- Email: [email protected]
Line shift and mixing in the ν4 and 2ν2 band of NH3 perturbed by H2 and Ar
Journal of Molecular Spectroscopy 233 (2005) 138–148 www.elsevier.com/locate/jms
Line shift and mixing in the m4 and 2m2 band of NH3 perturbed by H2 and Ar M. Dhib a,*, M.A. Echargui a, H. Aroui a, J. Orphal b, J.-M. Hartmann b a
Laboratoire de Physique Mole´culaire, Ecole Supe´rieure des Sciences et Techniques de Tunis, 5 Av Taha Hussein 1008 Tunis, Tunisia b Laboratoire de Photophysique Mole´culaire, UPR 3361 du CNRS, Universite´ de Paris-Sud, baˆt. 350, 91405 Orsay Cedex, France Received 26 April 2005
Abstract Pressure induced line shift and line mixing parameters have been measured for 66 rovibrational lines in the m4 band and for 10 lines in the 2m2 band of NH3 perturbed by H2 and Ar at room temperature (T = 296 K). These lines with J values ranging from 2 to 10 are located in the spectral range 1450–1600 cm1. Experiments were made with a high-resolution Fourier transform spectrometer. The line shifts and line mixing parameters have been derived from the non-linear least-square multi-pressure fitting technique. The shift coefficients are compared with those calculated from the Robert–Bonamy formalism (RB). The results are generally in satisfactory agreement with the experimental data. 2005 Elsevier Inc. All rights reserved. Keywords: Shift; Line mixing; Ammonia; H2; Ar
1. Introduction Knowledge of the lineshape parameters of molecular transitions and of their dependence upon pressure is useful both to fundamental and to applied spectroscopical studies. It gives an insight into intermolecular forces and is also essential for monitoring the composition of planetary atmospheres and for quantitative analysis of pollutants. The ammonia molecule has always played an important role in the field of spectroscopy because of its peculiar properties. Indeed, it has a large molecular dipole and an inversion spectrum, which are important properties for modeling intermolecular forces. Moreover, ammonia, which is present in many planetary atmospheres [1,2] and other celestial bodies, is commonly used as an interstellar thermometer and is considered as an industrial and biological pollutant [3].
*
Corresponding author. Fax: +216171391166. E-mail address: [email protected] (M. Dhib).
0022-2852/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2005.06.012
Broadening coefficients in the infrared spectra of ammonia have been the subject of numerous experimental and theoretical studies for different bands and collision partners (He, Ar, H2, O2, N2, CO2, air, . . .) [4–8]. On the other hand, the line shifts and especially line mixing have received much less attention in the past, mainly because they are expected to be small and their observation is therefore difficult. The situation is now completely different. A large number of shift measurements for the ammonia molecule have been published. Temperature dependence of self-shift and shifts of ammonia perturbed by N2 and CO2 in the m2 band were studied by Baldacchini et al. [9,10]. The self-shifts in the m1 band were studied by Markov et al. [4] using a difference frequency laser. Measurements of line shifts with a frequency-stabilized diode laser in the m2 and (2m2 m2) bands of NH3 were studied by Raynaud et al. [11]. Pine et al. [12] measured the shift coefficients of NH3 in the m1 band perturbed by He, Ar, O2, H2, and N2. On the other hand, measurements of line mixing effects are still lacking especially
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
for the m4 band because of its strong Coriolis interaction with the 2m2 band. However, it is well known that a rigorous treatment of vibration–rotation spectral line shapes must include interference effects caused by the overlapping of lines. Recently, Hadded et al. [13] have studied line mixing of 15 inversion doublets of NH3 perturbed by He, Ar, and H2. More recently, these authors [14,15] have measured line mixing effects in the m1 and m2 bands of NH3 at high pressure. They have demonstrated the necessity of take into account line mixing for the treatment of inversion-rotation spectra of NH3. On the theoretical side, semiclassical calculations of shift coefficients have been previously performed by Parson et al. [16] for the (J, K) = (12, 12) inversion line of ammonia. Buffa et al. [17] calculated the pressure shifts of ammonia using the Anderson–Tsao–Curnutte (ATC) theory [18] and the Quantum Fourier Transform (QFT) theory. Baldacchini et al. [10] used the ATC theory for calculation of shifts of NH3–N2 and NH3–CO2 in the m2 band. Markov et al. [4] calculated the self-shifts in the m1 band. The latter calculations were based on the ATC theory, in which only dipole–quadripole interaction is taken into account. The present paper is an experimental analysis of the line shift and line mixing parameters in the PP and RP branches of the m4 perpendicular band and QQ branch of the 2m2 parallel band of NH3 perturbed by H2 and Ar in the pressure range 0–170 Torr. In addition, the shift coefficients have been calculated on the basis of the semiclassical Robert–Bonamy (RB) formalism developed in [19]. The effect of the inversion movement of NH3 was taken into account [6].
139
2. Experimental and fitting procedures 2.1. Experiment All experiments were made with a high-resolution Fourier transform spectrometer (FTS) Bruker IFS 120 HR as described previously [20,21]. This spectrometer was equipped with a globar source, a KBr beam splitter, a filter eliminating infrared radiation for m > 2500 cm1, and a HgCdTe detector cooled to 77 K. The resolution of the spectrometer was about 0.0038 cm1. Samples of ammonia, argon and hydrogen in natural abundances were provided by Air Liquide France with stated purities of 98.5, 99.5, and 99.9%, respectively. The gas mixture was contained in a 10.5 cm absorption cell equipped with CaF2 windows. The cell was first filled with NH3 at a constant pressure of 7 Torr. Next, Ar or H2 was added in stages at pressures ranging 22–170 Torr. To allow equilibrium to occur, the sample was filled into the cell for several hours before high-resolution scans were recorded. During the scans, the sample pressures remained fairly constant and were measured with three Baratron capacitance gauges accurate to 0.5%, with full-scale readings of 10, 100, and 1000 Torr. The spectra recorded at room temperature, T = 296 ± 1 K, were obtained by averaging 100 scans and calculated using a triangular apodization function. The FTS was evacuated with a cryopump to remove residual H2O. Reference spectra were taken under the same conditions (alignment and resolution) but with the empty cell. The transmittance at wavenumber r was calculated from the measured intensities by the usual ratio of recordings with and without the gas sample.
Fig. 1. Results of multi-pressure fits in the case of the PP(4, 3)s line for NH3 perturbed by H2 at 296 K. (—) and (d) are the measured and calculated values, respectively. Measured minus calculated deviations are shown in the lower part of plots.
140
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
2.2. Fitting procedure The analyses of spectra were performed taking into account interference effects. Thus within the impact theory of the spectral shape and for moderately overlapping lines at low pressure as considered in this work, the collisional absorption coefficient a (r) can be written as [22,23], P NH3 X PY k ðr rk Þ þ P ck aðrÞ ¼ Sk ; ð1Þ p lines k ðr rk Þ2 þ ðP ck Þ2 where k represents the line vi Ji Ki fi vf Jf Kf, Sk its intensity, rk its wavenumber including the collisional shift dc (dc = rk r0, r0 being the unperturbed wavenumber), ck its halfwidth, and Yk its interference parameters related to the off-diagonal element of the relaxation matrix. The experimental spectra were analyzed by means of non-linear least-squares fitting procedures using the following theoretical expression sC (r) for the transmission and the collisional absorption coefficient in Eq. (1). Z þ1 sC ðrÞ ¼ F App ðr r0 Þ 1 Z þ1 exp l aDop ðr0 r00 Þaðr00 Þ dr00 dr0 ;
successively adjusted using Eq. (2). The parameters deduced from the fits for a line k are Pck, rk, Sk and PYk. Note that the linewidths ck and line intensities Sk were already published in [5,7,20]. An example of a multi-pressure fit in the case of PP(4, 3)s line for NH3 broadened by H2 is given in Fig. 1. The measured values of the collisional wavenumber rk and of the interference parameter Yk are well fitted by linear relationships, rk ¼ r0 þ P NH3 dNH3 NH3 þ P d0 ; PY k ¼ P NH3 Y NH3 NH3 þ PY 0 ; where d0 is the line shift coefficient, r0 is the unperturbed line-center frequency, Y0 the first-order line mixing parameter, dNH3 –NH3 and Y NH3 –NH3 are
1
ð2Þ where aDop is the Doppler profile, FAPP is the Fourier transform apparatus function (approximated here with a Gaussian shape), and l = 10.5 cm is the cell length. The collisional parameters for a given temperature were obtained by means of non-linear least-square multi-pressure fitting in which all spectra at various pressures are
Fig. 3. Line mixing coefficients in the symmetric (upper symbols) and antisymmetric (lower symbols) components of the PP (4, 4) doublets as a function of pressure.
Fig. 2. Collision-induced variation of the center wavenumber rk for the RP(2, 0)a line of the m4 band and QQ(10, 9)a line of the 2m2 band of NH3 perturbed by H2.
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
141
Table 1 Line shift d0 (in 103 cm1 atm1) and line mixing coefficients Y0 (in atm1) in the m4 band of NH3 perturbed by H2 at 296 K NH3–H2 Line
m0(cm1)
Y exp 0
m4 band P P(2, 1)s P P(2, 1)a P P(2, 2)s P P(2, 2)a
1590.6916 1591.1050 1594.7907 1595.0801
dexp 0
dcalc 0
0.16(0.01) 0.17(0.11) +0.21(0.04) 0.28(0.06)
4.16(1.03) 4.47(1.05) 4.15(0.82) 2.62(0.61)
5.25 5.25 3.68 3.68
P(3, 1)s P(3, 1)a P P(3, 2)s P P(3, 2)a P P(3, 3)s P P(3, 3)a
1571.8315 1572.4882 1575.8518 1576.3173 1579.3615 1579.6363
+0.05(0.03) 0.06(0.04) +0.20(0.03) 0.17(0.02) +0.21 (0.03) 0.21(0.04)
+0.19 0.19
3.42(0.42) 3.32(0.42) 4.63(0.79) 4.14(1.71) 4.61 (2.00) 4.85(0.67)
4.93 4.93 4.86 4.86 3.72 3.72
P
P(4, 1)s P(4, 1)a P P(4, 2)a P P(4, 3)s P P(4, 3)a P P(4, 4)s P P(4, 4)a
1553.6294 1554.7340 1558.2494 1560.8895 1561.3835 1563.8239 1564.0824
+0.09(0.05) 0.11(0.05) +0.16(0.03) +0.09(0.03) 0.12(0.02) +0.30(0.02) 0.34(0.03)
+0.10 0.10 +0.39 0.39
5.48(0.69) 4.42(0.66) 6.25(0.29) 3.92(0.72) 3.20(0.93) 3.04(0.52) 4.78(0.92)
4.84 4.84 4.88 4.02 4.02 3.69 3.69
P
P(5,1)s P(5, 1)a P P(5, 2)s P P(5, 2)a P P(5, 3)s P P(5, 3)a P P(5, 4)s P P(5, 4)a P P(5, 5)s P P(5, 5)a
1536.2088 1538.0102 1539.7596 1541.0041 1542.9798 1543.8550 1545.8043 1546.3315 1548.1839 1548.4290
0.09(0.03) 0.10(0.04) +0.14(0.01) 0.11(0.03) +0.11(0.01) 0.10(0.03) +0.08(0.03) 0.09(0.02) +0.33(0.03) 0.33(0.03)
+0.02 0.02 0.07 +0.07 +0.32 0.32
2.95(0.17) 4.33(0.48) 5.60(0.85) 5.11(0.91) 4.30(0.94) 4.02(0.46) 2.63(0.15) 4.24(1.36) 2.66(0.09) 5.52(0.87)
4.87 4.87 5.03 5.03 4.09 4.09 3.52 3.52 4.06 4.06
P
P(6,1)s P(6, 1)a P P(6, 3)s P P(6, 3)a P P(6, 4)s P P(6, 4)a P P(6, 5)s P P(6, 5)a P P(6, 6)s P P(6, 6)a
1519.6627 1522.3847 1525.7625 1527.0615 1528.3774 1529.2897 1530.6141 1531.1591 1532.4503 1532.6830
+0.07(0.01) 0.05(0.02) +0.06(0.03) 0.06(0.01) +0.07(0.02) 0.07(0.06) +0.09(0.04) 0.07(0.03) +0.34(0.01) 0.38(0.03)
+0.07 0.07 +0.45 0.45
2.79(0.27) 3.27(0.85) 5.21(0.50) 3.56(0.26) 3.24(0.63) 2.40(0.35) 2.29(0.27) 4.22(0.38) +2.96(0.53) 6.62(0.35)
4.99 4.99 4.39 4.39 3.52 3.52 3.58 3.58 4.43 4.43
P
P(7,1)s P(7, 2)a P P(7, 3)s P P(7, 3)a P P(7, 4)s P P(7, 4)a P P(7, 5)s P P(7, 5)a P P(7, 6)s P P(7, 6)a P P(7, 7)s P P(7, 7)a
1504.0218 1509.4479 1509.1379 1511.3131 1511.5985 1513.0439 1513.6480 1514.6055 1515.3243 1515.8819 1516.6309 1516.8521
0.10(0.05) 0.16(0.02) +0.07(0.01) +0.07(0.02) 0.10(0.01) 0.12(0.06) 0.10(0.05) 0.11(0.04) +0.10(0.02) 0.11(0.02) +0.49(0.09) 0.45(0.09)
+0.09 0.09 +0.46 0.46
3.09(0.53) +1.48(0.83) 4.50(0.79) 4.85(0.52) +1.44(0.66) 3.71 (1.68) +2.42 (0.36) 4.09(0.55) 2.74 (0.56) 3.13(0.41) +1.32 (0.52) 6.13(0.60)
5.18 5.37 4.69 4.69 3.81 3.81 3.42 3.42 3.70 3.70 4.74 4.74
P
1494.2421 1493.5269 1496.1740 1497.6750 1497.3332 1499.8082 1499.9436 1500.5103
0.10(0.03) 0.08(0.06) +0.10(0.02) 0.12(0.05) +0.13 (0.07) 0.08(0.04) +0.12(0.05) 0.14(0.01)
P P
P
P
P
P
P(8, 1)a P(8, 3)s P P(8, 3)a P P(8, 4)a P P(8, 5)s P P(8, 6)a P P(8, 7)s P P(8, 7)a P
Y exp (Ref. [13] ) 0
+0.14 0.14
2.91(1.00) 5.44 2.43 (0.63) 4.95 5.66(1.57) 4.95 4.64(0.98) 4.18 4.44 (1.50) 3.64 2.23 (0.96) 3.42 2.39(0.99) 3.87 3.21 (1.66) 3.87 (continued on next page)
142
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
Table 1 (continued) NH3–H2 Line
m0(cm1)
Y exp 0
Y exp (Ref. [13] ) 0
dexp 0
dcalc 0
P
1500.7334 1500.9439
+0.48(0.03) 0.53 (0.05)
+0.49 0.49
+4.53 (0.83) 4.37 (0.66)
5.04 5.04
P(2, 0)a P(3, 0)s R P(4, 0)a R P(5, 0)s R P(7, 0)s R P(8, 0)a R P(9, 0)s
1586.8714 1567.9930 1552.1574 1533.7968 1502.7553 1493.8633 1474.7257
+0.11(0.02) 0.09(0.03) 0.09(0.02) +0.11(0.04) 0.11(0.02) 0.10(0.02) +0.14(0.04)
8.50(0.49) 4.86 (1.27) 4.39 (0.77) 6.61(0.75) 4.17(1.69) 2.66 (0.41) 6.76(0.80)
5.89 8.08 8.77 8.97 8.82 8.74 8.59
2m2 band Q P(4, 3)a Q Q(3, 3)a Q Q(4, 3)a Q Q(4, 4)a Q Q(5, 5)a Q Q(6, 6)a Q Q(7, 7)a Q Q(8, 8)a Q Q(9, 9)a Q Q(10, 9)a
1515.4684 1594.8992 1596.7714 1593.1724 1590.8807 1588.0293 1584.6276 1580.6885 1576.2251 1587.8357
0.81(0.35) 0.29(0.11) 0.87(0.18) 0.39(0.09) 0.08(0.03) 0.44(0.05) 0.82(0.21) 0.34(0.09) 0.93(0.05) 0.60(0.05)
13.92(6.85) 12.31(0.92) 20.89(4.64) 19.40 (0.72) 15.94(0.89) 17.20(2.09) 17.81(4.38) 21.68(4.40) 15.78(1.22) 11.39(0.49)
10.81 11.73 11.80 12.48 13.13 13.74 14.26 14.67 15.00 15.55
P(8, 8)s P(8, 8)a
P
R R
respectively the shift and interference parameter of pure ammonia at low pressure (P NH3 ¼ 7 Torr) and P is the partial pressure of the perturber gas (H2 or Ar). Typical plots of the line center frequency rk and line mixing Yk as a function of the pressure P are shown in Figs. 2 and 3 respectively. Within the measurement scatter, the shift and line mixing varies linearly with pressure over the range considered here (0–170 Torr), and no non-linear behavior was observed. The H2 and Ar-shift coefficients d0 and line mixing coefficients Y0 are determined as the slopes of these lines and are presented in Tables 1 and 2 along with the estimated experimental errors. The main sources of uncertainties in the results arise from the perturbations due to interfering lines (mainly coming from H2O), the base line location, the line shape model used, and the approximations done in accounting for the instrumental line shape. The values given in parentheses correspond to the statistical errors expressed as one time standard deviation for line shifts coefficients and line mixing parameters.
3. Theoretical calculations of shifts Within the Robert–Bonamy formalism, the line shift coefficients for the transition f ‹ i are given by, Z 1 n2 X dif ¼ q vF ðvÞ dv 2pc J 2 J 2 0 Z 1 2pb Im ½SðbÞ db; ð3Þ 0
where n2 is the number density of the perturbing molecules, qJ 2 is the relative population of the perturber in the jJ2, m2 = 0æ states (this factor reduces to one and summation cancels out for monoatomic perturber), v the relative velocity of the absorber–perturber collision pair, F (v) the Maxwellian velocity distribution, and b the impact parameter. Im [S(b)] is the imaginary part of the differential cross section given by Im ½SðbÞ ¼ expbðRe S aniso ðbÞÞc sinbIm S aniso ðbÞ 2 2 þ S iso 1 ðbÞc;
ð4Þ
where • S iso 1 is a vibrational phase shift defined from the difference of the isotropic part of the potential in the initial and final states of transition [24]: S iso 1 ¼ S 1;f2 S 1;i2 ; • the real part of S aniso derived from the anisotropic 2 part of the potential is expressed as the second-order terms of the development of S2(b): Re ðS aniso Þ ¼ S 2;f2 þ S 2;i2 þ S 2;f2i2 ; 2 • the imaginary part of S aniso results from the non-com2 mutative character of the interaction at different times and is, like the first-order contribution, an additive quantity with respect to the shifts of the initial and final levels of the transitions: 0 0 Im ðS aniso Þ ¼ S S . 2 2;f2 2;i2 All the S1, S2, and S 02 terms are given by Eqs. (8)–(11) of [19]. The expressions of Re S aniso for the interaction be2 tween NH3 and atomic or diatomic molecules have been previously given by Eqs. (6) and (7) of [5] and Eqs. (10)
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
143
Table 2 Line shift d0 (in 103 cm1 atm1) and line mixing coefficients Y0 (in atm1) in the m4 band of NH3 perturbed by Ar at 296 K NH3–Ar Line
m0(cm1)
Y exp 0
m4 band P P(2, 1)s P P(2, 1)a P P(2, 2)s P P(2, 2)a
1590.6916 1591.1050 1594.7907 1595.0801
dexp 0
dcalc 0
0.09(0.05) 0.11(0.08) +0.16(0.02) 0.14(0.07)
6.05(0.93) 7.22(0.92) 8.77(1.22) 5.89(1.52)
5.79 5.79 5.68 5.68
P(3, 1)s P(3, 1)a P P(3, 2)s P P(3, 2)a P P(3, 3)s P P(3, 3)a
1571.8315 1572.4882 1575.8518 1576.3176 1579.3615 1579.6363
+0.04(0.01) 0.04(0.03) +0.08(0.06) 0.12(0.02) +0.09(0.03) 0.12(0.02)
+0.03 0.03
4.70(0.83) 4.68(1.11) 5.64(0.92) 7.35(1.03) 6.35(1.10) 5.17(1.36)
5.80 5.80 5.79 5.79 5.64 5.64
P
P(4, 1)s P(4, 1)a P P(4, 2)a P P(4, 3)s P P(4, 3)a P P(4, 4)s P P(4, 4)a
1553.6294 1554.7340 1558.2494 1560.8895 1561.3835 1563.8239 1564.0824
+0.09 (0.04) 0.08(0.01) 0.10(0.06) +0.09(0.04) 0.09(0.03) +0.07(0.04) 0.11(0.02)
+0.03 0.03 +0.10 0.10
6.63 (1.19) 3.03(0.45) 6.09(0.93) 5.27(0.48) 4.21(1.40) 4.03(0.71) 4.13(0.91)
5.68 5.68 5.75 5.73 5.73 5.62 5.62
P
P(5, 1)s P(5, 1)a P P(5, 2)s P P(5, 2)a P P(5, 3)s P P(5, 3)a P P(5, 4)s P P(5, 4)a P P(5, 5)s P P(5, 5)a
1536.2088 1538.0102 1539.7596 1541.0041 1542.9798 1543.8550 1545.8043 1546.3315 1548.1839 1548.4290
+0.08(0.03) 0.11(0.01) +0.04(0.01) 0.06(0.01) +0.09 (0.02) 0.04(0.02) 0.04(0.02) +0.03(0.02) +0.17(0.04) 0.17(0.03)
+0.02 0.02 +0.12 0.12
4.98(0.75) 3.51(1.06) 4.41(0.89) 5.75(0.92) 5.43 (0.61) 5.02(1.23) 2.82(0.98) 4.10(0.57) 5.37(0.70) 4.32(1.55)
5.46 5.46 5.57 5.57 5.68 5.68 5.67 5.67 5.60 5.60
P
P(6, 1)s P(6, 1)a P P(6, 3)s P P(6, 3)a P P(6, 4)s P P(6, 4)a P P(6, 5)s P P(6, 5)a P P(6, 6)s P P(6, 6)a P P(7, 1)s P P(7, 2)a P P(7, 3)s P P(7, 3)a P P(7, 4)s P P(7, 4)a P P(7, 5)s P P(7, 5)a P P(7, 6)s P P(7, 6)a P P(7, 7)s
1519.6627 1522.3847 1525.7625 1527.0615 1528.3774 1529.2897 1530.6141 1531.1591 1532.4503 1532.6830 1504.0218 1509.4479 1509.1379 1511.3131 1511.5985 1513.0439 1513.6480 1514.6055 1515.3243 1515.8819 1516.6309
+0.03(0.02) +0.05(0.03) +0.08(0.03) 0.07(0.03) +0.02(0.01) 0.04(0.01) 0.03(0.01) 0.02(0.02) +0.19(0.05) 0.22(0.038) +0.09(0.02) 0.08(0.01) +0.08(0.03) +0.01(0.01) +0.07(0.02) 0.04(0.07) +0.09(0.06) 0.07(0.05) +0.04(0.02) 0.05(0.03) +0.19(0.08)
3.41(0.72) 5.94(0.86) 5.05(1.09) 3.16(0.41) 4.21(0.53) 4.84(0.92) 5.86(1.14) 5.42(0.54) 2.23(0.66) 3.77(1.81) 5.80(0.95) 3.99(1.07) 2.03(0.65) 5.70(1.33) 3.90(1.62) 3.82(1.61) 5.04(0.39) 5.41(0.66) 3.46(0.75) 3.86(0.53) 4.69(0.28)
5.13 5.13 5.48 5.48 5.58 5.58 5.62 5.62 5.58 5.58 4.70 4.90 5.15 5.15 5.36 5.36 5.49 5.49 5.57 5.57 5.55
P
1516.8521 1494.2421 1493.5269 1496.1740 1497.6750 1497.3332 1499.8082 1499.9436 1500.5103
0.18(0.05) 0.12(0.05) +0.08(0.02) 0.15(0.10) 0.13(0.01) +0.08(0.05) +0.07(0.03) +0.09(0.06) 0.11(0.07)
P P
P
P
P
P(7, 7)a P(8, 1)a P P(8, 3)s P P(8, 3)a P P(8, 4)a P P(8, 5)s P P(8, 6)a P P(8, 7)s P P(8, 7)a P
Y exp (Ref. [13]) 0
+0.02 0.02 +0.15 0.15
+0.05 0.05 +0.20 0.20
+0.07 0.07
4.57(0.60) 5.55 2.90(0.65) 4.19 4.65(1.02) 4.76 4.95(1.35) 4.76 4.04(1.00) 5.06 7.57(0.91) 5.36 5.95(1.06) 5.42 3.73(1.19) 5.59 4.54(1.50) 5.59 (continued on next page)
144
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
Table 2 (continued) NH3–Ar Line
m0(cm1)
Y exp 0
Y exp (Ref. [13]) 0
dexp 0
dcalc 0
P
P(8, 8)s P(8, 8)a R P(2, 0)a R P(3, 0)a R P(4, 0)a R P(5, 0)s R P(7, 0)a R P(8, 0)a R S ð9; 0ÞS
1500.7334 1500.9439 1586.8714 1567.9930 1552.1574 1533.7968 1502.7553 1493.8633 1474.7257
+0.27(0.03) 0.27(0.03) 0.11(0.01) 0.09(0.03) 0.05(0.02) +0.09(0.03) 0.04(0.01) 0.11(0.04) +0.12(0.07)
+0.23 0.23
3.73(1.22) 2.44(1.05) 8.85(1.16) 3.26(0.90) 5.06(0.93) 5.99(0.50) 3.88(0.71) 3.67(0.42) 5.36(1.49)
5.55 5.55 5.64 5.80 5.72 5.46 4.67 4.25 3.82
2m2 band P(4, 3)a Q Q(3, 3)a Q Q(4, 3)a Q Q(4, 4)a Q Q(5, 5)a Q Q(6, 6)a Q Q(7, 7)a Q Q(8, 8)a Q Q(9, 9)a Q Q(10, 9)a
1515.4684 1594.8992 1596.7714 1593.1724 1590.8807 1588.0293 1584.6276 1580.6885 1576.2251 1587.8357
0.81(0.13) 0.16(0.04) 0.85(0.26) 0.34(0.06) 0.32(0.18) 0.11(0.09) 0.76(0.13) 0.60(0.28) 0.53(0.03) 0.44(0.22)
20.27(2.00) 14.96(2.00) 18.29(5.16) 18.45(2.87) 14.64(3.50) 20.42(1.18) 27.11(3.28) 16.70(3.76) 6.28(0.42) 10.57(1.98)
14.42 14.60 14.91 15.07 15.65 16.04 16.28 16.41 16.46 18.57
P
Q
and (11) of [6] and for collision induced transitions with DK = 0 and DK = ±3. Because of the inversion motions (e = ±1 denoting the symmetry of wave function with respect to the inversion), S2,f2i2 = 0 for l1 = 1 or l1 = 3, l representing the order of spherical harmonics considered for absorber. The imaginary part Im ðS aniso Þ may 2 be easily obtained from Re ðS aniso Þ by replacing the reso2 nance function fn(k) by Ifn(k) defined in [25]. The trajectory model used [26] accounts for influence of the isotropic potential, taken as a Lennard-Jones 6– 12 potential, in energy conservation and in the equation of motion around the distance of closest approach rc. A straight-line trajectory tangential to the real trajectory near rc and described at the relative velocity v0c has been assumed. The Maxwell–Boltzmann distribution of relative velocity F(v) in Eq. (6) was considered by using a method previously described [27] which involves a 15point Laguerre integration of velocities. The LennardJones parameters for the molecular pair are evaluated pffiffiffiffiffiffiffiffi 2 from the usual rules e ¼ e1 e2 and r ¼ r1 þr . 2 3.1. H2-shift calculation The total intermolecular potential V includes anisotropic and isotropic induction and dispersion contributions obtained by Leavitt [28], such as disp V ¼ V aniso þ V ind iso þ V iso ;
ð5Þ
where V aniso ¼ V l1 Q2 þ V Q1 Q2 þ V X1 Q2 þ V l1 U2 þ V Q1 U2 þ V X1 U2 þ V l2 a2 þ V l2 a2 c2 þ V l1 Q1 a2 1
1
þ V l1 Q1 a2 c2 þ V a1 c1 a2 c2 þ V a1 c1 a2 þ V a1 c2 a2 þ V A1k a2 þ V A1? a2 þ V A1k a2 c2 þ V A1? a2 c2 þ V a2 A01
ð6Þ
V ind iso ¼
l21 a2 r6
ð7Þ
and 3 U 1 U 2 a1 a2 . ð8Þ 2 ðU 1 þ U 2 Þ r6 Here, the index 1 refers to the absorber (NH3) and 2 to the perturber (H2); l, Q, X, and U are the dipole, quadrupole, octupole, and hexadecapole moments of the molecules; a, c, Ai, and A^ are, respectively, the average polarizability, the polarizability anisotropy, and the hyperpolarizabilities of the molecules. Ui is the first ionization energy for molecule i. The electrostatic interactions from the octupole and hexadecapole moments of the molecules may be found in [29]. The dispersion potential V a2 A01 , introduced by Bonamy and Robert [30] gives rise to DK = ±3 transitions. The analytic contributions to the real and imaginary differential cross sections l1 l2 S 2 ½rc ðbÞ (l1 and l2 represent the order of the spherical harmonics considered for the absorber and perturber) of the electrostatic dipole–quadrupole and quadrupole– quadrupole interactions and of the induction and dispersion energy are, except the last term in Eq. (6), given by Leavitt [31]. The contributions from the octupole and hexadecapole moments of the molecules may be found in [29] and those derived from V a2 A01 are given in [30]. The selection rules for optical transitions studied in the m4 perpendicular and 2m2 parallel bands, and for the collisionally induced changes in the rotational energy of NH3 composed of symmetric (s) and antisymmetric (a) states 0 may0 be deduced from the factor l þJ J þK K b1 þ ei e0i ð1Þ 1 i i i i c occurring in Eq. (8) of [6] and from the properties of the Clebsch–Gordan coefficients. In the P and R branches of the m4 band, these selection rules are DJ = Jf Ji = ±1, DK = Kf Ki = V disp iso ¼
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
145
±1, s fi s, a fi a. In the Q branch of the 2m2 band, these selection rules are DJ = Jf Ji = 0, DK = Kf Ki = 0, a fi s, s fi a. The first-order term S iso 1 in Eq. (4) depends only on the difference in the isotropic part of the interaction potential between the initial and final vibrational states, mi and mf, of radiator: Z 1 þ1 ¼ dt½hmf jV iso jmf i hmi jV iso jmi i; ð9Þ S iso 1 h 1
The vibrational dependence of the isotropic interaction is approximated from the isotropic induction and dispersion potentials (Eqs. (7) and (8)). The vibrational dependence of the dipole moment of ammonia was determined by Marchal et al. [32] and is given in Debyes by
where the time integral is evaluated along the relative trajectories of the radiator and perturber. For a ro-vibrational transition of radiating molecule, the first-order term can be written [31] 3p 3 U 1U 2 iso 2 2 ða1;f a1;i Þ a2 . S1 ¼ ðl1;f l1;i Þ þ 8ðhv0c Þr5c 2 ðU 1 þ U 2 Þ ð10Þ
ð11Þ
Table 3 Molecular parameters for NH3, H2 and Ar used in the calculations of shift coefficients Molecule
NH3
H2
Ar
M (amu) li (D) lf (D) m4 lf (D) 2m2 ˚) Q (D A ˚ 2) X (D A ˚ 3) U (D A ˚ r (A) e (K) ˚ 3) ai (A c U (ev) ˚ 4) Ai(A ˚ 4) A^(A ˚ 4) A 0 (A
17.03 1.4715a 1.4554a 1.015a 2.32b 1.20b — 3.018c 294.3c 2.18b 0.054b 10.16d 0.0633e 0.793e 0.81e
2.0158 0 0 0 0.6522f +0.6522f 0.1264f 2.944g 32.0g 0.806b 0.116b 15.426d 0 0 0
39.948 0 0 0 0 0 0 3.504g 117.7g — — — 0 0 0
a b c d e f g
Ref. Ref. Ref. Ref. Ref. Ref. Ref.
lm1 m2 m3 m4 ¼ 1.5610 þ 7.2 103 ðm1 þ 12Þ 2.271 101 ðm2 þ 12Þ þ 3.75 102 ðm3 þ 1Þ 1.65 102 ðm4 þ 1Þ;
where mi is the number of quanta in the ith normal mode. In the absence of any information about the vibrational dependence of the polarizability of NH3, it was hoped that it would be possible to choose a value of Da = a1,f a1,i which would give a reasonable agreement between experimental and theoretical results. For the vibrational dephasing contribution, we have consid˚ 3 in the m4 band. In the 2m2 band, for ered Da = 0.05 A which the shift is positive, we have used only the positive contribution of S iso 1 ðDa ¼ 0Þ arising from the difference of the dipole moment of ammonia in the initial and final states. The H2-shift coefficients at 296 K were computed in the PP and RP branches of the m4 band and in the QQ branch of the 2m2 by including the contribution from H2 in the ground state with J2 values varying from 0 to 7 that were weighted by the Boltzmann factors and by J þ1 the nuclear spin factor 2 þ ð1Þ 2 . We considered the parameters of NH3 for symmetric (s) and antisymmetric (a) levels to compare the shift coefficients for a fi a and s fi s allowed transitions in the m4 band as well as for a fi s transitions in the 2m2 band. The molecular constants involved in the computation are given in Tables 3 and 4. The calculated values are compared in Table 1 with the experimental data. 3.2. Ar-shift calculation
[32]. [35]. [36]. [37]. [30]. [38]. [39].
For NH3–Ar we have considered the intermolecular potential of Smith, Giraud, and Cooper (SGC) [33] developed in Legendre polynomials limited to the second-order terms,
Table 4 Rovibrational parameters used in the calculation for NH3 in the ground and m4 and 2m2(s) vibrational states, and for H2 in the ground vibrational state Molecule NH3
State a
Ground m4b 2m2b
Groundc
H2 a b c
Ref. [40]. Ref. [41]. Ref. [42].
s a s a s
B (cm1)
(C–B) (cm1)
9.94664 9.94159 10.17702 10.16501 10.31580
3.71828 3.71123 4.00729 3.99276 4.38068
59.3345
—
D (103 cm1) 0.84953 0.832742 1.04216 1.0220 0.4324 45.651
DJK (103 cm1)
DK (103 cm1)
1.5783 1.53197 2.05445 1.96035 0.4814
1.0107 0.97894 1.2066 1.1300 0.1374
—
—
146
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
Table 5 Coefficients of Smith–Giraud–Cooper (SGC) potential
NH3–Ar m4a 2m2b a b
4. Results and discussion
A1
A2
R1
R2
0.20 0.20
0.20 0.20
0.50 0.40
0.40 0.30
Ref. [5]. This work.
V ¼ V iso þ V aniso r7 r 12 r6 r 12 ¼ 4e A1 þ R1 P 1 ðcoshÞ r r r r r6 r 12 þ R2 A2 ð12Þ P 2 ðcoshÞ ; r r where r is the intermolecular distance, h is the angle between the symmetric axis of absorbing molecule and intermolecular axis, and Pl(l = 1 or 2) are Legendre polynomials of order l. The parameters R1, A1, R2, and A2 that were calculated to obtain a reasonable agreement with the experimental values of broadening coefficient are given in Table 5. e and r are the Lennard-Jones parameters for the molecular pair NH3–Ar. The analytical contributions to the differential cross section are given in [19] for the anisotropic part of atomlinear molecule potential used. They have been modified to include the quantum numbers K (Ki, Kf) in the Clebsch–Gordan coefficients. The inversion motion in NH3 was considered through Eqs. (6) and (7) of [5] so that S middle ¼ 0 for l = 1 (contribution of P1(cos h)). 2 The Lennard-Jones isotropic part of the potential can be written as C 12 C 6 6 with C 6 ¼ 4er6 r12 r 3 U 1U 2 and C 12 ¼ 4er12 . 2 ðU 1 þ U 2 Þ
V iso ¼
The vibrational dephasing contribution is obtained from S iso 1 given by [34] 5 11 3 DC 6 per r 63 DC 6 per r iso þ y. ð13Þ S1 ¼ 2 C6 hv0c rc 64 C 6 hv0c rc Here
DC 6 ¼ ðC 6 Þmf ðC 6 Þmi
and
y¼
The new results for line shift and line mixing parameters obtained from the present analysis are presented in this section, where they are compared with previous measurements when available and with the calculations described above. 4.1. Line shifts The line shift values obtained for the two collisional systems NH3–H2 and NH3–Ar are reported in Tables 1 and 2 along with the absolute errors. For the two perturbers all shift coefficients in the m4 band are negative (except for six lines for H2 perturber), so that the center frequencies of the lines decrease with increasing pressure. These shifts are typically 1–2 orders of magnitude smaller than the broadening coefficients published in [5] and [7] for Ar and H2 respectively. This makes them rather difficult to determine as evidenced from the relatively large error found. For the 2m2 band the shifts coefficients are positive and are much greater than those obtained in the m4 one. Therefore the temptation is great to explain the observed behavior by predominant vibrational dephasing effect. Moreover these shifts appear to weakly depend on J and K quantum number. The prediction of line shifts using a semiclassical approach (which is not perfectly appropriate for a molecule such as NH3 with large rotational constants) leads to a reasonable agreement, even though poor knowledge of the polarizability for vibrational transitions produces inaccuracies in the computed values. These calculations reproduce the sign of line shifts. Although we have considered two sets of rotational constants (for symmetric and antisymmetric levels), the predicted values of line shift coefficients are practically identical for a ‹ s and s ‹ a transitions. For the two perturbers, the
DC 12 =C 12 . DC 6 =C 6
The values of DC6/C6 and y are not directly available for ammonia. In our calculation, we have systematically considered the coefficients as adjustable parameters and taken as DC6/C6 = 0.014 and y = 2.0, in the m4 band and DC6/C6 = 0.03 and y = 5.0 in the 2m2 band. The molecular parameters introduced in the computation are given in Tables 3–5. The line shifts coefficients d0 (J, K) at 296 K were computed for J 6 10 in the PP and RP branches of m4 band and QQ branch of the 2m2 band. The calculated values are compared in the Table 2 with the experimental data.
Fig. 4. Line shifts in the PP branch of the m4 vibrational band of NH3 perturbed by H2 as a function of J + 0.1 · (J K). (m) Experimental values; (s) calculated values.
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
Fig. 5. Line shifts for NH3 transitions broadened by Ar in the m4 vibrational band as a function of J + 0.1 · (J K). (m) Experimental values; (s) calculated values.
Im ðS aniso Þ values are small. Thus, for the two systems, 2 the line shift is mostly due to the isotropic part of aniso S iso Þ 1 with small corrections coming from the Im ðS 2 terms. The comparison of the results is shown by Figs. 4 and 5, where the measured and theoretical line shifts of PP (J, K) transitions are plotted as a function of J + 0.1(J K). As may be seen by these figures and Tables 1 and 2, the experimental and calculated line shifts appear to depend weakly on J and K. These evolutions are less pronounced for predicted values than for the observed. Moreover for Ar, the results obtained from the Smith–Giraud–Cooper (SGC) potential with the values of vibrational parameters indicated above provide overestimated line shifts. Our H2-shift values in the m4 band are larger than those obtained by Pine et al. [12] in the R and Q branches of the m1 band and smaller for the Ar perturber. For the 2m2 band, a satisfactory agreement for the sign of shifts is observed when comparison is done with the results obtained by Raynaud et al. [11] in the P branch of the 2m2 m2 combination band of NH3 perturbed by H2. For the Q branch however our values are greater than those obtained by these authors. Furthermore, as expected, the present values of line shifts are smaller than those obtained by Baldacchini et al. for self-shifts in the 2m2 m2 parallel band. 4.2. Line mixing parameters For lines whose line mixing parameters are statistically significant, the a ‹ s transitions have mostly positive Y0 values and the s ‹ a transitions have mostly a negative ones. Nevertheless there are some exceptions to this sign ordering for the lines for which Y0 parameters have the same magnitude of standard error. The observed lines appear to be shifting towards each other, whereas at low pressures the lines are shifting apart. This mutual
147
attraction is characteristic of line mixing of the collisionally-coupled overlapped lines. Moreover for a given J, the line mixing parameter Y0 seems to increase with K quantum number (as seen in Tables 1 and 2, Y0 of the P P(3, 1)s line is smaller than Y0 of PP(3, 2)s line and very weak compared with PP(3, 3)s result). This evolution is more pronounced for H2 than for Ar perturber. Note that the splitting 2d between the inversion components decreases with K for a given J. The most striking result is the very large amount of coupling between the symmetric and antisymmetric components for J close or equal to K. The largest line mixing parameters observed are those for the J = K lines. For these lines the line mixing parameters decrease with 2d. In fact parameter Y0 of the PP(3, 3) doublet of 2d = 0.275 cm1 is very weak compared to those of PP(8, 8) doublet with 2d = 0.210 cm1.
5. Conclusion We have measured H2 and Ar pressure-induced line shifts and line interference parameters of 66 PP and R P selected lines in the m4 band and 10 lines in the 2m2 band of NH3 at T = 296 K using a high-resolution Fourier transform spectrometer. The measured and predicted values of line shift are in reasonable agreement if one takes into account the various uncertainties both in the experiments and in the theory. It should be noted that the pure rotational contribution is quite negligible and the shifts are mostly due to the vibrational dependence of the isotropic potential. These values are mostly negative in the m4 band and positive in the 2m2 band. On the contrary the inversion doublets line mixing parameters are, on the hole, of opposite sign.
Acknowledgment The authors are grateful to C. Boulet for helpful discussions.
References [1] V. Kunde, R. Hanel, W. Maguire, J.P. Baluteau, A. Marten, A. Chedin, N. Husson, N.S. Scott, Astrophys. J. 263 (1982) 443–467. [2] P.T.P. Ho, C.H. Townes, Annu. Rev. Astron. Astrophys. 21 (1983) 239–270. [3] D.J. Brassington, in : Proceedings of the International Symposium on Monitoring of Gaseous Pollutants by Diode Lasers , Freiburg, Germany, 17 October, 1988. [4] V.N. Markov, A.S. Pine, G. Buffa, O. Tarrini, J. Quant. Spectrosc. Radiat. Transfer 50 (1993) 167–178. [5] M. Dhib, J.P. Bouanich, H. Aroui, M. Broquier, J. Mol. Spectrosc. 202 (2000) 83–88. [6] M. Dhib, J.-P. Bouanich, H. Aroui, A. Picard-Bersellini, J. Quant. Spectrosc. Radiat. Transfer 68 (2001) 163–178.
148
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
[7] J-P. Bouanich, H. Aroui, S. Nouri, A. Picard-Bersellini, J. Mol. Spectrosc. 206 (2001) 104–110. [8] V. Nemtchinov, K. Sung, P. Varanasi, J. Quant. Spectrosc. Radiat. Transfer 83 (2004) 243–265. [9] G. Baldacchini, F. Damato, M. De Rosa, G. Buffa, O. Tarrini, J. Quant. Spectrosc. Radiat. Transfer 55 (1996) 745– 753. [10] G. Baldacchini, A. Bizzarri, L. Nencini, V. Sorge Tarrini, J. Quant. Spectrosc. Radiat. Transfer 43 (1990) 371–380. [11] F. Raynaud, B. Lemoine, F. Rohart, J. Mol. Spectrosc. 168 (1994) 584–592. [12] S. Pine, V.N. Markov, G. Buffa, O. Tarrini, J. Quant. Spectrosc. Radiat. Transfer 50 (1993) 337–348. [13] S. Hadded, H. Aroui, J. Orphal, J.-P. Bouanich, J.-M. Hartmann, J. Mol. Spectrosc. 210 (2001) 275–283. [14] S. Hadded, F. Thibault, P.-M. Flaud, H. Aroui, J.-M. Hartmann, J. Chem. Phys. 116 (2002) 7544–7557. [15] S. Hadded, F. Thibault, P.-M. Flaud, H. Aroui, J.-M. Hartmann, J. Chem. Phys. 120 (2002) 217–223. [16] P.W. Parson, V.I. Metchnik, I.C. Story, J. Phys. B: Atom. Mol. Phys. 5 (1972) 1221–1233. [17] G. Buffa, O. Tarrini, Appl. Optics 28 (1989) 1800–1805. [18] C.J. Tsao, B. Curnutte, J. Quant. Spectrosc. Radiat. Transfer 2 (1962) 41–91. [19] D. Robert, J. Bonamy, J. Phys. 40 (1979) 923–943. [20] H. Aroui, M. Broquier, A. Picard-Berselini, J-P. Bouanich, M. Chevalier, S. Gherissi, J. Quant. Spectrosc. Radiat. Transfer 60 (1998) 1011–1023. [21] H. Aroui, A. Picard-Bersellini, M. Chevalier, M. Broquier, S. Gherissi, J. Mol. Spectrosc. 176 (1996) 162–168. [22] A. Le´vy, N. Lacome, C. Chackerian Jr., in: Spectroscopy of the EarthÕs Atmosphere and of the Interstellar Medium, Academic Press, New York, 1992, pp. 261–337. [23] P.W. Rosenkranz, IEEE Trans. Antenn. Propag. 23 (1975) 498–506.
[24] F. Thibault, J. Boissoles, R. Le Doucen, J.-P. Bouanich, Phys. Areas, and C. Boulet, J. Chem. Phys. 96 (1992) 4945-4953. [25] C. Boulet, D. Robert, L. Galatry, J. Chem. Phys. 65 (1976) 5302– 5314. [26] J. Bonamy, L. Bonamy, D. Robert, J. Chem. Phys. 67 (1977) 4441–4453. [27] J.P. Bouanich, C. Campers, G. Blanquet, J. Walrand, J. Quant. Spectrosc. Radiat. Transfer 39 (1988) 353–365. [28] R.P. Leavitt, J. Chem. Phys. 72 (1980) 3472–3482. [29] J.-P. Bouanich, C. Brodbeck, J. Quant. Spectrosc. Radiat. Transfer 14 (1974) 141–151. [30] J. Bonamy, D. Robert, J. Quant. Spectrosc. Radiat. Transfer 15 (1975) 855–862. [31] R.P. Leavitt, J. Chem. Phys. 73 (1980) 5432–5450. [32] M.D. Marshal, K.C. Izgi, J.S. Muenter, J. Chem. Phys. 107 (1997) 1037–1044. [33] E.W. Smith, M. Giraud, J. Cooper, J. Chem. Phys. 65 (1976) 1256–1267. [34] L. Bonamy, J. Bonamy, D. Robert, B. Lavorel, R. Saint-Loup, R. Chaux, J. Santos, H. Berger, J. Chem. Phys. 89 (1988) 5568–5577. [35] C.G. Gray, K.E. Gubbins, Theory of Molecular Fluids, Oxford University Press, London/New York, 1984. [36] S.V. Khristenko, A.I. Maslov, V.P. Shevelko, Molecules and their Spectroscopic Properties, Springer, Berlin, 1998. [37] J. Komasa, A.J. Thakkar, Mol. Phys. 78 (1993) 1039–1046. [38] J.-P. Bouanich, C. Brodbek, J. Quant. Spectrosc. Radiat. Transfer 17 (1977) 777–782. [39] M. Lepe`re, G. Blanquet, J. Walrand, J.P. Bouanich, J. Mol. Spectrosc. 192 (1998) 231–234. [40] S. Urban, V. Spirko, D. Papousek, J. Kauppinen, S.P. Belov, L.I. Gershtein, A.F. Krupnov, J. Mol. Spectrosc. 88 (1981) 274–292. [41] H. Sasada, Y. Endo, E. Hirota, R.L. Poynter, J.S. Margolis, J. Mol. Spectrosc. 151 (1992) 33–53. [42] S.L. Bragg, J.W. Brault, W.H. Smith, Astrophys. J. 263 (1982) 999–1004.
Line shift and mixing in the m4 and 2m2 band of NH3 perturbed by H2 and Ar M. Dhib a,*, M.A. Echargui a, H. Aroui a, J. Orphal b, J.-M. Hartmann b a
Laboratoire de Physique Mole´culaire, Ecole Supe´rieure des Sciences et Techniques de Tunis, 5 Av Taha Hussein 1008 Tunis, Tunisia b Laboratoire de Photophysique Mole´culaire, UPR 3361 du CNRS, Universite´ de Paris-Sud, baˆt. 350, 91405 Orsay Cedex, France Received 26 April 2005
Abstract Pressure induced line shift and line mixing parameters have been measured for 66 rovibrational lines in the m4 band and for 10 lines in the 2m2 band of NH3 perturbed by H2 and Ar at room temperature (T = 296 K). These lines with J values ranging from 2 to 10 are located in the spectral range 1450–1600 cm1. Experiments were made with a high-resolution Fourier transform spectrometer. The line shifts and line mixing parameters have been derived from the non-linear least-square multi-pressure fitting technique. The shift coefficients are compared with those calculated from the Robert–Bonamy formalism (RB). The results are generally in satisfactory agreement with the experimental data. 2005 Elsevier Inc. All rights reserved. Keywords: Shift; Line mixing; Ammonia; H2; Ar
1. Introduction Knowledge of the lineshape parameters of molecular transitions and of their dependence upon pressure is useful both to fundamental and to applied spectroscopical studies. It gives an insight into intermolecular forces and is also essential for monitoring the composition of planetary atmospheres and for quantitative analysis of pollutants. The ammonia molecule has always played an important role in the field of spectroscopy because of its peculiar properties. Indeed, it has a large molecular dipole and an inversion spectrum, which are important properties for modeling intermolecular forces. Moreover, ammonia, which is present in many planetary atmospheres [1,2] and other celestial bodies, is commonly used as an interstellar thermometer and is considered as an industrial and biological pollutant [3].
*
Corresponding author. Fax: +216171391166. E-mail address: [email protected] (M. Dhib).
0022-2852/$ - see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2005.06.012
Broadening coefficients in the infrared spectra of ammonia have been the subject of numerous experimental and theoretical studies for different bands and collision partners (He, Ar, H2, O2, N2, CO2, air, . . .) [4–8]. On the other hand, the line shifts and especially line mixing have received much less attention in the past, mainly because they are expected to be small and their observation is therefore difficult. The situation is now completely different. A large number of shift measurements for the ammonia molecule have been published. Temperature dependence of self-shift and shifts of ammonia perturbed by N2 and CO2 in the m2 band were studied by Baldacchini et al. [9,10]. The self-shifts in the m1 band were studied by Markov et al. [4] using a difference frequency laser. Measurements of line shifts with a frequency-stabilized diode laser in the m2 and (2m2 m2) bands of NH3 were studied by Raynaud et al. [11]. Pine et al. [12] measured the shift coefficients of NH3 in the m1 band perturbed by He, Ar, O2, H2, and N2. On the other hand, measurements of line mixing effects are still lacking especially
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
for the m4 band because of its strong Coriolis interaction with the 2m2 band. However, it is well known that a rigorous treatment of vibration–rotation spectral line shapes must include interference effects caused by the overlapping of lines. Recently, Hadded et al. [13] have studied line mixing of 15 inversion doublets of NH3 perturbed by He, Ar, and H2. More recently, these authors [14,15] have measured line mixing effects in the m1 and m2 bands of NH3 at high pressure. They have demonstrated the necessity of take into account line mixing for the treatment of inversion-rotation spectra of NH3. On the theoretical side, semiclassical calculations of shift coefficients have been previously performed by Parson et al. [16] for the (J, K) = (12, 12) inversion line of ammonia. Buffa et al. [17] calculated the pressure shifts of ammonia using the Anderson–Tsao–Curnutte (ATC) theory [18] and the Quantum Fourier Transform (QFT) theory. Baldacchini et al. [10] used the ATC theory for calculation of shifts of NH3–N2 and NH3–CO2 in the m2 band. Markov et al. [4] calculated the self-shifts in the m1 band. The latter calculations were based on the ATC theory, in which only dipole–quadripole interaction is taken into account. The present paper is an experimental analysis of the line shift and line mixing parameters in the PP and RP branches of the m4 perpendicular band and QQ branch of the 2m2 parallel band of NH3 perturbed by H2 and Ar in the pressure range 0–170 Torr. In addition, the shift coefficients have been calculated on the basis of the semiclassical Robert–Bonamy (RB) formalism developed in [19]. The effect of the inversion movement of NH3 was taken into account [6].
139
2. Experimental and fitting procedures 2.1. Experiment All experiments were made with a high-resolution Fourier transform spectrometer (FTS) Bruker IFS 120 HR as described previously [20,21]. This spectrometer was equipped with a globar source, a KBr beam splitter, a filter eliminating infrared radiation for m > 2500 cm1, and a HgCdTe detector cooled to 77 K. The resolution of the spectrometer was about 0.0038 cm1. Samples of ammonia, argon and hydrogen in natural abundances were provided by Air Liquide France with stated purities of 98.5, 99.5, and 99.9%, respectively. The gas mixture was contained in a 10.5 cm absorption cell equipped with CaF2 windows. The cell was first filled with NH3 at a constant pressure of 7 Torr. Next, Ar or H2 was added in stages at pressures ranging 22–170 Torr. To allow equilibrium to occur, the sample was filled into the cell for several hours before high-resolution scans were recorded. During the scans, the sample pressures remained fairly constant and were measured with three Baratron capacitance gauges accurate to 0.5%, with full-scale readings of 10, 100, and 1000 Torr. The spectra recorded at room temperature, T = 296 ± 1 K, were obtained by averaging 100 scans and calculated using a triangular apodization function. The FTS was evacuated with a cryopump to remove residual H2O. Reference spectra were taken under the same conditions (alignment and resolution) but with the empty cell. The transmittance at wavenumber r was calculated from the measured intensities by the usual ratio of recordings with and without the gas sample.
Fig. 1. Results of multi-pressure fits in the case of the PP(4, 3)s line for NH3 perturbed by H2 at 296 K. (—) and (d) are the measured and calculated values, respectively. Measured minus calculated deviations are shown in the lower part of plots.
140
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
2.2. Fitting procedure The analyses of spectra were performed taking into account interference effects. Thus within the impact theory of the spectral shape and for moderately overlapping lines at low pressure as considered in this work, the collisional absorption coefficient a (r) can be written as [22,23], P NH3 X PY k ðr rk Þ þ P ck aðrÞ ¼ Sk ; ð1Þ p lines k ðr rk Þ2 þ ðP ck Þ2 where k represents the line vi Ji Ki fi vf Jf Kf, Sk its intensity, rk its wavenumber including the collisional shift dc (dc = rk r0, r0 being the unperturbed wavenumber), ck its halfwidth, and Yk its interference parameters related to the off-diagonal element of the relaxation matrix. The experimental spectra were analyzed by means of non-linear least-squares fitting procedures using the following theoretical expression sC (r) for the transmission and the collisional absorption coefficient in Eq. (1). Z þ1 sC ðrÞ ¼ F App ðr r0 Þ 1 Z þ1 exp l aDop ðr0 r00 Þaðr00 Þ dr00 dr0 ;
successively adjusted using Eq. (2). The parameters deduced from the fits for a line k are Pck, rk, Sk and PYk. Note that the linewidths ck and line intensities Sk were already published in [5,7,20]. An example of a multi-pressure fit in the case of PP(4, 3)s line for NH3 broadened by H2 is given in Fig. 1. The measured values of the collisional wavenumber rk and of the interference parameter Yk are well fitted by linear relationships, rk ¼ r0 þ P NH3 dNH3 NH3 þ P d0 ; PY k ¼ P NH3 Y NH3 NH3 þ PY 0 ; where d0 is the line shift coefficient, r0 is the unperturbed line-center frequency, Y0 the first-order line mixing parameter, dNH3 –NH3 and Y NH3 –NH3 are
1
ð2Þ where aDop is the Doppler profile, FAPP is the Fourier transform apparatus function (approximated here with a Gaussian shape), and l = 10.5 cm is the cell length. The collisional parameters for a given temperature were obtained by means of non-linear least-square multi-pressure fitting in which all spectra at various pressures are
Fig. 3. Line mixing coefficients in the symmetric (upper symbols) and antisymmetric (lower symbols) components of the PP (4, 4) doublets as a function of pressure.
Fig. 2. Collision-induced variation of the center wavenumber rk for the RP(2, 0)a line of the m4 band and QQ(10, 9)a line of the 2m2 band of NH3 perturbed by H2.
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
141
Table 1 Line shift d0 (in 103 cm1 atm1) and line mixing coefficients Y0 (in atm1) in the m4 band of NH3 perturbed by H2 at 296 K NH3–H2 Line
m0(cm1)
Y exp 0
m4 band P P(2, 1)s P P(2, 1)a P P(2, 2)s P P(2, 2)a
1590.6916 1591.1050 1594.7907 1595.0801
dexp 0
dcalc 0
0.16(0.01) 0.17(0.11) +0.21(0.04) 0.28(0.06)
4.16(1.03) 4.47(1.05) 4.15(0.82) 2.62(0.61)
5.25 5.25 3.68 3.68
P(3, 1)s P(3, 1)a P P(3, 2)s P P(3, 2)a P P(3, 3)s P P(3, 3)a
1571.8315 1572.4882 1575.8518 1576.3173 1579.3615 1579.6363
+0.05(0.03) 0.06(0.04) +0.20(0.03) 0.17(0.02) +0.21 (0.03) 0.21(0.04)
+0.19 0.19
3.42(0.42) 3.32(0.42) 4.63(0.79) 4.14(1.71) 4.61 (2.00) 4.85(0.67)
4.93 4.93 4.86 4.86 3.72 3.72
P
P(4, 1)s P(4, 1)a P P(4, 2)a P P(4, 3)s P P(4, 3)a P P(4, 4)s P P(4, 4)a
1553.6294 1554.7340 1558.2494 1560.8895 1561.3835 1563.8239 1564.0824
+0.09(0.05) 0.11(0.05) +0.16(0.03) +0.09(0.03) 0.12(0.02) +0.30(0.02) 0.34(0.03)
+0.10 0.10 +0.39 0.39
5.48(0.69) 4.42(0.66) 6.25(0.29) 3.92(0.72) 3.20(0.93) 3.04(0.52) 4.78(0.92)
4.84 4.84 4.88 4.02 4.02 3.69 3.69
P
P(5,1)s P(5, 1)a P P(5, 2)s P P(5, 2)a P P(5, 3)s P P(5, 3)a P P(5, 4)s P P(5, 4)a P P(5, 5)s P P(5, 5)a
1536.2088 1538.0102 1539.7596 1541.0041 1542.9798 1543.8550 1545.8043 1546.3315 1548.1839 1548.4290
0.09(0.03) 0.10(0.04) +0.14(0.01) 0.11(0.03) +0.11(0.01) 0.10(0.03) +0.08(0.03) 0.09(0.02) +0.33(0.03) 0.33(0.03)
+0.02 0.02 0.07 +0.07 +0.32 0.32
2.95(0.17) 4.33(0.48) 5.60(0.85) 5.11(0.91) 4.30(0.94) 4.02(0.46) 2.63(0.15) 4.24(1.36) 2.66(0.09) 5.52(0.87)
4.87 4.87 5.03 5.03 4.09 4.09 3.52 3.52 4.06 4.06
P
P(6,1)s P(6, 1)a P P(6, 3)s P P(6, 3)a P P(6, 4)s P P(6, 4)a P P(6, 5)s P P(6, 5)a P P(6, 6)s P P(6, 6)a
1519.6627 1522.3847 1525.7625 1527.0615 1528.3774 1529.2897 1530.6141 1531.1591 1532.4503 1532.6830
+0.07(0.01) 0.05(0.02) +0.06(0.03) 0.06(0.01) +0.07(0.02) 0.07(0.06) +0.09(0.04) 0.07(0.03) +0.34(0.01) 0.38(0.03)
+0.07 0.07 +0.45 0.45
2.79(0.27) 3.27(0.85) 5.21(0.50) 3.56(0.26) 3.24(0.63) 2.40(0.35) 2.29(0.27) 4.22(0.38) +2.96(0.53) 6.62(0.35)
4.99 4.99 4.39 4.39 3.52 3.52 3.58 3.58 4.43 4.43
P
P(7,1)s P(7, 2)a P P(7, 3)s P P(7, 3)a P P(7, 4)s P P(7, 4)a P P(7, 5)s P P(7, 5)a P P(7, 6)s P P(7, 6)a P P(7, 7)s P P(7, 7)a
1504.0218 1509.4479 1509.1379 1511.3131 1511.5985 1513.0439 1513.6480 1514.6055 1515.3243 1515.8819 1516.6309 1516.8521
0.10(0.05) 0.16(0.02) +0.07(0.01) +0.07(0.02) 0.10(0.01) 0.12(0.06) 0.10(0.05) 0.11(0.04) +0.10(0.02) 0.11(0.02) +0.49(0.09) 0.45(0.09)
+0.09 0.09 +0.46 0.46
3.09(0.53) +1.48(0.83) 4.50(0.79) 4.85(0.52) +1.44(0.66) 3.71 (1.68) +2.42 (0.36) 4.09(0.55) 2.74 (0.56) 3.13(0.41) +1.32 (0.52) 6.13(0.60)
5.18 5.37 4.69 4.69 3.81 3.81 3.42 3.42 3.70 3.70 4.74 4.74
P
1494.2421 1493.5269 1496.1740 1497.6750 1497.3332 1499.8082 1499.9436 1500.5103
0.10(0.03) 0.08(0.06) +0.10(0.02) 0.12(0.05) +0.13 (0.07) 0.08(0.04) +0.12(0.05) 0.14(0.01)
P P
P
P
P
P
P(8, 1)a P(8, 3)s P P(8, 3)a P P(8, 4)a P P(8, 5)s P P(8, 6)a P P(8, 7)s P P(8, 7)a P
Y exp (Ref. [13] ) 0
+0.14 0.14
2.91(1.00) 5.44 2.43 (0.63) 4.95 5.66(1.57) 4.95 4.64(0.98) 4.18 4.44 (1.50) 3.64 2.23 (0.96) 3.42 2.39(0.99) 3.87 3.21 (1.66) 3.87 (continued on next page)
142
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
Table 1 (continued) NH3–H2 Line
m0(cm1)
Y exp 0
Y exp (Ref. [13] ) 0
dexp 0
dcalc 0
P
1500.7334 1500.9439
+0.48(0.03) 0.53 (0.05)
+0.49 0.49
+4.53 (0.83) 4.37 (0.66)
5.04 5.04
P(2, 0)a P(3, 0)s R P(4, 0)a R P(5, 0)s R P(7, 0)s R P(8, 0)a R P(9, 0)s
1586.8714 1567.9930 1552.1574 1533.7968 1502.7553 1493.8633 1474.7257
+0.11(0.02) 0.09(0.03) 0.09(0.02) +0.11(0.04) 0.11(0.02) 0.10(0.02) +0.14(0.04)
8.50(0.49) 4.86 (1.27) 4.39 (0.77) 6.61(0.75) 4.17(1.69) 2.66 (0.41) 6.76(0.80)
5.89 8.08 8.77 8.97 8.82 8.74 8.59
2m2 band Q P(4, 3)a Q Q(3, 3)a Q Q(4, 3)a Q Q(4, 4)a Q Q(5, 5)a Q Q(6, 6)a Q Q(7, 7)a Q Q(8, 8)a Q Q(9, 9)a Q Q(10, 9)a
1515.4684 1594.8992 1596.7714 1593.1724 1590.8807 1588.0293 1584.6276 1580.6885 1576.2251 1587.8357
0.81(0.35) 0.29(0.11) 0.87(0.18) 0.39(0.09) 0.08(0.03) 0.44(0.05) 0.82(0.21) 0.34(0.09) 0.93(0.05) 0.60(0.05)
13.92(6.85) 12.31(0.92) 20.89(4.64) 19.40 (0.72) 15.94(0.89) 17.20(2.09) 17.81(4.38) 21.68(4.40) 15.78(1.22) 11.39(0.49)
10.81 11.73 11.80 12.48 13.13 13.74 14.26 14.67 15.00 15.55
P(8, 8)s P(8, 8)a
P
R R
respectively the shift and interference parameter of pure ammonia at low pressure (P NH3 ¼ 7 Torr) and P is the partial pressure of the perturber gas (H2 or Ar). Typical plots of the line center frequency rk and line mixing Yk as a function of the pressure P are shown in Figs. 2 and 3 respectively. Within the measurement scatter, the shift and line mixing varies linearly with pressure over the range considered here (0–170 Torr), and no non-linear behavior was observed. The H2 and Ar-shift coefficients d0 and line mixing coefficients Y0 are determined as the slopes of these lines and are presented in Tables 1 and 2 along with the estimated experimental errors. The main sources of uncertainties in the results arise from the perturbations due to interfering lines (mainly coming from H2O), the base line location, the line shape model used, and the approximations done in accounting for the instrumental line shape. The values given in parentheses correspond to the statistical errors expressed as one time standard deviation for line shifts coefficients and line mixing parameters.
3. Theoretical calculations of shifts Within the Robert–Bonamy formalism, the line shift coefficients for the transition f ‹ i are given by, Z 1 n2 X dif ¼ q vF ðvÞ dv 2pc J 2 J 2 0 Z 1 2pb Im ½SðbÞ db; ð3Þ 0
where n2 is the number density of the perturbing molecules, qJ 2 is the relative population of the perturber in the jJ2, m2 = 0æ states (this factor reduces to one and summation cancels out for monoatomic perturber), v the relative velocity of the absorber–perturber collision pair, F (v) the Maxwellian velocity distribution, and b the impact parameter. Im [S(b)] is the imaginary part of the differential cross section given by Im ½SðbÞ ¼ expbðRe S aniso ðbÞÞc sinbIm S aniso ðbÞ 2 2 þ S iso 1 ðbÞc;
ð4Þ
where • S iso 1 is a vibrational phase shift defined from the difference of the isotropic part of the potential in the initial and final states of transition [24]: S iso 1 ¼ S 1;f2 S 1;i2 ; • the real part of S aniso derived from the anisotropic 2 part of the potential is expressed as the second-order terms of the development of S2(b): Re ðS aniso Þ ¼ S 2;f2 þ S 2;i2 þ S 2;f2i2 ; 2 • the imaginary part of S aniso results from the non-com2 mutative character of the interaction at different times and is, like the first-order contribution, an additive quantity with respect to the shifts of the initial and final levels of the transitions: 0 0 Im ðS aniso Þ ¼ S S . 2 2;f2 2;i2 All the S1, S2, and S 02 terms are given by Eqs. (8)–(11) of [19]. The expressions of Re S aniso for the interaction be2 tween NH3 and atomic or diatomic molecules have been previously given by Eqs. (6) and (7) of [5] and Eqs. (10)
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
143
Table 2 Line shift d0 (in 103 cm1 atm1) and line mixing coefficients Y0 (in atm1) in the m4 band of NH3 perturbed by Ar at 296 K NH3–Ar Line
m0(cm1)
Y exp 0
m4 band P P(2, 1)s P P(2, 1)a P P(2, 2)s P P(2, 2)a
1590.6916 1591.1050 1594.7907 1595.0801
dexp 0
dcalc 0
0.09(0.05) 0.11(0.08) +0.16(0.02) 0.14(0.07)
6.05(0.93) 7.22(0.92) 8.77(1.22) 5.89(1.52)
5.79 5.79 5.68 5.68
P(3, 1)s P(3, 1)a P P(3, 2)s P P(3, 2)a P P(3, 3)s P P(3, 3)a
1571.8315 1572.4882 1575.8518 1576.3176 1579.3615 1579.6363
+0.04(0.01) 0.04(0.03) +0.08(0.06) 0.12(0.02) +0.09(0.03) 0.12(0.02)
+0.03 0.03
4.70(0.83) 4.68(1.11) 5.64(0.92) 7.35(1.03) 6.35(1.10) 5.17(1.36)
5.80 5.80 5.79 5.79 5.64 5.64
P
P(4, 1)s P(4, 1)a P P(4, 2)a P P(4, 3)s P P(4, 3)a P P(4, 4)s P P(4, 4)a
1553.6294 1554.7340 1558.2494 1560.8895 1561.3835 1563.8239 1564.0824
+0.09 (0.04) 0.08(0.01) 0.10(0.06) +0.09(0.04) 0.09(0.03) +0.07(0.04) 0.11(0.02)
+0.03 0.03 +0.10 0.10
6.63 (1.19) 3.03(0.45) 6.09(0.93) 5.27(0.48) 4.21(1.40) 4.03(0.71) 4.13(0.91)
5.68 5.68 5.75 5.73 5.73 5.62 5.62
P
P(5, 1)s P(5, 1)a P P(5, 2)s P P(5, 2)a P P(5, 3)s P P(5, 3)a P P(5, 4)s P P(5, 4)a P P(5, 5)s P P(5, 5)a
1536.2088 1538.0102 1539.7596 1541.0041 1542.9798 1543.8550 1545.8043 1546.3315 1548.1839 1548.4290
+0.08(0.03) 0.11(0.01) +0.04(0.01) 0.06(0.01) +0.09 (0.02) 0.04(0.02) 0.04(0.02) +0.03(0.02) +0.17(0.04) 0.17(0.03)
+0.02 0.02 +0.12 0.12
4.98(0.75) 3.51(1.06) 4.41(0.89) 5.75(0.92) 5.43 (0.61) 5.02(1.23) 2.82(0.98) 4.10(0.57) 5.37(0.70) 4.32(1.55)
5.46 5.46 5.57 5.57 5.68 5.68 5.67 5.67 5.60 5.60
P
P(6, 1)s P(6, 1)a P P(6, 3)s P P(6, 3)a P P(6, 4)s P P(6, 4)a P P(6, 5)s P P(6, 5)a P P(6, 6)s P P(6, 6)a P P(7, 1)s P P(7, 2)a P P(7, 3)s P P(7, 3)a P P(7, 4)s P P(7, 4)a P P(7, 5)s P P(7, 5)a P P(7, 6)s P P(7, 6)a P P(7, 7)s
1519.6627 1522.3847 1525.7625 1527.0615 1528.3774 1529.2897 1530.6141 1531.1591 1532.4503 1532.6830 1504.0218 1509.4479 1509.1379 1511.3131 1511.5985 1513.0439 1513.6480 1514.6055 1515.3243 1515.8819 1516.6309
+0.03(0.02) +0.05(0.03) +0.08(0.03) 0.07(0.03) +0.02(0.01) 0.04(0.01) 0.03(0.01) 0.02(0.02) +0.19(0.05) 0.22(0.038) +0.09(0.02) 0.08(0.01) +0.08(0.03) +0.01(0.01) +0.07(0.02) 0.04(0.07) +0.09(0.06) 0.07(0.05) +0.04(0.02) 0.05(0.03) +0.19(0.08)
3.41(0.72) 5.94(0.86) 5.05(1.09) 3.16(0.41) 4.21(0.53) 4.84(0.92) 5.86(1.14) 5.42(0.54) 2.23(0.66) 3.77(1.81) 5.80(0.95) 3.99(1.07) 2.03(0.65) 5.70(1.33) 3.90(1.62) 3.82(1.61) 5.04(0.39) 5.41(0.66) 3.46(0.75) 3.86(0.53) 4.69(0.28)
5.13 5.13 5.48 5.48 5.58 5.58 5.62 5.62 5.58 5.58 4.70 4.90 5.15 5.15 5.36 5.36 5.49 5.49 5.57 5.57 5.55
P
1516.8521 1494.2421 1493.5269 1496.1740 1497.6750 1497.3332 1499.8082 1499.9436 1500.5103
0.18(0.05) 0.12(0.05) +0.08(0.02) 0.15(0.10) 0.13(0.01) +0.08(0.05) +0.07(0.03) +0.09(0.06) 0.11(0.07)
P P
P
P
P
P(7, 7)a P(8, 1)a P P(8, 3)s P P(8, 3)a P P(8, 4)a P P(8, 5)s P P(8, 6)a P P(8, 7)s P P(8, 7)a P
Y exp (Ref. [13]) 0
+0.02 0.02 +0.15 0.15
+0.05 0.05 +0.20 0.20
+0.07 0.07
4.57(0.60) 5.55 2.90(0.65) 4.19 4.65(1.02) 4.76 4.95(1.35) 4.76 4.04(1.00) 5.06 7.57(0.91) 5.36 5.95(1.06) 5.42 3.73(1.19) 5.59 4.54(1.50) 5.59 (continued on next page)
144
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
Table 2 (continued) NH3–Ar Line
m0(cm1)
Y exp 0
Y exp (Ref. [13]) 0
dexp 0
dcalc 0
P
P(8, 8)s P(8, 8)a R P(2, 0)a R P(3, 0)a R P(4, 0)a R P(5, 0)s R P(7, 0)a R P(8, 0)a R S ð9; 0ÞS
1500.7334 1500.9439 1586.8714 1567.9930 1552.1574 1533.7968 1502.7553 1493.8633 1474.7257
+0.27(0.03) 0.27(0.03) 0.11(0.01) 0.09(0.03) 0.05(0.02) +0.09(0.03) 0.04(0.01) 0.11(0.04) +0.12(0.07)
+0.23 0.23
3.73(1.22) 2.44(1.05) 8.85(1.16) 3.26(0.90) 5.06(0.93) 5.99(0.50) 3.88(0.71) 3.67(0.42) 5.36(1.49)
5.55 5.55 5.64 5.80 5.72 5.46 4.67 4.25 3.82
2m2 band P(4, 3)a Q Q(3, 3)a Q Q(4, 3)a Q Q(4, 4)a Q Q(5, 5)a Q Q(6, 6)a Q Q(7, 7)a Q Q(8, 8)a Q Q(9, 9)a Q Q(10, 9)a
1515.4684 1594.8992 1596.7714 1593.1724 1590.8807 1588.0293 1584.6276 1580.6885 1576.2251 1587.8357
0.81(0.13) 0.16(0.04) 0.85(0.26) 0.34(0.06) 0.32(0.18) 0.11(0.09) 0.76(0.13) 0.60(0.28) 0.53(0.03) 0.44(0.22)
20.27(2.00) 14.96(2.00) 18.29(5.16) 18.45(2.87) 14.64(3.50) 20.42(1.18) 27.11(3.28) 16.70(3.76) 6.28(0.42) 10.57(1.98)
14.42 14.60 14.91 15.07 15.65 16.04 16.28 16.41 16.46 18.57
P
Q
and (11) of [6] and for collision induced transitions with DK = 0 and DK = ±3. Because of the inversion motions (e = ±1 denoting the symmetry of wave function with respect to the inversion), S2,f2i2 = 0 for l1 = 1 or l1 = 3, l representing the order of spherical harmonics considered for absorber. The imaginary part Im ðS aniso Þ may 2 be easily obtained from Re ðS aniso Þ by replacing the reso2 nance function fn(k) by Ifn(k) defined in [25]. The trajectory model used [26] accounts for influence of the isotropic potential, taken as a Lennard-Jones 6– 12 potential, in energy conservation and in the equation of motion around the distance of closest approach rc. A straight-line trajectory tangential to the real trajectory near rc and described at the relative velocity v0c has been assumed. The Maxwell–Boltzmann distribution of relative velocity F(v) in Eq. (6) was considered by using a method previously described [27] which involves a 15point Laguerre integration of velocities. The LennardJones parameters for the molecular pair are evaluated pffiffiffiffiffiffiffiffi 2 from the usual rules e ¼ e1 e2 and r ¼ r1 þr . 2 3.1. H2-shift calculation The total intermolecular potential V includes anisotropic and isotropic induction and dispersion contributions obtained by Leavitt [28], such as disp V ¼ V aniso þ V ind iso þ V iso ;
ð5Þ
where V aniso ¼ V l1 Q2 þ V Q1 Q2 þ V X1 Q2 þ V l1 U2 þ V Q1 U2 þ V X1 U2 þ V l2 a2 þ V l2 a2 c2 þ V l1 Q1 a2 1
1
þ V l1 Q1 a2 c2 þ V a1 c1 a2 c2 þ V a1 c1 a2 þ V a1 c2 a2 þ V A1k a2 þ V A1? a2 þ V A1k a2 c2 þ V A1? a2 c2 þ V a2 A01
ð6Þ
V ind iso ¼
l21 a2 r6
ð7Þ
and 3 U 1 U 2 a1 a2 . ð8Þ 2 ðU 1 þ U 2 Þ r6 Here, the index 1 refers to the absorber (NH3) and 2 to the perturber (H2); l, Q, X, and U are the dipole, quadrupole, octupole, and hexadecapole moments of the molecules; a, c, Ai, and A^ are, respectively, the average polarizability, the polarizability anisotropy, and the hyperpolarizabilities of the molecules. Ui is the first ionization energy for molecule i. The electrostatic interactions from the octupole and hexadecapole moments of the molecules may be found in [29]. The dispersion potential V a2 A01 , introduced by Bonamy and Robert [30] gives rise to DK = ±3 transitions. The analytic contributions to the real and imaginary differential cross sections l1 l2 S 2 ½rc ðbÞ (l1 and l2 represent the order of the spherical harmonics considered for the absorber and perturber) of the electrostatic dipole–quadrupole and quadrupole– quadrupole interactions and of the induction and dispersion energy are, except the last term in Eq. (6), given by Leavitt [31]. The contributions from the octupole and hexadecapole moments of the molecules may be found in [29] and those derived from V a2 A01 are given in [30]. The selection rules for optical transitions studied in the m4 perpendicular and 2m2 parallel bands, and for the collisionally induced changes in the rotational energy of NH3 composed of symmetric (s) and antisymmetric (a) states 0 may0 be deduced from the factor l þJ J þK K b1 þ ei e0i ð1Þ 1 i i i i c occurring in Eq. (8) of [6] and from the properties of the Clebsch–Gordan coefficients. In the P and R branches of the m4 band, these selection rules are DJ = Jf Ji = ±1, DK = Kf Ki = V disp iso ¼
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
145
±1, s fi s, a fi a. In the Q branch of the 2m2 band, these selection rules are DJ = Jf Ji = 0, DK = Kf Ki = 0, a fi s, s fi a. The first-order term S iso 1 in Eq. (4) depends only on the difference in the isotropic part of the interaction potential between the initial and final vibrational states, mi and mf, of radiator: Z 1 þ1 ¼ dt½hmf jV iso jmf i hmi jV iso jmi i; ð9Þ S iso 1 h 1
The vibrational dependence of the isotropic interaction is approximated from the isotropic induction and dispersion potentials (Eqs. (7) and (8)). The vibrational dependence of the dipole moment of ammonia was determined by Marchal et al. [32] and is given in Debyes by
where the time integral is evaluated along the relative trajectories of the radiator and perturber. For a ro-vibrational transition of radiating molecule, the first-order term can be written [31] 3p 3 U 1U 2 iso 2 2 ða1;f a1;i Þ a2 . S1 ¼ ðl1;f l1;i Þ þ 8ðhv0c Þr5c 2 ðU 1 þ U 2 Þ ð10Þ
ð11Þ
Table 3 Molecular parameters for NH3, H2 and Ar used in the calculations of shift coefficients Molecule
NH3
H2
Ar
M (amu) li (D) lf (D) m4 lf (D) 2m2 ˚) Q (D A ˚ 2) X (D A ˚ 3) U (D A ˚ r (A) e (K) ˚ 3) ai (A c U (ev) ˚ 4) Ai(A ˚ 4) A^(A ˚ 4) A 0 (A
17.03 1.4715a 1.4554a 1.015a 2.32b 1.20b — 3.018c 294.3c 2.18b 0.054b 10.16d 0.0633e 0.793e 0.81e
2.0158 0 0 0 0.6522f +0.6522f 0.1264f 2.944g 32.0g 0.806b 0.116b 15.426d 0 0 0
39.948 0 0 0 0 0 0 3.504g 117.7g — — — 0 0 0
a b c d e f g
Ref. Ref. Ref. Ref. Ref. Ref. Ref.
lm1 m2 m3 m4 ¼ 1.5610 þ 7.2 103 ðm1 þ 12Þ 2.271 101 ðm2 þ 12Þ þ 3.75 102 ðm3 þ 1Þ 1.65 102 ðm4 þ 1Þ;
where mi is the number of quanta in the ith normal mode. In the absence of any information about the vibrational dependence of the polarizability of NH3, it was hoped that it would be possible to choose a value of Da = a1,f a1,i which would give a reasonable agreement between experimental and theoretical results. For the vibrational dephasing contribution, we have consid˚ 3 in the m4 band. In the 2m2 band, for ered Da = 0.05 A which the shift is positive, we have used only the positive contribution of S iso 1 ðDa ¼ 0Þ arising from the difference of the dipole moment of ammonia in the initial and final states. The H2-shift coefficients at 296 K were computed in the PP and RP branches of the m4 band and in the QQ branch of the 2m2 by including the contribution from H2 in the ground state with J2 values varying from 0 to 7 that were weighted by the Boltzmann factors and by J þ1 the nuclear spin factor 2 þ ð1Þ 2 . We considered the parameters of NH3 for symmetric (s) and antisymmetric (a) levels to compare the shift coefficients for a fi a and s fi s allowed transitions in the m4 band as well as for a fi s transitions in the 2m2 band. The molecular constants involved in the computation are given in Tables 3 and 4. The calculated values are compared in Table 1 with the experimental data. 3.2. Ar-shift calculation
[32]. [35]. [36]. [37]. [30]. [38]. [39].
For NH3–Ar we have considered the intermolecular potential of Smith, Giraud, and Cooper (SGC) [33] developed in Legendre polynomials limited to the second-order terms,
Table 4 Rovibrational parameters used in the calculation for NH3 in the ground and m4 and 2m2(s) vibrational states, and for H2 in the ground vibrational state Molecule NH3
State a
Ground m4b 2m2b
Groundc
H2 a b c
Ref. [40]. Ref. [41]. Ref. [42].
s a s a s
B (cm1)
(C–B) (cm1)
9.94664 9.94159 10.17702 10.16501 10.31580
3.71828 3.71123 4.00729 3.99276 4.38068
59.3345
—
D (103 cm1) 0.84953 0.832742 1.04216 1.0220 0.4324 45.651
DJK (103 cm1)
DK (103 cm1)
1.5783 1.53197 2.05445 1.96035 0.4814
1.0107 0.97894 1.2066 1.1300 0.1374
—
—
146
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
Table 5 Coefficients of Smith–Giraud–Cooper (SGC) potential
NH3–Ar m4a 2m2b a b
4. Results and discussion
A1
A2
R1
R2
0.20 0.20
0.20 0.20
0.50 0.40
0.40 0.30
Ref. [5]. This work.
V ¼ V iso þ V aniso r7 r 12 r6 r 12 ¼ 4e A1 þ R1 P 1 ðcoshÞ r r r r r6 r 12 þ R2 A2 ð12Þ P 2 ðcoshÞ ; r r where r is the intermolecular distance, h is the angle between the symmetric axis of absorbing molecule and intermolecular axis, and Pl(l = 1 or 2) are Legendre polynomials of order l. The parameters R1, A1, R2, and A2 that were calculated to obtain a reasonable agreement with the experimental values of broadening coefficient are given in Table 5. e and r are the Lennard-Jones parameters for the molecular pair NH3–Ar. The analytical contributions to the differential cross section are given in [19] for the anisotropic part of atomlinear molecule potential used. They have been modified to include the quantum numbers K (Ki, Kf) in the Clebsch–Gordan coefficients. The inversion motion in NH3 was considered through Eqs. (6) and (7) of [5] so that S middle ¼ 0 for l = 1 (contribution of P1(cos h)). 2 The Lennard-Jones isotropic part of the potential can be written as C 12 C 6 6 with C 6 ¼ 4er6 r12 r 3 U 1U 2 and C 12 ¼ 4er12 . 2 ðU 1 þ U 2 Þ
V iso ¼
The vibrational dephasing contribution is obtained from S iso 1 given by [34] 5 11 3 DC 6 per r 63 DC 6 per r iso þ y. ð13Þ S1 ¼ 2 C6 hv0c rc 64 C 6 hv0c rc Here
DC 6 ¼ ðC 6 Þmf ðC 6 Þmi
and
y¼
The new results for line shift and line mixing parameters obtained from the present analysis are presented in this section, where they are compared with previous measurements when available and with the calculations described above. 4.1. Line shifts The line shift values obtained for the two collisional systems NH3–H2 and NH3–Ar are reported in Tables 1 and 2 along with the absolute errors. For the two perturbers all shift coefficients in the m4 band are negative (except for six lines for H2 perturber), so that the center frequencies of the lines decrease with increasing pressure. These shifts are typically 1–2 orders of magnitude smaller than the broadening coefficients published in [5] and [7] for Ar and H2 respectively. This makes them rather difficult to determine as evidenced from the relatively large error found. For the 2m2 band the shifts coefficients are positive and are much greater than those obtained in the m4 one. Therefore the temptation is great to explain the observed behavior by predominant vibrational dephasing effect. Moreover these shifts appear to weakly depend on J and K quantum number. The prediction of line shifts using a semiclassical approach (which is not perfectly appropriate for a molecule such as NH3 with large rotational constants) leads to a reasonable agreement, even though poor knowledge of the polarizability for vibrational transitions produces inaccuracies in the computed values. These calculations reproduce the sign of line shifts. Although we have considered two sets of rotational constants (for symmetric and antisymmetric levels), the predicted values of line shift coefficients are practically identical for a ‹ s and s ‹ a transitions. For the two perturbers, the
DC 12 =C 12 . DC 6 =C 6
The values of DC6/C6 and y are not directly available for ammonia. In our calculation, we have systematically considered the coefficients as adjustable parameters and taken as DC6/C6 = 0.014 and y = 2.0, in the m4 band and DC6/C6 = 0.03 and y = 5.0 in the 2m2 band. The molecular parameters introduced in the computation are given in Tables 3–5. The line shifts coefficients d0 (J, K) at 296 K were computed for J 6 10 in the PP and RP branches of m4 band and QQ branch of the 2m2 band. The calculated values are compared in the Table 2 with the experimental data.
Fig. 4. Line shifts in the PP branch of the m4 vibrational band of NH3 perturbed by H2 as a function of J + 0.1 · (J K). (m) Experimental values; (s) calculated values.
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
Fig. 5. Line shifts for NH3 transitions broadened by Ar in the m4 vibrational band as a function of J + 0.1 · (J K). (m) Experimental values; (s) calculated values.
Im ðS aniso Þ values are small. Thus, for the two systems, 2 the line shift is mostly due to the isotropic part of aniso S iso Þ 1 with small corrections coming from the Im ðS 2 terms. The comparison of the results is shown by Figs. 4 and 5, where the measured and theoretical line shifts of PP (J, K) transitions are plotted as a function of J + 0.1(J K). As may be seen by these figures and Tables 1 and 2, the experimental and calculated line shifts appear to depend weakly on J and K. These evolutions are less pronounced for predicted values than for the observed. Moreover for Ar, the results obtained from the Smith–Giraud–Cooper (SGC) potential with the values of vibrational parameters indicated above provide overestimated line shifts. Our H2-shift values in the m4 band are larger than those obtained by Pine et al. [12] in the R and Q branches of the m1 band and smaller for the Ar perturber. For the 2m2 band, a satisfactory agreement for the sign of shifts is observed when comparison is done with the results obtained by Raynaud et al. [11] in the P branch of the 2m2 m2 combination band of NH3 perturbed by H2. For the Q branch however our values are greater than those obtained by these authors. Furthermore, as expected, the present values of line shifts are smaller than those obtained by Baldacchini et al. for self-shifts in the 2m2 m2 parallel band. 4.2. Line mixing parameters For lines whose line mixing parameters are statistically significant, the a ‹ s transitions have mostly positive Y0 values and the s ‹ a transitions have mostly a negative ones. Nevertheless there are some exceptions to this sign ordering for the lines for which Y0 parameters have the same magnitude of standard error. The observed lines appear to be shifting towards each other, whereas at low pressures the lines are shifting apart. This mutual
147
attraction is characteristic of line mixing of the collisionally-coupled overlapped lines. Moreover for a given J, the line mixing parameter Y0 seems to increase with K quantum number (as seen in Tables 1 and 2, Y0 of the P P(3, 1)s line is smaller than Y0 of PP(3, 2)s line and very weak compared with PP(3, 3)s result). This evolution is more pronounced for H2 than for Ar perturber. Note that the splitting 2d between the inversion components decreases with K for a given J. The most striking result is the very large amount of coupling between the symmetric and antisymmetric components for J close or equal to K. The largest line mixing parameters observed are those for the J = K lines. For these lines the line mixing parameters decrease with 2d. In fact parameter Y0 of the PP(3, 3) doublet of 2d = 0.275 cm1 is very weak compared to those of PP(8, 8) doublet with 2d = 0.210 cm1.
5. Conclusion We have measured H2 and Ar pressure-induced line shifts and line interference parameters of 66 PP and R P selected lines in the m4 band and 10 lines in the 2m2 band of NH3 at T = 296 K using a high-resolution Fourier transform spectrometer. The measured and predicted values of line shift are in reasonable agreement if one takes into account the various uncertainties both in the experiments and in the theory. It should be noted that the pure rotational contribution is quite negligible and the shifts are mostly due to the vibrational dependence of the isotropic potential. These values are mostly negative in the m4 band and positive in the 2m2 band. On the contrary the inversion doublets line mixing parameters are, on the hole, of opposite sign.
Acknowledgment The authors are grateful to C. Boulet for helpful discussions.
References [1] V. Kunde, R. Hanel, W. Maguire, J.P. Baluteau, A. Marten, A. Chedin, N. Husson, N.S. Scott, Astrophys. J. 263 (1982) 443–467. [2] P.T.P. Ho, C.H. Townes, Annu. Rev. Astron. Astrophys. 21 (1983) 239–270. [3] D.J. Brassington, in : Proceedings of the International Symposium on Monitoring of Gaseous Pollutants by Diode Lasers , Freiburg, Germany, 17 October, 1988. [4] V.N. Markov, A.S. Pine, G. Buffa, O. Tarrini, J. Quant. Spectrosc. Radiat. Transfer 50 (1993) 167–178. [5] M. Dhib, J.P. Bouanich, H. Aroui, M. Broquier, J. Mol. Spectrosc. 202 (2000) 83–88. [6] M. Dhib, J.-P. Bouanich, H. Aroui, A. Picard-Bersellini, J. Quant. Spectrosc. Radiat. Transfer 68 (2001) 163–178.
148
M. Dhib et al. / Journal of Molecular Spectroscopy 233 (2005) 138–148
[7] J-P. Bouanich, H. Aroui, S. Nouri, A. Picard-Bersellini, J. Mol. Spectrosc. 206 (2001) 104–110. [8] V. Nemtchinov, K. Sung, P. Varanasi, J. Quant. Spectrosc. Radiat. Transfer 83 (2004) 243–265. [9] G. Baldacchini, F. Damato, M. De Rosa, G. Buffa, O. Tarrini, J. Quant. Spectrosc. Radiat. Transfer 55 (1996) 745– 753. [10] G. Baldacchini, A. Bizzarri, L. Nencini, V. Sorge Tarrini, J. Quant. Spectrosc. Radiat. Transfer 43 (1990) 371–380. [11] F. Raynaud, B. Lemoine, F. Rohart, J. Mol. Spectrosc. 168 (1994) 584–592. [12] S. Pine, V.N. Markov, G. Buffa, O. Tarrini, J. Quant. Spectrosc. Radiat. Transfer 50 (1993) 337–348. [13] S. Hadded, H. Aroui, J. Orphal, J.-P. Bouanich, J.-M. Hartmann, J. Mol. Spectrosc. 210 (2001) 275–283. [14] S. Hadded, F. Thibault, P.-M. Flaud, H. Aroui, J.-M. Hartmann, J. Chem. Phys. 116 (2002) 7544–7557. [15] S. Hadded, F. Thibault, P.-M. Flaud, H. Aroui, J.-M. Hartmann, J. Chem. Phys. 120 (2002) 217–223. [16] P.W. Parson, V.I. Metchnik, I.C. Story, J. Phys. B: Atom. Mol. Phys. 5 (1972) 1221–1233. [17] G. Buffa, O. Tarrini, Appl. Optics 28 (1989) 1800–1805. [18] C.J. Tsao, B. Curnutte, J. Quant. Spectrosc. Radiat. Transfer 2 (1962) 41–91. [19] D. Robert, J. Bonamy, J. Phys. 40 (1979) 923–943. [20] H. Aroui, M. Broquier, A. Picard-Berselini, J-P. Bouanich, M. Chevalier, S. Gherissi, J. Quant. Spectrosc. Radiat. Transfer 60 (1998) 1011–1023. [21] H. Aroui, A. Picard-Bersellini, M. Chevalier, M. Broquier, S. Gherissi, J. Mol. Spectrosc. 176 (1996) 162–168. [22] A. Le´vy, N. Lacome, C. Chackerian Jr., in: Spectroscopy of the EarthÕs Atmosphere and of the Interstellar Medium, Academic Press, New York, 1992, pp. 261–337. [23] P.W. Rosenkranz, IEEE Trans. Antenn. Propag. 23 (1975) 498–506.
[24] F. Thibault, J. Boissoles, R. Le Doucen, J.-P. Bouanich, Phys. Areas, and C. Boulet, J. Chem. Phys. 96 (1992) 4945-4953. [25] C. Boulet, D. Robert, L. Galatry, J. Chem. Phys. 65 (1976) 5302– 5314. [26] J. Bonamy, L. Bonamy, D. Robert, J. Chem. Phys. 67 (1977) 4441–4453. [27] J.P. Bouanich, C. Campers, G. Blanquet, J. Walrand, J. Quant. Spectrosc. Radiat. Transfer 39 (1988) 353–365. [28] R.P. Leavitt, J. Chem. Phys. 72 (1980) 3472–3482. [29] J.-P. Bouanich, C. Brodbeck, J. Quant. Spectrosc. Radiat. Transfer 14 (1974) 141–151. [30] J. Bonamy, D. Robert, J. Quant. Spectrosc. Radiat. Transfer 15 (1975) 855–862. [31] R.P. Leavitt, J. Chem. Phys. 73 (1980) 5432–5450. [32] M.D. Marshal, K.C. Izgi, J.S. Muenter, J. Chem. Phys. 107 (1997) 1037–1044. [33] E.W. Smith, M. Giraud, J. Cooper, J. Chem. Phys. 65 (1976) 1256–1267. [34] L. Bonamy, J. Bonamy, D. Robert, B. Lavorel, R. Saint-Loup, R. Chaux, J. Santos, H. Berger, J. Chem. Phys. 89 (1988) 5568–5577. [35] C.G. Gray, K.E. Gubbins, Theory of Molecular Fluids, Oxford University Press, London/New York, 1984. [36] S.V. Khristenko, A.I. Maslov, V.P. Shevelko, Molecules and their Spectroscopic Properties, Springer, Berlin, 1998. [37] J. Komasa, A.J. Thakkar, Mol. Phys. 78 (1993) 1039–1046. [38] J.-P. Bouanich, C. Brodbek, J. Quant. Spectrosc. Radiat. Transfer 17 (1977) 777–782. [39] M. Lepe`re, G. Blanquet, J. Walrand, J.P. Bouanich, J. Mol. Spectrosc. 192 (1998) 231–234. [40] S. Urban, V. Spirko, D. Papousek, J. Kauppinen, S.P. Belov, L.I. Gershtein, A.F. Krupnov, J. Mol. Spectrosc. 88 (1981) 274–292. [41] H. Sasada, Y. Endo, E. Hirota, R.L. Poynter, J.S. Margolis, J. Mol. Spectrosc. 151 (1992) 33–53. [42] S.L. Bragg, J.W. Brault, W.H. Smith, Astrophys. J. 263 (1982) 999–1004.