Ab initio calculations for the far infrared collision induced absorption by N2 gas Béatrice Bussery-Honvault and Jean-Michel Hartmann Citation: The Journal of Chemical Physics 140, 054309 (2014); doi: 10.1063/1.4863636 View online: http://dx.doi.org/10.1063/1.4863636 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Dissipation of alignment in CO2 gas: A comparison between ab initio predictions and experiments J. Chem. Phys. 139, 024306 (2013); 10.1063/1.4812770 Can theory quantitatively model stratospheric photolysis? Ab initio estimate of absolute absorption cross sections of ClOOCl J. Chem. Phys. 133, 174303 (2010); 10.1063/1.3499599 Ab initio calculation of electrostatic multipoles with Wannier functions for large-scale biomolecular simulations J. Chem. Phys. 120, 4530 (2004); 10.1063/1.1644800 Determination of an ethane intermolecular potential model for use in molecular simulations from ab initio calculations J. Chem. Phys. 114, 6058 (2001); 10.1063/1.1356003 Determination of a methane intermolecular potential model for use in molecular simulations from ab initio calculations J. Chem. Phys. 110, 3368 (1999); 10.1063/1.478203
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THE JOURNAL OF CHEMICAL PHYSICS 140, 054309 (2014)
Ab initio calculations for the far infrared collision induced absorption by N2 gas Béatrice Bussery-Honvault1,a) and Jean-Michel Hartmann2 1
Laboratoire ICB, UMR 6303, CNRS-Université de Bourgogne, BP 47870 F-21078 Dijon cedex, France Laboratoire Interuniversitaire des Systèmes Atmosphériques (LISA), UMR CNRS 7583, Université Paris Est Créteil, Université Paris Diderot, Institut Pierre-Simon Laplace, 94010 Créteil cedex, France 2
(Received 19 November 2013; accepted 17 January 2014; published online 4 February 2014) We present (far-infrared) Collision Induced Absorption (CIA) spectra calculations for pure gaseous N2 made for the first time, from first-principles. They were carried out using classical molecular dynamics simulations based on ab initio predictions of both the intermolecular potential and the induced-dipole moment. These calculations reproduce satisfactory well the experimental values (intensity and band profile) with agreement within 3% at 149 K. With respect to results obtained with only the long range (asymptotic) dipole moment (DM), including the short range overlap contribution improves the band intensity and profile at 149 K, but it deteriorates them at 296 K. The results show that the relative contribution of the short range DM to the band intensity is typically around 10%. We have also examined the sensitivity of the calculated CIA to the intermolecular potential anisotropy, providing a test of the so-called isotropic approximation used up to now in all N2 CIA calculations. As all these effects interfere simultaneously with quantitatively similar influences (around 10%), it is rather difficult to assert which one could explain remaining deviations with the experimental results. Furthermore, the rather large uncertainties and sometimes inconsistencies of the available measurements forbid any definitive conclusion, stressing the need for new experiments. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4863636] I. INTRODUCTION
Collision Induced Absorption (CIA) spectra1, 2 arise when two or more molecules collide. The intermolecular forces distort the symmetry of the electronic cloud of each colliders and the system acquires a temporary dipole moment. The strength of the induced dipole depends on the mutual distance and orientation of the colliding molecules. The resulting absorption spectra appear in the far infrared when the induced dipole is modulated by the translational and rotational motions of the molecules or at shorter wavelengths when vibrational transitions are also involved. In this paper, we focus on the far infrared CIA spectra at the low density limit, where binary collisions dominate and when the absorption coefficient therefore is proportional to the gas-density squared. Various theoretical methods with differing precisions exist nowadays for the computation of CIA spectra, which are reviewed in Refs. 1 and 2. Each has its advantages and limitations. In general, the methods can be divided into classical and quantum mechanical treatments. The most rigorous technique is a close coupling method which fully takes into account the anisotropy of the intermolecular potential but it is extremely computer-time consuming. Speed limitations of present computers make these computations possible only for very small and light molecules (H2 ) and/or at very low temperatures. For heavier or more complex molecules (such as N2 3 ) and/or higher temperatures (e.g., room temperature), it is nevertheless possible to carry quantum mechanical a) Author to whom correspondence should be addressed. Electronic mail:
[email protected]
0021-9606/2014/140(5)/054309/6/$30.00
calculations using the approximation that the translation is governed by the isotropic intermolecular potential. While this so-called “isotropic approximation” is totally inadequate for the CIA of CO2 pairs,4, 5 it leads to the underestimation of the pure N2 CIA band integrated intensity by about 10%.6 However, its consequences on the spectral shape of pure N2 CIA remain unknown. An interesting alternative is brought by classical molecular dynamics simulations (CMDS). Indeed, these are tractable for heavy or complex molecular systems, even when the potential anisotropy is taken into account. The available results, obtained for CO2 ,7, 8 show that CMDS is a powerful method. With a concentration of roughly 97%, nitrogen is the most abundant species in the atmosphere of Titan and the collision-induced dipole spectrum of N2 -N2 pairs contributes substantially to the atmospheric absorption below 200 cm−1 . As a result, precise knowledge of N2 CIA is required for optical remote sensing studies (e.g., Refs. 9 and 10) as well as for studies of the heat balance11 of the atmosphere of Titan. Despite these important applications in planetary science, relatively few experimental and theoretical studies of the far infrared pure N2 CIA have been made. To the best of our knowledge, the most recent laboratory measurements were made about 30 years ago.12, 13 They cover a broad temperature range but have significant uncertainties and provide limited information on the CIA wing. From the theoretical side, quantum mechanical calculations were made in Ref. 3, while, in Ref. 14 and those cited therein, empirical line shapes15 were used. These attempts present severe limitations since: (i) they use the isotropic approximation and thus disregard
140, 054309-1
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J. Chem. Phys. 140, 054309 (2014)
the influence of the intermolecular potential anisotropy on the translational and rotational dynamics. (ii) They rely on the adjustment of some parameters (the short range induced dipole in Ref. 3, the line shape in Ref. 14) on measured spectra. On the opposite, in this paper, we present the first calculations conducted using an anisotropic intermolecular potential and an induced dipole, both ab initio predicted, and thus free of any adjusted parameter. For this, CMDS have been carried out, as in Ref. 8, using the anisotropic N2 -N2 intermolecular potential of Ref. 16 or its purely isotropic component. These simulations provide the positions and orientations of all of the many molecules treated at each time step. From these, the interaction induced dipole is calculated, based on an accurate fit of the ab initio values of Ref. 17 or on some long range asymptotic developments. The time autocorrelation of this dipole vector is then obtained whose Fourier-Laplace transform yields the spectrum. Such calculations enable to a test of the influence of the isotropic approximation as well as a quantification of the contribution of the short range induced dipole. The induced dipole fitting procedure is described in Sec. II while the way CMDS are carried out is the subject of Sec. III. Comparisons between measured and predicted CIA in the (far infrared) roto-translational band of pure N2 at various temperatures are then presented in Sec. IV where the influences of the short range DM and of the intermolecular potential anisotropy are also discussed. A conclusion is given at the end of this paper.
the dimer after taking into account the symmetry (see Fig. 1 of Ref. 17 for the definitions of the θ and φ angles). It is compared here with the asymptotic long-range cartesian components (μx , μy , μz ), calculated using Eqs. (1), (2) and (A1)– (A15) of Ref. 8. For these calculations, the values of the static polarisability components (α // , α ⊥ ), of the quadrupole () and hexadecapole () moments were taken from Ref. 18, i.e., α // = 14.91, α ⊥ = 10.16, = −1.052, and = −7.5, all in atomic units. Note that the values of α // and α ⊥ lead to an isotropic polarisability α of 11.74 a.u. and an anisotropic polarisability γ of 4.75 a.u. From Table 4 of Ref. 19, we can see that experimental values are dispersed around −1.09 a.u. for (= Q20 ), around −7.97 a.u. for (= Q40 ), around 14.98 a.u. 1,1 1,1 for α// (= α0,0 ) and around 10.304 a.u. for α⊥ (= α±1,±1 ), so that, the presently used values are in good agreement with these averaged experimental quantities. The ab initio and asymptotic dipole moments are presented in Fig. 1, as functions of the intermolecular distance R, for selected values of θ 1 , θ 2 , and φ 2 . A good agreement between asymptotic and ab initio dipole moments is observed at large intermolecular distances (typically further than 7 bohr) that proves the accuracy of the ab initio calculations in this region. Deviations from the asymptotic behavior occur at shorter range, increasing with decreasing distances, which result from the short range contribution to the DM, not included in the asymptotic one. Note that, in some cases, changes in the sign of the dipole moment appear at small distances. B. Spherical expansion of the dipole moment
II. THE AB INITIO DIPOLE MOMENT
In order to include the ab initio dipole moment into the collision-induced spectra calculations, it is convenient to represent it through Eq. (2) of Ref. 8. Such an expansion of the induced dipole presents the advantage to offer some physical understanding of the various contributions, separated into radial and angular factors. Several previous
A. Ab initio versus asymptotic dipole moments
The ab initio dipole moment of N2 -N2 was calculated in Ref. 17, for four intermolecular distances between 5 and 11 bohrs, with θ a , θ b = 0◦ , 30◦ , 60◦ , 90◦ and φ = 0◦ , 45◦ , 90◦ , 135◦ , 180◦ , resulting in 42 angular arrangements of X
Y
01 0
φ2=45
0
04
-0. 8
10
0.03 φ2=90
0.02
0
06
6
8
10
φ2=90
0
8
10
0
6
1
0 -0.
0.04
10
φ2=135
0.02 6
8
10
-
03
-0.
θ1=30
0
θ2=30
8
0.0
10 θ2=90
0
8 θ1=90
0
10 θ2=30
φ2=90
0
0
0
6
.04
0
φ2=135
2 0.0
0
φ2=45
0
8
8 θ1=60
1
-0.
6
6
0.0
0.06
0
2
0.0
04
0.01
0
-0.
02 -0.
0
φ2=0
-0.
3 6
-0. 0
N2-N2 Dipole Moment (a.u.)
0.01
0
02
-0.
-0.
φ2=45
02
0.02
0 0.04
Z 0
0
0.03
0
0
0
6 8 10 Intermolecular distance (Bohr)
0
6
8
10
FIG. 1. Ab initio (circles) and asymptotic (dashed lines) dipole moment (in a.u.) of N2 -N2 as a function of the intermolecular distance (in Bohr) for various geometric arrangements. When not stated, θ 1 = 30◦ and θ 2 = 60◦ (see Fig. 1 of Ref. 17 for the definitions of the θ and φ angles).
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J. Chem. Phys. 140, 054309 (2014)
works3, 6 have discussed the contributions and the physical significations of the various terms so that we will not discuss that point here again. A straightforward adaptation of the dipole moment of Eq. (2) of Ref. 8, written in the space-fixed coordinate system, to the dimer-fixed coordinate system, is obtained by fixing φ 1 = θ = φ = 0 in the equation. The radial coefficients, Al1 ,l2 ,,l (R12 ), are obtained by solving, for each intermolecular distance, a set of linear equations associated with the geometries of the dimer used in the ab initio calculations. This set includes 3Ng (with Ng = 42 geometric arrangements) equations, each involving Nt unknown (the Al1 ,l2 ,,l (R12 )) radial terms, associated with the various angular terms. The factor 3 arises because we consider the three cartesian components of the dipole moment simultaneously. Following various tests, we have retained an optimized set of Nt = 28 (l1 , l2 , , l) components, restrained by the conditions: l1 ≤ 10, l2 ≥ l1 with Al2 ,l1 ,,l = Al1 ,l2 ,,l if is even and Al2 ,l1 ,,l = −Al1 ,l2 ,,l if is odd, ≤ 7 with odd for l1 = l2 terms and even for l1 = l2 terms. The associated radial coefficients, Al1 ,l2 ,,l (R) for each of the four calculated intermolecular distances have been obtained for all the 28 sets of (l1 , l2 , , l). With these values, we obtained root mean square (rms) deviations between the adjusted and ab initio values of the dipole moment of 2.7 × 10−3 a.u. for the x component, 2.3 × 10−3 a.u. for the y component, and 2 × 10−4 a.u. for the z component at R = 5 bohr. These deviations are typically one order of magnitude smaller than the values of the DM components (see Fig. 1). C. Analytical fit of the short range radial functions
In order to get an analytical representation of the dipole moment suitable for spectra calculations through CMDS, we have fitted the radial coefficients by analytical expressions optimized for each (l1 , l2 , , l) set. For this, we first subtract the asymp known asymptotic behavior from the values of Al1 ,l2 ,,l (R), in order to get short-range (SR) coefficients such that: asymp
ASR l1 ,l2 ,,l (R) = Al1 ,l2 ,,l (R) − Al1 ,l2 ,,l (R),
(1)
asymp
where Al1 ,l2 ,,l (R) is computed as explained before, neglecting the contributions given by Eqs. (A4)–(A6) of Ref. 8 due to missing data. Various analytical expressions have been employed for best fits, i.e., ASR 1 (R) = a exp(−bR) + c exp(−dR), ASR 2 (R) = a exp(−cR) +
b , Rd
b exp(−cR − dR 2 ), (R) = a + (2) ASR 3 R b exp(−dR), ASR (R) = a + 4 Rc b exp(−c(R − d)). ASR (R) = a + 5 R The a, b, c, and d coefficients are given in Table I for distances in bohr and radial functions A(R) in a.u., together with the indices of the expression used [i.e., from 1 to 5 following Eq. (2)], in the last column of the table.
D. Quality of the global fit of the dipole moment
With the values of Table I, Eqs. (1) and (2) of Ref. 8 and the molecular parameters given in Sec. II A for the asymptotic contributions, the DM can now be generated for any conformation of the molecular pair. We can check its quality by comparing it with the input ab initio DM value. This exercise leads to root mean square errors of 10.8 × 10−5 a.u. for the x component, 6.8 × 10−5 a.u. for the y component, and 21.1 × 10−5 a.u. for the z component, which is quite satisfactory in regards of the ab initio DM values (Fig. 1) and their precision. III. CLASSICAL MOLECULAR DYNAMICS SIMULATIONS
CMDS have been carried out exactly as previously done for the pure CO2 CIA,8 for which very satisfactory results have been obtained. 288 sets of 20 000 N2 molecules inside cubic boxes with periodic boundary conditions20 have been treated in parallel. First, proper initialisation (random orientations and Boltzmann statistics for energies) is made for the translational and rotational parameters of the molecules. Then, the time evolutions of the center of mass position and velocity as well as of the molecular axis orientation and of the rotational angular momentum of each molecule are calculated step by step using an intermolecular potential as input. From the (relative) positions and orientations of the molecules, the interaction-induced dipole is then computed. Having stored this dipole vector at time zero, its auto-correlation function (ACF) can be obtained at each time. Then, as in Ref. 8, the Fourier-Laplace transform of this ACF directly yields the spectrum. For the calculations, the anisotropic intermolecular potential described in Refs. 16 has been used. Averaging this potential over all molecular orientations provides the isotropic component for a test of the widely used isotropic approximation on the CIA spectra. For the interaction-induced dipole, two calculations were also made. In the first, the full dipole is used, including both the long range asymptotic dipoles and the short distance terms described in Sec. II. In the second, only the long range components are taken into account. IV. RESULTS A. Experimental versus calculated collision-induced absorption spectra
Figure 2 presents comparisons of experimental results at various temperatures with predictions obtained with the ab initio N2 -N2 anisotropic potential of Ref. 16 and full dipole moment of Sec. II. As can be seen, the agreement is very satisfactory at 149 K but deteriorates (moderately) with increasing temperature. Indeed, the ab initio CIA spectrum overestimates the experimental peak values by 3% at 149 K, 5% at 228 K, and 11% at 296 K. Nevertheless, one should be cautious in definitive conclusion about the model quality from such results for two reasons: first, because, as already mentioned, the experimental data are tainted of uncertainties of typically 10% or more, as shown in Refs. 3 and 6 where various measurements are compared. Second, because input data
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J. Chem. Phys. 140, 054309 (2014)
TABLE I. Numerical values of the a, b, c, and d coefficients of the analytical radial functions (see Relations (2)) whose expression number is given in the last column. (l1 , l2 , , l) (2021) (2023) (2211) (2233) (4043) (4045) (4221) (4223) (4243) (4245) (4265) (4267) (4411) (4433) (4455) (4477) (6065) (6067) (6243) (6245) (6265) (6267) (6421) (6423) (6443) (6445) (6465) (6467)
a
b
c
d
N◦
0.18832437 − 2.50142847 − 1.61490065 − 2.99460545 − 0.83306643 − 141.64218797 − 0.08051585 − 21.00000000 − 69.99989585 47.15217189 571.15008359 − 210.99997920 − 3.57511979 − 1.38906391 5.48949315 − 2.38671320 0.00000002 − 2.32539535 1391.39686204 − 2.39613048 − 91.15987451 1175.05951604 1263.28178232 − 209.99965065 − 79.08944016 8596.82185691 6.72995727 − 209.99958391
− 1.42358996 13.21490525 8.89655956 0.00156483 9.19937445 − 0.02023686 7.67472780 − 0.02000000 − 0.02000000 0.01505213 0.27296950 − 0.02000000 0.00188879 0.00634065 0.10809706 9.10225749 1.00000000 9.15333577 55.87867034 9.12546170 0.00014934 3.54333579 2.99961994 − 0.02000000 0.00104647 157.69016961 0.00051409 − 0.02000000
0.25442614 0.93859007 2.11325460 1.99391664 1.58280645 8.39999662 2.03633265 2.20000000 8.40000000 1.87218790 1.99960252 8.40000000 2.11868380 1.50414756 1.78491363 2.86920632 0.00000002 2.59341823 2.41961282 2.72572068 2.06611153 2.53181425 2.69045621 8.00000000 2.20407844 3.08337869 2.0238256 8.00000000
0.03658907 0.00154809 2.68576430 0.70000000 2.73208244 1.85684522 0.96148340 11.0000000 1.89666485 2.44096603 3.43464339 1.82209539 2.20010917 2.54201951 4.29630926 3.34693218 1.00000000 3.60319165 6.96222480 3.52768862 0.80436446 5.74710873 6.29915695 2.26854414 1.81603196 7.92622703 1.61674424 2.33874232
3 3 5 2 5 4 4 2 4 2 2 4 2 2 2 5 1 5 2 5 2 2 2 4 2 2 2 4
of the CMDS (i.e., dipole moment and intermolecular potential), though obtained through ab initio calculations, are not exact values and uncertainties are also attached to these quantities. Increasing the induced dipole moment by 5% increases the CIA by 10%. Furthermore, as well known,6, 8 the results are sensitive to the intermolecular potential. However, the quality of the presently used ab initio potential16 has previously been confirmed by the calculations of line-broadening coefficients21 down to low temperature range, and those of total integral scattering cross-sections16 (test of the well depth, of the repulsive wall and of the asymptotic part of the potential). From the confrontation between calculated and experimental results,16, 21 it has been concluded that the present potential is of good quality, though the isotropic part may be slightly overestimated. From the above given uncertainty estimations, it is clear that calculated and measured CIA spectra both fall well within error bars, as presented in Fig. 2. Following the work of Gruszka and Borysow,6 an analysis in terms of spectral moments has been conducted through the evaluation of γ 1 and α 1 , defined as ∞ α(ω) ¯ dω (3) γ1 = 2kT 0 ω tanh(¯ω/2kT ) and α1 =
1 n2
∞
α(ω)dω, 0
(4)
where α(ω) is the squared-density normalized CIA coefficient (as plotted in Fig. 2). These two spectral moments are plotted in Fig. 3 and compared with the experimental values of Refs. 12 and 13. As can be seen, the agreement between experimental and calculated values of γ 1 is excellent while the calculated predictions of α 1 overestimate the experimental ones by 10% or slightly more. This discrepancy may be partly explained by the fact that α 1 is much more sensitive to the area of the CIA wing where the absorption is weak and not at all or poorly determined experimentally. B. Influence of the short range induced dipole
In order to quantify the influence of the short range induced dipole (SRID) on the CIA spectra, we compare in Fig. 4 CIA spectra calculated with the full dipole with results obtained by taking into account only the asymptotic long range one. To our knowledge, this is the first paper offering an ab initio quantification of such effects as the previous tentatives have proposed fitting procedure to estimate them. From Fig. 4, we note that, for both temperatures presented here (i.e., 149 and 296K), the SRID contributions are about 10%-14% greater than the pure asymptotic which contribute for about 90% of the peak absorption at both temperatures. Detailed analysis shows that the relative contribution of the SRID is larger at high temperature and in the far wing of the band. In this region, it results in an increase of the CIA by a
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054309-5
B. Bussery-Honvault and J.-M. Hartmann
J. Chem. Phys. 140, 054309 (2014)
8e-06
8e-06 (a)
6e-06
(a) 6e-06
4e-06 2e-06
4e-06 0
100
50
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350
6e-06 5e-06
2e-06
(b)
4e-06
2
3e-06 2e-06
0
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250
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300
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-1
1e-06 0
CIA coefficient (cm /amagat )
-1
2
CIA coefficient (cm /amagat )
0
0
100
50
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200
300
250
350
5e-06 4e-06
(c)
3e-06 2e-06
5e-06 (b)
4e-06
3e-06
1e-06 0
350
2e-06
FIG. 2. Collision-induced absorption spectrum (in cm−1 /amagat2 ) of N2 by N2 (a) at 149 K, (b) at 228 K, and (c) at 296 K, as obtained from measurements12, 13 (circles) and from the CMDS calculations using the present ab initio dipole moment and the intermolecular potential of Ref. 16 (continuous lines). The error bars correspond to ± 10%.
1e-06
0
100
50
200 150 -1 ω (cm )
300
250
factor of more than 2 beyond 300 cm−1 . This can be explained by the fact that large frequency detunings (in the spectrum) correspond to short times (in the dipole ACF) which involve close distance collisions, and then a greater influence of the
0
0
50
100
200 150 -1 ω (cm )
250
FIG. 4. Collision-induced absorption spectrum (in cm−1 /amagat2 ) of N2 by N2 (a) at 149 K and (b) at 296 K, as obtained by present ab initio dipole moment (continuous lines) or by the asymptotic dipole moment only (dashed lines), both with the ab initio intermolecular potential of Ref. 16.
18 cm s)
16 5
14
γ1 (10
-58
12 10 8 6
α1 (10
-31
5
cm /s)
4 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1
150
200
150
200
250
250 Temperatue (K)
300
350
300
350
FIG. 3. Comparison between experimental and computed spectral moments of N2 pairs. Experimental data are from Ref. 13 (full circles) or Ref. 12 (open circles). Indicative error bars of ±10% have been added to the measured values. Computed values (continuous lines) have been evaluated with the present ab initio dipole moment and the ab initio intermolecular potential of Ref. 16.
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054309-6
B. Bussery-Honvault and J.-M. Hartmann
J. Chem. Phys. 140, 054309 (2014)
8e-06
(a) 6e-06
4e-06
2
CIA coefficient (cm /amagat )
2e-06
0
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-1
0
5e-06 (b)
4e-06
3e-06
first principles with the help of classical molecular dynamics based on ab initio calculations of both the intermolecular potential and the induced-dipole moment. The calculated results reproduce well the experimental values (intensity and band profile) with agreement within 3% at 149 K. Including short range overlap improves the band intensity and band profile at 149 K while it deteriorates them at 296 K when compared to results obtained with the pure asymptotic DM. The short range dipole moment contributes between 9% and 14% of the band intensity. Due to unknown uncertainties and sometimes inconsistencies in the experimental values and ab initio data, we cannot give a definitive conclusion about the final agreement between measurements and simulations and we recall for the need for more accurate experimental data. We have also examined the sensitivity of the CIA bands to the anisotropy of the intermolecular potential. This shows that the isotropic approximation used up to now leads to an underestimation of the calculated CIA absorption. The anisotropy contributes up to 18% of the band intensity which confirms the finding of previous works. Its contribution is larger at low temperatures.
2e-06
ACKNOWLEDGMENTS
The authors acknowledge the computational support of the Computer Center of the University of Burgundy (CCUB).
1e-06
0
0
50
100
200 150 -1 ω (cm )
250
300
350
FIG. 5. Collision-induced absorption spectrum (in cm−1 /amagat2 ) of N2 by N2 (a) at 149 K and (b) at 296 K, as obtained with the full ab initio intermolecular potential of Ref. 16 (continuous lines) or with its isotropic part only (dashed lines), both with the present ab initio dipole moment.
overlap contributions. Concerning the effect of the temperature which increases the relative SRID contribution, it can also be explained by the greater influence of close collisions. C. Test of the isotropic approximation
The widely used isotropic approximation1, 2 assumes that the intermolecular potential anisotropy has a negligible contribution to the CIA spectra. To the best of our knowledge, this approximation has been used in all previous calculations of the N2 CIA band shape. Its influence on the integrated intensity (but not the shape) has nevertheless been studied in Ref. 6. It was shown that the isotropic approximation underestimates the band intensity by about 10% at room temperature with errors increasing with decreasing temperature. We confirm this fact in Fig. 5 as the CIA spectral intensities are reduced by 18% at 149K and 10% at 296 K. V. CONCLUSION
In this paper, we present far-infrared CIA spectra simulations for pure gaseous N2 , conducted for the first time from
1 L.
Frommhold, Collision Induced Absorption in Gases, Cambridge Monographs on Atomic, Molecular, and Chemical Physics (Cambridge University Press, Cambridge, 2006). 2 J.-M. Hartmann, C. Boulet, and D. Robert, Collisional Effects on Molecular Spectra: Laboratory Experiments and Model, Consequences for Applications (Elsevier, Amsterdam, 2008). 3 A. Borysow and L. Frommhold, Astrophys. J. 311, 1043 (1986). 4 A. Borysow and M. Moraldi, Phys. Rev. Lett. 68, 3686 (1992). 5 M. Gruszka and A. Borysow, J. Chem. Phys. 101, 3573 (1994). 6 M. Gruszka and A. Borysow, Mol. Phys. 88, 1173 (1996). 7 M. Gruszka and A. Borysow, Mol. Phys. 93, 1007 (1998). 8 J.-M. Hartmann, C. Boulet, and D. Jacquemart, J. Chem. Phys. 134, 094316 (2011). 9 C. M. Anderson and R. E. Samuelson, Icarus 212, 762 (2011). 10 R. de Kok, P. G. J. Irwin, N. A. Teanby, C. A. Nixon, D. E. Jennings, L. Fletcher, C. Howett, S. B. Calcutt, N. E. Bowles, F. M. Flasar, and F. W. Taylor, Icarus 191, 223 (2007). 11 M. G. Tomasko, B. Bézard, L. Doose, S. Engel, E. Karkoschka, and S. Vinatier, Planet. Space Sci. 56, 648 (2008). 12 N. W. B. Stone, L. A. A. Read, A. Anderson, I. R. Dagg, and W. Smith, Can. J. Phys. 62, 338 (1984). 13 I. R. Dagg, A. Anderson, S. Yan, W. Smith, and L. A. A. Read, Can. J. Phys. 63, 625 (1985). 14 J. Boissoles, C. Boulet, R. H. Tipping, A. Brown, and Q. Ma, J. Quant. Spectrosc. Radiat. Transfer 82, 505 (2003). 15 G. Birnbaum and E. R. Cohen, Can. J. Phys. 54, 593 (1976). 16 L. Gomez, B. Bussery-Honvault, T. Cauchy, M. Bartolomei, D. Cappelletti, and F. Pirani, Chem. Phys. Lett. 445, 99 (2007). 17 S. E. Lokshtanov, B. Bussery-Honvault, and A. A. Vigasin, Mol. Phys. 106, 1227 (2008). 18 J. Boissoles, R. H. Tipping, and C. Boulet, J. Quant. Spectrosc. Radiat. Transfer 51, 615 (1994). 19 M. Bartolomei, E. Carmona-Novillo, M. I. Hernandez, J. CamposMartinez, and R. Hernandez-Lamoneda, J. Comput. Chem. 32, 279 (2011). 20 M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon Press, Oxford, 1987). 21 F. Thibault, L. Gomez, S. V. Ivanov, O. G. Buzykin, and Ch. Boulet, J. Quant. Spectrosc. Radiat. Transfer 113, 1887 (2012).
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THE JOURNAL OF CHEMICAL PHYSICS 140, 054309 (2014)
Ab initio calculations for the far infrared collision induced absorption by N2 gas Béatrice Bussery-Honvault1,a) and Jean-Michel Hartmann2 1
Laboratoire ICB, UMR 6303, CNRS-Université de Bourgogne, BP 47870 F-21078 Dijon cedex, France Laboratoire Interuniversitaire des Systèmes Atmosphériques (LISA), UMR CNRS 7583, Université Paris Est Créteil, Université Paris Diderot, Institut Pierre-Simon Laplace, 94010 Créteil cedex, France 2
(Received 19 November 2013; accepted 17 January 2014; published online 4 February 2014) We present (far-infrared) Collision Induced Absorption (CIA) spectra calculations for pure gaseous N2 made for the first time, from first-principles. They were carried out using classical molecular dynamics simulations based on ab initio predictions of both the intermolecular potential and the induced-dipole moment. These calculations reproduce satisfactory well the experimental values (intensity and band profile) with agreement within 3% at 149 K. With respect to results obtained with only the long range (asymptotic) dipole moment (DM), including the short range overlap contribution improves the band intensity and profile at 149 K, but it deteriorates them at 296 K. The results show that the relative contribution of the short range DM to the band intensity is typically around 10%. We have also examined the sensitivity of the calculated CIA to the intermolecular potential anisotropy, providing a test of the so-called isotropic approximation used up to now in all N2 CIA calculations. As all these effects interfere simultaneously with quantitatively similar influences (around 10%), it is rather difficult to assert which one could explain remaining deviations with the experimental results. Furthermore, the rather large uncertainties and sometimes inconsistencies of the available measurements forbid any definitive conclusion, stressing the need for new experiments. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4863636] I. INTRODUCTION
Collision Induced Absorption (CIA) spectra1, 2 arise when two or more molecules collide. The intermolecular forces distort the symmetry of the electronic cloud of each colliders and the system acquires a temporary dipole moment. The strength of the induced dipole depends on the mutual distance and orientation of the colliding molecules. The resulting absorption spectra appear in the far infrared when the induced dipole is modulated by the translational and rotational motions of the molecules or at shorter wavelengths when vibrational transitions are also involved. In this paper, we focus on the far infrared CIA spectra at the low density limit, where binary collisions dominate and when the absorption coefficient therefore is proportional to the gas-density squared. Various theoretical methods with differing precisions exist nowadays for the computation of CIA spectra, which are reviewed in Refs. 1 and 2. Each has its advantages and limitations. In general, the methods can be divided into classical and quantum mechanical treatments. The most rigorous technique is a close coupling method which fully takes into account the anisotropy of the intermolecular potential but it is extremely computer-time consuming. Speed limitations of present computers make these computations possible only for very small and light molecules (H2 ) and/or at very low temperatures. For heavier or more complex molecules (such as N2 3 ) and/or higher temperatures (e.g., room temperature), it is nevertheless possible to carry quantum mechanical a) Author to whom correspondence should be addressed. Electronic mail:
[email protected]
0021-9606/2014/140(5)/054309/6/$30.00
calculations using the approximation that the translation is governed by the isotropic intermolecular potential. While this so-called “isotropic approximation” is totally inadequate for the CIA of CO2 pairs,4, 5 it leads to the underestimation of the pure N2 CIA band integrated intensity by about 10%.6 However, its consequences on the spectral shape of pure N2 CIA remain unknown. An interesting alternative is brought by classical molecular dynamics simulations (CMDS). Indeed, these are tractable for heavy or complex molecular systems, even when the potential anisotropy is taken into account. The available results, obtained for CO2 ,7, 8 show that CMDS is a powerful method. With a concentration of roughly 97%, nitrogen is the most abundant species in the atmosphere of Titan and the collision-induced dipole spectrum of N2 -N2 pairs contributes substantially to the atmospheric absorption below 200 cm−1 . As a result, precise knowledge of N2 CIA is required for optical remote sensing studies (e.g., Refs. 9 and 10) as well as for studies of the heat balance11 of the atmosphere of Titan. Despite these important applications in planetary science, relatively few experimental and theoretical studies of the far infrared pure N2 CIA have been made. To the best of our knowledge, the most recent laboratory measurements were made about 30 years ago.12, 13 They cover a broad temperature range but have significant uncertainties and provide limited information on the CIA wing. From the theoretical side, quantum mechanical calculations were made in Ref. 3, while, in Ref. 14 and those cited therein, empirical line shapes15 were used. These attempts present severe limitations since: (i) they use the isotropic approximation and thus disregard
140, 054309-1
© 2014 AIP Publishing LLC
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054309-2
B. Bussery-Honvault and J.-M. Hartmann
J. Chem. Phys. 140, 054309 (2014)
the influence of the intermolecular potential anisotropy on the translational and rotational dynamics. (ii) They rely on the adjustment of some parameters (the short range induced dipole in Ref. 3, the line shape in Ref. 14) on measured spectra. On the opposite, in this paper, we present the first calculations conducted using an anisotropic intermolecular potential and an induced dipole, both ab initio predicted, and thus free of any adjusted parameter. For this, CMDS have been carried out, as in Ref. 8, using the anisotropic N2 -N2 intermolecular potential of Ref. 16 or its purely isotropic component. These simulations provide the positions and orientations of all of the many molecules treated at each time step. From these, the interaction induced dipole is calculated, based on an accurate fit of the ab initio values of Ref. 17 or on some long range asymptotic developments. The time autocorrelation of this dipole vector is then obtained whose Fourier-Laplace transform yields the spectrum. Such calculations enable to a test of the influence of the isotropic approximation as well as a quantification of the contribution of the short range induced dipole. The induced dipole fitting procedure is described in Sec. II while the way CMDS are carried out is the subject of Sec. III. Comparisons between measured and predicted CIA in the (far infrared) roto-translational band of pure N2 at various temperatures are then presented in Sec. IV where the influences of the short range DM and of the intermolecular potential anisotropy are also discussed. A conclusion is given at the end of this paper.
the dimer after taking into account the symmetry (see Fig. 1 of Ref. 17 for the definitions of the θ and φ angles). It is compared here with the asymptotic long-range cartesian components (μx , μy , μz ), calculated using Eqs. (1), (2) and (A1)– (A15) of Ref. 8. For these calculations, the values of the static polarisability components (α // , α ⊥ ), of the quadrupole () and hexadecapole () moments were taken from Ref. 18, i.e., α // = 14.91, α ⊥ = 10.16, = −1.052, and = −7.5, all in atomic units. Note that the values of α // and α ⊥ lead to an isotropic polarisability α of 11.74 a.u. and an anisotropic polarisability γ of 4.75 a.u. From Table 4 of Ref. 19, we can see that experimental values are dispersed around −1.09 a.u. for (= Q20 ), around −7.97 a.u. for (= Q40 ), around 14.98 a.u. 1,1 1,1 for α// (= α0,0 ) and around 10.304 a.u. for α⊥ (= α±1,±1 ), so that, the presently used values are in good agreement with these averaged experimental quantities. The ab initio and asymptotic dipole moments are presented in Fig. 1, as functions of the intermolecular distance R, for selected values of θ 1 , θ 2 , and φ 2 . A good agreement between asymptotic and ab initio dipole moments is observed at large intermolecular distances (typically further than 7 bohr) that proves the accuracy of the ab initio calculations in this region. Deviations from the asymptotic behavior occur at shorter range, increasing with decreasing distances, which result from the short range contribution to the DM, not included in the asymptotic one. Note that, in some cases, changes in the sign of the dipole moment appear at small distances. B. Spherical expansion of the dipole moment
II. THE AB INITIO DIPOLE MOMENT
In order to include the ab initio dipole moment into the collision-induced spectra calculations, it is convenient to represent it through Eq. (2) of Ref. 8. Such an expansion of the induced dipole presents the advantage to offer some physical understanding of the various contributions, separated into radial and angular factors. Several previous
A. Ab initio versus asymptotic dipole moments
The ab initio dipole moment of N2 -N2 was calculated in Ref. 17, for four intermolecular distances between 5 and 11 bohrs, with θ a , θ b = 0◦ , 30◦ , 60◦ , 90◦ and φ = 0◦ , 45◦ , 90◦ , 135◦ , 180◦ , resulting in 42 angular arrangements of X
Y
01 0
φ2=45
0
04
-0. 8
10
0.03 φ2=90
0.02
0
06
6
8
10
φ2=90
0
8
10
0
6
1
0 -0.
0.04
10
φ2=135
0.02 6
8
10
-
03
-0.
θ1=30
0
θ2=30
8
0.0
10 θ2=90
0
8 θ1=90
0
10 θ2=30
φ2=90
0
0
0
6
.04
0
φ2=135
2 0.0
0
φ2=45
0
8
8 θ1=60
1
-0.
6
6
0.0
0.06
0
2
0.0
04
0.01
0
-0.
02 -0.
0
φ2=0
-0.
3 6
-0. 0
N2-N2 Dipole Moment (a.u.)
0.01
0
02
-0.
-0.
φ2=45
02
0.02
0 0.04
Z 0
0
0.03
0
0
0
6 8 10 Intermolecular distance (Bohr)
0
6
8
10
FIG. 1. Ab initio (circles) and asymptotic (dashed lines) dipole moment (in a.u.) of N2 -N2 as a function of the intermolecular distance (in Bohr) for various geometric arrangements. When not stated, θ 1 = 30◦ and θ 2 = 60◦ (see Fig. 1 of Ref. 17 for the definitions of the θ and φ angles).
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054309-3
B. Bussery-Honvault and J.-M. Hartmann
J. Chem. Phys. 140, 054309 (2014)
works3, 6 have discussed the contributions and the physical significations of the various terms so that we will not discuss that point here again. A straightforward adaptation of the dipole moment of Eq. (2) of Ref. 8, written in the space-fixed coordinate system, to the dimer-fixed coordinate system, is obtained by fixing φ 1 = θ = φ = 0 in the equation. The radial coefficients, Al1 ,l2 ,,l (R12 ), are obtained by solving, for each intermolecular distance, a set of linear equations associated with the geometries of the dimer used in the ab initio calculations. This set includes 3Ng (with Ng = 42 geometric arrangements) equations, each involving Nt unknown (the Al1 ,l2 ,,l (R12 )) radial terms, associated with the various angular terms. The factor 3 arises because we consider the three cartesian components of the dipole moment simultaneously. Following various tests, we have retained an optimized set of Nt = 28 (l1 , l2 , , l) components, restrained by the conditions: l1 ≤ 10, l2 ≥ l1 with Al2 ,l1 ,,l = Al1 ,l2 ,,l if is even and Al2 ,l1 ,,l = −Al1 ,l2 ,,l if is odd, ≤ 7 with odd for l1 = l2 terms and even for l1 = l2 terms. The associated radial coefficients, Al1 ,l2 ,,l (R) for each of the four calculated intermolecular distances have been obtained for all the 28 sets of (l1 , l2 , , l). With these values, we obtained root mean square (rms) deviations between the adjusted and ab initio values of the dipole moment of 2.7 × 10−3 a.u. for the x component, 2.3 × 10−3 a.u. for the y component, and 2 × 10−4 a.u. for the z component at R = 5 bohr. These deviations are typically one order of magnitude smaller than the values of the DM components (see Fig. 1). C. Analytical fit of the short range radial functions
In order to get an analytical representation of the dipole moment suitable for spectra calculations through CMDS, we have fitted the radial coefficients by analytical expressions optimized for each (l1 , l2 , , l) set. For this, we first subtract the asymp known asymptotic behavior from the values of Al1 ,l2 ,,l (R), in order to get short-range (SR) coefficients such that: asymp
ASR l1 ,l2 ,,l (R) = Al1 ,l2 ,,l (R) − Al1 ,l2 ,,l (R),
(1)
asymp
where Al1 ,l2 ,,l (R) is computed as explained before, neglecting the contributions given by Eqs. (A4)–(A6) of Ref. 8 due to missing data. Various analytical expressions have been employed for best fits, i.e., ASR 1 (R) = a exp(−bR) + c exp(−dR), ASR 2 (R) = a exp(−cR) +
b , Rd
b exp(−cR − dR 2 ), (R) = a + (2) ASR 3 R b exp(−dR), ASR (R) = a + 4 Rc b exp(−c(R − d)). ASR (R) = a + 5 R The a, b, c, and d coefficients are given in Table I for distances in bohr and radial functions A(R) in a.u., together with the indices of the expression used [i.e., from 1 to 5 following Eq. (2)], in the last column of the table.
D. Quality of the global fit of the dipole moment
With the values of Table I, Eqs. (1) and (2) of Ref. 8 and the molecular parameters given in Sec. II A for the asymptotic contributions, the DM can now be generated for any conformation of the molecular pair. We can check its quality by comparing it with the input ab initio DM value. This exercise leads to root mean square errors of 10.8 × 10−5 a.u. for the x component, 6.8 × 10−5 a.u. for the y component, and 21.1 × 10−5 a.u. for the z component, which is quite satisfactory in regards of the ab initio DM values (Fig. 1) and their precision. III. CLASSICAL MOLECULAR DYNAMICS SIMULATIONS
CMDS have been carried out exactly as previously done for the pure CO2 CIA,8 for which very satisfactory results have been obtained. 288 sets of 20 000 N2 molecules inside cubic boxes with periodic boundary conditions20 have been treated in parallel. First, proper initialisation (random orientations and Boltzmann statistics for energies) is made for the translational and rotational parameters of the molecules. Then, the time evolutions of the center of mass position and velocity as well as of the molecular axis orientation and of the rotational angular momentum of each molecule are calculated step by step using an intermolecular potential as input. From the (relative) positions and orientations of the molecules, the interaction-induced dipole is then computed. Having stored this dipole vector at time zero, its auto-correlation function (ACF) can be obtained at each time. Then, as in Ref. 8, the Fourier-Laplace transform of this ACF directly yields the spectrum. For the calculations, the anisotropic intermolecular potential described in Refs. 16 has been used. Averaging this potential over all molecular orientations provides the isotropic component for a test of the widely used isotropic approximation on the CIA spectra. For the interaction-induced dipole, two calculations were also made. In the first, the full dipole is used, including both the long range asymptotic dipoles and the short distance terms described in Sec. II. In the second, only the long range components are taken into account. IV. RESULTS A. Experimental versus calculated collision-induced absorption spectra
Figure 2 presents comparisons of experimental results at various temperatures with predictions obtained with the ab initio N2 -N2 anisotropic potential of Ref. 16 and full dipole moment of Sec. II. As can be seen, the agreement is very satisfactory at 149 K but deteriorates (moderately) with increasing temperature. Indeed, the ab initio CIA spectrum overestimates the experimental peak values by 3% at 149 K, 5% at 228 K, and 11% at 296 K. Nevertheless, one should be cautious in definitive conclusion about the model quality from such results for two reasons: first, because, as already mentioned, the experimental data are tainted of uncertainties of typically 10% or more, as shown in Refs. 3 and 6 where various measurements are compared. Second, because input data
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054309-4
B. Bussery-Honvault and J.-M. Hartmann
J. Chem. Phys. 140, 054309 (2014)
TABLE I. Numerical values of the a, b, c, and d coefficients of the analytical radial functions (see Relations (2)) whose expression number is given in the last column. (l1 , l2 , , l) (2021) (2023) (2211) (2233) (4043) (4045) (4221) (4223) (4243) (4245) (4265) (4267) (4411) (4433) (4455) (4477) (6065) (6067) (6243) (6245) (6265) (6267) (6421) (6423) (6443) (6445) (6465) (6467)
a
b
c
d
N◦
0.18832437 − 2.50142847 − 1.61490065 − 2.99460545 − 0.83306643 − 141.64218797 − 0.08051585 − 21.00000000 − 69.99989585 47.15217189 571.15008359 − 210.99997920 − 3.57511979 − 1.38906391 5.48949315 − 2.38671320 0.00000002 − 2.32539535 1391.39686204 − 2.39613048 − 91.15987451 1175.05951604 1263.28178232 − 209.99965065 − 79.08944016 8596.82185691 6.72995727 − 209.99958391
− 1.42358996 13.21490525 8.89655956 0.00156483 9.19937445 − 0.02023686 7.67472780 − 0.02000000 − 0.02000000 0.01505213 0.27296950 − 0.02000000 0.00188879 0.00634065 0.10809706 9.10225749 1.00000000 9.15333577 55.87867034 9.12546170 0.00014934 3.54333579 2.99961994 − 0.02000000 0.00104647 157.69016961 0.00051409 − 0.02000000
0.25442614 0.93859007 2.11325460 1.99391664 1.58280645 8.39999662 2.03633265 2.20000000 8.40000000 1.87218790 1.99960252 8.40000000 2.11868380 1.50414756 1.78491363 2.86920632 0.00000002 2.59341823 2.41961282 2.72572068 2.06611153 2.53181425 2.69045621 8.00000000 2.20407844 3.08337869 2.0238256 8.00000000
0.03658907 0.00154809 2.68576430 0.70000000 2.73208244 1.85684522 0.96148340 11.0000000 1.89666485 2.44096603 3.43464339 1.82209539 2.20010917 2.54201951 4.29630926 3.34693218 1.00000000 3.60319165 6.96222480 3.52768862 0.80436446 5.74710873 6.29915695 2.26854414 1.81603196 7.92622703 1.61674424 2.33874232
3 3 5 2 5 4 4 2 4 2 2 4 2 2 2 5 1 5 2 5 2 2 2 4 2 2 2 4
of the CMDS (i.e., dipole moment and intermolecular potential), though obtained through ab initio calculations, are not exact values and uncertainties are also attached to these quantities. Increasing the induced dipole moment by 5% increases the CIA by 10%. Furthermore, as well known,6, 8 the results are sensitive to the intermolecular potential. However, the quality of the presently used ab initio potential16 has previously been confirmed by the calculations of line-broadening coefficients21 down to low temperature range, and those of total integral scattering cross-sections16 (test of the well depth, of the repulsive wall and of the asymptotic part of the potential). From the confrontation between calculated and experimental results,16, 21 it has been concluded that the present potential is of good quality, though the isotropic part may be slightly overestimated. From the above given uncertainty estimations, it is clear that calculated and measured CIA spectra both fall well within error bars, as presented in Fig. 2. Following the work of Gruszka and Borysow,6 an analysis in terms of spectral moments has been conducted through the evaluation of γ 1 and α 1 , defined as ∞ α(ω) ¯ dω (3) γ1 = 2kT 0 ω tanh(¯ω/2kT ) and α1 =
1 n2
∞
α(ω)dω, 0
(4)
where α(ω) is the squared-density normalized CIA coefficient (as plotted in Fig. 2). These two spectral moments are plotted in Fig. 3 and compared with the experimental values of Refs. 12 and 13. As can be seen, the agreement between experimental and calculated values of γ 1 is excellent while the calculated predictions of α 1 overestimate the experimental ones by 10% or slightly more. This discrepancy may be partly explained by the fact that α 1 is much more sensitive to the area of the CIA wing where the absorption is weak and not at all or poorly determined experimentally. B. Influence of the short range induced dipole
In order to quantify the influence of the short range induced dipole (SRID) on the CIA spectra, we compare in Fig. 4 CIA spectra calculated with the full dipole with results obtained by taking into account only the asymptotic long range one. To our knowledge, this is the first paper offering an ab initio quantification of such effects as the previous tentatives have proposed fitting procedure to estimate them. From Fig. 4, we note that, for both temperatures presented here (i.e., 149 and 296K), the SRID contributions are about 10%-14% greater than the pure asymptotic which contribute for about 90% of the peak absorption at both temperatures. Detailed analysis shows that the relative contribution of the SRID is larger at high temperature and in the far wing of the band. In this region, it results in an increase of the CIA by a
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054309-5
B. Bussery-Honvault and J.-M. Hartmann
J. Chem. Phys. 140, 054309 (2014)
8e-06
8e-06 (a)
6e-06
(a) 6e-06
4e-06 2e-06
4e-06 0
100
50
150
200
300
250
350
6e-06 5e-06
2e-06
(b)
4e-06
2
3e-06 2e-06
0
0
50
100
150
200
250
300
350
300
350
-1
1e-06 0
CIA coefficient (cm /amagat )
-1
2
CIA coefficient (cm /amagat )
0
0
100
50
150
200
300
250
350
5e-06 4e-06
(c)
3e-06 2e-06
5e-06 (b)
4e-06
3e-06
1e-06 0
350
2e-06
FIG. 2. Collision-induced absorption spectrum (in cm−1 /amagat2 ) of N2 by N2 (a) at 149 K, (b) at 228 K, and (c) at 296 K, as obtained from measurements12, 13 (circles) and from the CMDS calculations using the present ab initio dipole moment and the intermolecular potential of Ref. 16 (continuous lines). The error bars correspond to ± 10%.
1e-06
0
100
50
200 150 -1 ω (cm )
300
250
factor of more than 2 beyond 300 cm−1 . This can be explained by the fact that large frequency detunings (in the spectrum) correspond to short times (in the dipole ACF) which involve close distance collisions, and then a greater influence of the
0
0
50
100
200 150 -1 ω (cm )
250
FIG. 4. Collision-induced absorption spectrum (in cm−1 /amagat2 ) of N2 by N2 (a) at 149 K and (b) at 296 K, as obtained by present ab initio dipole moment (continuous lines) or by the asymptotic dipole moment only (dashed lines), both with the ab initio intermolecular potential of Ref. 16.
18 cm s)
16 5
14
γ1 (10
-58
12 10 8 6
α1 (10
-31
5
cm /s)
4 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1
150
200
150
200
250
250 Temperatue (K)
300
350
300
350
FIG. 3. Comparison between experimental and computed spectral moments of N2 pairs. Experimental data are from Ref. 13 (full circles) or Ref. 12 (open circles). Indicative error bars of ±10% have been added to the measured values. Computed values (continuous lines) have been evaluated with the present ab initio dipole moment and the ab initio intermolecular potential of Ref. 16.
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054309-6
B. Bussery-Honvault and J.-M. Hartmann
J. Chem. Phys. 140, 054309 (2014)
8e-06
(a) 6e-06
4e-06
2
CIA coefficient (cm /amagat )
2e-06
0
50
100
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300
250
350
-1
0
5e-06 (b)
4e-06
3e-06
first principles with the help of classical molecular dynamics based on ab initio calculations of both the intermolecular potential and the induced-dipole moment. The calculated results reproduce well the experimental values (intensity and band profile) with agreement within 3% at 149 K. Including short range overlap improves the band intensity and band profile at 149 K while it deteriorates them at 296 K when compared to results obtained with the pure asymptotic DM. The short range dipole moment contributes between 9% and 14% of the band intensity. Due to unknown uncertainties and sometimes inconsistencies in the experimental values and ab initio data, we cannot give a definitive conclusion about the final agreement between measurements and simulations and we recall for the need for more accurate experimental data. We have also examined the sensitivity of the CIA bands to the anisotropy of the intermolecular potential. This shows that the isotropic approximation used up to now leads to an underestimation of the calculated CIA absorption. The anisotropy contributes up to 18% of the band intensity which confirms the finding of previous works. Its contribution is larger at low temperatures.
2e-06
ACKNOWLEDGMENTS
The authors acknowledge the computational support of the Computer Center of the University of Burgundy (CCUB).
1e-06
0
0
50
100
200 150 -1 ω (cm )
250
300
350
FIG. 5. Collision-induced absorption spectrum (in cm−1 /amagat2 ) of N2 by N2 (a) at 149 K and (b) at 296 K, as obtained with the full ab initio intermolecular potential of Ref. 16 (continuous lines) or with its isotropic part only (dashed lines), both with the present ab initio dipole moment.
overlap contributions. Concerning the effect of the temperature which increases the relative SRID contribution, it can also be explained by the greater influence of close collisions. C. Test of the isotropic approximation
The widely used isotropic approximation1, 2 assumes that the intermolecular potential anisotropy has a negligible contribution to the CIA spectra. To the best of our knowledge, this approximation has been used in all previous calculations of the N2 CIA band shape. Its influence on the integrated intensity (but not the shape) has nevertheless been studied in Ref. 6. It was shown that the isotropic approximation underestimates the band intensity by about 10% at room temperature with errors increasing with decreasing temperature. We confirm this fact in Fig. 5 as the CIA spectral intensities are reduced by 18% at 149K and 10% at 296 K. V. CONCLUSION
In this paper, we present far-infrared CIA spectra simulations for pure gaseous N2 , conducted for the first time from
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