[6]. Experimental results observed in situ mass spectrometry show the existence of
atmospheric negative ion NO
−
3 HNO 3
ð
Þ 2 in the upper troposphere (altitude between
9 and 12 km) [7, 8]. This negative ion is also known as a dominant negative ion at
the upper troposphere region [7].
Recently, Sekimoto and Takayama established the atmospheric pressure corona
discharge ionization (APCDI) technique, which enables us to reproducibly generate
negative ions [9]. They reported the existence of stable negative ion water clusters,
NO
−
3 HNO 3
ð
Þ 2 H 2 O
ð
Þ n , and the specific stability referred to as a magic number for
n = 8 [10]. Geometric structures of these water clusters are, however, still unclear
even for the core ion and its monohydrate (n = 1).
From theoretical points of view, Drenck and coworkers reported stable structures
of NO
−
3 HNO 3
ð
Þ 2 H 2 O
ð
Þ n (n = 0–4) obtained at B3LYP/6-31++G** level of
density functional theory (DFT) calculations [1]. They also reported the stable
structures of NO
−
3 HNO 3
ð
Þ m H 2 O
ð
Þ n up to n + m = 6, and assessed the validity of
theoretical calculations by comparing theoretical dissociation energies of the
NO
−
3 HNO 3
ð
Þ m H 2 O
ð
Þ n cluster into NO
−
3 , mHNO 3 , and nH 2 O fragments to the
experimental results with mass-analyzed ion kinetic energy (MIKE) spectra measurement [11]. Their theoretical results agree with the experiments reasonably, but
assumed only one kind of geometry for each NO
−
3 HNO 3
ð
Þ m H 2 O
ð
Þ n clusters despite
that a water cluster should generally have various kinds of conformers. In order to
elucidate the stable geometries of NO
−
3 HNO 3
ð
Þ 2 and its hydrates, a more comprehensive geometry searching with first-principles calculations must be
indispensable.
In this study, to elucidate stable geometries of these ionic clusters in details, we
theoretically analyzed stable geometries of the negative core ion NO
−
3 HNO 3
ð
Þ 2 and
its monohydrate in consideration of a lot of possible conformers with the post
Hartree-Fock ab initio method. We also discussed the relative abundance of conformers of these ionic clusters under a finite temperature.
2 Computational Details
We employed the second order Møller-Plesset perturbation theory (MP2) with 6-31
++G** Gaussian type basis sets in ab initio calculations of the negative core ion,
and its monohydrate. The basis set superposition error (BSSE) is not corrected
because of the less convergence in BSSE corrected geometrical optimization procedure. The harmonic approximation was used to evaluate the zero-point vibration
energy (ZPE) and Gibbs free energy. Natural Population Analysis (NPA) [12] was
used to analyze electronic populations on each atom. All calculations were performed with GAUSSIAN 09 program package [13].
In the comformational searching, we picked up the initial geometries to be a
molecular cluster consisting of one NO
−
3 , two HNO 3 ’s, and one H 2 O fragments,
and optimized all the geometric degrees of freedom of the cluster simultaneously.
194
A. Ueda et al.
atmospheric negative ion NO
−
3 HNO 3
ð
Þ 2 in the upper troposphere (altitude between
9 and 12 km) [7, 8]. This negative ion is also known as a dominant negative ion at
the upper troposphere region [7].
Recently, Sekimoto and Takayama established the atmospheric pressure corona
discharge ionization (APCDI) technique, which enables us to reproducibly generate
negative ions [9]. They reported the existence of stable negative ion water clusters,
NO
−
3 HNO 3
ð
Þ 2 H 2 O
ð
Þ n , and the specific stability referred to as a magic number for
n = 8 [10]. Geometric structures of these water clusters are, however, still unclear
even for the core ion and its monohydrate (n = 1).
From theoretical points of view, Drenck and coworkers reported stable structures
of NO
−
3 HNO 3
ð
Þ 2 H 2 O
ð
Þ n (n = 0–4) obtained at B3LYP/6-31++G** level of
density functional theory (DFT) calculations [1]. They also reported the stable
structures of NO
−
3 HNO 3
ð
Þ m H 2 O
ð
Þ n up to n + m = 6, and assessed the validity of
theoretical calculations by comparing theoretical dissociation energies of the
NO
−
3 HNO 3
ð
Þ m H 2 O
ð
Þ n cluster into NO
−
3 , mHNO 3 , and nH 2 O fragments to the
experimental results with mass-analyzed ion kinetic energy (MIKE) spectra measurement [11]. Their theoretical results agree with the experiments reasonably, but
assumed only one kind of geometry for each NO
−
3 HNO 3
ð
Þ m H 2 O
ð
Þ n clusters despite
that a water cluster should generally have various kinds of conformers. In order to
elucidate the stable geometries of NO
−
3 HNO 3
ð
Þ 2 and its hydrates, a more comprehensive geometry searching with first-principles calculations must be
indispensable.
In this study, to elucidate stable geometries of these ionic clusters in details, we
theoretically analyzed stable geometries of the negative core ion NO
−
3 HNO 3
ð
Þ 2 and
its monohydrate in consideration of a lot of possible conformers with the post
Hartree-Fock ab initio method. We also discussed the relative abundance of conformers of these ionic clusters under a finite temperature.
2 Computational Details
We employed the second order Møller-Plesset perturbation theory (MP2) with 6-31
++G** Gaussian type basis sets in ab initio calculations of the negative core ion,
and its monohydrate. The basis set superposition error (BSSE) is not corrected
because of the less convergence in BSSE corrected geometrical optimization procedure. The harmonic approximation was used to evaluate the zero-point vibration
energy (ZPE) and Gibbs free energy. Natural Population Analysis (NPA) [12] was
used to analyze electronic populations on each atom. All calculations were performed with GAUSSIAN 09 program package [13].
In the comformational searching, we picked up the initial geometries to be a
molecular cluster consisting of one NO
−
3 , two HNO 3 ’s, and one H 2 O fragments,
and optimized all the geometric degrees of freedom of the cluster simultaneously.
194
A. Ueda et al.