BROADENING PRESSURE PARAMETERS FOR NITRIC ACID IN THE
5
BAND
Anne Laraia and Robert Gamache
Abstract: A number of satellite instruments are measuring nitric acid, HNO3, in the Earths atmosphere. In order to do retrievals of temperature and concentration profiles, the spectral parameters for many thousands of HNO3 transitions must be known. Currently the pressure-broadened half-width is estimated on the HITRAN database. To help ameliorate this situation, complex Robert-Bonamy calculations were made to determine N2-broadened half-widths and line shifts for some 5000 transitions of HNO3 in the 5 band. The intermolecular potential is a sum of electrostatic terms (dipole-quadrupole and quadrupole-quadrupole), isotropic induction and London dispersion terms, and the atom-atom potential expanded to eighth order. The trajectory parameters were adjusted to yield better agreement with measurement. Velocity integrated calculations were made at seven temperatures in order to determine the temperature dependence of the half-widths. The data are compared with measurements of Goyette et al. (J. Quant. Spectrosc. Radiat. Transfer 60, 77,1998). The average percent difference between the measured and calculated half-widths is -0.31. The temperature, vibrational, and rotational state dependence of the half-width are investigated.
Preliminary Calculations
In the parabolic trajectory approximation the isotropic part of the interaction potential is taken into account in determining the distance, effective velocity, and force at closest approach . To simplify the trajectory calculations the isotropic part of the atom-atom expansion is fit to an isotropic Lennard-Jones 6-12 potential. In order to improve agreement with measurement the isotropic Lennard-Jones parameters were adjusted so the calculations would better agree with eight transitions measurements by Goyette et al. (J. Quant. Spectros. Radiat. Transfer 60 (1998) 77-84). Results for adjusting the trajectory parameters. Initial parameters: Final parameters: =369.99 =165.0
Exp Transition 16 0 16 14 2 12 13 3 10 12 5 8 11 6 6 24 8 16 25 9 16 26 10 16 * 300 K 15 0 15 13 2 11 12 3 9 * 11 5 7 10 6 5 24 8 17 25 9 17 * 26 10 17 * 0.11966 0.12676 0.13385 0.12650 0.13335 0.11053 0.11915 0.11433
HNO3-N2 half-widths in units of cm-1 atm-1 versus J"+0.1(J"-Ka")
Complex Robert-Bonamy Theory
The model chosen is the semiclassical complex formalism of Robert and Bonamy (CRB) for several reasons. 1) The formalism is complex valued, yielding halfwidths and line shifts from a single calculation. 2) The cumulant expansion incorporated in the RB formalism allows for the inclusion of higher order terms in the S matrix, eliminating an awkward cutoff procedure that characterized earlier theories. 3) The intermolecular dynamics are treated more realistically than in earlier theories, i.e. using curved rather than straight line trajectories. 4) Connected to item (3) is the incorporation in the CRB theory of a short range (Lennard-Jones 6-12) atom-atom component to the intermolecular potential. This component has been shown to be essential for a proper description of pressure broadening.
=3.178 =3.117
calinitial 0.13299 0.13493 0.13346 0.13564 0.13556 0.12590 0.12394 0.12368 calfinal 0.12641 0.12832 0.12697 0.12899 0.12885 0.11702 0.11479 0.11427
Half-width and Line Shift in CRB theory
In computational form the half-width and line shift are usually expressed in terms of the Liouville scattering matrix
HNO3-N2 half-widths in units of cm-1 atm-1 versus Ka"+0.1(J"-Ka")
(
i
)
=
n2 2 c
v 1 e
[
R
S 2 ( f , i, J2 , v, b )
e
i IS 2 ( f , i, J2 , v, b )
]
v, J
Calculations
A b, list of 15 609 5 transitions in the 841.5-930.9 cm-1 region was provided by the Laboratoire Interuniversitaire des Systemes Atmospheriques (LISA) in Paris. From this list we extracted transitions with line intensities greater than 5 x 10-22 cm-1/(moleculecm-2) and J 45. This yields a list of 5011 transitions. Due to limitations in the wavefunction codes calculations could only be made for 4979 of these transitions.
Temperature exponents of HNO3 -N2 half-widths versus J"+0.1(J"-Ka")
where n2 is the number density of perturbers and b,v,J represents an average over all trajectories (impact parameter b and initial relative velocity v) and initial rotational state J2 of the collision partner.
Spherical Tensor Expansion of the Potential
V=
w, q l 1l 2 n1 m1m2 l m
U (l 1l 2 l, n1wq ) R q + l1 + l 2 + 2 w
C (l 1l 2 l, m1m2 m )D l11n1 ( m
1
)D lm 0 ( 2 )Ylm ( )
2 2
where C(l1 l 2 l; m1 m2 m) is a Clebsch-Gordan coefficient, 1 =( 1 , 1, 1 ) and 2=( 2 , 2 , 2) are the Euler angles describing the molecular fixed axis relative to the space fixed axis. = ( , ) describes the relative orientation of the centers of mass. Electrostatic interactions: q=1 and w=0 Atom-atom interactions: q=12 or 6 and w defined by the order of the expansion where Order=l1 +l2+2w
parameter
* *
min 0.0924 -0.0017 0.751
max* 0.1316 0.00086 0.935
Wavefunctions
The wavefunctions used to evaluate the reduced matrix elements are obtained by diagonalizing the Watson Hamiltonian in a symmetric top basis. The wavefunctions for the ground vibrational state are determined using the WatsonHamiltonian constants of Goldman et al. (J. Mol. Spectrosc. 131 (1988) 195200) and those for the 5 vibrational state use the Watson constants of Maki and Wells (J. Mol. Spectrosc. 152 (1992) 69-79). The molecular constants for N2 are from Huber and Herzberg (Molecular Spectra and Molecular Structure: Constants of Diatomic Molecules. Van Nostrand, New York 1979)
n
Minimum and maximum values of the half-width, line shift, and temperature dependence of the half-width (temperature exponent) for N2-broadening of HNO3.
Temperature exponents of HNO3 -N2 half-widths versus Ka"+0.1(J"...