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Possible configurations of clusters of H3 and H2
and their energies  L. Ziemczonek1, T.
Wróblewski1 and G. P. Karwasz1,2  1 Institute of
Physics, Pedagogical University of Slupsk,
Arciszewskiego 22 B, 76-200 Slupsk, Poland 2
Institut für Chemie Physikalische und
Theoretische Chemie, Freie Universität Berlin,
14195 Berlin, Germany
Configurations of the H3(H2)n clusters for n1
up to n12 are presented. Total energies with
zero point vibration corrections and
stabilization energies (the differences between
the energy of the cluster and the energy of the
individual molecules) are given. Calculations
have been performed with ab initio method using
6-311G molecular basis set. This basis set
includes diffuse and polarization functions. The
advantage of using Gaussian 6-311 molecular basis
set is that calculations are relatively fast if
compared to more extended basis sets, so numerous
configurations can be easily optimized, but the
precision of calculations, in terms of
dissociation energies of cluster, is still high
9. The H3(H2)n clusters can be considered as
a structure with a core of H3 and two shells of
H2 molecules. The most stable structure for the
bigger n is with three molecules on the first
shell and nine molecules on the second one.
Influence of increasing of size of clusters on
changing of IR spectrum is also discussed
especially for ?1 and ?2 frequencies.
H3(H2)1-2
The triatomic hydrogen ion H3 is the simplest
of all polyatomic molecules 1. It consists of
three protons and two electrons only. In its
ground state it is forming an equilateral
triangle. It was discovered in a rudimentary mass
spectrum in 1911 by J. J. Thompson 2. Its
electronic structure, rovibrational dynamics and
spectroscopic properties have been the subject of
theoretical and experimental studies 3. The H3
ion has high symmetry so it offers many dynamical
phenomena in its internal excitation modes and
its collisional processes especially with
low-energy electrons, see in 4 and 5. Also
the molecular ion H3 is considered the
cornerstone of interstellar chemistry because it
initiates the reaction responsible for the
production of many larger molecules. Now it is
observed in many places of the interstellar
medium 6. Interaction and clustering of H3
with molecular hydrogen is very important too,
see in 7 and 8.
bigger structures are not flat
1.9 Å
4.9 Å
H3(H2)12
Influence of increasing of size of clusters on
changing of ?1 and ?2 frequencies in IR spectrum
Energies of H3(H2)n clusters

1. H. Kreckel, J. Tennyson, D. Schwalm, D. Zajman
   and A. Wolf New J. Phys. 6 (2004) 151.
2. J.J. Thomson Phil. Mag. 21 (1911) 225.
3. A. Wolf et al Physica Scripta T110 (2004) 193.
4. V. Kokoouline and C.H. Greene Phys. Rev. A 68
   (2003) 012703.
5. B.J. McCall et al Nature 422 (2003) 500.
6. B.J. McCall, T.R. Geballe, K.H. Hinkle, T. Oka
   Science 279 (1998) 1910.
7. A. Qayyum et al Physica Scripta T103 (2003) 29.
8. Zhen Xie, B.J. Braams, J.M. Bowman J. Chem.
   Phys. 122 (2005) 224307.
9. T. Wróblewski, L. Ziemczonek, E. Gazda and G.P.
   Karwasz Radiation Physics and Chemistry 68
   (2003) 313.
10. K. Hiraoka J. Chem. Phys. 87 (1987) 7.
11. B. Diekmann, P. Borrmann, E.R. Hilf Condensed
    Matter, abstract cond-mat/9412123 (1994).

n ?1 (cm-1) ?2 (cm-1) ??1 (cm-1) ??2 (cm-1)
H3 3321.57 2730.49
H3(H2)n 1 3445.16 2433.72 123.59 -296.77
H3(H2)n 2 3427.23 2482.64 105.66 -247.85
H3(H2)n 3 3253.69 2584.69 -67.88 -145.80
H3(H2)n 4 3254.86 2574.63 -66.71 -155.86
H3(H2)n 5 3253.44 2588.68 -68.13 -141.81
H3(H2)n 6 3261.39 2585.89 -60.18 -144.60
H3(H2)n 7 3259.93 2571.32 -61.64 -159.17
H3(H2)n 8 3255.76 2591.15 -65.81 -139.34
H3(H2)n 9 3253.34 2567.83 -68.23 -162.66
H3(H2)n 10 3251.04 2564.94 -70.53 -165.55
H3(H2)n 11 3249.97 2566.63 -71.60 -163.86
H3(H2)n 12 3249.49 2568.93 -72.08 -161.56
n Etot (a.u.) ZPEV (a.u.) E (a.u.) SE (a.u.)
H3 -1.27654 0.02011 -1.25643
H2 -1.12804 0.01051 -1.11753
H3(H2)n 1 -2.40967 0.03437 -2.37530 -0.00134
H3(H2)n 2 -3.53897 0.04545 -3.49352 -0.00203
H3(H2)n 3 -4.67232 0.06080 -4.61152 -0.00250
H3(H2)n 4 -5.80059 0.07132 -5.72927 -0.00272
H3(H2)n 5 -6.92880 0.08237 -6.84643 -0.00235
H3(H2)n 6 -8.05702 0.09315 -7.96387 -0.00226
H3(H2)n 7 -9.18505 0.10376 -9.08129 -0.00215
H3(H2)n 8 -10.31294 0.11610 -10.19684 -0.00017
H3(H2)n 9 -11.44102 0.12555 -11.31547 -0.00127
H3(H2)n 10 -12.56908 0.13754 -12.43154 0.00019
H3(H2)n 11 -13.69722 0.14824 -13.54898 0.00028
H3(H2)n 12 -14.82528 0.15717 -14.66811 -0.00132

• minimal shift for n 6 for ?1 frequency
  (attracting mode)
• periodical shift for ?2 frequency (deformation
  mode) depending on the symmetry of cluster

where Etot (a.u.) ZPEV (a.u.) E (a.u.) SE (a.u.)
- total energy of structure - zero point energy
of vibrations - corrected total energy -
stabilization energy
Calculated energies are in good agreement with
other models, see for example in 10 and 11.
Stabilization energies (SE) show that the most
stable clusters are with three and twelve
hydrogen molecules, Fig.1 and Fig.2. The radius
of the H3(H2)3 cluster is 1.9 Å and the radius
of the second shell of H3(H2)12 cluster is 4.9 Å
. So difference between shells equals 2 Å.
Positions of hydrogen molecules may vary from
parallel to perpendicular to the plane of H3
ion. Energies of the conformes are hardly ever
the same. From table above we see that for
small clusters, n1,2, the ?1 frequency of
attractive mode of vibration increased what gives
evidence of magnitude of forces between H3 ion
and hydrogen molecules. For the bigger clusters
the fundamental ?1 and ?2 frequencies are
smaller. This is result of the polarization
effect which we can understand as follows the
positive central H3 ion attracts the electrons
of the attaching hydrogen molecules. It reduces
the screening of the protons by electrons and
enlarges the repulsion between protons.
H3(H2)4-5