Structure and Other Molecular Properties of Actinide Trichlorides

Article pubs.acs.org/JPCA

Structure and Other Molecular Properties of Actinide Trichlorides AnCl3 (An = Th−Cm) Attila Kovács,*,† Rudy J. M. Konings,† Zoltán Varga,‡ and Dénes Szieberth§ †

European Commission, Joint Research Centre, Institute for Transuranium Elements, P.O. Box 2340, 76125 Karlsruhe, Germany Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, United States § Department of Inorganic and Analytical Chemistry, Budapest University of Technology and Economics, Szent Gellért tér 4, H-1111 Budapest, Hungary ‡

ABSTRACT: The ground-state molecular properties of the trichlorides of light actinides (An = Th−Cm) have been predicted by state-of-the-art quantum chemical calculations. The ground electronic states have been determined by multireference calculations at the CASPT2 level including both scalar and spin− orbit relativistic effects. These studies supported the expected single-configuration character of ThCl3 and CmCl3 with their well-defined 6dσ/7s hybrid and 5f7 configurations, respectively. In contrast, the intermediate actinides (PaCl3− AmCl3) with partly filled 5f shells have numerous very low-lying excited states and consequently a mixed character of the spin−orbit ground states. Apart from the planar ThCl3 the ground-state molecular geometries proved to be pyramidal with C3v symmetry. The gradually decreasing An−Cl bond distances reveal the actinide contraction known for the atomic and ionic radii of these actinide atoms. Other ground-state molecular properties as vibrational frequencies and natural charges have been obtained by density functional theory calculations using the B3LYP exchange-correlation functional in conjunction with small-core relativistic energy-consistent pseudopotentials for the actinides.

1. INTRODUCTION One of the most characteristic structural features of f-elements is the systematic contraction of their atomic and ionic radii1 along the lanthanide and actinide rows of the periodic system2 due to the less effective shielding of nuclear charge by f electrons. This results in the valence s electrons (6s and 7s in lanthanides and actinides, respectively) drawn toward the nucleus, thus leading to smaller atomic radii.3−7 The relativistic effects were found to contribute by about 10% of the contraction in lanthanide compounds.8 This contraction can be expected in the compounds of felements with strong ionic character, in which the bond distances are determined primarily by the ionic radii. In compounds with considerable covalent character the bond distances are strongly influenced by the molecular orbital interactions. The trend can be altered when the occupied molecular orbitals change along the row which happens at different involvement of atomic valence s, d, and f orbitals in the bonding and nonbonding orbitals. This is why an overall contraction trend could not be found in the actinide monoxides and dioxides.9 The contraction was observed only in a small segment of actinide dioxides (PaO2−UO2−NpO2−PuO2), in which the bonding scheme was consistent enough; that is, the only difference was the gradual population of the nonbonding 5f atomic orbitals of the actinides.9 The “lanthanide contraction” in lanthanide trihalides is well documented both from experiment and quantum chemical © 2013 American Chemical Society

calculations (see, e.g., refs 6,10−13). In contrast, very limited information is available for actinide trihalides. Due to the gasphase experimental difficulties on these compounds (radioactivity, low abundance, multiple oxidation states leading to sensitivity to oxidation and moisture) the only experimental geometry known is that of UCl3 from a gas electron diffraction study ca. 20 years ago.14 From the side of theory, a few papers reported quantum chemical calculations on actinide trihalides: these are the DFT calculations of Joubert and Maldivi on uranium trihalides (UF3, UCl3, UBr3, UI3),15 the DFT calculations of Batista et al. on uranium fluorides and chlorides (UXn, n = 1−6)16 and that of Vetere et al. using multireference and DFT methods on AmF3 and AmCl3.17 These limited data and the different theoretical levels do not facilitate any conclusion on the trends in actinide halides. The goal of the present study is the elucidation of the electronic ground-state properties of actinide trichlorides by means of state-of-the-art relativistic multireference calculations. Selection of the chlorides is reasoned by the potential application of thorium and uranium chlorides in molten salt nuclear reactors,18−20 leading to the formation of other actinide (Pa, Np, Pu, Am, Cm) chlorides during the nuclear process. As another application, actinide chlorides play a role in reprocessing technologies.21,22 The molecular geometries Received: August 6, 2013 Published: October 4, 2013 11357

dx.doi.org/10.1021/jp407855j | J. Phys. Chem. A 2013, 117, 11357−11363

The Journal of Physical Chemistry A

Article

Spin−orbit (SO) effects were taken into account by using the complete active space state interaction method (CASSI-SO),32 which allows CASSCF wave functions for different electronic states to interact under the influence of a spin−orbit Hamiltonian. The CASSCF/CASPT2/CASSI-SO methods and the basis set used here have been successfully applied in a number of studies on actinide-containing systems.33−47 The DFT calculations were carried out using the Gaussian 09 code.48 We note that while DFT was proved to be inferior in several cases to multireference theory,49−51 our recent studies using the above B3LYP/ECP level provided comparable performance with SO-CASPT2 for both the geometries and the ionization and dissociation energies of actinide oxides.9,52 Therefore we used in the present study a similar DFT level as previously for the oxides, i.e., the B3LYP exchange−correlation functional53,54 in conjunction with the actinide small-core quasi-relativistic pseudopotentials of the Stuttgart−Cologne group (ECP60MWB)55,56 and the 14s13p10d8f6g valence basis set contracted to 10s9p5d4f3g (ECP60MWB_SEG basis),56 while for Cl the correlation-consistent cc-pVTZ basis set.57 In the cases when the initial DFT calculations converged to an electronic state different from that obtained by spin-free (SF) CASPT2, we altered the orbital populations accordingly. Thus the DFT states reported in this paper are consistent with the SF-CASPT2 ground states. We note that in the case of UCl3 we found that the SF-CASPT2 ground state was a lowlying excited state at the B3LYP level. This is not surprising for such systems with very low-lying excited states (see Table 1).

obtained in our systematic study provide a reliable basis for studying the contraction effect along the actinide row. Furthermore, the computed molecular parameters (geometry, vibrational frequencies, electronic properties) can be used to update existing (mostly estimated) gas-phase thermodynamic data being required to design efficient safety arrangements for nuclear processes.

2. COMPUTATIONAL DETAILS The multireference calculations on ThCl3, PaCl3, UCl3, NpCl3, PuCl3, AmCl3 and CmCl3 were performed using the software MOLCAS 7.8.23 As the code can handle only Abelian groups (the D2h point group and its subgroups), we used C1 symmetry which facilitates also the exploration of eventual deformation from C3v geometry. The complete active space (CAS) SCF method24 was used to generate molecular orbitals and reference functions for subsequent multiconfigurational second-order perturbation theory calculations of the dynamic correlation energy (CASPT2).25,26 The atomic orbitals required for the active space have been tested carefully. Initially we included the three σ bonding orbitals (having major Cl 3p contributions) and the 7s, five 6d and seven 5f orbitals of the actinides, altogether 16 orbitals, in the active space. These orbitals in the active space were occupied by 7−13 electrons in the AnCl3 species (An = Th−Cm), respectively. In test CASSCF calculations we investigated the static correlation behavior of the lone pair Cl orbitals (from which one π type orbital of each Cl tends to donate some electron density to empty 5f/6d orbitals of the actinides). The populations of the 2-electron bonding and lone pair orbitals (dominated by the atomic orbitals of Cl) were always larger than 1.98 e, hence they could be moved to the inactive space.27 The orbitals beyond the 5f ones in the active space (having generally antibonding character) showed populations below 0.02 e. Based on the above experience, i.e., that the 2-electron orbitals are not important for the ground state properties, the geometry optimizations were performed with a small active space including only the seven 5f orbitals for UCl3−CmCl3. Because of technical (SCF convergence) problems in our calculations for ThCl3 and PaCl3 we extended the active space with the two highest-energy 2-electron orbitals. Thus, for these latter molecules we used 11 orbitals with five and six electrons, respectively. Test geometry optimizations on UCl3 and NpCl3 with a 16-orbital active space (including three 2-electron orbitals) confirmed the reliability of the geometries obtained with the smaller active space. The ground and low-lying excited states of the molecules were studied by multiconfigurational state-averaged calculations including the 5−13 lowest electronic states for a given spin multiplicity and symmetry. Beside the ground-state spin multiplicity the neighboring multiplicities were checked too. The active space in these calculations contained 13 orbitals (7s, 6d, 5f) and the 5f electrons of the given actinide element. All electron basis sets of atomic natural orbital type, developed for relativistic calculations (ANO-RCC), were used for all the atoms. For the actinides a primitive set of 26s23p17d13f5g3h was contracted to 9s8p6d4f2g1h,28 whereas for Cl a primitive set of 17s12p5d4f2g was contracted to 5s4p2d1f29 achieving TZP quality. The Douglas−Kroll−Hess Hamiltonian30,31 was used in the CASSCF calculations in order to account for scalar relativistic effects.

3. RESULTS AND DISCUSSION 3.1. Electronic Structure from Multireference Calculations. The SF ground electronic and lowest excited states of the studied AnCl3 molecules are compiled in Table 1. The spin multiplicities are in agreement with those of the An3+ ions.58 As found for U3+/Np3+/Pu3+/Am3+/Cm3+,58 the nonbonding (unpaired) valence electrons occupy the pure 5f orbitals. On the other hand, some deviations were observed for ThCl3 and PaCl3. In Th3+ the single valence electron occupies the 5fϕ orbital (state is 2F2.5),58 while in ThCl3 the nonbonding (unpaired) valence electron populates a 6dσ/7s hybrid orbital. In Pa3+ the 5fδ and 5fϕ orbitals are populated,58 while in the SF ground state of PaCl3 the two unpaired valence electrons populate the nonbonding 6dσ/7s hybrid and 5fσ orbitals (cf. Table 1). The SF ground electronic states of most studied AnCl3 molecules are characterized by a single dominant electron configuration, its contribution being near 100%. The exception is PuCl3, its SF ground state consisting of two major configurations in 1:1 ratio (see Table 1). We note that also the lowest-lying excited states (compiled in Table 1) have only one major electron configurations. The ground electronic states are straightforward for ThCl3 and CmCl3, where the first SF excited states appear much higher in energy: in the case of ThCl3 this difference is 140 kJ/ mol (the 6dσ electron excited to 6dπ) while in the case of CmCl3 322 kJ/mol (having spin multiplicity of 6 due to the switch of the spin of an 5f electron, thus resulting in a double population of the 5fσ orbital). In the other studied AnCl3 molecules the lowest SF excited states appear already at a few kJ/mol above the ground state. We note that, having the lowest excited states so close in energy to the ground state, the ground state and its geometry should be determined with particular care. Small changes in the 11358



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Table 1. Low-Lying Electronic States of AnCl3 Molecules from Spin-Free CASPT2 Calculations AnCl3 ThCl3

PaCl3

UCl3

NpCl3

PuCl3

AmCl3

CmCl3

ΔE kJ/mol

state

0.0 139.7 323.5 0.0 4.8 12.7 72.0 0.0 2.1 6.9 8.8 13.6 14.4 16.0 17.1 20.3 0.0 3.0 7.7 8.6 10.1 12.1 17.0 17.9 0.0

2

8.3 16.3 19.0 19.0 21.4 22.6 23.1 0.0 0.4 15.5 22.3 27.3 0.0 322.4 615.4

6

A′1 E″ 2 E′ 3 A1(1) 3 E(1) 3 E(2) 3 A1(2) 4 A1(1) 4 E(1) 4 E(2) 4 A1(2) 4 A2(1) 4 A1(3) 4 E(3) 4 E(4) 4 A2(2) 5 A1(1) 5 A1(2) 5 A1(3) 5 E(1) 5 A1(4) 5 E(2) 5 A2(1) 5 A2(2) 6 E(1)b 2

E(2) A1 6 A2(1) 6 E(3) 6 A2(2) 6 A2(3) 6 A2(4) 7 A2(1) 7 A1 7 E(1) 7 E(2) 7 A2(2) 8 A2 6 E 8 E 6

Scheme 1. Pyramidal Structure of AnCl3 Molecules

character of major electron configurationa 6dσ/7s 6dπ 6dδ 6dσ/7s, 5fσ 6dσ/7s, 5fπ 6dσ/7s, 5fδ 5fπ, 5fπ 5fσ, 5fδ, 5fδ 5fσ, 5fδ, 5fϕ 5fσ, 5fπ, 5fϕ 5fπ, 5fπ, 5fϕ 5fδ, 5fδ, 5fϕ 5fδ, 5fδ, 5fϕ 5fσ, 5fπ, 5fϕ 5fσ, 5fδ, 5fϕ 5fπ, 5fπ, 5fϕ 5fσ, 5fπ, 5fδ, 5fϕ 5fσ, 5fδ, 5fδ, 5fϕ 5fσ, 5fπ, 5fδ, 5fϕ 5fπ, 5fδ, 5fδ, 5fϕ 5fσ, 5fπ, 5fδ, 5fϕ 5fπ, 5fπ, 5fδ, 5fϕ 5fσ, 5fπ, 5fδ, 5fϕ 5fσ, 5fδ, 5fδ, 5fϕ 51% 5fσ, 5fπ, 5fπ, 5fδ, 5fϕ 49% 5fσ, 5fπ, 5fπ, 5fδ, 5fϕ 5fσ, 5fπ, 5fδ, 5fδ, 5fϕ 5fπ, 5fπ, 5fδ, 5fδ, 5fϕ 5fσ, 5fπ, 5fδ, 5fϕ, 5fϕ 5fπ, 5fπ, 5fδ, 5fϕ, 5fϕ 5fσ, 5fπ, 5fδ, 5fϕ, 5fϕ 5fσ, 5fπ, 5fδ, 5fϕ, 5fϕ 5fσ, 5fπ, 5fπ, 5fϕ, 5fϕ 5fσ, 5fπ, 5fπ, 5fδ, 5fδ, 5fϕ 5fσ, 5fπ, 5fπ, 5fδ, 5fδ, 5fϕ 5fσ, 5fπ, 5fπ, 5fδ, 5fϕ, 5fϕ 5fσ, 5fπ, 5fδ, 5fδ, 5fϕ, 5fϕ 5fπ, 5fπ, 5fδ, 5fδ, 5fϕ, 5fϕ 5fσ, 5fπ, 5fπ, 5fδ, 5fδ, 5fϕ, 5fϕ (5fσ)2, 5fπ, 5fδ, 5fδ, 5fϕ, 5fϕ 5fσ, 5fπ, 5fδ, 5fδ, 5fϕ, 5fϕ, 6dσ

Table 2. Ground and Selected Low-Lying Electronic States of AnCl3 Molecules from Spin−Orbit CASPT2 Calculations AnCl3 ThCl3 PaCl3

UCl3

NpCl3

PuCl3

AmCl3

a

The orbitals are singly occupied except for 5fσ in the 6E state of CmCl3. bIn this state of PuCl3 the two given configurations differ in the sign of the magnetic quantum numbers of the 5fδ and 5fϕ orbitals.

geometry may change the energetic ordering of these states. Therefore we performed first a geometry optimization of the state-averaged system containing seven states, and the obtained geometry was used as initial one for the optimization of the ground electronic state. These low-lying electronic states differ from each other in the population of the 5f orbitals (cf. Table 1). From them 5fσ and 5fϕ seem to be preferred, being populated in most low-energy states. All our geometry optimizations at the SF-CASPT2 level starting from asymmetric C1 structures converged to pyramidal C3v ones (Scheme 1) except for ThCl3, for which a planar D3h structure was obtained for the SF ground state. The symmetry

CmCl3

ΔE kJ/mol

major spin-free components

0.0 0.0 4.0 10.7 28.4 30.5 33.6 38.8 0.0 3.7 6.6 12.1 14.6 41.7 43.0 45.9 0.0 6.2 12.5 15.1 18.7 25.6 30.0 0.0 11.6 18.1 22.0 30.7 34.5 37.1 48.0 0.0 0.9 10.2 21.4 22.1 22.7 37.3 37.5 0.0

100% 2A′1 54% 3E(1) + 44% 3A1(1) 46% 3E(1) + 36% 3A1(1) 48% 3E(1) + 30% 3E(2) + 21% 3A1(1) 51% 3E(2) + 34% 3E(1) 50% 3E(1) + 45% 3E(2) 54% 3E(1) + 29% 3A1(1) 43% 3E(1) + 36% 3E(2) + 20% 3A1(1) 34% 4A1(1) + 46% 4E(1) 31% 4E(2) + 30% 4E(1) 24% 4A1(2) + 34% 4E(2) 39% 4E(4) + 20% 4A2(1) + 20% 4A1(3) 41% 4E(3) + 31% 4A2(2) 43% 4E(1) + 34% 4E(2) 33% 4A1(1) + 27% 4A1(2) 36% 4E(2) + 29% 4E(1) 36% 5A1(2) + 31% 5A1(1) 32% 5E(2) + 22% 5E(1) + 20% 5A1(3) + 18% 5A1(4) 18% 5E(1) + 17% 5A2(2) + 17% 5A2(1) + 15% 5A1(4) 19% 5A2(1) + 18% 5A2(2) + 15% 5E(1) + 15% 5A1(3) 29% 5A1(3) + 28% 5E(1) + 18% 5A1(1) 21% 5E(2) + 18% 5A1(1) + 18% 5A1(2) 39% 5E(2) + 22% 5A1(4) + 16% 5A1(2) 74% 6E(1) 48% 6E(2) + 15% 6A1 + 14% 6A2(1) 32% 6E(3) + 17% 6A2(3) + 17% 6A2(4) 58% 6E(1) + 26% 6E(2) 16% 6A2(1) + 16% 6A1 + 12% 6E(3) + 10% 6A2(2) 28% 6E(2) + 21% 6A2(4) + 17% 6E(3) + 17% 6A2(3) 29% 6E(3) + 16% 6A2(2) + 16% 6A1 + 15% 6A2(1) 58% 6E(1) +32% 6E(2) 38% 7A1 + 38% 7A2(1) 42% 7A1 + 41% 7A2(1) 29% 7A2(1) + 29% 7A1 + 26% 7E(1) 35% 7E(1) + 17% 7A2(1) + 15% 7E(2) 43% 7E(2) + 23% 7A2(2) 28% 7E(1) + 22% 7E(2) + 17% 7A1 + 14% 7A2(1) 45% 7A1 + 34% 7E(1) 46% 7A2(1) + 34% 7E(1) 100% 8A2

of the ground states (Table 1) corresponds to A1 in the case of PaCl3, UCl3 and NpCl3 while to A′1 in the case of ThCl3. PuCl3, AmCl3 and CmCl3 have different SF ground-state symmetries corresponding to 6E, 7A2 and 8A2, respectively. Due to its E symmetry PuCl3 is a proper candidate for Jahn−Teller effect, therefore we investigated a possible Jahn−Teller distortion of its geometry at the SF-CASPT2 level. The 11359



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geometry optimization resulted in a C3v structure as lowestenergy one, but the potential energy surface in its vicinity seems to be rather flat. The lowest energy SO states of the studied AnCl3 molecules are compiled in Table 2. The SO ground states correspond exclusively to the SF ones in the case of ThCl3 and CmCl3, due to the very high energies of the lowest excited states in these molecules. One dominant SF component (74%) appears in the SO ground state of PuCl3, which can be derived from its degenerate SF ground state (cf. Table 1). In these cases the geometries of the SO ground states are expected to be in good agreement with those of the SF ones. In all the other studied AnCl3 molecules the SO ground states are mixed, the two major contributions being the SF ground and first excited states (cf. Tables 1 and 2). For the latter molecules we optimized the geometries in state-averaged calculations including the first two SF states (SA2). As seen in Table 3, they are quite close to both

Figure 1. Comparison of computed ClAnCl and FLnF bond angles in actinide and lanthanide trihalides. The FLnF data were taken from ref 12.

a

Table 3. Geometrical Parameters of AnCl3 Molecules from SF-CASPT2 Calculations AnCl3

sym

ThCl3 PaCl3 UCl3 NpCl3 PuCl3 AmCl3 CmCl3

D3h C3v C3v C3v C3v C3v C3v

SA7b 2.596, 2.532, 2.524, 2.496, 2.484,

113.4 105.5 108.3 108.2 108.6

single-state 2.573, 2.532, 2.532, 2.510, 2.500, 2.491, 2.478,

120.0 117.4 107.8 107.7 109.7 113.2 110.9

SA2b 2.532, 117.5 2.532, 107.7 2.518, 108.3 2.493, 113.9

a

Bond distances are given in angstroms, bond angles in degrees. State-averaged calculations using the seven and two lowest-energy states, respectively.

b

the ground-state geometries and the ones obtained in the stateaveraged calculations using seven states. This suggests that the geometries of the low-lying excited SF states do not differ much from those of the ground states. The geometries obtained from the SA2 calculations are expected to approach the SO groundstate geometries of the latter AnCl3 molecules. 3.2. DFT Calculations. The main goal of our DFT calculations was to obtain the vibrational data of the target AnCl3 molecules. These calculations were guided by the abovediscussed CASPT2 results, as we had to reproduce the reliable ground states determined by the multireference method. By the procedure described in Computational Details we could quite well reproduce the above-reported SF-CASPT2 ground electronic states of the AnCl3 molecules. The only minor deviation arose in the case of the mixed ground state of PuCl3, where in the B3LYP orbital populations one of the 5fϕ contributions is missing. The unbalanced 5fϕ population of the orbitals can be the reason that these B3LYP geometry optimizations resulted in a Cs geometry instead of C3v obtained in the multireference calculations for PuCl3. As the symmetry of the CASPT2 ground state of PuCl3 is E, the B3LYP results are in agreement with Jahn−Teller effect. We note that except for UCl3 the SF-CASPT2 ground electronic states agreed with the obtained lowest-energy electronic states at the B3LYP level. In the case of UCl3, however, at the B3LYP level we found a state with lower energy than the 4A1 state (ground state at the SF-CASPT2 level). This lower-energy B3LYP state has an electron configuration of 5fσ, 5fδ, 5fϕ (4E). Its optimized geometry is Cs (with bond distances

Figure 2. Computed An−Cl bond distances and the An3+ ionic radii from ref 1.

of 2 × 2.556, 2.550 Å), implying a Jahn−Teller distortion from C3v. Our B3LYP results are compiled in Table 4. In agreement with the multireference results, ThCl3 was found to be planar, while the other studied AnCl3 molecules proved to be pyramidal. Similarly to the CASPT2 geometries, there is no gradual change of the pyramidality from ThCl3 to CmCl3. The bond angles computed at both levels of theory are presented in Figure 1 where a good agreement in the trend of the two sets of data can be observed. As the properties of related actinide and lanthanide compounds are often compared, we added also the recently computed bond angles of the pyramidal LnF3 molecules (Ln = Ce−Gd, the LnCl3 molecules are planar)12 to Figure 1. These LnF3 bond angles are in agreement with the 4f asphericity model of Molnár and Hargittai,59 based on the shape of the gradually filled inert 4f shell. It is interesting that the trend of the AnCl3 and LnF3 data is just the opposite. This contradiction is probably accidental, because the bonding character of the 4f and 5f shells is different: while in the lanthanides the 4f shell forms usually a nonbonding electron density distribution (and by steric interactions has some effect on the shape of the molecule), in the actinides (from Pa) the 5f electrons take part in the bonding interactions. 11360



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Table 4. Electronic Ground-State Properties of AnCl3 Molecules from B3LYP Calculations AnCl3

state

sym

ThCl3 PaCl3 UCl3 NpCl3 PuCl3e AmCl3 CmCl3

2

D3h C3v C3v C3v Cs C3v C3v

A′1 A1 4 A1 5 A1 6 A′ 7 A2 8 A2

3

geometrya 2.569, 2.551, 2.567, 2.545, 2.538, 2.532, 2.518,

120.0 115.1 111.9 112.2 2 × 2.531; 110.9, 2 × 113.4 116.5 112.9

qAnb

nAnc

vibrational frequenciesd

1.44 1.43 1.62 1.65 1.67 1.72 1.74

7s(0.60)5f(0.40)6d(1.51) 7s(0.51)5f(1.84)6d(1.11) 7s(0.15)5f(3.23)6d(0.95) 7s(0.20)5f(4.18)6d(0.92) 7s(0.18)5f(5.20)6d(0.90) 7s(0.17)5f(6.21)6d(0.85) 7s(0.20)5f(7.11)6d(0.90)

328(97), 331(0), 60(3), 36(4) 324(86), 314(13), 58(2), 31(11) 313(100), 317(9), 67(3), 47(14) 317(97), 317(9), 68(2), 44(16) 317(81), 313(81), 321(43), 62(3), 53(3), 33(16) 316(107) 313(29), 26(19), 2(7) 319(93), 322(8), 74(3), 42(18)

a Bond distances are given in angstroms, bond angles in degrees. bNatural charges of the actinide atom (e) from NBO analysis. cPopulations (e) of the actinide valence orbitals from NBO analysis. dIn cm−1. IR intensities (km/mol) in parentheses. The sequence of the frequencies corresponds to the irreducible representations: E, A1, E, A2 (C3v), and the corresponding ones of D3h. eDue to the single electron configuration treatment at the DFT level of theory, the degenerate ground electronic state at CASPT2 level undergoes the Jahn−Teller distortion. Therefore besides the geometrical changes the degenerated vibrational frequencies split up (e.g., 317(81) and 313(81)) and shifted a few cm−1 from the real C3v ground state.

The computed bond distances are depicted in Figure 2. The trends obtained at the two levels are in good agreement with minor deviations at ThCl3 and PaCl3, their B3LYP bond distances being relatively smaller. In these two molecules the 7s and 6d orbitals are more populated and play some role in the bonding, and presumably these features are somewhat differently described by the CASPT2 and B3LYP levels. Nevertheless, from UCl3 the bond distances show a gradually decreasing trend similarly to that of the An3+ ionic radii (cf. Figure 2). Hence, the “actinide contraction” appears clearly in the trichlorides of early actinides, which can be the result of two main reasons: (i) considerable ionic component of bonding; (ii) very similar covalent interactions (composition of bonding molecular orbitals) in these molecules. The NBO60 atomic charges of the actinides in the studied AnCl3 compounds are listed in Table 4. They are in agreement with a considerable ionic contribution in the An−Cl bonding and show a gradual increasing trend from UCl3 to CmCl3. The ionic character of bonding seems to be somewhat weaker in ThCl3 and PaCl3, as the actinide charges in these AnCl3 molecules are smaller by 0.2−0.3 e than those in the other ones. The natural actinide valence orbital populations in Table 4 show the expected gradual increase of 5f population from ThCl3 to CmCl3. In agreement with the energetic proximity of the 5f and 6d orbitals in Th and Pa, in these trichlorides the 6d orbitals are somewhat more, while the 5f ones somewhat less populated than in the other AnCl3 molecules. Similarly, the 7s orbital of the former two actinides is somewhat more populated than that of the other ones. The 7p orbitals are practically empty in the studies AnCl3 molecules. In order to gain insight into the orbital interactions, we investigated the bonding molecular orbitals. We found six molecular orbitals with bonding character. We depicted those of UCl3 in Figure 3; the orbitals of the other pyramidal AnCl3 molecules are very similar. The first two orbitals demonstrate σ interactions between An and Cl, while the third orbital is a mixture of σ and π interactions. The three orbitals in the second row contain various π interactions. The shape of these orbitals and their higher energy suggest that they represent donor−acceptor interactions in the form of charge transfer from the chlorine lone pairs to the empty valence orbitals of An. The remaining 3p and the 3s orbitals of Cl form nonbonding lone pair orbitals. 3.3. Assessment of Literature Data on UCl3 and AmCl3. For these two molecules some literature information is available, and in this section we assess them compared with our present results (Table 5). We start with UCl3, for which

Figure 3. Characteristic bonding orbitals of UCl3.

Table 5. Comparison of Selected Results on the Geometrya of UCl3 and AmCl3 AnCl3 UCl3

AmCl3

method

sym

bond

angle

ref

EDb SF-CASPT2/AE B3LYP/SC-PP PBE0/SC-PP MP2/LC-PP B3LYP/LC-PP BP/ZORA/AE SF-CASPT2/AE B3LYP/SC-PP SF-CASPT2/AE SF-CASPT2/SC-PP BP/ZORA/AE

C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v C3v

2.549(8) 2.532 2.567 2.553 2.521 2.592 2.524 2.491 2.532 2.440 2.480 2.482

95(3) 107.8 111.9 108.2 106.9 114.5 109.6 113.2 116.5 109.4 110.9 109.3

14, 61 this work this work 16 15 15 15 this work this work 17 17 17

a Bond distances are given in angstroms, bond angles in degrees. bGas electron diffraction. Experimental errors are given in parentheses.

molecule both experimental and quantum chemical results have been reported. The molecular geometry has been determined by gas electron diffraction at 800 K by Bazhanov et al.14,61 The molecule was reported to have a strongly pyramidal structure (C3v symmetry, bond angle 95 ± 3°). From the vibrational amplitudes derived at the analysis of the electron diffraction data the authors estimated the fundamental frequencies. Another set of vibrational frequencies was estimated from spectroscopic constants.62 In addition, the asymmetric stretching frequency has been reported from a gas-phase IR spectroscopic study.63 11361



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UCl3 results, we can observe some systematic deviations between the theoretical levels. Thus, the B3LYP/SC-PP bond distances are larger by ca. 0.04 Å than our SF-CASPT2 ones, while the BP/ZORA/AE bond distances are shorter by ca. 0.01 Å. Noteworthy is the difference of 0.05 Å in the Am−Cl bond distance obtained by the two SF-CASPT2/AE calculations. This difference reflects the importance of the basis sets: The ANO-RCC basis sets,28,29 optimized for relativistic calculations, were not yet available for the study of Vetere et al.,17 and in addition they used for Cl a smaller basis (DZP in contrast to our TZP one for both Cl and Am). The smaller bond distance is accompanied by smaller bond angles in the study of Vetere et al. (cf. Table 5).

Two quantum chemical studies have been published dealing with UCl3 among other uranium halides. The study of Joubert and Maldivi15 was performed at seven different theoretical levels including relativistic all electron density functional theory calculations as well as MP2 and various exchange-correlation functionals in conjunction with the large-core (78 e) pseudopotential of the Stuttgart−Cologne group.64 They reported the symmetry of the ground state (4A1), but lacking additional information we were not able to correlate it with the CASPT2 ground or one of the low-lying 4A1 excited states. Batista et al. performed calculations using the small-core (60 e) Stuttgart−Cologne pseudopotential in conjunction with the B3LYP and PBE0 hybrid functionals.16 They did not gave a detailed electronic characterization of the ground state either, just that the electron configuration is 5f3. Selected results on UCl3 including our present CASPT2 and B3LYP/SC-PP ones are compiled in Table 5. From the computed data the bond distance obtained by Batista et al.16 at the PBE0/SC-PP level is in excellent agreement with the experimental bond distance, which lies between our B3LYP/ SC-PP and SF-CASPT2 ones. The other literature data have larger deviations. We note, however, that the experimental data originate from a time when assistance from quantum chemical calculations was not yet available. Particularly the missing reliable vibrational data may call for a larger experimental uncertainty than that given by Bazhanov et al.14,61 The latter deficiency is clearly shown by the bond angles, where the computed ones are considerably larger than that reported in the gas electron diffraction study.14,61 The overestimation of pyramidal character of such floppy molecules17 occurred frequently in past high-temperature gas electron diffraction studies as a result of insufficient description of the large amplitude deformation vibrations resulting in too small Cl···Cl interatomic distances (leading to too small bond angles). Therefore we believe that the bond angles computed recently at adequate theoretical levels are more reliable than the (probably underestimated) experimental ones. The computed harmonic vibrational frequencies reported by Joubert and Maldivi for UCl315 are in good agreement with our present results. The computations support also the estimated frequencies by Gurvich and Dorofeeva.62 However, the reported experimental asymmetric stretching frequency (275.0 ± 0.5 cm−1)63 is lower by ca. 40 cm−1 than our computed harmonic value. Taking into account the anharmonicity (computed to be about 1 cm−1 for this mode) does not improve the situation. It seems very likely that the band assigned to (the moisture and oxygen sensitive) UCl3 in the gas-phase IR spectrum belongs to another gas-phase species, while the stretching bands of UCl3 are hidden by the intense band of UCl4 being the major component in the vapor. The electronic structure of AmCl3 has been investigated in detail by Vetere et al.17 using relativistic multireference and DFT methods. In agreement with our present results, they reported the 7A2 state as the SF ground electronic state with a pyramidal C3v structure. The first excited state, 7A1, was found by them at somewhat higher energy (2 kJ/mol) than in our present study (0.4 kJ/mol, cf. Table 1). They reported also a planar D3h geometry being a transition state higher by a few kJ/ mol in energy above the C3v global minimum. The small energy difference supports the flexible nature of AnCl3 molecules, similarly to that found for lanthanide trihalides.6 Geometrical parameters obtained at selected theoretical levels are compiled in Table 5. Assessed together with the

4. CONCLUSIONS Using state-of-the-art relativistic multireference calculations we determined the ground and low-lying excited states of the trichlorides of early actinides (Th−Cm). Our spin−orbit calculations revealed the pure character of the SO ground states of ThCl3 and CmCl3, the nearly pure one of PuCl3, while the mixed character of those of other actinide trihalides. Except for ThCl3 and CmCl3, the trihalides of the early actinides have several very low-lying excited states, which can be populated at high-temperature gas-phase experiments. Apart from the planar ThCl3, the ground-state molecular geometries proved to be pyramidal with C3v symmetry. The gradually decreasing An−Cl bond distances reveal the “actinide contraction” known for the atomic and ionic radii of these actinide atoms. That well recognizable contraction is due to the considerable ionic character of bonding in these actinide trihalides and to the very similar covalent interactions. The analysis of molecular orbitals supported the multiple character of bonding: beyond the actinide−halogen single (mostly sigma) bonds π-type donor−acceptor interactions appear, representing charge transfer from the chlorine lone pairs to the empty valence orbitals of the central An atom.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS The Hungarian Scientific Research Foundation (OTKA No. 75972) is acknowledged for financial support. REFERENCES

(1) Shannon, R. D. Acta Crystallogr. 1976, A32, 751−767. (2) Edelstein, N. M.; Fuger, J.; Katz, J. J.; Morss, L. R. Summary and Comparison of Properties of the Actinide and Transactinide Elements. In The Chemistry of the Actinide and Transactinide Elements; Edelstein, N. M., Fuger, J., Morss, L. R., Eds.; Springer: Dordrecht, 2006; Vol. 3; pp 1753−1835. (3) Cotton, F. A.; Wilkinson, G. Advanced Inorganic Chemistry; Wiley: New York, 1988. (4) Wang, S. G.; Schwarz, W. H. E. J. Phys. Chem. 1995, 99, 11687− 11695. (5) Laerdahl, J. K.; Fægri, K.; Visscher, L.; Saue, T. J. Chem. Phys. 1998, 109, 10806. (6) Hargittai, M. Chem. Rev. 2000, 100, 2233−2301. (7) Housecroft, C. E.; Sharpe, A. G. Inorganic Chemistry; Prentice Hall: New Jersey, 2004. (8) Pyykkö, P. Chem. Rev. 1988, 88, 563−594. (9) Kovács, A.; Pogány, P.; Konings, R. J. M. Inorg. Chem. 2012, 51, 4841−4849. 11362



Article

(10) Hargittai, M. Coord. Chem. Rev. 1988, 91, 35−88. (11) Kovács, A.; Konings, R. J. M. J. Phys. Chem. Ref. Data 2004, 33, 377−404. (12) Pantazis, D. A.; Neese, F. J. Chem. Theor. Comput. 2009, 5, 2229−2238. (13) Dolg, M. J. Chem. Theor. Comput. 2011, 7, 3131−3142. (14) Bazhanov, V. I.; Ezhov, Y. S.; Komarov, S. A. J. Struct. Chem. 1990, 31, 986. (15) Joubert, L.; Maldivi, P. J. Phys. Chem. A 2001, 105, 9068−9076. (16) Batista, E. R.; Martin, R. L.; Hay, P. J. J. Chem. Phys. 2004, 121, 11104−11111. (17) Vetere, V.; Roos, B. O.; Maldivi, P.; Adamo, C. Chem. Phys. Lett. 2004, 396, 452−457. (18) Taube, M. Fast Reactors Using Molten Chloride Salts as Fuel; EIRBericht Nr-332; Eidgenö ssisches Institut für Reaktorforschung Wurenlingen: 1978. (19) Forsberg, C. W. Thermal-and Fast-Spectrum Molten Salt Reactors for Actinide Burning and Fuel Production; Report, American Nuclear Society: 2007. (20) LeBlanc, D. Nucl. Eng. Des. 2010, 240, 1644−1656. (21) Souček, P.; Malmbeck, R.; Nourry, C.; Glatz, J.-P. Energy Procedia 2011, 7, 396−404. (22) Volkovich, V. A.; May, I.; Griffiths, T. R.; Charnock, J. M.; Lewin, B. The Reprocessing of Nuclear Waste Using Molten Salts: Selective Precipitation Using Phosphate and Solving Problems of Speciation. In Proc. Electrochem. Soc.; Mantz, R. A., Trulove, P. C., De Long, H. C., Stafford, G. R., Hagiwara, R., Costa, D. A., Eds.; Electrochemical Society: Pennington, NJ, 2004; Vol. 24; pp 729. (23) Karlström, G.; Lindh, R.; Malmqvist, P.-Å.; Roos, B. O.; Ryde, U.; Veryazov, V.; Widmark, P.-O.; Cossi, M.; Schimmelpfennig, B.; Neogrady, P.; Seijo, L. Comput. Mater. Sci. 2003, 287, 222. (24) Roos, B. O. In Advances in Chemical Physics, Ab Initio Methods in Quantum Chemistry - II; Lawley, K. P., Ed.; John Wiley & Sons Ltd.: Chichester, 1987; Chapter 69; p 399. (25) Andersson, K.; Malmqvist, P.-Å.; Roos, B. O.; Sadlej, A.; Wolinski, K. J. Phys. Chem. 1990, 94, 5483. (26) Andersson, K.; Malmqvist, P.-Å.; Roos, B. O. J. Chem. Phys. 1992, 96, 1218. (27) Veryazov, V.; Malmqvist, P. Å.; Roos, B. O. Int. J. Quantum Chem. 2011, 111, 3329−3338. (28) Roos, B. O.; Lindh, R.; Malmqvist, P.-Å.; Veryazov, V.; Widmark, P.-O. Chem. Phys. Lett. 2005, 409, 295−299. (29) Roos, B. O.; Lindh, R.; Malmqvist, P.-Å.; Veryazov, V.; Widmark, P.-O. J. Phys. Chem. A 2005, 108, 2851. (30) Douglas, N.; Kroll, N. M. Ann. Phys. 1974, 82, 89. (31) Hess, B. Phys. Rev. A 1986, 33, 3742. (32) Roos, B. O.; Malmqvist, P.-Å. Phys. Chem. Chem. Phys. 2004, 6, 2919−2927. (33) Gagliardi, L.; La-Manna, G. F.; Roos, B. O. Faraday Discuss. 2003, 124, 63−68. (34) Gagliardi, L.; Roos, B. O. Inorg. Chem. 2003, 42, 1599−1603. (35) Gagliardi, L. J. Am. Chem. Soc. 2003, 125, 7504−7505. (36) Ferrante, F.; Gagliardi, L.; Bursten, B. E.; Sattelberger, A. P. Inorg. Chem. 2005, 44, 8476−8480. (37) Gagliardi, L.; Heaven, M. C.; Krogh, J. W.; Roos, B. O. J. Am. Chem. Soc. 2005, 127, 86−91. (38) Gagliardi, L.; Pyykkö, P.; Roos, B. O. Phys. Chem. Chem. Phys. 2005, 7, 2415−2417. (39) Roos, B. O.; Malmqvist, P.-Å.; Gagliardi, L. J. Am. Chem. Soc. 2006, 128, 17000−17006. (40) Gagliardi, L.; Cramer, C. J. Inorg. Chem. 2006, 45, 9442−9447. (41) Gagliardi, L. Theor. Chem. Acc. 2006, 116, 307−315. (42) Gagliardi, L.; Roos, B. O. Chem. Soc. Rev. 2007, 36, 893−903. (43) Roos, B. O.; Borin, A.; Gagliardi, L. Angew. Chem., Int. Ed. 2007, 46, 1469−1472. (44) Infante, I.; Raab, J.; Lyon, J. T.; Liang, B.; Andrews, L.; Gagliardi, L. J. Phys. Chem. A 2007, 111, 11996−12000. (45) Infante, I.; Gagliardi, L.; Scuseria, G. E. J. Am. Chem. Soc. 2008, 130, 7459−7465.

(46) Infante, I.; Gagliardi, L.; Wang, X. F.; Andrews, L. J. Phys. Chem. A 2009, 113, 2446−2455. (47) Gagliardi, L. Int. J. Quantum Chem. 2011, 111, 3302−3306. (48) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery Jr., J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Keith, T.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, Revision B.01; Gaussian, Inc.: Wallingford, CT, 2010. (49) Réal, F.; Vallet, V.; Marian, C.; Wahlgren, U. J. Chem. Phys. 2007, 127, 214302. (50) Wei, F.; Wu, G.; Schwarz, W. H. E.; Li, J. Theor. Chem. Acc. 2011, 129, 467−481. (51) Tecmer, P.; Gomes, A. S. P.; Ekström, U.; Visscher, L. Phys. Chem. Chem. Phys. 2011, 13, 6249−6259. (52) Averkiev, B.; Mantina, M.; Valero, R.; Infante, I.; Kovács, A.; Truhlar, D. G.; Gagliardi, L. Theor. Chem. Acc. 2011, 129, 657−666. (53) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (54) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (55) Küchle, W.; Dolg, M.; Stoll, H.; Preuss, H. J. Chem. Phys. 1994, 100, 7535−7542. (56) Cao, X. Y.; Dolg, M.; Stoll, H. J. Chem. Phys. 2003, 118, 487− 496. (57) Dunning, J., T. H. J. Chem. Phys. 1989, 90, 1007−1023. (58) Blaise, J.; Wyart, J.-F. Energy Levels and Atomic Spectra of Actinides, International Tables of Selected Constants; CNRS: Paris, 1992; Vol. 20. (59) Molnár, J.; Hargittai, M. J. Phys. Chem. 1995, 99, 10780−10784. (60) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899. (61) Bazhanov, V. I.; Ezhov, Y. S.; Komarov, S. A. Zh. Strukt. Khim. 1990, 31, 152. (62) Fuger, J.; Parker, V. B.; Hubbard, W. N.; Oetting, F. L. The Chemical Thermodynamics of Actinide Elements and Compounds Part 8. The Actinide Halides. Part 8. The Actinide Halides; IAEA: Vienna, 1983. (63) Kovács, A.; Booij, A. S.; Cordfunke, E. H. P.; Kok-Scheele, A.; Konings, R. J. M. J. Alloys Compd. 1996, 241, 95−97. (64) Küchle, W., et al., unpublished results.

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Structure and Other Molecular Properties of Actinide Trichlorides

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