- Email: [email protected]
An inelastic rotational transfer study of NH, colliding with H2, and He
Volume 136, number 6
22 May 1987
CHEMICAL PHYSICS LETTERS
AN INELASTIC ROTATIONAL TRANSFER STUDY OF NH3 COLLIDING WITH H2 AND He M. BROQUIER, A. PICARD-BERSELLINI Laboratoire de Photophysique Molkulaire du CNRS, Britiment 213, Universitk de Paris&d,
91405 Orsay Cedex, France
and J. HALL Rice Quantum Institute, Houston, TX 77001, USA
Received 10 October 1986; in final form 9 March 1987
We have studied the absorption profile of ammonia in the 6 l.trn (diode laser) and 3 pm (color center laser) regions, and in collisions with H2 and He, in order to obtain new experimental results at room and low temperatures. The behaviour of the different collision gases is discussed.
1. Introduction We have studied the absorption profile of ammonia in the 6 and 3 pm regions. The aim of this paper is to present new experimental results on the NH,-H,(para) collision and to make comparisons with previous results for NH3-H*(normal) and NH,-He.
2. Experimental We used a diode laser in the 6 pm region, and a color center laser in the 3 pm region. The experimental apparatus has been described in detail elsewhere [l]. We have studied the absorption lineshape of the vibrational lines of NH3 perturbed by para-HZ. From the line profiles we have evaluated the pressure broadening coefficient y( MHz/Torr) by measuring the Lorentz hwhm as a function of the pressure of the collision gas. The pressure broadening cross sections are then given by a=2nx106yINor7(A2), where N,, is the number of molecules per m3 at a 0 009-2614/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
pressure of 1 Torr, B= ( 8kT17r~)1’2 is the average velocity and p the reduced mass of the two collision partners. For all our measurements the experimental error is around 2 to 3%. A study of the collision pairs NH,-He and NH3-Hz (para-hydrogen) has the double advantage of providing information on the most probable collisions in the interstellar medium and of testing the validity of the hypothesis that the behaviour of helium is identical to that of para-hydrogen [ 21. Ortho- and para-hydrogen are distinguished by the parity of their rotational states. The rotational level population distribution at a temperature T, is
-= n
cJg(J)(IJ+
l)eXp( -EJ/kBTl) ’
(1)
where g(J) is the nuclear degeneracy. Since the nuclear spin of each proton is l/2, the nuclear spin T of the molecule can take the values T= 1 and T= 0, corresponding to spins parallel and antiparallel respectively. The nuclear degeneracy is equal to 2T+ 1, and is 3 for the triplet states (T= 1) and 1 for the singlet states ( T= 0). The symmetric spin function of the triplet state is associated with an antisymmetric rotational function corresponding to an odd value of the rotational quantum number. The 531
Volume 136, number
6
CHEMICAL
PHYSICS
antisymmetric spin function in the singlet state is associated with a symmetric rotational function with J even, g(J) is equal to 3 for J odd and 1 for J even. Except at very high temperatures, singlet-triplet transitions are extremely rare due to the weakness of the intermolecular magnetic interactions which produce such transitions. The group of levels with J odd and those with J even essentially behave as two different species. The ortho species occurs with the greater statistical weight. Transitions with AJ odd are not rigorously forbidden and the system evolves very slowly under the effect of those rare collisions with J odd, towards the equilibrium distribution given by eq. (1) at 300 K, n(ortho)=in and n(para)=fn; but at 20 K n(para)=n and n(ortho)=O (all the rotational population is in the state J=O). It is possible to obtain para-H, by liquefaction of the gas in the presence of a catalyst whose role is to facilitate the magnetic interactions permitting the transitions J= l--t J= 0. The CEA laboratory (DPC) provided us with (100% para) hydrogen. The reconversion time para+ortho is slow in comparison with the time scale of our measurements (we have compared results obtained at the beginning of the day with those obtained under the same conditions at the end of the day).
LETTERS
22 May 1987
Table 1 NH,-He experimental sections Transition %J&J’)
Table 1 presents our results as a function of the rotational quantum numbers J and IC,and as a function of the temperature.
parameters
and cross
T(K)
Y (MHz/Torr )
0 (A*)
300 163
1.24 1.86
17 19
300 188
1.44 1.66
20 18
300 173
1.1 1.33
15 14
173
1.32
14
300 176 145
3.4 5.2 5.5
35 41 40
pP-,(2)
300 173
4.2 6
43 47
pP-I(2)
300
3.9
40
RQ+7(8)
300
3.8
39
300 173
2.75 4.5
29 36
173
4.2
33
300 163
2.85 3.4
30 26
pP-s(5)
300
2.68
28
pP+I(2)
300 186
3 4.1
31 34
NH,-He, pP-s(s)
vq
pP+,(2)
NH3-He, pP+k5)
v,
pP-,(3) NHJ-H2, pP-s(5)
NH~-Hz, ‘P-2(5)
~4
~3
pP-I(3)
3. Results
pressure broadening
NH,-H,(para), pP+5(5)
~4
3.1. Comparison of the results We will compare our results with those already obtained by other authors using alternative methods. Similarly we will compare the experimental results for the two bands. To our knowledge there are no previous results for collisions at 6 or 3 pm. However, numerous results exist in the microwave region. Note that in the infrared region the transitions are rovibrational while in the microwave they are purely rotational. Firstly, we compare the results obtained with normal hydrogen; these cross sections are always larger than those obtained with para-H,. We next 532
compare our results for the collision NH3-Hz ( para) with those obtained by Oka [ 21 (table 2). In effect it was from these results that Green put forward the hypothesis that the collision NH3-H2( para) is iden, tical to that with He. The comparison, though difficult because we have not studied the same transitions, shows that for the same J, the cross seo tion for the transition (J,K) = (2,2) in the microwave region is the same as that found for the collision with helium and not for the collision with parahyThe cross section obtained for drogen.
22 May 1987
CHEMICAL PHYSICS LETTERS
Volume 136, number 6
Table 2 Comparison of our experimental results with those obtained by Oka [ 21 and Townes [ 51
J”=2 K”=l NH,-He microwave V3 Va
J”=5
J”=3 K”=2 lS(2)
K”=l
K”=3
K”=2
K”=5 18(2)
18(2) 15.3
17.2 20 21(2)
NHX-H*(pam) microwave
20(2) 29
v3
V4 NH,-Hz microwave JJ3 Vd
31 31(2)
30(2) 29 35.1
43
NH,-Hz(para) is 3 1 A*, whereas Oka found 21 A*. As has been noted previously, this result is significant since it justifies a posteriori the calculations undertaken by Valiron and co-workers [ 31 and Billing et al. [4]. Conversely, the results with helium are more or less identical to those of Townes and co-workers [ 5 1, since they confirm that the Jdependence of the cross section is very weak and has a value equal to 18 AZ. Now it is necessary to note that there is a depen: dence of the cross sections on the vibrational level studied. We consider it likely that the difference in the measurements is due to this dependence. The variation of the cross sections as a function of the temperature shows that, in general, there is an increase in the cross section as the temperature decreases. But for the collision NH3-He and for the transition ‘P, (2) (upper P denotes the condition AK= - 1, lower P denotes AJ= - 1; (2) denotes the initial J level of the transition, and (1) the initial K level), the cross section decreases with T, likewise for the collision NH,-H2(para) and for the transition ‘P,( 5). It is interesting to note that the calculations of Billing et al. [ 41 for the NHs-He collision show the same evolution. Thus the intermolecular potential and the semi-classical calculations seem to be valid.
3.2. Comparison with theoretical calculations Quantum-mechanical close coupling calculations have been performed on rotational energy transfer in collisions of para-ammonia with ground state (j= 0) para-hydrogen by Valiron and co-workers [ 31. Rate coefficients are given for the temperature range 15 Q Tg 300 K. The calculations employed an ab initio potential energy surface derived from separate determinations of the SCF and dispersion energies. The MOLSCAT computer package was used to perform the scattering calculations. They have calculated pressure broadening cross sections for a selection of inversion transitions in ammonia. These theoretical results are compared with the experimental values obtained by us (see table 3). The theoretical broadening cross sections are too low, and Table 3 Comparison between theoretical NH3-HZ (para) cross sections
pp+,(2)
and
experimental
T
= (4
163 186 207 294
17.6 34 a> 18 18.7, 31 a)
a) Our experimental result. The theoretical results are given by Danbyetal. [3].
$33
Volume 136, number 6
CHEMICAL PHYSICS LETTERS
this could be due to a number of reasons: - potential insufficiently anisotropic; - vibrational effect in our experiment; - elastic part not taken into account in the calculations; - rotational excitation of the hydrogen not taken into account in the calculations. Acknowledgement The authors wish to thank Professor R.F. Curl and Professor F. Tittel for their interest in this research and for helpful discussions. A part of the work has been supported by a grant from NATO. References [ 1] M. Broquier and A. Picard-Bersellini, Chem. Phys. Letters 111 (1984) 602; 121 (1985) 437;
534
22 May 1987
M. Broquier, A. Picard-Bersellini and H. Aroui, Opto 86 ES1 Publications; M. Broquier, A. Picard-Bersellini, G.D. Billing and J. Hall, Proceedings of the Fifteenth International Symposium on Rarefied Gas Dynamics, Vol. 1, II, Grado (1986). [2] T. Oka, private communication, as quoted in: S. Green, J. Chem. Phys. 73 (1980) 2740. [ 31 G. Danby, D. Flower, E. Kochanski, L. Kurdi, P. Valiron and G.H.F. Diercksen, J. Phys. B, to be published; G. Danby, D. Flower, P. Valiron, E. Kochanski, L. Kurdi and G.H.F. Diercksen, J. Phys. B, to be published. [4] G.D. Billing, L. Poulsen and G.H.F. Diercksen, Chem. Phys. 98 (1985) 397; 105 (1986) 145; Chem. Phys. Letters 121 (1985) 94. [ 51 C.H. Townes, Phys. Rev. 70 (1946) 109A, 665; B. Bleaney and R.P. Penrose, Proc. Roy. Sot. Al89 (1947) 358; P.T.P. Ho and C.H. Townes, Ann. Rev. Astron. Astrophys. 21 (1983) 239.
22 May 1987
CHEMICAL PHYSICS LETTERS
AN INELASTIC ROTATIONAL TRANSFER STUDY OF NH3 COLLIDING WITH H2 AND He M. BROQUIER, A. PICARD-BERSELLINI Laboratoire de Photophysique Molkulaire du CNRS, Britiment 213, Universitk de Paris&d,
91405 Orsay Cedex, France
and J. HALL Rice Quantum Institute, Houston, TX 77001, USA
Received 10 October 1986; in final form 9 March 1987
We have studied the absorption profile of ammonia in the 6 l.trn (diode laser) and 3 pm (color center laser) regions, and in collisions with H2 and He, in order to obtain new experimental results at room and low temperatures. The behaviour of the different collision gases is discussed.
1. Introduction We have studied the absorption profile of ammonia in the 6 and 3 pm regions. The aim of this paper is to present new experimental results on the NH,-H,(para) collision and to make comparisons with previous results for NH3-H*(normal) and NH,-He.
2. Experimental We used a diode laser in the 6 pm region, and a color center laser in the 3 pm region. The experimental apparatus has been described in detail elsewhere [l]. We have studied the absorption lineshape of the vibrational lines of NH3 perturbed by para-HZ. From the line profiles we have evaluated the pressure broadening coefficient y( MHz/Torr) by measuring the Lorentz hwhm as a function of the pressure of the collision gas. The pressure broadening cross sections are then given by a=2nx106yINor7(A2), where N,, is the number of molecules per m3 at a 0 009-2614/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
pressure of 1 Torr, B= ( 8kT17r~)1’2 is the average velocity and p the reduced mass of the two collision partners. For all our measurements the experimental error is around 2 to 3%. A study of the collision pairs NH,-He and NH3-Hz (para-hydrogen) has the double advantage of providing information on the most probable collisions in the interstellar medium and of testing the validity of the hypothesis that the behaviour of helium is identical to that of para-hydrogen [ 21. Ortho- and para-hydrogen are distinguished by the parity of their rotational states. The rotational level population distribution at a temperature T, is
-= n
cJg(J)(IJ+
l)eXp( -EJ/kBTl) ’
(1)
where g(J) is the nuclear degeneracy. Since the nuclear spin of each proton is l/2, the nuclear spin T of the molecule can take the values T= 1 and T= 0, corresponding to spins parallel and antiparallel respectively. The nuclear degeneracy is equal to 2T+ 1, and is 3 for the triplet states (T= 1) and 1 for the singlet states ( T= 0). The symmetric spin function of the triplet state is associated with an antisymmetric rotational function corresponding to an odd value of the rotational quantum number. The 531
Volume 136, number
6
CHEMICAL
PHYSICS
antisymmetric spin function in the singlet state is associated with a symmetric rotational function with J even, g(J) is equal to 3 for J odd and 1 for J even. Except at very high temperatures, singlet-triplet transitions are extremely rare due to the weakness of the intermolecular magnetic interactions which produce such transitions. The group of levels with J odd and those with J even essentially behave as two different species. The ortho species occurs with the greater statistical weight. Transitions with AJ odd are not rigorously forbidden and the system evolves very slowly under the effect of those rare collisions with J odd, towards the equilibrium distribution given by eq. (1) at 300 K, n(ortho)=in and n(para)=fn; but at 20 K n(para)=n and n(ortho)=O (all the rotational population is in the state J=O). It is possible to obtain para-H, by liquefaction of the gas in the presence of a catalyst whose role is to facilitate the magnetic interactions permitting the transitions J= l--t J= 0. The CEA laboratory (DPC) provided us with (100% para) hydrogen. The reconversion time para+ortho is slow in comparison with the time scale of our measurements (we have compared results obtained at the beginning of the day with those obtained under the same conditions at the end of the day).
LETTERS
22 May 1987
Table 1 NH,-He experimental sections Transition %J&J’)
Table 1 presents our results as a function of the rotational quantum numbers J and IC,and as a function of the temperature.
parameters
and cross
T(K)
Y (MHz/Torr )
0 (A*)
300 163
1.24 1.86
17 19
300 188
1.44 1.66
20 18
300 173
1.1 1.33
15 14
173
1.32
14
300 176 145
3.4 5.2 5.5
35 41 40
pP-,(2)
300 173
4.2 6
43 47
pP-I(2)
300
3.9
40
RQ+7(8)
300
3.8
39
300 173
2.75 4.5
29 36
173
4.2
33
300 163
2.85 3.4
30 26
pP-s(5)
300
2.68
28
pP+I(2)
300 186
3 4.1
31 34
NH,-He, pP-s(s)
vq
pP+,(2)
NH3-He, pP+k5)
v,
pP-,(3) NHJ-H2, pP-s(5)
NH~-Hz, ‘P-2(5)
~4
~3
pP-I(3)
3. Results
pressure broadening
NH,-H,(para), pP+5(5)
~4
3.1. Comparison of the results We will compare our results with those already obtained by other authors using alternative methods. Similarly we will compare the experimental results for the two bands. To our knowledge there are no previous results for collisions at 6 or 3 pm. However, numerous results exist in the microwave region. Note that in the infrared region the transitions are rovibrational while in the microwave they are purely rotational. Firstly, we compare the results obtained with normal hydrogen; these cross sections are always larger than those obtained with para-H,. We next 532
compare our results for the collision NH3-Hz ( para) with those obtained by Oka [ 21 (table 2). In effect it was from these results that Green put forward the hypothesis that the collision NH3-H2( para) is iden, tical to that with He. The comparison, though difficult because we have not studied the same transitions, shows that for the same J, the cross seo tion for the transition (J,K) = (2,2) in the microwave region is the same as that found for the collision with helium and not for the collision with parahyThe cross section obtained for drogen.
22 May 1987
CHEMICAL PHYSICS LETTERS
Volume 136, number 6
Table 2 Comparison of our experimental results with those obtained by Oka [ 21 and Townes [ 51
J”=2 K”=l NH,-He microwave V3 Va
J”=5
J”=3 K”=2 lS(2)
K”=l
K”=3
K”=2
K”=5 18(2)
18(2) 15.3
17.2 20 21(2)
NHX-H*(pam) microwave
20(2) 29
v3
V4 NH,-Hz microwave JJ3 Vd
31 31(2)
30(2) 29 35.1
43
NH,-Hz(para) is 3 1 A*, whereas Oka found 21 A*. As has been noted previously, this result is significant since it justifies a posteriori the calculations undertaken by Valiron and co-workers [ 31 and Billing et al. [4]. Conversely, the results with helium are more or less identical to those of Townes and co-workers [ 5 1, since they confirm that the Jdependence of the cross section is very weak and has a value equal to 18 AZ. Now it is necessary to note that there is a depen: dence of the cross sections on the vibrational level studied. We consider it likely that the difference in the measurements is due to this dependence. The variation of the cross sections as a function of the temperature shows that, in general, there is an increase in the cross section as the temperature decreases. But for the collision NH3-He and for the transition ‘P, (2) (upper P denotes the condition AK= - 1, lower P denotes AJ= - 1; (2) denotes the initial J level of the transition, and (1) the initial K level), the cross section decreases with T, likewise for the collision NH,-H2(para) and for the transition ‘P,( 5). It is interesting to note that the calculations of Billing et al. [ 41 for the NHs-He collision show the same evolution. Thus the intermolecular potential and the semi-classical calculations seem to be valid.
3.2. Comparison with theoretical calculations Quantum-mechanical close coupling calculations have been performed on rotational energy transfer in collisions of para-ammonia with ground state (j= 0) para-hydrogen by Valiron and co-workers [ 31. Rate coefficients are given for the temperature range 15 Q Tg 300 K. The calculations employed an ab initio potential energy surface derived from separate determinations of the SCF and dispersion energies. The MOLSCAT computer package was used to perform the scattering calculations. They have calculated pressure broadening cross sections for a selection of inversion transitions in ammonia. These theoretical results are compared with the experimental values obtained by us (see table 3). The theoretical broadening cross sections are too low, and Table 3 Comparison between theoretical NH3-HZ (para) cross sections
pp+,(2)
and
experimental
T
= (4
163 186 207 294
17.6 34 a> 18 18.7, 31 a)
a) Our experimental result. The theoretical results are given by Danbyetal. [3].
$33
Volume 136, number 6
CHEMICAL PHYSICS LETTERS
this could be due to a number of reasons: - potential insufficiently anisotropic; - vibrational effect in our experiment; - elastic part not taken into account in the calculations; - rotational excitation of the hydrogen not taken into account in the calculations. Acknowledgement The authors wish to thank Professor R.F. Curl and Professor F. Tittel for their interest in this research and for helpful discussions. A part of the work has been supported by a grant from NATO. References [ 1] M. Broquier and A. Picard-Bersellini, Chem. Phys. Letters 111 (1984) 602; 121 (1985) 437;
534
22 May 1987
M. Broquier, A. Picard-Bersellini and H. Aroui, Opto 86 ES1 Publications; M. Broquier, A. Picard-Bersellini, G.D. Billing and J. Hall, Proceedings of the Fifteenth International Symposium on Rarefied Gas Dynamics, Vol. 1, II, Grado (1986). [2] T. Oka, private communication, as quoted in: S. Green, J. Chem. Phys. 73 (1980) 2740. [ 31 G. Danby, D. Flower, E. Kochanski, L. Kurdi, P. Valiron and G.H.F. Diercksen, J. Phys. B, to be published; G. Danby, D. Flower, P. Valiron, E. Kochanski, L. Kurdi and G.H.F. Diercksen, J. Phys. B, to be published. [4] G.D. Billing, L. Poulsen and G.H.F. Diercksen, Chem. Phys. 98 (1985) 397; 105 (1986) 145; Chem. Phys. Letters 121 (1985) 94. [ 51 C.H. Townes, Phys. Rev. 70 (1946) 109A, 665; B. Bleaney and R.P. Penrose, Proc. Roy. Sot. Al89 (1947) 358; P.T.P. Ho and C.H. Townes, Ann. Rev. Astron. Astrophys. 21 (1983) 239.