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Procedia Chemistry 7 ( 2012 ) 460 – 465

ATALANTE 2012 International Conference on Nuclear Chemistry for Sustainable Fuel Cycles Structural and electronic properties of actinides fluorides: a density functional study

Cheng Chenga*, Chang-Ying Wanga, Ping Huaia and Zhi-Yuan Zhua

aShanghai Institute of Applied Physics, Chinese Academy of Sciences,Jia Luo Street no.2019, Shanghai 201800, China

Abstract

Using local density approximation and generalized gradient approximation functions, we carried out relativistic density functional studies on the molecular structure and vibrational frequencies of actinides fluorides (ThF4, UF4 and UF6). Bonding lengths are in good agreement with available experimental data. Bonding energies and vibrational frequencies are predicted with relativistic scalar ZORA effects.

©© 2012 2012 Elsevier The Authors. B.V...Selection Published and/or by Elsevier peer-review B.V. under responsibility of the Chairman of the ATALANTE 2012 ProgramSelection Committee and/or peer-review under responsibility of the Chairman of the ATALANTE 2012 Program

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1. Introduction

Chemical bonding in actinide compounds is an important topic for both fundamental and application-oriented studies. The complicated behavior of 5f-orbital leads to unique electronic structure of actinide compounds [1-2]. For instance, typical oxidation states of actinides range from 3 to 6 for uranium and 3 to 7 for neptunium and plutonium [3]. In the candidate of generation IV nuclear reactors, Molten Salt Reactor (MSR) is the only one based on liquid fuel i.e. actinides fluorides. One of the biggest challenges of MSR is the control of material corrosion by molten salt, which is composed of FLiBe and actinides fluorides (ThF4 and UF4). Furthermore, in the nuclear fuel reprocessing industry, hydrolysis of uranium hexafluoride (UF6) in the gas phase is applied to

* Corresponding author. Tel.: +086-021-39194032 E-mail address: [email protected].

1876-6196 © 2012 Elsevier B.V...Selection and/or peer-review under responsibility of the Chairman of the ATALANTE 2012 Program Committee doi: 10.1016/j.proche.2012.10.070 Cheng Cheng et al. / Procedia Chemistry 7 ( 2012 ) 460 – 465 461

produce pure nuclear fuel, uranium dioxide (UO2) [18]. Because of the difficulty in experimental study for actinide fluorides, computational actinide chemistry provides one useful tool for elucidating the mechanisms of corrosion process induced by actinides and other metal fluorides. Despites some progresses on actinides fluorides e.g. hexafluorides AnF6 and pentafluorides AnF5 [4-6], the nature of chemical bonding is still open question. The first experimental electron diffraction studies for thorium and uranium tetrahedral geometries [7] were performed in 1958. Since that time, many experimental and theoretical studies indicated a tetrahedral geometry for the thorium tetrahalides, but some cases suggested a distorted tetrahedral geometry for the uranium tetrahalides, which is explained by Jahn-Teller distortion due to the f2 electronic configuration of U4+. These molecular geometry distortion calculations are usually treated in a non-relativistic theoretical framework. The situation for the thorium tetrahalides is much clear than for the uranium tetrahalides. Koning et al [13] described in detail the state-of-art of the experimental and theoretical studies on actinide tetrahalides. In their paper, experimental information from electron-diffraction measurements [14, 15] and thermochemical studies [16, 17] confirm the tetrahedral geometry for ThF4 and UF4. For the experimental study of UF6, Burke et al [19] already investigated the infrared and Raman Spectra in 1952, and McDowell et al [20] measured the infrared and Raman spectra of UF6 in 1974. In the past decade, lots of experimental and theoretical studies have been obtained for molecular structures and vibrational frequencies of UF6 [21-33]. With abundant experimental data of UF6, the molecule served as a benchmark to test computational method which is applied to the study of actinide compounds. In this paper, we carry out theoretical calculations on structural and electronic properties of the actinides fluorides with relativistic density functional theory. The geometries, bonding energies and vibrational frequencies are compared with available experimental values and other theoretical results. Relativistic effects due to the high atomic number of the thorium and uranium atoms are taken into account with scalar ZORA effects.

Nomenclature

FLiBe a mixture of lithium fluoride (LiF) and beryllium fluoride (BeF2) LDA local density approximation GGA generalized gradient approximation MSR Molten Salt Reactor ZORA the zero-order regular approximation

2. Methods of Calculation

The Amsterdam Density Functional Program (ADF) is based on the Hohenberg-Kohn theorems [8] and the Kohn-Sham molecular orbital method [9]. The Kohn-Sham method implies a one-electron picture of the many- electron systems to get the exact electron density and the total energy. Slater type orbitals have been chosen as basis functions. In order to avoid the classical n4 problem in the two- electron integral evaluations, an auxiliary STO basis set has been introduced to expand the electron density in atom-centered functions. Since the exchange-correlation potential can be evaluated from the electron density and its derivatives at each sample point of the numerical integration grid, the density fitting only serves to obtain the matrix elements of the Coulomb potential of the electronic charge density. In ADF program, scalar and spin-orbit coupling relativistic effects are taken into account via ZORA approximation in the Dirac equation [10-12]. In this paper, we employ a triple-Slater type basis set augmented with one set of polarization functions, i.e. the triple-zeta polarized (TZP) basis set. The spin restricted DFT scheme is used. With a frozen core approximation, core electrons (U 5d) are frozen for uranium and thorium. The calculation are performed by using exchange-correlation functionals of LDA and GGA (PW91, PBE, BP86, BLYP and RPBE) respectively. 462 Cheng Cheng et al. / Procedia Chemistry 7 ( 2012 ) 460 – 465

3. Results and discussion

For heavy-element compounds relativistic effects play an important role in their geometries, electronic structures and spectrum properties. In this work, the calculated Th-F and U-F bonding length of three molecules (ThF4, UF4 and UF6) are presented in Table 1. The comparison between different exchange-correlation functionals shows a benchmark for DFT calculation. Due to the relativistic effects, bond lengths of these molecules are led to be shorter. As shown in Table 1, the GGA results of ThF4 agree better with experimental data, comparing with the LDA results. However, the LDA results of UF4 and UF6 show fewer differences with experimental data. The relativistic effects usually scale with the square of the atomic number. The ZORA results of UF6 with LDA agree well with the experimental data. In Zhang et al [38] work, the calculated geometries and vibration frequencies of uranium tetrahalides have little difference between the results obtained from scalar and spin-orbit relativistic effect. Due to the same calculated bench mark, only the results with scalar ZORA and with non-relativistic effects are compared with experimental data. Meanwhile, the vibrational frequencies of ThF4, UF4 and UF6 are calculated. The octahedral UF6 molecule has four normal modes of vibration: A1g, Eg, T1u, T2g and T2u. As shown in Table 5, the results of non-relativistic effects and scalar ZORA are compared with experimental data [20]. The optimized geometries of UF6 are calculated by using LDA and GGA functions (PW91, PBE, BP86, BLYP and RPBE). The “Avg. error” line implicates the average error of the four normal modes. These relativistic methods give reasonable results for the structure and electronic properties of actinides fluorides.

Table 1. Th-F and U-F bonding length (Å) for thorium tetrefluoride, uranium tetrefluoride and uranium hexafluoride NR stands for non-relativistic results and ZORA stands for spin-orbit ZORA results.

LDA PW91 PBE BP86 BLYP RPBE Expt

ThF4 NR 2.099 2.127 2.126 2.128 2.148 2.137 2.140[13] SR-ZORA 2.096 2.122 2.121 2.122 2.142 2.131 2.140[13]

UF4 NR 2.073 2.105 2.106 2.107 2.133 2.127 2.056[34] SR- ZORA 2.040 2.068 2.067 2.070 2.089 2.079 2.056[34]

UF6 NR 2.032 2.067 2.069 2.070 2.093 2.085 1.994[35] SR- ZORA 1.995 2.022 2.024 2.024 2.024 2.034 1.994[35]

Table 2. The bonding energy (eV) for thorium tetrefluoride, uranium tetrefluoride and uranium hexafluoride. NR stands for non-relativistic results and ZORA stands for scalar-ZORA results.

LDA PW91 PBE BP86 BLYP RPBE Expt

[36] ThF4 NR 37.33 35.54 35.31 35.14 34.44 34.51 27.70 ZORA 35.69 32.02 33.80 33.60 33.03 33.04 27.70[36] [37] UF4 NR 32.42 30.69 30.47 30.31 29.65 29.67 25.58 ZORA 35.80 34.03 33.81 33.61 32.99 33.01 25.58[37] [35] UF6 NR 40.94 38.01 37.74 37.47 36.47 36.42 31.91 44.90[6] 44.70[6] 44.30[6] ZORA 48.46 45.41 43.86 44.84 43.85 43.76 31.91[35] 45.20[6] 44.90[6] 44.40[6]

Table 3 The vibrational frequencies of thorium tetrafluoride. NR stands for non-relativistic results and ZORA stands for scalar-ZORA results (in cm-1). Cheng Cheng et al. / Procedia Chemistry 7 ( 2012 ) 460 – 465 463

A1 E T2 T2 Avg. error

ThF4 NR LDA 568 77 514 94 24 PW91 548 77 495 93 33 PBE 547 78 494 96 32 BP86 543 76 493 88 36 BLYP 538 69 489 81 42 RPBE 531 76 481 89 41 ZORA LDA 594 105 545 102 19 PW91 575 106 523 105 12 PBE 547 106 522 106 15 BP86 570 108 523 102 13 BLYP 562 104 513 102 17 RPBE 561 105 511 104 16 Expt[13] 618 121 520 116

Table 4 The vibrational frequencies of uranium tetrafluoride. NR stands for non-relativistic results and ZORA stands for scalar-ZORA results (in cm-1).

A1 E T2 T2 Avg. error

UF4 NR LDA 554 119 520 119 13 PW91 548 73 510 63 43 PBE 524 115 492 116 26 BP86 524 115 483 116 26 BLYP 504 27 459 63 75 RPBE 509 113 478 115 32 ZORA LDA 622 114 575 172 35 PW91 592 91 548 97 17 PBE 602 139 555 134 16 BP86 600 140 554 135 17 BLYP 587 138 540 133 12 RPBE 587 137 541 133 12 Expt[13] 605 123 537 114

4. Summary

We have carried out benchmark calculations on the geometries, vibrational frequencies of ThF4, UF4 and UF6 using relativistic DFT methods by using the TZP basis set. The scalar ZORA effects are important for structural properties of actinide fluorides. The bonding lengths are in good agreement with the experimental data. However, both relativistic and scalar relativistic calculations on bonding energies are higher than the experimental data. We compare the performance of the widely used LDA and GGA functions (PW91, PBE, BPB6, BLYP, RPBE) with non-relativistic and scalar ZORA relativistic approximation. Among the vibrational frequencies results, the LDA functions give the better value than the GGA functions. 464 Cheng Cheng et al. / Procedia Chemistry 7 ( 2012 ) 460 – 465

Table 5 The vibrational frequencies of uranium hexafluoride. NR stands for non-relativistic results and ZORA stands for scalar- ZORA results (in cm-1).

A1g Eg T1u T1u T2g T2u Avg. error

UF6 NR LDA 558 439 555 175 115 111 58 PW91 519 406 518 172 121 108 71 PBE 522 411 516 174 124 107 69 BP86 522 415 519 172 124 109 68 BLYP 505 404 501 168 126 105 74 RPBE 502 400 501 171 121 106 77 ZORA LDA 663 551 633 167 181 133 19 PW91 631 525 598 171 184 134 23 PBE 614 514 584 169 186 132 29 BP86 631 524 600 172 187 136 23 BLYP 613 513 583 169 186 133 29 RPBE 615 514 585 174 184 133 28 Expt[20] 667 534 626 186 200 143

Acknowledgements

Supported by National Basic Research Program of China Grant No.2010CB934504, National Natural Science Foundation of China Grant No.10905040, the CAS Hundred Talent Program, and Strategic Priority Research Program of the Chinese Academy of Sciences Grant no. XDA02040104.

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