Full configuration interaction calculation of BeH adiabatic states
J. Pitarch-Ruiz,
1
J. Sánchez-Marin,
1,a͒
A. M. Velasco,
2
and I. Martin
2
1
Institut de Ciència Molecular, Universitat de València, Edifici d’Instituts Campus de Paterna,
E-46980 Valencia, Spain
2
Departamento de Química Física y Químíca Inorgánica, Facultad de Ciencias, Universidad de Valladolid,
E-47005 Valladolid, Spain
͑Received 28 April 2008; accepted 11 June 2008; published online 6 August 2008͒
An all-electron full configuration interaction ͑FCI͒ calculation of the adiabatic potential energy
curves of some of the lower states of BeH molecule is presented. A moderately large ANO basis set
of atomic natural orbitals ͑ANO͒ augmented with Rydberg functions has been used in order to
describe the valence and Rydberg states and their interactions. The Rydberg set of ANOs has been
placed on the Be at all bond distances. So, the basis set can be described as
4s3p2d1f /3s2p1d͑Be /H͒+4s4p2d͑Be͒. The dipole moments of several states and transition dipole
strengths from the ground state are also reported as a function of the R
Be–H
distance. The position
and the number of states involved in several avoided crossings present in this system have been
discussed. Spectroscopic parameters have been calculated from a number of the vibrational states
that result from the adiabatic curves except for some states in which this would be completely
nonsense, as it is the case for the very distorted curves of the 3s and 3p
2
⌺
+
states or the double-well
potential of the 4p
2
⌸ state. The so-called “D complex” at 54 050 cm
−1
͑185.0 nm͒ is resolved into
the three 3d substates ͑
2
⌺
+
,
2
⌸,
2
⌬͒. A diexcited valence state is calculated as the lowest state of
2
⌺
−
symmetry and its spectroscopic parameters are reported, as well as those of the 2
2
⌬ ͑4d͒ state The
adiabatic curve of the 4
2
⌺
+
state shows a swallow well at large distances ͑around 4.1 Å͒ as a result
of an avoided crossing with the 3
2
⌺
+
state. The probability that some vibrational levels of this well
could be populated is discussed within an approached Landau–Zerner model and is found to be high.
No evidence is found of the E͑4s
͒
2
⌺
+
state in the region of the “D complex”. Instead, the
spectroscopic properties obtained from the ͑4s
͒ 6
2
⌺
+
adiabatic curve of the present work seem to
agree with those of the experimental F͑4p
͒
2
⌺
+
state. The FCI calculations provide benchmark
results for other correlation models for the open-shell BeH system and evidence both the limitations
and capabilities of the basis set. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2953584͔
I. INTRODUCTION
A continued effort is being done to develop and improve
theoretical methods of high quality for the calculations of
electronic excitation energies
1–4
and well adapted for calcu-
lation in large systems and at geometries far from equilib-
rium. Most of these methods face the difficulties by means of
multireference ͑MR͒ approaches ͓e.g., multireference con-
figuration interaction ͑CI͒ more or less corrected for size-
consistency error effects
5–11
or multireference perturbation
theory
12–15
͔. The extension of the single-reference configura-
tions interaction ͑SR-CI͒ to the MR case is conceptually
straightforward. However, because of the rapidly increasing
size of the hamiltonian matrices, these approaches are com-
monly restricted to single and double ͑SD͒ excitations out of
the chosen model space ͑MR-SDCI͒. Consequently, the so-
called static and nondynamic correlation effects are to some
extent taken into account efficiently, but, generally, there is
an incomplete consideration of the multitude of higher than
double hole-particle substitutions that contribute to the dy-
namic correlation. Multireference formulations can also be
conceived for the approaches based in the coupled-cluster
͑CC͒ formulation.
3,16–23
However, the generalization of the
SR-CC ansatz to the MR case is not unambiguous,
24,25
and,
also, the resulting formalisms for all genuine MR-CC ap-
proaches are computationally very demanding. Moreover,
some of the approximate methods yield excellent results in
the neighborhood of the equilibrium geometry, but, unfortu-
nately, breaks down entirely when dissociating the molecule
into open-shell fragments ͑Ref. 26 and references therein͒.
The extension of the approximate methods to general open-
shell systems offers additional challenges related, in most
cases, to the optimal selection of the one-electron basis, and
in some cases is demanding, both theoretically and
computationally.
24,25,27–32
Full configuration interaction ͑FCI͒ calculations are very
appealing because they are free of a number of formal dis-
advantages that affect approximate methods which truncate
the space of excitations. Within the limits imposed by the
Born–Oppenheimer ͑BO͒ approximation and the choice of
the one-particle functions basis, FCI provides nonrelativistic
exact results. Of course, only basis set of comparatively re-
duced size can be used and only systems with small number
of electrons are eligible for a systematic FCI study. However,
on the other hand, the results from such a study provide
durable benchmarks for approximate methods.
a͒
Electronic mail: jose.sanchez@uv.es.
THE JOURNAL OF CHEMICAL PHYSICS 129, 054310 ͑2008͒
0021-9606/2008/129͑5͒/054310/19/$23.00 © 2008 American Institute of Physics129, 054310-1