Numerical analyses based on the F and G intensity sum rules show that recently published experimental values for the fundamental vibrational intensities of CH4, CH3D, CH2D2, CHD3, and CD4 are internally consistent within experimental errors. Effective charge values for the carbon and hydrogen atoms obtained using the intensity sums for all these isotopically related molecules are almost in exact agreement with reported values obtained from the polar tensors of CH4 and CD4. The G sum rule allows a determination of the signs of the dipole moment derivatives using the fundamental intensity sum for CH4 (or CD4) and the polar tensor values for CD4 (or CH4). © 1978 American Institute of Physics.6994147414

Bruns R.E.

De Barros Neto B.

English

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F and G intensity sum rule applications: the CH x D4−x molecules
Benício de Barros Neto and Roy E. Bruns 
 
Citation: The Journal of Chemical Physics 69, 4147 (1978); doi: 10.1063/1.437093 
View online: http://dx.doi.org/10.1063/1.437093 
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/69/9?ver=pdfcov 
Published by the AIP Publishing 
 
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F and G intensity sum rule applications: the CHx D4_ x 
molecules 
Benlcio de Barros Neto and Roy E. Bruns 
Instituto de Quimica. Universidade Estadual de Campinas. C. P. 1170. Campinas. SP. Brazil 
(Received 27 June 1978) 
Numerical analyses based on the F and G intensity sum rules show that recently published experimental 
values for the fundamental vibrational intensities of CH4• CH3D. CH2D2• CHD3• and CD4 are internally 
consistent within experimental errors. Effective charge values for the carbon and hydrogen atoms obtained 
using the intensity sums for all these isotopically related molecules are almost in exact agreement with 
reported values obtained from the polar tensors of CH4 and CD4• The G sum rule allows a determination 
of the signs of the dipole moment derivatives using the fundamental intensity sum for CH4 (or CD4) and 
the polar tensor values for CD4 (or CH4). 
In recent articlesl-. the authors have suggested that 
the F and G intensity sum rules5 allow several useful 
applications in studies involving fundamental vibrational 
intensities. Most importantly, perhaps, these rules 
serve as a check on the internal consistency of the ex-
perimental intensity results for a series of isotopically 
related molecules. Also, the G sum rule allows a de-
termination of the relative signs of the dipole moment 
derivatives of those molecules from a knowledge of the 
individual fundamental intensities of one member of 
this series and only the sum of these intensities for 
another member. Studies with these objectives can be 
accomplished without reference to the sum rules. A 
main advantage in their use, however, is a minimiza-
tion of the dependence on normal coordinate informa-
tion which contains experimental errors of varying mag-
nitudes for the different members of the isotopically re-
lated family of molecules. In this report the above-
mentioned applications are tested for the CH"D4-" mole-
cules. 
For these molecules the G intensity sum rule in terms 
of the carbon and hydrogen effective charges, ~e and 
~H' can be expressed ass (~H = ~D and mD = 2mH) 
(l/K)LA j = ~~me + (4 +x)~V2mH , 
where 2;A" me and m H are the fundamental intenSity 
sum, and the atomic masses of carbon and hydrogen. 
A graph of ~Ume against ~~ leads to G sum rule lines 
with slopes of - (4+x)/2mH and intercepts of (l/K)2;Aj> 
where K=N1T/3c2, Nand c being Advogadro's number 
and the velocity of light. 
In Table I fundamental intensity sums and their error 
limits as calculated from the data of Saeki, Mizuno, 
and Kond07 are presented for CH4, CHaD, CH2~' and 
CD.. As their data are incomplete for CHDs' the in-
tensity sum for this molecule in Table I was taken from 
Heicklen. 8 In Fig. 1, the possible ranges in the G sum 
rule lines for CH4, CHaD, CH2~' and CD., as deter-
mined by the 2:Aj values and their errors, are pre-
sented in a graph of ~~/me vs ~~. Each pair of lines 
represents the upper and lower limits for the G sum rule 
lines, the lines corresponding to the 2:Aj values in 
Table I being equidistant between the limiting lines. 
Clearly, the data of Saeki et aZ. 1 appear to be quite ac-
curate within their estimated experimental errors as 
the sets of parallel lines containing the experimentally 
allowed G sum rule lines converge quite nicely around 
~~ =0 and ~~ =0. 026 ~. 
As the effective charges are real quantities, ~~ > O. 
With this limitation the region of common overlap for 
the experimentally allowable G sum rule lines of these 
four CH"D • ..,; molecules corresponds to values of the 
effective charges within the ranges O<~e/me< 10-4 e 
and 0.0261 e2 < ~~ < O. 0265 e2 • Assuming that the G -sum 
rule line for CHDa passes tiirough the point with ~~ = 0 
and ~i = 0.0263 e2 a fundamental intensity sum of 63.6 
km mol"l is predicted for this molecule. This value is 
in excellent agreement with the intenSity sum of 60. 8 
± 1. 8 km mol"l calculated from the experimental inten-
sities reported by Heicklen. 8 Indeed the predicted val-
ue is probably too large as it reflects a sum of funda-
mental intensities which appears to be a bit too high. 
Clearly, Fig. 1 shows that although the experimentally 
permissible G sum rule lines for CHaD, CHaDa, and 
CD. show a large region of overlap, the ones for CH. 
are just barely in common with this region. A slightly 
lower value for the CH. sum would result in improved 
convergence of all G sum rule lines. 
The F sum rule also indicates that the intensity sum 
for CH. may be slightly too high. The values for the F 
sum rule invariant, 2;A/ w~, for methane and its deu-
terated derivatives are also given in Table I. These 
values were calculated using the intenSity data in Ref. 
TABLE 1. F and G sum rule results for 
methane and its deuterated analogues. a 
2:A j b 2;A/w~c 
CH, 104.0±3.0 26.4 ± O. 7 
CHaD 86.7 ± 1. 9 23.2±0.5 
CH2D2 73.2±2.2 23.1±0.6 
CHDa 60.8±1.8 24.0±0.7 
CD, 49.9±1.3 24.3 ± O. 5 
aThe intenSity values are taken from Ref. 
7 for all the molecules except for CHDa• 
for which data were taken from Ref. 8. 
The frequency values used to calculate 
the F sum rule invariant were taken 
from Ref. 9. 
J>units of km mol "I. 
"Units of 10-16 km3 morl. 
J. Chem. Phys. 69(9), 1 Nov. 1978 0021·9606178/6909-4147$01.00 © 1978 American Institute of PhysiCS 4147 
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4148 B. de Barros Neto and R. E. Bruns: F and G intensity sum rule 
-~-~-~ ~- -~ - ~ ----~----l 
10 
9 
8 
-, 
:lI 
• 7 
.. 
, 6 
Q 
eU 5 
3 
2 
2 3 
2 _ 2 2 
~H/D.IO e 
FIG. 1. Ranges due to experimental errors for the G sum ru1e 
lines of CH4, CH3D, CH2D2, and CD4• The dashed line is the 
predicted G sum ru1e line for CHD3 based on the region of in-
tersection of the experImentally permissible G sum rule lines 
for the other molecules. 
7 except for CHD3, where the data of Heicklen8 were 
used. The frequencies were taken from the book by 
Sverdlov. 9 Although all the values of LA/ w~ are in ex-
cellent agreement, the value for CH4 appears to be 
about 2 x 10-18 km3 mol-1 too high when compared with 
all of the other F sum rule values. 
Based on comparisons of experimental intensity data 
for all the isotopically related methanes7 and theoret-
ically (CNDO and ab initio) calculated results10 the 
signs of ap/aQ3 and ap/aQ4 have been found to be iden-
tical. The G intensity sum rule provides a very 
straightforward method for verifying this result. New-
ton and Personl1 have calculated average values for the 
polar tensor of methane and its carbon and hydrogen 
effective charges using the individual fundamental in-
tensities of CH. and CD.. For the (- -) sign combina-
tion (ap/aQ3 and ap/aQ4 both <0) average values of 
~~ == 0.0006 and ~~ == 0.027 e2 are reported. These val-
ues are in excellent agreement with effective charge 
values corresponding to the region of overlap defined 
by the experimental ranges in the four G sum rule lines 
shown in Fig. 1. On the other hand, the alternative 
sign combination, (+ -), leads to average values of 
~~==0.271 and ~~==0.018 e2 • Reference to Fig. 1 shows 
that this value of ~~ corresponds to four different val-
ues for ~~ for the CH4 • CR3D, CR2D2 , and CD4 intensity 
sums. As ~~ should be invariant for these molecules 
within the Born-Oppenheimer approximation, the (+ -) 
sign combination can be confidently eliminated. 
Average values of ~~ and ~~ have been used here as 
effective charge values based on only the CR4 or CD. 
intensity data have not been reported for the two possi-
ble sign combinations of the ap/aQ;'s. However, the 
effective charge values obtained from either the CH. 
and CD4 individual intensities, via the polar tensor, 
must be in reasonable agreement with the average val-
ues quoted here. Rence it is easily seen that the rela-
tive signs of ap/aQ3 and ap/aQ 4 can be determined from 
a knowledge of the polar tensors for CH4 (or CD4) and 
a sum of the fundamental vibrational intensities of 
CD4 (or CR4). 
ACKNOWLEDGMENTS 
Financial support from the Fundac;ao de Amparo a 
Pesquisa do Estado de Sao Paulo (FAPESP) and the 
Financiadora de Estudos e Projetos (FINEP) is grate-
fully appreCiated. One of us (BBN) is indebted to the 
Conselho Nacional de Desenvolvimento Cientffico e 
Tecnologico (CNPq) for a fellowship. 
l R. E. Bruns and B. de Barros Neto, J. Chern. Phys. 68, 
847 (1978). 
2B. de Barros Neto and R. E. Bruns, J. Chern. Phys. 68, 
5451 (1978). 
3R. E. Bruns and A. B. M. S. Bassi, J. Chern. Phys. 68, 
5448 (1978). 
4R. E. Bruns and B. de Barros Neto, J. Chern. Phys. (to be 
published) . 
5B. L. Crawford, Jr., J. Chern. Phys. 20, 977 (1952). 
6W. T. King, G. B. Mast, and P. P. Blanchette, J. Chern. 
Phys. 56, 4440 (1972). 
7S. Sl1eki, M. Mizuno, and S. Kondo, Spectrochim. Acta A 
32, 403 (1976). 
8J. Heicklen, Spectrochim. Acta A 17, 201 (1961). 
9L. M. Sverdlov, M. A. Kovner, and E. P. Krainov, Vibra-
tional Spectra of Polyatomic Molecules (Wiley, New York, 
1974). 
lOG. A. Segal and M. L. Klein, J. Chern. Phys. 47, 4236 
(1967); W. Meyer and P. Pulay, J. Chern. Phys. 56, 2109 
(1972). 
l1J. H. Newton and W. B. Person, J. Phys. Chern. 82, 226 
(1978). 
J. Chem. Phys., Vol. 69, No.9, 1 November 1978 
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F And G Intensity Sum Rule Applications: The Chxd4-x Molecules

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F And G Intensity Sum Rule Applications: The Chxd4-x Molecules

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