Theoretical study of the electronic spectra of neutral and cationic NpO and NpO2

The electronic spectra of neutral NpO and NpO 2 as well as of their mono- ( NpO + , NpO 2 + ) and dications ( NpO 2 + , NpO 22 + ) were studied using multiconfigurational relativistic quantum chemical calculations at the complete active space self-consistent field / CASPT2 level of theory taking into account spin-orbit coupling. The active space included 16 orbitals: all the 7s, 6d, and 5f orbitals of neptunium together with selected orbitals of oxygen. The vertical excitation energies on the ground state geometries have been computed up to ca. 35 000 cm − 1 . The gas-phase electronic spectra were evaluated on the basis of the computed Einstein coe ffi cients at 298 K and 3000 K. The computed vertical transition energies show good agreement with previous condensed-phase results on NpO 2 + and NpO 22 + . C 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http: // dx.doi.org / 10.1063 / 1.4928588]


I. INTRODUCTION
Neptunium oxides are present in notable amount in spent nuclear fuel, for which several reprocessing and recycling technologies have been developed, including oxide-based transmutation fuels. [1][2][3][4][5][6] However, these technologies can gain from optimization of the conditions, requiring an accurate knowledge of the molecular properties of all actinide compounds present in the fuel.
In contrast to the detailed experimental description of the solid neptunium oxides, 7 their molecular properties are less explored. To obtain them requires difficult and expensive gas-phase experiments which were performed hitherto for the ionization energies (NpO 8-10 and NpO 2 9,10 ) and dissociation energies of both the neutral oxides and their cations. 10,11 Structural and vibrational data on the NpO and NpO 2 molecules are available from quantum chemical calculations only. 12,13 Experimental studies of the electronic structure were performed for the ions NpO 2 + and NpO 2 2+ and only in condensed phases. Early absorption spectra of Np oxides (and also other actinide compounds) were reviewed in Ref. 14 and 15. Both ions were investigated by UV/VIS absorption spectroscopy in aqueous acidic solutions, [16][17][18] accompanied by separate studies on NpO 2 +19 and on NpO 2 2+ . 20 The absorption spectrum of NpO 2 2+ was also recorded in the form doped into Cs 2 UO 2 Cl 4 and CsUO 2 (NO 3 ) 3 crystals. [21][22][23][24][25] These latter spectra were similar to the solution ones implying that the transition energies are not much affected by the environment. The ground electronic states could be well determined on the basis of the above experiments: they are the 3  . 23,24,26 The electronic spectra of the solutions were first assigned using semi-empirical ligand-field theory (NpO 2 +27 and NpO 2 2+ 28 ) and were revised later by quantum chemical calculations. 19,25,[29][30][31][32][33][34][35] Matsika et al. 19,25,29 used configuration interaction methods in conjunction with relativistic effective core potentials that incorporate also spin-orbit coupling 36 (SO-MRCI). In one of these studies, 19 coordination models with five explicit coordinating water molecules and chloride ions, respectively, were tested. Infante et al. 30 5 ] + ) ions. 32 The ground and the four lowest-energy excited states of NpO 2 2+ and of the NpO 2 Cl 4 2− complex ion (model for the Cs 2 NpO 2 Cl 4 solidphase spectra) were investigated by Gomes et al. using IHFSCC. 31 They considered further environmental effects on NpO 2 Cl 2− 4 by means of density functional theory (DFT) embedding. The hitherto most complete assessment of the electronic spectrum of Cs 2 NpO 2 Cl 4 at an adequate level of theory was performed by Su et al. 33 who calculated both the vertical and adiabatic transitions of NpO 2 2+ and NpO 2 Cl 4 2− up to 21 000 cm −1 using the SO-RASPT2 method. The electronic structure and magnetic properties of NpO 2 2+ and a few complexes: NpO 2 Cl 4 2− , [NpO 2 (NO 3 ) 3 ] − , and [NpO 2 (CO 3 ) 3 ] 4− were studied by Gendron et al. 34,35 using a combination of theoretical (among them SO-CASPT2) methods. The studies included a detailed analysis of SO coupling involving the first four electronic states of the given molecules.
In other recent studies, only the ground-state electronic structure and molecular properties were investigated: Liao et al. computed NpO 2 and NpO 2 2+ using relativistic DFT calculations. 37 They reported the electronic ground states of NpO 2 and NpO 2 2+ (that of NpO 2 erroneously as 4 Σ g ) as well as the first and second ionization energies of NpO 2 . Several computational studies were performed on neutral and ionic neptunium mono-and dioxides at SO-CASPT2 and various DFT levels resulting in theoretical ionization energies, 12,38 vibrational frequencies, 13 and dissociation energies. 38,39 The hydration and oxidation reactions of NpO 2 + in the gaseous phase were studied by DFT assisting electrospray experiments, 40 while NpO 2 2+ served as model compound (focusing on the bond distance and vibrational frequencies) in a benchmark study of two-component relativistic DFT methods. 41 The goal of the present study is the systematic evaluation of the gas-phase electronic spectra of the neutral and ionic NpO and NpO 2 species by means of multireference relativistic ab initio calculations on the basis of our previous studies on the electronic ground states of these species. 12,38 Other important results from the present calculations are the energies of the excited states, required for a reliable evaluation of the thermodynamic functions of the gaseous oxides. Such thermodynamic data are utilized in developing safety procedures in nuclear industry.

II. COMPUTATIONAL DETAILS
The calculations were performed using the software MOLCAS 7.4. 42 The complete active space self-consistent field (CASSCF) method 43 was used to generate molecular orbitals and reference functions for subsequent multiconfigurational second-order perturbation theory calculations of the dynamic correlation energy (CASPT2). 44,45 In the case of the monoxides, the active space consisted of 7s, 6d, and 5f orbitals of the actinide atoms as well as of the 2p orbitals of oxygen. This means 16 orbitals occupied by 11, 10, and 9 electrons for NpO, NpO + , and NpO 2+ , respectively. An analogous construction of the active space of the dioxides would result in 19 orbitals occupied by 13-15 electrons in the studied dioxide species, which is nowadays computationally unfeasible due to the large amount of configuration state functions. Therefore, we used a truncated space of 14 orbitals, omitting the two lowest π g bonding and the corresponding antibonding orbitals and one σ g * antibonding orbital. This active space included 11, 10, and 9 electrons for NpO 2 , NpO 2 + , and NpO 2 2+ , respectively. We neglected the Np 7p orbitals due to their relatively high energy with respect to the 5f, 6d, and 7s orbitals, 30 which makes them less important in low-energy excitations. Accordingly, previous studies of the electronic spectra of NpO 2 + and NpO 2 2+ did not find any significant excitations to Np 7p orbitals. 19,25,29 As MOLCAS can handle only Abelian point groups, the point groups of the target molecules (D ∞h and C ∞v ) could not be applied. In order to be consistent for the mono-and dioxides, we used the C 2v approach in our calculations. This might lead to symmetry breaking effects resulting in some cases to spurious orbital mixing. After investigation of the trial orbitals, the CLEAnup keyword of MOLCAS was applied to minimize as much as possible this shortcoming.
The ground state molecular geometries of the title Np oxides reported in Ref. 12 were applied in the present study. The vertical excited electronic states were explored by multiconfigurational state-averaged calculations using up to 30 roots for a given spin multiplicity and symmetry. In addition to the ground-state spin multiplicity (4, 3, 2, 6, 5, and 4 for NpO 2 , NpO 2 + , NpO 2 2+ , NpO, NpO + , and NpO 2+ , respectively), generally the two neighbouring (lower and higher) ones were considered too. For details, see the supplementary material. 76 All electron basis sets of atomic natural orbital type, developed for relativistic calculations (ANO-RCC) with the Douglas-Kroll-Hess Hamiltonian 46,47 were used for all the atoms. For neptunium, a primitive set of 26s23p17d13f5g3h basis functions was contracted to 9s8p6d5f2g1h, 48 whereas for O, a primitive set of 14s9p4d3f2g functions was contracted to 4s3p2d1f 49 achieving TZP quality. The Douglas-Kroll-Hess Hamiltonian was used in the CASSCF calculations in order to take into account scalar relativistic effects.
Spin-orbit (SO) effects were taken into account by using the complete active space state interaction (CASSI) method, 50 which allows CASSCF wave functions for different electronic states to interact under the influence of a spinorbit Hamiltonian. Dynamic electron correlation is taken into account using the CASPT2 energies as spin-orbit free (SF) energies in the spin-orbit Hamiltonian (SO-CASPT2). The above described multireference methods and the ANO-RCC basis set were successfully applied in a number of studies on actinide-containing systems. 12,13,[51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70] The electronic spectra have been evaluated from the Einstein coefficient values (being directly related to the spectral intensities) computed at the SO-CASPT2 level. 71 The spectra were evaluated utilizing the relative populations of all computed SO states obtained by the Boltzmann equation. We note that our computed electronic transitions model the (unperturbed) gas-phase electronic spectra. When, however, electronic spectra are recorded in condensed phases, considerable environmental effects can appear. These effects can introduce drastic changes in the spectral intensities, while the transition energies suffer less from them.

2+
Literature information on these molecules involves the ground electronic states of all three species and the electronic spectra of the NpO 2 + and NpO 2 2+ ions. 12,19,[23][24][25][26][29][30][31][32][33][34][35]38,39 We computed the excited electronic states up to ca. 35 000 cm −1 using the SO-CASPT2 method. As these states were obtained on the ground state geometries, the computations provided us the vertical excitation energies. On the basis of the excited states and the computed Einstein coefficients, we could model the gas-phase electronic spectra. The spectra were calculated at two temperatures, 298 K (to be compared with reported solution and solid-phase spectra at room temperature) and 3000 K (modeling high-temperature gas-phase studies). The calculated electronic spectra are presented in Figure 1. In Tables I-III,  between the donor and acceptor SO states. The full lists of the obtained SF and SO states are given in the supplementary material. 76 In the spectra at 298 K, only excitations from the ground states appear with considerable intensity. Due to the population of low-lying excited states at high temperatures, the spectra simulated for 3000 K contain several additional lines compared to those at 298 K.
In the ground and the studied excited states of NpO 2 + , the Np 7s orbital is not populated and the doubly occupied 5f σ seems to be very stable; thus, the electronic transitions correspond essentially to population transfer mostly from orbitals having major 5f δ and 5f φ contributions to ones having major 5f π contributions (cf. Table II). These originally electric dipole forbidden f → f transitions may become possible because the affected states contain minor contributions from 2p orbitals of oxygen.
Transitions accompanied with spin inversion appear at very high energy (e.g., the one at 34 697 cm −1 ). We note that the Einstein coefficients (and accordingly the expected absolute intensities in the spectrum) of NpO 2 + are generally smaller by one order of magnitude than those of neutral NpO 2 . This is due to the parity character of the states involved in the transitions. In the case of NpO 2 , all the donor states in Table I have gerade (g) and the acceptor states ungerade (u) parity satisfying the Laporte rule. 72  , where all the states have a dominant ungerade character (cf . Table III).
Due to the decreased number of non-bonded valence electrons in NpO 2 2+ , its electronic spectra ( Figure 1) are poor in signals. There are three intense transitions at 298 K, while an additional one at 3000 K. Several lower-energy transitions (below 20 000 cm −1 ) involve the excitation of a 5f σ electron to an anti-bonding (2p,5f) orbital. The higher-energy transitions involve excitations of (mostly) a 5f σ electron to another 5f orbital, but some double excitations appear also here.
Having reliable gas-phase electronic transition energies of the neutral and ionic NpO 2 species, it can be interesting to see how they compare to previous experimental and theoretical investigations of the condensed-phase spectra of NpO 2 + and NpO 2
Selected experimental 17,19 and theoretical results 29,30,32 of NpO 2 + are compiled in Table IV. The most recent study by Danilo et al. 32 used SO-CASPT2 but with a considerably smaller active space (2 electrons in 6 orbitals) than ours. Yet, the agreement with our present SO-CASPT2 data is acceptable, the energy ordering of the excited states is the same in almost all cases, while the energy difference is mostly below 1000 cm −1 . The agreement is better with the SO-MRCI results from that study (obtained by the small 2 electrons in 4 orbitals active space, corrected for size-extensivity according to Davidson 73 ), though the latter results lack several high energy states.
Danilo et al. 32 studied also the electronic states of hydrated NpO 2 + modelled by the NpO 2 (H 2 O) 5 + structure using SO-CASPT2 in conjunction with the smaller (2,4) active space. They showed that the H 2 O ligand field around NpO 2 + resulted generally in minor changes in the excitation energies, while the average deviation between the calculated and experimental excitation energies was 1234 cm −1 . The main advantage of this solvation model is, however, the intensity information. The ligands attached to NpO 2 + can promote mixing of 5f φ and 6d δ orbitals, which can increase considerably certain transition probabilities. The computed oscillator strengths in Ref. 32 agree well with the experimental ones determined from the perchloric acid solution 19 facilitating a reliable assignment.
As can be seen from model, confirming our above concern about the suitability of these intensity data of naked NpO 2 + for the interpretation of condensed-phase spectra. On the other hand, the average deviation between the NpO 2 + calculated and the experimental excitation energies is 1108 cm −1 , slightly better than for those of the NpO 2 (H 2 O) 5 + model 32 obtained by the smaller active space. Particularly, our low-energy data are in good agreement with experiment 19 (cf. Table IV).
The latest (our present and those of Danilo et al. 32 ) computed data support generally the assignment proposed in the earlier IHFSCC study by Infante et al. 30 Our calculations support also the findings of Infante et al. 30 that the 5f π orbital appears only in higher-lying excited states; hence, transitions lower in energy than 19 000 cm −1 are unlikely to such orbitals.
Selected experimental 20,23,24 and theoretical 29-31,33,34 results of NpO 2 2+ are compared in Table V. In the experimental spectra, five bands (two in solution 20 and five in the Cs 2 UO 2 Cl 4 crystal 23 ) have been identified as 5f-5f electronic transitions from the ground state to low-lying excited states. The assignments of the charge transfer bands between 13 000 and 20 000 cm −1 have been done in terms of symmetry on the basis of crystal and Zeeman effect and magnetic circular dichroism measurements on the Cs 2 UO 2 (NO 3 ) 3 crystal and semi-empirical calculations. 24 The theoretical studies compared in Table V    , providing information on the effect of chloride ligands on the transition energies. Another advantage of this study (making it the best model for the doping experiment of NpO 2 2+ into Cs 2 UO 2 Cl 4 crystal 23,24 ) is the evaluation of the adiabatic transition energies. As can be expected, this study achieved the best average deviation (947 cm −1 ) from experiment. Those of the SO-CI and SO-CASPT2 energies of the naked NpO 2 2+ are around 2400 cm −1 . Considering the 0-10 000-cm −1 region of the spectrum, the best agreement with the experimental data of Cs 2 UO 2 Cl 4 (515 cm −1 ) has been obtained by Gendron et al., who computed only the three lowest excitations of this molecule using SO-CASPT2. 34 We note that to the better agreement in the latter limited study, the following character of CASPT2 may also contribute: the energies of excited states become less accurate with increasing number of states considered in the state-averaged calculations.
The assignments of the experimental transitions to the acceptor (excited) states are generally in agreement with our and in the listed literature studies. 24,[29][30][31]33,34 Instead of the Ω = 0.5 u excited states suggested for the experimental transitions at 19 510 and 17 844 cm −1 by Denning, 23,24 our and the other recent computations predicted more suitable excited states with Ω values of 1.5.

B. NpO, NpO + , and NpO 2+
The electronic ground states of these species were reported recently by Infante et al. 12 from SO-CASPT2 calculations. The ground and low-lying excited states are strongly mixed. We observed in the composition of the ground states of the three molecules determined in our present study some minor differences from those in Ref. 12 which, however, do not affect the Ω quantum number of these states. We attribute these differences to the inclusion of more states in the CASSCF and CASSI calculations, which result in more extensive mixing than occurred between the few ones (three states for each species) in Ref. 12.
The details of the electronic ground and excited states are given in the supplementary material. 76 With exception of the ground states, nothing is known about these monoxides; therefore, we briefly discuss here a few important characteristics of their electronic structure.
The major components of the SO ground state of NpO arrive from the SO coupling of the 6 Φ and 6 ∆ low-energy SF excited states (ca. 1000 cm −1 above the SF ground state). Accordingly, the major Np orbital populations include the 7s and the four 5f (σ, π, δ, φ) orbitals. These are the major orbitals in the low-lying excites states too, only with somewhat different contributions. The 6d δ orbitals appear with notable (but still minor) contribution above 13 000 cm −1 . Their importance is increased in the higher excited states. These characteristics can be compared with those of the isoelectronic PuO + . 12,74 The latter species has a simpler electronic structure than NpO: it has one major (79%) contribution with no 7s occupation and also the 5f σ orbital has only a minor role in its electronic ground state. This character is preserved in the reported few low-energy (0-3000 cm −1 ) excited states of PuO + . 74 The SO ground state of NpO + consists mainly of the SO-coupled 5 Φ SF ground and 5 ∆ SF low-energy excited states. The major Np orbital populations include the four 5f (σ, π, δ, φ) orbitals. The 7s orbital, being important in the neutral NpO, became a minor contributor in the ion and gains importance in some high-energy excited states only. The same refers to the 6d δ orbitals too. Compared to the characteristics of isoelectronic UO, the main difference is the monoconfigurational character and dominant 7s contribution in the uranium oxide, in the ground state of which the 5f σ orbital plays no role. 12,75 However, the 7s and 5f σ orbitals appear as minor contributions in some high-energy excited states of UO. 75 The case is similar in the isoelectronic PuO 2+ with a major (70%) SF state of 5f δ 2 , 5f φ 1 , 5f π 1 character. In the ground and excited states of the latter species, 5f σ has been found as a minor contributor. 12,74 The SO ground state of NpO 2+ consists mainly of the 4 I SF ground state with major Np 5f π 1 , 5f δ 1 , 5f φ 1 populations. The 5f σ , and 5f φ ′ mean the orbitals with magnetic quantum number of the opposite sign to that of the donor one.
orbital gains importance in the first excited state having a 4 H character, then in a few strongly mixed states above 8000 cm −1 .
The 6d π orbital appears as minor contributor in strongly mixed excited states above 10 000 cm −1 . The only isoelectronic actinide oxide with available literature data is UO + with analogous ground and first excited states. 75 However, the 5f σ orbital seems to have a larger role in the excited states of UO + than found in NpO 2+ . The calculated electronic spectra for 298 K and for 3000 K are presented in Figure 2. In Tables VI-VIII, the most intense transitions for NpO, NpO + , and NpO 2+ , respectively, are compiled and characterized.
In contrary to the previous two monoxide species, the computed electronic spectra of the NpO 2+ ion at both 298 K and 3000 K are poor of intense transitions. They include a single intense line only (at 27 273 cm −1 , cf. Figure 2 and Table VIII) attributed to a 5f π → 6d δ population transfer. The Einstein coefficient of this transition is comparable to the intense ones in the spectra of NpO but is smaller by ca. one order of magnitude than those of NpO + . Differences with respect to NpO and NpO + appear in the Np orbitals important in the transitions: In NpO 2+ , the 5f π orbital does not play an important role; the most frequent donor orbital is 5f π . The acceptor ones cover 6d σ , 6d δ , and all the four types of 5f. As 7s is poorly populated in NpO 2+ , it does not have any important role in its transitions.

IV. CONCLUSIONS
We studied the low-lying excited states and corresponding gas-phase electronic spectra of the neutral and ionic NpO and NpO 2 molecules. Our computations at the SO-CASPT2 level of theory elucidated the parameters and characters of electronic transitions. Spectral intensities were estimated on the basis of the computed Einstein coefficients for room temperature (298 K) and for 3000 K, being more relevant for the gas-phase experiments. From the six studied species, the dioxides (NpO 2 , NpO 2 + , NpO 2 2+ ) and NpO 2+ have quite simple electronic spectra possessing only a few intense peaks. On the other hand, the spectra of NpO and NpO + are very dense. The electronic states of these two species are strongly mixed and in several cases only small population transfers between various Np orbitals could be recognized. The computed vertical transition energies show good agreement with the previous results on NpO 2 + and NpO 2 2+ .

ACKNOWLEDGMENTS
The 7th Framework Programme of the European Commission under Grant No. 323300 (TALISMAN), the Hungarian Scientific Research Foundation (OTKA No. 75972), is acknowledged for financial support.