Theoretical Study of 1Σ+ States of Alkali Hydride XH Molecule (X ) Na, K and Rb) in Adiabatic and Nonadiabatic Representations


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Theoretical Study of 1Σ+ States of Alkali Hydride XH Molecule (X ) Na, K and Rb) in Adiabatic and Nonadiabatic Representations
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Alkali hydrides have been the object of intense theoretical
and experimental interest for many years.1-12 Such molecules
are at the intersection of various theoretical and experimental
challenges, and now are tractable with high reliability via ab
initio techniques. Using appropriate methods, it is possible to
approach the experimental results with an overall good agreement
for the ground and excited states. Their ground state is
known to be of ionic character but dissociates to neutral
A charge-transfer crossing is therefore expected to occur,
making this problem attractive for diabatization. The nonadiabatic
approach brings physical insight as shown in the previous
studies of the LiH molecule,1,13,14 suggesting further calculations
of non Bo
-Oppenheimer effects such as transitions occurring
in collisions,15-17 estimation of vibronic effects (vibronic shifts
and nonradiative lifetime).12,18-20 In addition, the nonadiabatic
picture can be used to improve the accuracy of calculations, by
overcoming basis set limitations on the electron affinity of H,
which is among the main limitations in the ab initio approach,
particularly for the binding energy of the ground state.1
Undulations in the potential of the highly excited states were
revealed and analyzed in the previous study of LiH1 and further
confirmed in various recent works.11,21-23 These undulations
were shown to be magnified in the nonadiabatic curves and to
be related to intrinsic characteristics of the Rydberg atomic
Although realistic all-electron calculations are now feasible
for the XH (X ) Na, K, Rb) molecule, we prefer to use the
pseudopotential approach for the core and large basis sets for
the valence and Rydbergs states, which allows accurate descriptions
of the highest excited states for the whole alkali hydride
series. The two electrons are then treated at the full configuration-
interaction level (here CISD: singles-doubles configuration
interaction). Core-valence correlation effects are quite
important. Here we used the well-established operatorial approach
proposed by Mu¨ller, Flesh, and Meyer.24 This paper
presents the first ab initio calculations on highly excited states
of the XH alkali hydride molecule (X ) Na, K, Rb), treating
nearly all states dissociating below the ionic one [Na (3s, 3p,
4s, 3d, 4p, 5s, 4d, 4f), K(4s, 4p, 5s, 3d, 5p, 4d, 6s, 4f) and Rb
(5s, 5p, 4d, 6s, 6p, 5d, 7s, 4f)]. The accuracy of the results can
be judged by a comparison with the numerous theoretical and
experimental data for the two lowest states. In addition to the
adiabatic potential curves and dipoles moments, nonadiabatic
curves are also derived. A further interest of this work is an
improvement of both potential curves and dipole moments
related to the H electron affinity correction effects allowed by
the use of an efficient diabatization method. Therefore a rather
complete set of data is presented about the XH (X ) Na, K,
Rb) molecule from ground to highly excited states including
adiabatic potential energy in 1Σ+ and permanent dipole and
transition dipole moments, as well as potential electronic
couplings, for the corresponding nonadiabatic states. This set
of data will be further used to perform detailed spectroscopic
studies including vibronic effects, radiative and nonradiative life
In section 2 we briefly present the computational method and
give numerical details. Section 3 is devoted to the presentation
and discussion of the nonadiabatic and adiabatic results. Section
4 presents the permanent dipole moment for the adiabatic and
nonadiabatic representations. Suggestions of spectroscopic interest
are proposed in section 5. Finally, we summarize our results
and conclude in section 6.
2. Methods
2.1. Computational Details. The alkali (sodium, potassium
and rubidium) is treated as a one-electron system using the
nonempirical pseudopotential of Barthelat and Durand,25 in its
semilocal form,4 and as in LiH1 we used the abinitio package
developed in Toulouse. We have used basis set 6s/5p/4d/2f for
Na atom, 8s/5p/5d/2f for K atom and 8s/6p/6d/3f for Rb atom,
where diffuse orbital exponents have been optimized to reproduce
all the (3s, 3p, 4s, 3d, 4p, 5s, 4d, and 4f) atomic states for
Na, (4s, 4p, 5s, 3d, 5p, 4d, 6s and 4f) atomic states for K and
(5s, 5p, 4d, 6s, 6p, 5d, 7s and 4f) atomic states for Rb, while a
* E-mail: more restricted basis set has been employed for hydrogen.
J. Phys. Chem. A XXXX, xxx, 000 A
10.1021/jp9040138 CCC: $40.75  XXXX American Chemical Society
Downloaded by AUSTRIA CONSORTIA on July 6, 2009
Published on July 1, 2009 on | doi: 10.1021/jp9040138
This 5s, 3p, 2d basis set can be considered as a reasonable
compromise, able to describe both neutral and negatively
charged (H-) hydrogen. A larger basis set for H could not be
used because of numerical problems during the diabatization
process, the main effect of this rather small H basis being an
error (405 cm-1) in the H electron affinity, which however is
corrected due to the nonadiabatic approach used. An extensive
range of inte
uclear distances has been considered, ranging
from 2.45 to 500 bohr, in order to cover all the ionic-neutral
crossings in the 1Σ+ symmetry. For the simulation of the
interaction between the polarizable X+ (X ) Na, K, Rb) core
with the valence electrons and H nucleus a core polarization
potential is used, according to the operatorial approach of
Mu¨ller, Flesh, and Meyer.24 Following the formulation of
Foucrault, Millie, and Daudey26 cutoff functions with ldependent
adjustable parameters are fitted to reproduce not only
the first experimental ionization potential but also the lowest
excited states of each l, namely, [2S(3s), 2P(3p), 2D(3d) and
2F(4f)] for Na, [2S(4s), 2P(4p), 2D(3d) and 2F(4f)] for K and
[2S(5s), 2P(5p), 2D(4d) and 2F(4f)] for Rb. In the present work,
the core polarizability of alkali and the optimized cutoff
parameters are given in Table 1. The resulting atomic spectra
are reported in Table 2 for X (Na, K and Rb) atom (in cm-1).
The neutral dissociation limits reach a good accuracy for all
the 3s, 3p, 4s, 3d, 4p, 5s, 4d and 4f states for Na atom, 4s, 4p,
5s, 3d, 5p, 4d, 6s and 4f states for K atom and 5s, 5p, 4d, 6s,
6p, 5d, 7s and 4f states for Rb atom, the largest error being 36
2.2. Diabatization. We briefly recall the principal lines of
the method used; more details can be found in previous
publications.1,29-31 The strategy is to compute a numerical
estimate of the nonadiabatic coupling between the relevant
adiabatic states and to cancel it by an appropriate unitary
transformation according to the effective Hamiltonian theory.28,31
The estimate is however obtained using the large inte
intervals used in the molecular calculation instead of infinitesimal
ones, and an effective overlap matrix is employed, in order
to asymptotically ensure vanishing radial couplings and to get
stable results. This nonadiabatic coupling calculation is closely
related to an overlap matrix29,30 between the R-dependent
adiabatic multiconfigurational states and an Ro fixed set of
reference states.
This diabatization method was shown to be among the most
effective for molecular ab initio calculations.32 The set of
reference states are the nonadiabatic states calculated for the
larger neighboring distance. The calculation is performed from
the largest distance where the nonadiabatic states are initialized
to the adiabatic ones to the shortest one, similar to an integration
scheme. This method leads to smaller residual couplings
between the nonadiabatic states.33


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