Multiconfigurational Calculations Research Articles

A Four-Coordinate Pr4+ Imidophosphorane Complex.

The imidophosphorane ligand, [NPtBu3]- (tBu = tert-butyl), enables isolation of a pseudo-tetrahedral, tetravalent praseodymium complex, [Pr4+(NPtBu3)4] (1-Pr), which is characterized by a suite of physical characterization methods including single-crystal X-ray diffraction, electron paramagnetic resonance, and L3-edge X-ray near-edge spectroscopies. Variable-temperature direct-current magnetic susceptibility data, supported by multiconfigurational quantum chemical calculations, demonstrate that the electronic structure diverges from the isoelectronic Ce3+ analogue, driven by increased crystal field. The four-coordinate environment around Pr4+ in 1-Pr, which is unparalleled in reported extended solid systems, provides a unique opportunity to study the interplay between crystal field splitting and spin-orbit coupling in a molecular tetravalent lanthanide within a pseudo-tetrahedral coordination geometry.

A Four‐Coordinate Pr4+ Imidophosphorane Complex

The imidophosphorane ligand, [NPtBu3]– (tBu = tert‐butyl), enables isolation of a pseudo‐tetrahedral, tetravalent praseodymium complex, [Pr4+(NPtBu3)4] (1‐Pr), which is characterized by a suite of physical characterization methods including single‐crystal X‐ray diffraction, electron paramagnetic resonance, and L3‐edge X‐ray near‐edge spectroscopies. Variable‐temperature direct‐current magnetic susceptibility data, supported by multiconfigurational quantum chemical calculations, demonstrate that the electronic structure diverges from the isoelectronic Ce3+ analogue, driven by increased crystal field. The four‐coordinate environment around Pr4+ in 1‐Pr, which is unparalleled in reported extended solid systems, provides a unique opportunity to study the interplay between crystal field splitting and spin‐orbit coupling in a molecular tetravalent lanthanide within a pseudo‐tetrahedral coordination geometry.

Natural Orbitals and Targeted Non-Orthogonal Orbital Sets for Atomic Hyperfine Structure Multiconfiguration Calculations

Hyperfine structure constants have many applications, but are often hard to calculate accurately due to large and canceling contributions from different terms of the hyperfine interaction operator, and also from different closed and spherically symmetric core subshells that break up due to electron correlation effects. In multiconfiguration calculations, the wave functions are expanded in terms of configuration state functions (CSFs) built from sets of one-electron orbitals. The orbital sets are typically enlarged within the layer-by-layer approach. The calculations are energy-driven, and orbitals in each new layer of correlation orbitals are spatially localized in regions where the weighted total energy decreases the most, overlapping and breaking up different closed core subshells in an irregular pattern. As a result, hyperfine structure constants, computed as expectation values of the hyperfine operators, often show irregular or oscillating convergence patterns. Large orbital sets, and associated large CSF expansions, are needed to obtain converged values of the hyperfine structure constants. We analyze the situation for the states of the {2s22p3,2s22p23p,2s22p24p} odd and {2s22p23s,2s2p4,2s22p24s,2s22p23d} even configurations in N I, and show that the convergence with respect to the increasing sets of orbitals is radically improved by introducing separately optimized orbital sets targeted for describing the spin- and orbital-polarization effects of the 1s and 2s core subshells that are merged with, and orthogonalized against, the ordinary energy-optimized orbitals. In the layer-by-layer approach, the spectroscopic orbitals are kept frozen from the initial calculation and are not allowed to relax in response to the introduced layers of correlation orbitals. To compensate for this lack of variational freedom, the orbitals are transformed to natural orbitals prior to the final calculation based on single and double substitutions from an increased multireference set. The use of natural orbitals has an important impact on the states of the 2s22p23s configuration, bringing the corresponding hyperfine interaction constants in closer agreement with experiment. Relying on recent progress in methodology, the multiconfiguration calculations are based on configuration state function generators, cutting down the time for spin-angular integration by factors of up to 50, compared to ordinary calculations.

ExROPPP: Fast, accurate, and spin-pure calculation of the electronically excited states of organic hydrocarbon radicals.

Recent years have seen an explosion of interest in organic radicals due to their promise for highly efficient organic light-emitting diodes and molecular qubits. However, accurately and inexpensively computing their electronic structure has been challenging, especially for excited states, due to the spin-contamination problem. Furthermore, while alternacy or "pseudoparity" rules have guided the interpretation and prediction of the excited states of closed-shell hydrocarbons since the 1950s, similar general rules for hydrocarbon radicals have not to our knowledge been found yet. In this article, we present solutions to both of these challenges. First, we combine the extended configuration interaction singles method with Pariser-Parr-Pople (PPP) theory to obtain a method that we call ExROPPP (Extended Restricted Open-shell PPP) theory. We find that ExROPPP computes spin-pure excited states of hydrocarbon radicals with comparable accuracy to experiment as high-level general multi-configurational quasi-degenerate perturbation theory calculations but at a computational cost that is at least two orders of magnitude lower. We then use ExROPPP to derive widely applicable rules for the spectra of alternant hydrocarbon radicals, which are completely consistent with our computed results. These findings pave the way for highly accurate and efficient computation and prediction of the excited states of organic radicals.

A comprehensive exploration of structural and electronic properties of molybdenum clusters

Molybdenum clusters, characterized by their unique structure and intriguing catalytic properties, have gained significant attention in recent years. In several existing studies, density functional theory (DFT) methods have been used to find the lowest energy Mo clusters and explore their electronic and magnetic structure. In all cases, with the exception of a single recent study, where a genetic algorithm was employed, initial geometries of the clusters, prior to geometry optimization, were chosen using heuristic approaches based on symmetry considerations and known structures. DFT calculations were performed using different types of pseudopotentials, from soft to hard, and different types of basis sets. However, no comprehensive study has yet been carried out in which a DFT method with the best control on its precision would be complemented by a reliable global minimum search method to find the lowest energy Mo clusters. In this work, we employ a combination of a plane wave-based DFT method and ab initio random structure searching technique to find the lowest energy clusters of up to 10 Mo atoms. In each case, the search has been performed for clusters with different spin multiplicities, which enabled us to explore their magnetic structure. The results are compared for both hard and soft pseudopotentials stressing the importance of treating more electrons explicitly, in agreement with some of the previous studies. For most of the low-energy magnetic structures found, we investigate the distribution of their spin densities, and for all low energy clusters, we confirm their stability by calculating their vibrational structure. For a few smallest clusters, the results of multiconfigurational quantum chemistry calculations are also discussed. Finally, free energies of the Mo clusters, within the quasi-harmonic approximation, are also calculated and discussed.

Time dependent vibrational electronic coupled cluster (VECC) theory for non-adiabatic nuclear dynamics.

A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photo-electron/UV-VIS absorption spectra as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born-Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation for the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only a few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favorable computational cost. In benchmark applications to small models and molecules, the VECC method provides accurate results compared to multi-configurational time-dependent Hartree calculations when predicting short-time dynamical properties (i.e., photo-electron/UV-VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities, the VECC method is also successfully applied to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Aranda and Santoro [J. Chem. Theory Comput. 17, 1691, (2021)].

Iron Kβ X-ray Emission Spectroscopy: The Origin of Spectral Features from Atomic to Molecular Systems Using Multi-configurational Calculations.

Kβ X-ray emission spectroscopy (XES) is widely used to fingerprint the local spin of transition-metal ions, including in pump-probe experiments, to identify excited states or in chemical and biological reactions to characterize short-lived intermediates. In this study, the spectra of ferrous and ferric complexes for various spin states were measured experimentally and described theoretically through restricted active space (RAS) calculations including dynamic correlations. Through the RAS calculations from simple atomic models to complex molecular systems, spectral effects such as the exchange interactions, crystal-field strength, and covalent orbital mixing were evaluated and discussed. The calculations find that only the spectral features of low-spin cases show a dependence on the crystal-field strength, particularly for ferrous low spin. The effect of the covalent orbital mixing strength on the first moment of the Kβ1,3 main line and the Kβ1,3-Kβ' energy splitting is quantitatively described. Clear relationships are found within a given nominal spin but less between different spin states, which calls for careful selection of reference spectra in future experiments. This study further advances our understanding of the correlation between changes in experimental spectral features and their corresponding electronic structure information.

Carbene Complexes of Plutonium: Structure, Bonding, and Divergent Reactivity to Lanthanide Analogs.

Organoplutonium chemistry was established in 1965, yet structurally authenticated plutonium-carbon bonds remain rare being limited to π-bonded carbocycle and σ-bonded isonitrile and hydrocarbyl derivatives. Thus, plutonium-carbenes, including alkylidenes and N-heterocyclic carbenes (NHCs), are unknown. Here, we report the preparation and characterization of the diphosphoniomethanide-plutonium complex [Pu(BIPMTMSH)(I)(μ-I)]2 (1Pu, BIPMTMSH = (Me3SiNPPh2)2CH) and the diphosphonioalkylidene-plutonium complexes [Pu(BIPMTMS)(I)(DME)] (2Pu, BIPMTMS = (Me3SiNPPh2)2C) and [Pu(BIPMTMS)(I)(IMe4)2] (3Pu, IMe4 = C(NMeCMe)2), thus disclosing non-actinyl transneptunium multiple bonds and transneptunium NHC complexes. These Pu-C double and dative bonds, along with cerium, praseodymium, samarium, uranium, and neptunium congeners, enable lanthanide-actinide and actinide-actinide comparisons between metals with similar ionic radii and isoelectronic 4f5 vs 5f5 electron-counts within conserved ligand fields over 12 complexes. Quantum chemical calculations reveal that the orbital-energy and spatial-overlap terms increase from uranium to neptunium; however, on moving to plutonium the orbital-energy matching improves but the spatial overlap decreases. The bonding picture that emerges is more complex than the traditional picture of the bonding of lanthanides being ionic and early actinides being more covalent but becoming more ionic left to right. Multiconfigurational calculations on 2M and 3M (M = Pu, Sm) account for the considerably more complex UV/vis/NIR spectra for 5f5 2Pu and 3Pu compared to 4f5 2Sm and 3Sm. Supporting the presence of Pu═C double bonds in 2Pu and 3Pu, 2Pu exhibits metallo-Wittig bond metathesis involving the highest atomic number element to date, reacting with benzaldehyde to produce the alkene PhC(H)═C(PPh2NSiMe3)2 (4) and "PuOI". In contrast, 2Ce and 2Pr do not react with benzaldehyde to produce 4.

Divergent Bimetallic Mechanisms in Copper(II)-Mediated C-C, N-N, and O-O Oxidative Coupling Reactions.

Copper-catalyzed aerobic oxidative coupling of diaryl imines provides a route for conversion of ammonia to hydrazine. The present study uses experimental and density functional theory computational methods to investigate the mechanism of N-N bond formation, and the data support a mechanism involving bimolecular coupling of Cu-coordinated iminyl radicals. Computational analysis is extended to CuII-mediated C-C, N-N, and O-O coupling reactions involved in the formation of cyanogen (NC-CN) from HCN, 1,3-butadiyne from ethyne (i.e., Glaser coupling), hydrazine from ammonia, and hydrogen peroxide from water. The results reveal two different mechanistic pathways. Heteroatom ligands with an uncoordinated lone pair (iminyl, NH2, OH) undergo charge transfer to CuII, generating ligand-centered radicals that undergo facile bimolecular radical-radical coupling. Ligands lacking a lone pair (CN and CCH) form bridged binuclear diamond-core structures that undergo C-C coupling. This mechanistic bifurcation is rationalized by analysis of spin densities in key intermediates and transition states, as well as multiconfigurational calculations. Radical-radical coupling is especially favorable for N-N coupling owing to energetically favorable charge transfer in the intermediate and thermodynamically favorable product formation.

Revisiting the role of octahedral symmetry in the interpretation of spectroscopic properties of [OsF6]2- and PtF6 complexes.

The electronic structure of [OsF6]2- and PtF6 complexes was studied by means of CASSCF/NEVPT2 multiconfigurational calculations, including spin-orbital coupling, which is very relevant in the case of these metals. From these calculations, it is possible to establish that in the octahedral symmetry (Oh), the ground state is non-magnetic (Jeff = 0) because of the strong ligand field, and the interaction with paramagnetic excited states is almost negligible, resulting in a non-magnetic behavior, which is in agreement with the experimental evidence.

Multiconfigurational Calculations and Experimental Resonant Raman/SERRS of a Donor-Acceptor Thiadiazole Dye.

The resonant Raman (RR) and resonant SERS spectra of the thiadiazole-based dye dibromobenzo[c]-1,2,5-thiadiazole (DBTD) were studied through multiconfigurational XMS-CASPT2/CASSCF and experimental methods in solution. The results indicate that the S1 excited state of DBTD is described by π → π* with internal CT from the benzene ring to the thiadizole. In resonance conditions at 364 nm, the RR spectrum shows intensifications in modes that describe extensive geometrical changes at both the benzene ring and the thiadiazole region, indicating an internal CT character to the S1. The SERS spectra observed on gold and silver nanoparticles indicate different adsorption geometries, which leads to distinct enhancement patterns on the spectra with varying excitation energy. It evidences the major contribution of the chemical enhancement mechanism on the spectra from a metal → DBTD CT state, as confirmed by the simulated spectra. This theoretical approach proved strong in the prediction of the main features of the observed experimental resonant Raman and SERS spectra indicating a potential for adequate description of the chemical mechanism of SERS.

Theoretical study of time-resolved photoelectron circular dichroism in the photodissociation of a chiral molecule.

Photoelectron circular dichroism (PECD), the forward-backward asymmetry of the photoelectron angular distribution when ionizing randomly oriented chiral molecules with circularly polarized light, is an established method to investigate chiral properties of molecules in their electronic ground state. Here, we develop a computational strategy for predicting time-resolved PECD (TRPECD) of chemical reactions and demonstrate the method on the photodissociation of 1-iodo-2-methylbutane. Our approach combines multi-configurational quantum-chemical calculations of the relevant potential-energy surfaces of the neutral and singly ionized molecule with ab initio molecular-dynamics (AIMD) calculations. The PECD parameters along the AIMD trajectories are calculated with the aid of electron-molecule scattering calculations based on the Schwinger variational principle implemented in ePolyScat. Our calculations have been performed for two probe wavelengths (133 and 160 nm) accessible through low-order harmonic generation in gases. Our results show that the TRPECD is a highly sensitive probe of photochemical reaction dynamics. Most interestingly, the TRPECD is found to change sign multiple times along the photodissociation coordinate, in agreement with recent experiments on CHBrFI [Svoboda et al., "Femtosecond photoelectron circular dichroism of chemical reactions," Sci. Adv. 8, eabq2811 (2022)]. The computational protocol introduced in the present work is general and readily applicable to other chiral photochemical processes.

Simulations of the Aqueous "Brown-Ring" Complex Reveal Fluctuations in Electronic Character.

Ab initio molecular dynamics (AIMD) simulations of the aqueous [Fe(H2O)5(NO)]2+ "brown-ring" complex in different spin states, in combination with multiconfigurational quantum chemical calculations, show a structural dependence on the electronic character of the complex. Sampling in the quartet and sextet ground states show that the multiplicity is correlated with the Fe-N distance. This provides a motivation for a rigid Fe-N scan in the isolated "brown-ring" complex to investigate how the multiconfigurational wave function and the electron density change around the FeNO moiety. Our results show that subtle changes in the Fe-N distance produce a large response in the electronic configurations underlying the quartet wave function. However, while changes in spin density and potential energy are pronounced, variations in charge are negligible. These trends within the FeNO moiety are preserved in structural sampling of the AIMD simulations, despite distortions present in other degrees of freedom in the bulk solution.

Machine learning accelerated photodynamics simulations

Machine learning (ML) continues to revolutionize computational chemistry for accelerating predictions and simulations by training on experimental or accurate but expensive quantum mechanical (QM) calculations. Photodynamics simulations require hundreds of trajectories coupled with multiconfigurational QM calculations of excited-state potential energies surfaces that contribute to the prohibitive computational cost at long timescales and complex organic molecules. ML accelerates photodynamics simulations by combining nonadiabatic photodynamics simulations with an ML model trained with high-fidelity QM calculations of energies, forces, and non-adiabatic couplings. This approach has provided time-dependent molecular structural information for understanding photochemical reaction mechanisms of organic reactions in vacuum and complex environments (i.e., explicit solvation). This review focuses on the fundamentals of QM calculations and ML techniques. We, then, discuss the strategies to balance adequate training data and the computational cost of generating these training data. Finally, we demonstrate the power of applying these ML-photodynamics simulations to understand the origin of reactivities and selectivities of organic photochemical reactions, such as cis–trans isomerization, [2 + 2]-cycloaddition, 4π-electrostatic ring-closing, and hydrogen roaming mechanism.

Modeling the Mg I from the NUV to MIR

Context. Reliable atomic data are mandatory ingredients to obtain a realistic semiempirical model of any stellar atmosphere. Due to their importance, we further improved our recently published Mg I atomic model. Aims. We tested the new atomic model using atmospheric models of stars of different spectral types: the Sun (dG2), HD 22049 (dK2, Epsilon Eridani), GJ 832 (dM2), and GJ 581 (dM3). Methods. Significant improvements have been included in the atomic model, mainly to the electron impact excitation (ϒij) values. We used new Breit-Pauli distorted-wave (DW) multiconfiguration calculations, which proved to be relevant for many transitions in the mid-infrared (MIR) range. The new atomic model of Mg I includes the following: (i) recomputed (ϒij) data through the DW method, including the superlevels. (ii) For the nonlocal thermodynamic equilibrium (NLTE) population calculations, 5676 theoretical transitions were added (3001 term-to-term). (iii) All of these improvements were studied in the Sun and the stars listed above. Comparisons for the distribution of magnesium among the first ionization states and the formation of molecules, as well as for the population of the different energy levels and atmospheric heights, were carried out. Several lines, representative of the spectral ranges, were selected to analyze the changes that were produced. In particular, we exemplify these results with the problematic line 2853.0 Å, a transition between the third level and the ground state. Results. The magnesium distribution between ionization states for stars with different effective temperatures was compared. For the Sun and Epsilon Eridani, Mg II predominates with more than 95%, while for GJ 832 and GJ 581, Mg I represents more than 72% of the population. Moreover, in the latter stars, the amount of magnesium forming molecules in their atmosphere is at least two orders of magnitude higher. Regarding the NLTE population, a noticeable lower variability in the departure coefficients was found, indicating a better population coupling for the new model. Comparing the synthetic spectrum calculated with the older and new Mg I atomic model, these results show minimal differences in the visible range but they are stronger in the infrared (IR) for all of the stars. This aspect should be considered when using lines from this region as indicators. Nevertheless, some changes in the spectral type were found, also emphasizing the need to test the atomic models in different atmospheric conditions. The most noticeable changes occurred in the far-ultraviolet (FUV) and near-ultraviolet (NUV), obtaining a higher flux for the new atomic model regardless of the spectral type. The new model did not prevent the formation of the core emission in the synthetic NUV line 2853.0 Å. However, by including other observations, we could note that the emission indeed exists, although with a much lower intensity. Further tests have shown that to reduce the emission, the population of its upper level (3s3p 1P) should be reduced by a factor of about 100.

Understanding the Excited-State Relaxation Mechanisms of Xanthophyll Lutein by Multi-configurational Electronic Structure Calculations.

The contradictory behaviors in light harvesting and non-photochemical quenching make xanthophyll lutein the most attractive functional molecule in photosynthesis. Despite several theoretical simulations on the spectral properties and excited-state dynamics, the atomic-level photophysical mechanisms need to be further studied and established, especially for an accurate description of geometric and electronic structures of conical intersections for the lowest several electronic states of lutein. In the present work, semiempirical OM2/MRCI and multi-configurational restricted active space self-consistent field methods were performed to optimize the minima and conical intersections in and between the 1Ag-, 2Ag-, 1Bu+, and 1Bu- states. Meanwhile, the relative energies were refined by MS-CASPT2(10,8)/6-31G*, which can reproduce correct electronic state properties as those in the spectroscopic experiments. Based on the above calculation results, we proposed a possible excited-state relaxation mechanism for lutein from its initially populated 1Bu+ state. Once excited to the optically bright 1Bu+ state, the system will propagate along the key reaction coordinate, i.e., the stretching vibration of the conjugated carbon chain. During this period of time, the 1Bu- state will participate in and forms a resonance state between the 1Bu- and 1Bu+ states. Later, the system will rapidly hop to the 2Ag- state via the 1Bu+/2Ag- conical intersection. Finally, the lutein molecule will survive in the 2Ag- state for a relatively long time before it internally converts to the ground state directly or via a twisted S1/S0 conical intersection. Notably, though the photophysical picture may be very different in solvents and proteins, the current theoretical study proposed a promising calculation protocol and also provided many valuable mechanistic insights for lutein and similar carotenoids.

A numerically exact correlation discrete variable representation for multi-configurational time-dependent Hartree calculations.

The correlation discrete variable representation (CDVR) enables (multilayer) multi-configurational time-dependent Hartree (MCTDH) calculations with general potentials. The CDVR employs a set of grids corresponding to single-particle functions to efficiently evaluate all potential matrix elements appearing in the MCTDH equations of motion. In standard CDVR approaches, the number of grid points employed is tied to the number of corresponding single-particle functions. This limits the accuracy of the quadrature, which can be achieved for a given single-particle function basis. In this work, an extended CDVR approach that facilitates a numerically exact quadrature of all potential matrix elements is introduced. The number of grid points employed can be increased independent of the number of corresponding single-particle function to achieve any desired quadrature accuracy. The properties of the new scheme are illustrated by numerical calculations studying the photodissociation of NOCl and the vibrational states of CH3. Fast convergence with respect to the number of additional quadrature points is observed: Employing a single additional point in each physical or logical coordinate already ensures negligible quadrature errors.

First-principles calculations of electronic and optical properties of Ce3+-activated phosphors toward evaluating valence stability of Eu ions

The valence stability of activator ions with multiple stable valence states has always been a major concern in the field of luminescent materials. Here we present a computational protocol that is able to predict the valence stability of the europium (Eu) ion in its activated phosphors, in terms of the energy difference between the ground-state level of Eu2+ and the Fermi level of the host. The protocol is based on hybrid density functional theory (DFT) and wavefunction-based multiconfigurational ab initio calculations of the dopant Ce3+, in conjunction with the established relationship between energy levels of Ce3+ and Eu2+. The predictions are in good agreements with experimental findings. It is demonstrated that across the study set consisting of five borate-containing phosphors, the valence stability of the dopant Eu2+ is positively correlated with the host band gap, and this positive correlation is more significant than the negative correlation with the energy level of Eu2+ within the host band gap. Microscopic analysis reveals that a strong bonding of electrons within the anion groups together with a large dopant site is beneficial for the reduction of Eu3+ into Eu2+. The influence of hybrid DFT functional on the predicted valence stability of a given compound was found be negligible due to cancellation of changes in the host band gap and the Eu2+ ground level. This study clarifies the reasons for the stabilization of Eu2+ in phosphors synthesized in air at high temperature and is expected to help to screen out the host compounds that could stabilize Eu2+ activators for diverse optical applications.

Synthesis and isolation of a triplet bismuthinidene with a quenched magnetic response.

Large spin-orbit coupling (SOC) is an intrinsic property of the heavy elements that directly affects the electronic structures of the compounds. In this work, we report the synthesis and characterization of a monocoordinate bismuthinidene that features a rigid and bulky ligand. All magnetic measurements [superconducting quantum interference device (SQUID), nuclear magnetic resonance (NMR)] point to a diamagnetic compound. However, multiconfigurational quantum chemical calculations predict the ground state of the compound to be dominated (76%) by a spin triplet. The apparent diamagnetism is explained by an extremely large SOC-induced positive zero-field splitting of more than 4500 wavenumbers that leaves the MS = 0 magnetic sublevel thermally isolated in the electronic ground state.

Electron Trap Depths in Cubic Lutetium Oxide Doped with Pr and Ti, Zr or Hf─From Ab Initio Multiconfigurational Calculations.

We propose a universal approach to model intervalence charge transfer (IVCT) and metal-to-metal charge transfer (MMCT) transitions between ions in solids. The approach relies on already well-known and reliable ab initio RASSCF/CASPT2/RASSI-SO calculations for a series of emission center coordination geometries (restricted active space self-consistent field, complete active space second-order perturbation theory, and restricted active space state interaction with spin-orbit coupling). Embedding with ab initio model potentials (AIMPs) is used to represent the crystal lattice. We propose a way to construct the geometries via interpolation of the coordinates obtained using solid-state density functional theory (DFT) calculations for the structures where the activator metal is at specific oxidation (charge) states of interest. The approach thus takes the best of two worlds: the precision of the embedded cluster calculations (including localized excited states) and the geometries from DFT, where the effects of ionic radii mismatch (and eventual nearby defects) can be modeled explicitly. The method is applied to the Pr activator and Ti, Zr, Hf codopants in cubic Lu2O3, in which the said ions are used to obtain energy storage and thermoluminescence properties. Electron trap charging and discharging mechanisms (not involving a conduction band) are discussed in the context of the IVCT and MMCT role in them. Trap depths and trap quenching pathways are analyzed.