Relativistic Multireference Quantum Chemical Study of the Electronic

Article pubs.acs.org/JPCA

Relativistic Multireference Quantum Chemical Study of the Electronic Structure of Actinide Trioxide Molecules Attila Kovács* European Commission, Joint Research Centre, P.O. Box 2340, 76125 Karlsruhe, Germany S Supporting Information *

ABSTRACT: Actinide trioxide (AnO3, An = U, Np, Pu, Am, Cm) molecules have been investigated by relativistic multireference quantum chemical calculations with the goal to elucidate their electronic structures. The molecular geometries of the ground and selected excited electronic states have been optimized at the spin−orbit-free complete active space secondorder perturbation theory (SF-CASPT2) level. The low-lying vertical excitation states have been computed and characterized by CASPT2 calculations taking into account spin−orbit coupling. The reason for the considerable lengthening of the equatorial An−O bond in AmO3 and CmO3 with respect to the other trioxides has been analyzed on the basis of valence molecular orbitals of the SF ground electronic states. For the bond in question a singly occupied π orbital has been identified, this orbital is doubly occupied in the other (An = U, Np, Pu) trioxides. The clarified electronic structures of the investigated AnO3 molecules confirmed the pentavalent character of Am and Cm in their trioxides in contrast to the hexavalent character of U, Np, and Pu.

1. INTRODUCTION

orbitals based on B3LYP calculations using a large(78e)-core for U.10,11 The formation of gaseous NpO3 in thermochromatographic experiments has been reported,12 but no data have been published for the neutral molecule hitherto. Theoretical studies on the NpO3+ cation have been performed in the course of researches focusing on heptavalent Np.13,14 A weak signal in the mass spectrum recorded upon sublimation of plutonium dioxide with excess O2 has been assigned to the PuO3 molecule.15 In addition, several theoretical studies have been published on PuO3. However, the early theoretical results are somewhat controversial, reflecting the difficulty to treat the complex electronic structure of this molecule. In the first theoretical study a 1A1 state has been calculated at the B3LYP level, and limited structural data without any discussion have been reported.16 The study of Gao et al.17 has covered low-energy quintet, septet, and nonet states using the Hartree−Fock method and two DFT exchangecorrelation functionals with a large(78e)-core relativistic pseudopotential for Pu. As a result, a septet 7B1 Y-shaped C2v structure has been reported as the ground electronic state and a 5 B2 Y-shaped C2v structure as an excited state higher in energy by 25 kJ/mol. Recently more sophisticated two-component relativistic DFT calculations have resulted in a T-shape structure18−20 with bond distances similar to those of UO3 and to the geometry reported in ref 16. The septet ground state

Actinides (An) occur rarely in the oxidation state of VI. The best known An(VI) molecules are the trioxides, yet the molecular information even on them is rather scarce. Similarly to other An compounds, the most studied trioxide is that of U, which has been analyzed by both experiment and theory and is thus fairly well characterized. The molecule has been first reported by a matrix-isolation IR spectroscopic study.1 Subsequent matrix-isolation IR experiments using 18O substitution have shown that UO3 has a unique T-shaped C2v structure involving a near-linear OUO moiety and a third oxygen attached equatorially to U (Scheme 1).2−6 This structure has been supported later by Hartree−Fock7,8 and DFT calculations.6,9 Shundalau et al. have analyzed the bonding of T- and Y-shaped conformers in terms of localized molecular Scheme 1. Structure of AnO3 Molecules

Received: February 10, 2017 Revised: March 9, 2017

© XXXX American Chemical Society

A

DOI: 10.1021/acs.jpca.7b01344 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A

corresponding to TZP quality. In the CASSCF calculations the scalar relativistic effects were taken into account using the Douglas−Kroll−Hess Hamiltonian.31,32 The spin−orbit-free (SF) ground-state molecular geometries were optimized in the present study using numerical gradients. The vertical excited electronic states were explored by multiconfigurational state-averaged calculations. In addition to the ground-state spin multiplicities (1, 2, 3, 6, 7 for An = U to Cm, respectively) the neighboring lower and higher ones were considered too. Spin−orbit (SO) effects were computed by means of the complete active space state interaction (CASSI) method,35 which allows CASSCF wave functions for different electronic states to interact under the influence of a spin−orbit Hamiltonian. Dynamic electron correlation was taken into account using the CASPT2 energies in the spin−orbit Hamiltonian (SO-CASPT2). The number of SF states considered in these calculations corresponded to 11, 13, 14, 12, and 13 for UO3, NpO3, PuO3, AmO3, and CmO3, respectively. The above-described multireference methods and the ANO-RCC basis set were successfully applied in a number of studies on actinide-containing systems.36−45

from ref 17 has not been confirmed by Zaitsevskii et al., who have obtained a chemically more reasonable triplet.21 The latter spin multiplicity has been confirmed by recent multireference calculations predicting the spin-free ground electronic state of PuO3 to be 3B2.22 From the trioxides of heavier actinides only CmO3 has presumably been detected in thermochromatographic experiments.23 Two-component relativistic DFT calculations have been performed recently by Zaitsevskii et al. on AmO3,19,20 CmO3,20,24 BkO3, and CfO3.20 The main information from these calculations are the dissociation energies, vibrational frequencies, and geometries resembling those of the UO3 and PuO3 molecules except for the considerably elongated equatorial An−O bond. However, the electronic structure of the latter trioxides, including the character of the ground state, has not been studied in detail hitherto. The aim of the present work is to elucidate the electronic structure of the trioxides of early actinides (An = U−Cm) by relativistic multireference calculations including spin−orbit (SO) coupling. The study involves the determination and characterization of the ground as well as low-lying excited electronic states. Additional important goal of the study is to uncover the electronic origin of the lengthening of the equatorial An−O′ bond in the trioxides of the heavier actinides.

3. RESULTS AND DISCUSSION The computed relative energies of the lowest-energy SF states from each spin multiplicity and symmetry species covered by the present study are compiled in Table 1. All energies belong

2. COMPUTATIONAL DETAILS The calculations have been performed using the code MOLCAS 8.0.25,26 The complete active space self-consistent field (CASSCF) method27 has been used to generate molecular orbitals and reference functions for subsequent multiconfigurational second-order perturbation theory calculations of the dynamic correlation energy (CASPT2)28,29 with frozen 1s for O and up to 4f for An. The active space was constructed on the basis of state-averaged test calculations using five roots. Based on the observed occupations30 four bonding AnO orbitals were selected for the active space of each trioxide, one from both A1 and B1 symmetries and two from B2 symmetry. The active space was completed up to 16 orbitals to facilitate the contribution of all 6d and 5f orbitals of the actinides. Hence, these active spaces contained 8, 9, 10, 11, and 12 electrons for UO3, NpO3, PuO3, AmO3, and CmO3, respectively. We note that, on the basis of orbital entanglement and correlation measures obtained from DMRG calculations, Boguslawski et al. suggested an optimal active space of (14,14) for the ground state of PuO3.22 The most significant orbitals from it are included also in the present active space. However, due to our goal to elucidate the lowest-lying excited states, our active space needed more virtual orbitals. This means that, because of feasibility reasons, we had to neglect two less important doubly occupied orbitals. In agreement with the reported C2v symmetry of AnO3 molecules, we applied the C2v point group in our calculations. Accordingly, the z axis corresponds to the axis of the C2 symmetry operation (cf. Scheme 1). This defines the magnetic quantum numbers of the 6d and 5f orbitals given in the tables. The notations σ, π, δ, ϕ in the discussion represent the magnetic quantum numbers 0, ±1, ±2, ±3, respectively. All electron basis sets of atomic natural orbital type, developed for relativistic calculations (ANO-RCC) with the Douglas−Kroll−Hess Hamiltonian31,32 were used for all the a t o m s . B a s i s se t s w i t h co n t r a c t i o n s c h e m e s o f 26s23p17d13f5g3h/9s8p6d5f2g1h 33 and 14s9p4d3f2g/ 4s3p2d1f34 were used for the actinides and O, respectively,

Table 1. Relative Adiabatic Energies (cm−1) of Selected SF States of AnO3 Molecules Obtained by SF-CASPT2 Calculations symmetry AnO3 UO3 NpO3 PuO3

AmO3

CmO3

spin multiplicity 1 3 2 4 1 3 5 2 4 6 8 3 5 7 9

A1

B1

A2

B2

0 20678 1958 11353 8408 14756 15838 8624 9967 9635 16127 31142 3891 4764 18975

17326 13799 1678 10194 7790 3641 15455 11329 1985 4991 13896 30082 8149 2608 5223

19112 17085 0 11876 7045 1650 10189 13588 10378 8283 18564 37367 19313 0 14761

17571 15576 5315 14024 8921 0 6230 12373 9730 0 15951 22026 3545 4836 7798

to geometries optimized at the same SF-CASPT2 level. The optimized geometrical parameters of selected SF states are given in Table 2. The geometrical parameters of all the above SF states are given in the Supporting Information. 3.1. UO3. The ground electronic state of UO3 is 1A1. Its geometry is compared in Table 2 with literature data. All the methods predicted correctly the equatorial U−O′ bond being longer than the uranyl U−O bonds, but the difference between the two types of bonds scatter between 0.015 and 0.083 Å, the SF-CASPT2 value (0.049 Å) being in the middle of the range. For the bending of the uranyl moiety a fair agreement can be observed between the presented theoretical levels. B


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The main electron configurations have contributions around 90%, while the minor configurations remain generally below 1%. In the excited states various 5f orbitals are singly populated by electrons from excitations of π orbitals. U 6d orbitals appear as minor contributors in some bonding orbitals. The SO coupling did not affect the ground-state character of the 1A1 state, and as expected, the lowest-energy excited SO states are triplets with generally one major SF component. Notable mixing can be seen in the SO states above 15000 cm−1. Shundalau et al. analyzed the characters of the bonding orbitals in the T-shaped ground electronic state on the basis of localized molecular orbitals from DFT calculations.11 Three bonding orbitals, two σ and one π, were reported for the equatorial U−O′ bond. The most characteristic molecular orbitals from our SF-CASSCF level are depicted in Figure 1. For the U−O′ bond we identified one σ orbital (A1 symmetry) and three π orbitals (2xB1, B2), from which one of the B1 ones and B2 are localized over all the four atoms of UO3. No second σ bonding orbital for the U−O′ interaction was found in our more sophisticated study. The additional characteristic bonding molecular orbitals in Figure 1 comprise two σ (2xB2) and two π ones (A2, B2) for the OUO moiety. 3.2. NpO3. The SF ground electronic state of NpO3 is the doublet 2A2 (cf. Table 1). Its geometry shows slight bond contractions with respect to the ground state of UO3 and a slightly larger O−Np−O angle (cf. Table 2). The other doublet states are also quite low in energy (cf. Table 1). The lowest energy quartet is the 4B1 state lying higher in energy by ca. 10000 cm−1. The characterization of selected low-lying (vertical) electronic states of NpO3 is given in Table 4. The ground state is dominated by the 5fδ configuration (89%, cf. Table 4), but also the other low-lying doublet SF states have a predominant electron configuration. The quartet states are somewhat more mixed (60−75% major configuration). In these excited states additional singly populated 5f orbitals appear from excitations of π orbitals.

Table 2. Optimized Geometrical Parameters of the SF Ground and a Few Selected States of AnO3 Moleculesa AnO3

method

An−O

An− O′

OAnO

ref

UO3

SF-CASPT2

1

A1

1.789

1.838

161.3

1

A1 A1

1.75 1.810

1.83 1.853

161 158.8

NpO3

HF/LCPP B3LYP/ SCPP HF/SCCP PBE0/SCPP SF-CASPT2

present study 7 6

A1 n.a. 2 A2

1.745 1.771 1.766

1.828 1.786 1.836

165.2 161 166.6

PuO3

SF-CASPT2

3

B2

1.763

1.842

171.0

PBE0/SCPP B3LYP/ SCPP SF-CASPT2

3

X X

1.749 1.749

1.853 1.858

170 169

1

A1

1.743

1.833

172.2

1

A1

1.752

1.811

n.a.

7

B1

2.206

1.914

102.2

17

AmO3

B3LYP/ SCPP B3LYP/ LCPP SF-CASPT2

present study 16

6

B2

1.721

2.101

180.0

CmO3

PBE0/SCPP SF-CASPT2

n.a. A2

1.747 1.746

2.067 2.115

179 173.1

n.a.

1.768

2.069

176

present study 20 present study 20

PBE0/SCPP a

SF state

1

1

3

7

8 9 present study present study 18,21 18,21

Bond distances are given in angstroms, bond angles in degrees.

Due to the closed-shell nature of this molecule, the SF excited electronic states start at high energies (near 14000 cm−1, cf. Table 1). The first excited state is a triplet (3B1), while the first singlet excited state (1B1) appears above 17000 cm−1. The studied SF states show only a slight mixing (cf. Table 3). Table 3. Selected Low-Energy Electronic States of UO3 from SF- and SO-CASPT2 Calculations term symbol SF

1

A1 B1 3 B2 3 A2 1 B1 1 B2 1 A2 3

SO

Ea (cm−1) 0 14982 18524 19409 20733 21315 21552 0 13729 14043 15720 17466 20961 22451

Table 4. Selected Low-Energy Electronic States of NpO3 from SF- and SO-CASPT2 Calculations

characterb 89% closed shell 92% 5f2−, (2p,6py) 90% 5f0, (2p,5f3−) 90% 5f1+, (2p,5f3−) 93% 5f2−, (2p,6py)β 89% 5f0, (2p,6py)β 90% 5f1+, (2p,6py)β 100% 1A1 61% 3B1 + 19% 3A2 + 18% 3B2 79% 3B1 49% 3B2 + 43% 3A2 56% 3B2 + 22% 1A2 + 21% 3B1 61% 1B1 + 31% 3B2 71% 1B2

term symbol SF

2

A2 B1 2 A1 2 B2 4 A1 4 B1 4 A2 2

SO

a

Vertical excitation energies obtained on the geometry of the 1A1 ground state. Additional states are given in the Supporting Information. bSF section: Character of the unpaired electrons in the main electron configuration. The primary spin of the unpaired electrons is α; β means electrons with opposite spin according to the singlet spin multiplicity of the given states. The notation of atomic orbitals corresponds to the coordinate system depicted in Scheme 1. SO section: composition in terms of SF states.

Ea (cm−1) 0 637 1554 5808 9973 10115 12421 0 2615 7781 8446 10068 13991 15845

characterb 89% 76% 76% 89% 75% 67% 76% 42% 55% 50% 49% 61% 40% 32%

5f2− 5f1+ 5f0 5f1− 5f1+, 5f2−, (2p,5f3−) 5f0, 5f2−, (2p,5f3−) 5f1−, 5f2−, (2p,5f3−) 2 B1 + 32% 2A1 + 23% 2A2 2 A2 + 19% 2B2 2 A1 + 46% 2B1 4 A1 + 48% 4B1 2 B2 + 16% 2A2 4 A2 + 22% 4B1 + 15% 4A1 4 A1 + 26% 4A2 + 15% 4B1

a

Vertical excitation energies obtained on the geometry of the 2A2 ground state. Additional states are given in the Supporting Information. The SO states are doubly degenerate. bSF section: Character of the unpaired electrons in the main electron configuration. The notation of atomic orbitals corresponds to the coordinate system depicted in Scheme 1. SO section: composition in terms of SF states. C


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Figure 1. Characteristic bonding molecular orbitals of UO3.

The SO coupling results in a considerable mixing of the SF states (cf. Table 4). The SO ground state consists of three major doublet contributions (2B1, 2A1, 2A2) from which the first excited SF state 2B1 has the largest, while the ground state 2A2 has the smallest contribution. This suggests that for modeling of the NpO3 molecule single-reference methods are less suitable. 3.3. PuO3. The 3B2 SF ground state determined by Boguslawski et al. using a small (two electrons in four orbitals) active space in CASSCF calculations22 is confirmed by our more sophisticated study using a considerably larger (10,16) active space and account for dynamic correlation. From the other spin multiplicities the quintet 5B2 has the lowest-energy (ca. 6200 cm−1, cf. Table 1), the lowest-energy singlet 1A2 being somewhat higher (ca. 7000 cm−1). The 7B1 state reported by Gao et al. from large-core pseudopotential B3LYP calculations17 should be completely wrong for a ground state. Six unpaired electrons cannot facilitate a plutonyl-type structure (hence the bond angle of 102.2°17) and without its stabilizing effect the state must be very high in energy. The computed geometry of the SF-CASPT2 ground state compares well with the DFT result of Zaitsevskii et al.:18−20 the bond distances agree within 0.02 Å, the bond angles within 2° (cf. Table 2). Beyond the advanced two-component relativistic DFT technique and the good quality pseudopotentials, the success of the DFT calculations can be attributed to the predominance of the 5fπ1,5fδ1 electron configuration in the 3B2 ground electronic state (79%, cf. Table 5), which makes a good description of this SF state by single-reference methods possible. The same refers to the 1A1 excited state containing 78% of the main 5fδ2 configuration (cf. Table 5). Accordingly, the B3LYP bond distances from the early study of Straka et al.16 are in good agreement with our SF-CASPT2 results (cf. Table 2). We note that the vertical excitation energies collected in Table 5 are considerably higher for several excited states than their adiabatic counterparts in Table 2. This is due to the considerable differences between the reference (SF ground state) and optimized geometries of these states. This feature was not observed for the electronic states of UO3 and NpO3 covered by the present study, where the two types of energies are in fair agreement (cf. Tables 1, 3, and 4 and Supporting Information).

Table 5. Selected Low-Energy Electronic States of PuO3 from SF- and SO-CASPT2 Calculations term symbol SF

3

B2 A2 3 B1(1) 3 B1(2) 1 A2 1 B1 3 B1(3) 1 A1 1 B2 5 B2 5 A2 3

SO

Ea (cm−1) 0 1644 4619 7118 8989 9544 10143 10265 10674 12236 18012 0 471 2833 9558 9700 10817 15391 16079

characterb 79% 66% 31% 36% 83% 73% 29% 78% 78% 92% 90% 52% 53% 75% 84% 41% 45% 44% 61%

5f1+, 5f2− 5f0, 5f2− 5f1−, 5f2− + 30% 5f1+, (5f2+,5f0) (5f0,5f2+), 5f1+ + 29% 5f1‑, 5f2‑ (5f0,5f2+), 5f2‑β 5f2−, 5f1‑β 5f1+, (5f2+,5f0) + 18% (5f0,5f2+), 5f1+ (5f2−)2 5f1+, 5f2−β 5f1+, 5f1−, 5f2−, (2p,5f3−) (5f0,5f2+), 5f1−, 5f2−, (2p,5f3−) 3 B2 + 37% 3A2 3 B2 + 38% 3A2 3 B2 + 15% 3B1(1) 3 B1(1) 3 A2 + 40% 3B2 3 B1(2) + 26% 1A2 5 B2 + 29% 3B1(3) 5 B2 + 13% 5A2

a

Vertical excitation energies obtained on the geometry of the 3B2 ground state. Additional states are given in the Supporting Information. bSF section: Character of the unpaired electrons in the main electron configuration. The primary spin of the unpaired electrons is α; β means electrons with opposite spin according to the singlet spin multiplicity of the given states. The notation of atomic orbitals corresponds to the coordinate system depicted in Scheme 1. SO section: composition in terms of SF states.

In the SO ground state the major character of 3B2 is preserved with a minor (37%) contribution of 3A2. In fact, also the first two SO excited states are dominated by 3B2. Quintet states appear above 15000 cm−1 as major contributions in the SO vertical states, while singlet ones above 18000 cm−1 (cf. Supporting Information). Mixing is moderate in these lowenergy SO states, in the majority of them the main component has a contribution over 40%. 3.4. AmO3. The SF ground electronic state is a sextet (6B2, cf. Table 1). The lowest-energy quartet state, 4B1, is the first excited state lying higher by 2000 cm−1 above the SF ground D


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Figure 2. Characteristic bonding molecular orbitals of AmO3.

other lighter AnO3 molecules. The obvious consequence of this electronic structure is the pentavalent character of Am and the larger Am−O′ bond length. We note that both the sextet and octet SF states of AmO3 have Am−O′ bond lengths above 2.0 Å (cf. Table S1 in Supporting Information). They are in agreement with singly occupied π bonding orbitals in these states formed by excitation of electrons from doubly occupied bonding orbitals. Selected low-lying (vertical) electronic states of AmO3 are given in Table 6. In the sextet states the other four singly occupied orbitals correspond to nonbonding 5f orbitals. The low-energy quartet states contain a doubly occupied orbital with mainly 5fπ character. The 6B2 ground state is dominated

state. We note that the other quartet states appear at around 10000 cm−1, while the first doublets (except for 2A1) and particularly the octet states are considerably higher in energy. The sextet ground state of AmO3 broke the gradually increasing spin multiplicity of the ground electronic states from UO3 to PuO3 (singlet to triplet, vide supra). Thus, AmO3 differs significantly from the lighter AnO3 (An = U, Np, Pu) molecules. The latter trioxides possess 58 doubly occupied orbitals in their ground states in accordance with the hexavalent character of An in them. In the sextet AmO3 there are only 57 doubly occupied orbitals and five unpaired electrons. The peculiar electronic structure of AmO3 has already been noted by Zaitsevskii, who doubted the hexavalent character of Am in this trioxide on the basis of the geometrical parameters and dissociation enthalpies.19 In his subsequent paper, the analysis of spin magnetization densities gave −1 as the formal charge of the equatorial oxygen. This would be in agreement with single-bonding to Am, i.e., with a pentavalent character of the actinide.20 In the geometrical parameters the equatorial single bond is manifested in the Am−O′ bond distance being longer by ca. 0.25 Å than the An−O′ bonds in UO3, NpO3, and PuO3. Another characteristic feature is the linear uranyl moiety in AmO3 (180° O−Am−O bond angle in contrast to 161−171° in UO3, NpO3, and PuO3, cf. Table 2), indicating the lack of distorting electron density by the equatorial Am−O′ bond in this electron configuration. Our SO-CASPT2 calculations confirmed the considerably longer Am−O′ bond as compared to the An-O′ bonds with An = U, Np, and Pu. In order to elucidate the origin of this feature we analyzed the valence molecular orbitals of AmO3 in detail. Selected orbitals are presented in Figure 2. They are similar to the molecular orbitals of UO3 shown in Figure 1 with the exception of the A1 orbital: it is delocalized over the four atoms in AmO3 in contrast to UO3, where it is localized on the U−O′ bond. Additional minor differences compared to UO3 are manifested in the pure character of the AmO3 orbitals, lacking a mixing with lone pair densities. The main point is, however, that all the eight orbitals of UO3 shown in Figures 1 are doubly occupied orbitals, while the third B2 orbital of AmO3 (Figure 2) is populated by one electron only. This orbital corresponds to a π Am−O′ bond. As a result of the lower population, the Am− O′ bond is weaker than the equatorial bonds in UO3 and in the

Table 6. Selected Low-Energy Electronic States of AmO3 from SF- and SO-CASPT2 Calculations term symbol SF

6

B2(1) B1 6 B1(1) 6 A2 6 B2(2) 6 A1 6 B1(2) 4 A1 4 A2 4

SO

Ea (cm−1) 0 2333 5931 6649 7296 9453 9767 11592 12556 0 2353 3525 7306 7505 9088 11705 14815

characterb 89% 59% 90% 57% 72% 77% 82% 60% 60% 86% 47% 96% 37% 95% 36% 60% 77%

(5f0,5f2+), 5f1+, 5f1−, 5f2−, (2p,5f3−) (5f0,5f2+), (5f1+,2p)2, 5f1−, 5f2− (5f0,5f2+), 5f1+, 5f1−, 5f2−, (2p,6d1+) 5f1+, (5f1−,5f3−), 5f2−, 5f3+, (2p,5f1−) (5f0,5f2+), 5f1−, 5f2−, 5f3+, (2p,5f3−) 5f0, 5f1+, 5f2+, 5f2−, (2p,5f3−) (5f0,5f2+), 5f1+, 5f3+, 5f2−, (2p,5f3−) (5f1+,2p)2, 5f1−, (5f2+,5f0), 5f3+ (5f1+,2p)2, 5f1−, (5f2+,5f0), 5f3+ 6 B2(1) 6 A2 + 40% 6B2(2) 4 B1 6 B1(2) + 36% 6A1 6 B1(1) 6 A1 + 24% 6B2(2) 4 A1 + 34% 4A2 4 A2 + 15% 4A1

a

Vertical excitation energies obtained on the geometry of the 6B2(1) ground state. Additional states are given in the Supporting Information. The SO states are doubly degenerate. bSF section: Character of the unpaired electrons in the main electron configuration. The notation of atomic orbitals corresponds to the coordinate system depicted in Scheme 1. SO section: composition in terms of SF states. E


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determinant configuration indicating the possibility for singlereference methods for efficient modeling the SF ground state of CmO3 too. Some of the low-lying SF states have one major electron configuration (around 90%), but most of them are strongly mixed suggesting the necessity of multireference methods for successful description of (these) excited states of CmO3. In the heptet states there are five singly occupied orbitals with 5f character; the sixth singly occupied orbital, however, consists of major O 2p and minor Cm contributions. In the 7A2 ground state this singly occupied orbital corresponds to the same singly occupied B2 orbital, which characterizes the pentavalent character of Am in the SF ground state of AmO3 (vide supra). Accordingly, this singly occupied B2 orbital confirms the pentavalency of Cm in CmO3. The geometry of the SF ground state, 7A2, is similar to that of the SF ground state of AmO3: the equatorial Cm−O′ bond is ca. 2.1 Å and the O−Cm−O angle is close to linear (173°, cf. Table 2). Both types of bonds in CmO3 are slightly longer than those in AmO3. The close geometrical parameters are the consequence of the close electronic structures of the SF ground states of the two molecules: essentially the main electron configuration of the AmO3 6B2(1) state appears in the 7A2 state of CmO3 with addition of a singly occupied Cm 5fϕ orbital. The latter one, being nonbonded, has no significant effect on the geometry. As noted for PuO3 and AmO3, also for CmO3, there is a good agreement with the DFT result of Zaitsevskii et al.20 (cf. Table 2). A slight difference is manifested in DFT failing to predict the slight elongation of the equatorial Cm−O′ bond with respect to the Am−O′ one, as observed in the SF-CASPT2 geometries. Similarly to the previously discussed actinides, the high-spin multiplicity nonet states of CmO3 are generally formed by excitation of electrons from doubly occupied bonding orbitals to Cm 5f orbitals. In part of the low-energy quintets there is a singly occupied (2p,5f) bonding orbital with opposite-spin electron. The presence of singly occupied bonding orbitals in these states is in agreement with the long equatorial Cm−O′ bonds (cf. Table S1 in Supporting Information). The high energy 9A1 and 9A2 states are formed by excitations of electrons from the uranyl Cm−O bonds with the consequence of the uranyl moiety getting destroyed (cf. Supporting Information). The SO ground state of CmO3 consists essentially (94%) of the 7A2 SF ground state. Hence, the above-mentioned expected good performance of advanced single-reference methods for the SF ground state can be transferred to the SO ground state of CmO3 too. Most excited states, however, have one major (around 60%) and one minor (around 30%) contributors.

(89%) by a single determinant configuration, but also the other low-lying SF states have one major electron configuration (57− 90%, cf. Table 6). The SO interaction did not change the ground state character of the 6B2 SF ground state, which is the predominant contributor (86%) in the SO ground state. This indicates that for modeling the ground state of AmO3 single-reference methods can be suitable. In addition, there are a few quite pure low-energy SO states (cf. Table 6). Considerably mixed states start to appear above 8000 cm−1 (cf. Supporting Information). Comparing the geometrical parameters in Table 2 we note the good agreement of the SF-CASPT2 geometry with the DFT result of Zaitsevskii et al.20 Beyond the importance of the above-mentioned single-reference character of the 6B2 state this is a further evidence of the good performance of the twocomponent relativistic DFT technique applied in ref 20. 3.5. CmO3. The SF ground electronic state is the heptet 7A2 (cf. Table 1). From the other spin multiplicities the quintet states have the lowest energy, the first quintet excited state, 5B2, lying higher by ca. 3500 cm−1 above the SF ground state. Two nonet SF states have also quite low adiabatic energies (the lowest one being at ca. 5200 cm−1). The triplet states are considerably less stable; they appear above 22000 cm−1. Selected low-lying (vertical) electronic states of CmO3 are given in Table 7. The 7A2 state is dominated (88%) by a single Table 7. Selected Low-Energy Electronic States of CmO3 from SF- and SO-CASPT2 Calculations term symbol SF

7

A2

5

B2

7

B1

7

A1

7

B2(1) B1 5 A1 5 B1 7 B2(2) 9

9

B2

SO

Ea (cm−1)

characterb

0 88% (5f0,5f2+), 5f1+, (5f1−,5f3−), 5f2−, 5f3+, (2p,6p) 3984 30% 5f0, 5f1+, 5f2+, 5f2− + 20% 5f0, 5f1+, 5f2+, 5f2−, (2p,5f1−), (2p,5f1−)β 5377 30% 5f0, 5f1+, 5f1−, 5f2+, 5f2−, 5f3+, 5f3−, (2p,5f1−)β + 26% 5f0, 5f1+, 5f1−, 5f2+, 5f2−, 5f3+ 5733 87% (5f0,5f2+), 5f1+, (5f−‑,5f3−) 5f2−, 5f3+, (2p,5f1+) 5751 56% 5f0, 5f1+, 5f1−, 5f2+, 5f2−, (2p,5f3−) 8882 91% 5f0, 5f1+, 5f1−, 5f2+, 5f2−, 5f3+, 5f3−, (2p,6d1−) 9781 45% (5f0,5f2+), 5f1+, 5f1−, 5f2−, 5f3+, (2p,5f1+)β 10113 36% 5f0, 5f1−, 5f2+, 5f2− 10803 29% 5f0, 5f1+, 5f1−, 5f2+, 5f2−, 5f3+, (2p,5f3−), (2p,5f1+)β + 26% 5f0, 5f1+, 5f1−, 5f2+, 5f2−, 5f3+, (2p,5f3−), (2p,5f1+)β 13162 91% 5f0, 5f1+, 5f1−, 5f2+, 5f2−, 5f3+, 5f3−, (2p,6d1+) 0 94% 7A2 2288 65% 5B2 + 33% 7B1 4507 70% 7B2(1) + 29% 9B1 5821 95% 7A1 6211 72% 7B1 8262 61% 5A1 + 31% 7B2(2) 8478 49% 5B1 + 48% 7B2(2) 9636 97% 9B1 13891 97% 9B2

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CONCLUSIONS In the article we presented the first sophisticated multireference quantum chemical study of actinide trioxides. The main results include the first reliable characterization of the ground as well as low-lying excited electronic states of the studied AnO3 (An = U, Np, Pu, Am, Cm) molecules, the molecular geometries optimized at the SF-CASPT2 level and the confirmation of the pentavalent character of Am and Cm in contrast to the hexavalent U, Np, and Pu in their trioxides. The pentavalency of Am and Cm has been suggested in the literature on the basis of the considerable lengthening of the equatorial An−O′ bond in AmO3 and CmO3 with respect to the trioxides of the lighter actinides, as well as by the smaller charge of the equatorial oxygen.20 A difference in the oxidation

a

Vertical excitation energies obtained on the geometry of the 7A2 ground state. Additional states are given in the Supporting Information. bSF section: Character of the unpaired electrons in the main electron configuration. The primary spin of the unpaired electrons is α; β means electrons with opposite spin according to the singlet spin multiplicity of the given states. The notation of atomic orbitals corresponds to the coordinate system depicted in Scheme 1. SO section: composition in terms of SF states. F


Article


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state was indicated in the present study by the break of the gradually increasing spin multiplicities of the ground electronic states between PuO3 and AmO3. The evidence for the pentavalency was provided by analysis of the valence molecular orbitals of the ground electronic states. For the equatorial An− O′ bond a singly occupied π orbital was identified in AmO3 and CmO3, which has doubly occupied counterparts in the other (An = U, Np, Pu) trioxides. The present results supported the good performance of twocomponent relativistic DFT methods for this type of compounds providing reliable molecular geometries. An important prerequisite is that the ground electronic states of the studied Pu, Am, and Cm trioxides have one dominant (80− 90%) electron configuration; hence, advanced single-reference methods can successfully model the ground-state molecular properties.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b01344. Six tables listing all the optimized geometries and computed SF and SO electronic states (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Attila Kovács: 0000-0001-8169-3547 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS The author is grateful to Dr. Zs. Soti for technical assistance in the analysis of the computed results. REFERENCES

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Relativistic Multireference Quantum Chemical Study of the Electronic

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