The Electronic Structure of ScAl
+
. Ground and Low-Lying Excited States
Demeter Tzeli and Aristides Mavridis*
Laboratory of Physical Chemistry, Department of Chemistry, National and Kapodistrian UniVersity of Athens,
P.O. Box 64 004, 157 10 Zografou, Athens, Greece
ReceiVed: March 7, 2000; In Final Form: May 5, 2000
Using semiquantitative basis sets and ab initio multireference methods, we have investigated the electronic
structure of scandium aluminide cation, ScAl
+
. In addition to the ground state (X
2
Δ), we have constructed
potential energy curves for 20 more states spanning an energy range of no more than 1.5 eV. The first three
states, X
2
Δ,1
2
Π, and 2
2
Σ
+
, are practically degenerate within the accuracy of our calculations. They have
similar binding modes and a binding energy of about 30 kcal/mol with respect to their adiabatic fragments
Sc(
2
D) + Al
+
(
1
S). The rest of the states correlate to Sc
+
(
3
D or
3
F) + Al(
2
P). For all states we report bond
lengths, dissociation energies, harmonic frequencies, Mulliken charges, and energy gaps.
1. Introduction
The 3d transition metal aluminides form an important class
of high-temperature materials with some of them being candi-
dates for permanent magnets.
1
A systematic study through
electronic spectroscopy of 3d transition metal aluminides but
with the exception of the ScAl species is given in ref 2, while
for ScAl alloys there are some limited experimental data on
enthalpies of formation.
3-5
Given the increasing importance of
these materials, our interest in the isovalent metal borides,
M-B
+
(M ) Sc, Ti, V, Cr),
6
and the complete lack of
experimental and/or theoretical information on ScAl
+
, we have
decided to probe the electronic structure of this diatomic cation
by ab initio quantum methods.
In the present work the electronic structure of ScAl
+
is
investigated via complete active space SCF (CASSCF) and
multireference configuration interaction (MRCI ) CASSCF +
single + double replacements ) CASSCF +1 + 2) methods.
In addition to the ground state (X
2
Δ, vide infra), 20 low-lying
excited states have been also examined: 10 doublets {2
2
Σ
+
,
11
2
Σ
+
,7
2
Σ
-
, 20
2
Σ
-
,1
2
Π,9
2
Π, 13
2
Π,8
2
Δ, 14
2
Δ, 12
2
Φ} and
10 quartets {15
4
Σ
+
, 19
4
Σ
+
,3
4
Σ
-
, 18
4
Σ
-
,4
4
Π, 10
4
Π, 17
4
Π,6
4
Δ,
16
4
Δ,5
4
Φ}. One of the interesting aspects of the present report
is the comparable ionization potentials of Sc and Al atoms, 6.56
and 5.98 eV, respectively;
7
as a result the ground (X
2
Δ) and
the first two excited states (1
2
Π,2
2
Σ
+
) of ScAl
+
correlate to
Sc(
2
D) + Al
+
(
1
S), while the rest of the states correlate to Sc
+
-
(
3
D or
3
F) + Al(
2
P).
For all 21 states examined we report full potential energy
curves (PEC), binding energies (D
e
), bond distances (R
e
),
harmonic frequencies (ω
e
), Mulliken populations, and energy
gaps (T
e
), while emphasis has been given in deciphering the
bonding mechanism(s) with the help of simple valence bond
Lewis (vbL) diagrams.
2. Methods
For the Sc atom the ANO basis set of Bauschlicher
8
(21s16p9d6f4g) has been used but with the functions of g
angular momentum removed. For the Al atom, the cc-pVTZ
(15s9p2d1f) basis set of Dunning
9
was employed. Both sets were
generally contracted to [(7s6p4d3f)
Sc
/(5s4p2d1f)
Al
], numbering
100 spherical Gaussians.
As already indicated, the complete active space SCF (CASS-
CF) methodology was employed to describe the reference space,
followed by single and double configuration interaction out of
the CASSCF space (CASSCF + 1 + 2 ) MRCI). Five
“valence” (active) electrons were distributed to 10 orbital
functions for the quartets (one 4s and five 3d’s on Sc + one 3s
and three 3p’s on Al), and to 11 orbitals (+ one 4p
z
) for the
doublets. The additional 4p
z
orbital function was deemed
necessary for the X
2
Δ,1
2
Π, and 2
2
Σ
+
states correlating to Sc
+ Al
+
, but for reasons of uniformity the 11 orbital space was
maintained in all doublets. Depending on the number of orbitals
and the symmetry of the state, our reference spaces range from
432 to 1354 configuration functions (CF), with corresponding
CI numbers ranging from 431 318 to 871 611 CFs at the MRCI
level. By applying the internal contraction (icMRCI) technique,
10
the number of CFs is reduced by about half. All calculations
were done under C
2V
symmetry constraints; however care was
exercised for the CASSCF wave functions to display correct
axial angular momentum symmetry, i.e., |Λ| ) 0, 1, 2, and 3
or Σ
(
, Π, Δ, and Φ, respectively. This means that Δ states are
linear combinations of A
1
and A
2
symmetries, Π and Φ states
are combinations of B
1
and B
2
symmetries, and Σ
+
and Σ
-
states
correspond to the A
1
and A
2
symmetry species, respectively.
MRCI wave functions do not display in general pure axial
symmetry, being calculated as A
1
or A
2
and B
1
or B
2
. With the
exception of the X
2
Δ,1
2
Π,2
2
Σ
+
, and 3
4
Σ
-
states, the state
average (SA) approach
11,12
was used for the computation of all
other states. Numerical experiments performed for some of the
lowest states with and without the SA method and with and
without internal contraction showed absolute energy losses of
no more than 2 mhartrees collectively. Finally, the size
nonextensivity errors of our SA-icMRCI wave functions are
less than 1 mhartree.
All calculations were performed with the MOLPRO suite of
codes,
13
while some of the lower states were also checked with
the COLUMBUS code.
14
3. Description of the Atoms
Absolute energies of Sc(
2
D), Sc
+
(
3
D,
1
D,
3
F), and Al(
2
P), Al
+
-
(
1
S), atomic energy separations, and ionization potentials are
listed in Table 1. The SCF and CASSCF calculations were done
6861 J. Phys. Chem. A 2000, 104, 6861-6870
10.1021/jp000894+ CCC: $19.00 © 2000 American Chemical Society
Published on Web 07/01/2000