A Neoteric Neodymium Model: Ground and Excited Electronic State Analysis of NdF²⁺ Page: 4
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The Journal of Physical Chemistry A
MCSCF (5,8)
175
150
125
100
C6 75
50
25-- X41
-U- A4cD
-~B4Ai
~-C~F
--all)
b2H
c2F
d2A
e6H0
-25
1.41.6
1.8
2
2.2
2.6
2.4
Internuclear Distance (A)
Figure 2. Potential energy curves obtained with a (5,8) active space at the MCSCF level of theory. Relative energies are in kcal/mol, and the zero of
the energy scale is set to the lowest point on the MCSCF ground state potential energy curve.occupied at all internuclear distances. Thus, the (5,8) active
space allows for homolytic dissociation (Nd2+ + F'), while the
(3,7) active space forces heterolytic dissociation (Nd3+ + F-), a
process that is not stable in the gas phase in the absence on an
external field to stabilize the charge separation. The natural
orbital occupation numbers highlight differences between the
two active spaces along the ground state potential energy curves
(Table 1). In Table 1, it is clear that the F 2pz orbital is always
doubly occupied with the (3,7) active space, whereas the F 2pz
orbital occupation varies gradually from 1.99 electrons at 1.6 A
to 1.90 electrons at 2.6 A with the (5,8) active space. Likewise,
the Nd 4f orbitals react to the variation in F 2pz occupation. In
the case of the (3,7) active space, electrons are simply
transferred from the bulk of the Nd 4f set to the 4fZ orbital
(orbital f(7) in Table 1). However, the electrons are transferred
from the F 2pz orbitals to the Nd 4fZ orbital (orbital f(7) in
Table 1) when the (5,8) active space is used. All the remaining f
orbitals maintain an occupation of 0.5 electrons for all
internuclear distances when the (5,8) active space is used. In
both cases, there is a relatively large change in the Nd 4fZ3
orbital occupation between 2.6 and 2.8 A where the occupation
is 0.33 electrons with the (3,7) active space and 0.26 electrons
with the (5,8) active space.
Potential energy curves for NdF2+ obtained at the MCSCF
level of theory with the (5,8) active space is shown in Figure 2.
Four quartet states are shown, but each of the quartet states is
also doubly degenerate. The MCSCF quartet states, in order of
increasing energy at the equilibrium distance, re, are X41, A4t,
B4A, and C4F, and their energies relative to the ground state
(X4I) are 7.1, 14.1, and 30.6 kcal/mol, respectively. Inclusion of
dynamic correlation via MCQDPT2 calculations does not
change the ordering of the quartet states, but the energydifferences relative to the ground state of the A4t, B4A, and
C4F states are lowered to 5.6, 10.5, and 22.5 kcal/mol,
respectively, and the ground state energy is lowered by 14.5
kcal/mol relative to the MCSCF ground state energy. Four
doublet states are also shown, and these states are all doubly
degenerate as well. The doublet states (a2, b211, c2F, and d20)
are much higher in energy than the quartet states, which should
be expected according to Hund's rule. The MCSCF energy
differences between the doublet states and the quartet ground
state are 50.1, 55.3, 55.5, and 57.0 kcal/mol for the a2t, b211,
c2F, and d2A states, respectively. As with the quartet states,
inclusion of dynamic correlation via MCQDPT2 calculations
lowers the doublet states relative to the ground state energy.
The MCQDPT2 energies of the doublet states at re are 44.6,
46.6, 48.2, and 49.8 kcal/mol for the a2k, b211, c2F, and d20
states, respectively. In addition to lowering the relative energies
of the doublet states, the energy gap between the lowest and
highest doublet states closes by approximately 2 kcal/mol.
Equilibrium bond lengths for each of the quartet and doublet
states are shown in Table 2. At the MCSCF level the
equilibrium bond lengths are approximately the same for each
state and range from 1.905 to 1.912 A. Inclusion of dynamic
correlation shortens the bond slightly; the MCQDPT2 bond
lengths vary between 1.900 and 1.905 A. For comparison, the
bond lengths of NdF3 and NdF4- are 2.09 A5 (or 2.15 A42) and
2.63 A,43 respectively. At re, the F 2pz orbital is doubly occupied
in all of the dominant configuration state functions (CSFs), i.e.,
all CSFs with a coefficient greater than 0.07. The quartet states
differ from each other by permutations of f orbital occupations
localized solely on Nd, and therefore the quartet potential
energy curves are all roughly parallel to each other. The F 2pz
orbital is doubly occupied near re for all dominant CSFs for thedx.doi.org/10.1021/jp404654d Ii. Phys. Chem. A 2013, 117, 10881-10888
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10884
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Schoendorff, George; South, Christopher & Wilson, Angela K. A Neoteric Neodymium Model: Ground and Excited Electronic State Analysis of NdF²⁺, article, September 19, 2013; Washington, DC. (https://digital.library.unt.edu/ark:/67531/metadc991016/m1/4/: accessed April 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Arts and Sciences.