ARTICLE pubs.acs.org/JPCA
Computed Vibrational Frequencies of Actinide Oxides AnO0/þ/2þ and AnO20/þ/2þ (An = Th, Pa, U, Np, Pu, Am, Cm) Attila Kovacs*,†,‡ and Rudy J.M. Konings† † ‡
European Commission, Joint Research Centre, Institute for Transuranium Elements, P.O. Box 2340, 76125 Karlsruhe, Germany Materials Structure and Modeling Research Group of the Hungarian Academy of Sciences, Budapest University of Technology and Economics, H-1111 Budapest, Szt. Gellert ter 4
bS Supporting Information ABSTRACT: The vibrational frequencies of the actinide oxides AnO and AnO2 (An = Th, Pa, U, Np, Pu, Am, Cm) and of their mono- and dications have been calculated using advanced quantum chemical techniques. The stretching fundamental frequencies of the monoxides have been determined by fitting the potential function to single-point energies obtained by relativistic CASPT2 calculations along the stretching coordinate and on this basis solving numerically the ro-vibrational Schr€odinger equation. To obtain reliable fundamental frequencies of the dioxides, we developed an empirical approach. In this approach the harmonic vibrational frequencies of the AnO20/þ/2þ species were calculated using eight different exchange-correlation DFT functionals. On the basis of the good correlation found between the vibrational frequencies and computed bond distances, the final frequency values were derived for the CASPT2 reference bond distances from linear regression equations fitted to the DFT data of each species. As a test, the approach provided excellent agreement with accurate experimental data of ThO, ThOþ, UO, and UOþ. The joint analysis of literature experimental and our computed data facilitated the prediction of reliable gas-phase molecular properties for some oxides. They include the stretching frequencies of PuO, ThO2, UO2, and UO2þ and the bond distance of PuO (1.818 Å, being likely within 0.002 Å of the real value). Also the derived equilibrium bond distances of ThO2, UO2, and UO2þ (1.896, 1.790, and 1.758 Å, respectively) should approximate closely the (yet unknown) experimental values. On the basis of the present results, we suggest that the ground electronic state of PuO2 in Ar and Kr matrices is probably different from that in the gaseous phase, similarly to UO2 observed previously.
1. INTRODUCTION Actinide oxides are of high relevance in nuclear technology: the uranium and plutonium dioxides are important nuclear fuels, while the other (minor) actinides are formed in the fuel during irradiation as a result from neutron capture processes. Because of the long-term perspective of nuclear energy, considerable activities are in progress for the development of safer and more economic nuclear reactors. Several of the promising Generation IV reactor types are fast reactors in which the fuel operates at extreme conditions. The temperature in the middle zone of the fuel can reach 2500 K,13 where the actinide oxides have already a substantial vapor pressure. Hence, for a proper thermodynamic description of the high-temperature fuel restructuring processes in these nuclear fuels, the vapor species have to be taken into account, requiring the knowledge of molecular data of the actinide oxides. Due to the complications handling actinide, particularly other than Th and U, material experimental information is available only for a few actinide oxides. Previous experimental investigations of gaseous oxides include the microwave spectroscopic investigations of ThO,46 the high-resolution photoelectron r 2011 American Chemical Society
spectroscopic studies of ThO/ThOþ,7 UO,8 UOþ,9 UO2,10 and UO2þ,11 and the matrix-isolation IR spectroscopic measurements of ThO/ThO2,1215 UO/UO2,1618 UO2þ,1719 and PuO/PuO220 in various matrices. The microwave and highresolution photoelectron spectroscopic studies provided accurate values for the bond lengths, harmonic vibrational frequencies, and first anharmonicities of the studied species, while the matrix-isolation IR measurements provided anharmonic frequencies of the IR active stretching fundamentals. Note that the latter data suffer from matrix shifts and occurrently from perturbation effects (vide infra), requiring caution at their interpretation. For the rest of the actinide oxides there is no direct experimental information available, only estimates based on the properties of the above actinide or related lanthanide compounds.2125 Attempts to fill the gaps in the data of gaseous actinide oxides came from the field of quantum chemical calculations. Our Received: March 17, 2011 Revised: May 5, 2011 Published: May 23, 2011 6646
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The Journal of Physical Chemistry A literature search found computed vibrational data for ThO,7,15,2633 ThOþ,7 UO,18,3437 UOþ,35,37 PuO,3840 PuOþ,39,41,42 PuO2þ,39,41 AmO,43 AmOþ,43 CmO,43 ThO2,13,15,44 PaO2þ,44 UO2,18,4549 UO2þ,18,19,47,50 UO22þ,18,44,47,4952 NpO2,49 NpO22þ,49 PuO2,39,40,49,53,54 PuO2þ,39 and PuO22þ,39,49,51,55,56 obtained at various levels of theory. The computed bond distances and vibrational frequencies depend strongly on the computational level (and on the sometimes different electronic state) and in most cases differ considerably from the available experimental results. Very recently we performed a systematic theoretical study for all the title species at the relativistic spinorbit CASPT2 (SO-CASPT2) level and reported the electronic ground states, reliable molecular geometries, and ionization energies.57 The goal of our present work is the evaluation of reliable vibrational frequencies for AnO and AnO2 (An = Th, Pa, U, Np, Pu, Am, Cm) molecules as well as for their mono- and dications by means of sophisticated quantum chemical calculations. The work is based on the electronic ground states reported recently.57 The vibrational data of the monoxides are evaluated by analysis of the potential energy curve along the stretching coordinate. We paid special attention to the accuracy of the curve, and therefore we used 2030 sampling points and a very narrow sampling rate around the minimum. In a few cases, we found a strong dependence of the vibrational frequency and anharmonicity values on the sampling parameters. Due to difficulties to obtain vibrational frequencies of triatomic species at the CASPT2 level, we chose for the dioxide species a different approach. The recently found nearly singledeterminant character of the ground-state electronic structures of the title species57 suggested a promising application of the DFT technique. However, the DFT-computed geometries deviate more or less from the reference CASPT2 data, which leads consequently to errors of the DFT vibrational frequencies. Moreover, the deviations of DFT data are not consistent in the actinide row. Therefore, instead of selecting a single “best performing” DFT method we computed each species with eight different exchange-correlation functionals, and on the basis of the found empirical relationships between the optimized bond distances and vibrational frequencies, we evaluated the frequencies for SO-CASPT2 bond distances available from the literature. The reliability of our evaluated molecular parameters is assessed by comparison with available experimental data of the thorium, uranium, and plutonium oxides.420
2. COMPUTATIONAL DETAILS The calculations on the monoxides were performed using the code MOLCAS 7.4 patch 045.5860 The complete active space (CAS) SCF method61 was used to generate molecular orbitals and reference functions for subsequent multiconfigurational second-order perturbation theory calculations of the dynamic correlation energy (CASPT2).62,63 The active space consisted of the 7s, 6d, and 5f orbitals of the actinide atoms as well as of the unoccupied 2p orbitals of oxygen, altogether 16 orbitals occupied by the appropriate number of valence electrons in the various species. All-electron basis sets of atomic natural orbital type developed for relativistic calculations (ANO-RCC) with the Douglas KrollHess Hamiltonian64,65 were used for all the atoms. For the actinides a primitive set of 26s23p17d13f5g3h was contracted to 9s8p6d5f2g1h,66 whereas for O a primitive set of 14s9p4d3f2g
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was contracted to 4s3p2d1f67 achieving VTZP quality. The DouglasKrollHess Hamiltonian was used in the CASSCF calculations to account for scalar relativistic effects. In the second-order perturbation treatment (CASPT2), the orbitals up to 5d of the actinides and 1s of oxygen were kept frozen, while the remaining valence and semivalence orbitals (including 6s and 6p of the actinides and 2s of oxygen) were correlated. These CASPT2 calculations have been performed on the recently reported electronic ground states of the monoxide species.57 The potential energy curves were obtained by singlepoint calculations using steps of 0.1 Å between 1.5 and 2.3 Å. The sampling distance was decreased to 0.02 Å in a range of 0.2 Å around the equilibrium bond distance. In a few cases we obtained unrealistic values for the anharmonicity ωexe which could be corrected by further refinement of the sampling to steps of 0.002 Å in the 0.02 Å range around the equilibrium bond distance. (This is the reason why we did not consider spinorbit effects: the calculation of such numerous data points using the complete active space interaction (CASSI) method68 would require enormous computational costs.) to avoid the change of electronic state along the potential curve, we used the SUPSym keyword of MOLCAS, allowing orbital rotations in the active space between the defined 16 orbitals only. The equilibrium bond distances, the harmonic vibrational frequencies, and other spectroscopic constants of the monoxides were determined by using the program VIBROT available in the MOLCAS package. In the VIBROT run the potential is fitted to an analytical form using cubic splines, and then the ro-vibrational Schr€odinger equation is solved numerically.59 The frequencies of the dioxide species have been calculated by the code Gaussian 0369 using the following exchange-correlation functionals: B3LYP,70,71 B3P86,70,72 mPW1PW91,73 TPSSTPSS,74 PBE1PBE (alias PBE0),75 BLYP,71,76 BP86,72,76 PBEPBE,77,78 and HCTH.79 A linear equation was fitted to the optimized bond distances and computed harmonic vibrational frequencies (one model for all the computed data of a fundamental), and using this equation we evaluated the frequencies for the SOCASPT2 bond distances. This procedure was validated on the experimental data of ThO, ThOþ, UO, and UOþ. Note that the vibrational frequencies obtained by the HCTH functional have been omitted from our analysis because of their considerable deviation from the frequencybond distance relationships shown by the other results. In the DFT calculations, the small-core relativistic effective core potentials of the CologneStuttgart group (ECP60MWB) were used for the actinides28,80 in conjunction with a 14s13p10d8f6g valence basis set contracted to 10s9p5d4f3g (ECP60MWB_SEG basis).80 For oxygen, the correlation-consistent augcc-pVTZ basis set81 was used. Particular care was taken on the electronic states in the DFT calculations. After the SCF cycle reached convergence, orbital population analyses have been performed for each species, and the results were compared to the ground-state electronic configurations known from the literature.57 In the few cases when the SCF converged to a different (generally higher-lying) electronic state, the DFT orbital populations were altered to the reference (literature) ground states.
3. RESULTS AND DISCUSSION 3.1. Vibrational Frequencies of the Monoxides. The computed spin-free CASPT2 bond distances and selected computed 6647
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Table 1. Equilibrium Bond Distances, Harmonic Vibrational Frequencies, and Anharmonicitiesa of the Monoxide Species Computed at the Spin-Free CASPT2 Level species
ωe
ωexe
Σ
1.861
878.9
2.3
Σ
1.827
930.8
2.6
Σ
1.792
987.6
2.7
Φ
ThO ThOþ
2
ThO2þ
1
PaO
2
1.811
926.7
2.1
PaOþ PaO2þ
3
H 2 Φ
1.805 1.752
932.3 1040.0
2.6 2.6
5
1.837
857.9
1.2
UO
4
1.799
910.9
2.4
UO2þ
3
H
1.728
1047.2
2.8
NpO
6
Δ
1.837
899.8
3.0
NpOþ
5
Γ
1.797
966.8
2.7
NpO2þ
4
I
1.722
1082.0
3.4
PuO PuOþ
7
Π 6 Π
1.818 1.777
858.2 918.5
2.8 2.2
Γ
1.720
1012.5
1.0
Σ
1.800
872.2
3.4
Σ
1.776
964.9
3.6
Π
1.774
810.6
6.0
Σ
1.835
834.9
2.9
Σ
1.795
951.3
2.2
Σ
1.788
819.5
12.3
þ
b
re
1
UO
a
stateb
I I
PuO2þ
5
AmO
8
AmOþ
7
AmO2þ
6
CmO
9
CmOþ
8
CmO2þ
7
The vibrational data are given in cm1 and the bond distances in Å. From ref 57.
vibrational parameters of the monoxides (in the electronic ground state57) are compiled in Table 1. We note that our optimized spin-free bond distances agree well with those from the spinorbit CASPT2 calculations of Infante et al.,57 as minor deviations were found only for PaO2þ, PuOþ, PuO2þ, and AmO2þ attributed to the differences in the theoretical level. Experimental data on spectroscopic constants have been reported previously for ThO, ThOþ, UO, UOþ, and PuO. They are compared with our and selected theoretical results from the literature in Table 2. Dewberry et al. determined the bond distance in ThO with very high accuracy using microwave spectroscopy.6 The bond distance of ThOþ has been derived from pulsed field ionizationzero-kinetic-energy photoelectron spectroscopic (PFIZEKE) measurements.7 As the data in Table 2 show, our calculations (similarly to the previous ones including spinorbit coupling57) overestimate the bond distance in ThO and ThOþ by 0.02 Å. This error is accompanied by an underestimation of the harmonic vibrational frequencies4,5,7 of the two species by ca. 20 cm1. On the other hand, the computed first anharmonicities (2.3 and 2.6 cm1 for ThO and ThOþ, respectively) agree well with the experimental values of 2.39 and 2.45 cm1, respectively.4,5,7 We note that most earlier theoretical results show similar (or larger) errors for the bond distances and vibrational frequencies of ThO (cf. Table 2). Better agreement has been achieved only by the DFT calculations of Goncharov7 and Andrews 15 and by the CCSD(T) calculations of Buchachenko. 33 Additional IR data on ThO include the IR absorptions of the species isolated in neon13,15 and argon12,14 matrices. On the basis of the experimental gas-phase harmonic frequency and
anharmonicity,4,5 we can derive the matrix shifts of 4 and 12 cm1 for the Ne and Ar matrices, respectively. Experimental data for the bond distances in UO and UOþ have been reported by Heaven et al. using high-resolution photoelectron spectroscopy.8,9 In contrast to the above shown deviations for the bond distances in the ThO species, the agreement of our CASPT2 results with the experimental ones of UO and UOþ is excellent (cf. Table 2). We comment briefly on the experimental vibrational spectrum of UO, which showed a significant vibronic perturbation of the first vibrational interval for the ground state due to the interactions between the three lowest energy Ω = 4 states. The observed vibrational interval in the gaseous phase was 882.4 cm1.8 Kaledin et al. derived the deperturbed ground state vibrational interval to be 841.9 cm1 and the deperturbed harmonic vibrational constant to be ωe = 846.5 cm1.8 We used this latter value in our comparison with the computed data because the routine quantum chemical frequency calculations do not account for vibronic effects. The vibronic perturbation appears also in the matrix-isolated species; however, there the guesthost interactions affect the magnitude of perturbations, and hence the vibronic effect is different in the various matrices. This can be seen in the anomalous band at 889.5 cm1 in the IR spectrum of UO isolated in the Ne matrix18 being somewhat larger than the perturbed frequency observed in the gaseous phase. On the other hand, the absorptions in the Ar and Kr matrices (820 and 815 cm1, respectively,16,17 cf. Table 2) seem to be quite reasonable compared to the deperturbed gas-phase value. The derived shift in the Ar matrix, ca. 20 cm1, is somewhat larger than that observed for ThO (12 cm1, vide supra). The matrix shift of Kr is ca. 25 cm1. Comparing our computed data with the previous theoretical results on UO, the SO-CASPT2 results by Paulovic et al.37 match well for both the bond distances and vibrational frequencies. We note, however, that their spin-free CASPT2 bond distances deviate slightly, while these vibrational frequencies deviate considerably (e.g., ωeUOþ by 163 cm1, cf. Table 2) from our and the experimental values. (The difference between our and their theoretical level was that Paulovic et al. used a somewhat smaller active space.) In the other theoretical studies listed in Table 2, the bond distances are overestimated. Good agreement was found with the vibrational frequency computed by Krauss and Stevens.35,36 The only experimental information found on plutonium monoxide is the matrix-isolation IR study of Green and Reedy.20 We note the resemblance of the matrix IR data of UO and PuO in Ar and Kr, in both cases the matrix shift from Ar to Kr being 5 cm1 (cf. Table 2). On this basis we assume analogous matrix shifts for UO and PuO and estimate the harmonic fundamental of PuO to be ca. 849 cm1 in the gaseous phase. The data of UO and PuO compiled in Table 2 suggest that our calculations performed similarly for the two oxides: like obtained for UO, our computed harmonic frequency for the PuO stretching is larger by 36 and 41 cm1 than the experimental values from the Ar and Kr matrices, respectively. With respect to our above estimated “gas-phase frequency” of PuO, our computed value is larger by the same magnitude (9 cm1) as obtained in the case of UO. These resemblances suggest that our computed bond distance for PuO possesses a reliability comparable to that of UO (within 0.002 Å of the experimental equilibrium bond distance). 6648
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Table 2. Available Experimental and Selected Computed Resultsa on the AnO0/þ/2þ Species species ThO
method
phase/state
re
frequency
ref
PFI-ZEKE
gas
1.840
MW
gas
1.84018613(24)
7
electron spectroscopy
gas
ωe = 895.77
IR
Ne matrix
887.1
13,15
IR
Ar matrix
878.8
12,14
6 4,5
ωexe = 2.39
ωexe = 1.9(9) 1 þ
Σ Σ
CCI DiracFockRoothaan
1 þ 1 þ
Σ
MRCIb
1.862
28
1.886
29
882
1.853
15
937
1.874
30
Σ
866
1.877
31
Σ0þ
856
1.866
32
898 898.7
1.846 1.845
7 33
879
1.863
present study
894
(1.840)
present study
1.807
7
960
1.814
7
931 941
1.827 (1.807)
present study present study
Σ
1 þ
Σ
1 þ
CASSCF DK3-SO-CASPT2b
1
1 þ
Σ 1 þ Σ
B3PW91 CCSD(T)
26 27
867
1 þ
MRCI
1.923 1.873
865
CASSCF PW91
852 923
ωexe = 3.19 1 þ
Σ
CASPT2 empiricald ThOþ
PFI-ZEKE
ωe = 954.97(6)
gas
ωexe = 2.45(3) 2 þ
Σ
B3PW91
2 þ
Σ
CASPT2 empiricald UO
photoelectron spectroscopy
ωe = 846.5(6)c
gas
1.8383(6)
8
(ω = 882.4) IR
Ne matrix
889.5
18
IR
Ar matrix
819.8
17,18
IR
Ar matrix
820
16
ωexe = 2.5(8) IR B3LYP
Kr matrix 5 Γ 3
Σ
MP2
16 18
1035.9
1.833
34
845
1.889
35,36
5
CASPT2
5
920
1.850
37
SO-CASPT2
5
855
1.842
37
CASPT2
5
858
1.837
present study
840
(1.8383)
present study
I I I4 I
empirical
photoelectron spectroscopy
gas
ωe = 911.9(2) ωexe = 2.39(4)
1.801(5)
9
MCSCF
4
935
1.842
35
CASPT2
4
1074
1.796
37
SO-CASPT2
4
912
1.802
37
CASPT2
4
911
1.799
present study
900
(1.801)
present study
I I I4.5 I
d
empirical PuO
1.850
MCSCF
d
UOþ
815.45 846
IR
Ar-matrix
822.3
20
IR estimatedf
Kr-matrix gas
817.27 849
20 present study
5
Σ
QCISD
781
1.83
38 39
ωexe = 2.77 SO-CASPT2b
856
1.820
Π
820
1.834
39
734
1.89
40
7
B3LYP
B3LYP
Π0
7
b e
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Table 2. Continued species PuOþ
method CASPT2 B3LYP b
AmO
present study
Π
899
1.788
39b
Π0.5
881
1.789
39
Π
919
1.777
present study
Σ
525
1.96
41
Γ
961
1.720
39b
6
5
41,42
B3LYP
5
SO-CASPT2b
5
Γ2
872
1.731
39
CASPT2 CASPT2
5
Γ 8 þ Σ
1013 917
1.720 1.803
present study 43
872
1.800
present study
924
1.758
43
Σ
965
1.776
present study
Σ
858
1.824
43
Σ
835
1.835
present study
CASPT2 CASPT2
CmO
1.818 1.875
SO-CASPT2
CASPT2 þ
858 652
CASPT2 b
AmO
Π Σ
6
B3LYP
ref
6 6
B3LYP
re
frequency
7
b
PuO2þ
phase/state
8 þ
Σ
7 þ
Σ
7 þ
CASPT2
9
CASPT2
9
a The vibrational data are given in cm1 and the bond distances in Å. The harmonic experimental vibrational frequencies are indicated by the ωe symbol (the computed values are in all the cases the harmonic ones). Experimental uncertainties are given in parentheses. b From the numerous calculated data from the given reference, only selected high-level results are shown here. For the full set of results see the reference. c UO suffers from strong perturbation effects. The ωe value is the derived unperturbed result. d Harmonic frequencies evaluated at the experimental reference bond distances (indicated in parentheses) from the trendlines fitted to data obtained with eight exchange-correlation DFT functionals. For details see text. e Electronic state not given in the original paper. f Estimated by assuming analogous general matrix shifts for UO and PuO on the basis of the same shifts from Ar to Kr.
Previous theoretical data on Pu monoxides include the SOCASPT2 calculations of La Macchia et al.39 and the DFT calculations of Gao et al.38 and Li et al.82 Our computed results are in good agreement with the SO-CASPT2 results of La Macchia et al.39 except for the vibrational frequency of PuO2þ, for which the value of La Macchia et al. seems to be too small. Therefore, the increasing trend of frequencies with the decreasing bond distance from PuO to PuO2þ seen in our computer results (cf. Table 1) does not appear in the computed frequencies of that work. The DFT frequencies of Gao et al.38 and Li et al.82 are smaller than the CASPT2 ones and thus deviate more from the experimental values. Regarding the previous theoretical study of AmO, AmOþ, and CmO43 performed at a level of theory similar to the present one, the differences in the computational details can account for the deviations from the present data (cf. Table 2). Our consistent calculations on the light actinide monoxides allow us to draw some general conclusions. Most obvious is the trend in the bond distances when the neutral molecule is ionized. The AnO bond becomes gradually shorter with the loss of one and two electrons, respectively. However, no clear trend can be observed in the spin-free CASPT2 bond distances from ThO to CmO (neither in the ions) similarly to the recently reported spinorbit distances.57 This is the consequence of the somewhat different electronic structures of these actinide oxides. Hence, the frequently supposed analogy within the actinide row or with the lanthanide series2125 may often fail for actinides. Our most important observation on the computed harmonic vibrational frequencies is that they are generally in agreement with the changes in the bond distances. The species with shorter (=stronger) bonds require generally larger energy for the stretching motion. The only exceptions are AmO2þ and CmO2þ where the ωe values are quite low. Inspecting the potential energy curves of these dications, we found that their curves have a flatter character around the minimum compared to the curves of the other dications. The
case is demonstrated by the potential energy curves of PuO0/þ/2þ and CmO0/þ/2þ in Figure 1. In agreement with the flatter character of their curves, AmO2þ and CmO2þ have larger first anharmonic constants (6.2 and 12.3 cm1, respectively) as compared to the other monoxides having values generally around 23 cm1. To clarify the electronic basis of this feature we checked the populations of the bonding orbitals of all the AnO species under study. We found that around the equilibrium bond distance the bonding orbitals in AmO2þ and CmO2þ are less populated by ca. 0.3 e than the bonding orbitals in the other monoxides. This missing ca. 0.3 e populates in AmO2þ and CmO2þ an antibonding orbital consisting of mainly 2pz of O and 5fσ of An. This should be responsible for the relatively longer equilibrium bond distances and the larger anharmonic character of the potential energy curve in the vicinity of the minimum. 3.3. Vibrational Frequencies of the Dioxides. For actinide dioxides, there is less experimental gas-phase information available than for the monoxides. No experimental bond distance has been reported for these molecules, while the only experimental vibrational data on gaseous species are the bending fundamental of UO2 from resonance-enhanced multiphoton ionization (REMPI)10 and the symmetric stretching and bending fundamentals of UO2þ from PFI-ZEKE measurements.11 In addition, some stretching frequencies of ThO2, UO2, UO2þ, and PuO2 have been reported from matrix-isolation IR experiments.1220 The molecular geometries and vibrational frequencies of the dioxide species obtained by eight DFT exchange-correlation functionals are given in the Supporting Information. We note that most of these bond distances were reported recently,83 where DFT data (including other exchange-correlation functionals like PW91, M05, M06, M06-L, MOHLYP, and MPW3LYP) were compared to bond distances and dissociation energies obtained by sophisticated multiconfigurational ab initio methods. In that comparison, none from the tested DFT levels showed a uniform agreement with the reference SO-CASPT2 6650
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Figure 1. Potential energy curves of PuO0/þ/2þ and CmO0/þ/2þ around the equilibrium bond distances. The scale of the y axis was the same for all six curves, but due to the large differences in the absolute energies of the species the curves of the ions were shifted to fit into one graph with those of the neutral oxides.
Figure 2. DFT frequencybond distance correlation for the three fundamentals of UO2.
bond distances. Thus, to obtain reliable vibrational frequencies for the title dioxides, we cannot pick a single DFT level. We analyzed here jointly the DFT equilibrium bond distances and vibrational frequencies and observed a good correlation between the two parameters. We demonstrate this in Figure 2 with the three fundamentals of UO2. In the bond distance (re) range covered by our computations, a trendline can be fitted to the computed data, on which basis the harmonic vibrational frequencies can be evaluated to any bond distance within (and near) the range. The quality of these empirical frequencies depends on two main factors: (i) the accuracy of the reference bond distance and (ii) the accuracy of the DFT potential energy surfaces around the computed equilibrium bond distances. For example, if the potential energy surface is too flat, we obtain too small frequencies at the accurate bond distance. This empirical approach has been tested on the monoxides with available experimental bond distances: ThO, ThOþ, UO, and UOþ. The empirical harmonic vibrational frequencies are included in Table 2 in the rows indicated by “empirical”. There is an excellent agreement with the gas-phase experimental frequencies of ThO and UO (within 2 cm1) for which very accurate experimental bond distances are available (cf. Table 2). For ThOþ and UOþ the deviations are 14 and 8 cm1, respectively, but here the reference bond distances may be less accurate: the experimental bond distance of UOþ has a larger uncertainty, while that of ThOþ is not given in ref 7. Note that with the exception of UOþ the empirical vibrational frequencies are closer to the experimental results than the frequencies computed on the basis of the spin-free CASPT2 potential energy curve.
In the lack of proper gas-phase experimental data on the dioxides, we cannot be sure of the same excellent performance of the empirical approach on these latter molecules. However, the similar bonding in the actinide monoxides and dioxides suggests a pretty good reliability of the empirical dioxide frequencies as far as the reference bond distance is correct. Hence the selection of the reference bond may be the critical issue here. From the numerous computations13,15,18,19,40,4457,84 we selected the recently reported SO-CASPT2 results of Infante et al.57 for this purpose. The only exception is UO2, for which we used the bond distance of 1.770 Å obtained recently by four-component DCIHFSCCSD calculations85 being in good agreement with an earlier SO-CASPT2 result of 1.766 Å.46 The vibrational frequencies of the dioxides obtained for the reference bond distances are summarized in Table 3. The parameters of the trendlines are given as Supporting Information. We note the different character of the trendlines for the stretching frequencies of ThO2þ and PaO22þ (cf. Supporting Information), which may result in a larger uncertainty of the frequency data of these ions. We calculated also the anharmonic vibrational frequencies at the B3LYP or B3P86 levels by calculation of the quartic force fields using the “Freq=Anharmonic” keyword of Gaussian 03. The empirical harmonic frequencies in Table 3 have been corrected by the obtained anharmonic effects and are presented in separate columns in Table 3. A compilation of literature data on the vibrational frequencies of actinide dioxides (both experimental and theoretical) is given in Table 4. We start our discussion with UO2þ for which most experimental information is available for the gaseous phase.11 The empirical anharmonic frequencies evaluated on the basis of the 6651
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Table 3. Empirical Harmonic and Anharmonic Vibrational Frequencies of the Dioxide Species on the Basis of DFT Calculationsa DFT anharmonicc
DFT harmonic r eb
νas
νs
β
νas
νs
β
1.923
719
772
151
715
767
151
1.896d
766
818
151
762
813
151
ThO2þ
1.832
635
790
63
623
780
51
ThO22þ
1.903
736
701
107
727
695
107
PaO2 PaO2þ
1.816 1.767
855 994
900 935
79 106
852 989
899 931
82 108
PaO22þ
1.726
602
981
138
594
961
144
UO2
1.770
959
907
150
956
904
150
1.790d
923
868
136
920
865
136
1.745
1019
951
155
1013
946
155
species ThO2
UO2þ
1.758d
991
921
144
985
916
144
2þ
1.710
1089
993
127
1082
987
127
NpO2 NpO2þ
1.761 1.723
942 1031
882 954
188e 216
939 1023
880 947
185 215
NpO22þ
1.700
1092
983
154
1085
977
154
PuO2
1.744
940
870
188
934
862
184
PuO2þ
1.704
1035
945
262
1027
938
261
PuO22þ
1.675
1110
992
239e
1102
984
237
AmO2
1.807
819
761
102
815
757
105
AmO2þ
1.721
981
862
264
970
851
262
AmO22þ CmO2
1.679 1.832
1057 788
918 731
293 92
1045 778
906 721
291 90
CmO2þ
1.746
895
778
193
870
752
192
CmO22þ
1.674
996
817
313
964
783
309
UO2
The fundamentals (in cm1) νas, νs, and β correspond to asymmetric stretching, symmetric stretching, and bending, respectively. All the species except for ThO2 are linear, in which β is doubly degenerated. The harmonic frequencies have been evaluated at the SO-CASPT2 reference bond distance using the presently developed empirical approach. For details see text. b The reference bond distances (Å) were taken from ref 57 except for UO2. The 1.770 Å bond distance of UO2 has been computed at the four-component DC-IHFSCCSD level in ref 85. c Anharmonic effects were calculated by the Freq=Anharmonic keyword of Gaussian 03, and the corrections were added to the empirical harmonic values given in columns 35. d The values of 1.896, 1.790, and 1.758 Å were estimated in the present study for ThO2, UO2, and UO2þ, respectively, on the basis of the experimental vibrational data. They are likely more reliable for the equilibrium bond distances than the SO-CASPT2 values. e The DFT calculations with Gaussian03 gave erroneously two close frequency values for the degenerate bending fundamentals (difference of 20 cm1 for NpO2 and 9 cm1 for PuO22þ). The data given in the Table are the average values. a
SO-CASPT2 bond distance (946 and 155 cm1) compare reasonably well with the experimental values of 921(4) and 145.5 cm1 (Table 4): the stretching fundamental is overestimated by ca. 25 cm1, the bending fundamental by ca. 7 cm1. The anharmonic parameters derived by Merritt et al.11 are in excellent agreement with the anharmonic effects from our DFT calculations (cf. Tables 3 and 4). From the reported matrix-isolation IR1719 and computed19 data on UO2þ we can estimate the gas-phase value of the asymmetric stretching (νas) fundamental. The matrix-isolation IR data show the following matrix shifts: with respect to Ne there
is a red-shift of 28 cm1 in Ar, 40 cm1 in Kr, and 51 cm1 in Xe. Wang et al.19 carried out DFT calculations on the UO2þ, UO2(Ne)6þ, UO2(Ar)5þ, UO2(Kr)5þ, and UO2(Xe)5þ species to model the effect of matrix on the vibrational frequencies. From their data, we derived somewhat smaller matrix shifts for νas than found experimentally, viz., 27, 32, and 42 cm1 in Ar, Kr, and Xe matrices, respectively, with respect to the frequency in the Ne matrix. The calculations of Wang et al.19 predicted matrix shifts in Ne with respect to the isolated UO2þ molecule values of 2 and 5 cm1 for the asymmetric and symmetric stretching fundamentals, respectively. On the basis of the above information, we estimate the gas-phase νas frequency to be ca. 983 cm1, which is overestimated by our empirical νas by 30 cm1, slightly more than the νs fundamental (vide supra). The consistent overestimation of all three fundamentals by our empirical approach implies that the main source of error lies in the reference bond distance. We get an excellent agreement with the three gas-phase fundamental frequencies using a bond distance of 1.758 Å instead of the SO-CASPT2 value (cf. Tables 3 and 4). The amount and quality of experimental vibrational data on UO2 facilitates a straightforward analysis of these data as well. However, not all the matrix-isolation IR data are useful for our purpose because those obtained in the heavier rare gas matrices suffer from the change of electronic ground state upon interactions with the rare gas atoms.18,48,86 It has been clarified by quantum chemical calculations and new matrix-isolation IR experiments that while the gas-phase electronic ground state (3Φu) is retained in the Ne matrix the interactions with the more polarizable Ar and Kr atoms stabilize the low-lying 3Hg state in those matrices.18,48,86 This is the reason that the observed frequency of UO2 in Ar16,17,86 (775.7 cm1) is considerably lower than the frequency in the Ne matrix15,18,86 (914.8 cm1). Therefore, only the latter value will be discussed in the following. A joint analysis of the 3Φu experimental and theoretical data of UO2 facilitates the estimation of the gas-phase asymmetric stretching frequency and a (possibly) reliable equilibrium bond distance. Assuming a matrix shift of 5 cm1 by Ne, the “gas-phase anharmonic value” of νas would be 920 cm1. The empirical νas frequency using the literature reference bond distance85 is considerably (by 39 cm1) larger, similar to the empirical bending frequency as compared to the gas-phase value from REMPI experiments.10 Utilizing the frequencybond distance relationship (see Supporting Information) and the computed anharmonicity, an equilibrium bond distance of 1.790 Å would fit to the “gas-phase νas value”. In turn, based on this bond distance, the empirical νs and β fundamental frequencies would be 865 and 136 cm1, respectively. This empirical bending frequency is larger by only 15 cm1 than the gas-phase REMPI value, which may partly be attributed to RennerTeller vibronic coupling10 not taken into account by the theoretical model in the DFT calculations. Regarding the other actinide dioxides, some matrix-isolation IR data have been reported for ThO21215 and PuO2.20 The fundamental stretching frequencies of ThO2 have been observed in Ne13,15 and Ar12,14 matrices. The matrix shifts of 21.1 and 21.8 cm1 (Ar with respect to Ne) are consistent for the two stretching fundamentals of ThO2 and are somewhat smaller than the value of 28 cm1 observed for the νas of UO2þ (vide supra). Note that also for ThO somewhat smaller matrix shifts were found than for UO (vide supra), hence the interaction with the matrix seems to depend more on the bonding characteristics of 6652
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Table 4. Available Experimental and Selected Computed Resultsa on the AnO20/þ/2þ Species frequency species ThO2
PaO2þ UO2
UO2
þ
UO22þ
method b
phase/state
νs
νas
β
re
ref
estimated
gas
762
813
IR
Ne matrix
756.8
808.4
IR
Ar matrix
735.0
787.3
PW91
1
759
812
157
1.911
15
DHF
1
761
896
139
1.898
44
B3LYP
1
760
802
159
1.906
13
empirical
1
715
767
151
1.923
present study
empirical DHF
1
A1 Σgþ
762 1158
813 1029
151 130
1.896 1.742
present study 44
empirical
1
Σ0gþ
989
931
108
1.767
present study
REMPI
gas
estimatedb
gas
920
IR
Ne matrix
914.8
18
IR
Ar matrix
776
17
IR
Ar matrix
776.10(5)
IR MP2
Kr matrix 3 þ Σu
B3LYP
3
CASPT2c
3
SO-CASPT2c
3
B3LYPc
3
CCDc
3
MP2c B3LYPc PW91
3
SO-VWN-BP
3
VWN-BP
3
empirical
3
empirical
3
PFI-ZEKE
gas
A1 A1 A1 A1
1
present study 13,15 12,14
121
10 present study
16
767.95 1022
947
294
1.779
16 45
Φu
931
874
138
1.800
18
Φu
932
809
1.806
46
Φ2u
923
948
1.766
46
Φu
937
875
1.794
46
Φu
958
927
168
1.766
47
3
Φu
913
896
149
1.795
47
Φu 3 Φu
933 919
880 856
222
1.764 1.807
47 48
Φu
934
863
1.803
49
Φu
948
853
1.813
49
Φ2u
956
904
150
1.770
present study
Φ2u
920
865
136
1.790
present study
ω = 921(4)
ω = 145.5
ωx = 2.0(22)
ωx = 0.3
11
estimatedb IR
gas Ne matrix
IR
Ar matrix
952.3
17,19
IR
Kr matrix
940.6
17,19
IR
Xe matrix
B3LYP
2
CCDc
2
MP2c
2
B3LYPc CASPT2
2
PW91
2
empirical
2
empirical
2
DHF
1
4-CCSD
1
4-CCSD(T)
1
CCSDc B3LYPc
983 980.1
present study 18,19
929.0
19
Φu
1010
Φu
1031
971
146
1.744
47
Φu
955
901
101
1.80
47
Φu Φu
1001 942
916 858
191
1.746 1.773
47 50
2
Φu
936
148
1.764
18
987
911
1.773
19
1013
946
155
1.745
present study
Φ2.5u
985
916
144
1.758
present study
Σgþ
1294
1234
246
1.650
44
Σ0gþ
1168
1040
180
1.696
52
1.715
52
1.702 1.706
51 51
Φ2.5u
Σ0gþ
974
Σgþ Σgþ
1148 1143
1063 1041
180 150
Σgþ
1140
1041
161
Σgþ
1066
959
Σgþ
1179
1100
1 1
B3LYP
1
CASPT2
1
CCDc
1
6653
194
1.705
18
1.705
50
1.678
47
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Table 4. Continued frequency species
method
phase/state
1095
997
1082
987
Σg
892
Σg
869 939
880
2
1075
969
1.717
49
Φ2.5u Ar matrix
1085 794.2
977
154
1.700
present study 20
1.800
53
SO-VWN-BP
4
VWN-BP
4
empirical
4
NpO22þ
VWN-BP
2
PuO2
empirical IR
H3.5g Φu
IR
Kr matrix
MP2
5
PuO2
PuO22þ
present study
870
1.778
49
868
1.773
49
1.761
present study
185
786.8
20 306
Σgþ
828
792
109
1.870
54
Σgþ
781
772
1.833
49
Σgþ
866
791
1.812
49
758
614
1.88
40
1.818 1.744
39 39
1.744
present study
VWN-BP SO-VWN-BP
5 d
Σgþ 5 Φ1u
5
Φ1u
5
934
862
Φ1.5u
SO-CASPT2 empirical
4
1027
B3LYPc
3
1144
AQCC
3
Φ1.5u Hg
3
Hg
B3LYP SO-CASPT2 SO-CASPT2
3
empirical
3
938
261
1014
229
1005 1100
Hg 3 H4g H4g H4g
184
962
Hg
3
181
773 837
4
c
49
1.710
656
5
VWN-BP
1.720 127
744
5
c
126 144
Σgþ
CCSD(T)c
empirical
47 47
Σ0gþ
empirical
1
þ
ref
Σgþ
1
B3LYPc SO-CASPT2c
re 1.728 1.687
923 1027
VWN-BP
B3LYP
β
1024 1126
1
NpO2
νs
νas
Σgþ 1 þ Σg
MP2c B3LYPc
39
1.704
present study
1.688
51
1.670
55
953
1.703
49
1004 1065
1.678 1.699
39 56
1019 1102
1.704
984
237
1.675
39
1.675
present study
a The vibrational data are given in cm1 and the bond distances in Å. In the rows “empirical” we repeat the empirical anharmonic frequencies from Table 3. In the case of ThO2, UO2, and UO2þ the first set of empirical data refers to the literature reference bond distance, while the second set is based on reference bond distances estimated in the present study. The harmonic experimental vibrational frequencies are indicated by the ωe symbol. Experimental uncertainties are given in parentheses. b Estimated on the basis of matrix shifts. c From the numerous calculated data from the given reference, only selected high-level results are shown here. For the full set of results, see the reference. d Electronic state is not given in the original paper.
the actinide than on the different shape of the molecules (UO2þ is linear while ThO2 is bent57). These two examples suggest that the uranium valence 5f orbitals are more favorable for interaction with the rare gas atoms than the valence 6d orbitals predominating in thorium. Due to this larger interaction, the heavier actinides may generally be more sensitive to matrix effects. Assuming a matrix shift of 5 cm1 in Ne, the “gas-phase anharmonic stretching frequencies” of ThO2 can be estimated to be around 762 and 813 cm1. With respect to these frequencies, the empirical stretching values based on the SO-CASPT2 bond distance are underestimated by ca. 45 cm1. The consistent underestimation of the two fundamentals suggests that the main source of error lies again in the SO-CASPT2 bond distance. This suggestion is supported by our previous experience on ThO and ThOþ, where the theoretical SO-CASPT2 bond distances proved to be larger by ca. 0.02 Å than the experimental ones.57 These examples indicate a general error of this SO-CASPT2 level for thorium oxides. On the basis of the frequencybond distance relationship derived from the DFT calculations and taking into account the
matrix shift and anharmonicity effects, we predict the equilibrium bond distance of ThO2 to be around 1.896 Å. We note that from our DFT calculations the B3LYP results differ only marginally from the “gas-phase frequencies” estimated from the IR data in the Ne matrix using a correction of 10 cm1 for matrix shift and anharmonicity effects. Accordingly, the B3LYP optimized bond distance is 1.898 Å, and the bond angle is 119.0°, being in excellent agreement with the value of 122.5 ( 2° derived from isotope-substitution IR experiments.12 The IR spectra of PuO2 recorded in Ar and Kr matrices call also for a careful interpretation. At first sight our empirical anharmonic asymmetric stretching frequency is considerably larger than the reported values from the matrix-IR spectra.20 Assuming 30 cm1 for the matrix effect in Ar, the “gas-phase value” derived from the matrix-IR data would be lower by ca. 110 cm1 than our empirical frequency. It is unlikely that the SOCASPT2 bond distance of PuO2 would have such a large error. We suspect a change of the electronic ground state upon interaction with the rare gas atoms in the matrix, as shown for UO2 (vide supra). Indeed, recent theoretical results obtained by 6654
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The Journal of Physical Chemistry A SO-CASPT2 computations indicate that the 5Φ1u ground and the 5Σ0gþ excited states are very close in energy (at the spin-free level, 5Σgþ is the ground state, while the energy ordering is interchanged upon inclusion of spinorbit effects39), while the bond distances in the two electronic states differ considerably (cf. Table 4). On this basis we suggest that upon interaction with the more polarizable Ar and Kr rare gas atoms the 5Σ0gþ state is stabilized (and is present) in the Ar and Kr matrices. The asymmetric stretching frequencies computed recently for the 5 þ Σg state by Archibong and Ray54 and Liao et al.49 agree reasonably with the matrix-IR values (cf. Table 4) supporting the hypothesis of interchanging ground states in the matrix. In addition to the above-discussed cases, there are a few computed data on PaO2þ, UO22þ, NpO2, NpO22þ, PuO2þ, and PuO22þ as listed in Table 4. Most previous papers report bond distances longer than the reference ones accompanied generally by smaller vibrational frequencies. Liao et al. reported their NpO2 data for the 4Σg state,49 while the ground state of the molecule has been determined to be 4H3.5g by recent SOCASPT2 calculations.57 Nevertheless, the bond distances from the two papers are quite close as are the vibrational frequencies in Table 4.
4. CONCLUSIONS In the present paper, we reported the vibrational frequencies for the electronic ground states of the actinide oxides AnO and AnO2 (An = Th, Pa, U, Np, Pu, Am, Cm). Our consistent CASPT2 calculations on the monoxides revealed no trend in the actinide row but showed a decreasing trend in the bond distance from the neutral molecule to the dication. The frequencies increase generally in this order except for AmO2þ and CmO2þ, which possess a somewhat larger anharmoncity compared to those (mostly 23 cm1) of the others. The fundamental frequencies of the dioxides have been evaluated by an empirical approach which was tested on the accurate gas-phase experimental data of ThO, ThOþ, UO, and UOþ. For the dioxides, the SO-CASPT2 bond distances57 are presently the most sophisticated geometrical data, hence we used them as reference bond distances in the empirical approach. We believe that the reliability of our empirical stretching frequencies is comparable to those of the SO-CASPT2 bond distances (except where vibronic effects appear). The empirical bending frequencies are also promising, as we obtained a very good agreement for UO2þ. We analyzed the available literature experimental data and the found characteristics combined with our computed data facilitated the prediction of molecular properties of several gas-phase species. On the basis of the observed analogous matrix shift in the IR spectra of UO and PuO, we estimated the harmonic gas-phase frequency of PuO. Utilizing the small matrix shifts in Ne and the computed anharmonicities, we derived reliable gas-phase stretching frequencies for ThO2, UO2, and UO2þ. The same differences between the computed and experimental frequencies of UO and PuO suggest that our computed bond distance for PuO (1.818 Å) is likely within 0.002 Å of the experimental equilibrium bond distance. On the basis of the experimental vibrational data and the derived frequencybond distance relationships, we provided good-quality estimates for the equilibrium bond distances of ThO2, UO2, and UO2þ (1.896, 1.790, and 1.758 Å, respectively). We believe that they are a
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better approximation of the (yet unknown) experimental values than the SO-CASPT2 bond distances. Further important information from the present joint analysis is that the electronic ground state of PuO2 in Ar and Kr matrices is probably different from that in the gaseous phase, as observed previously for UO2.18,86
’ ASSOCIATED CONTENT
bS
Supporting Information. The computed molecular geometries and vibrational frequencies of the dioxide species obtained by the eight DFT exchange-correlation functionals, the parameters of the fitted trendlines for the frequency-geometry data, and calculated anharmonic corrections for the dioxides. This material is available free of charge via the Internet at http:// pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The Seventh Framework Programme of the European Commission (Collaboration Project No. 211690, F-BRIDGE) and the Hungarian Scientific Research Foundation (OTKA No. 75972) are acknowledged for financial support. The authors thank Dr. I. Infante and Dr. M. Klipfel for helpful discussions. ’ REFERENCES (1) Konings, R. J. M.; Wiss, T.; Gueneau, C. Nuclear Fuels. In The chemistry of the actinide and transactinide elements; Edelstein, N. M., Fuger, J., Morss, L. R., Eds.; Springer: Berlin, 2010; Vol. 6. (2) Olander, D. Fundamental aspects of nuclear reactor fuel elements. Tech. Rep. 3561 TID-26711- P1, Technical Information Center, Office of Public Affairs Energy Research and Development Administration, 1976. (3) Maeda, K.; Sasaki, S.; Kato, M.; Kihara, Y. J. Nucl. Mater. 2009, 389, 78. (4) Edvinsson, G.; Selvin, L.-E.; Aslund, N. Ark. Fys. 1965, 30, 28. (5) Edvinsson, G.; Lagerqvist, A. Phys. Scr. 1984, 30, 309. (6) Dewberry, C. T.; Etchison, K. C.; Cooke, S. A. Phys. Chem. Chem. Phys. 2007, 9, 4895. (7) Goncharov, V.; Heaven, M. C. J. Chem. Phys. 2006, 124, 064312. (8) Kaledin, L. A.; McCord, J. E.; Heaven, M. C. J. Mol. Spectrosc. 1994, 164, 27. (9) Goncharov, V.; Kaledin, L. A.; Heaven, M. C. J. Chem. Phys. 2006, 125, 133202. (10) Han, J.; Kaledin, L. A.; Goncharov, V.; Komissarov, A. V.; Heaven, M. C. J. Am. Chem. Soc. 2003, 125, 7176. (11) Merritt, J. M.; Han, J.; Heaven, M. C. J. Chem. Phys. 2008, 128, 084304. (12) Gabelnick, S. D.; Reedy, G. T.; Chasanov, M. G. J. Chem. Phys. 1974, 60, 1167. (13) Zhou, M.; Andrews, L. J. Chem. Phys. 1999, 111, 11044. (14) Kushto, G. P.; Andrews, L. J. Phys. Chem. A 1999, 103, 4836. (15) Andrews, L.; Zhou, M.; Liang, B.; Li, J.; Bursten, B. E. J. Am. Chem. Soc. 2000, 122, 11440. (16) Gabelnick, S. D.; Reedy, G. T.; Chasanov, M. G. J. Chem. Phys. 1973, 58, 4468. (17) Hunt, R. D.; Andrews, L. J. Chem. Phys. 1993, 98, 3690. (18) Zhou, M.; Andrews, L.; Ismail, N.; Marsden, C. J. Phys. Chem. A 2000, 104, 5495. 6655
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