Intensity, transition moment, and bandshapes for the second overtone of compressed CO

J. Qumr. Speclrosc. Radiaf. Printed in Great Britain.

Transfer

Vol. 30, No.

1, pp. 9-15,

00224073/83/07000%07SO340/0 Q 1983 Pergamon Press Ltd.

1983

INTENSITY, TRANSITION MOMENT, AND BANDSHAPES FOR THE SECOND OVERTONE OF COMPRESSED CO

Laboratoire

J.-P. BOUANICH, d’Infrarouge, Associt

NGUYEN-VAN-THANH, au C.N.R.S., Universitk Orsay, France

and I. ROSSI de Paris-Sud,

BLtiment

350, 91405

(Received 22 September 1982) Abstract-Infrared spectra of the CO second overtone absorption band have been studied for pressures up to 156 bar. The absolute intensity, obtained from direct measurements of the total band, is found to be (1.27 + 0.04) x 10 _’ cm - 2 Am - ’ at 298 K. Using the vibrational moments for the ground state and the transitions l&l to &4, we have evaluated the coefficients M, to M4 of the quartic dipole moment function for CO and the coefficients of the vibration-rotation interaction functions. The normalized IS3 band contours of compressed CO were first generated by summing the pressure-broadened rotational lines with Lorentz profiles. A discrepancy appears between calculated and observed bandshapes and increases with density. An empirical model, which involves the sum of CO self-broadened lines with profile described as the product of a Lorentz function by a fitted exponential function, gives reasonable agreement with the experiments. The interference effects resulting from overlapping lines have been estimated within the impact approximation. 1. INTRODUCTION

The absolute intensity of the &3 band of CO has been measured by various investigators1-5 using different experimental and analytical techniques. The measured band intensity values fall between 0.0 102 and 0.0 135 cm -2 Am - ‘. The transition moment generally adopted6t7 for the O-3 band is derived from the intensity value recommended by Toth et al4 (i.e., 0.0132cm-2Am-‘). In the present work, we determine that band intensity from high pressure spectra. Using the rotationless transition moments derived from recent values of vibration-rotation line strengths or absolute band intensities, we evaluate the coefficients M,, to M4 of the electric dipole moment function for the ground electronic state of CO. Next, the vibration-rotation interaction functions F:(m) are calculated for the transitions O-l to O-4 and the coefficients of the quartic polynomials fitting these functions are deduced. In order to generate the &3 band profiles, we use the models previously developed for spectra of the CO first overtone band. ‘y9The normalized band contours are calculated by summing the pressure-broadened lines, assuming for these lines successively a Lorentz shape (model 0) and a modified Lorentz shape (model II). If the interference line effects are not negligible, they are taken into account implicitly in model II, which contains an adjustable parameter. Thus, we have estimated these effects by using, in the frame of the impact and classical path approximations, an extension of the Anderson-TsaeCurnutte formalism to overlapping lines. 2. EXPERIMENTAL

PROCEDURE

The spectra were recorded on a Czerny-type spectrometer working with appropriate filters in the second order of the grating. We made sure that no superposition with a different order occurred by scanning a saturated spectrum of the (2v, + 2~; + v3)band of compressed CO, situated at 6348 cm-‘. The spectral slitwidth used was about 1.Ocm -’ and the spectral region was calibrated with emission lines of neon in higher orders. The CO sample, as supplied by L’Air Liquide, had a stated purity of 99.995%. The gas was introduced in a high-pressure, stainless steel absorption cell with an optical pathlength of 43.1 cm. The windows were made of synthetic sapphire, 2 cm in diameter and 0.6 cm thick. The CO gas pressures ranged from 3 1 bar to 156 bar and were measured with Bourdon tube gauges with an accuracy of better than 1%. The spectra were recorded at an ambient temperature of 298 + 1 K. The densities of CO were determined from the PVT data given by Michels et ~1.” 9

IO

J~OUANICH

J.-P.

et al

and are expressed either in Amagat units (d) or in atmosphere units (of density) defined by 6 = n(P, T)/n(P = 1 atm, T = 298 K), where n is the number of CO moles per unit volume. 3. INTENSITY

MEASUREMENTS

The integrated absorption coefficient S in cm-’ is calculated from the relation S = f

k(o) da,

s where 1is the optical pathlength in cm and the absorption coefficient at the wavenumber 0, k(o), is given by k(a) = ln

V&W(~)l.

(2)

Here, Y0 is the radiation intensity transmitted by the evacuated cell and Y the intensity transmitted by the cell filled with CO. The appropriate background curve, which is obtained with the cell evacuated, is superimposed on each spectral curve. The measurements include the totality of the isotopic bands of CO. The values of S plotted as a function of CO gas densities are shown in Fig. 1. Within experimental errors, the intensities are proportional to the densities. The intensity value per unit density of CO which was determined by a least squares technique is S, = 0.0127 cm-’ Am-’ at 298 K. Assuming that the absorption of the isotopes is roughly equal, at the same density, to that of 12C160,this value corresponds to the band intensity normalized to 100% 12C’60. Our provious result’ which was determined from line-intensity measurements is notably lower. A review of the former spectra shows that we had underestimated the overlapping of the lines and we had not checked that the spectral region of the band was perfectly filtered. The absolute error in S,, is mainly caused by uncertainties in the determination of the background curve and is value of band intensity + 0.0004 cm-’ Am-‘. The estimated to be (1.27 f O.O4)lO-2 cm-2Am-1 is in excellent agreement with the value reported by Schurin and Ellis2 and lies within the limits of experimental errors of the values of Burch and Gryvnak3 and Toth et a1.4 4. VIBRATIONAL

TRANSITION MOMENTS, AND HERMAN-WALLIS

DIPOLE MOMENT COEFFICIENTS

FUNCTION

Using for the dipole moment function of CO a power series expansion about the equilibrium internuclear separation re such as M(r)

+

=

1 Mi(r - rj, i=O

S(cm3

l.S-

l.O_

O.S_

0

Fig.

1. Variation

25

of the integrated

I 50

absorption

1 75

coefficient

I 100

I 125

l

d(Am)

S of the &3 band of CO with gas density.

Intensity,

transition

moment,

and bandshapes

of compressed

11

CO

the dipole moment coefficients Mi can be calculated from the vibrational transition moments Rt=, through the relations R; = 1 M,u - ‘12Ry,

(4)

i

where the expressions for the rotationless matrix elements RF, including the sixth-order contributions from perturbation theory, are given in Ref. 11, and a = w,/(2B,r,2). The vibrational transition moments are related to the band intensities SF (in cme2 Am-‘) by

(5) where m = - J or J + 1 for P or R-branch transitions, respectively, NL is the number of CO molecules per cm3 at 1 Am, Q, the rotational partition function, E, the rotation energy, a(m) the vibration-rotation transition wavenumber, and F:(m) the vibration-rotation interaction function for the transition O-v’. The summation over m is extended from - 44 to + 45, which corresponds to the convergence for J = 44 of the partition function calculated with eight digits. To obtain the transition moments Rt from the band intensities, we have used an iterative procedure since the F:(m) functions depend on the Mi coefficients and on the Rt values. The values considered for Rf with u’ < 4 (Table 1) are somewhat different, except for o’ = 0, from the set of values previously used12 since they are based on new intensities measurements. The absolute intensity for the fundamental band is obtained by averaging the results of Varghese and Hanson,13 Varanasi and Sarangil (their results have been normalized to lOOok12PO) and Lowry and Fisher,” i.e., SE’ = 279 cm-’ Am-‘. For the O-2 band, we have considered the intensity previously obtained* from spectra of compressed CO, SE2 = 2.09 cmm2 Am-‘, which is in very good agreement with the recent result of Chandraiah and HeberP (2.11 cmm2 Am-‘). The transition moment Ri deduced from our band intensity, 4.18 (fO.07) 10m4D, is slightly smaller than the value generally adopted: 4.24 x 10P4D. For the WI band, the transition moment used by us and obtained by Chackerian and Valero”, 2.011 x 10e5D, is in good agreement with the determination of Spellicy.’ The Rz moment for the ground state of CO is taken from Muenter.” The choice of signs for the matrix elements R$, which alternate with u’, seems to have been definitely established.’ The coefficients M,-M4 of the dipole moment expansion are determined by solving the system of Eqs. (4), with i and a’ varying from 1 to 4; the matrix elements Ry are calculated from the anharmonic potential coefficients al-u6 obtained in Table 1 of Ref. 20. Then MO can be evaluated from the relation M,=R;-

i~~~-il2~“.

(6)

i=l

Using the data in Table 1, the dipole moment function of CO, expressed in Debye (with r - re in A) is found to be M(r) = -0.1226 + 3.2109(r - rJ - O.l98(r - re)2- 2.553(r - re)3+ 1.18l(r - r,)4. (7)

Table

1. Values of the rotationless transition moments Rg (in Debye) used in the determination dipole moment function and the vibration-rotation interaction functions. 0

v’ R;’ CD)

-

0.1098

1 O.lca

2 -6.59

x 1o-3

3 4.18

x 10-l

4 -2.01

x 10-5

of the

12

BOUANICH

J.-P.

The vibration-rotation transition moment level v’, J has been expressed2’ in the form Rt;

c

=

et al

R$” between the initial level U, J and the final

-“2(&H

&ficr

+

xf”-“‘J’),

(8)

where general expressions of the rovibrational matrix elements XyJ ““, including order contributions, have been obtained in Refs. 21 and 22. The vibration-rotation action functions Ft’ may be calculated from the relation i (py2=

1 +

M,~

i=O

fourthinter-

-ilIzxpJ-dJ R",

(9)

0

and can be very well represented

by quartic

in m such as

polynomials

F:(m)= 1 + Cusrn + Ducm2+ E,,,m3 + G,m4.

(10)

The coefficients C, D, E, and G have been calculated for the transitions &l to O-4 by applying a least-squares fit to F:(m) with m varying from - 30 to 30. As may be seen in Table 2, the results obtained for the Herman-Wallis coefficients C,., and D,.(with o’ = 2, 3, 4) are in reasonable agreement with experimental results. It should be noted that slightly different values of C,, and D, arise from quadratic polynomials although such polynomials cannot be adequately fitted to the calculated F;(m)functions; the r.m.s. deviation increases notably with u’. For the second overtone band, we obtain

F:(m)N 1 + 1.2 x 10P2m + 1.0 x 10-4m2. This function

has been used in the calculation

5. EXPERIMENTALLY The normalized

OBSERVED

spectral

densities

of bandshapes. AND

k(a)

have been

determined

CALCULATED

BANDSHAPES

Z(a) are given by

Z(a) = -

and

(11)

k(a) ~

c

do

(12)

rJ

for the O-3 band

spectra

of ‘2C’60 by subtracting,

in the

Table 2. Experimental and calculated Herman-Wallis coefficients for the transitions f&l to t&4 of CO. The experimental values for the O-2, f&3 and &I bands are taken from Refs. 23, 4, and 17, respectively. For the @I band, the quoted errors are statistical and not a measure of the absolute accuracy.

Transition

C

(5.4

=P

C CalC

1.911

x 10 -4

talc

E c&c

G talc L

+ 0.4) 5.113

(4 + 2)

Dexp D

6.97

x lo+

0+3

o-2

0+1

3.44

x 10-3 (I.16 x 10-3

x 10-5 x 10-5

0+4

+ 0.07) 1.187

(18 +

x 10 -2

10)

3.34

x 16

x lO-5 x

10-5

1 -2

(3.55

5 o.ca)xlo-2

3.432

(4.81

x lO-2

5 0.48)x10-4

3.70

x 10-4

1 .48 x 10 -6

4.73

I

x 10 -9

Intensity, transition moment, and bandshapes of compressed CO

13

experimentally measured k(a), the weak absorption coefficient calculated for the ‘3C’60 band centered at about 6212 cm -‘. Moreover, we have generated Z(g) by considering the sum of pressure-broadened lines with a Lorentz shape (model 0) or a modified Lorentz shape (model II) such as 8,9

K(lm1)

’ K(lml)*+ b -

Cexp[-E,(m)lk,TlF(m)lmI.

dm)l’ ,,,

(13)

Here, a(m) is the wavenumber of the pressure-broadened line m, including the frequency shift; a2 is an adjustable parameter, which implies that the overlapping effects of the lines and/or the influence of the finite duration of collisions are not negligible; C(a,) = [l - cp(ail’)]n exp az, where q(x) is the probability integral; for a2 < 0.5, K(\m)) is given, in good approximation, by

K(lmI)= r(lml)(l + 2a2)/(l+ a21r

(14)

where the ~(1m 1)are the [ml-dependent halfwidths of the lines. The summation over m has been extended from -44 to 45. Model 0 is a particular case of model II in which a2 = 0, C(0) = n and K(lm I) = y((m I). The halfwidths of the lines are assumed to be proportional to the density such that y = y06, where y0refers to halfwidths measured at 1 atm and 298 K. However, the use of Eq. (14) for a2 2 0.5 implies the presence of a slight nonlinearity of the linewidths with density (deviation of 8.2% for a2 = 1). We have shown9 that the linewidths considered for d > 200 Am should be notably smaller than y06. Within experimental errors, the vibrational effects in CO self-broadening are negligible. 24Therefore, the values of yo(lmI) extrapolated to [ml = 45 are taken from accurate results obtained in the &2 band.* Compared to experimental profiles, the calculated spectral densities Z(a) have similar behaviour to that previously described8x9for the (r2 band of compressed CO. As may be seen in Fig. 2, a discrepancy between experimental and calculated bandshapes for Lorentzian lines (model 0), which appears for d N 30 Am, increases with density. The results are greatly improved with model II by adjusting the a2 parameter. In the density range 28.6-140 Am, the fitted a2 values vary from 0.02 to 1. This model yields a reasonable description of the experimental results and the use of Eq. (11) for F(m) is appropriate. The observed relative intensities for the peaks of the P and R-branches and for the band center are well represented for d < 100 Am. However, at high density (d > 100 Am), the calculated profile of the R-branch is slightly lowered in its central range and notably shifted from the experimental profile. The wavenumbers of the maximum absorption for the P- and R-branches, as well as for the minimum absorption corresponding to the band center, have been evaluated with model II. The wavenumbers a(m) are calculated from the frequencies of the unperturbed CO lines in the &3 band and from the m-dependent lineshifts which are estimated for - 19 < m < 22 in Ref. 25. We have assumed that these lineshifts are equal to a constant value of - 0.0075 cm-’ atm-’ for m < - 19 and - 0.0085 cm-’ atm-’ for m > 22 and are proportional to the density 6. The results are compared (Table 3) with experimental wavenumbers determined with an accuracy of about + 1 cm - ‘. Satisfactory agreement is obtained for d < 50 Am. The small discrepancy between wavenumbers, which appears for higher densities in the P-branch and in the band center, may be caused by large uncertainties in the lineshifts considered. As for the O-2 band of compressed C0,8*g the peak of the R-branch is notably displaced from the calculated wavenumber (3.5 cm- 1 at 140 Am). We estimate that this displacement cannot be entirely explained by inaccuracies in the calculated line positions. In order to estimate the interference effects which do not appear explicitly in model II, we have considered an extension of the Anderson-Tsar-Curnutte theory to overlapping

14

J.-P. BOUANICH et a2

6250

5850

5300

6400

Fig. 2. Spectral densities Z(c) for the O-3 band of compressed ‘2C’60; (a) d = 47.2 Am; (b) d = 92.1 Am; (c) d = 140.4 Am; -, experimental data; x , model 0 (sum of Lorentzians); + , model II with c(r = 0.05 (a), a, = 0.5 (b) and a, = 1 (c); o, model including overlapping effects.

Table 3. Experimental

and calculated wavenumbers R-branches and the minimum

d (run)

(in cm-‘) absorption

47.2

of maximum absorption at the band center. 92.1

for the P and

140.4

I 6321.6

6320.9

6319.5

6321.2

6322.1

6320.5

6349.5

6347.0

6345.6

6349.4

6348.2

6346.5

6379.5

6378.1

6376.9

6380.1

6380.2

6380.4

0.05

0.5

P-branch

bard center

a2[cf. Es. (1311

lines. The formalism used has been presented in Refs. 8 and 9. We have evaluated the cross-term contributions arising from the couplings between nearby rotational lines such as AJ = If: 1, f 2, f 3 caused by the electrostatic interactions (p1--p2, p,-Q*, ~,-L&, Q,-P~, Q,-Q2, Q,-R,, R,--,+, R,-Q,, LI-R,) and the dispersion energy. The parameters used for the dipole, quadrupole and octopole moments of CO and for the dispersion potential have been given in Ref. 8. The cross-term contributions appear to decrease even faster than the linewidths with increasing J values. The normalized profiles of the &3 band have been generated by considering the experimental lineshifts and assuming that the negative crossterm contributions, the diagonal contributions (i.e., halfwidths of isolated lines) and the lineshifts are proportional to the density. Except around the band centers where the

Intensity,

transition

moment,

and bandshapes

of compressed

CO

15

calculated spectral densities are lowered too much (Fig. 2), good agreement is obtained with the experimental profiles. In the wings, the agreement is even better than with model II and the calculated R-branch does not exhibit any significant shift. Assuming that absorption by the pressure-induced Q-branch is negligible, the discrepancy observed around the band center is possibly caused by overestimation of the cross-term contributions, especially for small Jvalues. Actually, whatever these contributions may be, it seems that our calculation cannot provide satisfactory band contours. Thus, consideration of overlapping effects within the impact approximation, which yields improved band profiles over those deduced from the simple sum of Lorentz lines, is an important contribution but is still insufficient. The influence of the finite duration of collisions and, at high density, of quadratic contributions in density are probably not negligible. Since model II gives reasonable agreement with experiments, we estimate that the introduction of a parameter (a2) which increases with density arises only partly from the nonadditivity contributions which are proportional to the density. 6. CONCLUSION

The absolute intensity of the O-3 band of CO has been accurately determined. From the vibrational transition moments Ri to Ri (Riand Ri are deduced from our measurements) and using the matrix elements derived from perturbation theory, we have obtained Herman-Wallis coefficients in good agreement with experimental results. A simple model, which involves summing of pressure-broadened lines with a modified Lorentz profile, reproduces well the bandshapes of compressed ‘2C’60, especially for moderate densities (d < 100 Am). REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

E. K. Plyler, W. S. Benedict, and S. Silverman, J. Chem. Phys. 20, 175 (1952). B. Schurin and R. E. Ellis, J. Chem. Phys. 45, 2528 (1966). D. E. Burch and D. A. Gryvnak, J. Chem. Phys. 47, 4930 (1967). R. A. Toth, R. H. Hunt, and E. K. Plyler, J. Molec. Spectrosc. 32, 85 (1969). J. P. Bouanich and C. Brodbeck, JQSRT 14, 1199 (1974). R. H. Tipping, J. Molec. Spectrosc. 61, 272 (1976). C. Chackerian, J. Chem. Phys. 65, 4228 (1976). J. P. Bouanich, Nguyen-Van-Thanh, and H. Strapelias, JQSRT 26, 53 (1981). J. P. Bouanich, JQSRT27, 131 (1982). A. Michels, J. M. Lupton, T. Wassenaar, and W. De Graaff, Physica 18, 121 (1952). J. P. Bouanich, JQSRT 20, 419 (1978). J. P. Bouanich, JQSRT 16, 1119 (1976). P. L. Varghese and R. K. Hanson, JQSRT 24, 479 (1980). P. Varanasi and S. Saran& JQSRT 15, 473 (1975). H. S. Lowry and C. J. Fisher, JQSRT 27, 585 (1982). G. Chandraiah and G. R. Hebert, Can. J. Phys: 59,‘1367 (1981). C. Chackerian and F. P. J. Valero. J. Molec. Soectrosc. 62. 338 (1976). R. L. Spellicy, Report, Environmental Research Institute of Michigan: private communication. J. S. Muenter, J. Molec. Spectrosc. 55, 490 (1975). J. P. Bouanich, JQSRT 19, 381 (1978). J. P. Bouanich and C. Brodbeck, JQSRT 16, 153 (1976). J. B. Bouanich, JQSRT 17, 639 (1977). C. L. Korb, R. H. Hunt, and E. K. Plyler, J. Chem. Phys. 48, 4252 (1968). J. P. Bouanich and C. Haeusler, JQSRT 12, 695 (1972). J. P. Bouanich and C. Brodbeck, Rev. Phys. Appl. 9, 475 (1974).