Formation of HF through radiative association in the early universe

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Abstract

Rate constants for the formation of HF through radiative association have been calculated from potential energy surfaces and dipole moments determined by accurate quantum chemistry calculations. This rate constant is about 10−20–10−19 cm3 s−1 depending of temperature, of the same order of magnitude than rate constants calculated for other hydride molecules (LiH, BeH).

Graphical abstract

Rate constants for the formation of HF through radiative association have been calculated from potential energy surfaces and dipole moments determined by accurate quantum chemistry calculations. As far as no low-lying excited electronic states could be accessible, only transitions to the rovibrational levels of the ground state have to be considered. The cross-sections, averaged over all values of the collision energy and impact parameter, are determined in a semi-classical scheme from the transition probability for spontaneous emission.

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Introduction

Although hydrogen fluoride, is known in the interstellar medium since 1997 [1], it is only recently that a systematic theoretical study of the chemistry of the interstellar fluorine-bearing molecules has been undertaken [2], after quantal calculations of the rate coefficient for the F + H2  H + HF reaction [3] have suggested that HF abundances could be large in various environments of the interstellar medium.

The fluorine chemistry is also of interest for the cosmological community. Indeed, some models of the big bang nucleo synthesis have suggested that in the early universe, fluorine could have been formed with the consequence that hydrogen fluorine could have already existed in the early stages of the universe. In the astrochemical model used to describe the early universe fluorine chemistry [4], two reactions for the formation of HF are considered: the F + H2  H + HF process, which reaction rate is known [3], [5] and the F + H  HF +  radiative association process for which a reaction rate has been deduced from the HF photodissociation cross-section using the principle of detailed balance [4]. The possible importance of this reaction for the HF abundances at these early stages of the universe has motivated the present study for the calculation of a more accurate rate constant for the F + H  HF +  reaction, a work that we have undertaken using highly accurate electronic calculations.

Section snippets

Einstein coefficients and rate constants

The only known bound electronic state of HF is the X1Σ+ ground state correlating to the lowest energy asymptote F(2P) + H(2S). There are three other states correlating to the same asymptote, i.e., the 1Π, 3Π and 3Σ+ states but all of them are repulsive in nature [6]. Since in the present study we are mainly interested on the formation of HF at low temperature (below 1000–2000 K) we do not expect the 1Π state of HF to have a significant role in the formation of HF from the F(2P) and H(2S)

Conclusions

Using accurate electronic ab initio calculations for the HF molecule, we have calculated the rate constant for the formation of HF through the radiative association of F(2P) and H(2S). This reaction rate is of the order of 10−20–10−19 cm3 s−1, in agreement with previous calculations on the formation of hydride molecules (LiH, BeH) [8], [22], [23] through the same mechanism. This value is low as expected for the formation of a diatomic molecule through a radiative association mechanism, which does

Acknowledgements

Prof. Robert J. Le Roy is gratefully acknowledged for providing us with his Computer program and Dr. Amanda Ross for very fruitful discussions. The National French Program PCMI and the computing facilities of IDRIS are acknowledged for support.

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