Spectroscopy and metastability of BeO+

Abstract

The potential energy curve of the ground electronic state of BeO and those of the lowest electronic states of the BeO+ cation are computed using the CASSCF/MRCI methods and a large basis set. For the cation, the spin–orbit coupling and the transition momentum integrals are also evaluated. These data are used later to deduce an accurate set of spectroscopic constants and to investigate the spin–orbit-induced predissociation of the lowest electronic excited states of BeO+. Our calculations show that the high-rovibrational levels of the BeO+ (12Σ+) electronic state exhibit rapid predissociation processes forming Be+(2S) + O(3P). Our curves are also used for predicting the single ionization spectrum of BeO.

Full text

IOP PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS
J. Phys. B: At. Mol. Opt. Phys. 41 (2008) 205101 (7pp) doi:10.1088/0953-4075/41/20/205101
Spectroscopy and metastability of BeO+
H Ghalila1, S Lahmar1, Z Ben Lakhdar1and M Hochlaf2
1Laboratoire de Spectroscopie Atomique, Mol´
eculaire et Application, D´
epartement de Physique,
Facult´
e des sciences de Tunis, Universit´
e Tunis El Manar, 1060, Tunisia
2Laboratoire Mod´
elisation et Simulation Multi Echelle, Universit´
e Paris-Est, MSME FRE 3160 CNRS,
5 bd Descartes, 77454 Marne-la-Vall´
ee, France
E-mail: ghalila.sevestre@planet.tn and hochlaf@univ-mlv.fr
Received 4 August 2008, in final form 5 August 2008
Published 1 October 2008
Online at stacks.iop.org/JPhysB/41/205101
Abstract
The potential energy curve of the ground electronic state of BeO and those of the lowest
electronic states of the BeO+cation are computed using the CASSCF/MRCI methods and a
large basis set. For the cation, the spin–orbit coupling and the transition momentum integrals
are also evaluated. These data are used later to deduce an accurate set of spectroscopic
constants and to investigate the spin–orbit-induced predissociation of the lowest electronic
excited states of BeO+. Our calculations show that the high-rovibrational levels of the BeO+
(12+) electronic state exhibit rapid predissociation processes forming Be+(2S) + O(3P). Our
curves are also used for predicting the single ionization spectrum of BeO.
1. Introduction
Alkaline earth oxides, such as BeO, are known as thermal
conductors and electrical insulators. Their structural and
electric properties and transport performances have been
widely investigated both experimentally and theoretically
allowing very interesting applications of such materials (see
[1] for more details). The nature of the bonding in
these compounds was subject to several controversies. A
pronounced ionic character was established for most of them,
such as in BeO. Many spectroscopic features of the gas
phase isolated molecules were deduced after analysing the
chemiluminescence Fourier transform spectra [2–6] and from
ab initio theoretical studies [7–9].
The present theoretical investigations treat the
spectroscopy and the metastability of beryllium oxide
cation, BeO+. Very few are known on this ionized species.
In contrast, the neutral molecule has been widely studied
because of the importance of beryllium and its derivatives
in medical standpoint [10], in plasma physics and in nuclear
physics, where they are used as protection layers. Very
recently, JET Tokamak experiments showed the effectiveness
of the beryllium neutral and multi-ionized states near the
surface metal in contact with the plasma [1]. These tests were
so successful that the next generation fusion Tokamaks will
most likely use beryllium as a wall coating material.
In order to fill the gap on the structure, the spectroscopy
and the metastability of the gas phase of BeO+cation, large
ab initio calculations are currently being performed dealing
with the electronic states of this ion. Highly correlated
wavefunctions are used to deduce the transition moments
and the spin–orbit coupling matrix elements between these
electronic states. A set of accurate spectroscopic data is then
deduced for the bound electronic states of BeO+. For the upper
electronic states, rapid spin–orbit-induced predissociation
processes are identified. Finally, the BeO+potential curves
together with those of BeO (X1+) are used to predict the
single ionization spectrum of beryllium monoxide.
2. Computational approaches
As widely discussed in the literature, electronic computations
of metallic bearing compounds are not obvious because of
the importance of electron correlation for a good description
of their electronic states and properties and the irregular
behaviour of their wavefunctions. This is associated with a
sudden change from ionic to covalent character even for the
lowest electronic states of these species. Only configuration
interaction methods, similar to those used currently, are viewed
as providing accurate data for them. Here the potential energy
curves of the electronic states of BeO+correlating to the
four lowest dissociation limits and that of BeO(X1+)were
computed using the full valence complete active space self-
consistent field (CASSCF) approach [11]followedbythe
internally contracted multireference configuration interaction
technique including the Davidson correction (MRCI+Q)
[12,13]. Both of them are implemented in the MOLPRO
0953-4075/08/205101+07$30.00 1© 2008 IOP Publishing Ltd Printed in the UK

J. Phys. B: At. Mol. Opt. Phys. 41 (2008) 205101 H Ghalila et al
program suite [14]. For beryllium and oxygen, the spdfgh
cc-pV5Z basis set of Dunning [15], resulting in 182 contracted
Gaussian functions, was used. The calculations were carried
out in the C2v point group where the B1and B2representations
were equivalently described.
At the CASSCF level of theory, all electrons were
correlated and the active space comprised all configuration
state functions (CSFs) obtained after excitations of these
electrons in valence orbitals. All electronic states having
the same spin multiplicity were averaged together with
equal weights. For MRCI calculations, all CSFs from the
CASSCF approach were taken as reference, resulting in
616, 588, 588, 560 uncontracted CSFs to be treated in the
A1,B
1,B
2and A2symmetries of the C2v point group when
computing the doublets and in 4832, 4960, 4960, 5048 CSFs
to be considered when treating the quartets. The spin–orbit
couplings in Cartesian coordinates were evaluated at the spdf
cc-pV5Z/CASSCF level of theory. The accuracy of the
electronic structure calculations and the spin–orbit evaluations
using our methodologies were widely discussed previously.
Readers are referred to [16–19] for more details.
For the bound electronic states of BeO+, our calculated
potentials were incorporated into variational treatment of the
nuclear motion problem using the method of Cooley [20]. A
set of spectroscopic constants, including the harmonic wave
numbers, anharmonic terms, rotation–vibration terms, ...,
was also deduced using standard perturbation theory and using
the derivatives of our potentials at equilibrium geometries.
Finally, the potentials, the spin–orbit couplings and the
dipole transition moments we were computing, were used later
with the LEVEL and BCONT programs of Le Roy [21,22]to
deduce the radiative lifetimes of the vibrational levels of BeO+
(12+) and their spin–orbit-induced predissociation lifetimes,
and the single ionization spectrum of BeO.
3. Results
Figure 1provides an overview on the evolution of the potential
energy curves of the electronic states of BeO+correlating
to the Be+(2Sg)+O(
3Pg), Be+(2Sg)+O(
1Dg), Be+(2Pu)+
O(3Pg) and Be+(2Sg)+O(
1Sg) dissociation limits along the
internuclear separation, RBeO. These potentials are computed
at the cc-pV5Z/CASSCF/MRCI+Q level of theory and they
are given in energy with respect to the minimum of the ground
state of this cation. Table 1lists the dominant electronic
configurations of the cationic states, which are quoted at
the equilibrium distance for the ground state (i.e. RBeO =
1.43 ˚
A). The equilibrium distances and the adiabatic excitation
energies (=difference between the energy of the minimum of
the ground BeO+state and the corresponding minimum of the
BeO+excited state) are also listed in this table.
3.1. On the nature of the ground electronic state of BeO+
Figure 1shows clearly that the ground state of BeO+is of 2
symmetry, which is mainly described by the 4σ21π3electronic
configuration (see table 1). This electronic state is followed
by the 2+state at 9384 cm−1, dominantly described by the
Figure 1. MRCI+Q potential energy curves of the electronic states
of BeO+correlating to the four lowest dissociation limits. The
vertical line corresponds to the middle of the Franck–Condon (FC)
region i.e. the maximum of the BeO (X2,v=0) wavefunction.
Table 1. Dominant electron configuration of the electronic states of
the BeO+ion investigated currently. We are also quoting, for the
bound states, the equilibrium distances (Re,in ˚
A) and the MRCI+Q
adiabatic excitation energies (Ta,incm
−1).
State Electron configurationaReTab
X23σ24σ21π31.43 0
12+3σ24σ11π41.35 9384
14−3σ24σ25σ11π21.85 23 529
12−3σ24σ25σ11π21.85 25 402
223σ24σ15σ11π31.72 39 655
123σ24σ25σ11π21.77 40 678
22+3σ24σ25σ11π21.85 49 273
243σ24σ21π22π11.69 49 497
323σ24σ15σ11π31.88 50 085
423σ24σ21π22π11.88 55 744
14+3σ24σ11π32π11.85 59 199
143σ24σ11π32π11.85 60 579
24−3σ24σ11π32π12.12 61 020
223σ24σ11π32π12.12 62 790
22−3σ24σ11π32π12.12 63 114
14c3σ24σ15σ11π3––
32+c 3σ24σ◦5σ11π4––
34−c3σ24σ25σ◦6σ11π2––
34c3σ24σ15σ◦6σ11π3––
44−c3σ24σ15σ21π2––
aDominant configuration at the equilibrium distance of the ground
state.
bCalculated as the difference between the energy of the minimum of
the ground state and the minimum of the considered electronic state.
cRepulsive state.
4σ11π4electron configuration and then by the 4−quartet
state. The quartet is associated with the promotion of a valence
2

J. Phys. B: At. Mol. Opt. Phys. 41 (2008) 205101 H Ghalila et al
Table 2. MRCI+Q spectroscopic constants of the ground electronic state of BeO and those of the electronic states of BeO+including the
harmonic wavenumber (ωe,incm
−1), the anharmonic terms (ωexe,ωeye;incm
−1), the rotational constants (Be,αe;incm
−1), the dissociation
energies (De, in eV) and spin–orbit constant at equilibrium geometry (ASO,incm
−1).
State ωeωexeωeyeBeαeDeASOa
BeO (X1+) 1473.5b10.67 0.08 1.63 0.017 6.4 –
1487.3c11.83 0.02 1.65 0.019 –
1463d
BeO+(X2) 1242.4 7.65 1.01 1.443 0.017 4.0 117.8
BeO+(2 2) 587.0 0.28 0.49 0.975 0.015 1.0 96.5
BeO+(3 2) 416.2 11.34 0.95 0.740 0.014 1.7 5.4
BeO+(4 2) 385.5 17.26 1.90 0.812 0.019 1.0 −34.1
BeO+(1 2+) 1427.9 9.45 0.03 1.622 0.017 4.8 –
BeO+(2 2+) 475.9 4.65 0.68 0.888 0.021 2.0 –
BeO+(1 4−) 502.4 9.04 0.02 0.900 0.024 1.0 –
BeO+(2 4−) 291.2 42.18 4.55 0.731 0.070 0.3 –
BeO+(1 2−) 495.7 10.95 0.27 0.887 0.024 0.8 –
BeO+(2 2−) 86.4 18.06 4.30 0.147 0.003 0.1 –
BeO+(2 4) 661.8 7.77 0.02 0.946 0.016 1.7 −4.3
BeO+(1 2) 494.8 10.75 0.08 0.893 0.025 0.9 −1.2
BeO+(2 2) 261.2 11.82 0.74 0.687 0.039 0.2 52.7
aThe values of ASO are calculated at the equilibrium distance of BeO+
(X2).
bThis work.
cExp. [7].
dTheor. [9].
electron from the 1πmolecular orbital (MO) into the vacant
5σMO and simultaneous removal of a second electron from
the 1πMO. This ordering for the lowest electronic states is not
the same for all seven electrons isovalent diatomic molecules,
where a change in the symmetry of the ground state is noticed.
For instance, the BeO+electronic states pattern is as for LiO,
NaO, MgO+and LiS [23–25]. For AlC, LiP−, BC, the ground
electronic state is, however, of 4−nature and the doublets
are located well above in energy and separated from each other
[24,26]. The situation is rather more critical when it comes
to the KO, BN+and C2+molecules where the lowest 2+,
the 2and 4−states are lying close in energy complicating
rather more the pattern of the corresponding electronic spectra
[27–29]. As widely discussed in the literature for the
molecules given above, the dipole and quadrupole interactions
in BeO+, that stabilize the 2state, are probably overwhelming
the Pauli repulsion which is critical for the stabilization of the
2+and the 4−states.
3.2. Electronic states of BeO+: potentials, spectroscopy and
spin–orbit integrals
Figure 1shows that the X2and the 12+electronic states
possess deep potential wells of several eV. However, the
lowest 4−state has a shallow potential well. Several
avoided crossings are remarkable between the BeO+states
e.g. those between the 2+states for RBeO distance of
∼4 bohr. Figure 1also shows that the 14,3
4−,3
4
and 44−are repulsive in nature. The later electronic states
are crossing the cationic-bound electronic states either in the
molecular or at large internuclear distances and therefore,
they are probably participating into their predissociation (see
below). For internal energies >50 000 cm−1, a high density
of electronic states is noticeable, favouring rather more their
mutual interactions by spin–orbit and vibronic couplings.
Inter-conversions to the low-lying states are also expected to
occur.
Table 2gives a set of spectroscopic constants for BeO+.
This includes the rotational constants (Be,αe), the dissociation
energies (De) evaluated at the equilibrium geometry of the
corresponding electronic states, the harmonic wave numbers
(ωe) and anharmonic terms (ωexe,ωeye), which are deduced
from the derivatives of the potentials at their respective
minima. We are also giving the spectroscopic parameters
for BeO (X1+) computed at the same level of theory. The
main aim of the calculations on the neutral species, for which
accurate theoretical and experimental data are available in the
literature, is to allow judging the accuracy of the spectroscopic
constants of the so-far unknown states of BeO+. For instance,
the equilibrium distance of BeO (X1+) is calculated to
be 1.337 ˚
A, which is in good accord with the experimental
value 1.3309 ˚
Agivenin[7]. The spectroscopic constants of
BeO (X1+) agree with those given in [7]. For example, our
BeO(X1+)ωevalue (of 1473.5 cm−1) differs by less than
14 cm−1from the experimentally determined ωeharmonic
wave number [7]. Accordingly, we believe that our predictive
data for the BeO+cation should be of similar precision.
The spin–orbit coupling evolutions between the electronic
states of BeO+are depicted in figure 2and specified in
table 3. Close examination of this figure reveals that the
integrals involving the 2,the2+and the 4electronic
states are presenting non-monotonic behaviour: they are
changing drastically for RBeO distances around 3.5–4.5 bohr.
At these internuclear ranges, figure 1shows that the set of
electronic states having the same spin and symmetry nature
are interacting mutually (cf the avoided crossings occurring
at these internuclear separations), resulting in mixings of
their electronic wavefunctions, which are accompanied by
3

J. Phys. B: At. Mol. Opt. Phys. 41 (2008) 205101 H Ghalila et al
(a)
(b)
(c)
Figure 2. Evolution of the non-vanishing spin–orbit couplings
between the doublets and the quartet states of BeO+versus the
internuclear distance. These terms are specified in table 4.(a)
Diagonal coupling terms; (b) doublet-doublet off-diagonal
couplings; (c) doublet–quartet and quartet–quartet off-diagonal
couplings.
Table 3. Definition of the spin–orbit matrix elements computed in
this work together with our schematic representation given in
figure 2.
iX2;ms=1/2|LZSZ|X2;ms=1/2=X2–X2
i12;ms=1/2|LZSZ|12;ms=1/2=12–12
i22;ms=1/2|LZSZ|22;ms=1/2=22–22
i22;ms=1/2|LZSZ|22;ms=1/2=22–22
i32;ms=1/2|LZSZ|32;ms=1/2=32–32
i42;ms=1/2|LZSZ|42;ms=1/2=42–42
i14;ms=3/2|LZSZ|14;ms=3/2=14–14
i14;ms=1/2|LZSZ|14;ms=1/2=14–14
i24;ms=1/2|LZSZ|24;ms=1/2=24–24
i34;ms=1/2|LZSZ|34;ms=1/2=34–34
iX2;ms=−1/2|LXSX|12−;ms=1/2=X2–12−
iX2;ms=1/2|LZSZ|22;ms=1/2=X2–22
iX2;ms=−1/2|LXSX|22;ms=1/2=X2–22
iX2;ms=1/2|LXSX|14−;ms=3/2=X2–14−
iX2;ms=1/2|LZSZ|14;ms=1/2=X2–14
i12+;ms=1/2|LYSY|X2;ms=1/2=12+–X2
i12+;ms=1/2|LZSZ|12−;ms=1/2=12+–12−
i12+;ms=1/2|LYSY|22;ms=1/2=12+–22
i12+;ms=1/2|LYSY|14;ms=3/2=12+–14
i12+;ms=1/2|LZSZ|14−;ms=3/2=12+–14−
i12−;ms=−1/2|LXSX|22:ms=1/2=12−–22
i22;ms=−1/2|LXSX|22;ms=1/2=22–22
i14;ms=1/2|LXSX|14−;ms=3/2=14–14−
i22;ms=1/2|LXSX|14−;ms=3/2=22–14−
i22;ms=1/2|LXSX|14;ms=1/2=22–14
i12;ms=1/2|LXSX|14;ms=3/2=12–14
i12−;ms=1/2|LXSX|14;ms=3/2=12−–14
such spin–orbit integral changes. The diagonal spin–orbit
integrals are used for deducing the spin–orbit constants
(ASO) of the corresponding electronic states evaluated at their
corresponding equilibrium geometries and using the formula
given in [30]. These constants are quoted at the right side of
table 2.
4. Discussion
Our potential energy curves together with the spin–orbit and
the transition moment functions are used: (1) for treating the
predissociation of the high-rovibrational levels of BeO+(12+)
as illustration for state-to-state unimolecular decomposition
processes that can occur on BeO+and (2) for deducing the
single ionization spectrum of BeO.
4.1. Predissociation of BeO+(12+)
The first excited state 12+presents a deep potential well
of ∼4.8 eV and it correlates adiabatically to the second
dissociation limit Be+(2Sg)+O(
1Dg). It is crossed by the
repulsive 14state at internuclear distance around 3.7 bohr
allowing predissociation phenomena to take place leading to
the formation of Be+and O species in their electronic ground
state. Figure 3, which is an enlargement of figure 1in the 0–
50 000 cm−1energy domain, gives the potential energy curves
of the X2,1
2+and 14states (in (a)), the spin–orbit
coupling between the 12+and 14(in (b), cf figure 2) and
4

J. Phys. B: At. Mol. Opt. Phys. 41 (2008) 205101 H Ghalila et al
(a)
(b)
(c)
Figure 3. Enlargement of figure 1showing the potentials of the
X2,1
2+and 14states (a), the spin–orbit coupling between the
12+and 14(b) and the transition moment between the 12+and
the X2states (c), versus the internuclear distance. In (a), the
horizontal lines correspond to the vibrational levels of the 12+as
deduced variationally. See the text for more details.
the transition moment between the 12+and the X2states
{in (c)}, versus the internuclear distance. These data are used
for deducing the natural lifetime of the rovibrational levels of
the 2+state using Le Roy’s set of programs [21,22].
At the 12+and 14crossing, the 12+|LZSZ|14
integral is evaluated to be ∼21 cm−1, which is high enough to
allow converting the doublet into the quartet. Figure 3(a)
reveals that the predissociation of the 2+rovibrational
levels, via the repulsive 4state is effective for v+
18. It is also worth noticing that the rovibrational levels of
this 2+state can decay via radiative transitions populating
the Xstate. The natural lifetime τnatural is related to the
radiative τradiative and the predissoviative τpredissociative lifetimes
by: 1
τnatural =1
τradiative +1
τpredissociative . Here, τradiative is calculated,
using LeRoy’s LEVEL code [21] and our computed transition
moment integral between the 12+and the X2(cf
figure 3(c)), as the inverse of the sum of the Einstein transition
rates Avv between the v+(12+) vibrational level and all the
v+levels of the X2state (i.e. τradiative =(v Avv)−1).
τpredissociative is computed, using the LeRoy’s BCONT code
Table 4. Radiative, predissociative and natural lifetimes of the v+=
0upto21vibrationallevelsofBeO
+(12+). See the text for more
details. All values are in ns.
v+τradiative τpredissociative τnatural
0 21 747.90 21 747.90
1 9877.72 9877.72
2 5758.68 5758.68
3 3774.39 3774.39
4 2651.00 2651.00
5 1947.98 1947.98
6 1478.82 1478.82
7 1151.33 1151.33
8 913.99 913.99
9 736.52 736.52
10 599.46 599.46
11 488.42 488.42
12 393.84 393.84
13 315.12 315.12
14 255.32 255.32
15 226.67 226.67
16 326.31 326.31
17 190.35 190.35
18 175.04 304.55 111.15
19 163.90 0.01 0.012
20 153.21 0.02 0.017
21 143.64 0.03 0.031
[22], by Fermi Golden rule calculations of the predissociation
rates for the BeO+(12+) vibrational levels v+=18 up to 21.
Table 4lists the radiative, the predissociative and the
natural lifetimes of the vibrational levels of BeO+(12+)0
v+21. For the v+17 levels, only the radiative transitions
contribute to the reduction of their lifetimes, since they are
located below the Be+(2Sg)+O(
3Pg) asymptote. The v+=
18 state is however located slightly above this asymptote so
that both radiative and non-radiative transitions are expected to
contribute. For this level, the radiative and the predissociative
lifetimes are calculated 175 and 304 ns, respectively. They are
of the same order of magnitude and therefore they contribute
to the reduction of τnatural of BeO+(v+=18). The situation is
quite different for the v+>18 states. Indeed, our calculations
show that their natural lifetimes are reduced to the ps scale
mainly due to the rapid spin–orbit-induced predissociation via
the 4electronic state. The non-monotonic evolution of the
predissociative lifetimes is associated with the overlap of the
corresponding wavefunctions of the bound vibrational states
and those of the continuum.
4.2. Single-ionization spectrum of BeO
At the cc-pV5Z/CASSCF/MRCI+Q level of theory, the
adiabatic ionization potential (IP) of beryllium oxide is
computed to be 9.82 eV. Our IP agrees with the mass
spectrometric value of 10.4 ±0.4 eV [31], but it is slightly
higher than the 9.46–9.43 B3LYP and MP2 determinations of
Srnec and Zahradnik [32]. The BeO+(12+) state is located
in the Franck–Condon zone (denoted as FC in figure 1). A
short-vibrational progression is expected for the BeO+(12+)
v++e
−←BeO(X1+)v=0+hνionization transitions,
whereas long-vibrational progressions should be associated
5

J. Phys. B: At. Mol. Opt. Phys. 41 (2008) 205101 H Ghalila et al
Figure 4. Simulation of the ionization spectrum of the neutral BeO (X1+) at a resolution of 50 cm−1. The Franck–Condon factors and
frequencies of transitions between the v=0 vibrational level of the ground electronic state of neutral BeO and calculated electronic states
of BeO+were calculated using LEVEL. Convolution of the output from this program was carried out using a Gaussian function with a
FWHM of 50 cm−1to simulate the resolution achieved by current available experiments. Above the simulated spectrum we show the
electronic states that contribute. The inset is a zoom of the right part of the spectrum for more clarity.
with the population of the other electronic states from
BeO(X1+)v=0.
In order to provide the ionization intensity distribution for
ionization of BeO (X1+)fromthe(v =0, N ) rovibrational
states to the (v+,N+) levels of BeO+(X2,1
2+,2
2,3
2
and 22+), we have computed, using our MRCI+Q potential
energy curves and the LEVEL Program, the Franck–Condon
factors for all transitions including rotational levels up to
N=10. A ‘Q-Branch’ approximation (N=0) was adopted.
A simulated photoionization spectrum, where the transitions
are fitted by LEVEL to a Gaussian function, with a full-width
at half-maximum (FWHM) =50 cm−1, is shown in figure 4.
As pointed out above, and because of favourable Franck–
Condon overlaps, the spectrum is dominated by the transition
populating the 12+v+=0 level and a long progression
is associated with the ground state of BeO+. For ionization
energies >120 000 cm−1, the shape of the spectrum is rather
complicated because of the overlap of several vibrational series
corresponding to the population of the doublet electronic states
located in the top of figure 1. For more clarity we are giving
in the inset of figure 4an enlargement of this spectrum region.
The spectrum of figure 4is predictive in nature and should
be helpful for the identification of the bands associated with
the formation of this cation by photoionization or electron
impact ionization of the neutral molecule. Moreover, the
comparison of our synthetic spectrum, corresponding mainly
to direct ionization mechanism, with the experimental ones
whenever measured should give an insight into the eventual
contributions of indirect processes, such as autoionization.
5. Conclusion
The spectroscopy and the metastability of the lowest electronic
states of the BeO+cation have been investigated using
configuration interaction methods and a large basis set, where
our potential energy curves and our couplings are used in Fermi
Golden rate computations using the Le Roy programs [21,22]
in order to deduce the lifetimes of these rovibrational levels
and to propose plausible spin–orbit-induced predissociation
mechanisms for the short-lived ones. The data deduced
presently are mostly predictive in nature. This theoretical work
should motivate new experimental studies on the beryllium
oxide cation and derivatives.
Acknowledgments
Professor R J Le Roy is acknowledged for kindly providing us
with the LEVEL and BCONT programs. M H would like to
thank a visiting fellowship at the University of Tunis El Manar
from the Tunisian Ministry of High Education and Research.
References
[1] Brooks J N, Allain J P, Alman D A and Ruzicb D N 2005
Fusion Eng. Des. 72 363–375 and references therein
[2] Jonah C D, Zare R N and Ottinger C H 1972 J. Chem. Phys.
56 263–74
[3] Engelke F, Sander R K and Zare R N 1976 J. Chem. Phys.
65 1146–55
[4] Focsa C, Poclet A, Pinchemel B, Le Roy R J and Bernath P F
2000 J. Mol. Spectrosc. 203 330–8
6

J. Phys. B: At. Mol. Opt. Phys. 41 (2008) 205101 H Ghalila et al
[5] Li H, Skelton R H, Focsa C, Pinchemel B and Bernath P F
2000 J. Mol. Spectrosc. 203 188–95
[6] Griffiths P R and de Haseth J A 1986 Fourier Transform
Infrared Spectrometry (New York: Wiley)
[7] Herzberg G 1989 Molecular Spectra and Molecular Structure,
vol I—Spectra of Diatomic Molecules 2nd edn (Malabar,
FL: Kreiger) p 573
[8] Mallard W G and Lindstrom P J (eds) 1998 NIST Chemistry
WebBook NIST Standard Reference Data-base 69,
November 1998 (Gaithersburg, MD: National Institute of
Standards and Technology) 20899 (http://webbook.nist.gov)
[9] Buenker R J, Liebergmann H-P, Pichl L, Tachikawa M and
Kimura M 2007 J. Chem. Phys. 126 104305, 1–7
[10] Reeves A L 1967 Cancer Res. 27 1895–9
[11] Knowles P J and Werner H-J 1985 Chem. Phys. Lett. 115 259
[12] Werner H-J and Knowles P J 1988 J. Chem. Phys. 89 5803
[13] Knowles P J and Werner H-J 1988 Chem. Phys. Lett. 145 514
[14] MOLPRO is a package of ab initio programs written by H-J
Werner and PJ Knowles; further details at
http://www.molpro.net
[15] Dunning T H Jr 1989 J. Chem. Phys. 90 1007
[16] Ben Yaghlane S, Lahmar S, Ben Lakhdar Z and Hochlaf M
2005 J. Phys. B: At. Mol. Opt. Phys. 38 3395
[17] Ben Houria A, Ben Lakhdar Z and Hochlaf M 2006 J. Chem.
Phys. 124 054313
[18] Khadri F, Ndome H, Lahmar S, Ben Lakhdar Z and Hochlaf M
2006 J. Mol. Spectrosc. 237 232
[19] Edhay B, Lahmar S, Ben Lakhdar Z and Hochlaf M 2007
Prog. Theor. Chem. Phys. 16 273
[20] Cooley J W 1961 Math. Comput. 15 363
[21] Le Roy R J 2002 LEVEL 7.2, University of Waterloo,
Chemical Physics Research Report CP-642
[22] Le Roy R J 1993 BCONT, University of Waterloo, Chemical
Physics Research Report CP-329R3
[23] Maatouk A, Ben Houria A, Yazidi O, Ben Lakhdar Z and
Hochlaf M 2008 in preparation
[24] Boldyrev A I, Simons J and Schleyer P von R 1993 J. Chem.
Phys. 99 8793
[25] Lee E P F, Soldan P and Wright T G 2001 Chem. Phys. Lett.
347 481
[26] Tzeli D and Mavridis A 2001 J. Phys. Chem. A105 7672
[27] Watts J D and Bartlett R J 1992 J. Chem. Phys. 96 6073
[28] Bauschlicher C W Jr, Partridge H and Pettersson L G M 1993
J. Chem. Phys. 99 3654
[29] Mawhinney R C, Bruna P J and Grein F 1995 Chem. Phys.
199 163
[30] Lefebvre-Brion H and Field R W 2004 The Spectra and
Dynamics of Diatomic Molecules (Amsterdam: Elsevier)
[31] Theard L P and Hildenbrand D L 1964 J. Chem. Phys. 41 3416
[32] Srnec M and Zahradnik R 2005 Chem. Phys. Lett. 407 283
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