A CASPT2 Computational Study of
the Ce + O and Ce + O2 Chemiionization Reactions:
Assignment of the observed chemielectron bands
Tanya K. Todorova, Ivan Infante, Laura Gagliardi*)
Department of Physical Chemistry, University of Geneva, 30 Quai Ernest Ansermet CH-1211 Geneva,
Switzerland
John M. Dyke*
Department of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
Multiconfigurational quantum chemical methods (CASSCF/CASPT2) have been used to study the
chemiionization reactions Ce + O  CeO+
+ e and Ce + O2 
CeO2+ + e. Selected
spectroscopic constants for CeOn and CeOn+ (n = 1, 2), as well as reaction enthalpies of the
chemiionization reactions of interest, have been computed and compared with experimental values.
In contrast to the lanthanum case, for both Ce + O2(X3Σg) and Ce + O2(a1g),
the Ce + O2  CeO2+ + e reaction is shown to be exothermic, and thus, contributes to the
experimental chemielectron spectra. The apparent discrepancy between the computed reaction
enthalpies and the high kinetic energy offset values measured in the chemielectron spectra is
rationalized by arguing that chemielectrons are produced mainly via two sequential reactions (Ce +
O2  CeO + O, followed by Ce + O  CeO+ + e-) as occurs in the lanthanum case. For Ce +
1
O2(a1g), a chemielectron band with higher kinetic energy than that recorded for Ce + O2(X3Σg) is
obtained. This is attributed to production of O(1D) from the reaction Ce + O2(a1g)  CeO +
O(1D), followed by chemiionization via the reaction Ce + O(1D)  CeO+ + e Accurate potential
energy curves for the ground and a number of excited states of CeO and CeO+ have been computed
and a mechanism for the chemiionization reactions investigated experimentally was proposed.
)
Authors to whom correspondence should be addressed.
E-mail: laura.gagliardi@chiphy.unige.ch; jmdyke@soton.ac.uk
2
Introduction
In a recent publication, the chemiionization reactions that occur for the La + O(3P), La +
O2(X3g), and La + O2(a1g) reaction conditions have been established by quantum chemical
methods.1 It has been shown that for La + O2(X3g) and La + O2(a1g), the chemiionization
reaction La + O2  LaO2+ + e- is endothermic and does not contribute to the experimental
chemielectron spectra. Instead, chemiionization occurs via a two-step process, a rapid first step La
+ O2  LaO + O, followed by LaO + O  LaO+ + e-. For all reaction conditions studied, (i.e. La +
O2(X3g), La + O2(a1g) and La + O(3P)) production of LaO+ was attributed to the primary
chemiionization reaction (LaO + O  LaO+ + e-), whereas LaO2+, observed in the mass spectra,
does not arise from a chemiionization process, but from ion-molecule reactions involving LaO+.
This work is now extended to the Ce + O and Ce + O2 chemiionization reactions. Experimentally,
electron spectroscopy was employed to study the chemiionization reactions of cerium with the
oxidants O(3P), O2(X3g), and O2(a1g).2,3 As in the study on lanthanum1, an effusive beam of
cerium was crossed with an effusive beam from (A) a microwave discharge of flowing oxygen
which contains O2(X3Σg), O2(a1g) or O(3P), (B) the above microwave discharge conditions but
with O(3P) deactivated, or (C) pure O2(X3Σg). The Ce + O2(X3Σg) reaction gave a chemielectron
band, which showed resolved vibrational structure, with a most probable kinetic energy (MPKE)
(band maximum) of (0.90 ± 0.04) eV and a high kinetic energy offset (HKEO) of (2.4 ± 0.1) eV.
For the Ce + O2(a1g) reaction, these values were (1.83 ± 0.10) and (3.1 ± 0.3) eV, whereas for the
Ce + O(3P) reaction they were (0.13 ± 0.06) and (0.9 ± 0.1) eV.
In the experimental work
2,3
, although assignment of a chemielectron band to a particular
chemiionization reaction was made, the measured HKEO values showed large differences with
reaction enthalpies derived from available thermodynamic values. This was partly because
3
available thermodynamic values for CeO, CeO+, CeO2 and CeO2+ are not sufficiently well
determined to allow reaction enthalpies for the chemiionization reactions to be reliably determined.
For example, for Ce + O2(X3Σg)  CeO2+ + e
and Ce + O2(a1g)  CeO2+ + e , the heats of
reaction were calculated as – (0.2± 1.0) and – (1.2±1.0) eV compared to HKEO values of (2.4 ±
0.1) and (3.1 ± 0.3) eV. Hence, although the chemielectron bands observed under the Ce +
O2(X3Σg) and the Ce + O2(a1g) reaction conditions were assigned to the above chemiionization
reactions, the discrepancy between the HKEO values and the available reaction enthalpies was
large. The objective of this work, therefore, is to compute selected spectroscopic constants for CeO,
CeO+, CeO2 and CeO2+, to make a comparison with available experimental values, and to compute
the standard reaction enthalpies for Ce + O and Ce + O2 chemiionization reactions in order to
assign the experimental chemielectron bands. Also, by computing relevant parts of the potential
energy curves for the relevant neutral and cationic states, it was hoped that a mechanism for the Ce
+ O 
CeO+ + e and Ce + O2 
CeO2+ + e chemiionization reactions investigated
experimentally could be proposed. Comparison with the lanthanum case can then be made.
Computational Details
The study was performed using the complete active space (CAS) SCF method4 followed by
multiconfigurational second-order perturbation theory (CASPT2).5 Scalar relativistic effects were
included using the Douglas-Kroll Hamiltonian6,7 and the relativistic ANO-RCC basis set,8 where
the primitive set of 25s22p15d11f4g2h functions was contracted to 9s8p5d4f3g2h for cerium and
the primitive set of 14s9p4d3f2g basis functions was contracted to 5s4p3d2f for oxygen. Spin-orbit
coupling effects were computed using the Complete Active Space State Interaction (CASSI)
method,9,10 in which an effective one-electron spin-orbit Hamiltonian, based on the atomic mean
field approximation of the two-electron part, is employed. This approach has been shown to work
successfully
in
a
number
of
applications.11,12,13,14,15,16,17
earlier
4
All
calculations
were performed using the MOLCAS 7.0 program package. 18 In the CASSCF treatment, the
molecular orbitals formed by linear combinations of 6s, 5d and 4f orbitals of Ce with 2p orbitals of
O were included in the active space, resulting in an active space of 8 electrons in 16 orbitals for
CeO and an active space of 12 electrons in 12 orbitals for CeO2. The complete valence active space
in the case of CeO2 consists of 19 orbitals with 12 electrons (all the linear combinations of Ce 6s,
5d and 4f with O 2p). Such an active space however is unaffordable and thus we used a truncated
space constructed of the six bonding and six antibonding Ce-O orbitals. In the subsequent CASPT2
calculations, the [Xe] 4d orbitals of Ce and 1s orbitals of O were kept frozen. In total, 18 electrons
were correlated for CeO, and 24 electrons were correlated for CeO2. C2v symmetry was imposed for
all the species considered. In addition, density functional theory (DFT) calculations were performed
with the hybrid B3LYP functional19 using the same basis sets for Ce and O. The potential energy
curves for several electronic states of CeO and CeO+ were calculated at the CASPT2 level of
theory. The spectroscopic constants for their ground states were determined by using the program
VIBROT in the MOLCAS 7.0 package. CASPT2 geometry optimizations were performed for CeO 2
and CeO2+ followed by vibrational frequency calculations.
To ensure consistency of the results, we also performed calculations with the relativistic
four-component Dirac-Coulomb (DC) Hamiltonian as implemented in the DIRAC code, 20 which
includes spin-orbit coupling effects from the outset, so that mixing of orbitals with different orbital
angular momenta is included already at the Hartree-Fock (HF) level. To facilitate analysis, and for
comparison with results from other conventional approaches, DC-CCSD and DC-CCSD(T)
calculations21 were performed which employed the same active space as in the CASPT2
calculations, with 18 electrons correlated for CeO and 24 electrons correlated for CeO2. The
uncontracted double-zeta basis set consisting of 24s19p13d8f2g basis functions was used, which
has already been shown to be sufficiently large to predict with high accuracy excited states of
metal oxide species. The ionization energies were computed using total energies obtained at the
5
geometries optimized at the CASPT2 level of theory.
Results and Discussion
CeO and CeO+. As the first 4f-element, cerium represents a bridge between the lanthanide and the
5d-block elements. The ground state electronic configurations of Ce, Ce+, and O atoms are [Xe]
6s25d14f1, 1G4, [Xe] 5d24f1, 4H7/2, and [He] 2s22p4, 3P2, respectively. It is worth-mentioning the
“strange” ground state of the Ce atom, which violates the Hund’s rule (the unnatural parity rule).
Moreover, the first ionization is also very unusual, i.e., the ground state of the ion is 4f5d2. The
ionization energy IE(Ce) is strongly influenced by spin-orbit coupling (SOC) effects. As evident
from Table 2, the IE value is 5.67 eV without SOC and 5.53 eV with SOC included (the
experimental value is 5.54 eV27). The ground states of CeO and CeO+ are 3 and 2, respectively.
The computed equilibrium spectroscopic constants (equilibrium bond distance Re, dissociation
energy De, and harmonic vibrational constant e) for the ground states of CeO and CeO+ are
summarized in Table 2, along with the computed first ionization energies of Ce and CeO. The
CASPT2 computed equilibrium distance and vibrational constant of CeO are 1.821 Å and 823 cm -1,
respectively, in good agreement with the experimental values of 1.82009 Å and 829 cm-1.31 Tables
3 and 4 report the spin-free and spin-orbit vertical excitation energies for CeO computed at the
equilibrium bond distance (1.821 Å), along with the composition of each spin state in terms of spinfree states. The 3 ground state has an electron in the 6s and an electron in the 4f orbital of cerium.
The spin-orbit calculation shows that it is a 32 state with  = 2. It is composed of 93 % 3, 5.5 %
3
 and 1.5 % 1. The first ionization energy of CeO computed at the CASPT2 level of theory is
5.26 eV (5.25 eV including SOC), which agrees well with the CCSD(T) value of 5.53 eV as well as
the experimentally obtained values as evident from Table 2. The spin-free dissociation energy (De)
of CeO is 7.69 eV which increases slightly to 7.73 eV due to spin-orbit interaction. However, the
value is lower than the experimental De(CeO) values. An even lower value (6.49 eV) is obtained at
6
the CCSD(T) level of theory. A possible explanation for the high experimentally measured value is
that at the high temperature conditions at which CeO is produced in the experimental studies (e.g.
the vapourization conditions used in high temperature mass spectrometry experiments), low-lying
excited states of CeO are populated. The CISD calculations of Dolg at al., 29 indicate that the 3
excited state has a dissociation energy of 8.14 eV, in close agreement with the experimental De
values. Moreover, according to our CASPT2 calculations this state is only 0.13 eV higher in energy
than the 3 ground state. The computed equilibrium distance of CeO+ is 1.776 Å; experimental
information on the equilibrium bond length of CeO+ is not available. The vibrational wavenumber
e is computed as 885 cm-1, approximately 36 cm-1 higher than the reported experimental value
measured in an argon matrix. The 2 ground state arises from removal of an electron from the 6s
orbital of the 3 state of neutral CeO, and thus the single unpaired electron is left in a nonbonding
4f orbital of cerium. The spin-orbit calculation reveals that it is a 2 state with  = 2.5. Table 5
summarizes the computed spectroscopic constants (equilibrium bond distance Re and harmonic
vibrational constant e) for the ground state and the low-lying excited states of CeO+, along with
the spin-free vertical excitation energies (in cm-1) evaluated at the ground-state equilibrium bond
length (1.776 Å). The corresponding excitation energies obtained on including spin-orbit coupling
effects and the total angular momentum quantum number () of each state are given in Table 6.
Figure 1 shows the low-lying CeO+ states in the CeO bond length range 1.5 – 2.0 Å. The first
electronically excited state of CeO+ has 2 symmetry and is only 0.07 eV higher in energy than the
ground state. In this state, the equilibrium cerium-oxygen bond distance is 1.771 Å and the
harmonic vibrational frequency is 880 cm-1. It should be noted that the 2 state has been found to
be the ground state for CeO+ within the DFT scheme.5 The second excited state has 2 symmetry
and is only 0.19 eV higher than the 2 state. For this 2 state, the equilibrium bond distance is
1.767 Å and the harmonic vibrational frequency is 886 cm-1. Finally, very close in energy is a 2
7
state (0.21 eV higher than the 2 state), for which the Re(Ce-O) is 1.771 Å and e is 882 cm-1. The
fact that these low-lying electronically excited states are so close in energy changes the computed
dissociation energy of CeO+ from 8.10 (spin-free) to 8.01 eV upon including spin-orbit coupling
effects. This value, however, is significantly lower than the experimentally reported values of the
dissociation energy (see Table 2).
CeO2 and CeO2+. From the observed deflection of a molecular beam of CeO2 in an electric
quadrupole field22 and infrared spectroscopy data,23 the neutral CeO2 molecule is known to have a
bent geometry. The angle θ(O-Ce-O) = 146 ± 2 has been derived from the infrared spectrum of
CeO2 in an Ar matrix.23 This value does not include corrections for anharmonicity effects which are
estimated to reduce θ(O-Ce-O) by 5 ± 10.23 Experimental information on the structure of CeO2+ is
not available. Previous nonrelativistic DFT calculations performed by Heinemann at al.24 reported a
linear geometry of CeO2, which upon including a scalar quasirelativistic treatment adopts a bent
structure with a cerium-oxygen bond length of 1.843 Å and bond angle (O-Ce-O) of 131.5. The
CASPT2 optimized geometries for CeO2 and CeO2+, their computed bond dissociation energies
with respect to Ce + O2 and Ce+ + O2, respectively, and the first ionization energy of CeO2 as
obtained in this work are given in Table 7. Neutral CeO2 molecule is computed to have a bent C2v
structure with a cerium-oxygen bond length of 1.816 Å and bond angle θ(O-Ce-O) of 126. The
Ce-O equilibrium bond lengths are virtually the same as the equilibrium bond distance in CeO
(1.821 Å). The geometry is in good agreement with MRCI (Re = 1.813 Å; θ(O-Ce-O) = 115) and
ACPF (Re = 1.838 Å; θ(O-Ce-O) = 118) results reported in reference 24. Energetically, the
optimized linear structure is only 0.18 eV less stable than the bent geometry. According to our
calculations, CeO2 has a 1A1 electronic ground state. CeO2+ is formed by removal of an electron
from the O 2p orbital with concomitant relaxation of the O-Ce-O angle to 180 and shortening of
8
the cerium-oxygen bond length to 1.765 Å.
The ground state of CeO2+ is a 2u+ state. Quasirelativistic DFT and ACPF calculations24
give bond lengths CeO2+ of 1.784 and 1.789 Å, respectively, whereas the bond length at the MRCI
level of theory is 1.756 Å,24 very close to our CASPT2 value. The first excited state (2u) is
computed in this work to be 2.19 eV higher in energy, followed by a 2g+ state (2.64 eV) and 2g
state (3.08 eV). The CASPT2 computed harmonic vibrational wavenumbers for the ground state of
CeO2 are 102, 784 and 822 cm-1. The 102 cm-1 value is the deformation mode (2) and the latter two
values correspond to the antisymmetric (3) and symmetric stretching (1) modes involving the CeO bonds, respectively. For the linear CeO2+, the computed wavenumbers are 141(2), 748(1) and
780(3) cm-1. Neutral CeO2 has been observed in argon matrices and fundamental absorptions
have been measured at 737 cm-1, the 3 stretch and 757 cm-1, the 1 stretch. Experimental
information on the vibrational wavenumbers of CeO2+ is not available.
A bent geometry is also obtained for neutral CeO2 molecule at the DFT/B3LYP level of theory,
with a bond angle of 140 (compared to the CASPT2 value of 126) and a cerium-oxygen bond
length of 1.822 Å (compared to the CASPT2 value of 1.816 Å). Even better agreement is obtained
for the CeO2+ molecule, for which a linear structure is obtained at the DFT/B3LYP level with a
Ce-O bond length (1.758 Å) which deviates by only 0.007 Å from the corresponding CASPT2
value. The DFT computed harmonic vibrational frequencies for CeO2 are 59(2), 790(3) and
794(1) cm-1 and for CeO2+ are 165(2), 772(3) and 752(1) cm-1.
The adiabatic ionization energy (AIE) of CeO2 computed at the CASPT2 and DFT/B3LYP
levels of theory is 8.43 and 8.58 eV, respectively, in very good agreement with the DC-CCSD(T)
result of 8.50 eV. They are all below the experimentally reported IE(CeO2) of 9.7 ± 0.5 eV as
derived in Ref. 2. Nevertheless, the results are very similar to the adiabatic ionization energies
computed at CISD (8.52 eV) and ACPF (8.57 eV) levels of theory published in Ref. 24. Spin-orbit
9
effects on the AIE have been found to be of minor importance. As far as the dissociation energy of
CeO2 is concerned, the calculated CASPT2 De values, relative to Ce and O2(X3g), are 9.28 eV
(spin-free) and 9.19 eV (spin-orbit). The DC-CCSD value is 9.34 eV which increases to 9.96 eV
upon including the perturbative triple excitations, a result which is in excellent agreement with the
experimental value of 9.9 ± 0.5 eV (as derived in Ref. 2). The corresponding De values with respect
to O2(a1g) computed at the CASPT2 level of theory are 10.24 eV (spin free) and 10.15 eV (spinorbit), whereas the DC-CCSD and DC-CCSD(T) energies are 10.39 and 10.89 eV, respectively.
The experimentally derived value is (10.9  0.5) eV2. The energy to dissociate CeO2+ to Ce+ and
O2(X3g) is 6.52 eV (spin free) and 6.28 eV (spin-orbit), compared to the values of 6.39 eV
(CCSD) and 6.77 eV (CCSD(T)). The experimental vale is (5.7  0.5) eV40. The dissociation
energy with respect to O2(a1g) computed at the CASPT2 level of theory is 7.48 eV which
decreases to 7.24 eV upon including spin-orbit effects. The corresponding values with CCSD and
CCSD(T) are 7.52 and 7.83 eV, respectively. The experimental value is (6.7  0.5) eV . Compared
to LaO+ which has a closed shell ground state (1+), in CeO+(3) the additional electron occupies a
nonbonding 4f orbital. Upon formation of the second cerium-oxygen bond, this electron becomes
involved in chemical bonding with the result that CeO2+ is energetically more stabilized compared
to LaO2+. Indeed, the dissociation energy De(CeO2+) of 6.28 eV is much higher than the
corresponding value De(LaO2+) of 3.99 eV.1
Interpretation of the Experimental Chemielectron Spectra
On the basis of the experimentally available values for CeO2 (De(CeO2) = (9.9 ± 0.5) eV
and IE(CeO2) = (9.7 ± 0.5) eV)2,3 , it is not possible to establish if the chemiionization reaction Ce
+ O2  CeO2+ + e- is exothermic. However, the CASPT2 results (De(CeO2) = 9.19 eV and
IE(CeO2) = 8.43 eV) clearly indicate that this chemiionization reaction is exothermic. Similarly,
10
De(CeO) > IE(CeO) from both experiment and theory, indicating that the Ce + O  CeO+ + ereaction is also exothermic (see Table 1). However, the computed enthalpy for the Ce + O2(X3g)
 CeO2+ + e- reaction is -0.76 eV (the corresponding experimental value is -0.2 ± 1.0 eV), which
does not fit the high kinetic energy offset of (2.4 ± 0.1) eV (see Table 1) measured under the Ce +
O2(X3g) reaction conditions. Under these conditions the observed chemielectron band is too high
in electron kinetic energy to be attributed to Ce + O2  CeO2+ + e-, although the low kinetic energy
part will have a contribution from this reaction. Hence the original assignment of the chemielectron
bands in references (2) and (3) for the Ce + O2(X3g) and Ce + O2(a1g) reaction conditions to
reaction (5) for O2(X3Σg), and the corresponding reaction for O2(a1g) respectively, cannot be
correct. Instead, as in the La case (see Ref. 1), it is likely that the following reactions take place
under the Ce + O2(X3g) reaction conditions
Ce + O2(X3Σg)  CeO + O(3P) ------------(5),
H = -2.50 eV
Ce + O(3P)  CeO+ + e-
H = -2.48 eV
then
------------(6),
It is significant that the HKEO value of (2.4 ± 0.1) eV measured under the Ce + O2(X3Σg)
reaction conditions agrees very well with the computed value of -2.48 eV for reaction (6). This
means that the chemielectron band observed under the Ce + O2(X3Σg) conditions should have a
high energy part (from 0.8 to 2.5 eV) that is the same as that for the Ce + O(3P) reaction.
Therefore, it appears that the Ce + O reaction is contributing to the Ce + O2(X3Σg) experimental
band and significantly affecting the shape of the high kinetic energy side. Unfortunately the
experimental values for the chemielectron band from Ce + O(3P) (MPKE=(0.13 ± 0.06) eV and
HKEO = (0.90 ± 0.1)eV) differ significantly from the Ce + O2(X3g) values. However, the signalto-noise obtained for the Ce +O reaction conditions is much lower than that obtained from the Ce +
O2(X3g) reaction conditions (and from the Ce
+ O2(a1g) reaction conditions) and it is clear
11
now that these Ce + O spectra are not good enough to be taken as representative of the Ce + O 
CeO+ + e- chemiionization reaction.
For the Ce + O2(a1g) reaction, as for the La + O2(a1g) reaction, a more intense
chemielectron band is observed at higher electron kinetic energy than under the Ce + O2(X3g)
reaction conditions. It has a MPKE value of (1.83 ± 0.10) eV and a HKEO value of (3.1 ± 0.3) eV.
The chemiionization reaction Ce + O2(a1g)  CeO2+ + e- is exothermic with a computed reaction
enthalpy of -1.72 eV obtained from CASPT2 calculations. The only possible explanation for the
significantly higher HKEO value as compared to the calculated enthalpy of the Ce + O2(a1g) 
CeO2+ + e- reaction, is that reaction (5)
Ce + O2(a1g)  CeO + O(1D, 3P) ------(5),
H = -3.46 eV
is again followed by
Ce + O(1D)  CeO+ + e- ------------
(6),
H = -4.42 eV
Again as in the La case, in order for the HKEO value from the Ce + O2(a1g) reaction conditions
to be higher than for the Ce + O2(X3g) reaction conditions, some of the excess energy from
reaction (5) must be available for reaction (6). It is proposed that, as in the La + O2(a1g) case, this
is achieved by O(1D) production. O(1D) is known to be long-lived with respect to the O(3P) ground
state. The reaction enthalpy of -4.42 eV of reaction (6) compares with the observed HKEO value
of (3.1 ± 0.30) eV implying that the chemielectron onset has not been observed because of
unfavourable Franck-Condon factors in the band onset region.
Hence, the results from our calculations indicate the same overall interpretation of the
chemiionization reactions as we put forward for the La case applies to the reactions of cerium with
O2(X3g), O2(a1g), and O(3P), with the only difference being that the Ce + O2  CeO2+ + ereaction is also contributing to the lower kinetic energy region of the chemielectron bands observed
under the Ce + O2(X3Σg) and Ce + O2(a1g) reaction conditions. Reaction (5) for Ce + O2(X3Σg) is
12
sufficiently exothermic to produce O(3P) and O(1D) but a higher O(1D):O(3P) ratio must be
produced in the more exothermic Ce + O2(a1g) reaction.
Also, the CeO+ observed in the mass spectra from the Ce + O2(X3Σg) and Ce + O2(a1g) reaction
conditions must arise from chemiions produced from reaction (5) followed by reaction (6), whereas
the CeO2+ observed in the mass spectra must be produced both from the chemiionization reaction
Ce + O2  CeO2+ + e- as well as ion-molecule reactions involving CeO+ which occur in the ion
extraction region of the mass spectrometer (e.g. reaction (7) and reaction(11); see Table 1).
Finally, we can provide an assignment for the vibrational structure observed in the Ce + O2
chemielectron band 2,3. The structure observed with separations of (790 ± 30) cm-1 in the region of
the band maximum (0.98 ± 0.04) eV (HKEO value (2.4 ± 0.1) eV) must be due to chemiionization
from a turning point in the incoming channel to high vibrational levels of the ground state of CeO+
i.e. Ce + O  CeO*  CeO+ + e. The computed harmonic vibrational wavenumber for the
ground state of CeO+, a 2 state, is 885 cm-1 and the separation between the vibrational levels of
CeO+ must be reduced to (790 ± 30) cm-1 by anharmonicity in the region of the chemielectrom
band maximum.
Potential Curves for CeO, CeO*, CeO+ and CeO+*.
A number of excited states of CeO and CeO+ were investigated in order to understand the
chemiionization mechanisms of the Ce + O  CeO+ + e- reaction. Singlets, triplets and quintets
have been computed for CeO, and doublets and quartets have been computed for CeO+. As
discussed above, CeO and CeO+ have many low-lying excited states of the , , , and  types.
The low-lying electronic states of CeO+, which are likely to be important for the chemiionization
study, are shown in Figure 1. For CeO, 10 singlets, 10 triplets and 4 quintets were computed for
each of the above irreducible representations and were included in the spin-orbit calculations. So
many states had to be included because of the need to describe the chemiionization region
13
occurring at ca. 6.5 eV above the CeO ground state. The potential energy curves of the ground
states of CeO and CeO+ as well as the low-lying excited states of CeO+ are shown in Figure 2 and
an enlarged region of this figure of particular interest (the region where the chemiionization occurs)
is given in Figure 3. The reactants Ce and O approach each other (the horizontal lines shown for
the Ce and O(3P) reagents and the Ce and O(1D) reagents) until the left-hand turning point of a
CeO* curve is reached. Autoionization then occurs in accordance with the Franck-Condon principle
and the most intense transition from the left-hand turning point of the CeO* curve is the vertical
transition onto the CeO+ ground state curve where the overlap of the initial and final vibrational
wavefunctions is largest. Thus, the maximum intensity of the chemielectron band will occur at an
energy corresponding to the vertical energy difference between the CeO* curve and the CeO+ curve
at the CeO* classical turning point. From spin conservation, reaction between Ce(1G) + O(1D) can
only give singlet CeO* excited states for chemiionization, whereas Ce(1G) and O(3P) can give rise
to triplet CeO* states. The autoionization process CeO*  CeO+(2) + e- is a spin-allowed process
if S between the initial (CeO excited state) and final (ion plus electron) states is zero. Moreover,
the  = 0 selection rule has to be fulfilled between the initial and the final state.
For the Ce + O(3P) chemiionization reaction, the horizontal (solid) line from the reactants
crosses CeO* states at internuclear distances at ca. 1.62 Å. These are quintet states of CeO located
ca. 1.66 eV vertically above the CeO+ ground state. However, the autoionization process 5CeO* 
CeO+(2) + e- is spin-forbidden as the S = 0 selection rule is not satisfied. The first CeO* state
that fulfills both selection rules is encountered at ca. 1.55 Å and is located 0.68 eV above the CeO+
ground state, in reasonable agreement with the experimental MPKE value of (0.90 ± 0.04) eV.
For the Ce + O(1D) chemiionization reaction… this part is not finished since the singlet
states I have computed so far are not crossing the dissociation limit. I am running calculations with
14
more states.
The calculations show that the reaction Ce(1G) + O2(X3Σg)  CeO(X3) + O is sufficiently
exothermic to produce O(3P) and O(1D), with O(3P) being the dominant product. Chemiionization
occurs via Ce(1G) + O(3P)  CeO+(X2) + e- to give a chemielectron band with a MPKE value of
0.90 ± 0.04 eV. In contrast, Ce(1G) + O2(a1g)  CeO(X3) + O produces a significant amount of
O(1D) as indicated by the higher energy chemielectron band from the reaction Ce(1G) + O(1D) 
CeO+(X2) + e-, with an experimental MPKE value of 1.83 ± 0.10 eV.
Conclusions
Multiconfigurational quantum chemical methods (CASSCF/CASPT2) have been used to
establish the chemiionization reactions that occur for the Ce + O(3P), Ce + O2(X3Σg), and Ce +
O2(a1g) reaction conditions. As was found for the U + O2 reaction25 and the La + O2 reaction,1
chemiionization for Ce + O2(X3Σg) occurs predominantly via a two-step process, a rapid first step
Ce + O2  CeO + O(3P) (reaction (5)) followed by Ce + O(3P)  CeO+ + e- (reaction (6)). For Ce
+ O2(a1g), chemiionization occurs via the same two step mechanism. In this case, the experimental
chemielectron spectra can be explained by production of O(1D) from reaction (5) followed by
production of chemielectrons via Ce + O(1D)  CeO+ + e-. For all reaction conditions studied, the
primary chemiionization reaction is Ce + O  CeO+ + e-. However, in contrast to the La case, the
reaction Ce + O2  CeO2+ + e- is exothermic for both O2(X3Σg) and O2(a1g) , and therefore
contributes in the lower kinetic energy regions of the chemielectron spectra recorded for the Ce +
O2(X3Σg) and Ce + O2(a1g) reaction conditions.
Accurate potential energy curves have been computed for the ground states of CeO and
CeO+, and a number of excited states of CeO, to determine the mechanisms of the Ce + O(3P) and
Ce + O(1D) chemiionization reactions which give CeO+ and electrons. Calculated chemielectron
band maxima (MPKE values) and high kinetic
energy offsets (HKEO values) for the Ce + O
15
 CeO+ + e- reactions considered provide strong support for the chemiionization mechanisms
proposed.
Acknowledgment. This work was supported by the Swiss National Science Foundation (grants n.
200021-111645/1 and 200020-120007). JMD thanks NERC UK for support.
Table 1: Experimental and Computed Reaction Enthalpies (eV) for Possible Reactions (see
text).
16
Reaction
1.
2.
3.
4.
Ce + O2  CeO2+ + eCe + O2  CeO+ + OCe + O2  CeO+ + O + eCe + O2  Ce+ + O2-
Reaction Enthalpy
from Ref. [2]
-0.2 ± 1.0
0.6 ± 1.0
2.1 ± 1.0
5.1 ± 0.1
5. Ce + O2  CeO + O
6. Ce + O  CeO+ + e7. CeO+ + O2  CeO2+ + O
8. CeO2+ + Ce  CeO+ + CeO
9. CeO2+ + M  CeO+ + O + M
10. CeO + O  CeO2+ + e11. CeO+ + O + M  CeO2+ + M
Note that the first four reactions (1) – (4)
Computed values
w.r.t O2 (X3g)
-0.76
1.39
2.76
5.23
Computed values
w.r.t O2 (a1g)
-1.72
0.42
1.79
4.27
-3.1 ± 0.2
-3.0 ± 0.7
2.8 ± 1.7
-5.9 ± 1.9
2.9 ± 1.7
2.9 ± 1.2
-2.50
-3.46
-2.48
-4.42
1.73
0.76
-4.22
3.51
1.74
-3.51
are primary ionization reactions, whereas reactions (5) –
(11) are neutral or ion-molecule processes. The separation of the reactions in this way follows the
approach used in the previous experimental paper (Ref. 2).
Table 2. Computed spectroscopic constants for the ground states of CeO and CeO+. Equilibrium
bond distances (Re) in Å, dissociation energy (De) in eV, and harmonic vibrational constants (e) in
17
cm-1. First ionization energy (IE) for Ce and CeO is in eV. Previous calculations along with
available experimental data are also listed.
System
Ce
Method
CASPT2
CASPT2 + SO
ACPF
ACPF + SO
Expt.
Re
CeO
CASPT2
CASPT2 + SO
CCSD(T)
DC-CCSD(T)
CISD
DFT/B3LYP
Expt.
1.821
CASPT2
CASPT2 + SO
DC-CCSD(T)
DFT/B3LYP
Expt.
1.776
CeO+
1.819c)
1.827d)
1.806e)
1.820f)
De
e
IE
5.67
5.53
6.07a)
5.86a)
5.54b)
7.69
7.73
8.26c)
6.49
7.28d)
8.23e)
8.23f)
8.19 ± 0.18g)
8.20 ± 0.22h)
8.22 ± 0.08i)
8.24 ± 0.08j)
8.30 ± 0.14k)
823
5.26
5.25
5.53
5.53
8.10
8.01
6.25
g)
8.80 ± 0.16
8.94 ± 0.17k)
8.83p)
a) Ref. [26]
b) Ref. [27]
c) Ref. [28]
d) Ref. [29]
e) Ref. [30]
f) Ref. [31]
g) Ref. [32]
18
838d)
821e)
f)
862 /829l)/808m)
885
1.759e)
This work unless otherwise indicated.
849c)
912e)
849m)
5.48e)
4.9 ± 0.1k),n)
5.2 ± 0.2o)
5.2 ± 0.5h)
4.90p)
h) Ref. [2]
i) Ref. [33]
j) Ref. [34]
k) Ref. [35]
l) Ref. [36], taking wexe = 2.5 cm-1
m) Ref. [37], from measurements in an argon matrix
n) Ref. [38]
o) Ref. [39]
p) Ref. [40]
Table 3. Spin-free vertical excitation energies (cm-1) for CeO and the electronic configuration for
each spin-free state. The computed energies are evaluated at the equilibrium bond distance (1.821
Å).
19
State
3

1

3

3

1

1

3

3

1

1

Composition
(6s)1(4f)1
(6s)1(4f)1
(6s)1(4f)1
(6s)1(4f)1
(6s)1(4f)1
(6s)1(4f)1
(6s)1(4f)1
(6s)1(4f)1
(6s)1(4f)1
(6s)1(4f)1
E (cm-1)
0
453
1066
1411
1533
1648
1980
2583
2855
2976
Table 4. Spin-orbit vertical excitation energies (cm-1) for CeO and composition of each spin-state
in terms of spin-free states.
20
 value
2
3
1
2
3
2
4
3
3
2
3
2
0
1
2
1
0
Composition (%)
3
(93), 3(5.5), 1(1.5)
3
(55), 1(37), 3(8)
3
(87), 3(7), 1(5)
3
(51), 1(34), 3(13)
3
(53), 3(26), 3(21)
3
(38), 1(19), 3(15), 3(14), 1(13)
3
(89), 3(7), 1(4)
3
(30), 3(47), 3(23)
1
(42), 3(31), 3(16), 1(5), 3(5)
1
(31), 3(58), 3(10)
3
(91), 1(6), 3(2)
1
(51), 3(40), 3(6), 3(1)
3
(44), 3(56)
3
(64), 3(31), 3(4), 1(1)
3
(86), 3(8), 1(6)
1
(74), 3(10), 3(6), 3(8)
1
(65), 3(35)
E (cm-1)
0
171
1378
1503
1971
2089
2079
2333
2517
2671
3300
3453
4428
4447
4509
4668
4978
Table 5. Computed spectroscopic constants for the ground state and the low-excited states of CeO+,
along with the vertical excitation energies evaluated at the equilibrium bond distance (1.776 Å).
21

we
E
(cm-1) (cm-1)
885
0
2
Re
(Å)
1.776

we
E
(cm-1) (cm-1)
882
526
2
Re
(Å)
1.771

we
E
(cm-1) (cm-1)
882
1655
2
Re
(Å)
1.771

we
E
(cm-1) (cm-1)
886
1560
2
Re
(Å)
1.767
Table 6. Vertical excitation energies (cm-1) for CeO+ calculated at the CASPT2 level of theory
including spin-orbit coupling effects. The computed energies are evaluated at the equilibrium bond
distance (1.776 Å).
22

2.5
1.5
1.0
3.5
2.5
1.5
0.5
E (cm-1)
0
821
1446
2276
2832
3625
3792
Table 7. Spectroscopic constants for the ground state of CeO2 and CeO2+. Equilibrium bond
distance (Re) in Å, angles in (deg), dissociation energy (De) and ionization energy (IE) in eV, and
harmonic vibrational constant (e) in cm-1. The dissociation energies of CeO2 and CeO2+ are given
23
with respect to Ce + O2 and Ce+ + O2, respectively. The available experimental data are also listed.
System
Method
CeO2
C2v
CASPT2
1.816
CASPT2 - SO
DC-CCSD
DC-CCSD(T)
DFT/B3LYP
1.822
Expt.
1.88a)
CeO2+
linear
Re
(O-Ce-O)
126
140
146 ± 2a)
CASPT2
1.765
180
CASPT2 - SO
DC-CCSD
DC-CCSD(T)
DFT/B3LYP
1.758
180
Expt.
This work unless otherwise indicated.
De
O2(X g) O2(a1g)
9.28
10.24
9.19
10.15
9.34
10.39
9.96
10.89
3
10.07 ± 0.65b)
9.81 ± 0.22c)
9.9 ± 0.5d)
6.52
6.28
6.39
6.77
7.48
7.24
7.52
7.83
e
IE
102(2), 784(3), 822(1)
8.43
59(2), 790(3), 794(1)
264(2), 737(3), 757(1)a),e)
141(2), 748(1), 780(3)
165(2), 752(1), 772(3)
5.68h)
a) Ref. [41]
b) Ref. [42]
c) Ref. [43]
d) Ref. [2]
e) Ref. [37]
f) Ref. [39]
g) Ref. [44]
h) Ref. [40]
i) Ref. [24]
24
8.15
8.50
8.58
9.7 ± 0.5b),d)
10.3 ± 0.2f)
9.5 ± 0.5g)
9.80h)
9.1 ± 0.3i)
Figure 1. Spin-free potential-energy curves for the ground state (black) and the low-lying excited
states of CeO+.
25
Figure 2. Spin-free potential-energy curves for the ground states of CeO (red) and CeO+ (black) as
well as the low-lying excited states of CeO+. The solid and dotted lines correspond to Ce + O(3P)
and Ce + O(1D) calculated dissociation limit, respectively.
26
Figure 3. Enlarged region of the spin-free potential-energy curves for the ground and low-lying
states of CeO+ and a number of excited states of CeO in the region where the chemiionization
reactions occur. The solid and dotted horizontal lines correspond to Ce + O(3P) and Ce + O(1D)
calculated dissociation limits, respectively.
27
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