Gas-Phase Energetics of Thorium Fluorides and Their Ions - The

Article pubs.acs.org/JPCA

Gas-Phase Energetics of Thorium Fluorides and Their Ions Karl K. Irikura* Computational Chemistry Group, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8320, United States S Supporting Information *

ABSTRACT: Gas-phase thermochemistry for neutral ThFn and cations ThFn+ (n = 1−4) is obtained from large-basis CCSD(T) calculations, with a small-core pseudopotential on thorium. Electronic partition functions are computed with the help of relativistic MRCI calculations. Geometries, vibrational spectra, electronic fine structure, and ion appearance energies are tabulated. These results support the experimental results by Lau, Brittain, and Hildenbrand for the neutral species, except for ThF. The ion thermochemistry is presented here for the first time.

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INTRODUCTION Thorium is best known as a nuclear fuel. Its merits relative to uranium are debated, but one cited advantage is the intrinsic safety of designs based upon molten-salt mixtures that include ThF4.1 Thermodynamic properties of the salt mixtures are clearly important for reactor design, and chemical properties may either be exploited or may lead to corrosion problems. The intrinsic stability of ThF4 molecules, the primary topic of the present study, represents an ancillary aspect of this larger story. The positive ions are also considered here for their relevance to the mass spectrometry of ThF4. Throughout this report, T = 298.15 K and the ideal-gas law are implicit. Experimental measurements have been reviewed by Fuger et al.2 and subsequently by Rand et al.3 The latter recommended ΔfH(ThF4, c) = −2100.0 ± 10.0 kJ/mol for the enthalpy of formation of the solid and Δgc H = 349.3 ± 2.0 kJ/mol for the enthalpy of sublimation. From this, they derived ΔfH(ThF4, g) = −1750.7 ± 10.2 kJ/mol. For elemental thorium vapor, ΔfH(Th, g) = 602 ± 6 kJ/mol has been recommended3−5 based upon a single reliable measurement.6 Combining these data with ΔfH(F, g) = 79.38 ± 0.30 kJ/mol,4 the enthalpy of atomization of ThF4 is found to be 2670 ± 12 kJ/mol, for an average bond dissociation enthalpy of 668 ± 3 kJ/mol. There have been two thermochemical studies of the lower fluorides.7,8 Both used Knudsen-cell effusion with mass spectrometric monitoring. Based upon this work, Rand et al. recommended Δ fH(ThF3 , g) = −1165 ± 15 kJ/mol, ΔfH(ThF2, g) = −590 ± 20 kJ/mol, and ΔfH(ThF, g) = 30 ± 15 kJ/mol.3 These values correspond to bond dissociation enthalpies D(F3Th−F) = 665 ± 18 kJ/mol, D(F2Th−F) = 654 ± 25 kJ/mol, D(FTh-F) = 699 ± 25 kJ/mol, and D(Th−F) = 651 ± 16 kJ/mol. Hildenbrand and Lau have emphasized the problematic ignorance of the electronic and vibrational energy levels that are needed for third-law computations.9 These energy levels are determined as part of the present work. In additional to neutral thermochemistry, the mass spectrometric studies yielded appearance energies for the ions ThFn+ (n = 0−3; parent ion has not been detected) from electron ionization of the vapor. Typical uncertainties are between 30 and 100 kJ/mol, but serious errors, such as that for © 2012 American Chemical Society

ThF2 (see Discussion), can arise from mistaken assignments of neutral precursors. Thermochemistry of these positive ions, including appearance energies, is determined as part of the present work. Negative ions, however, are not included.10,11

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COMPUTATIONAL METHODS12 Thorium is a heavy atom (Z = 90), so relativistic effects are expected to be important. Scalar relativistic effects, such as the contraction of s-orbitals, can be modeled efficiently using core pseudopotentials designed for this purpose. Here, the WoodBoring pseudopotential by Küchle et al. was used to replace the 60 core electrons (i.e., a 60e pseudopotential).13 The remaining orbitals were described using two basis sets. The smaller basis, denoted B1, is the contracted [6s6p5d4f 3g] set (104 functions; ECP60MWB_ANO) by Cao et al., in combination with the aug-cc-pVQZ [6s5p4d3f 2g] set (80 functions) on fluorine atoms.14−16 Harmonic vibrational frequencies and initial geometries were computed at the MP2/B1 level. Correlating only the valence electrons (thorium has four) leads to a bond length of 217.9 pm in ThF4. The fluorine K-shell energies are approximately −26 Eh (hartree), while the lowest metalcentered orbital lies much higher, near −12 Eh. Correlating everything except the fluorine K-shells leads to a bond length of 210.5 pm, substantially shorter. Because of this sensitivity, all post-Hartree−Fock (post-HF) calculations described below have only the K-shells frozen (denoted “fK”). Geometries were refined at the CCSD(T) level, but not vibrational frequencies. For single-point energy calculations, the larger basis set, denoted B2, was used. The basis on fluorine centers was unchanged. On thorium, the two most diffuse primitives were decontracted for each value of the angular momentum, and three uncontracted shells of polarization functions were added, leading to a [8s8p7d6f5g2hi] set with 189 functions. The exponents, ζh = (4.57, 1.575) and ζi = 4.687, were obtained by Special Issue: Peter B. Armentrout Festschrift Received: June 22, 2012 Revised: November 8, 2012 Published: November 8, 2012 1276

dx.doi.org/10.1021/jp3061703 | J. Phys. Chem. A 2013, 117, 1276−1282

The Journal of Physical Chemistry A

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minimizing the MP2 energy of ThF at a fixed geometry. The most reliable energies here are CCSD(T)/B2//CCSD(T)/B1. For ThF4+, the CCSD(T)/B1 geometry optimization was prohibitively expensive. Instead, the MP2/B1 geometry was adopted for the single-point CCSD(T)/B2 calculation. Considering ThF4+ as a complex between F and ThF3+, one may estimate (by comparing Table 1 with Table S1 in the Supporting Information) that the CCSD(T)/B1 bond lengths would be about 0.4 pm greater than the MP2 values.

Uncontracted large-component basis sets were used: Dyall’s double-ζ set26 on Th and the aug-cc-pVDZ basis set,16 supplemented by a tight p-function (ζ = 135), on F. The small-component basis functions were generated by kinetic balance, following the software default, which led to a total of 1152 functions on Th and 138 functions on F. In earlier computations on atomic Th, a double-ζ basis set gave similar results to larger basis sets,27 justifying its use here. Calculations were multireference CISD (using state-averaged Dirac−Fock orbitals) with four orbital spaces: frozen (uncorrelated), doubly occupied in the reference, full-CI in the reference, and unoccupied in the reference. Such calculations are described here as (N2/N3/N4), where these are the numbers of orbitals in the three active spaces. Fock-space coupled cluster (FSCC) and intermediate-Hamiltonian FSCC were attempted in two appropriate situations, but no convergence was achieved in the sector 2 part of the computations (addition of the second electron). For ThF+, N2 = 13 was chosen (2s2p on fluorine and 6s6p5d on thorium), N3 = 5 (nonbonding orbitals on thorium), and N4 = 26 (up to 0.19 Eh). For ThF, N2 = 3 (2p on fluorine), N3 = 5, and N4 = 40 (up to 0.84 Eh). Larger values of N4 (and N2, for ThF) were desired but infeasible for technical reasons. Thermochemical computations adopted the rigid-rotor/ harmonic-oscillator ideal-gas model. Vibrational frequencies were scaled by 0.96 for the computation of harmonic zero-point energies (ZPE)28 but were not scaled for the computation of vibrational partition functions. Electronic partition functions were computed using experimental data when available and ab initio data otherwise. When including electronically excited states, the changes in vibrational and rotational properties were ignored, i.e., the electronic, vibrational, and rotational partition functions were taken as separable. The ion convention is adopted here for the thermochemistry of charged species.29 For the atomic partition functions, experimental energy levels were used: 2P1/2 and 2P3/2 for F,19 and levels up to about 15000 cm−1 for Th and Th+.22 This represents 42 different energies for Th and 54 different energies for Th+. To probe anharmonic effects, the geometry and anharmonic (VPT2) vibrational frequencies of ThF4 were computed at the fK-MP2/B1 level. The anharmonic density of states was obtained by a combination of direct enumeration (7.4 × 109 levels up to 8000 cm−1) and Monte Carlo estimation (up to 25 000 cm−1, 5.4 × 1012 levels).

Table 1. Molecular Geometries Obtained from fKCCSD(T)/B1 Calculations, except ThF4+ molecule ThF4 ThF3 ThF2 ThF ThF+ ThF2+ ThF3+ ThF4+a a

point group Td D3h D∞h C2v C∞v C∞v C∞v C∞v C2v C3v Cs

state 1

A1 2 A1′ ã3Δg X̃ 1A1 X 2Δ a 4Σ− 1 + Σ 3 Δ 2 A1 1 A1 2 A′

r(Th−F)/pm 210.6 209.2 209.3 204.8 201.6 204.8 196.7 198.1 199.6 202.4 281.1, 202.8, 202.6, 202.6

θ(F−Th−F)/degree 109.4712 120 180 130.5

108.3 111.9 69.7, 125.5, 125.5, 106.2

Geometry from fK-MP2/B1 calculation.

Calculations were spin-unrestricted. In some cases, SCF stability following was required, which sometimes led to a reduction in orbital symmetry. An unusual problem was found in calculations on atomic Th and Th+, wherein different results were obtained with different versions of the software, or even with the same version but different numbers of processors. This arises from multiple UHF minima, presumably due to the highJ core potential. The most consistent (IE variations ≤3 meV) and reasonable results were obtained by turning off the use of symmetry (keyword “nosymm”), which was done here for final, single-point energies [fK-CCSD(T)/B2] of open-shell systems. Conventional electronic structure calculations were done using version B.01 of the Gaussian 09 software package.17 The calculations described above are nonrelativistic, which means that energies are spin−orbit averages. For classically degenerate electronic states, the energy must therefore be lowered by an amount equal to the difference between the term average and the actual ground state, as is standard practice.18 For the F atom, the 2P average energy is 1.61 kJ/mol above the 2 P3/2 ground level.19 For the Th atom, the 3F average is 36.88 kJ/mol above the 3F2 ground level.20 For Th+, many energy levels are known, but their assignment to specific LS terms or configurations is ambiguous.21,22 Thus, the spin−orbit energy correction for Th + cannot be made with confidence. Fortunately, the ionization energy of Th is known precisely, IE = (6.3067 ± 0.0002) eV = (608.50 ± 0.02) kJ/mol, allowing ion energetics to be referenced to neutral Th.23 Among the molecules, experimental spin−orbit splittings for ThF and ThF+, along with theoretical calculations, were published recently (while this manuscript was being prepared) by Barker et al.24 To estimate unknown spin−orbit splittings, relativistic, fourcomponent calculations were done using the Dirac-Coulomb Hamiltonian, by means of the DIRAC software package.25

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RESULTS Geometries. The CCSD(T)/B1 geometries are summarized in Table 1. (MP2/B1 and HF/B1 geometries are summarized in the Supporting Information.) The most interesting observations are that ThF3+ is pyramidal, ThF3 is planar, and ThF4+ may be described as an asymmetrical complex between a F atom and ThF3+, with the long Th−F bond eclipsing one of the short Th−F bonds and coplanar with the other two short Th−F bonds. In some cases, low-level theory yields substantially different structures. In particular, HF predicts structures of lower symmetry for ThF3 (C3v) and triplet ThF2 (C2v). Bonds are slightly longer at the HF level. For example, r(Th−F) = 211.6 pm in ThF4 at the HF/B1 level. The CCSD(T) coordinates, energies, and values of ⟨S2⟩ are provided in the Supporting Information. As inferred from the fK-MP2/B1 calculations, anharmonic effects on the bond length are small: R0 − Re = 0.08 pm for ThF4 (see Supporting Information). 1277



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Table 2. Harmonic Vibrational Frequencies and Dipole Intensities from fK-MP2/B1 Calculations molecule ThF4

ThF2 (3Δg)

ThF (X 2Δ) ThF+ (1Σ+) ThF2+ (2A1)

ThF4+ (2A′)

mode

cm−1

km/mol

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

595 116 537 110. 549 39 543 604 687 678 109 649 663 613 164 113 100. 49 616 116 22

0 0 221 30 0 6.1 256 120 124 92 13 167 50 200 12 10 23 7.3 207 9.7 2.8

(a1) (e) (t2) (t2) (σg) (πu) (σu) (σ) (σ) (a1) (a1) (b2) (a′) (a′) (a′) (a′) (a′) (a′) (a″) (a″) (a″)

molecule ThF3

cm−1

km/mol

(a1′) (a2″) (e′) (e′) (a1) (a1) (b2) (σ) (σ) (a1) (a1) (e) (e)

583 64 547 101 590 37 585 571 674 670. 105 621 116

0 9.4 206 9.9 12 1.9 209 28 99 49 29 201 9.8

1 2 3 4 1 2 3 1 1 1 2 3 4

ThF2 (1A1)

ThF (a 4Σ−) ThF+ (3Δ) ThF3+ (1A1)

Electronic Structure. The electronic state symmetry labels are included in Table 1, as derived from inspection of the occupied orbitals. When the UHF orbitals are too distorted for symmetry labeling, the labels in Table 1 are based upon small CASSCF calculations. The singly occupied molecular orbital (SOMO) in ThF3 is 6dz2, perpendicular to the plane of the molecule. In triplet ThF2, the singly occupied orbitals are of δ and σ (6dx2+y2) symmetry. The singly occupied orbitals in quartet ThF are similar to those in triplet ThF2, with the addition of a second δ orbital. The orbitals in doublet ThF are of broken symmetry, but the open shell is essentially of δ symmetry. Among the ions, the SOMO in ThF2+ is mainly 6dx2, perpendicular to the molecular plane. In triplet ThF+, the SOMOs are of δ and σ (ds hybrid) symmetry. In ThF4+, the spin density is localized upon the F atom most distant from the Th center. Some cases show substantial spin contamination. In particular, ideal values of ⟨S2⟩ are exceeded by 0.45 (Th triplet), 0.52 (ThF doublet), 0.53 (Th+ doublet), 0.77 (ThF2 singlet), and 0.95 (ThF+ singlet). In such cases, it is expected that the energy is slightly too far in the direction of the higherspin electronic state (usually too high). Vibrational Spectra. Harmonic vibrational frequencies, computed at the MP2/B1 level, are summarized in Table 2, along with the corresponding infrared (i.e., dipole) intensities. HF/B1 frequencies and intensities are included in the Supporting Information. For ThF4, anharmonic calculations (second-order perturbation theory, VPT2) were also done; the resulting frequencies are listed in Table 3. Vibrational constants are listed in the Supporting Information. Electronic Fine Structure. Fine structure is needed for partition functions and to compute term averages (for spin− orbit corrections). The electronic ground state of ThF has been assigned as X 2Δ3/2, with 2Δ5/2 lying at T0 = 2575 ± 15 cm−1.24 Spin−orbit CI calculations predicted 2Π1/2 and 2Π3/2 states lying at 4253 cm−1 and 6134 cm−1, respectively.24 Additional low-lying states were sought here using a four-component

mode

Table 3. Harmonic (ω) and Fundamental (ν) Vibrational Frequencies for ThF4 from Anharmonic fK-MP2/B1 Calculations mode 1 2 3 4

(a1) (e) (t2) (t2)

ω (cm−1)

IR intensity (km/mol)

ν (cm−1)

595 116 537 110

0 0 221 30

589 112 532 107

multireference CISD calculation described as (3/5/40) (virtuals up to 0.8 Eh) at an internuclear distance of 203.2 pm. The spin−orbit corrections to the nonrelativistic energies are taken as (2575/2) cm−1 = 15.4 kJ/mol for the ground 2Δ state (from experimental levels) and 4.7 kJ/mol for the 4Σ− state (from the MR-CISD levels). The present, conventional CCSD(T) calculations (i.e., spin−orbit averages) place the 4Σ− state near 6395 cm−1 after applying these spin−orbit corrections. Experimental and theoretical energy levels, summarized in Table 4, are all consistent. The electronic partition function was constructed using the MR-CISD values, except that the experimental value was used for 2Δ5/2. The ground state of ThF+ is believed to be X 1Σ+, with 3ΔΩ lying at T0 = 315, 1053, and 3150 cm−1 for Ω = 1, 2, 3, Table 4. Electronic Energy Levels of ThF (in cm−1) label

Ω

expta

X 2Δ

3/2 5/2 1/2 3/2 1/2 3/2

0 2575 ± 15

A 2Π a 4Σ−

MRCI + SO-CIa CCSD(T)b 0 1939 4253 6134

[0]

[6395]

MRCISDc 0 2415 3132 6099 6124 6911

a Reference 24. bConventional ECP, after spin−orbit correction (see text). cFour-component relativistic calculation with Dirac-Coulomb Hamiltonian; vertical excitation energies.

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respectively (average = 1506 cm−1), and another state, tentatively 3Π0, at 3395 cm−1.24 The present, conventional CCSD(T) calculations (i.e., no spin−orbit coupling) place the lowest triplet state about 738 cm−1 above the lowest singlet state. After applying the experimental spin−orbit correction of (1506 cm−1 − 315 cm−1 =) 1191 cm−1, this puts the 3Δ1 level 453 cm−1 below the 1Σ+. Fine structure was computed using relativistic MR-CISD calculations (13/5/26) (virtuals up to 0.19 Eh), at the geometry (r = 197.5 pm) corresponding to the ground-state rotational constant.24 Experimental and theoretical energy levels, summarized in Table 5, disagree. Like the best

Table 6. Computed Bond Dissociation Enthalpies and Enthalpies of Formation (T = 298.15 K; kJ/mol; Literature Values between Parentheses) ThFn(+) Th ThF ThF2 ThF3

Table 5. Electronic Energy Levels of ThF+ (in cm−1) labela

Ω

expta

X 1Σ+ A 3Δ B C D 3Π

0 1 2 3 0 1 0

0 315.0 ± 0.5 1052.5 ± 0.5 3150 ± 15 3395 ± 15

CCSDT(Q) + SOCIa,b 0 66 955 2223

CCSD(T)c [453] [0]

D298(Fn−1Th(+)−F)

ThF4

676 ± 12 (651 ± 16)b 679 ± 12 (699 ± 25)b 653 ± 12 (654 ± 25)b 672 ± 12 (665 ± 18)b

Th+ ThF+ ThF2+ ThF3+ ThF4+

MRCISDd 197 0 1126 2899 6239 6766 6405

666 ± 12 670 ± 12 656 ± 12 40 ± 12

ΔfH [reference] (602 ± 6)a 5 ± 13 (30 ± 15)b −594 ± 13 (−651 ± 21;c −590 ± 20;b −574 ± 21d) −1168 ± 13 (−1165 ± 15;b −1084 ± 21d) −1761 ± 13 (−1751 ± 10)b 1211 ± 6e 624 ± 13 33 ± 13 −543 ± 13 −503 ± 13

a e

Reference 24. bSelected, higher-level calculations placed 3Δ1 lower than 1Σ+ by about 240 cm−1. cConventional ECP, after experimental spin−orbit correction. dFour-component, Dirac-Coulomb (relativistic) Hamiltonian; vertical excitation energies. a

References 2−6. bReference 3. cReference 2. Experimental value derived here using eq 1.

d

Reference 7.

then yields ΔfH(Th+) = 1211 ± 6 kJ/mol, a purely experimental value. For ThF, the present computations yield an (adiabatic) value IE(ThF) = 6.35 eV, close to the precise experimental value IE(ThF) = 6.3952 ± 0.0004 eV.24 As pointed out by Barker et al.,24 the bond dissociation enthalpy in ThF+ can be inferred from that in ThF when both IE(Th) and IE(ThF) are available. Applying eq 2 with the experimental ionization energy results in D298(Th+−F) = 666 ± 12 kJ/mol. This corresponds to ΔfH(ThF+) = 624 ± 13 kJ/mol. Results for ThF2+, ThF3+, and ThF4+ are straightforward and are included in Table 6. All thermochemical results in this report are for the ideal gas.

calculations by Barker et al. (not included in their tables),24 the present calculations place the 3Δ1 state below the 1Σ+. This suggests reassigning the ground state as 3Δ1, which is interesting for application of ThF+ to measurements of the dipole moment of the electron.30 However, the present calculations are not good enough to justify replacing the experimental assignment. Consequently, the experimental levels are used here to compute the electronic partition function, plus the two highest calculated levels that are listed in Table 5. For ThF2, the lowest triplet state is predicted to be linear (3Δ). To estimate its fine structure, an MR-CISD calculation (6/4/67) (virtuals up to 1.5 Eh) was done at the geometry described in Table 1. The lowest level is calculated to be 3Δ1, followed by 3Δ2 (779 cm−1) and then 3Δ3 (1884 cm−1). This corresponds to a spin−orbit correction of 10.6 kJ/mol. After applying this correction, the conventional CCSD(T) calculations place the 3Δ1 state about 46 kJ/mol (3825 cm−1) above X̃ 1A1. ThF2+ has a bent, nondegenerate ground state for which no spin−orbit splitting is expected. EOM-CCSD calculations predict no vertical excitation energies below 0.8 eV. No lowlying electronically excited states are expected for ThF4 or ThF3+. Thermochemistry. The computed bond dissociation enthalpies (T = 298.15 K) are summarized in Table 6. Enthalpies of formation, also in Table 6, are computed with reference to atomic Th, since its enthalpy of formation has a smaller associated uncertainty than that for ThF4. The computed atomization enthalpy of ThF4 is 2680 kJ/mol, in good agreement with the experimental value of (2671 ± 12) kJ/mol. As stated earlier, it is problematic to determine the spin− orbit correction to apply to the computed electronic energy of Th+. Thus, the experimental value is used here for the ionization energy of atomic Th.23 The identity shown in eq 1

+ Δf H298(Th+) = Δf H298(Th) + IE(Th) + Δ298 0 H(Th )

− Δ298 0 H(Th)

(1)

D298(ThF+) = D298(ThF) + IE(Th) − IE(ThF) + + + Δ298 0 H(Th − Th + ThF − ThF )

(2)

From the temperature dependence of gas-phase equilibria, Lau et al. determined the absolute entropies of ThFn (n = 1−4) at elevated temperature.8 These experimental values are compared with the present results in Table 7. Results agree within the experimental uncertainties except for ThF4, for which the theoretical value is too high by 7 ± 4 J mol−1 K−1 (at 1150 K). Table of thermodynamic functions for all species are provided in the Supporting Information. Table 7. Comparison of Experimental and Computed GasPhase Entropies (J mol−1 K−1) of Neutral ThFn

a

molecule

T (K)

expta

computedb

ThF ThF2 ThF3 ThF4

2200 2200 1900 1150

337 ± 8 411 ± 10 484 ± 12 483 ± 4

330 419 483 490 (514)c

Reference 8. function.

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b

Present work.

c

Anharmonic vibrational partition



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Table 8. Appearance Energies of Ions (at Left) from Neutral Precursors (at Top)a Th+ ThF+

Th

ThF

ThF2

ThF3

ThF4

(6.3067 ± 0.0002)b (6.0 ± 0.3)e

13.28 ± 0.12 (14.2 ± 0.5)e 6.35 ± 0.12 (6.3952 ± 0.0004)d (6.0 ± 0.3)e

20.28 ± 0.12

27.03 ± 0.12

13.36 ± 0.12 (14.2 ± 1.0)e

20.10 ± 0.12

33.97 ± 0.12 (39 ± 1)c 27.04 ± 0.12 (30 ± 1)c

6.46 ± 0.12 (13.1 ± 0.6)c (6.0 ± 0.3)e

13.21 ± 0.12 (14.0 ± 0.5)e

ThF2+

6.43 ± 0.12 (7.8 ± 0.3)c (6.2 ± 0.3)e

ThF3+

ThF4+ a

Literature values are between parentheses. Values are in eV. bReference 23. cReference 7. dReference

Appearance Energies. The appearance energy of an ion, A+, from a neutral molecule, B, is denoted AE(A+/B) and defined here as the minimum, zero-temperature energy required to produce A+ from B, disregarding any kinetic barriers. Combining the computed atomization energy with the experimental value of IE(Th),23 AE(Th+/ThF4) = 3278 kJ/mol = 33.97 eV if the F4 coproduct is assumed to be atomic. In the unlikely event that the fluorine is lost as two molecules of F2, the appearance energy would be lower by 2D0(F2) = 309.1 ± 1.2 kJ/mol = 3.204 ± 0.012 eV.31 Table 8 summarizes appearance energies (assuming that fluorine is lost as F atoms), along with experimental values from the literature. Uncertainties. Since these are small molecules with simple bonds, large-basis CCSD(T) thermochemistry is estimated to be reliable to about 8 kJ/mol. However, there are at least three additional sources of uncertainty here. (1) A core pseudopotential is used to mimic scalar relativistic effects, but cannot be perfect. Moreover, spin−orbit coupling is included only as a simple, open-shell energy adjustment; it is absent in the CCSD(T) calculations. (2) Because of technical limitations, some of the energy levels used in the electronic partition functions are computed using a relativistic configuration interaction with a space that may be too small. (3) Small inconsistencies in atomic energies may also be present in the open-shell molecules. Including these considerations, the present thermochemical predictions have an uncertainty estimated to be 12 kJ/mol.

20.15 ± 0.12 (23.2 ± 0.6)c (21 ± 1)e 13.38 ± 0.12 (14.5 ± 0.5)c (13.5 ± 0.5)e 12.97 ± 0.12 (12.75 ± 0.01)f

24 e

Reference 8. fReference 39.

present MP2 and HF values are slightly shorter than these earlier results, which may be ascribed to the larger basis sets and subvalence correlation included here. Gagliardi et al. were primarily concerned with the performance of density functional theory (DFT) calculations, and obtained r(Th−F) values ranging from 210.7 pm (LSDA) to 214.3 pm (BLYP). DFT computations by Adamo and Barone, using the PBE0 functional and a 78e pseudopotential, gave r(Th−F) ≈ 211.5 pm, with minor dependence upon basis set.35 For the lower fluorides and the ions, the only previous information is from the closed-shell calculations by Buz’ko et al., cited above. For ThF3+, they reported C3v symmetry with r(Th−F) = 205.0 and 204.8 pm at the MP2 and HF levels, respectively. The bond angle was not reported. These values are slightly longer than those from the present study, as for ThF4. Vibrational Spectra. Konings and Hildenbrand have summarized experimental data for actinide tetrahalides, including ThF4.36 Values for ν3 (520 cm−1)37 and ν4 (116 cm−1)38 are available from high-temperature, gas-phase, infrared measurements, but ν1 and ν2 are inactive (see Table 2). Their values have been estimated when needed for computing thermodynamic partition functions, e.g., ν1 ≈ 618 cm−1 and ν2 ≈ 121 cm−1.36 All these values are in reasonably good agreement (∼ 5%) with the present, theoretical values (Table 2). Previous calculations have provided vibrational data for ThF4. Gagliardi et al. reported frequencies and intensities from a variety of theoretical methods; their MP2 results are close to those in Table 2.34 Likewise, the PBE0 results by Adamo and Barone also agree reasonably well with the present MP2 calculations.35 The present anharmonic calculations are the first for this molecule. No earlier data are available for the lower fluorides or for the ions. Thermochemistry. The computed atomization enthalpy for ThF4 differs from the experimental value by only 9 ± 17 kJ mol−1, lending confidence to the theoretical predictions for other species. The second neutral bond (i.e., F2Th−F) is slightly weaker than the others, which are remarkably uniform. This is in contrast to the conclusions of Lau et al., who found the FTh−F bond to be markedly stronger than the others.8 For standard entropies, the theoretical results agree with experiment except for ThF4,8 for which theory appears too high by 7 ± 4 J mol−1 K−1 at 1150 K. To investigate whether anharmonic effects could explain the discrepancy, entropies were computed

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DISCUSSION Geometries. The structure of crystalline ThF 4, as determined by X-ray diffraction, is not molecular but ionic, with Th−F distances mostly greater than 230 pm.32 In contrast, gas-phase electron diffraction yielded a tetrahedral structure with a thermally averaged distance of (212.4 ± 0.5) pm at T = 1370 K.33 The present CCSD(T) value in Table 1 (210.6 pm) is somewhat shorter, as may be expected for an equilibrium (Re) value when compared with a high-temperature value. No experimental data are available for the structures of the other molecules. There have been earlier, more approximate structural calculations on ThF4. The most recent are by Buz’ko et al.10 They obtained r(Th−F) = 212.9 and 212.5 pm at the MP2 and HF levels, respectively, using a 78e pseudopotential. Gagliardi et al., using a 60e pseudopotential, obtained r(Th−F) = 213.0 and 213.4 pm at the MP2 and HF levels, respectively.34 The 1280



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(2) Fuger, J.; Parker, V. B.; Hubbard, W. N.; Oetting, F. L. The Chemical Thermodynamics of Actinide Elements and Compounds. Part 8. The Actinide Halides; International Atomic Energy Agency: Vienna, Austria, 1983. (3) Rand, M.; Fuger, J.; Grenthe, I.; Neck, V.; Rai, D. Chemical Thermodynamics of Thorium; OECD Publishing: Paris, 2008. (4) Cox, J. D.; Wagman, D. D.; Medvedev, V. A. CODATA Key Values for Thermodynamics; Hemisphere: New York, 1989. (5) Konings, R. J. M.; Benes, O. J. Phys. Chem. Ref. Data 2010, 39, 043102:1−47. (6) Ackermann, R. J.; Rauh, E. G. J. Chem. Thermodyn. 1972, 4, 521− 532. (7) Zmbov, K. F. J. Inorg. Nucl. Chem. 1970, 32, 1378−1381. (8) Lau, K. H.; Brittain, R. D.; Hildenbrand, D. L. J. Chem. Phys. 1989, 90, 1158−1164. (9) Hildenbrand, D. L.; Lau, K. H. Pure Appl. Chem. 1992, 64, 87− 92. (10) Buz’ko, V. Y.; Kushkhov, K. B.; Buz’ko, M. B. Russ. J. Inorg. Chem. 2010, 55, 395−400. (11) Sidorov, L. N.; Zhuravleva, L. V.; Varkov, M. V.; Skokan, E. V.; Sorokin, I. D.; Korenev, Y. M.; Akishin, P. A. Int. J. Mass Spectrom. Ion Phys. 1983, 51, 291−311. (12) Certain commercial materials and equipment are identified in this paper in order to specify procedures completely. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the material or equipment identified is necessarily the best available for the purpose. (13) Küchle, W.; Dolg, M.; Stoll, H.; Preuss, H. J. Chem. Phys. 1994, 100, 7535−7542. (14) Cao, X. Y.; Dolg, M.; Stoll, H. J. Chem. Phys. 2003, 118, 487− 496. (15) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007−1023. (16) Kendall, R. A.; Dunning, T. H., Jr. J. Chem. Phys. 1992, 96, 6796−6806. (17) 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. et al. Gaussian 09; version B.01; Gaussian, Inc.: Wallingford, CT, 2010. (18) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. J. Chem. Phys. 1998, 109, 7764−7776. (19) Ralchenko, Y.; Kramida, A. E.; Reader, J.; NIST ASD Team NIST Atomic Spectra Database, version 4.1.0; National Institute of Standards and Technology: Gaithersburg, MD, 2011; http://physics. nist.gov/asd. Accessed February 1, 2012. (20) Zalubas, R. J. Res. Natl. Bur. Stand. 1959, 63A, 275−278. (21) Palmer, B. A.; Engleman, R., Jr. Atlas of the Thorium Spectrum, Los Alamos National Laboratory Report LA-9615, Los Alamos, NM, 1983. (22) Blaise, J.; Wyart, J.-F. Selected Constants, Energy Levels and Atomic Spectra of Actinides; http://www.lac.u-psud.fr/Database/Contents.html (accessed March 29, 2012). (23) Köhler, S.; Deiβenberger, R.; Eberhardt, K.; Erdmann, N.; Herrmann, G.; Huber, G.; Kratz, J. V.; Nunnemann, M.; Passler, G.; Rao, P. M.; et al. Spectrochim. Acta B 1997, 52, 717−726. (24) Barker, B. J.; Antonov, I. O.; Heaven, M. C.; Peterson, K. A. J. Chem. Phys. 2012, 136, 104305−104309. (25) Bast, R.; Jensen, H. J. A.; Saue, T.; Visscher, L.; Bakken, V.; Dyall, K. G.; Dubillard, S.; Ekström, U.; Eliav, E.; Enevoldsen, T. et al. DIRAC, A Relativistic Ab Initio Electronic Structure Program, vers. DIRAC11, Vrije Universiteit Amsterdam: Amsterdam, 2011. (26) Dyall, K. Theor. Chem. Acc. 2007, 117, 491−500. (27) Knecht, S. Parallel Relativistic Multiconfiguration Methods: New Powerful Tools for Heavy-Element Electronic-Structure Studies. Ph.D. Thesis, Heinrich-Heine-Universität Düsseldorf, 2009. (28) Irikura, K. K.; Johnson, R. D., III; Kacker, R. N.; Kessel, R. J. Chem. Phys. 2009, 130, 114102:1−11. (29) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17, Suppl. 1.

using an anharmonic vibrational partition function. All the anharmonicity constants (xij) are negative-valued, leading to a higher density of states than in the harmonic model. This raises the value of S(1150) by 24 J mol−1 K−1, moving it farther from the experimental value. Thus, anharmonic effects do not explain the small disagreement with the experimental entropy. Appearance Energies. Compared with the values reported by Lau et al.,8 the calculated appearance energies are all in good agreement, or in marginal agreement (i.e., between 1 and 2 times the estimated standard uncertainty). They are consistently lower than the values reported by Zmbov.7 In particular, the present results support the conclusion that the neutral precursor of ThF2+ in Zmbov’s experiment was ThF3, not ThF2.8 The parent ion, ThF4+, has not been observed by mass spectrometry. However, the ultraviolet photoelectron spectrum of ThF4 has been reported.39 The adiabatic ionization energy is assumed here to represent AE(ThF4+/ThF4), since the ab initio calculations indicate that the ion is stable. However, the current result is higher than the photoelectron value by 0.23 ± 0.16 eV. Although this is marginal agreement, common difficulties in extracting adiabatic ionization energies from photoelectron spectra may apply in this case. In particular, the experiment was done at high temperature (1120 to 1300 K), at which the internal energy of ThF4 exceeds 1 eV, based upon the present partition function. Contributions from hot bands will skew the apparent ionization energy to a lower value. For this reason, it is not clear whether the theoretical or the photoelectron value should be preferred. Better calculations would resolve this.

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CONCLUSIONS For neutral ThFn, the present results generally support the experimental measurements by Lau, Brittain, and Hildenbrand.8 Enthalpies of formation are first reported here for the ions ThFn+. Vibrational and electronic energy levels are computed, and the corresponding thermodynamic functions are tabulated. High-temperature, experimental entropies are matched surprisingly well by rigid-rotor/harmonic-oscillator calculations. In post-HF calculations, freezing all core electrons appears to be too strong an approximation.

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ASSOCIATED CONTENT

S Supporting Information *

Full citations for refs 17 and 25, optimized molecular geometries, vibrational frequencies, coordinates, energies, and thermodynamic functions (24 pages). This information is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS I am grateful to Dr. Stefan Knecht for generous help in using the DIRAC software package, and for pointing out ref 24. I also thank Dr. Gary W. Trucks for help in diagnosing the UHF inconsistency problem, and the anonymous reviewers for helpful comments.

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REFERENCES

(1) LeBlanc, D. Nucl. Eng. Des. 2010, 240, 1644−1656. 1281



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