A theoretical study of the ground state and lowest excited states of PuO0/+/+2 and PuO20/+/+2

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Reference

A theoretical study of the ground state and lowest excited states of PuO0/+/+2 and PuO20/+/+2

LA MACCHIA, Giovanni, et al.

Abstract

The ground and excited states of neutral and cationic PuO and PuO2 have been studied with multiconfigurational quantum chemical methods followed by second order perturbation theory, the CASSCF/CASPT2 method. Scalar relativistic effects and spin–orbit coupling have been included in the treatment. As literature values for the ionization energy of PuO2 are in the wide range of B6.6 eV to B10.1 eV, a central goal of the computations was to resolve these discrepancies; the theoretical results indicate that the ionization energy is near the lower end of this range. The calculated ionization energies for PuO, PuO+ and PuO2+ are in good agreement with the experimental values.

LA MACCHIA, Giovanni, et al . A theoretical study of the ground state and lowest excited states of PuO0/+/+2 and PuO20/+/+2. Physical Chemistry Chemical Physics , 2008, vol. 10, no. 40, p. 7278-7283

DOI : 10.1039/b810744k

Available at:

http://archive-ouverte.unige.ch/unige:3566

Disclaimer: layout of this document may differ from the published version.

A theoretical study of the ground state and lowest excited states of PuO

and PuO

w

Giovanni La Macchia,

Ivan Infante,

Juraj Raab,

John K. Gibson*

and Laura Gagliardi*

Received 24th June 2008, Accepted 24th September 2008

First published as an Advance Article on the web 3rd November 2008 DOI: 10.1039/b810744k

The ground and excited states of neutral and cationic PuO and PuO2have been studied with multiconfigurational quantum chemical methods followed by second order perturbation theory, the CASSCF/CASPT2 method. Scalar relativistic effects and spin–orbit coupling have been included in the treatment. As literature values for the ionization energy of PuO₂are in the wide range ofB6.6 eV toB10.1 eV, a central goal of the computations was to resolve these discrepancies; the theoretical results indicate that the ionization energy is near the lower end of this range. The calculated ionization energies for PuO, PuO⁺and PuO₂⁺are in good agreement with the experimental values.

Introduction

The spectroscopy and thermodynamics of actinide-containing molecules pose great challenges to both experimentalists and computational chemists. Among actinides, uranium and thorium species are certainly widely studied. Plutonium sys- tems have also been the subject of extended research. In particular, thermodynamics of elementary plutonium oxide molecules PuO_x(x= 1,2) have been studied experimentally by one of us (Gibson and co-workers^1–4), and also recently by Capone and co-workers.^5,6

The value of the first ionization energy (IE) of PuO2 has recently become an issue of particular controversy. An early Knudsen effusion electron impact (EI) study⁷ provided a IE(PuO₂) = 9.4 0.5 eV; a more recent EI study⁵yielded IE(PuO2) = 10.10.1 eV. These two values are remarkably some 3–4 eV higher than the spectroscopically measured IE(UO2) = 6.128 0.003 eV.⁸Also, they are not consistent with the recently determined bond energy of PuO2+

.¹In view of the anomalously high literature values resulting from EI experiments, Santoset al.¹employed an electron-transfer bracketing approach to establish that IE(PuO2) is in the range 6.91–7.14 eV, and thus assigned IE(PuO2) = 7.030.12 eV;

this latter value is in full accord with the known thermo- dynamics values of neutral and ionized plutonium oxides.

Given the reduced propensity for transneptunium actinides to exist in oxidation states above IV, particularly as compared with uranium, and that plutonium is in the IV oxidation state in PuO2, it seems reasonable that IE(PuO2) should be some- what higher than both IE(PuO) = 6.1 0.2 eV^2,4 and IE(UO₂) = 6.13 eV.⁸ Furthermore, the following trend for

the ionization energies across the series of actinide dioxides, IE(AnO₂)/eV, appears entirely reasonable, where the cited values (ranges), except that for IE(UO₂), were obtained by Santos and co-workers using the electron-transfer bracketing method:

UO₂/6.13 eV⁸oNpO₂/6.330.18 eV⁴ oPuO2/7.030.12 eV¹ oAmO2/7.230.15 eV²

Considering the substantial discrepancy between the value for IE(PuO₂) determined from their EI measurements, 10.1 eV, and the range for IE(PuO₂) subsequently established by electron-transfer bracketing, Capone et al. carried out additional high-temperature Knudsen effusion experiments.⁶ To arrive at IE(PuO2), approximate values for D(Pu–O) = 7.1 eV and IE(PuO) = 6.2 eV were assumed;⁶this latter value for IE(PuO) is close to the experimental value of 6.10.2 eV determined by Santoset al.^2,4A value for IE(PuO2) was then derived by presuming that equilibrium was achieved between PuO⁺and PuO2+

ions at high temperature in a Knudsen cell, and further that their equilibrium concentrations in the cell could be measured by monitoring with a mass spectrometer the ions which were purported to be effusing from the cell.⁶ From this so-called ‘‘new type of experiment’’⁶ it was ulti- mately inferred that IE(PuO2) = (IE(PuO) + 0.420.005 eV) E(6.2 eV + 0.42 eV)E6.6 eV, which is only 0.3 eV below the lower limit of the previously established range of 6.91–7.14 eV.¹ The validity of the experiment performed by Capone et al.,⁶ and particularly the evaluation by which IE(PuO2) = 6.6 eV was obtained, has been a matter of discussion.⁹ Of particular concern is the necessary and novel assumption that thermodynamic equilibrium between PuO⁺ and PuO₂⁺ was achieved and measured under the conditions of the high- temperature Knudsen effusion experiments.^6,9 In view of the uncertainties associated with the derivation of IE(PuO2) = 6.6 eV, the somewhat higher experimental range, 6.91–7.14 eV, as obtained from the well-established and demonstrated

aDepartment of Physical Chemistry, University of Geneva, 30 Quai Ernest Ansermet, CH-1211 Geneva, Switzerland.

E-mail: laura.gagliardi@unige.ch

bChemical Sciences Division, Lawrence Berkeley National

Laboratory, Berkeley, CA 94720, USA. E-mail: JKGibson@lbl.gov wElectronic supplementary information (ESI) available: Total energy (a.u.) for the species reported in Table 1. See DOI: 10.1039/b810744k

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

technique of electron-transfer bracketing¹should be consid- ered the more reliable. A direct spectroscopic determination of IE(PuO2) would definitively resolve this issue. The accuracy of most current computational methods may not be fully adequate to definitively resolve the 0.3 eV discrepancy between the two low-range experimental values for IE(PuO₂), 7.03 0.12 eV¹ andB6.6 eV,⁶ but their accuracy is certainly ade- quate to resolve theB3–4 eV discrepancy between this lower range and the much higher values obtained from the earlier EI experiments, 9.4 eV¹and 10.1 eV.⁵

Computationally, Archibong and Ray¹⁰ have performed a study of the ground state and some excited states of PuO₂and PuN₂ using the coupled cluster method CCSD(T) and the complete active space second-order perturbation theory method (CASPT2). They have predicted the ground state of PuO₂to be a⁵S⁺_g, the ground state of PuN₂to be a³P_g, and computed a vertical ionization energy of 9.92 eV for PuO₂at the CCSD(T) level of theory; they did not report an adiabatic ionization energy, but implied that it should not be signifi- cantly lower than the vertical value. Clavague´ra-Sarrioet al.¹¹ have performed density functional theory (DFT) and CASPT2 calculations on PuO₂²⁺and PuN₂and they have predicted a

3H_gground state for PuN₂, in disagreement with the ground state predicted by Archibong and Ray.¹⁰ More recently Infanteet al.¹²computed the electronic spectrum of PuO22+

using the novel intermediate Hamiltonian Fock-space coupled cluster (IH-FSCC) method and achieved a significant improvement with respect to the CASPT2 results of Clavague´ra-Sarrioet al.¹¹Previous theoretical work has also been performed by Ismail et al.¹³ and Maronet al.¹⁴on the PuO22+

species.

It seems that many unresolved questions still exist for Pu-containing small molecules, particularly the elementary monoxide and dioxide molecules. We have thus decided to perform accurate quantum chemical calculations on PuO and PuO2in order to explore the nature of their ground and lowest excited states, and determine their first and second ionization energies.

Computational methods

All the calculations were performed using the MOLCAS 7.1 package.¹⁵ Basis sets of atomic natural type (ANO)^16,17 including relativistic corrections were employed. They were contracted to 9s8p6d5f2g1h and 4s3p2d1f on plutonium and oxygen, respectively. We performed density functional theory (DFT) based calculations using the B3LYP functional and also multiconfigurational calculations followed by second order perturbation theory, CASSCF/CASPT2. The complete active space CASSCF method¹⁸ is used to generate wave functions for a predetermined set of electronic states. Dynamic correlation is added using second-order perturbation theory, CASPT2.¹⁹ Scalar relativistic effects were included using a Douglas–Kroll–Hess Hamiltonian. Spin–orbit coupling effects were estimated using the complete active space state interac- tion (CASSI) method,²⁰ in which an effective one-electron spin–orbit (SO) Hamiltonian, based on the atomic mean field approximation of the two-electron part, is employed. All CASSCF wave functions of the appropriate symmetries are

used as basis functions to set up the SO Hamiltonian, and CASPT2 energies are used in the diagonal elements. This approach has been shown to work successfully in a number of earlier applications.^21–34 In the CASSCF calculations the complete active space for PuO, PuO⁺ and PuO²⁺ contains 12, 11 and 10 electrons, respectively, distributed into 16 orbitals, which are linear combinations of the thirteen orbitals coming from the 5f, 6d and 7s shells of plutonium, and the three 2p orbitals of oxygen. In the PuO2, PuO2+

, PuO22+

cases the ideal active space would contain again thirteen Pu orbitals and six 2p orbitals from the two oxygen atoms. This would yield a complete active space of 19 orbitals with 16 electrons (in case of PuO₂): 8 electrons from plutonium and the other 8 from the oxygen atoms. Such an active space is too big, and we thus decided to truncate the space by removing twop_gbonding orbitals and the corresponding antibonding orbitals, and ones* antibonding orbital. This gives a complete active space that contains 12, 11 and 10 electrons for PuO₂, PuO2+

, PuO22+

, respectively, distributed into 14 orbitals (see the discussion below of the nature of the orbitals in details). In all subsequent CASPT2 calculations the orbitals up to and including the 5d on plutonium and 1s on oxygen have been kept frozen, while the remaining valence orbitals have been correlated. In order to be more definitive on the value of the ionization energy of PuO2, we have also per- formed a series of CASSCF/CASPT2 calculations on PuO2

with active spaces of increasing size: 4/10, 8/12, 12/14, 12/15 and 12/17. The last three active spaces represent increasing size truncations of the full valence 16/19 active space (all the linear combinations of Pu 5f, 6d and 7s with O 2p), which is unaffordable.

We computed electronically excited states lying at most about 0.5 eV above the ground state. All calculations were performed imposingC_2vsymmetry.

Results

In Table 1 the spectroscopic constants of the ground states of neutral and cationic PuO and PuO₂are reported. PuO has a

7P(O= 0) ground state with a bond distance of 1.82, 1.83 A˚

according to CASPT2 and B3LYP, respectively; PuO⁺has a

6P (O = 0.5) ground state with a bond distance of 1.78, 1.79 A˚, according to CASPT2 and B3LYP, respectively. PuO2

has a⁵S⁺_g (O= 1_g) ground state. The molecule is linear and the Pu–O bond distance is, according to our best estimate, 1.74 A˚. This compares with 1.77 A˚ previously obtained for the U–O distance in UO2,^25,30and with previous but less accurate calculations which predicted the Pu–O bond distance to be longer than 1.85 A˚.¹⁰PuO₂⁺has a⁴F_uO= 1.5_uground state and a Pu–O bond distance of 1.70 A˚. PuO₂²⁺has a³H_gO= 4g ground state and a Pu–O bond distance of 1.68 A˚. In Tables 2 and 3 the spin–orbit (SO) and spin-free (SF) excita- tion energies, respectively, of the lowest electronic states of PuO, PuO⁺and PuO²⁺are reported. In Tables 4 and 5 the SO and SF excitations, respectively, of PuO₂, PuO₂⁺ and PuO₂²⁺ are reported. In Table 6 the vertical excitation en- ergies (in cm ¹) for PuO22+

calculated at the SO-CASPT2 level are reported, together with values obtained by previous theoretical and experimental studies. We note the better

agreement of the present values with experiment overall, compared to previous theoretical studies. Table 7 shows the calculated values for the first and second ionization energies

for PuO and PuO₂. Comparisons with available experimental values and previous theoretical estimations are also presented there.

Discussion

PuO, PuO⁺and PuO²⁺

To our knowledge this is the first theoretical work that studies the plutonium monoxide species. The first IE of PuO from SO-CASPT2, 6.17 eV (see Table 7), is in good agreement with the experimental value of 6.10.2 eV obtained by Santoset al.,^2,4 who employed a reactivity method developed and demonstrated by Schwarz and co-workers for lanthanide oxide ions.³⁵ The ground state of PuO, O = 0, is mainly made up of two dominant spin-free electronic states, 44% of⁷Pand 26% of⁷S.

The ⁷P state is characterized by two electronic config- urations: (7s)¹(5fp)¹(5fd)²(5fj)² and (7s)¹(5fs)¹(5fd)¹(5fp)¹(5fj)². The electron removed in the process of ionization in order to form PuO⁺ belongs to the Pu 7s orbital, which has only little SO coupling. For this reason, the IE of PuO does not change very much if one includes spin–orbit coupling in the calculation: the SF-CASPT2 value is 6.16 eV and the SO-CASPT2 value is 6.17 eV. The ground state of PuO⁺,O= 0.5, has a composition that resembles the neutral species,⁶P(44%) and⁶S(24%), with the only absence of the 7s electron. The Pu–O bond distance is similar in the neutral and ionic species, 1.820 A˚ in PuO and 1.789 A˚ in PuO⁺. The IE of PuO computed at the SF-DFT/

B3LYP level is equal to 6.31 eV, a value which is very close to the multi-reference SF-CASPT2 result and well inside the experimen- tal uncertainty range, 5.9–6.3 eV.^2,4

Table 1 Pu–O bond distance (R in A˚) and harmonic vibrational frequency (oin cm ¹) for the ground state of neutral and cationic PuO and PuO2wcalculated with different methods, without and with the inclusion of spin–orbit (SO) coupling

Species State Method R(Pu–O) o

PuO ⁷P B3LYP 1.834 820

7P CASPT2(12,16) 1.818 767

O= 0 SO-CASPT2 1.820 856

PuO^{+ 6}P B3LYP 1.788 899

6P CASPT2(11,16) 1.784 1046

O= 0.5 SO-CASPT2 1.789 881

PuO^{2+ 6}G B3LYP 1.720 961

6G CASPT2(10,16) 1.724 872

O= 2.0 SO-CASPT2 1.731 872

PuO2 5S⁺g HF¹⁰ 1.883 —

5S⁺g B3LYP 1.818 773

5S⁺g CCSD¹⁰ 1.866 769

5S⁺g CCSD(T)¹⁰ 1.870 792

5S⁺g CASSCF(8,8)¹⁰ 1.866 751

5S⁺g CASPT2(8,8)¹⁰ 1.846 —

5S⁺g CASPT2(12,14) 1.792 812

O= 1g SO-CASPT2 1.744 837

PuO2+ 4

Fu B3LYP 1.718 949

4Fu CASPT2(11,14) 1.703 957

O= 1.5u SO-CASPT2 1.704 962

PuO22+ 3Hg B3LYP 1.678 1004

3Hg CASSCF(2,4)¹³ 1.609 —

3Hg CASSCF(8,10)¹³ 1.639 1110

3Hg CASPT2(2,4)¹⁴ 1.685 —

3Hg CASPT2(2,4)¹¹ 1.697 1074

O= 4g SO-CASPT2¹¹ 1.699 1065

3Hg IHFSCC²³ 1.644 1144

3Hg CASPT2(10,14) 1.675 1017

O= 4g SO-CASPT2 1.675 1019

Table 2 Spin–orbit vertical excitation energies (cm ¹) for PuO, PuO⁺and PuO²⁺, and composition of each spin-state in terms of spin-free states.

The analysis has been performed at the equilibrium bond distance (in parentheses) of the ground state for each species

PuO (1.820 A˚) PuO⁺(1.789 A˚) PuO²⁺(1.731 A˚)

O Composition (%) DE O Composition (%) DE O Composition (%) DE

0 ⁷P(44),⁷S(26),⁷D(12),⁷D(10) 0 0.5 ⁶P(44),⁶S(24),⁶D(12),⁶D(9) 0 2 ⁵F(37),⁵G(36),⁵D(20) 0 1 ⁷P(41),⁷S(23),⁷D(12),⁷D(9) 209 1.5 ⁶P(28),⁶S(12),⁶D(14),⁶F(12) 324 1 ⁵F(29),⁵P(21),⁵D(21),⁵D(14) 469 2 ⁷P(30),⁷D(25),⁷S(15),⁷F(9) 868 2.5 ⁶F(30),⁶D(14),⁶D(11),⁶P(10) 1401 3 ⁵H(24),⁵G(43),⁵F(21) 677 0 ⁷F(36),⁷D(21),⁷D(16),⁷P(9) 1264 0.5 ⁶F(34),⁶D(17),⁶P(28) 1793 0 ⁵P(48),⁵S(31),⁵D(10),⁵D(10) 1129 1 ⁷F(28),⁷D(12),⁷P(10),⁷G(10) 1474 1.5 ⁶P(30),⁶S(23),⁶G(14),⁶G(11) 2131 4 ⁵G(42),⁵H(32),⁵F(16) 2747 3 ⁷F(26),⁷P(21),⁷D(14),⁷D(12) 2029 3.5 ⁶F(38),⁶D(16),⁶D(9),⁶G(10) 3158 2 ⁵P(24),⁵D(22),⁵G(42) 3292 2 ⁷F(20),⁷S(19),⁷G(13),⁷G(11) 2276 2.5 ⁶P(28),⁶S(21),⁶G(15),⁶G(11) 3648 1 ⁵S(33),⁵F(30),⁵P(33) 3483 0 ⁷F(60),⁷S(13),⁷D(6),⁷D(4) 2622 0.5 ⁶F(34),⁶D(16),⁶P(30) 3886 3 ⁵H(40),⁵F(21),⁵D(25) 3854

Table 3 Spin-free vertical excitation energies (cm ¹) for PuO, PuO⁺and PuO²⁺, and dominating electronic configuration for each spin-free state.

The analysis has been performed at the equilibrium bond distance (in parentheses) of the ground state for each species

PuO (1.818 A˚) PuO⁺(1.784 A˚) PuO²⁺(1.724 A˚)

7P (7s)¹(5fp)¹(5fd)²(5fj)² (7s)¹(5fs)¹(5fd)¹(5fp)¹(5fj)²

0 ⁶P (5fp)¹(5fd)²(5fj)² 0 ⁵G (5fp)¹(5fd)²(5fj)¹ 0

7S (7s)¹(5fs)¹(5fd)²(5fj)² 67 ⁶S (5fs)¹(5fd)²(5fj)² 453 ⁵F (5fs)¹(5fd)²(5fj)¹ 150

7D (7s)¹(5fp)²(5fd)¹(5fj)² 715 ⁶D (5fp)²(5fd)¹(5fj)² 1078 ⁵P (5fp)¹(5fd)¹(5fj)² 950

7F (7s)¹(5fp)²(5fd)²(5fj)¹ 885 ⁶F (5fp)²(5fd)²(5fj)¹ 1092 ⁵D (5fs)¹(5fd)¹(5fj)² +(5fp)¹(5fd)²(5fj)¹

1234

7D (7s)¹(5fp)²(5fd)¹(5fj)² 1467 ⁶D (5fp)²(5fd)¹(5fj)² 2217 ⁵D (5fs)¹(5fd)¹(5fj)² +(5fp)¹(5fd)²(5fj)¹

1284

7G (7s)¹(5fs)¹(5fp)¹(5fd)²(5fj)¹ 1890 ⁶F (5fp)²(5fd)²(5fj)¹ +(5fs)¹(5fp)¹(5fd)¹(5fj)²

2872 ⁵S (5fp)²(5fj)²+(5fd)²(5fj)² 1620

7G (7s)¹(5fs)¹(5fp)¹(5fd)²(5fj)¹ 2923 ⁶G (5fs)¹(5fp)¹(5fd)²(5fj)¹ 3139 ⁵H (5fp)²(5fd)¹(5fj)¹ 2405

5S (7s)¹(5fs)¹(5fd)²(5fj)² 2954 ⁶G (5fs)¹(5fp)¹(5fd)²(5fj)¹ 3809

The second ionization energy of PuO (or first ionization energy of PuO⁺), computed at the SO-CASPT2 level, is equal to 14.36 eV, which should be compared to the experimental mean value, 13.7(0.8) eV, based on a thermodynamic evaluation.³ In that evaluation, the Pu²⁺–O bond energy, and thereby DHf(PuO²⁺), were estimated from oxidation reactions of the Pu²⁺ion. The value for IE(PuO⁺) was then obtained as the difference between DH_f(PuO⁺) and DH_f(PuO²⁺). In the ionization of PuO⁺, an electron is removed from a 5fjorbital, which has a larger orbital angular momentum compared to the 7s, from which the ionization of PuO occurs. This gives a different spin–orbit coupling of the valence electrons for the ground state of PuO²⁺, O = 2.

One would thus imagine that the SO effect is larger in PuO²⁺

than in PuO and PuO⁺. This is indeed what occurs, in the sense that SO-CASPT2 predicts a IE of PuO⁺of 14.36 eV, a value 0.2 eV lower than the value predicted by SF-CASPT2, 14.56 eV.

The ground state of PuO²⁺, O= 2, is mainly composed by the spin-free states⁵G and⁵F. The⁵G state has a strong single-reference character and is dominated by the configura- tion (5fd)²(5fj)¹(5fp)¹. It thus seems appropriate to compute also the second IE of PuO at the SF-DFT/B3LYP level of theory. We obtain a value of 14.52 eV, which is in reasonable agreement with the SF-CASPT2 value. This agreement may however be fortuitous.

PuO2, PuO2+

and PuO22+

Our most accurate value, SO-CASPT2, for the first ionization energy for PuO₂is equal to 6.20 eV, and we are thus confident that the Knudsen effusion electron impact experimental values in theB9–10 eV range^5,7must be significantly too high; the actual value is almost certainly in the region of the more recent experimental values, 7.030.12 eV¹andB6.6 eV.⁶It would also appear that the vertical ionization energies previously Table 4 Spin–orbit vertical excitation energies (cm ¹) for PuO2, PuO2+and PuO22+, and composition of each spin-state in terms of spin-free states. The analysis has been performed at the equilibrium bond distance (in parentheses) of the ground state for each species

PuO2(1.744 A˚) PuO2+(1.704 A˚) PuO22+(1.675 A˚)

Ovalue Composition (%) DE O Composition (%) DE O Composition (%) DE

1u 5Fu(96),⁵Du(2),⁵Du(1) 0 1.5u 4Fu(63),⁴Du(14),²Du(8),⁴Du(7) 0 4g 3Hg(98),¹Gg(2) 0 2u

5Fu(88),³Fu(7),⁵Du(5) 535 2.5u

4Fu(79),⁴Du(9),⁴Du(7),²Du(2) 2867 0g

3Sg(59),¹Sg(21),³Pg(20) 2268 0g 5S⁺g(86),³Dg(13) 1794 3.5u 4Fu(76),⁴Du(18),²Fu(3) 5635 1g 3Pg(46),³Sg(37),¹Pg(16) 5065

3u 5

Fu(85),³Fu(7),⁵Du(3)⁵Du(2),³Fu(2) 2133 1.5u 4

Fu(36),⁴Du(28),⁴Du(15),²Du(8) 5986 5g 3

Hg(99) 6955

1g 5S⁺g(88),³Dg(11) 2315 1.5u 4Du(49),⁴Du(37),⁴Fu(11) 6717 0g 3Pg(100) 10436

2g 5

S⁺g(100) 4131 2.5u 4

Du(32),⁴Fu(31),⁴Du(22),²Du(6) 8753 1g 3

Sg(59),¹Pg(23),³Pg(16),³Sg(2) 10450 4u 5Fu(86),³Fu(5),⁵Du(5) 4491 4.5u 4Fu(77),⁴Du(8),⁴Du(6),²Gu(2) 8873 0g 3Pg(67),¹Sg(30),³Sg(2) 11262 2u 3Fu(72),⁵Du(14),³Du(5),³Fu(4) 5876 3.5u 4Du(59),⁴Du(29),²Fu(6),⁴Fu(2) 11903 6g 3Hg(89) 12257

Table 5 Spin-free vertical excitation energies (cm ¹) for PuO2, PuO2

+and PuO2

2+, and dominating electronic configuration for each spin-free state. The analysis has been performed at the equilibrium bond distance (in parentheses) of the ground for each species

PuO2(1.792 A˚) PuO2

+(1.703 A˚) PuO2

2+(1.675 A˚)

5S⁺g (5fd)²(5fj)² 0 ⁴Fu (5fd)²(5fj)¹ 0 ³Hg (5fd)¹(5fj)¹ 0

5Fu (7s)¹(5fd)²(5fj)¹ 1800 ⁴Du (5fd)¹(5fj)² 2390 ³Sg (5fd)²+ (5fj)² 1772

5Du (7s)¹(5fd)¹(5fj)² 4797 ⁴Du (5fd)¹(5fj)² 4250 ³Pg (5fd)¹(5fj)¹ 4878

5Du (7s)¹(5fd)¹(5fj)² 8548 ²Fu (5fd)²(5fj)¹ 11766 ¹Sg (5fd)²+ (5fj)² 6009

3Fu (7s)¹(5fd)²(5fj)¹ 8843 ²Du (5fd)¹ 11980 ¹Pg (5fd)¹(5fj)¹ 9532

3S g (5fd)²+ (5fj)² 9457 ¹Gg (5fd)¹(5fd)¹ 12462

5Hu (6dd)¹(5fd)²(5fj)¹ 10919

3Du (7s)¹(5fd)¹(5fj)² 11699

Table 6 Vertical excitation energies (cm ¹) for PuO22+calculated at the CASPT2 level including the spin–orbit coupling. The computed energies are evaluated at 1.675 A˚ (equilibrium bond length). For comparison, results obtained at different level of theory as well as adiabatic experimental data have been included

SDCI + Q + SO CASPT2 + SO IHFSCC

This work Experiment³⁶

Maronet al.¹⁴ Clavague´ra-Sarrioet al.¹¹ Infanteet al.¹²

State E/cm ¹ State E/cm ¹ State E/cm ¹ State E/cm ¹ State E/cm ¹

4g 0 4g 0 4g 0 4g 0 4g 0

0g 4295 0g 4190 0g 2530 0g 2268 0g —

5g 6593 1g 6065 1g 4870 1g 5065 1g —

1g 7044 5g 8034 5g 6700 5g 6955 5g —

0g 7393 0g 12 874 0g 10 334 0g 10 436 0g 10 185

6g 7848 1g 12 906 1g 10 983 1g 10 450 1g 10 500

0g 9415 6g 14 326 0g 11 225 0g 11 262 0g 10 700

1g 12 874 0g 14 606 6g 11 651 6g 12 257 6g —

calculated by CCSD and CCSD(T), 9.7 and 9.9 eV,¹⁰ are substantially higher than the actual (adiabatic) value. The value for IE(PuO2) computed by SO-CASPT2, 6.20 eV, is 0.4 eV below the Caponeet al.value,⁶and 0.7 eV below the lower end of the range established by the electron-transfer bracketing technique.¹We have verified that the SO-CASPT2 method did not substantially underestimate IE(PuO2) by performing a series of calculations with an increasing active space. The results are summarized in Fig. 1. The spin-free first IE of two different electronic states of PuO2, namely⁵S⁺g and

5F_u, is reported as a function of the active space. The IE for both states converges to the value of 6.5 eV without SO coupling. We can state that our calculations are converged with the active spaces of increasing size and we have no reason to believe that the value predicted by the SO-CASPT2 method of 6.20 eV represents a significant underestimation of the IE of PuO₂.

As already mentioned above, this computed value of IE(PuO2) is not in full agreement with the range of 6.91–7.14 eV previously established by electron transfer bracketing experi- ments.¹ A crucial requirement for such ‘‘bracketing’’ experi- ments is that the reactant ion, in this case PuO₂⁺, must be thermalized prior to electron transfer reactions. The presence of excited state PuO2+

ions could result in otherwise endothermic abstraction of an electron from a neutral mole- cule, which would give an apparent ionization energy higher

than the actual value. Although the validity of the ‘‘bracketing’’

experiments was carefully confirmed by accurately determining IE[Mo⁺],¹it is feasible that molecular PuO2+

ions, in contrast to atomic Mo⁺ions, were not completely thermalized under the conditions of the electron transfer experiments. This possibility was explicitly acknowledged by Santos et al.,¹ where the following is stated: ‘‘Doubts could arise concerning the possibility of an ineffective thermalization of the PuO2+

ions in the charge-transfer reactions, but, if this was the case, it would mean that IE(PuO₂⁺) was even lower than the

‘bracketed’ value.’’ The key point made by Santos et al.¹ was that IE(PuO2) is approximately 2–3 eV lower than the previously reported values, which are in the range of 9–10 eV.^5,7This conclusion is clearly validated by the present theoretical results. It should be noted that the discrepancy of 0.7 eV between the computed value of 6.20 eV and the lower limit of 6.9 eV¹determined from the electron transfer reactions is minor relative to the large correction,42 eV, to previously reported experimental^5,7and theoretical¹⁰values.

Another aspect that requires some consideration is the large difference between the SF, 6.73 eV, and SO, 6.20 eV values of the IE of PuO2. This difference is significantly larger than the one found for PuO. Like in the PuO case, also for PuO2

the electron released in the ionization process belongs to the 7s shell, but in this case the SO effect seems to be considerably more significant. In order to understand this feature, we have analyzed the ground state of PuO₂,O= 1_u, which is mainly formed by the⁵Fuspin-free state. This state is not the ground state, according to the spin-free calculation, but the second state, composed mainly by (7s)¹(5fd)²(5fj)², and lying about 0.3 eV above the⁵S⁺_g state. When we compute the spin-free ionization energy, we are thus not considering the ionization from the true ground state of the neutral species,⁵Fu, but the ionization from the⁵S⁺gstate of PuO2to the ground state of PuO2+

, a ⁴Fu state, mainly composed of (5fd)²(5fj)¹. This happens because ⁵S⁺_g state does not couple with spin–orbit terms and remains substantially unaffected, while the ⁵F_u mixes with other states and is further stabilized by SOC. This analysis is confirmed by considering that the energy difference between the PuO25

Fustate and the PuO2+ 4

Fustate is equal to 6.43 eV. Such a value is closer to the SO IE of 6.20 eV, Table 7 Ionization energies (eV): this work unless otherwise speci-

fied. The calculated values are vertical and the experimental values are adiabatic

Species IE/eV Ref. Method

PuO 6.60.1 5 Knudsen effusion/electron

impact

5.80.5 7 Knudsen effusion/electron impact

6.10.2 2 and 4 FTICR-MS/‘‘Schwarz method’’

6.31 DFT(B3LYP)

6.16 CASPT2(12,16)

6.17 SO-CASPT2(12,16)

PuO⁺ 13.70.8 3 Thermodynamic evaluation

14.52 DFT(B3LYP)

14.56 CASPT2(11,16)

14.36 SO-CASPT2(11,16)

PuO2 9.4 7 Knudsen effusion/electron

impact

10.10.1 5 Knudsen effusion/electron impact

7.030.12 1 FTICR-MS/electron transfer bracketing

6.6 6 Knudsen effusion/ion

equilibrium 6.70 B3LYP (⁵S⁺g to⁴Fu) 6.28 B3LYP (⁵Futo⁴Fu)

9.72 10 CCSD

9.92 10 CCSD(T)

6.73 CASPT2(12,14) (⁵S⁺g to⁴Fu) 6.43 CASPT2(12,14) (⁵Futo⁴Fu)

6.20 SO + CASPT2(12,14)

PuO2+ 15.10.4 3 FTICR-MS/electron transfer kinetics

16.3 B3LYP

15.48 CASPT2(11,14)

15.37 CASPT2(11,14) + SO

Fig. 1 The spin-free first IE of PuO2(in eV) as a function of the size of the active space for the⁵S⁺g (upper curve dashed) and⁵Fu(lower curve solid) states. The five points 1 to 5 represent the following active spaces: 4/10, 8/12, 12/14, 12/15 and 12/17.

indicating that the actual loss of a 7s electrons leads to a SO effect on IE of 0.23 eV.

The SF-DFT/B3LYP method predicts a vertical IE(PuO2) of 6.28 eV for the⁵Futo⁴Fuionization, a value just 0.15 eV different from the one obtained at the SF-CASPT2 level of theory. The agreement between the two methods is not surprising because both the ⁵F_u (PuO₂) and ⁴F_u (PuO₂⁺) ground states have a strong single reference character.

Inspection of Table 7 shows that the SO-CASPT2 value for the IE of PuO2+

, 15.37 eV, is in good agreement with the experimental value, 15.10.4 eV. The SO effect on the IE is equal to 0.11 eV. The IE of PuO₂⁺ computed at the SF-DFT/B3LYP level, 16.3 eV, is higher by about 0.8 eV than the SF-CASPT2 value.

The PuO22+

ion has been the subject of earlier theoretical studies due to the availability of experimental absorption spectra measured in water solution and for which the first excited states seem unaffected by the presence of the environ- ment. Our study represents a drastic improvement not only in detection of the correct ordering of the experimental bands, but also in the evaluation of the transition energies. If we compare our data to the values obtained with the IH-FSCC method,¹²we notice that SO-CASPT2 performs very well with differences of the order of only 100–200 cm ¹.

Conclusions

The results of the present computational study confirm that IE(PuO₂) is in the general region of the recent experimental values, B6.6–7.0 eV, and not in the B9–10 eV range previously reported. Our best theoretical estimate for the IE(PuO2), 6.20 eV, is lower than the currently most reliable experimental value,¹ 7.03 0.12 eV. For the other three calculated ionization energies, IE(PuO), IE(PuO⁺), and IE(PuO₂⁺), the SO-CASPT2 method gives good agreement with available experimental values. The SO-CASPT2 method employed here provides ionization energies for small actinide molecules which are typically accurate to withinB0.2 eV. The discrepancy of B0.5 eV between the currently best available experimental¹ and theoretical values for IE(PuO₂) (present work) remains unresolved. Refinement of both experiment and theory for such elementary molecules, as well as application to additional types of species, should remain a key focus of actinide science.

Acknowledgements

This work was supported by the Swiss National Science Foun- dation (grant no. 200020-120007); and by the Director, Office of Science, Office of Basic Energy Sciences, of the U. S. Depart- ment of Energy under Contract No. DE-AC02-05CH11231.

The absolute energies (a.u.) corresponding to the species described in Table 1 are available in the ESI.w

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