Scholarly article on topic 'Electronic structure and spectroscopic properties of mixed sodium actinide oxides Na2AnO4 (An = U, Np, Pu, Am)'

Electronic structure and spectroscopic properties of mixed sodium actinide oxides Na2AnO4 (An = U, Np, Pu, Am) Academic research paper on "Physical sciences"

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Abstract of research paper on Physical sciences, author of scientific article — Attila Kovács

Abstract Multireference relativistic post-HF and DFT calculations have been performed on four Na2AnO4 (An = U, Np, Pu, Am) molecules. Beyond the electronic characteristics of the ground and excited electronic states, the molecular geometries and vibrational frequencies have been determined.

Academic research paper on topic "Electronic structure and spectroscopic properties of mixed sodium actinide oxides Na2AnO4 (An = U, Np, Pu, Am)"

Journal of Molecular Structure xxx (2016) 1—7

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Journal of Molecular Structure

journal homepage: http://www.elsevier.com/locate/molstruc

Electronic structure and spectroscopic properties of mixed sodium actinide oxides Na2AnO4 (An = U, Np, Pu, Am)

Attila Kovacs

European Commission, Joint Research Centre, P. O. Box 2340, 76125 Karlsruhe, Germany

ARTICLE INFO

ABSTRACT

Article history: Received 29 June 2016 Received in revised form 19 September 2016 Accepted 22 September 2016 Available online xxx

Dedicated to Prof. Georgiy V. Girichev on the Occasion of his 70th birthday.

Multireference relativistic post-HF and DFT calculations have been performed on four Na2AnO4 (An = U, Np, Pu, Am) molecules. Beyond the electronic characteristics of the ground and excited electronic states, the molecular geometries and vibrational frequencies have been determined.

© 2016 The Author. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND

license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Actinides

Relativistic multireference calculations DFT

Electronic structure Molecular geometry Vibrational frequencies

1. Introduction

In order to reduce the radioactive waste of nuclear reactors, the reactors under recent development are planned to operate in a closed fuel cycle, in which the highly radioactive minor actinides are re-used for energy generation. One of the new designs is the Sodium cooled Fast Reactor (SFR). The main advantages of the sodium melt as coolant are the high heat capacity resulting in a high margin to overheating and the high boiling point (T = 1156 K) being well above the reactor's planned operating temperature (around 850 K).

The nuclear reactors have to obey to very high safety standards, therefore possible accidents have to be carefully explored. Such an accident can be the breach of the fuel clad, in which case the sodium coolant and fuel can react with each other forming mixed sodium actinide oxides. Beside U and Pu (components of the MOX fuel) the most relevant actinides in these fuels are Np and Am. From the Na-An-O systems the An = U and Pu ones have been studied extensively in the literature. The published properties include the crystal structures [1,2], thermodynamic [3—5], magnetic [6,7], and spectroscopic properties of the solids [8—10]. In the solid phase

E-mail address: attila.kovacs@ec.europa.eu.

numerous compositions were reported: Na3UO4, NaUO3, Na2UO4, Na4UO5, Na2U2O7, Na6U7O24[1], Na2Np2O7, Na2NpO4, Na4NpO5, Na5NpO6, Na3NpO4 or Na4NpO4[11,12] and Na2PuO3, Na3PuO4, Na4PuO4, Na6PuO5, Na4Pu2O5, Na6PuO6, Na4PuO5[1,2,12,13]. For the gaseous phase scarce data indicate the possible appearance of Na2NpO4 as evaporation product on the basis of mass spectrometric measurements [14].

In the present paper we are dealing with Na2AnO4 species, which can form in the vapour at severe accident situations. In order to simulate their formation and behaviour, the knowledge of their thermodynamic characteristics is required. These data can be calculated from reliable structural and spectroscopic parameters obtained conveniently by means of advanced quantum chemical calculations [15—20]. In the following we present the electronic structure of the four Na2AnO4 (An = U, Np, Pu, Am) molecules determined by relativistic multireference calculations as well as some other structural and spectroscopic properties of the ground electronic states determined by B3LYP density functional theory (DFT) calculations.

2. Computational details

The calculations were performed using the software MOLCAS

http://dx.doi.org/10.1016/j.molstruc.2016.09.065

0022-2860/© 2016 The Author. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

8.0 [21]. The complete active space (CAS) SCF method [22] was used to generate molecular orbitals and reference functions for subsequent multiconfigurational second-order perturbation theory calculations of the dynamic correlation energy (CASPT2) [23,24]. The Douglas-Kroll-Hess Hamiltonian was used in the CASSCF calculations in order to take into account scalar relativistic effects.

All electron basis sets of atomic natural orbital type, developed for relativistic calculations (ANO-RCC) with the Douglas-Kroll-Hess Hamiltonian [25,26] were used for all the atoms. For the actinides a primitive set of 26s23p17d13f5g3h basis functions was contracted to 9s8p6d5f2g1h [27] achieving TZP quality. Analogous contracted basis sets were applied for O (14s9p4d3f2g/4s3p2d1f) [28] and for Na (17s12p5d4f2g/5s4p2d1f) [29].

To determine the optimal size of the active space, preliminary state-averaged calculations using five roots (i.e. considering five electronic states in CASSCF) were performed in C1 symmetry with various number of inactive electrons. We found for all the four actinides that only two 2-electron orbitals had populations below 1.96 e, hence only these two orbitals were included beyond the unpaired An valence electrons in the active spaces [30]. Accordingly, in the subsequent calculations the active spaces contained 4, 5, 6, 7 electrons on 16 orbitals for the U, Np, Pu, and Am derivatives, respectively.

The electronic structures of the title molecules were investigated using D2h symmetry, in which the eight symmetry species of the point group were treated separately. For the lowest-energy symmetry species (within 20 kJ/mol) geometry optimizations were performed in order to ensure the ground electronic states and the respective global minimum geometries of the four title compounds. The vertical excited electronic states were calculated on the optimized geometries of the ground electronic states. Beyond the ground-state spin multiplicities (1, 2, 3, 4 for the U, Np, Pu and Am compounds, respectively) the neighbouring spin multiplicities were also probed.

Spin-orbit (SO) effects were taken into account by using the complete active space state interaction (CASSI) method [31], which allows CASSCF wave functions for different electronic states to interact under the influence of a spin-orbit Hamiltonian. Dynamic electron correlation is taken into account using the CASPT2 energies as spin-orbit free (SF) energies in the spin-orbit Hamiltonian (SO-CASPT2). The above described multireference methods and the ANO-RCC basis set were successfully applied in a number of studies on actinide-containing systems [32—53].

The DFT calculations were carried out with the Gaussian 09 code [54]. Our main DFT method was the B3LYP exchange—correlation functional [55,56] which provided previously very good

performance for both actinide oxides [47,57,58] and mixed alkali transition metal oxides [20]. A few test calculations were performed with PBE0 [59,60], B2PLYP [61], MP2 [62] and CCSD(T) [63—65] theories. For the actinides the small-core quasi-relativistic pseudopotentials of the Stuttgart-Cologne group (ECP60MWB [66,67] and the 14s13p10d8f6g valence basis set contracted to 10s9p5d4f3g (ECP60MWB_SEG basis) [67]) was used, while for O and Na the aug-cc-pVTZ all-electron basis set [68]. Because the goal of these calculations was to get the ground-state spectroscopic properties, only the ground state spin multiplicities were calculated. The ground-state characters of the results were confirmed by applying the STABLE keyword of Gaussian 09, which checks for eventual lower-energy solutions of the wavefunction. The geometry optimizations were followed by the frequency calculations confirming the minimum characters of the obtained geometries. The anharmonic frequencies were calculated by evaluation of the quartic force field by means of numerical derivation (Freq = Anharmonic keyword in Gaussian 09). The assignment of the fundamentals was done on the basis of visual observation by means of the GaussView software [69], facilitating the recognition of their main vibrational components. The study of the bonding properties was based on atomic charges and orbital populations obtained by natural bond orbital analysis [70] using the NBO5.9 [71] code.

3. Results and discussion

3.1. Electronic structure

The electronic structure of the Na2AnO4 species was investigated on the double bidentate NaO2AnO2Na coordination structure, characteristic on hexavalent alkali transition metal mixed oxides [20,72—76]. However, the D2d geometry formed by the transition metal compounds proved to be a saddle-point for actinides according to our calculations. The minimum structure for all the four Na2AnO4 molecules is the planar D2h one (presented in Fig. 1), hence we optimized these structures at the SF CASPT2 level. The optimized geometries of the ground electronic states (except where noted) were used to evaluate the characteristics of the electronic structures.

The lowest-energy electronic states of Na2UO4 from SF- and SO-CASPT2 calculations are given in Table 1. In agreement with general experience on closed-shell hexavalent uranium-containing molecules [15,77—79], the ground state of Na2UO4 is 1Ag. This SF state forms exclusively the SO ground state. We note that contributions from another configurations (also in most low-lying excited states)

Fig. 1. The D2h minimum structure of the investigated molecules.

A. Kovacs / Journal of Molecular Structure xxx (2016) 1—7

Table 1

Lowest-energy electronic states of Na2UO4 from SF- and SO-CASPT2 calculations.

Table 2

Lowest-energy electronic states of Na2NpO4 from SF- and SO-CASPT2 calculations.

No. Term symbol Ea Characterb No. Term symbol Ea Characterb

cm-1 kJ/mol cm-1 kJ/mol

SF 1 ^Ag(1) 0.0 0.0 97% closed shell SF 1 2B3u(1) 0.0 0.0 92% (5f3+, 5f1+)

2 B2g 21274 254.5 96% 5f1+, (2py,6pz) 2 2B2u 3202 38.3 91% 5f3-

3 ^Ag(2) 22996 275.1 74% 5fc,b (2py,6pz) 3 B1u 5057 60.5 91% 5f0

4 B1g 24501 293.1 96% 5f3+, (2pz,6py) 4 2B3u(2) 8133 97.3 90% (5f1+, 5f3+)

5 B2g 24935 298.3 96% 5f3+, (2py,6pz)b 5 ^Au 9872 118.1 86% 5f,-

6 B1u 25395 303.8 94% 6d2+, (2py,5f2+) 6 B1u 15439 184.7 93% 5f3+, 5f1+, (2py,6pz)

7 B3g 25470 304.7 98% 5f3-, (2py,6pz) 7 2A1gu 16050 192.0 90% (6d2+, 7s)

8 3Ag(1) 25554 305.7 98% 5f0, (2py,6pz) 8 4Au 16576 198.3 93% 5f1+, 5f3-, (2py, 6pz)

9 B1u 25805 308.7 95% 6d2+, (2py,5f2+)b 9 4B3u 17061 204.1 94% 5f3+, 5f2+, 5f0

10 11 B3g 3Ag(2) 26557 27811 317.7 332.7 97% 5f3-, (2py, 6pz)b 95% 5f3-, (2pz, 6py) SO 1 2 0.0 5762 0.0 68.9 75% 2B3u(1) 40% 2B2u + 32% 2B3u(2) + 26% 2B1u 44% 2B1u + 34% 2B2u

SO 1 0.0 0.0 100% 1Ag(1) 3 8775 105.0

2 14027 167.8 58% 3B2g + 26% 3B1g 4 12849 153.7 58% 2B3u(2) + 22% 2B1u

3 14970 179.1 70% 3B2g + 26% 3B1g 5 14023 167.8 82% 2Au

4 15266 182.6 31% 1B2g + 30% 3B1g + 24% 3B3g 6 15419 184.5 57% 4B1u + 25% 4Au

5 16247 194.4 73% 3B2g 7 16853 201.6 62% 4B1u + 19% 4B3u + 18% 4Au

6 18838 225.4 49% 3B3g + 31% 3Ag(2) 8 19545 233.8 100% 2Ag

7 19832 237.2 41% 3Ag(2) + 36% 1B3g 9 20156 241.1 87% 4Au

8 20458 244.7 40% 3B3g + 23% 3B1g + 16% 3Ag(2) 10 20518 245.5 87% 4B3u

9 20603 246.5 49% 1Ag(2) + 42% 3B3g 11 22468 268.8 38% 4B1u + 33% 4B3u + 29% 4Au

10 21847 261.4 43% 3Ag(1) + 38% 3B1g 100% 3B1u 12 23852 285.3 42% 4B1u + 32% 4B3u + 26% 4Au

11 21894 261.9 a Vertical excitation energies obtained on the geometry of the 2B3u(1) ground

a Vertical excitation energies obtained on the geometry of the 1Ag(1) ground state. Additional (higher-energy) SO states are given in the Supplementary Material.

b SF section: Character of the unpaired electrons in the main electron configuration. The primary spin of the unpaired electrons is a, b means electrons with opposite spin according to the singlet spin multiplicity of the given states; SO section: composition in terms of SF states.

are negligible, hence the ground state of Na2UO4 can reliably be calculated by single-determinant methods.

As there are no excess U electrons in this molecule, the SF excited electronic states start at high energy (above 250 kJ/mol). They are formed by excitation of one electron from one of the bonding orbitals with O2p and (mostly) U6p character to anti-bonding orbitals with major 5f or 6d contributions (cf. Table 1). The first excited state is a triplet 3B2g, but also several singlet states (possessing electrons with switched spin) are among the lowest-lying excited states too. States with Au, B2u and B3u symmetry have very high energies, they are beyond the selected energy window for Na2UO4.

Due to spin-orbit coupling, the excited states have much lower energy than the SF ones (168 vs 250 kJ/mol). Among the SO excited states there are a few pure Ag and B1u ones, while most of the states contain a major electron configuration with around 50% contribution. Strongly mixed states appear scarcely in the investigated range.

The lowest-energy electronic states of Na2NpO4 from SF- and SO-CASPT2 calculations are given in Table 2. The SF ground electronic state is a doublet 2B3u state, in which the unpaired electron is located on a hybrid 5f (5f3+, 5f1+) molecular orbital. The lowest excited states are formed by doublet states, having the unpaired electron on various 5f orbitals. The quartet SF excited states start from 185 kJ/mol with unpaired electrons generally on 5f and 1-electron bonding orbitals (as exception, the 4B3u state has only 5f electrons as major contributions). The states with Bg-type symmetry have very high energies, they are beyond the energy window considered in the present study. We note that nearly all the states have a major electron configuration with contribution above 90%, hence single-determinant methods can be expected to be suitable for modelling Na2NpO4.

The SO ground state is dominated by 75% by the SF ground state 2B3u. The SO excited states start at 69 kJ/mol with the doublet

state.

SF section: Character of the unpaired electrons in the main electron configuration; SO section: composition in terms of SF states. Each SO state is doubly degenerated.

states, while the quartets appear from 185 kJ/mol. Most SO states have one major contribution. From the available (low-energy) SF states the Bu-types have a larger propensity for mixing.

The lowest-energy electronic states of Na2PuO4 from SF- and SO-CASPT2 calculations are given in Table 3. The SF ground electronic state is a triplet 3Ag state, in which the two unpaired electrons are located on two 5f (5f1+, and 5f3+) Pu orbitals. The three lowest-energy excited states are formed similarly by triplet states. The energy differences from the ground state are considerably smaller than observed in the case of Na2NpO4 and Na2UO4: e.g. the first excited state lies only by 5 kJ/mol higher vs the 38 kJ/mol in Na2NpO4. In order to treat more accurately the very close (within 11 kJ/mol) lying first two excited (3B1g and 3B2g) states, we optimized their geometries and the obtained adiabatic energies were used in the present study.

The lowest-energy singlet (1Ag) state has a closed-shell electronic structure, hence no unpaired electrons. It appears higher in energy by 50 kJ/mol above the triplet ground state. The other singlet states (from 83 kJ/mol) have open-shell electronic structures, one of the two unpaired electrons with a switched spin. In these low-energy triplet and singlet states the unpaired electrons occupy only non-bonding 5f orbitals of Pu. Single population of bonding and anti-bonding orbitals appears in the first quintet state (5B1g), which is formed by excitation of a bonding electron from the (5f2+, 2py) bonding orbital to an anti-bonding one. The quintet states lie quite high in energy above the ground state, thus our energy window contains only 5B1g. Very high relative energies have the ungerade states (Au, Bu) too, being beyond the energy window considered in the present study. We note that most of the SF states listed in Table 3 (including the ground state) have the main electron configurations with contributions above 85%, suggesting that single-determinant methods can work for the ground and low-lying excited SF states of Na2PuO4.

In contrast to the previously discussed U and Np derivatives, the SO ground state of Na2PuO4 is considerably mixed (cf. Table 3). Moreover, the 3Ag SF ground state does not have any contribution in

A. Kovacs / Journal of Molecular Structure xxx (2016) 1—7

Table 3

Lowest-energy electronic states of Na2PuO4 from SF- and SO-CASPT2 calculations.

No. Term symbol Ea cm-1 kJ/mol Characterb

SF 1 3Ag 0.0 0.0 87% 5f1+, 5f3+

2 3B1g(1) 401 4.8 88% 5f1+, 5f3-

3 3B2g(1) 945 11.3 88% 5f3+, 5f0

4 3B3g(1) 2809 33.6 86% 5f3-, 5f0

5 > 4196 50.2 81% closed shell

6 1B1g 6946 83.1 91% 5f1+, (5f3_)b

7 B2g 7507 89.8 91% 5f3+, (5fc)b

8 3B3g(2) 7557 90.4 81% 5f3+, 5f2_

9 1B3g 8317 99.5 89% 5f3_, (5f0)b

10 3B1g(2) 8602 102.9 76% 5f3+, 5f3_

11 3B2g(2) 9387 112.3 81% 5f3_, 5f2_

12 B1g 11903 142.4 90% 5f1+, 5f3_, (5f2+, 2py), (5f0, 2py)

SO 1 0.0 0.0 35% 3B1g(1) + 25% 3B2g(1) + 18% 1Ag

2 568 6.8 42% 3Ag + 28% 3B1g(1) + 19% 3B2g(1)

3 889 10.6 39% 3Ag + 37% 3B1g(1)

4 1396 16.7 38% 3Ag + 37% 3B2g(1)

5 5728 68.5 47% 3B2g(1) + 46% 3B1g(1)

6 6990 83.6 33% 3B2g(1) + 24% 3B3g(1) + 19% 3B1g(1)

7 7475 89.4 46% 3Ag + 39% 3B3g(1)

8 7823 93.6 48% 3Ag + 33% 3B3g(1)

9 8260 98.8 26% 3B3g(1) + 23% 3B1g(1) + 19% 3B2g(1)

10 9568 114.5 39% 3B1g(1) + 31% 3B3g(1) + 24% 1B2g

11 9994 119.6 39% 1B1g + 35% 3B2g(1) + 20% 3B3g(1)

12 10005 119.7 52% 3Ag + 24% 1B3g

a Vertical (except for 3B1g(1) and 3B2g(1) being adiabatic) excitation energies obtained on the geometry of the 3Ag ground state. Additional (higher-energy) SO states are given in the Supplementary Material.

b SF section: Character of the unpaired electrons in the main electron configuration. The primary spin of the unpaired electrons is a, b means electrons with opposite spin according to the singlet spin multiplicity of the given states; SO section: composition in terms of SF states.

the SO ground state, it forms the main contribution of the first excited state. Apparently, the SO coupling between the 3B1g and 3B2g states is very advantageous and decreased considerably the energy of the formed SO state. The strong mixing is characteristic on the low-energy excited SO states (dominated by the triplet SF states below 200 kJ/mol) as well. Hence, for the electronic properties of Na2PuO4 the SO coupling is very important.

The lowest-energy electronic states of Na2AmO4 from SF- and SO-CASPT2 calculations are given in Table 4. The SF ground electronic state at the level of our calculations is a quartet 4Au state, in which the three unpaired electrons are located on three 5f (5fi+, 5f3+, 5f0) Am orbitals. However, the first excited 4B2 u state is very close in energy (1.6 kJ/mol). Because of the energetic proximity we again optimized the geometries of the first two excited states in order to ensure the ground state and accurate relative energies of these three lowest-energy states.

The low-energy excited SF states up to 59 kJ/mol are formed similarly by quartet states. Sextet SF states with 1-electron bonding and antibonding orbitals appear from 59.6 kJ/mol (6B2u), while the much higher-energy doublets (2B2u) from 106 kJ/mol. Part of the latter ones contain 2-electron (lone pair) Am 5f orbitals. The gerade states (Ag, Bg) have high energies, being beyond the energy window considered in the present study. We note that most of the SF states listed in Table 4 (including the ground state) have the main electron configurations with contributions above 80%, suggesting that — similarly to the above discussed mixed actinide oxides - single-determinant methods may work for the ground and low-lying excited SF states of Na2AmO4.

Similarly to Na2PuO4, SO coupling is very important in Na2AmO4. Already the SO ground state is considerably mixed (cf. Table 4), formed dominantly by the ground (4Au) and first excited (4B2u) state. The first excited SO state has a similar character while it lies higher in energy by 16 kJ/mol. The strong mixing is characteristic on all the SO states of Na2AmO4 covered in the present

study (cf. Supplementary Material), below 100 kJ/mol dominated by the quartet SF states.

3.2. DFT calculations on the molecular properties

The first question in our DFT calculations was: how can they reproduce the ground state electronic structures of the title molecules? From the SF-CASPT2 results above we concluded that, due to the very large contributions of the main electron configurations, the ground states of all the four molecules may reliably be modelled by single-determinant methods.

The term symbols of the ground electronic states together with some natural bond orbital characteristics (natural atomic charges and actinide valence populations) from our B3LYP calculations are compiled in Table 5. They support the mentioned conclusion, as B3LYP predicted correctly the 1Ag, 2B3 u, and 4Au SF ground states of Na2UO4, Na2NpO4 and Na2AmO4, respectively. We recall, that these SF ground states compose also the main components of the respective SO ground states. Only the 3B1g DFT ground state of Na2PuO4 seems to be in contradiction with the 3Ag SF ground state of Na2PuO4. However, as shown above, in the SO ground state of Na2PuO4 the main contributor is 3B1g, while 3Ag is the main contributor of the first excited SO state. Though in our B3LYP calculations no SO coupling was taken into account, they provide a reasonable estimate of the real ground state of Na2PuO4. The good performance of advanced DFT methods in the prediction of the ground states of actinide oxides has been shown earlier [47,57,58]. They proved to be reliable for species with considerable energy gap between the ground and first excited states. Discrepancies were found only in a few cases with very close lying first excited state. This happens apparently in the B3LYP treatment of Na2PuO4 too, but the neglect of SO coupling seems to compensate for the error on the SF state.

The natural atomic charges given in Table 5 reflect the strong

Table 4

Lowest-energy electronic states of Na2AmO4 from SF- and SO-CASPT2 calculations.

No. Term symbol Ea Characterb

cm-1 kJ/mol

SF 1 4Au(1) 0.0 0.0 82% 5f1+, 5f3-, 5f0

2 4B2u(1) 134 1.6 80% 5f3+, 5f1+, 5f3-

3 4B1u(1) 894 10.7 80% 5f1+, 5f3+, 5f0

4 4Au(2) 3920 46.9 58% 5f1+, 5f3+, 5f2-

5 4B1u(2) 4873 58.3 81% 5f1+, 5f3-, 5f2-

6 6B B2u 4982 59.6 83% 5f1+, 5f3+, 5f3_, (5f2+, 2py), f 2py)

7 4B2u(2) 5124 61.3 80% 5f3+, 5f0, 5f2-

8 X(3) 5275 63.1 55% 5f3+, 5f3-, 5f0

9 B3u 6737 80.6 84% 5f3-, 5f0, 5f2-

10 6Au 8234 98.5 87% 5f1+, 5f3+, (5fc, 2py), (5f2+, 2py), 5f2-

11 6B1u 8292 99.2 86% 5f1+, 5f3-, (5f2+, 2py), (5f0, 2py), 5f2-

12 2B2u 8861 106.0 82% (5f1+)2, 5f3-

13 2Au 8928 106.8 82% 5f3+, 5f3-, (5f0)b

14 6B3u 8953 107.1 86% 5f1+, 5f3+, 5f3-, (2py, 5f2+), 5f2-

15 2B1u 9404 112.5 83% (5f3+)2, 5f0

SO 1 0.0 0.0 36% 4Au(1) + 25% 4B2u(1)

2 1323 15.8 51% 4Au(1) + 21%4B1u(1)

3 2197 26.3 41%4B2u(1) + 29%4B1u(1)

4 4373 52.3 28% 4B2u(1) + 19% 4B2u(2) + 11% 4B1u(2)

5 4771 57.1 25% 4B1u(2) + 23% 4Au(2) + 15% 4B1u(1)

6 5674 67.9 33% 4Au(2) + 25% 4B2u(2)

7 5982 71.6 55% 4B1u(1) + 13% 4Au(3)

8 7528 90.1 21% 4B2u(2) + 19% 4Au(1) + 13% 4B1u(2)

9 8499 101.7 26% 6B1u + 23% 6Au + 16% 6B2u

10 9042 108.2 35% 6B2u + 17%6B1u

11 9429 112.8 34% 6B2u + 17% 6B1u + 14% 4Au(2)

12 9639 115.3 33% 4B1u(2) + 19% 4B2u(2)

a Vertical (except for 4B2u(1) and 4B1u(1) being adiabatic) excitation energies obtained on the geometry of the 4Au ground state. Additional (higher-energy) SO states are given in the Supplementary Material.

b SF section: Character of the unpaired electrons in the main electron configuration. The primary spin of the unpaired electrons is a, b means electrons with opposite spin according to the singlet spin multiplicity of the given states; SO section: composition in terms of SF states. Each SO state is doubly degenerated.

Table 5

Atomic charges and valence population (e) of the central actinide from NBO analysis of the B3LYP results.

M2AnO4 State Na An O An population

Na2UO4 D2h 1Ag +0.96 +2.81 -1.18 7s°.°6 S/287 6d047

D2 1A +0.96 +2.81 -1.18 7s°.°6 5Z2.87 6da47

Na2NpO4 2B3u +0.96 +2.56 -1.12 7s0.06 5/"5 6da43

Na2PuO4 B1g +0.96 +2.48 -1.10 7s0.05 5f523 6da42

Na2AmO4 4Au +0.96 +2.49 -1.10 7s0.05 5f6.26 6d0.41

ionic character of the sodium — oxygen interaction with sodium charges close to +1. The considerable (around +2.7) positive charges of the actinides are in agreement with a considerable ionic character of the An — O bonding too. The population analyses indicate bonding molecular orbitals strongly delocalised around the AnO4 moiety. The population data of the An valence orbitals are in agreement with the trends found in actinide dioxides: the partial positive charge of An is formed mainly by the leave of the 7s electrons. From U to Am the 5f population shows a gradual increase parallel with the gradual slight decrease in the 6d population (cf. Table 5). We note the larger change between U and Np in agreement with the experience of the somewhat more substantial 6d contribution to bonding in U compounds as compared to the ones of the heavier actinides [57,80]. In general, the covalent contribution of bonding in oxides is formed by the 6p, 5f (mainly 5f2+, 5f1-) and 6d (mainly 6d1+) actinide electrons [57].

We start the discussion of the geometry with a peculiar result of the B3LYP optimizations. In the view of our previous good experience on this method it came as a surprise, that our (also in previous studies used [47,57,58]) B3LYP level predicted the D2h structure of Na2UO4 as a first-order saddle point on the potential energy

surface, being in contrast with the D2h CASPT2 minimum. The B3LYP minimum is a slightly (by 13°) twisted D2 geometry. We investigated this problem in more detail: Computations with different parameters (basis set, grid size) resulted likewise in a D2 B3LYP minimum. However, all other theories, CCSD(T), MP2, B2PLYP, PBE0 in conjunction with the same basis set agreed with CASPT2 for the D2h minimum structure. Hence we concluded that the D2 minimum is a failure of the B3LYP approach. The reason is probably an overestimated contribution of the 6d orbitals of U in the UO bonding orbitals. The different structural preference of 6d vs 5f orbitals in actinide compounds is well known [80—82]. In our case, the 5f orbitals support a planar D2h structure (obtained for the molecules with Np, Pu and Am, with in this order increasing importance of 5f orbitals in bonding) while the 6d orbitals prefer a perpendicular D2d arrangement (seen in the mixed alkaline transition metal oxides [20,72—76]). As shown above in the discussion of the valence orbital populations, from the title actinides U has the largest 6d population supporting the important role of these orbitals in the formation of the molecular geometry of Na2UO4.

The effect of this error of B3LYP on the molecular properties is, however, very small: the energy difference between D2 and D2h is 0.3 kJ/mol, the bond distances differ by max. 0.003 A (cf. Table 6) while the orbital populations are the same (cf. Table 5). The errors of the theoretical level (due to approximations in the exchange-correlation functional and truncated basis set) are larger. Hence, the structural and spectroscopic data of the D2h B3LYP geometry of Na2UO4 can be used for comparison with the data of the other (D2h) NaAnO4 molecules. The statement may not be valid for the vibra-tional frequencies, where the imaginary frequency can cause larger perturbations in the force field.

The geometrical parameters of the four Na2AnO4 molecules are presented in Table 6. We can compare for Na2UO4 the performance

A. Kovacs / Journal of Molecular Structure xxx (2016) 1—7

Table 6

Computed geometrical parameters of M2AnO4 molecules.a

Na2AnO4

An-O Na-O OAnO (OAnO)r ONaO NaAnO

Na2UO4 CCSD(T) 1.936 2.216 93.9 86.1 73.2 137.0

CASPT2 1.938 2.183 93.9 86.1 74.6 137.0

MP2 1.953 2.193 94.0 86.0 74.8 137.0

B2PLYP 1.953 2.193 94.0 86.0 74.8 137.0

B3LYP D2h 1.930 2.177 94.2 85.8 74.3 137.1

D2 1.932 2.180 95.4 86.1 74.5 136.9

PBE0 1.910 2.173 93.9 86.1 73.7 137.0

Na2NpO4 CASPT2 1.904 2.181 93.5 86.5 73.5 136.8

B2PLYP 1.919 2.172 93.5 86.5 74.5 136.7

B3LYP 1.912 2.175 93.8 86.2 73.9 136.9

PBE0 1.889 2.169 93.5 86.5 73.3 136.8

Na2PuO4 CASPT2 1.898 2.185 92.6 87.4 73.8 136.3

B2PLYP 1.889 2.166 93.6 86.4 73.3 136.8

B3LYP 1.909 2.170 94.4 85.6 73.4 137.2

PBE0 1.885 2.163 94.2 85.8 72.8 137.1

Na2AmO4 CASPT2 1.896 2.187 92.0 87.9 74.0 136.1

B2PLYP 1.879 2.176 92.3 87.7 73.6 136.1

B3LYP 1.913 2.181 92.8 87.2 74.4 136.4

PBE0 1.887 2.175 92.6 87.5 73.7 136.3

a Bond distances are given in angstroms, bond angles in degrees, the moments of inertia in kg3m6. The angle (OAnO)r corresponds to the one in the NaO2An rings.

Table 7

Calculated anharmonic frequencies (cm-1)a of the fundamentals.

Sym Na2UO4b Na2NpO4 Na2PuO4c Na2AmO4 Assignment

Ag 749 746 722 648 v sAnO

Ag 441 442 470 453 b s(OAnO)r, vsNaO

Ag 248 242 251 247 v sNaO, bs(OAnO)r

B1u 683 705 710 670 v asAnO

B1u 438 450 465 463 b as(OAnO)r, vsNaO

B1u 273 271 277 265 v sNaO, bas(OAnO)r

B2u 653 676 665 658 v asAnO

B2u 362 382 392 398 b asOAnO, vasNaO

B2u 121 131 133 148 b asOAnO

B3u 190 219 229 242 g sAnO

B3u 43 57 60 37 gNa

B2g 145 156 154 187 g asAnO

B3g 518 529 475 473 v asAnO

B3g 301 302 313 304 v asNaO

Au 175 142 127 142 g asAnO

a The symbols v, b, g, s, as mean stretching, in-plane bending, out-of-plane bending, symmetric, asymmetric, respectively. The angle (OAnO)r corresponds to the one in the NaO2An rings.

b According its D2 symmetry, the symmetry species of Na2UO4 do not have the g/u (geradelungerade) symbols.

c Harmonic frequencies, because the calculation of the anharmonic frequencies was erroneous.

of CCSD(T), MP2, CASPT2 (as post-HF) and B3LYP, B2PLYP and PBE0 (DFT). While the CASPT2 and B3LYP results for the U-O bond distance are in very good agreement with the CCSD(T) one, the Na-O bond distances are somewhat underestimated. MP2 and B2PLYP predict somewhat longer U-O bonds, but again shorter Na-O bonds. We note that these two latter methods produce exactly the same geometrical parameters, hence B2PLYP can replace effectively MP2 with a considerably smaller computational cost. The worst performance for these type of compounds was provided by PBE0, underestimating both bond distances.

For the other three Na2AnO4 molecules we assessed only B3LYP, B2PLYP and PBE0. Compared to CASPT2, both B3LYP and B2PLYP perform quite well, the B3LYP bond distances being slightly closer to the CASPT2 ones. From the two methods B3LYP would be preferred also from the point of view of computational cost, because the vibrational frequencies by B2PLYP with this large basis set are quite expensive. The shown good agreement supports the reliability of our B3LYP level for the title compounds. This is particularly necessary for the quality of the B3LYP vibrational frequencies, which parameters were obtained only at the DFT level. As for PBE0, similarly to the performance on Na2UO4, it predicts generally the shortest bond distances, thus deviating the most from CASPT2.

The computed fundamentals and their qualitative assignments are given in Table 7. The anharmonic vibrational frequencies were obtained by computing the quartic force field. Unfortunately, this failed for Na2PuO4 as the electronic state changed during the numerical derivation (shown by the unrealistic anharmonic data). Therefore for this molecule the harmonic frequencies are listed in Table 7. The harmonic vibrational frequencies and infrared intensities of all the title molecules are given in the Supplementary Material.

The frequency data are quite consistent for the four actinide derivatives. Only the AnO stretching frequencies of Na2AmO4 dropped considerably referring to unusually flat potential curves for these vibrations.

4. Conclusions

In the current study the molecular properties of Na2AnO4 (An = U, Np, Pu, Am) compounds have been predicted by multi-reference post-HF and DFT calculations. The computations support

a planar D2h structure for these molecules preferred by the contributing 5f actinide orbitals in the bonding. We found a minor failure of the B3LYP exchange-correlational functional for the geometry, due probably to the overestimated 6d contribution in the Na2UO4 molecule.

We determined the low-lying electronic states of the title molecules by means of SO-CASPT2 calculations. Except for Na2PuO4, the SO ground states consist of mainly (in Na2UO4 entirely) the SF ground state. In Na2PuO4 the SO coupling between the first and second SF excited states lowers the energy considerably, forming in this way the SO ground state.

From the four molecules Na2UO4 is practically a single-reference species with 97% contribution of the main electron configuration. Going towards Na2AmO4 this decreases gradually to 82%, which facilitates the modelling of the spin-free electronic structure of these species with single-determinant quantum chemical methods. Indeed, our B3LYP calculations reproduced the ground electronic states of the title Na2AnO4 molecules and predicted geometries in good agreement with the spin-free CASPT2 one.

Acknowledgement

The author thanks Prof. R. J. M. Konings for advice. Appendix A. Supplementary data

Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.molstruc.2016.09.065.

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