted for CD3F 9 r
i-i--
i--
-+-
0.381 0.948 1.183
0.726 0.720 1.272
0.742 0.912 1.169
0.397 0.756 1.287
+--
---
0.163 0.539
0.093 0.334
0.050 0.259
0.171 0.612
---
.+--
1 2 3 signs predicted for CDjCl
0.431 0.511 0.663
0.574 0.106 0.735
0.612 0.494 0.655
0.468 0.089 o-744
---
i-f-
+--
@ s
0.098 0.225
0.273 0.554
0.027 0.073
-+0.294 0.586
1 2
0.414 0.563
0.500 0.315
3 signs predicted for CDSBr
0.383
0.463
0.550 0.549 0.378
0.464 0.301 0.469
--0.072 0.160
++0.142 0.280
+-0.036 0.089
-+0.154 0.336
1 2 3 signs predicted for CD3 I
0.351 0.590 0.160
0.389 0.475 0.240
0.447 0.581 0.156
0.409 0.466 0.244
---
fi-
+--
-i--
* z
0.265 0.337
0.238 0.264
0.249 0.272
0.237 0.239
Q
z CD31
I aM*/K?ilobs
---
-.--
to author may cause a great confusion *.
From the data presented
0.727 0.994 1.332
0.599 0.509 0.609
0.512 0.520 O-401
0.425 0.333 0.154
in ?.Nes 4 and 5 we first
see that not always a given sign choice for a molecule * We wish to underline that sometimes it makes little physical sense to compare the signs of the SM/SQi; this happens when the different authors are using so different geometries and force fields (and thus so diierent eigenvectors) that the difference in sign must be regarded as a minor problem. When instead, the eigenvectors of different authors are nearly the same, with the only possible difference in phase, a comparison is possible. In the case of CH3X we have Carerully checked the choice of the Cartesiansystem, symmetry coordinates and phase of Qi; in particular we have seen that all papers on the normal coordinate on these molecules give the same desaip tion of the normal modes; we have also verified the phase relationships between our Qi’s and those of the other authors and found that the phases are the same.
corresponds to the same sign choice for the isotopic derivative of the same symmetry. The case of CH3F and CD3 F provides a particularly meaningful example: in tables 4 and 5 it can be seen that the (6M/6St)‘s computed from the (GM/SQi)‘s of CH3F in a given sign choice give sometimes (S~/SQi)‘S for CD3F with a different sign choice. In particular, in the A, species, any choice for CH3F gives (SMz/SQ2)/(SW/SQ3)> 0 in CD3 F; moreover, if the same procedure is applied from CD3F to CH3F (table 8) the quantities B and Cp
for those cases where @Nz/6Q~)(CD3F) and (Mfz/6Q3) (CD3F) have opposite signs, become ex-
S. Abbate, M. GussonifDipole momeni cierivatiires i? CH3X
390
Table 5 Calculated k%W/SQ$ (D/A amu1j2) of molecule. E species Sign choice for CH3X:
-CD3F
CD3Q
---
_.---
4 5 6 signs predicted for CD3F UJ z 4 5 6 signs predicted For CDBCl @ z
CD3Br
CD31
~_----.--_
deuterated methyl halides for all the possible sign chhoicesof the corresponding hydrogenated
-if+
--+
-EC-
--++
f--
0.594 0.139 0.268
0.696 0.224 0.106
0.630 0.206 0.002
0.732 0.292 0.160
0.591 0.254 0.083
0.693 0.168 0.246
0.183
---
+t+ 0.205
--++
0.394
0.065
--0.321 0.150
-I-+-
1.039
0.487 0.193
0.103 0.125
--++ 0.921 0.259
ii.,',, 0.230 0.07s 0.329
0.214 0.220 0.244
0.305 0.280 0.133
0.253 0.266
0.345 0.326 0.197
0.208 0.290 0.127
0.230 0.238
---
*++ 0.091
--+
d-f-
--++
0.273 0.214
0.066 0.055
0.266 0.328 0.243
0.135 0.280 0.191
0.275
---
0.086
--
-+-
i---f
0.555 0.321
0.657 0.236 0.020
0.168 0.335 0.203
0.260
0.250
0.275 0.092
0.289 0.115
*--
-+-
+--+
0.369 0.231
0.283 0.215
0.068 0.046
0.218 0.222
0.087 0.335 0.246
0.169 0.276 0.163
-+0.253 0.210
-I---+
0.107 0.263 0.200
0.299
0.082
0.091 0.055
4 5 6 signs predicted for CD3Br @ z
0.135 0.215 0.278
0.217 0.274 0.195
0.183 0.270 0.159
---
+++
--•+
++-
-i-i
+--
0.282 0.229
0.141 0.112
0.049
0.286 0.227
0.105 0.074
0.291
4 5 6 signs predicted for CD31 * z
0.084 0.205 0.288
0.154 0.255 0.223
0.134 0.258 0.198
0.204 0.309 0.264
0.069 0.260 0.220
0.158 0.210 0.286
0.038 0.313 0.265
---
+++
--•+
++-
-++
+--
-f-
t-i
0.180
0.232 0.108
0.158 0.061
0.429
0.047 0.043
0.300 0.222
0.232 0.162
0.060 0.032
0.169
tremely large. This happens because Qs(CH3F)
0.215
0.066
+-+
0.386 0.233
0.046
0.685 0.239
0.245
0.163 0.292 0.156
0.027 0.029 0.091
0.275 0.196
almost coincides with S,, while both Q?(CD,F) and &3(CD3F) are mostly determined by S3 (see table 7); moreover, (SMz/SQ3)(CH3F) is large and leads to a large value
results of all choices in molecule (b) 1261: indeed the only comparison of qauntities coming from the same
of @W/SS3);
performed using the total dipole moment values reported in table 2
therefore t5e signs of (SMZ/SQ2)
(CD3F) and (SMzlSQ3)(~!I13F) are conipletely determined by the choice of sign of (&W/SQ3) (CH, F). We
felt necessary to discuss in detail this particular feature, since often the isotopic invariance criterion is applied by comparing @M/G,) [or (Mfkix,)] derived separately for molecules (a) and (b) in any sign assumption The latter procedure is correct only if the results for a given choice in molecule (a) are compared with the
Table 6 v&b for a = CH3X and b = CD3Xi The calculations have been
ii Br I
V,x(D/N
VsAD/rad)
0.032 0.036 0.036 0.031
0.041 0.037 0.033 0.028
V&Dlrad) -0.112 -0.076 -0.058 -0.045
S. .&bate. M. GftssoJIi/LJipo!e JizoJJ~eJll
defiVnfiVeS
in
391
ctf3x
Table 7
Eigenvectorsfor CHaX and CDaX
PI k
s1 St s3
Cl
S,
Q3
91
_____-___~~--
1.005 0.0087 -0.004 -0.212 1.367 0.194 -0.050 0.068 0.359
Q2
0.717 0.078 -0.024 S;: -0.251 0.994 -0.324 SJ -0.081 0.241 0.267 S;
Q,”
Q_:
Qf
P3
1.051 0.013 -0.017 0.120 1.499 -0.181 -0.103 0.282 0.952
Q:
Q-:
Q,"
0.780 -0.006 0.003 0.198 1.097 0.064 -0.156 0.021 0.747
0.001 0.721 0.003 0.009 S,r 0.168 -0.133 1.060 0.021 S: 0.321 -0.066 0.149 0.292 s;
0.113 1.499 -0.101 0.314
-0.222 0.906
0.192 1.100 -0.085 -0.137 0.135 0.693
s3
1.007 -0.056 -0.041
-0.024 1.366 0.094
0.000 0.139 0.292
1.051 0.024 0.109 1.513 -0.090 0.282
-0.007 -0.176 0.907
0.781 0.190 -0.124
SZ Sl
-0.003 1.006
-0.040 1.358
S3
-0.039
0.091
s3
Sr s2
I
Q2
CD3X
1.008 -0.012 -0.075 1.375 -0.044 0.084
s2
Br
-~ CHsX
CD3X
CHaX
0.720 -0.112 -0.061
-0.008 1.052 0.149
0.006 0.029 0.265
S4” sz Ss”
0.000 0.130
_::;;‘:
-;:“024:
“,:g:
::
A::;:
0.283
-0.057
0.148
0.257
S;
-0.074
sign choice might lead to neglect some acceptable soiutions. Notice that the application of the isotopic invariance criterion as illustrated in this paper, namely via comparison of ISM/SQ$& with ISM/SQ&~ is free from this danger, at least as far as the experimental uncertainties are not too large. In tables 4,s and 8 the acceptability of a sign
choice according to isotopic invariance is rationalized in terms of Z [eq. (5)] and CD[eq. (6)] _The latter quantity seems to be more meaningful because it accounts also for the relative order of magnitude of the various (gJ@Qi)‘s; however, a quantity similar to Z has been used by other authors [S] in a comparison of the various @M/&x,,) computed with different sign choices. In some particular cases (such, for instance, when looking for a starting set of electrooptical parameters to be refined on the intensities of a series of molecules) it may be useful to know the average error over all the symmetry species; for the case of CH3X we have*: * This defiition 0 = (qj
1.051 0.020
‘r + nari+)“2 1@ 1
0.269
1::::: 0.905
::::: -0.107
0.000
0.010
0.003 0.003 1.108 -0.065 0.121 0.683
;:“1”:: ?J::; 0.123
0.677
choice ensures that (6MZ/6Rcx) is less than zero, which seems physically more reasonable since (SW/ 6R,,) approximates the highly localized negative charge on the halogen atom [4]. The classification presented in table 9 cannot have an absolute meaning because of the uncertainties in the experimental data. Table 8 Calculated kiMr/aQ~i (D/A amulR) for CHsF in ah the possible sign choices for CDaF. At species
sign choice
forCD3F:
,
when the numbers of normal modes n rr and nr2 of species r t and ra are different. The above defiition leads to a value of z which coincides with 0 calculated from eq. (6), in which all the normal modes of the molecule are included, independently of the species.
1”:5”;;
0.181
The values of a, in increasing order, are reported in table 9 for the four molecules. Even if a sign choice and its opposite are completely equivalent in the Al species, in table 9 we report only those sign choices for Al that show a (-) sign in the third position. This
should be replaced by:
+ nr2)-r(n;
-0.001
@Is predicted forCHgF 9 L:
(---) 1.281 0.076 1.659
(++-) (+--) (-+-) 1.059 0.733 0.955 0.782 2.110 0.114 2.148 0.147 0.740 1.698 0.700 1.512
(---) (++-) (t--) (-+-) 0.268 4.449 0.087 4.534 0.716 3.012 0.260 2.986
S. Abbare, M. Gussoni/Dipolemoment derivarivesin C&X
392 Table 9 Classification of the sign choices for
CHxXaccording
to increasing values of i defied
CHaCl
CHsF
in the text
CH3Br
CHJI
A1
E
5
41
E
5
AI
E
T
Al
E
B
0.057 0.069 0.096 0.100 0.106 0.112 0.118 0.124 0.131 0.133 0.141 0.143 0.165 0.170 0.183 0.185 0.244 0.248 0.257 0.258 0.305 0.308 0.315 0.316 0.461 0.463 0.468 0.468 0.520 0.522 0.526 0.526
+-i--+-+---------+-iiii+-+i-
-++ +-i--+ +++
0.037 0.037 0.047 0.047 0.060 0.060 0.067 0.067 0.137 0.140 0.141 0.142 0.144 0.144 0.145 0.150 0.151 0.151 0.154 0.154 0.185 0.191 0.193 0.193 0.197 0.199 0.201 0.204 0.230 0.236 0.236 0.243
+-+-----+---++-
*-• --+
+++
-+++-+if+-+------f+++--+i-f-i-------+-++++++-+------i-+++----++++----
-++
c-++-+---
0.022 0.030 0.038 0.044 0.056 0.064 0.072 0.073 0.075 0.078 0.079 0.081 0.088 0.093 0.100
0.121 0.121 0.122 0.122 0.127 0.128 0.135 0.136 0.142 0.142 0.146 0.149 0.149 0.154 0.154 0.!60 0.166 0.166 0.166 0.166 0.170 0.170 0.176 0.176 0.191 0.191 0.195 0.200 0.245 0.245 0.248 0.252
f--
-++
ci---+-
-ii -++ -+*
+-+++-i-i---+---++-i-f---
++t -I-++ i---l+-+ +++ +++ -F--f i-i --•+ --+ --+
--I--
---+
+--
++-
++-
ti-
---
++-
-+-
++-
+--
-+-
ii-
-+-
---
-i-
-+-
-C-
+--
+--
+-I----
+--
-+-
+--
-l---
---
ii-
-_-
---
---
-t-
---
+--
-3-f +--+ --+ +i+ ++-++ +-+ -f+
i-b---
ii+
---
-+-
it-
-+-
--++
-t-
+-+
-+-
--+
-+-
+++
+--
+--
c-+-++---
i-t---
-+---
-f-
++-
++-++----
-+-
f--
--it-
-+++-
-f-
However, at least one piece of information turns out with a fair certainty, namely the refusal of the (-) sign in the third position of the E species. This refusal originates from the important role played by VrD which has a large negative value (table 6). Indeed the experimental values of (&%fx/8&$cD3x and of (W/gS6)CH 3X are connected as follows: (sl%fx/ss6)cD3x = (sMx/ss6)CH3X+ Since the i?ikfx/&s61a3x than
i+lD .
arc systematically
-*++-*+-i--++---+-i--++---
-I---+ --+ -++ -i-i+-+
--+ +-•+ iii--+ -ii -4-t fff +++ --+-+---
0.142
++-
0.144
-+---
+----
+--
-+---
-+-
++++-+ff-t-+-
0.104 0.128 0.131
+-k-
+---++--f-+++--
0.145 0.146
0.147 0.147 0.148 0.150 0.158 0.160 0.161 0.162 0.162 0.165
-4-f f--f i-i -++ *--I-++ t-i --+ --+ --+ --------+ ---
4-i-i -++i-+ -++++ -++++ -++-+-+-+--t+i-i-++++-
CD,X (see also the eigenvectors in table 7). At this point the most cautious conclusion one can derive is that only two signs are fairly certain: (SMz/SQ3) must be negative for physical reasons and (sMx/sQ6) must be positive for isotopic invariance; these requirements are the same for the four molecules. Therefore any solution of the type (2 + -) for the A, species and (2 f +) for the E species should be acceptable.
w&r
the corresponding]bMX/6S61CH3X (see table lo), the above condition is fulfilled onIy for positive (sM”/ss~)CD3X and (&%fx/ss6)cH3x; this corresponds to the (+) choice in @&fx/SQ6) both in CH,X and in
2.1. Methylfluoride Laboda and Overend [16] have found, from the measurements of the average value of the dipole moment
S. Abbnte. M Gussoni/Dipole
393
moment derivatives in CHs X
Table 10 Experimental values of (6MZ/6Sg) from the intensities of E bands for the CHJF and CD3F in the same sign choice.
@/Iad)
-
----_--c++-)
(-++I
(+--I
c-+-j
(+-+I
-0.129 -0.110
0.207 0.073
-0.207 -0.073
-0.154 -0.066
0.154 0.066
-0.293 -0.200
-0.171 -0.126
0.171 0.126
(----I
c+++>
CH3F CD3F
-0.233 -0.066
0.233 0.066
(--+I _--0.129 0.110
CH3CI CD3Cl
-0.291 -0.192
0.291 0.192
0.173 0.135
-0.173 -0.135
0.293 0.200
CHsBr CDsBr
-0.362 -0.249
0.362 0.249
0161 0.201
-0.267
0.360
-0.360
-0.201
0.251
-0.251
-0.268 -0.199
CH31 CDs1
-0.395 -0.312
0.395 0.312
0.312 0.262
-0.312 -0.262
0.390 0.309
-0.390 -0.309
-0.317 -0.264
of CH,F in excited vibrational states, that (SMz/SQ1) should be positive, (SMz/SQ2) should be negative and that (SMZ/SQ3) must certainly be negative; the latter result gives an experimental support to the physical requirement previously discussed. Therefore the more likely choice for the A1 species should be (+ - -). However, Di Laura and Miis [7] from the analysis of the rovibrational spectra of CH,F have concluded that SMZ/SQ2
SMX/S Qs
>o,
SMZISQ3
sMxb&j
>o.
01)
The contradiction between this indication and that emerging from the simultaneous use of the isotopic invariance and of Laboda’s results is particularly evident for Q3 and Q6: the acceptance of Di Laura’s prescription would lead either to a refusal of the (-) sign in (SMZ/SQ3), against Laboda’s resuit and against
isotopic
CHsCl
~M=I~Q~
6.W6~~
exp.
0.573 ‘0.782
-0.230 * 0.147
-0.920 51.512
CNDO exp.
-0.302
to.729
+ 0.406
CHaBr
CNDO exp.
0.247 +-0.675
-0.241 ~0.582
0.591
0.199 0.317 0.264
invariance criterion would come out to be SO
CNDOfor C&F [81,CH3Cl
--
6W/6Ql CNDO
0.268
weak that any indication emerging from it would be unusable. Newton and Person [S], among the 64 possible sign choices for CH3 F, have discarded all those which do not obey eq. (11); among the remaining 16 choices, they have discarded those for which the (SM/Sx,) turned out to be rather dissimilar in CH,F and CD,F, thus 8 choices were left and 7 of them were discarded because they did not agree with the results of a CNDO calculation. The final choice turned out to be (t - -) (+ - -), which is strongly unfavoured by isotopic
[8], CHsBr [9]; the ekenvectors used are reported in table 7 ~_______ -_~--
’
physical feeling, or to a refusal of the (+) sign in (SMx/SQ6)_ However, let us stress that acceptance of a (-) sign in the third position of the E species does contradict strongly isotopic invariance; indeed all four molecules give the same indication. Therefore, if a (-)_ sign turned out to be the true one for (SW/SQ6), the
Table 1 I Comparison of the experimental values of (6ilf/6Qi) with those calculated from the (6M/6Sr) given by
CH3F
The units ye
@W6Qs
sMJ’l&Qs
0.822 +-0.868
-0.092 =0.323
-0.382 kO.178
0.115 kO.746
0.725 +-0.346
-0.120 iO.386
-0.009 io.221
1.230 +0.450
0.216 f 0.238
-0.312 f 0.380
0.977 zo.295
&MY/&Q4
394
S. Abbate. M. Gllssoni/DipoIe moment derivatives in CH3X
invariance (see table 9), but agrees with Laboda, with Di Laura and with CNDO results (see table 11). 2.2. Methyl chloricle Di Laura and Mills [7] from a study on CD3& again predict (12) but give no indication on Q3 and Q6. Thus no contradiction appears with isotopic invariance results: the second row as well as many other choices with low (3 in table 9 agree with their result. Newton and Person [S] assume that requirements (11) for methyl fluoride are both validalso for methyl chloride; thus the choice of signs is operated in a way similar to that for fluorine, even if the CNDO results do not agree with the choice (+ - -) (+ - -) which is the one they retain also for chlorine (see table 11). 2.3. Methv! bromide To our knowledge, no experimental data other than infrared intensities are available. A recent paper by van Straten and Smit [9] reports on a CNDO result indicating (+ - +) (+ - +); however, the authors believe that an error in the parametrizationof CNDO for the third-row atoms is responsible for the positive sign of (SMz/SQs) and they accept the choice (+ - -) (+ -+). as the most likely (see table 11). 24. Methyl iodide To our knowledge, no other experimental data or calculation are available, except the paper by Newton and Person [8] which extends also to bromine and iodine the same choice as for fluorine, namely (+--)(+--).
3. Conclusions It seems that two kinds of results contradict the indications of isotopic invariance, namely CNDO calculations (F, Cl, Br) and the study of the Coriolis coupling (F only). As for CNDO, we believe that the disagreement between the experimental values of intensities
and those predicted by CNDO are too large for these molec’ules to justify an acceptance of the prediction of CNDO even for the signs of dipole moment derivatives. As an illustration of this pessimistic statement we report in table 11 the values of the (SM/SQ& predicted by CNDO for CH3F [8], CH3Cl [S] and CH3Br [9] together with the corresponding experimental quantities. We believe that more sophisticated quantum mechardcal calculations, or a new parametrization of CNDO, could yield more realistic prediction of the intensities and therefore a more reliable indication of the signs. Notice that in our previous study on u-paraffins [lo] we found that ab initio predictions were closer to experimental values than those from CNDO, even though in CH, and C,H, the calculated CNDO signs did coincide with those predicted by “ab initio” methods. As for the results from rovibrational spectra we are still very puzzled. We notice that the indications of the signs of (SMz/SQ3) and (SM-‘/SQ6) presented in this paper from isotopic invariance are common to all four molecules, while the ratio (SMz/SQ3)/(SMx/SQ6) was experimentally determined only for CH3F. At the present stage of intensity studies we think that the acceptance or refusal of the results of isotopic invariance must wait for some additional experimental studies on the Coriolis or Stark effects. Another possible source of information on the signs of (SAf/SQ$ in CH3X comes from “overlay” calculations of electro-optical parameters on two sets of molecules for which the observed infrared intensities are available; (CH3F, CH3F2, CHF3, CF4), (CH,Cl, CH2C12, CHCl,, Ccl,). We are presently studying these two series of molecules, together with CH4, in hope of finding “one” set of electro-optical parameters for each series.
References. [I] J. Overend, in: Infrared Spec!ra and MolecuIar Structure, ed. hl. Davies (EIsevier, Amsterdam, 1963). [2] M. Cursoni and S. Abbate, J. Chem. Phys. 65 (1975) 3439_ [3] B. Crawford, .I. Chem. Phys. 20 (1952) 977. [4] A.J. Dickson, LM. MiIIs and B. Crawford, J. Chem. Phys. 27 (1957) 445. [5] J.F. Biarge, I. Heand J. MorciIIo, Anales de Fis. Quim. 157 (1961) 81. [6] J. Heicklen, Spectrochim. Acta 17 (1961) 201. [7] C. Di Laura and IX Mills, J. hfol. Spectry. 21 (1966) 386. [S] J.H. Newton and W-B. Person,J. Chem. Phys. 64 (1976)
3036.
S. Abbate. M. GussonilDipole [9] A.J. Van Straten and M.A. Smit. J. Chem. Phys. 67 (1977) 970. ]lO] M. Cussoni, S. Abbate and G. Zerbi, I. Chem. Phys., to be published. [ll] hf. Bornand R. Oppenheimer, Ann. Phys. 20 (1927)457. [12] E.B. Wilson, J.C. Dechrs and P.C. Cross, Molecular Vilxations (MC Craw-Hill, New York, 1955). [13] V.T. Aleksanyan and S.Kh.Samvelyian, I. Mol. Spectry. 4.5 (1973) 79. 1141 S.Kh. Samvelyain and V.T. Aleksanyan, Opt. Spectry. 39 (1975) 612. [15] S. Abbate and M. Gussoni, to be published. [16] M.L. Laboda and J. Overend, Spectrochim. Acta 32A (1976) 1033. [17] GA. SegaIand M.L. Klein, J. Chem. Phys. 47 (1967) 4236. [18] W. Meyer and P. Puiay, J. Chem. Phys. 56 (1972) 2109. [19] G. Jalsowsky and P. Pulay, J. hlol. Struct. 26 (1975) 277. [ZO] C. Cussoni and S. Abbate, J. hfol. Spectry. 62 (1976) 53.
moment dq-ivatives in CHOX
395
[21] R.C. Snyder, J. Chem. Phys. 47 (1967) 1316. [22] L.A. Gribov, Intensity theory for infrared spectra of polyatomic molecules (Consulfants’ Bureau, New York, 1964). [23] L.M. Sverdlov, M.A. Kovner and E.P. Krainov, Vibrational spectra of polyatomic molecules (Wiley, New York, 1964). j24) S. Abbate, M. Gussoni, G. Masetti and G. Zerbi, J. Chem. Phys. 67 (1977) 1519. [25] I. Overend and J.R. Scherer, I. Chem. Phys. 33 (1960) 446. [26] J.W. Russell, C.D. Needham and J. Overend, J. Chem. Phys. 45 (1966) 3383. [27] J.L. Duncan, A. ABan and DC. MC Kean, Mol. Phys. 18 (1970) 289. [28] J-L. Duncan, DC. MC Kean and G.K. Speirs, Mot. Phys. 24 (1972) 553. [29] C.H. Townes and A.L. Schawlow, Microwave spectroscopy (MC Graw-Hill, New York, 1955).
ON THE SIGN OF THE DIPOLE MOMENT DERIVATIVES IN CH3X (X= F, Cl, Br, I)
S. ABBATE and M. GUSSONI Centro CNR di Chimicae C’himica-Fisica dei Materiali di Geneva, Nucleo di Spettroscopia. c/o Istituto di Chimica Imiusttiale de1Politecnico, Milano. Italy Received 5 January 1979; in final form 28 February 1979
It is shown in this paper that the principal methods for reducing the indeterminacy of the sign of (6,4f/SQ$ (isotropic inmechanicalcalculations,determination of (6M/6Qi) via high resolution data or the Stark effect) lead. in the case of CHSX (X=F, Cl, Br, I) molecules, to contradictory conclusions. The discrepancies are illustrated and discussed. It is also pointed out that either a Ievision of the previous results or a calculation of electro+ptical parameters on a set of chemically similar molecules including CH3X oould pwiily lead to a unique determination of the signvaliance of M, quantum
1. Introduction
Let us briefly outline the most often used methods for determination of the sign.
The intensity Ai of an absorption band due to the ith normal mode Qi in a given molecule is essentiaUy determined [l] by the square of the derivative of the dipole moment M: NOT vi
6~
At = 3~2 “i I SQi I
2
cm/mole
(N= Avogadro’s number; c = light speed in vacuum; vi = observed frequency of the ith mode; Wi= harmonic frequency of the same mode). iMf/6QJ may be then regarded as an observed quantity and may be used ’ for two main purposes [2] : (a) to derive information on the electrical behaviour of the molecule during the motion; (b) to compute electro-optical parameters useful to predict the intensities of similar molecules. Unluckily only the absolute value of SM/SQ, is known; its sign cannot be determined by eq. (1). Therefore for a molecule showing n infrared active modes, 2” different choices of signs of 16M/6Qi\.can be made when the corresponding Als are measured. A number of investigations have been carried out by several authors [3-101 on various methods intended to restrict the indetermination of the sign of SM/liQi. We wish to present in this paper a case (CH3X molecules, X = F, Cl, Br, I) where the various criteria for the choice of the sign are somewhat in contrast.
I. I. Use of infrared intensitydata under the assumption of isotopic invariance of M
In the Born-Oppenheimer approximation [ 1 I] the dipole moment of a molecule is not altered by isotopic substitution. Therefore the quantities &V/S& and SM/Sx,, defmed by:
SM!SQj= C (SM}SX,)L~~, n
are isotopic invariants provided that the quantities S, (symmetry internal displacements [12]) or xn (Cartesian displacements [12]) represent the same motion of atoms in the parent molecule (a) tid in its isotopic derivative (b) -Crawford [3] has shown that this is always the case for SM/Sx, while some complications arise for SM/SS,: even when the same St’s are chosen for (a) and @), they correspond to different displacements of the atoms due to the different Eckart conditions in (a) and in (b), respectively. Therefore:
S Abbate. M. GursonilDipole
386
where vt(b,a) = ,@ x A@a)
_
(4)
fl is the dipole moment of the molecule at equilibrium and Aopal is the rotation that would be induced in (b) if the displacements re resenting the vibration S, in (a) were applied to (b). V,Pbsa) is completely determined when i@ is known because ~~~~~~~can be easily computed [2,3] when the dynamical behaviour of (a) and (b) is known. When all the intensities of molecules (a) and (b) have been measured * one may derive SM/Sx, of (SMi S,St)(a) in all possible sign choices for (~M/I~Q$~); these quantities (the &V/X?, may need to be corrected by V,‘“,“)) are used to compute (SM/SQi)@) by the eigenvectors (Lf)@) as in eq. (2); the best sign choice is then that which provides the closest values to ]SM/SQ&~_ Because of the unavoidable uncertaintiesboth inAp) and Ajb) this criterion:: not an absolute one; yet, such as: when some quantities N
I(SMlSQi)F& - (SM/SQi)scI
z =C i
,
(5)
moment derivatives in CH3 X
.
molecule has been examined. We refer to those papers for a detailed discussion on the subject; let us only recall that the minimum indeterminacy which can be reached within a symmetry species is 2(*op) except for symmetry species containing a rotation in polar molecules; in the latter case, provided that the versds of M” is known, the indeterminacy is completely removed. 1.2. Use of other independent experimental data Another way to obtain some information on the signes of 6M/6Qj from experimental data is provided by high resolution infrared spectra. From the shape of the spectrum of two interacting rovibrational bands one can derive the sign of the intensity perturbation between the two associated normal modes Qi, Qi and therefore the relative sign of 6M/SQi with respect to SM/SQ,. (see, for instance, ref. [7]). It has also been shown that the measurement of the average dipole moment in vibrationally excited states by Stark effect may provide useful information on the signs of the 6M/6Q;s (see, for instance, ref. [16]).
or
1.3. Use of quantum mechanics calculations
or any other
Quantum mechanics provides the way of computing, in a more or less sophisticated way, several observables of a molecular system, inclu$ng M for any relative position of the atoms. Therefore
uantity which represents the deviations of iSM/SQil@ s c from ISM/SQJ$$ turn out to be higher for a sign choice up than for all others, then up should be rejected. Let us stress that the use of this method for the determination of signs does not require any other hypothesis except that of the isotopic invariance; the choice comes only from experimental data. Some authors [ 13-1.51 have already discussed the minimum indeterminacy which can be attained by this method, neglecting experimental uncertainties; also the possible use of isotopic derivatives with symmetry lower than that of the parent * Far the application of the isotopic invticx aiterion in the particular way we suggesthere, it may be not necessary that all the intensities of the two moleculesbe known; for the semnd molecule the knowledge of the sum of the intensities of overlapping bands may be suftkient. ** Nis the number of experimental data; degenerate modes are counted once.
SM/SS, = Asho {[M(Q)
-
iMol/AS,l,
(7)
tcan be computed and the signs Of 6M/6Qi can be predicted. The CNDO is the method most widely used for this purpose, after the fast paper on the subject by Segal tid Klein [17], but also other more sophisticated methods have been applied on a number of molecules (see, for instance, refs. [l&19]). While applying this method, two points should be kept in mind: (i) A& must be performed in such a way that no rotational component appears in it [20]; (ii) it may happen that the values of intensities predicted by quantum mechanical calculations are very far from the observed ones; in this case one must be cautious in relying on the prediction of signs from the same calcula’tions [9].
S Abbatc, M. QmonilDipok
I.4 Useofthe intensities of similar molecdes as a constraint
Normal coordinate calculations on large sets of molecules have shown that often the same force constants explain the vibrational behaviour of the same group of atoms in different molecules; a classical example is the force field for n-paraffms [21]. We believe that, also in the case of intensities, a set of parameters can be found which simultaneously explains the features of the spectra of several molecules containing the same groups of atoms. For this purpose quantities such as 6M/&St or &M/6x,, seem to be not completely appropriate because they give the variation of the total dipole moment; it seems more advisable to look for parameters referring to local quantities. If we write M as a sum of bond dipole moments
(& is the unit vector giving the instantaneous direction of the kth bond) one has:
moment derivatives itz CHJX
387
rigorously proven [2] starting from the isotopic invariance ofM, was used as a probe for the choice of signs. While a study only on methanes indicated +(t-) as the best sign choice, a study only on ethanes indicated ?(+ -) (- + -) and + (+ -) (- + t) as equally likely; only the overlay calculations were able to indicate +(t -)(-+-) as the best choice for ethane together with +(+ -) for methane. The + corresponds to a complete reversal of the signs of all electro-optical parameters and could be resolved neither by isotopic invariance [ 151 nor by “overlay” calculations. However, a good agreement between the values of the (SM/SS,) corresponding to our electro-optical parameters and the values of (SM/GS,) calculated by “ab initio” methods [18,19] is found if the sign ‘It” is retained for both molecules: (+ -) for CH4 and (+ -) (- + -) for C&He. In this study, therefore, no contradiction appeared between the results of different criteria for the determination of the sign; it must be noticed, however, that the experimental information came only from infrared intensities: no data from Coriolis coupling are, to our knowledge, yet available.
2. The case of CH3X molecules where the R,‘s are the vibrational coordinates. The quantities +‘, (&.rk/&~r) are usually called electro-optical parameters [22,23] and seem more appropriate for transferability [24]. A simultaneous refinement of electro-optical parameters on the intensities of a series of similar molecules (“overlay” refinement *), if correctly carried out considering all the possible sign combinations for the 6M/6Qi of all the molecules included, can drastically reduce the indeterminacy in the sign. Following this criterion we have already completed the study of a small series of molecules; the infrared intensities of nine molecules (CH4 and four deuterated derivatives, C2H6 and three deuterated derivatives) provided a set of electro-optical parameters [IO] which successfully predicted the infrared intensities of polyethylene and perdeuteropolyethylene [24]. The isotopic invariance of the electro-optical parameters, which was * The “overlay” techniqueis largelyused in force constant caIculations [21,25] and may be well appliedto intensity parameters calculations[lo]: a set of parameters the largestpart of which are common to all moleculesincluded in the calculation, is refried simultaneously on all the experimental intensities of all molecules
We have recently undertaken a similar study on the halogenated methanes starting from CH3X and CD3X (X= F, Cl, Br, I). In this case, however, we are faced with an initial difficulty: the available information on the signs (infrared intensities [26], Coriolis data [7], Stark effect [ 161, CNDO calculations [8,9]) do not lead to a common solution of the problem. We believe it is worthwhile to discuss in detail this discrepancy in hope that new investigations may give a reason for it and may lead to the “true” solution. The intensity data were taken from a paper of Russell et al. [26] and are reported in table 1. The geometries of the four molecules are reported in table 2; the internal and symmetry ccordinates and the Cartesian system are reported in fig. 1 and table 3. The force fields for CH,X and CD,X (X= Cl, Br, I) were taken from Duncan et al. [27]; that one for CH,F and CD3F from a later paper of the same school [28]. Applying the isotopic invariance criterion we have calculated the ISM/SQiI’Sof CDxX by transferring the SM/SS,lscomputed from CH3X for all the possible sign choices of SM/SQiin CHsX. The results are reported in table 4 (A, species) and table 5 (E species). As expected, a complete reversal of aB signs
S Abbate. M_ GussonilDipoIe monfent derivatives in CHgX
388
Table 1 Calculated [27,28] ww numbers (cm-‘). observed [261 intensities r&cm2jmole) and “observed” 16M/&Ql (D/Aam@*) fur methyl halides
Molecule
E
AI w
r
16iW6Ql
w --
ISMl6Ql
I-
CH3F
3024 850 0.782 1488 61 0.147 1063 9056 1.512
3131 2030 0.868 1493 591 0.323 1207 221 0.178
CD3F
2178 1020 0.121 1137 3653 0.994 1009 7393 1.332
2323 1699 0.685 1086 442 0.239 924 39 0.066
CHsCl
3075 726 0.729 1383 502 0.406 738 3167 0.746
3164 1481 1039
318 0.346 846 0.386 396 0.221
CDJCI
2201 686 0.599 1041 1046 0.509 706 2210 0.609
2349 1072 780
224 0.250 653 0.289 143 0.115
CH3Br
3084 621 0.675 1331 1069 0.582 617 1414 0.455
3184 1471 974
150 0.238 828 0.380
753 0.295
2204 503 0.512 1004 1137 0.520 582 1167 0.401
2362 1068 725
94 0.163 670 0.292 281 0.156
CH3I
3081 427 0.559 1277 1651 0.708 539 362 0.215
70 0.163 3187 1465 736 0.358 902 1012 0.329
CD31
2200 963 506
2363 1064 668
CD3 Br
345 0.425 483 0.333 196 0.154
30 0.091 596 0.275 483 0.196
in At species gives the same results; therefore only four cases instead of eight are reported_ On the contrary, all the eight possible sign choices for E species are -reported; the SMjSS,‘s transferred for each molecule ,bave obviously been corrected by the appropriate VH,D
Fig- 1. Deftition of internal coordinates and cartesian axes for methyl halides.
terms reported in table 6. Notice that, just because of the existence of nonvanishing VjHPD) in this species, up and -up are not equivalent in this case. The eigenvectors are reported in table 7; let us stress that in a discussion of sign choices the knowledge of ah details of the calculations is essential: a possible different choice of the Cartesian system, of the symmetry coordinates or even of the phase of the eigenvectors (which fLvesthe phase of the normal modes Q) from author
Table 3 Deftiition of symmetry
coordinates for CHaXand CD3X [4,26~.(k=-3sin~“cos~o/sin~o) Sl
Table 2 E@ibrium geometries (27,281 and equilibrium dipole moments [29] for methyl halides
s2
-a+
E
C&F
1.095
1.382
llOO30’
1.79
cH3cl CH3Br CH3I
1.095 1.095 1.095
1.780 1.938 2.139
lloeso’ 111020’ 111040’
1.869 1.797 1.65
3-112(rl + r2 + ra) (3k2 i- 3)-ln [kq+ P2 ;
kq+
P3)l
s3
R
4 SY S? Ss:
6-ln(2r1 - ra - ?a) 2-q?* - ?a) 6-“*(2a, - P’L - ~3) 2-q,, - a3)
Ss”
6-‘“(21%
SX
2-932
-
02 -
- P3)
03)
kol3
S Abbate, M. Gussoni/Dipole moment derivatives in CHJX
389
Table 4
Calculated16Mz/6Qil(D/A amu”*) of deuterated methyl halides for all the possible sign choices of the correspcnding hydrogenated molecule. Al species Sign choice for CH3X: CD3F
CD&l
CDsBr
I aMZlaQil~c
1 2 3 signs p!edicted for CD3F 9 r
i-i--
i--
-+-
0.381 0.948 1.183
0.726 0.720 1.272
0.742 0.912 1.169
0.397 0.756 1.287
+--
---
0.163 0.539
0.093 0.334
0.050 0.259
0.171 0.612
---
.+--
1 2 3 signs predicted for CDjCl
0.431 0.511 0.663
0.574 0.106 0.735
0.612 0.494 0.655
0.468 0.089 o-744
---
i-f-
+--
@ s
0.098 0.225
0.273 0.554
0.027 0.073
-+0.294 0.586
1 2
0.414 0.563
0.500 0.315
3 signs predicted for CDSBr
0.383
0.463
0.550 0.549 0.378
0.464 0.301 0.469
--0.072 0.160
++0.142 0.280
+-0.036 0.089
-+0.154 0.336
1 2 3 signs predicted for CD3 I
0.351 0.590 0.160
0.389 0.475 0.240
0.447 0.581 0.156
0.409 0.466 0.244
---
fi-
+--
-i--
* z
0.265 0.337
0.238 0.264
0.249 0.272
0.237 0.239
Q
z CD31
I aM*/K?ilobs
---
-.--
to author may cause a great confusion *.
From the data presented
0.727 0.994 1.332
0.599 0.509 0.609
0.512 0.520 O-401
0.425 0.333 0.154
in ?.Nes 4 and 5 we first
see that not always a given sign choice for a molecule * We wish to underline that sometimes it makes little physical sense to compare the signs of the SM/SQi; this happens when the different authors are using so different geometries and force fields (and thus so diierent eigenvectors) that the difference in sign must be regarded as a minor problem. When instead, the eigenvectors of different authors are nearly the same, with the only possible difference in phase, a comparison is possible. In the case of CH3X we have Carerully checked the choice of the Cartesiansystem, symmetry coordinates and phase of Qi; in particular we have seen that all papers on the normal coordinate on these molecules give the same desaip tion of the normal modes; we have also verified the phase relationships between our Qi’s and those of the other authors and found that the phases are the same.
corresponds to the same sign choice for the isotopic derivative of the same symmetry. The case of CH3F and CD3 F provides a particularly meaningful example: in tables 4 and 5 it can be seen that the (6M/6St)‘s computed from the (GM/SQi)‘s of CH3F in a given sign choice give sometimes (S~/SQi)‘S for CD3F with a different sign choice. In particular, in the A, species, any choice for CH3F gives (SMz/SQ2)/(SW/SQ3)> 0 in CD3 F; moreover, if the same procedure is applied from CD3F to CH3F (table 8) the quantities B and Cp
for those cases where @Nz/6Q~)(CD3F) and (Mfz/6Q3) (CD3F) have opposite signs, become ex-
S. Abbate, M. GussonifDipole momeni cierivatiires i? CH3X
390
Table 5 Calculated k%W/SQ$ (D/A amu1j2) of molecule. E species Sign choice for CH3X:
-CD3F
CD3Q
---
_.---
4 5 6 signs predicted for CD3F UJ z 4 5 6 signs predicted For CDBCl @ z
CD3Br
CD31
~_----.--_
deuterated methyl halides for all the possible sign chhoicesof the corresponding hydrogenated
-if+
--+
-EC-
--++
f--
0.594 0.139 0.268
0.696 0.224 0.106
0.630 0.206 0.002
0.732 0.292 0.160
0.591 0.254 0.083
0.693 0.168 0.246
0.183
---
+t+ 0.205
--++
0.394
0.065
--0.321 0.150
-I-+-
1.039
0.487 0.193
0.103 0.125
--++ 0.921 0.259
ii.,',, 0.230 0.07s 0.329
0.214 0.220 0.244
0.305 0.280 0.133
0.253 0.266
0.345 0.326 0.197
0.208 0.290 0.127
0.230 0.238
---
*++ 0.091
--+
d-f-
--++
0.273 0.214
0.066 0.055
0.266 0.328 0.243
0.135 0.280 0.191
0.275
---
0.086
--
-+-
i---f
0.555 0.321
0.657 0.236 0.020
0.168 0.335 0.203
0.260
0.250
0.275 0.092
0.289 0.115
*--
-+-
+--+
0.369 0.231
0.283 0.215
0.068 0.046
0.218 0.222
0.087 0.335 0.246
0.169 0.276 0.163
-+0.253 0.210
-I---+
0.107 0.263 0.200
0.299
0.082
0.091 0.055
4 5 6 signs predicted for CD3Br @ z
0.135 0.215 0.278
0.217 0.274 0.195
0.183 0.270 0.159
---
+++
--•+
++-
-i-i
+--
0.282 0.229
0.141 0.112
0.049
0.286 0.227
0.105 0.074
0.291
4 5 6 signs predicted for CD31 * z
0.084 0.205 0.288
0.154 0.255 0.223
0.134 0.258 0.198
0.204 0.309 0.264
0.069 0.260 0.220
0.158 0.210 0.286
0.038 0.313 0.265
---
+++
--•+
++-
-++
+--
-f-
t-i
0.180
0.232 0.108
0.158 0.061
0.429
0.047 0.043
0.300 0.222
0.232 0.162
0.060 0.032
0.169
tremely large. This happens because Qs(CH3F)
0.215
0.066
+-+
0.386 0.233
0.046
0.685 0.239
0.245
0.163 0.292 0.156
0.027 0.029 0.091
0.275 0.196
almost coincides with S,, while both Q?(CD,F) and &3(CD3F) are mostly determined by S3 (see table 7); moreover, (SMz/SQ3)(CH3F) is large and leads to a large value
results of all choices in molecule (b) 1261: indeed the only comparison of qauntities coming from the same
of @W/SS3);
performed using the total dipole moment values reported in table 2
therefore t5e signs of (SMZ/SQ2)
(CD3F) and (SMzlSQ3)(~!I13F) are conipletely determined by the choice of sign of (&W/SQ3) (CH, F). We
felt necessary to discuss in detail this particular feature, since often the isotopic invariance criterion is applied by comparing @M/G,) [or (Mfkix,)] derived separately for molecules (a) and (b) in any sign assumption The latter procedure is correct only if the results for a given choice in molecule (a) are compared with the
Table 6 v&b for a = CH3X and b = CD3Xi The calculations have been
ii Br I
V,x(D/N
VsAD/rad)
0.032 0.036 0.036 0.031
0.041 0.037 0.033 0.028
V&Dlrad) -0.112 -0.076 -0.058 -0.045
S. .&bate. M. GftssoJIi/LJipo!e JizoJJ~eJll
defiVnfiVeS
in
391
ctf3x
Table 7
Eigenvectorsfor CHaX and CDaX
PI k
s1 St s3
Cl
S,
Q3
91
_____-___~~--
1.005 0.0087 -0.004 -0.212 1.367 0.194 -0.050 0.068 0.359
Q2
0.717 0.078 -0.024 S;: -0.251 0.994 -0.324 SJ -0.081 0.241 0.267 S;
Q,”
Q_:
Qf
P3
1.051 0.013 -0.017 0.120 1.499 -0.181 -0.103 0.282 0.952
Q:
Q-:
Q,"
0.780 -0.006 0.003 0.198 1.097 0.064 -0.156 0.021 0.747
0.001 0.721 0.003 0.009 S,r 0.168 -0.133 1.060 0.021 S: 0.321 -0.066 0.149 0.292 s;
0.113 1.499 -0.101 0.314
-0.222 0.906
0.192 1.100 -0.085 -0.137 0.135 0.693
s3
1.007 -0.056 -0.041
-0.024 1.366 0.094
0.000 0.139 0.292
1.051 0.024 0.109 1.513 -0.090 0.282
-0.007 -0.176 0.907
0.781 0.190 -0.124
SZ Sl
-0.003 1.006
-0.040 1.358
S3
-0.039
0.091
s3
Sr s2
I
Q2
CD3X
1.008 -0.012 -0.075 1.375 -0.044 0.084
s2
Br
-~ CHsX
CD3X
CHaX
0.720 -0.112 -0.061
-0.008 1.052 0.149
0.006 0.029 0.265
S4” sz Ss”
0.000 0.130
_::;;‘:
-;:“024:
“,:g:
::
A::;:
0.283
-0.057
0.148
0.257
S;
-0.074
sign choice might lead to neglect some acceptable soiutions. Notice that the application of the isotopic invariance criterion as illustrated in this paper, namely via comparison of ISM/SQ$& with ISM/SQ&~ is free from this danger, at least as far as the experimental uncertainties are not too large. In tables 4,s and 8 the acceptability of a sign
choice according to isotopic invariance is rationalized in terms of Z [eq. (5)] and CD[eq. (6)] _The latter quantity seems to be more meaningful because it accounts also for the relative order of magnitude of the various (gJ@Qi)‘s; however, a quantity similar to Z has been used by other authors [S] in a comparison of the various @M/&x,,) computed with different sign choices. In some particular cases (such, for instance, when looking for a starting set of electrooptical parameters to be refined on the intensities of a series of molecules) it may be useful to know the average error over all the symmetry species; for the case of CH3X we have*: * This defiition 0 = (qj
1.051 0.020
‘r + nari+)“2 1@ 1
0.269
1::::: 0.905
::::: -0.107
0.000
0.010
0.003 0.003 1.108 -0.065 0.121 0.683
;:“1”:: ?J::; 0.123
0.677
choice ensures that (6MZ/6Rcx) is less than zero, which seems physically more reasonable since (SW/ 6R,,) approximates the highly localized negative charge on the halogen atom [4]. The classification presented in table 9 cannot have an absolute meaning because of the uncertainties in the experimental data. Table 8 Calculated kiMr/aQ~i (D/A amulR) for CHsF in ah the possible sign choices for CDaF. At species
sign choice
forCD3F:
,
when the numbers of normal modes n rr and nr2 of species r t and ra are different. The above defiition leads to a value of z which coincides with 0 calculated from eq. (6), in which all the normal modes of the molecule are included, independently of the species.
1”:5”;;
0.181
The values of a, in increasing order, are reported in table 9 for the four molecules. Even if a sign choice and its opposite are completely equivalent in the Al species, in table 9 we report only those sign choices for Al that show a (-) sign in the third position. This
should be replaced by:
+ nr2)-r(n;
-0.001
@Is predicted forCHgF 9 L:
(---) 1.281 0.076 1.659
(++-) (+--) (-+-) 1.059 0.733 0.955 0.782 2.110 0.114 2.148 0.147 0.740 1.698 0.700 1.512
(---) (++-) (t--) (-+-) 0.268 4.449 0.087 4.534 0.716 3.012 0.260 2.986
S. Abbare, M. Gussoni/Dipolemoment derivarivesin C&X
392 Table 9 Classification of the sign choices for
CHxXaccording
to increasing values of i defied
CHaCl
CHsF
in the text
CH3Br
CHJI
A1
E
5
41
E
5
AI
E
T
Al
E
B
0.057 0.069 0.096 0.100 0.106 0.112 0.118 0.124 0.131 0.133 0.141 0.143 0.165 0.170 0.183 0.185 0.244 0.248 0.257 0.258 0.305 0.308 0.315 0.316 0.461 0.463 0.468 0.468 0.520 0.522 0.526 0.526
+-i--+-+---------+-iiii+-+i-
-++ +-i--+ +++
0.037 0.037 0.047 0.047 0.060 0.060 0.067 0.067 0.137 0.140 0.141 0.142 0.144 0.144 0.145 0.150 0.151 0.151 0.154 0.154 0.185 0.191 0.193 0.193 0.197 0.199 0.201 0.204 0.230 0.236 0.236 0.243
+-+-----+---++-
*-• --+
+++
-+++-+if+-+------f+++--+i-f-i-------+-++++++-+------i-+++----++++----
-++
c-++-+---
0.022 0.030 0.038 0.044 0.056 0.064 0.072 0.073 0.075 0.078 0.079 0.081 0.088 0.093 0.100
0.121 0.121 0.122 0.122 0.127 0.128 0.135 0.136 0.142 0.142 0.146 0.149 0.149 0.154 0.154 0.!60 0.166 0.166 0.166 0.166 0.170 0.170 0.176 0.176 0.191 0.191 0.195 0.200 0.245 0.245 0.248 0.252
f--
-++
ci---+-
-ii -++ -+*
+-+++-i-i---+---++-i-f---
++t -I-++ i---l+-+ +++ +++ -F--f i-i --•+ --+ --+
--I--
---+
+--
++-
++-
ti-
---
++-
-+-
++-
+--
-+-
ii-
-+-
---
-i-
-+-
-C-
+--
+--
+-I----
+--
-+-
+--
-l---
---
ii-
-_-
---
---
-t-
---
+--
-3-f +--+ --+ +i+ ++-++ +-+ -f+
i-b---
ii+
---
-+-
it-
-+-
--++
-t-
+-+
-+-
--+
-+-
+++
+--
+--
c-+-++---
i-t---
-+---
-f-
++-
++-++----
-+-
f--
--it-
-+++-
-f-
However, at least one piece of information turns out with a fair certainty, namely the refusal of the (-) sign in the third position of the E species. This refusal originates from the important role played by VrD which has a large negative value (table 6). Indeed the experimental values of (&%fx/8&$cD3x and of (W/gS6)CH 3X are connected as follows: (sl%fx/ss6)cD3x = (sMx/ss6)CH3X+ Since the i?ikfx/&s61a3x than
i+lD .
arc systematically
-*++-*+-i--++---+-i--++---
-I---+ --+ -++ -i-i+-+
--+ +-•+ iii--+ -ii -4-t fff +++ --+-+---
0.142
++-
0.144
-+---
+----
+--
-+---
-+-
++++-+ff-t-+-
0.104 0.128 0.131
+-k-
+---++--f-+++--
0.145 0.146
0.147 0.147 0.148 0.150 0.158 0.160 0.161 0.162 0.162 0.165
-4-f f--f i-i -++ *--I-++ t-i --+ --+ --+ --------+ ---
4-i-i -++i-+ -++++ -++++ -++-+-+-+--t+i-i-++++-
CD,X (see also the eigenvectors in table 7). At this point the most cautious conclusion one can derive is that only two signs are fairly certain: (SMz/SQ3) must be negative for physical reasons and (sMx/sQ6) must be positive for isotopic invariance; these requirements are the same for the four molecules. Therefore any solution of the type (2 + -) for the A, species and (2 f +) for the E species should be acceptable.
w&r
the corresponding]bMX/6S61CH3X (see table lo), the above condition is fulfilled onIy for positive (sM”/ss~)CD3X and (&%fx/ss6)cH3x; this corresponds to the (+) choice in @&fx/SQ6) both in CH,X and in
2.1. Methylfluoride Laboda and Overend [16] have found, from the measurements of the average value of the dipole moment
S. Abbnte. M Gussoni/Dipole
393
moment derivatives in CHs X
Table 10 Experimental values of (6MZ/6Sg) from the intensities of E bands for the CHJF and CD3F in the same sign choice.
@/Iad)
-
----_--c++-)
(-++I
(+--I
c-+-j
(+-+I
-0.129 -0.110
0.207 0.073
-0.207 -0.073
-0.154 -0.066
0.154 0.066
-0.293 -0.200
-0.171 -0.126
0.171 0.126
(----I
c+++>
CH3F CD3F
-0.233 -0.066
0.233 0.066
(--+I _--0.129 0.110
CH3CI CD3Cl
-0.291 -0.192
0.291 0.192
0.173 0.135
-0.173 -0.135
0.293 0.200
CHsBr CDsBr
-0.362 -0.249
0.362 0.249
0161 0.201
-0.267
0.360
-0.360
-0.201
0.251
-0.251
-0.268 -0.199
CH31 CDs1
-0.395 -0.312
0.395 0.312
0.312 0.262
-0.312 -0.262
0.390 0.309
-0.390 -0.309
-0.317 -0.264
of CH,F in excited vibrational states, that (SMz/SQ1) should be positive, (SMz/SQ2) should be negative and that (SMZ/SQ3) must certainly be negative; the latter result gives an experimental support to the physical requirement previously discussed. Therefore the more likely choice for the A1 species should be (+ - -). However, Di Laura and Miis [7] from the analysis of the rovibrational spectra of CH,F have concluded that SMZ/SQ2
SMX/S Qs
>o,
SMZISQ3
sMxb&j
>o.
01)
The contradiction between this indication and that emerging from the simultaneous use of the isotopic invariance and of Laboda’s results is particularly evident for Q3 and Q6: the acceptance of Di Laura’s prescription would lead either to a refusal of the (-) sign in (SMZ/SQ3), against Laboda’s resuit and against
isotopic
CHsCl
~M=I~Q~
6.W6~~
exp.
0.573 ‘0.782
-0.230 * 0.147
-0.920 51.512
CNDO exp.
-0.302
to.729
+ 0.406
CHaBr
CNDO exp.
0.247 +-0.675
-0.241 ~0.582
0.591
0.199 0.317 0.264
invariance criterion would come out to be SO
CNDOfor C&F [81,CH3Cl
--
6W/6Ql CNDO
0.268
weak that any indication emerging from it would be unusable. Newton and Person [S], among the 64 possible sign choices for CH3 F, have discarded all those which do not obey eq. (11); among the remaining 16 choices, they have discarded those for which the (SM/Sx,) turned out to be rather dissimilar in CH,F and CD,F, thus 8 choices were left and 7 of them were discarded because they did not agree with the results of a CNDO calculation. The final choice turned out to be (t - -) (+ - -), which is strongly unfavoured by isotopic
[8], CHsBr [9]; the ekenvectors used are reported in table 7 ~_______ -_~--
’
physical feeling, or to a refusal of the (+) sign in (SMx/SQ6)_ However, let us stress that acceptance of a (-) sign in the third position of the E species does contradict strongly isotopic invariance; indeed all four molecules give the same indication. Therefore, if a (-)_ sign turned out to be the true one for (SW/SQ6), the
Table 1 I Comparison of the experimental values of (6ilf/6Qi) with those calculated from the (6M/6Sr) given by
CH3F
The units ye
@W6Qs
sMJ’l&Qs
0.822 +-0.868
-0.092 =0.323
-0.382 kO.178
0.115 kO.746
0.725 +-0.346
-0.120 iO.386
-0.009 io.221
1.230 +0.450
0.216 f 0.238
-0.312 f 0.380
0.977 zo.295
&MY/&Q4
394
S. Abbate. M. Gllssoni/DipoIe moment derivatives in CH3X
invariance (see table 9), but agrees with Laboda, with Di Laura and with CNDO results (see table 11). 2.2. Methyl chloricle Di Laura and Mills [7] from a study on CD3& again predict (12) but give no indication on Q3 and Q6. Thus no contradiction appears with isotopic invariance results: the second row as well as many other choices with low (3 in table 9 agree with their result. Newton and Person [S] assume that requirements (11) for methyl fluoride are both validalso for methyl chloride; thus the choice of signs is operated in a way similar to that for fluorine, even if the CNDO results do not agree with the choice (+ - -) (+ - -) which is the one they retain also for chlorine (see table 11). 2.3. Methv! bromide To our knowledge, no experimental data other than infrared intensities are available. A recent paper by van Straten and Smit [9] reports on a CNDO result indicating (+ - +) (+ - +); however, the authors believe that an error in the parametrizationof CNDO for the third-row atoms is responsible for the positive sign of (SMz/SQs) and they accept the choice (+ - -) (+ -+). as the most likely (see table 11). 24. Methyl iodide To our knowledge, no other experimental data or calculation are available, except the paper by Newton and Person [8] which extends also to bromine and iodine the same choice as for fluorine, namely (+--)(+--).
3. Conclusions It seems that two kinds of results contradict the indications of isotopic invariance, namely CNDO calculations (F, Cl, Br) and the study of the Coriolis coupling (F only). As for CNDO, we believe that the disagreement between the experimental values of intensities
and those predicted by CNDO are too large for these molec’ules to justify an acceptance of the prediction of CNDO even for the signs of dipole moment derivatives. As an illustration of this pessimistic statement we report in table 11 the values of the (SM/SQ& predicted by CNDO for CH3F [8], CH3Cl [S] and CH3Br [9] together with the corresponding experimental quantities. We believe that more sophisticated quantum mechardcal calculations, or a new parametrization of CNDO, could yield more realistic prediction of the intensities and therefore a more reliable indication of the signs. Notice that in our previous study on u-paraffins [lo] we found that ab initio predictions were closer to experimental values than those from CNDO, even though in CH, and C,H, the calculated CNDO signs did coincide with those predicted by “ab initio” methods. As for the results from rovibrational spectra we are still very puzzled. We notice that the indications of the signs of (SMz/SQ3) and (SM-‘/SQ6) presented in this paper from isotopic invariance are common to all four molecules, while the ratio (SMz/SQ3)/(SMx/SQ6) was experimentally determined only for CH3F. At the present stage of intensity studies we think that the acceptance or refusal of the results of isotopic invariance must wait for some additional experimental studies on the Coriolis or Stark effects. Another possible source of information on the signs of (SAf/SQ$ in CH3X comes from “overlay” calculations of electro-optical parameters on two sets of molecules for which the observed infrared intensities are available; (CH3F, CH3F2, CHF3, CF4), (CH,Cl, CH2C12, CHCl,, Ccl,). We are presently studying these two series of molecules, together with CH4, in hope of finding “one” set of electro-optical parameters for each series.
References. [I] J. Overend, in: Infrared Spec!ra and MolecuIar Structure, ed. hl. Davies (EIsevier, Amsterdam, 1963). [2] M. Cursoni and S. Abbate, J. Chem. Phys. 65 (1975) 3439_ [3] B. Crawford, .I. Chem. Phys. 20 (1952) 977. [4] A.J. Dickson, LM. MiIIs and B. Crawford, J. Chem. Phys. 27 (1957) 445. [5] J.F. Biarge, I. Heand J. MorciIIo, Anales de Fis. Quim. 157 (1961) 81. [6] J. Heicklen, Spectrochim. Acta 17 (1961) 201. [7] C. Di Laura and IX Mills, J. hfol. Spectry. 21 (1966) 386. [S] J.H. Newton and W-B. Person,J. Chem. Phys. 64 (1976)
3036.
S. Abbate. M. GussonilDipole [9] A.J. Van Straten and M.A. Smit. J. Chem. Phys. 67 (1977) 970. ]lO] M. Cussoni, S. Abbate and G. Zerbi, I. Chem. Phys., to be published. [ll] hf. Bornand R. Oppenheimer, Ann. Phys. 20 (1927)457. [12] E.B. Wilson, J.C. Dechrs and P.C. Cross, Molecular Vilxations (MC Craw-Hill, New York, 1955). [13] V.T. Aleksanyan and S.Kh.Samvelyian, I. Mol. Spectry. 4.5 (1973) 79. 1141 S.Kh. Samvelyain and V.T. Aleksanyan, Opt. Spectry. 39 (1975) 612. [15] S. Abbate and M. Gussoni, to be published. [16] M.L. Laboda and J. Overend, Spectrochim. Acta 32A (1976) 1033. [17] GA. SegaIand M.L. Klein, J. Chem. Phys. 47 (1967) 4236. [18] W. Meyer and P. Puiay, J. Chem. Phys. 56 (1972) 2109. [19] G. Jalsowsky and P. Pulay, J. hlol. Struct. 26 (1975) 277. [ZO] C. Cussoni and S. Abbate, J. hfol. Spectry. 62 (1976) 53.
moment dq-ivatives in CHOX
395
[21] R.C. Snyder, J. Chem. Phys. 47 (1967) 1316. [22] L.A. Gribov, Intensity theory for infrared spectra of polyatomic molecules (Consulfants’ Bureau, New York, 1964). [23] L.M. Sverdlov, M.A. Kovner and E.P. Krainov, Vibrational spectra of polyatomic molecules (Wiley, New York, 1964). j24) S. Abbate, M. Gussoni, G. Masetti and G. Zerbi, J. Chem. Phys. 67 (1977) 1519. [25] I. Overend and J.R. Scherer, I. Chem. Phys. 33 (1960) 446. [26] J.W. Russell, C.D. Needham and J. Overend, J. Chem. Phys. 45 (1966) 3383. [27] J.L. Duncan, A. ABan and DC. MC Kean, Mol. Phys. 18 (1970) 289. [28] J-L. Duncan, DC. MC Kean and G.K. Speirs, Mot. Phys. 24 (1972) 553. [29] C.H. Townes and A.L. Schawlow, Microwave spectroscopy (MC Graw-Hill, New York, 1955).