Restricted Open-Shell Hartree–Fock Method for a General Configuration State Function Featuring Arbitrarily Complex Spin-Couplings

In this work, we present a general spin restricted open-shell Hartree–Fock (ROHF) implementation that is able to generate self-consistent field (SCF) wave functions for an arbitrary configuration state function (CSF). These CSFs can contain an arbitrary number of unpaired electrons in arbitrary spin-couplings. The resulting method is named CSF-ROHF. We demonstrate that starting from the ROHF energy expression, for example, the one given by Edwards and Zerner, it is possible to obtain the values of the ROHF vector-coupling coefficients by setting up an open-shell for each group of consecutive parallel-coupled spins dictated by the unique spin-coupling pattern of any given CSF. To achieve this important and nontrivial goal, we employ the machinery of the iterative configuration expansion configuration interaction (ICE-CI) method, which is able to tackle general CI problems on the basis of spin-adapted CSFs. This development allows for the efficient generation of SCF spin-eigenfunctions for systems with complex spin-coupling patterns, such as polymetallic chains and metal clusters, while maintaining SCF scaling with system size (quadratic or less, depending on the specific algorithm and approximations chosen)

Including vibrational effects in magnetic circular dichroism spectrum calculations in the framework of excited state dynamics

In this work, we present a computational approach that is able to incorporate vibrational effects in the computations of magnetic circular dichroism (MCD) spectra. The method combines our previous implementations to model absorption as well as fluorescence and phosphorescence spectra in the framework of excited state dynamics with a new technique to calculate MCD intensities, where molecular orientational averages are treated via semi-numerical quadrature. The implementation relies on a path integral approach that is employed to compute nuclear dynamics under the harmonic oscillator approximation (accounting for the nuclear potential energy surface) together with quasi-degenerate perturbative theory (to include the perturbation of an external magnetic field). We evaluate our implementation with a selected molecular set consisting of five aromatic organic molecules, namely, 1,4-benzoquinone, naphthalene, 2-naphthylamine, 2-naphthaldehyde, and benzene; we also included the MnO4− and the [Co(NH3)6]3+ transition metal complexes. This set is used to validate the ability of the approach to compute MCD A- and B-terms in conjunction with time-dependent density functional theory. The computed intensities are discussed in terms of the overall quality of the electronic structure treatments, vibrational modes, and the quality of the nuclear Hessians. It is shown that in the cases in which the potential energy surface is accurately represented, electric dipole-forbidden transitions are vibrationally activated, producing intensities relative to the dipole-allowed transitions in the same order of magnitude as the experimental measurements

General Spin-Restricted Open-Shell Configuration Interaction Approach: Application to Metal K-Edge X-ray Absorption Spectra of Ferro- and Antiferromagnetically Coupled Dimers

In this work, we present a generalized implementation of the previously developed restricted open-shell configuration interaction singles (ROCIS) family of methods. The new method allows us to treat high-spin (HS) ferro- as well as antiferromagnetically (AF) coupled systems while retaining the total spin as a good quantum number. To achieve this important and nontrivial goal, we employ the machinery of the iterative configuration expansion (ICE) method, which is able to tackle general configuration interaction (CI) problems on the basis of spin-adapted configuration state functions (CSFs). While ICE is designed to work in restricted orbital spaces, the new general-spin ROCIS (GS-ROCIS) method is designed to be applicable to larger molecules by employing a prototyping strategy. This new method can be applied to closed-shell, high-spin open-shell, as well as antiferromagnetic reference CSFs. In addition, GS-ROCIS can be combined with the pair natural orbital (PNO) machinery in the form of the PNO-GS-ROCIS method. With this extension, one can drastically reduce the required virtual space in the vicinity of the involved core orbitals, leading to computational savings of several orders of magnitude with negligible (<1%) loss in accuracy. To demonstrate the use of the new methodology, the metal K pre-edge X-ray absorption excitation problem of an antiferromagnetically coupled copper model dimer was investigated. By first analyzing a model copper dimer, it is shown that even for the minimum core excitation problem that involves the two antiferromagnetically coupled singly occupied orbitals and one virtual orbital, the resulting GS-ROCIS and broken-symmetry configuration interaction singles (BS-CIS) spectra may differ in terms of the number, energy position, and relative intensity of the computed bands. Furthermore, the methodology was validated to perform equally well in computing the K-edge spectra of antiferromagnetic nickel oxide dimers and mixed-valence cobalt oxide trimers. Collectively, the present development represents an important methodological advance in the application of theoretical X-ray spectroscopy

Extended Active Space Ab Initio Ligand Field Theory: Applications to Transition-Metal Ions

Ligand field theory (LFT) is one of the cornerstones of coordination chemistry since it provides a conceptual framework in which a great many properties of d- and f-element compounds can be discussed. While LFT serves as a powerful qualitative guide, it is not a tool for quantitative predictions on individual compounds since it incorporates semiempirical parameters that must be fitted to experiment. One way to connect the realms of first-principles electronic structure theory that has emerged as particularly powerful over the past decade is the ab initio ligand field theory (AILFT). The original formulation of this method involved the extraction of LFT parameters by fitting the ligand field Hamiltonian to a complete active space self-consistent field (CASSCF) Hamiltonian. The extraction was shown to be unique provided that the active space consists of 5/7 metal d/f-based molecular orbitals (MOs). Subsequent improvements have involved incorporating dynamical correlation using second-order N-electron valence state perturbation theory (NEVPT2) or second-order dynamical correlation dressed complete active space (DCDCAS). However, the limitation of past approaches is that the method requires a minimal space of 5/7 metal d- or f-based molecular orbitals. This leads to a number of limitations: (1) neglect of radial or semicore correlation would arise from the effect of a second d-shell or an sp-shell in the active space, (2) a more balanced description of metal–ligand bond covalency is lacking because the bonding ligand-based counterparts of the metal d/f orbitals are not in the active space. This usually leads to an exaggerated ionicity of the M–L bonds. In this work, we present an extended active space AILFT (esAILFT) that circumvents these limitations and is, in principle, applicable to arbitrary active spaces, as long as these contain the 5/7 metal d/f-based MOs as a subset. esAILFT was implemented in a development version of the ORCA software package. In order to help with the application of the new method, various criteria for active space extension were explored for 3d, 4d, and 5d transition-metal ions with varying charge. An interpretation of the trends in the Racah B parameter for these ions is also presented as a demonstration of the capabilities of esAILFT

On the possibility of magneto-structural correlations: detailed studies of di-nickel carboxylate complexes

A series of water-bridged dinickel complexes of the general formula [Ni&lt;sub&gt;2&lt;/sub&gt;(μ&lt;sub&gt;2&lt;/sub&gt;-OH&lt;sub&gt;2&lt;/sub&gt;)(μ2- O&lt;sub&gt;2&lt;/sub&gt;C&lt;sup&gt;t&lt;/sup&gt;Bu)&lt;sub&gt;2&lt;/sub&gt;(O&lt;sub&gt;2&lt;/sub&gt;C&lt;sup&gt;t&lt;/sup&gt;Bu)2(L)(L0)] (L = HO&lt;sub&gt;2&lt;/sub&gt;C&lt;sup&gt;t&lt;/sup&gt;Bu, L0 = HO&lt;sub&gt;2&lt;/sub&gt;C&lt;sup&gt;t&lt;/sup&gt;Bu (1), pyridine (2), 3-methylpyridine (4); L = L0 = pyridine (3), 3-methylpyridine (5)) has been synthesized and structurally characterized by X-ray crystallography. The magnetic properties have been probed by magnetometry and EPR spectroscopy, and detailed measurements show that the axial zero-field splitting, D, of the nickel(ii) ions is on the same order as the isotropic exchange interaction, J, between the nickel sites. The isotropic exchange interaction can be related to the angle between the nickel centers and the bridging water molecule, while the magnitude of D can be related to the coordination sphere at the nickel sites

A theoretical spectroscopy study of the photoluminescence properties of narrow band Eu²⁺-doped phosphors containing multiple candidate doping centers. Prediction of an unprecedented narrow band red phosphor

We have previously presented a computational protocol that is based on an embedded cluster model and operates in the framework of TD-DFT in conjunction with the excited state dynamics (ESD) approach. The protocol is able to predict the experimental absorption and emission spectral shapes of Eu2+-doped phosphors. In this work, the applicability domain of the above protocol is expanded to Eu2+-doped phosphors bearing multiple candidate Eu doping centers. It will be demonstrated that this protocol provides full control of the parameter space that describes the emission process. The stability of Eu doping at various centers is explored through local energy decomposition (LED) analysis of DLPNO-CCSD(T) energies. This enables further development of the understanding of the electronic structure of the targeted phosphors, the diverse interactions between Eu and the local environment, and their impact on Eu doping probability, and control of the emission properties. Hence, it can be employed to systematically improve deficiencies of existing phosphor materials, defined by the presence of various intensity emission bands at undesired frequencies, towards classes of candidate Eu2+-doped phosphors with desired narrow band red emission. For this purpose, the chosen study set consists of three UCr4C4-based narrow-band phosphors, namely the known alkali lithosilicates RbNa[Li3SiO4]2:Eu2+ (RNLSO2), RbNa3[Li3SiO4]4:Eu2+ (RNLSO) and their isotypic nitridolithoaluminate phosphors consisting of CaBa[LiAl3N4]2:Eu2+ (CBLA2) and the proposed Ca3Ba[LiAl3N4]4:Eu2+ (CBLA), respectively. The theoretical analysis presented in this work led us to propose a modification of the CBLA2 phosphor that should have improved and unprecedented narrow band red emission properties. Finally, we believe that the analysis presented here is important for the future rational design of novel Eu2+-doped phosphor materials, with a wide range of applications in science and technology

Electronic and Optical Properties of Eu²⁺-Activated Narrow-Band Phosphors for Phosphor-Converted Light-Emitting Diode Applications: Insights from a Theoretical Spectroscopy Perspective

In this work, we present a computational protocol that is able to predict the experimental absorption and emission spectral shapes of Eu2+-doped phosphors. The protocol is based on time-dependent density functional theory and operates in conjunction with an excited-state dynamics approach. It is demonstrated that across the study set consisting of representative examples of nitride, oxo-nitride, and oxide Eu2+-doped phosphors, the energy distribution and the band shape of the emission spectrum are related to the nature of the 4f–5d transitions that are probed in the absorption process. Since the 4f orbitals are very nearly nonbonding, the decisive quantity is the covalency of the 5d acceptor orbitals that become populated in the electronically excited state that leads to emission. The stronger the (anti) bonding interaction between the lanthanide and the ligands is in the excited state, the larger will be the excited state distortion. Consequently, the corresponding emission will get broader due to the vibronic progression that is induced by the structural distortion. In addition, the energy separation of the absorption bands that are dominated by states with valence 4f–5d and a metal to ligand charge transfer character defines a measure for the thermal quenching of the studied Eu2+-doped phosphors. Based on this analysis, simple descriptors are identified that show a strong correlation with the energy position and bandwidth of the experimental emission bands without the need for elaborate calculations. Overall, we believe that this study serves as an important reference for designing new Eu2+-doped phosphors with desired photoluminescence properties

Theoretical spectroscopy for unraveling the intensity mechanism of the optical and photoluminescent spectra of chiral Re(I) transition metal complexes

In this work, we present a computational study that is able to predict the optical absorption and photoluminescent properties of the chiral Re(I) family of complexes [fac-ReX(CO)3L], where X is either Cl or I and L is N-heterocyclic carbene extended with π-conjugated [5]-helicenic unit. The computational strategy is based on carefully calibrated time dependent density functional theory calculations and operates in conjunction with an excited state dynamics approach to treat in addition to absorption (ABS) and photoluminescence (PL), electronic circular dichroism (ECD), and circularly polarized luminescence (CPL) spectroscopies, respectively. The employed computational approach provides, an addition, access to the computation of phosphorescence rates in terms of radiative and non-radiative relaxation processes. The chosen molecules consist of representative examples of non-helicenic (NHC) and helicenic diastereomers. The agreement between theoretical and experimental spectra, including absorption (ABS, ECD) and emission (PL, CPL), is excellent, validating a quantitative interpretation of the spectral features on the basis of natural transition orbitals and TheoDore analyses. It is demonstrated that across the set of studied Re(I) diastereomers, the emission process in the case of NHC diastereomers is metal to ligand charge transfer in nature and is dominated by the easy-axis anisotropy of the emissive excited multiplet. On the contrary, in the cases of the helicenic diastereomers, the emission process is intra ligand charge transfer in nature and is dominated by the respective easy-plane anisotropy of the emissive excited multiplet. This affects remarkably the photoluminescent properties of the molecules in terms of PL and CPL spectral band shapes, spin-vibronic coupling, relaxation times, and the respective quantum yields. Spin-vibronic coupling effects are investigated at the level of the state-average complete active space self-consistent field in conjunction with quasi-degenerate second order perturbation theory. It is in fact demonstrated that a spin-vibronic coupling mechanism controls the observed photophysics of this class of Re(I) complexes

Experimental and theoretical correlations between vanadium K-edge X-ray absorption and Kβ emission spectra

A series of vanadium compounds was studied by K-edge X-ray absorption (XAS) and K[Formula: see text] X-ray emission spectroscopies (XES). Qualitative trends within the datasets, as well as comparisons between the XAS and XES data, illustrate the information content of both methods. The complementary nature of the chemical insight highlights the success of this dual-technique approach in characterizing both the structural and electronic properties of vanadium sites. In particular, and in contrast to XAS or extended X-ray absorption fine structure (EXAFS), we demonstrate that valence-to-core XES is capable of differentiating between ligating atoms with the same identity but different bonding character. Finally, density functional theory (DFT) and time-dependent DFT calculations enable a more detailed, quantitative interpretation of the data. We also establish correction factors for the computational protocols through calibration to experiment. These hard X-ray methods can probe vanadium ions in any oxidation or spin state, and can readily be applied to sample environments ranging from solid-phase catalysts to biological samples in frozen solution. Thus, the combined XAS and XES approach, coupled with DFT calculations, provides a robust tool for the study of vanadium atoms in bioinorganic chemistry

L edge X ray absorption study of mononuclear vanadium complexes and spectral predictions using a restricted open shell configuration interaction ansatz

A series of mononuclear V^(V), V^(IV) and V^(III) complexes were investigated by V L-edge near edge X-ray absorption fine structure (NEXAFS) spectroscopy. The spectra show significant sensitivity to the vanadium oxidation state and the coordination environment surrounding the vanadium center. The L-edge spectra are interpreted with the aid of the recently developed Density Functional Theory/Restricted Open Shell Configuration Interaction Singles (DFT/ROCIS) method. This method is calibrated for the prediction of vanadium L-edges with different hybrid density functionals and basis sets. For the B3LYP/def2-TZVP(-f) and BHLYP/def2-TZVP(-f) functional/basis-set combinations, good to excellent agreement between calculated and experimental spectra is obtained. A treatment of the spin–orbit coupling interaction to all orders is achieved by quasi-degenerate perturbation theory (QDPT), in conjunction with DFT/ROCIS for the calculation of the molecular multiplets while accounting for dynamic correlation and anisotropic covalency. The physical origin of the observed spectral features is discussed qualitatively and quantitatively in terms of spin multiplicities, magnetic sublevels and individual 2p to 3d core level excitations. This investigation is an important prerequisite for future applications of the DFT/ROCIS method to vanadium L-edge absorption spectroscopy and vanadium-based heterogeneous catalysts