Embedded Cluster Approach Research Articles

Nature of Scapolite Color: Ab Initio Calculations, Spectroscopy, and Structural Study

The article describes the results of a comprehensive study of the extra-framework components of scapolites using quantum–chemical calculations, electronic and vibrational spectroscopy, and single-crystal X-ray diffraction and crystal structure refinement. The ab initio calculations were performed using an embedded-cluster approach of extra-framework components in various cation surroundings. As a result, through comparing the experimental and ab initio calculation results, the energies of the electronic and vibrational transitions of various extra-framework components (CO3)2−, (CO3)·−, S3·−, S2·−—as well as the role of these components in the process of the lowering of the symmetry—were determined for scapolites belonging to the marialite–meionite solid–solution series. The nature of the various colors of the scapolites has also been established. Colors from purple to blue are a result of the presence of radiation-induced pairs of defects: carbonate radical anions (CO3)·− and F-centers. However, polysulfide S3·− radical anions are found in some violet scapolites.

Syngas Conversion over Co4 Cluster Grafted on HZSM‐5 Zeolite: Mechanistic Insights from DFT Modeling

AbstractWe present a detailed DFT‐based mechanistic investigation of syngas conversion mechanism over Co4 cluster grafted onto HZSM‐5 zeolite, [Co4H], employing a QM/MM embedded cluster approach. Starting from the [Co4H] complex, our results show that a favorable coordination of CO over H2, followed by CO hydrogenation leads to a stable −CH2O complex, [Co4(CH2O)(H)]. Coordination of a second CO molecule to [Co4(CH2O)(H)] complex, followed by CH2−O bond activation, and subsequent removal of CO as CO2 results in the formation of crucial methylene complex [Co4(CH2)(H)], serving as a branching point for the pathways leading to methane, ethene, and ethane. On the pathway to ethene formation, coordination of a third CO molecule to [Co4(CH2)(H)] complex yields the active [Co4(CH2)(CO)(H)] complex, which is 16.0 kcal mol−1 more stable than the methyl complex [Co4(CH3)] on the pathway to methane. From the active species [Co4(CH2)(CO)(H)], we demonstrate that the pathways to both methane and ethene are competing in nature, with the −CH3 hydrogenation barrier, 35.1 kcal mol−1, is lower by only 1.3 kcal mol−1 than the competing C−O bond activation barrier on the pathway to ethene, 36.4 kcal mol−1. However, the significant stability of the active species [Co4(CH2)(CO)(H)] effectively compensates for this minor difference in barriers, ultimately favoring the formation of ethene over methane. Finally, the ethene desorption barrier is 4.1 kcal mol−1 lower than the ethene hydrogenation barrier on the pathway to ethane, indicating the ease of ethene removal from the system. Overall, our DFT study describes that the syngas conversion mechanism catalyzed by [Co4H] system produces ethene selectively via 4CO+2H2→C2H4+2CO2.

Introducing the embedded random phase approximation: H2 dissociative adsorption on Cu(111) as an exemplar

The random phase approximation (RPA) as a means of treating electron correlation recently has been shown to outperform standard density functional theory (DFT) approximations in a variety of cases. However, the computational cost of the RPA is substantially more than DFT, especially when aiming to study extended surfaces. Properly accounting for sufficient surface ensemble size, Brillouin zone sampling, and vacuum separation of periodic images in standard periodic-planewave-based DFT code raises the cost to achieve converged results. Here, we show that sub-system embedding schemes enable use of the RPA for modeling heterogeneous reactions at reduced computational cost. We explore two different embedded RPA (emb-RPA) approaches, periodic emb-RPA and cluster emb-RPA. We use the (experimentally and theoretically) well-studied H2 dissociative adsorption on Cu(111) as our exemplar, and first perform full periodic RPA calculations as a benchmark. The full RPA results match well the semi-empirical barrier fit to experimental observables and others derived from high-level computations, e.g., from recent embedded n-electron valence second order perturbation theory [Zhao et al., J. Chem. Theory Comput. 16(11), 7078–7088 (2020)] and quantum Monte Carlo [Doblhoff-Dier et al., J. Chem. Theory Comput. 13(7), 3208–3219 (2017)] simulations. Among the two emb-RPA approaches tested, the cluster emb-RPA accurately reproduces the energy profile (maximum error of 50 meV along the reaction pathway) while reducing the computational cost by approximately two orders of magnitude. We therefore expect that the embedded cluster approach will enable wider RPA implementation in heterogeneous catalysis.

Magnetic Properties of Tetravalent Pu in the Perovskites BaPuO3 and SrPuO3.

BaPuO3 and SrPuO3 were synthesized, and their structures were refined in the orthorhombic space group Pbnm, a common distortion from the classic Pm3̅m cubic perovskite. Magnetic-susceptibility measurements, obtained as a function of temperature over the range of 1.8-320 K, exhibit temperature-dependent behavior, with evidence of long-range magnetic order at temperatures higher than their lanthanide and actinide analogues: BaPuO3 below 164(1) K and SrPuO3 below 76(1) K. Effective moments of 1.66(10)μB for BaPuO3 and 1.84(8)μB for SrPuO3 were obtained by fitting their paramagnetic susceptibilities using the Curie-Weiss law. Both are below the free-ion value of 2.68 μB expected for a Pu4+ 5I4 ground level. Ab initio wave function calculations, performed at the relativistic complete active space level including spin-orbit coupling and with an embedded cluster approach that neglects interactions between Pu centers, were used to generate embedded-cluster Pu4+ magnetic susceptibilities. The calculations agree well with experimental data at higher temperatures, providing evidence that a single-ion representation is sufficient to account for the observed paramagnetic behavior without the need to invoke charge transfer, disproportionation, strong covalent bonding, or other more complex electronic behavior.

An embedded cluster CASPT2 study of the Ce:YVO4 spectrum.

Multiconfigurational theory, in combination with the embedded cluster approach, is a precise and abinitio approach to describe the electronic structure of solids. In this work, the spectrum of a Ce(III) dopant in YVO4 has been studied by complete active space perturbation theory of the second order (CASPT2), with the host material represented as a set of abinitio model potentials and point-charges. We assess the sensitivity of the spectrum to the size of both the embedded cluster size as well as the size of the electronic basis set. A comparison of our best computational model with experimental results shows that the embedding approach is robust and can accurately model the spectrum of low-concentration dopants in complex host materials.

New Insights on Singlet Oxygen Release from Li-Air Battery Cathode: Periodic DFT Versus CASPT2 Embedded Cluster Calculations.

Li-air batteries are a promising energy storage technology for large-scale applications, but the release of highly reactive singlet oxygen (1O2) during battery operation represents a main concern that sensibly limits their effective deployment. An in-depth understanding of the reaction mechanisms underlying the 1O2 formation is crucial to prevent its detrimental reactions with the electrolyte species. However, describing the elusive chemistry of highly correlated species such as singlet oxygen represents a challenging task for state-of-the-art theoretical tools based on density functional theory. Thus, in this study, we apply an embedded cluster approach, based on CASPT2 and effective point charges, to address the evolution of 1O2 at the Li2O2 surface during oxidation, i.e., the battery charging process. Based on recent hypothesis, we depict a feasible O22-/O2-/O2 mechanisms occurring from the (112̅0)-Li2O2 surface termination. Our highly accurate calculations allow for the identification of a stable superoxide as local minimum along the potential energy surface (PES) for 1O2 release, which is not detected by periodic DFT. We find that 1O2 release proceeds via a superoxide intermediate in a two-step one-electron process or another still accessible pathway featuring a one-step two-electron mechanism. In both cases, it represents a feasible product of Li2O2 oxidation upon battery charging. Thus, tuning the relative stability of the intermediate superoxide species can enable key strategies aiming at controlling the detrimental development of 1O2 for new and highly performing Li-air batteries.

Hydroxyapatite and lead-substituted hydroxyapatite near-surface structures: Novel modelling of photoemission lines from X-ray photoelectron spectra

X-ray photoelectron spectroscopy (XPS) is one of the main tools for hydroxyapatite (HA) surface characterization in developing materials for biomedical and heterogeneous catalysis. Despite the XPS technique's potential to correlate binding energies with existing photo-emitter sites on near-surfaces, few previous studies analyzed this aspect for HA and metal-substituted HA surfaces. In this work, we theoretically reconstructed the XPS spectra of stoichiometric HA and lead-substituted hydroxyapatite (PbCaHA, Ca10-xPbx(PO4)6(OH)2; x = 2, 10) using a first-principles linear combination of atomic orbitals embedded cluster approach and periodic supercell band structures within the framework of Density Functional Theory (DFT). We take into account photoemission lines contributions from Ca(1), Ca(2), Pb(1) and Pb(2) sites located on surface and near-surface depths (up to ∼15 Å) along the (001) and (100) surfaces. The calculated DFT spectra of HA and PbCaHA were compared with high-resolution XPS spectra previously characterized by synchrotron X-ray diffraction (XRD), Fourier transforms infrared spectroscopy (FTIR), high-resolution transmission electron microscopy (HRTEM) and electron energy-loss spectroscopy (EELS). A combined theoretical and experimental approach enables decoding of the complex structure of HA and PbCaHA in XPS spectra. It was found that XPS binding energies profiles depend significantly on photo-emitters from near-surface sites and surface crystallographic orientation. The main Ca 2p3/2 envelope peak in HA is predominantly from Ca(1) and Ca(2) sites (∼347.4 eV), while the weaker peak is due to the Ca(2) site only (∼345.0 eV). Variations on HA nanoparticle morphology could be a critical factor for changes in XPS binding energies' profile.

Computation of NMR Shielding Constants for Solids Using an Embedded Cluster Approach with DFT, Double-Hybrid DFT, and MP2.

In this work, we explore the accuracy of post-Hartree–Fock (HF) methods and double-hybrid density functional theory (DFT) for the computation of solid-state NMR chemical shifts. We apply an embedded cluster approach and investigate the convergence with cluster size and embedding for a series of inorganic solids with long-range electrostatic interactions. In a systematic study, we discuss the cluster design, the embedding procedure, and basis set convergence using gauge-including atomic orbital (GIAO) NMR calculations at the DFT and MP2 levels of theory. We demonstrate that the accuracy obtained for the prediction of NMR chemical shifts, which can be achieved for molecular systems, can be carried over to solid systems. An appropriate embedded cluster approach allows one to apply methods beyond standard DFT even for systems for which long-range electrostatic effects are important. We find that an embedded cluster should include at least one sphere of explicit neighbors around the nuclei of interest, given that a sufficiently large point charge and boundary effective potential embedding is applied. Using the pcSseg-3 basis set and GIAOs for the computation of nuclear shielding constants, accuracies of 1.6 ppm for 7Li, 1.5 ppm for 23Na, and 5.1 ppm for 39K as well as 9.3 ppm for 19F, 6.5 ppm for 35Cl, 7.4 ppm for 79Br, and 7.5 ppm for 25Mg as well as 3.8 ppm for 67Zn can be achieved with MP2. Comparing various DFT functionals with HF and MP2, we report the superior quality of results for methods that include post-HF correlation like MP2 and double-hybrid DFT.

A quantum-mechanical tier model for phonon-driven vibrational relaxation dynamics of adsorbates at surfaces.

We present a quantum-mechanical tier model for vibrational relaxation of low-lying excited states of an adsorbate vibrational mode (system), coupled to surface phonons (bath), at zero temperature. The tier model, widely used in studies of intramolecular vibrational energy redistribution in polyatomics, is adapted here to adsorbate-surface systems with the help of an embedded cluster approach, using orthogonal coordinates for the system and bath modes, and a phononic expansion of their interaction. The key idea of the model is to organize the system-bath zeroth-order vibrational space into a hierarchical structure of vibrational tiers and keep therein only vibrational states that are sequentially generated from the system-bath initial vibrational state. Each tier is generated from the previous one by means of a successor operator, derived from the system-bath interaction Hamiltonian. This sequential procedure leads to a drastic reduction of the dimension of the system-bath vibrational space. We notably show that for harmonic vibrational motion of the system and linear system-bath couplings in the system coordinate, the dimension of the tier-model vibrational basis scales as ∼Nl×υ. Here, N is the number of bath modes, l is the highest-order of the phononic expansion, and υ is the size of the system vibrational basis. This polynomial scaling is computationally far superior to the exponential scaling of the original zeroth-order vibrational basis, ∼MN, with M being the number of basis functions per bath mode. In addition, since each tier is coupled only to its adjacent neighbors, the matrix representation of the system-bath Hamiltonian in this new vibrational basis has a symmetric block-tridiagonal form, with each block being very sparse. This favors the combination of the tier-model with iterative Krylov techniques, such as the Lanczos algorithm, to solve the time-dependent Schrödinger equation for the full Hamiltonian. To illustrate the method, we study vibrational relaxation of a D-Si bending mode, coupled via two- and (mainly) one-phonon interactions to a fully D-covered Si(100)-(2 × 1) surface, using a recent first-principles system-bath Hamiltonian. The results of the tier model are compared with those obtained by the Lindblad formalism of the reduced density matrix. We find that the tier model provides much more information and insight into mechanisms of vibration-phonon couplings at surfaces, and gives more reliable estimates of the adsorbate vibrational lifetimes. Moreover, the tier model might also serve as a benchmark for other approximate quantum-dynamics methods, such as multiconfiguration wavefunction approaches.

Hybrid-DFT Modeling of Lattice and Surface Vacancies in MnO

We have investigated the properties of defects in MnO bulk and at (100) surfaces, as used in catalytic applications, using hybrid-level density functional theory (i.e., inclusion of exact exchange within the exchange-correlation evaluation) in a hybrid QM/MM embedded-cluster approach. Initially, we calculate the formation energy for bulk Mn and O vacancies, comparing charged-defect compensation with charge carriers at the Fermi Level (ϵf) and through Schottky defect formation. Oxygen vacancies were also investigated at the (100) surface, where the vacancy formation energy is very similar to the bulk. Defect levels associated with the most stable vacancies are calculated using the ΔSCF method: all are positioned mid band gap, with surface environments failing to alter strongly the overall nature of the defect relative to bulk. Chemical activity of the (100) MnO surface was considered through the adsorption of a probe CO2 molecule, which is considered the initial step in the transformation of CO2 into hydro...

Restricted Open-Shell Configuration Interaction Singles Study on M- and L-edge X-ray Absorption Spectroscopy of Solid Chemical Systems.

In this study the M- and L-edge X-ray absorption spectra of a series of open- and closed-shell solids (TiO2 rutile, α-Fe2O3 hematite, FeS2 pyrite, and the spinel Co3O4) are investigated with the restricted open-shell configuration interaction singles methods (ROCIS/DFT and PNO-ROCIS/DFT) using the embedded cluster approach. ROCIS/DFT type of methods are grounded in wave function-based ab initio electronic structure theory and have shown great performance in the field of X-ray spectroscopy in particular in the field of transition metal L-edge spectroscopy. In this work we show that ROCIS/DFT can be used to calculate and interpret metal M- and L-edge XAS spectra of solids. To this end, clusters with up to 52 metal centers are considered. In all cases good to excellent agreement between theory and experiment is obtained. The experimentally probed local coordination environments are discussed in detail. The physical origin of the observed spectral features is explored through the machinery of natural difference orbitals. This analysis provides valuable information with respect to the core to valence, metal to metal charge transfer, and metal to ligand charge transfer characters of the relativistically corrected many particle states. The influence of the above electronic effects to the spectral shapes and the size of the treated clusters are thoroughly investigated.

Prediction of multiband luminescence due to the gallium vacancy–oxygen defect complex in GaN

Oxygen is the most common unintentional impurity found in GaN. We study the interaction between substitutional oxygen (ON) and the gallium vacancy (VGa) to form a point defect complex in GaN. The formation energy of the gallium vacancy is largely reduced in n-type GaN by complexing with oxygen, while thermodynamic and optical transition levels remain within the bandgap. We study the spectroscopy of this complex using a hybrid quantum-mechanical molecular-mechanical embedded-cluster approach. We reveal how a single defect center can be responsible for multiband luminescence, including possible contributions to the ubiquitous yellow luminescence signatures observed in n-type GaN, owing to the coexistence of diffuse (extended) and compact (localized) holes.

Deep vs shallow nature of oxygen vacancies and consequentn-type carrier concentrations in transparent conducting oxides

The source of n -type conductivity in undoped transparent conducting oxides has been a topic of debate for several decades. The point defect of most interest in this respect is the oxygen vacancy, but there are many conflicting reports on the shallow versus deep nature of its related electronic states. Here, using a hybrid quantum mechanical/molecular mechanical embedded cluster approach, we have computed formation and ionization energies of oxygen vacancies in three representative transparent conducting oxides: In 2 O 3 , SnO 2 , and ZnO. We find that, in all three systems, oxygen vacancies form well-localized, compact donors. We demonstrate, however, that such compactness does not preclude the possibility of these states being shallow in nature, by considering the energetic balance between the vacancy binding electrons that are in localized orbitals or in effective-mass-like diffuse orbitals. Our results show that, thermodynamically, oxygen vacancies in bulk In 2 O 3 introduce states above the conduction band minimum that contribute significantly to the observed conductivity properties of undoped samples. For ZnO and SnO 2 , the states are deep, and our calculated ionization energies agree well with thermochemical and optical experiments. Our computed equilibrium defect and carrier concentrations, however, demonstrate that these deep states may nevertheless lead to significant intrinsic n -type conductivity under reducing conditions at elevated temperatures. Our study indicates the importance of oxygen vacancies in relation to intrinsic carrier concentrations not only in In 2 O 3 , but also in SnO 2 and ZnO.

Isotopic effects in vibrational relaxation dynamics of H on a Si(100) surface

In a recent paper [U. Lorenz and P. Saalfrank, Chem. Phys. 482, 69 (2017)], we proposed a robust scheme to set up a system-bath model Hamiltonian, describing the coupling of adsorbate vibrations (system) to surface phonons (bath), from first principles. The method is based on an embedded cluster approach, using orthogonal coordinates for system and bath modes, and an anharmonic phononic expansion of the system-bath interaction up to second order. In this contribution, we use this model Hamiltonian to calculate vibrational relaxation rates of H-Si and D-Si bending modes, coupled to a fully H(D)-covered Si(100)-(2×1) surface, at zero temperature. The D-Si bending mode has an anharmonic frequency lying inside the bath frequency spectrum, whereas the H-Si bending mode frequency is outside the bath Debye band. Therefore, in the present calculations, we only take into account one-phonon system-bath couplings for the D-Si system and both one- and two-phonon interaction terms in the case of H-Si. The computation of vibrational lifetimes is performed with two different approaches, namely, Fermi's golden rule, and a generalized Bixon-Jortner model built in a restricted vibrational space of the adsorbate-surface zeroth-order Hamiltonian. For D-Si, the Bixon-Jortner Hamiltonian can be solved by exact diagonalization, serving as a benchmark, whereas for H-Si, an iterative scheme based on the recursive residue generation method is applied, with excellent convergence properties. We found that the lifetimes obtained with perturbation theory, albeit having almost the same order of magnitude-a few hundred fs for D-Si and a couple of ps for H-Si-, are strongly dependent on the discretized numerical representation of the bath spectral density. On the other hand, the Bixon-Jortner model is free of such numerical deficiencies, therefore providing better estimates of vibrational relaxation rates, at a very low computational cost. The results obtained with this model clearly show a net exponential decay of the time-dependent survival probability for the H-Si initial vibrational state, allowing an easy extraction of the bending mode "lifetime." This is in contrast with the D-Si system, whose survival probability exhibits a non-monotonic decay, making it difficult to define such a lifetime. This different behavior of the vibrational decay is rationalized in terms of the power spectrum of the adsorbate-surface system. In the case of D-Si, it consists of several, non-uniformly distributed peaks around the bending mode frequency, whereas the H-Si spectrum exhibits a single Lorentzian lineshape, whose width corresponds to the calculated lifetime. The present work gives some insight into mechanisms of vibration-phonon coupling at surfaces. It also serves as a benchmark for multidimensional system-bath quantum dynamics, for comparison with approximate schemes such as reduced, open-system density matrix theory (where the bath is traced out and a Liouville-von Neumann equation is solved) or approximate wavefunction methods to solve the combined system-bath Schrödinger equation.

Effect of doping and chemical ordering on the optoelectronic properties of complex oxides: Fe2O3-V2O3 solid solutions and hetero-structures.

The electronic and optical properties of α-(Fe1-xVx)2O3 at low (x = 0.04) and high (x = 0.5) doping levels are investigated using a combination of periodic and embedded cluster approaches, and time-dependent density functional theory. At low V concentrations the onset of the optical absorption is ∼0.5 eV (i.e., nearly 1.6 eV lower than that in pure α-Fe2O3) and corresponds to the electron transitions from V 3d to Fe 3d* orbitals. At high V concentrations, optical absorption energies and intensities are sensitive to specific arrangements of Fe and V atoms and their spin configuration that determine Fe-V hybridization. The onset of the lowest inter-vanadium absorption band in the case of Fe2O3/V2O3 hetero-structures is as low as ∼0.3 eV and the corresponding peak is at ∼0.7 eV. In contrast, in the case of solid solutions this peak has lower intensity and is shifted to higher energy (∼1.2 eV). Analysis of the orbital character of electronic excitation suggests that Fe2O3/V2O3 hetero-structures absorb light much more effectively than random alloys, thus promoting efficient photo-induced carrier generation. These predictions can be tested in α-(Fe1-xVx)2O3 thin films synthesized with well-controlled spatial distribution of Fe and V species.

A novel system-bath Hamiltonian for vibration-phonon coupling: Formulation, and application to the relaxation of Si–H and Si–D bending modes of H/D:Si(100)-(2 × 1)

We present a rigorous method to set up a system-bath Hamiltonian for the coupling of adsorbate vibrations (the system) to surface phonons (the bath). The Hamiltonian is straightforward to derive and exact up to second order in the environment coordinates, thus capable of treating one- and two-phonon contributions to vibration-phonon coupling. The construction of the Hamiltonian uses orthogonal coordinates for system and bath modes, is based on an embedded cluster approach, and generalizes previous Hamiltonians of a similar type, but avoids several (additional) approximations. While the parametrization of the full Hamiltonian is in principle feasible by a first principles quantum mechanical treatment, here we adopt in the spirit of a QM/MM model a combination of density functional theory (“QM”, for the system) and a semiempirical forcefield (“MM”, for the bath). We apply the Hamiltonian to a fully H-covered Si(100)-(2×1) surface, using Fermi’s Golden Rule to obtain vibrational relaxation rates of various H–Si bending modes of this system. As in earlier work it is found that the relaxation is dominated by two-phonon contributions because of an energy gap between the Si–H bending modes and the Si phonon bands. We obtain vibrational lifetimes (of the first excited state) on the order of 2ps at T=0K. The lifetimes depend only little on the type of bending mode (symmetric vs. antisymmetric, parallel vs. perpendicular to the Si2H2 dimers). They decrease by a factor of about two when heating the surface to 300K. We also study isotope effects by replacing adsorbed H atoms by deuterium, D. The Si–D bending modes are shifted into the Si phonon band of the solid, opening up one-phonon decay channels and reducing the lifetimes to few hundred fs.

Photodissociation of water on rutile (110): A wave packet approach based on first principles

The photodissociation of water on rutile (110) is studied from first principles. Using an embedded cluster approach, the motion of one hydrogen atom with a fixed OH group served as a model system. The ground and an electronically excited state are calculated on a CASSCF level of theory, explicitly accounting for the multi-reference character of the wave function during bond breaking. The dynamics is simulated by solving the time-dependent Schrödinger equation for a wave packet moving on the electronic potential energy surface. Photodissociation probabilities of water are calculated for hydrogen, deuterium and tritium, thereby revealing significant isotope effects.

Structure and optical properties of copper impurity in LiF and NaF crystals from ab initio calculations

This letter reports the results of ab initio calculations of absorption spectra of Cu+ ion embedded in LiF and NaF matrices. The calculations have been performed in embedded cluster approach at hybrid density functional theory (DFT) level. We propose the model of oscillator strength and absorption intensity calculations for forbidden 3d10→3d94s transitions based on the linear dependence between transitions dipole matrix elements and copper ion displacements. For LiF:Cu+ crystal one should expect two bands in absorption spectra at 5.32 and 5.88eV with different intensity ratios: the low energy band is more intense than the high energy band.

First-principles study of electronic structure of Ce3+ centres in alkaline-earth fluorides including spin-orbit and scalar relativistic effects

In this paper we present the results of ab initio calculations of Ce3+ impurity centres in CaF2 crystal. The cubic and tetragonal (interstitial fluorine compensated) configurations of centres were considered. The embedded cluster approach with polarizible crystalline lattice and CASSCF/CASPT2 methods were used to study the structural configurations and electronic properties of defects under consideration. Scalar relativistic corrections were taken into account at Douglas-Kroll-Hess level and spin-orbit effects were calculated with the RASSI approach. Calculated optical absorption spectra for cubic and tetragonal centres demonstrate good agreement with the experiment. Small symmetry breaking displacements of neighbouring ions were observed for cubic Ce3+ centre ground state.

Fcenter in lithium fluoride revisited: Comparison of solid-state physics and quantum-chemistry approaches

We revisit the theoretical description of the $F$ color center in lithium fluoride employing advanced complementary ab initio techniques. We compare the results from periodic supercell calculations involving density-functional theory (DFT) and post-DFT techniques with those from the embedded-cluster approach involving quantum-chemical many-electron wave-function techniques. These alternative approaches yield results in good agreement with each other and with the experimental data provided that correlation effects are properly taken into account.