The vibration-rotation bands v2 and v5 of methyl bromide

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The vibration-rotation bands v2 and v5 of methyl bromide

G. Graner, W.E. Blass

To cite this version:

G. Graner, W.E. Blass. The vibration-rotation bands v2 and v5 of methyl bromide. Journal de

Physique, 1975, 36 (9), pp.769-771. �10.1051/jphys:01975003609076900�. �jpa-00208314�

769

THE VIBRATION-ROTATION BANDS v2 AND v5 OF METHYL BROMIDE

G. GRANER

Laboratoire

d’Infrarouge,

Laboratoire Associé au

CNRS,

Université Paris

XI,

^Bâtiment

350,

⁹¹⁴⁰⁵

Orsay,

^France

and W. E. BLASS

Molecular

Spectroscopy Laboratory, Department

^of

Physics

^and

Astronomy,

The

University

^of

Tennessee, Knoxville,

^Tennessee

37916,

^U.S.A.

(Reçu

^le

20 février 1975, accepté

^{le 4 avril}

1975)

Résumé. ²⁰¹⁴ Le spectre infrarouge ^de

CH3Br

^{a été} analysé ^{entre 1 200 et 1 500 cm-1 en tenant} compte de la résonance de Coriolis en x- y entre les deux niveaux

fondamentaux v2

^{= 1 et} 03C55 ⁼ 1.

Les centres de bande ont été trouvés

respectivement

^à 1 305,907 ^et 1 442,885 cm-1 ^{et le terme de}

couplage 03B6x2,5

^{vaut 0,617.}

Abstract. ²⁰¹⁴ The infrared spectrum ^of

CH3Br

^has been analyzed between 1 200 and 1 500 cm-¹ taking ^{into account the} x - y Coriolis resonance between the two fundamental levels _03C52 ⁼ 1 and 03C55 ⁼ 1. The band centers were found

respectively

^{at 1 305.907} and 1 442.885 cm-1 and the

03B6x2,5 coupling

^{term was} determined to be 0.617.

LE JOURNAL DE PHYSIQUE TOME 36, ^SEPTEMBRE 1975, ¹

Classification Physics ^Abstracts

5.444

1. Introduction. ^- The infrared spectrum ^of

CH3Br

between 1200-1500

cm-1

has not so far been studied under a

high

resolution. In

1965,

Morino and Naka-

mura

[1] reported

^a

study

^{of the}

perpendicular

^fun-

damental _v-, with

only

the unresolved

Q-branch positions being

measured. In

1966, Jones, Popplewell

and

Thompson [2] reanalyzed

^{the same band with}

a somewhat

higher

resolution and

assigned

^about

one hundred ’P and RR lines.

They

^also

reported

^a

study

^{of the}

parallel fundamental v2

^without

being

able to resolve _any of the K structure,

fitting

^the

P(J)

^and

R(J)

^{lines to a}

polynomial

^{in m.}

In

1969,

^Kurlat

[3]

^recorded

the V2

^and vs

region

with

higher resolving

power ^at the Ohio State Univer-

sity, using

^a

path

^{of one meter} and pressures of ^one to two torr. The half-width of ^a

typical

recorded line

was 0.15

cm-1

and the transitions due to the

isotopes

of bromine were not resolved. The

spectra

^{were cali-} brated

using absorption

standards after the method of Rao et al.

[4]. Preliminary assignments

^{were made}

by

^Kurlat

exploring

^{the use of a}

generalized

^molecular

prediction

model for

assignment

^of

complicated

spectra

[3].

The results obtained

by

Kurlat indicated the existence of strong, non-localized resonance

between states

of v2 and v. ; using

^a

Taylor expansion

of _{the upper} state energy in terms of

J, K,

^and

lt,

^and

a

physical expression

^{for the}

ground

^state

[5],

^he

found that 32

parameters

^were

required

^to

represent

the

assigned vs

transitions for K

9,

^J

30,

^with

a standard deviation a ⁼ 35 ^x

10- 3 cm-’,

^and

17

parameters

^were

required

^to

represent v2 frequen-

cies for K

7,

^J

35,

^{with (1 = 17 x}

10-’ cm-’.

We have now decided to

reanalyze

^{the same}

experi-

mental data with the introduction of

the x - y

Coriolis interaction.

2.

Analysis

^{of the} spectrum. ^{- A}

complete

^re-

appraisal

of Kurlat’s

assignments

^was undertaken.

Weights

^were

given

^{to each}

line,

^some wrong ^or dubious

assignments

^were corrected and a few new ones were made

possible by

^the

predictions.

^The

R Ra

^and

RPo

^lines

of v.

which had been

assigned by

Kurlat but not used

by

^{him were} reintroduced. In contrast, ^{it was decided not to use K} > 5 lines in _v2 since

they

^are

overlapped by

low K lines.

A

difficulty

^{arose due to the fact that the lines}

belonging

^{to the two}

approximately equiabundant isotopic species, CH379Br

^and

CH381Br

^{were not}

resolved. From

high-resolution

studies of

2 vs [6]

and

2 v2 [7],

^we

expect

the band-center to be

slightly

lower for

81 Br

than for

79Br, by

about 0.009 cm-1

for vs

^{and 0.028}

^{cm -1}

^for v2, but because B-values are, smaller for

81 Br by

about 0.0012

cm -’,

^the

isotopic

^{shift should} grow rather

quickly

^{for the}

R(J)

^lines

(up

^{to 0.100}

^cm-1

^{around J =}

30)

^while

it cancels and

eventually changes sign

^{in the P-}

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01975003609076900

770

branches. We therefore used

throughout

^{this work}

an average bromine with

ground-state

^molecular

constants obtained

by averaging

the values

given

in

[8]

^{for the two}

species :

This

procedure

^{will of course .limit the} accuracy of our results. In the final

computational

stage, 346 transitions were

used, namely

¹¹⁰

for v2

^{and 236}

for _Vs.

3. Model used. ^- We have used the

least-squares

program described in reference

[9, 10].

^The energy-

expression

^includes

Maes’ qj and ’IK

^{terms from the}

third-order Hamiltonian. We solve 3 x 3 Hamilto- nian matrices

taking

^into account not

only

^{the x -} y Coriolis interaction

[11-13J,

but also the

l(2, 2)-type

resonance. All

computations

^were

performed

^at

Orsay ’on

^{a Univac}

1110 computer.

Although

¹⁷

parameters

^can vary in the _program,

we found that several of them are not

significantly

determined from the data. Therefore

Dj, D;’lK

^and

D’

were constrained to their

ground

^{state values for}

TABLE 1

Molecular constants

derived for

^an average bromine

Ground state values fixed. Distorsion constants fixed to ground

state values. All values except Cx2., ^{in cm-1. The errors} quoted ^are

standard deviations given by the least squares calculation.

both vibrational levels

and q

^{as well as} ilj ^{were set} to zero. A fit with the

remaining

⁹

parameiers gives

the results listed in Table 1 and a standard deviation

on residuals of 25.3 x

10-3 cm-l.

A somewhat better standard deviation was obtained with

D’

free to float but the fit

yields

^an

unacceptable

^value

of - 3 ^x

10-4 cm-l

for this

parameter.

In Table 1 we

quote

the standard deviations

given by

^the

least-squares

calculation. The real uncertainties

are

probably

^much

larger, especially

^for

A 2 - Ao

which is not well known because we could not find K values

larger

^{than 5 in}

the V2

^band.

TABLE II

Comparison

^with

previous

^studies

of

v2 and _{v 5}

(all

^cm-

1)

... ,

TABLE III

Comparison

with indirect determinations

of

a2 and _ce,

(all cm-1)

771

4. Discussion. ^- The values found in this work

can be

compared

^{with ones obtained}

previously

^from

direct studies

of v2

^and v.,

by

^infrared

[1, 2, 3]

^or

microwave

[14] spectroscopy

^{which have been sum-} marized in Table

II,

^{and also to} indirect determina- tions of the same constants

by

studies of overtones

[6, 7, 15]

^or combinations bands

[16],

^{which are collected}

in Table III.

As mentioned

above,

^Kurlat

[3] treated v2 and v5 independently.

^His

prediction

^model

required

⁴⁹ para- meters to fit the observed spectra

(32 for v5

^and

17 for

v2) compared

^{to the}

only

^{9 free} parameters and 5 fixed known

ground-state

values for the combin- ed _V2

and Vs

^{data set} used here. In an

attempt

^to

extract

physically meaningful

parameters ^{from the}

severely perturbed spectra,

Kurlat then used a

physical

model for each band

limiting

^the

input

^{data to} very low J and K-values.

Fitting

the thus restricted data

required only

three and five parameters

for v2

^and v.

respectively

^{- a result not}

unexpected

^{in the} presence of an x - y Coriolis ^resonance.

Morino and Hirose

[14]

^{recorded two micro-}

wave transitions of

CH3Br (J

^{= 1 -}

0,

^{K =}

0)

^and

(J

^{= 2 -}

1,

^{K =}

1)

ⁱⁿ

the V2

^{= 1 and} v5 ⁼ 1 vibra- tional states.

They

treated the Coriohs resonance.

explicitly, finding 2,5

values between 0.60 and

0.67,

as

compared

^with

0.616s

^here.

Table II shows that the band-centers are reaso-

nably

determined from _any model. For

a5,

^old

determinations as well as the

physical

^{model of}

Kurlat

give surprisingly good

results. For

a2,

^which

was taken as zero in reference

[2]

^the

prediction

model

gives

^a nonsensical

value ;

^the

surprising

^value

of + 23.1 ^x

10-3 given by

^the

physical

^model

[3]

is due to a clerical error in the value of

a2 - a2,

which should be - 0.021 instead of + 0.021

giving

a derived value of

a2

^{of - 18.9 x}

^10-3.

^The

major

effect of the Coriolis interaction is

apparent

^{in the}

aB values.

Previous values

of oc2 quoted

^{in Tablè II}

are too

large by

^{a factor of 2 or 3. Even}

though

^Morino

and Hirose treated the Coriolis

interaction,

^their

high

^{value is}

probably

^{due to} the fact that

only

^low

J lines were

used,

^{as was}

pointed

^out in reference

[17].

Similarly,

^{it seems}

likely

^{that the}

a’

^{are closer to}

zero than was

suggested by previous

^work.

Overtone and combination bands

yield

^similar

results. In reference

[1],

^the

2 v2

^{band was treated}

as if it were

unperturbed.

^{The same} data treated in reference

[15] by taking

^{into account a} Coriolis inter- action with

(V2

⁺

V.) gives a2

much closer to the present ^{results. In reference}

[16],

^{constants are deter-}

mined for the

(v3 + vs

⁺

v6) (A 1

⁺

A2)

^{band which}

interacts with _vl, but the _very

likely

Coriolis interac- tion between

(v3 + v_,

⁺

v6)

^and

(v2

⁺ V3 ⁺

v.)

^could

not be taken into account; ^moreover the values of

as

^and

as

obtained in reference

[16] rely

^{on the cor-}

rectness of _v3 and V6 - values from other works.

Finally,

^the

present

^results compare

reasonably

^with

the values obtained in reference

[6] by

at treatment of the interaction of 2

vs(A1)

^with

(v2

⁺

vs) although

the small values

of oej

^have

conflicting signs.

^These

could result from the limited resolution data used for

(v2

⁺

v.) [6]

^or the limited data set used

for v2

in this work.

5. Conclusions. ^- This work does not

by

any

means conclude the

analysis of v2

^and Vs. We have nevertheless shown for the first time

directly

^that

x - y Coriolis resonance is

actually present

^and

important.

The molecular constants

given here, although

^{not final are}

probably

^{closer to the real}

values than

previous

^{ones. We are}

planning

^extended

work with a

higher resolution,

^at

Orsay

^{as well as at}

Knoxville,

^on these fundamentals and their overtone and combination bands.

Acknowledgments.

^{- The} spectra ^{used in the ana-}

lysis

^were taken from the doctoral dissertation of M.

Kurlat, who,

^{while a student at the}

University

of

Tennessee,

^was

permitted

^{to use the}

spectroscopic

facilities at Ohio State

University

in 1969 with the

compliments

of Professor K. Narahari Rao of Ohio State

University.

^Portions of this work were

supported by

^NASA grant NGL-43-001-006.

References

[1] MORINO, ^{Y. and} NAKAMURA, J., Bull. Chem. Soc. Japan, ³⁸ (1965) 443.

[2] JONES, E. W., POPPLEWELL, ^{R. J. L. and} THOMPSON, ^H. W., Spectrochim. ^{Acta. 22} (1966) ^647.

[3] KURLAT, M., Ph. D. Dissertation, University ^of Tennessee, Knoxville, ^1969.

[4] ^NARAHARI RAO, K., HUMPHREYS, C. J. and RANK, D. H., Wavelength ^{Standards in the} Infrared (Academic Press, New York) ^1966.

[5] BLASS, ^W. E., NIELSEN, ^A. H., in Methods of Experimental Physics, 3A, 2nd ed. D. Williams, ^ed. (Academic Press, New York) ^1974.

[6] GRANER, G., ^{J. Mol.} Spectrosc., ⁵¹ (1974) ^238.

[7] BETRENCOURT-STIRNEMANN, ^{C. and} MORILLON-CHAPEY, M.,

J. Mol. Spectrosc., ⁴⁶ (1973) ^171.

[8] BETRENCOURT-STIRNEMANN, C., GRANER, G. and GUELACH- VILI, G., ^{J. Mol.} Spectrosc. ⁵¹ (1974) ^216.

[9] DEROCHE, J. C., GRANER, ^{G. and} ALAMICHEL, C., ^{J. Mol.}

Spectrosc., ⁴³ (1972) ^175.

[10] DEROCHE, ^J. C., Thèse de 3e Cycle, Paris 1971.

[11] ^DI LAURO, ^{C. and} MILLS, I. M., J. Mol. Spectrosc. ²¹ (1966) 386.

[12] DILLING, R. L. and PARKER, ^P. M., ^{J. Mol.} Spectrosc. ²⁸ (1967) 178.

[13] BLASS, W. E., J. Mol. Spectrosc. ³¹ (1969) ^196.

[14] MORINO, ^{Y. and} HIROSE, C., ^{J. Mol.} Spectrosc. ²⁴ (1967) ^204.

[15] BETRENCOURT-STIRNEMANN, C., Thèse, Orsay ^1975.

[16] BETRENCOURT, M., MORILLON-CHAPEY, M., GUELACHVILI, ^G.

and AMIOT, C., to be published ^{in J. Mol.} Spectrosc.

[17] GRANER, G., ^J. Physique ³¹ (1970) ^435.