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).

Correlating Valence and 2p3d RIXS Spectroscopies: A Ligand-Field Study of Spin-Crossover Iron(II).

The molecular spin-crossover phenomenon between high-spin (HS) and low-spin (LS) states is a promising route to next-generation information storage, sensing applications, and molecular spintronics. Spin-crossover complexes also provide a unique opportunity to study the ligand field (LF) properties of a system in both HS and LS states while maintaining the same ligand environment. Presently, we employ complementing valence and core-level spectroscopic methods to probe the electronic excited-state manifolds of the spin-crossover complex [FeII(H2B(pz)2)2phen]0. Light-induced excited spin-state trapping (LIESST) at liquid He temperatures is exploited to characterize magnetic and spectroscopic properties of the photoinduced HS state using SQUID magnetometry and magnetic circular dichroism spectroscopy. In parallel, Fe 2p3d RIXS spectroscopy is employed to examine the ΔS = 0, 1 excited LF states. These experimental studies are combined with state-of-the-art CASSCF/NEVPT2 and CASCI/NEVPT2 calculations characterizing the ground and LF excited states. Analysis of the acquired LF information further supports the notion that the spin-crossover of [FeII(H2B(pz)2)2phen]0 is asymmetric, evidenced by a decrease in eπ in the LS state. The results demonstrate the power of cross-correlating spectroscopic techniques with high and low LF information content to make accurate excited-state assignments, as well as the current capabilities of ab initio theory in interpreting these electronic properties.

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.

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.

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.

Going beyond the electric-dipole approximation in the calculation of absorption and (magnetic) circular dichroism spectra including scalar relativistic and spin-orbit coupling effects.

In this work, a time-dependent density functional theory (TD-DFT) scheme for computing optical spectroscopic properties in the framework of linearly and circularly polarized light is presented. The scheme is based on a previously formulated theory for predicting optical absorption and magnetic circular dichroism (MCD) spectra. The scheme operates in the framework of the full semi-classical field-matter interaction operator, thus generating a powerful and general computational scheme capable of computing the absorption, circular dichroism (CD), and MCD spectra. In addition, our implementation includes the treatment of relativistic effects in the framework of quasidegenerate perturbation theory, which accounts for scalar relativistic effects (in the self-consistent field step) and spin-orbit coupling (in the TD-DFT step), as well as external magnetic field perturbations. Hence, this formalism is also able to probe spin-forbidden transitions. The random orientations of molecules are taken into account by a semi-numerical approach involving a Lebedev numerical quadrature alongside analytical integration. It is demonstrated that the numerical quadrature requires as few as 14 points for satisfactory converged results, thus leading to a highly efficient scheme, while the calculation of the exact transition moments creates no computational bottlenecks. It is demonstrated that at zero magnetic field, the CD spectrum is recovered, while the sum of left and right circularly polarized light contributions provides the linear absorption spectrum. The virtues of this efficient and general protocol are demonstrated on a selected set of organic molecules where the various contributions to the spectral intensities have been analyzed in detail.

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.

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.

Magnetic Properties and Electronic Structure of the S = 2 Complex [MnIII{(OPPh2)2N}3] Showing Field-Induced Slow Magnetization Relaxation.

The high-spin S = 2 Mn(III) complex [Mn{(OPPh2)2N}3] (1Mn) exhibits field-induced slow relaxation of magnetization (Inorg. Chem. 2013, 52, 12869). Magnetic susceptibility and dual-mode X-band electron paramagnetic resonance (EPR) studies revealed a negative value of the zero-field-splitting (zfs) parameter D. In order to explore the magnetic and electronic properties of 1Mn in detail, a combination of experimental and computational studies is presented herein. Alternating-current magnetometry on magnetically diluted samples (1Mn/1Ga) of 1Mn in the diamagnetic gallium analogue, [Ga{(OPPh2)2N}3], indicates that the slow relaxation behavior of 1Mn is due to the intrinsic properties of the individual molecules of 1Mn. Investigation of the single-crystal magnetization of both 1Mn and 1Mn/1Ga by a micro-SQUID device reveals hysteresis loops below 1 K. Closed hysteresis loops at a zero direct-current magnetic field are observed and attributed to fast quantum tunneling of magnetization. High-frequency and -field EPR (HFEPR) spectroscopic studies reveal that, apart from the second-order zfs terms (D and E), fourth-order terms (B4m) are required in order to appropriately describe the magnetic properties of 1Mn. These studies provide accurate spin-Hamiltonian (sH) parameters of 1Mn, i.e., zfs parameters |D| = 3.917(5) cm-1, |E| = 0.018(4) cm-1, B04 = B42 = 0, and B44 = (3.6 ± 1.7) × 10-3 cm-1 and g = [1.994(5), 1.996(4), 1.985(4)], and confirm the negative sign of D. Parallel-mode X-band EPR studies on 1Mn/1Ga and CH2Cl2 solutions of 1Mn probe the electronic-nuclear hyperfine interactions in the solid state and solution. The electronic structure of 1Mn is investigated by quantum-chemical calculations by employing recently developed computational protocols that are grounded on ab initio wave function theory. From computational analysis, the contributions of spin-spin and spin-orbit coupling to the magnitude of D are obtained. The calculations provide also computed values of the fourth-order zfs terms B4m, as well as those of the g and hyperfine interaction tensor components. In all cases, a very good agreement between the computed and experimentally determined sH parameters is observed. The magnetization relaxation properties of 1Mn are rationalized on the basis of the composition of the ground-state wave functions in the absence or presence of an external magnetic field.

Kß X-Ray Emission Spectroscopic Study of a Second-Row Transition Metal (Mo) and Its Application to Nitrogenase-Related Model Complexes.

In recent years, X-ray emission spectroscopy (XES) in the Kß (3p-1s) and valence-to-core (valence-1s) regions has been increasingly used to study metal active sites in (bio)inorganic chemistry and catalysis, providing information about the metal spin state, oxidation state and the identity of coordinated ligands. However, to date this technique has been limited almost exclusively to first-row transition metals. In this work, we present an extension of Kß XES (in both the 4p-1s and valence-to-1s [or VtC] regions) to the second transition row by performing a detailed experimental and theoretical analysis of the molybdenum emission lines. It is demonstrated in this work that Kß2 lines are dominated by spin state effects, while VtC XES of a 4d transition metal provides access to metal oxidation state and ligand identity. An extension of Mo Kß XES to nitrogenase-relevant model complexes shows that the method is sufficiently sensitive to act as a spectator probe for redox events that are localized at the Fe atoms. Mo VtC XES thus has promise for future applications to nitrogenase, as well as a range of other Mo-containing biological cofactors. Further, the clear assignment of the origins of Mo VtC XES features opens up the possibility of applying this method to a wide range of second-row transition metals, thus providing chemists with a site-specific tool for the elucidation of 4d transition metal electronic structure.

Mechanism of L2,3-edge x-ray magnetic circular dichroism intensity from quantum chemical calculations and experiment-A case study on V(IV)/V(III) complexes.

In this work, we present a combined experimental and theoretical study on the V L2,3-edge x-ray absorption (XAS) and x-ray magnetic circular dichroism (XMCD) spectra of VIVO(acac)2 and VIII(acac)3 prototype complexes. The recorded V L2,3-edge XAS and XMCD spectra are richly featured in both V L3 and L2 spectral regions. In an effort to predict and interpret the nature of the experimentally observed spectral features, a first-principles approach for the simultaneous prediction of XAS and XMCD spectra in the framework of wavefunction based ab initio methods is presented. The theory used here has previously been formulated for predicting optical absorption and MCD spectra. In the present context, it is applied to the prediction of the V L2,3-edge XAS and XMCD spectra of the VIVO(acac)2 and VIII(acac)3 complexes. In this approach, the spin-free Hamiltonian is computed on the basis of the complete active space configuration interaction (CASCI) in conjunction with second order N-electron valence state perturbation theory (NEVPT2) as well as the density functional theory (DFT)/restricted open configuration interaction with singles configuration state functions based on a ground state Kohn-Sham determinant (ROCIS/DFT). Quasi-degenerate perturbation theory is then used to treat the spin-orbit coupling (SOC) operator variationally at the many particle level. The XAS and XMCD transitions are computed between the relativistic many particle states, considering their respective Boltzmann populations. These states are obtained from the diagonalization of the SOC operator along with the spin and orbital Zeeman operators. Upon averaging over all possible magnetic field orientations, the XAS and XMCD spectra of randomly oriented samples are obtained. This approach does not rely on the validity of low-order perturbation theory and provides simultaneous access to the calculation of XMCD A, B, and C terms. The ability of the method to predict the XMCD C-term signs and provide access to the XMCD intensity mechanism is demonstrated on the basis of a generalized state coupling mechanism based on the type of the excitations dominating the relativistically corrected states. In the second step, the performance of CASCI, CASCI/NEVPT2, and ROCIS/DFT is evaluated. The very good agreement between theory and experiment has allowed us to unravel the complicated XMCD C-term mechanism on the basis of the SOC interaction between the various multiplets with spin S' = S, S ± 1. In the last step, it is shown that the commonly used spin and orbital sum rules are inadequate in interpreting the intensity mechanism of the XAS and XMCD spectra of the VIVO(acac)2 and VIII(acac)3 complexes as they breakdown when they are employed to predict their magneto-optical properties. This conclusion is expected to hold more generally.

Accurate Band Gap Predictions of Semiconductors in the Framework of the Similarity Transformed Equation of Motion Coupled Cluster Theory.

In this work, we present a detailed comparison between wave-function-based and particle/hole techniques for the prediction of band gap energies of semiconductors. We focus on the comparison of the back-transformed Pair Natural Orbital Similarity Transformed Equation of Motion Coupled-Cluster (bt-PNO-STEOM-CCSD) method with Time Dependent Density Functional Theory (TD-DFT) and Delta Self Consistent Field/DFT (Δ-SCF/DFT) that are employed to calculate the band gap energies in a test set of organic and inorganic semiconductors. Throughout, we have used cluster models for the calculations that were calibrated by comparing the results of the cluster calculations to periodic DFT calculations with the same functional. These calibrations were run with cluster models of increasing size until the results agreed closely with the periodic calculation. It is demonstrated that bt-PNO-STEOM-CC yields accurate results that are in better than 0.2 eV agreement with the experiment. This holds for both organic and inorganic semiconductors. The efficiency of the employed computational protocols is thoroughly discussed. Overall, we believe that this study is an important contribution that can aid future developments and applications of excited state coupled cluster methods in the field of solid-state chemistry and heterogeneous catalysis.

Comparison of multireference ab initio wavefunction methodologies for X-ray absorption edges: A case study on [Fe(II/III)Cl4]2-/1- molecules.

In this work, we present a detailed comparison of wavefunction-based multireference (MR) techniques for the prediction of transition metal L-edge X-ray absorption spectroscopy (XAS) using [Fe(II)Cl4]2- and [Fe(III)Cl4]1- complexes as prototypical test cases. We focus on the comparison of MR Configuration Interaction (MRCI) and MR Equation of Motion Coupled Cluster (MREOM-CC) methods, which are employed to calculate valence excitation as well as core to valence Fe L-edge XAS spectra of [Fe(II)Cl4]2- and [Fe(III)Cl4]1- complexes. The two investigated approaches are thoroughly analyzed with respect to their information content regarding (1) metal-ligand covalency, (2) ligand field splittings, (3) relativistic effects, (4) electron correlation, (5) energy distribution, and (6) intensity modulation of the experimentally observed spectral features. It is shown that at the level of MRCI calculations in both [Fe(II)Cl4]2- and [Fe(III)Cl4]1- cases, very good agreement with the experimental Fe L-edge XAS spectra is obtained provided that the employed active space is extended to include ligand-based orbitals in addition to metal-based molecular orbitals. It is shown that this is necessary in order to correctly describe the important σ- and π- Fe-Cl covalent interactions. By contrast, MREOM-CC calculations yield excellent agreement relative to experiment even with small active spaces. The efficiency of the employed MR computational protocols is thoroughly discussed. Overall, we believe that this study serves as an important reference for future developments and applications of MR methods in the field of X-Ray spectroscopy.

Chemistry and Quantum Mechanics in 2019: Give Us Insight and Numbers.

This Perspective revisits Charles Coulson's famous statement from 1959 "give us insight not numbers" in which he pointed out that accurate computations and chemical understanding often do not go hand in hand. We argue that today, accurate wave function based first-principle calculations can be performed on large molecular systems, while tools are available to interpret the results of these calculations in chemical language. This leads us to modify Coulson's statement to "give us insight and numbers". Examples from organic, inorganic, organometallic and surface chemistry as well as molecular magnetism illustrate the points made.

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.

Ab Initio Wave Function-Based Determination of Element Specific Shifts for the Efficient Calculation of X-ray Absorption Spectra of Main Group Elements and First Row Transition Metals.

In this study, a detailed calibration of the performance of modern ab initio wave function methods in the domain of X-ray absorption spectroscopy (XAS) is presented. It has been known for some time that for a given level of approximation, for example, using time-dependent density functional theory (TD-DFT) in conjunction with a given basis set, there are systematic deviations of the calculated transition energies from their experimental values that depend on the functional, the basis set, and the chosen treatment of scalar relativistic effects. This necessitates a linear correlation for a given element/functional/basis set combination to be established before chemical applications can be performed. This is a laborious undertaking since it involves sourcing trustworthy experimental data, lengthy geometry optimizations, and detailed comparisons between theory and experiment. In this work, reference values for the element-specific shifts of all the first-row transition metal atoms and the main group elements C, N, O, F, Si, P, S, and Cl have been computed by using a protocol that is based on the complete active space configuration interaction in conjunction with second-order N-electron valence state perturbation theory (CASCI/NEVPT2). It is shown that by extrapolating the results to the basis set limit of the method and taking into account scalar relativistic effects via the second-order Douglas-Kroll-Hess (DKH2) corrections, the predicted element shifts are on average less than 0.75 eV across all the absorption edges and a very good agreement between theory and experiment in all the studied XAS cases is observed. The transferability of these errors to molecular systems is thoroughly investigated. The constructed CASCI/NEVPT2 database of element shifts is used to evaluate the performance and to automatically calibrate prior to comparison with the experiment two commonly used methods in X-ray spectroscopy, namely, DFT/Restricted open shell configuration interaction singles (DFT/ROCIS) and TD-DFT methods.

Investigations of the Magnetic and Spectroscopic Properties of V(III) and V(IV) Complexes.

Herein, we utilize a variety of physical methods including magnetometry (SQUID), electron paramagnetic resonance (EPR), and magnetic circular dichroism (MCD), in conjunction with high-level ab initio theory to probe both the ground and ligand-field excited electronic states of a series of V(IV) ( S = 1/2) and V(III) ( S = 1) molecular complexes. The ligand fields of the central metal ions are analyzed with the aid of ab initio ligand-field theory (AILFT), which allows for a chemically meaningful interpretation of multireference electronic structure calculations at the level of the complete-active-space self-consistent field with second-order N-electron valence perturbation theory. Our calculations are in good agreement with all experimentally investigated observables (magnetic properties, EPR, and MCD), making our extracted ligand-field theory parameters realistic. The ligand fields predicted by AILFT are further analyzed with conventional angular overlap parametrization, allowing the ligand field to be decomposed into individual σ- and π-donor contributions from individual ligands. The results demonstrate in VO2+ complexes that while the axial vanadium-oxo interaction dominates both the ground- and excited-state properties of vanadyl complexes, proximal coordination can significantly modulate the vanadyl bond covalency. Similarly, the electronic properties of V(III) complexes are particularly sensitive to the available σ and π interactions with the surrounding ligands. The results of this study demonstrate the power of AILFT-based analysis and provide the groundwork for the future analysis of vanadium centers in homogeneous and heterogeneous catalysts.

Pair Natural Orbital Restricted Open-Shell Configuration Interaction (PNO-ROCIS) Approach for Calculating X-ray Absorption Spectra of Large Chemical Systems.

In this work, the efficiency of first-principles calculations of X-ray absorption spectra of large chemical systems is drastically improved. The approach is based on the previously developed restricted open-shell configuration interaction singles (ROCIS) method and its parametrized version, based on a density functional theory (DFT) ground-state determinant ROCIS/DFT. The combination of the ROCIS or DFT/ROCIS methods with the well-known machinery of the pair natural orbitals (PNOs) leads to the new PNO-ROCIS and PNO-ROCIS/DFT variants. The PNO-ROCIS method can deliver calculated metal K-, L-, and M-edge XAS spectra orders of magnitude faster than ROCIS while maintaining an accuracy with calculated spectral parameters better than 1% relative to the original ROCIS method (referred to as canonical ROCIS). The method is of a black box character, as it does not require any user adjustments, while it scales quadratically with the system size. It is shown that for large systems, the size of the virtual molecular orbital (MO) space is reduced by more than 90% with respect to the canonical ROCIS method. This allows one to compute the X-ray absorption spectra of a variety of large "real-life" chemical systems featuring hundreds of atoms using a first-principles wave-function-based approach. Examples chosen from the fields of bioinorganic and solid-state chemistry include the Co K-edge XAS spectrum of aquacobalamin [H2OCbl]+, the Fe L-edge XAS spectrum of deoxymyoglobin (DMb), the Ti L-edge XAS spectrum of rutile TiO2, and the Fe M-edge spectrum of α-Fe2O3 hematite. In the largest calculations presented here, molecules with more than 700 atoms and cluster models with more than 50 metal centers were employed. In all the studied cases, very good to excellent agreement with experiment is obtained. It will be shown that the PNO-ROCIS method provides an unprecedented performance of wave-function-based methods in the field of computational X-ray spectroscopy.

A combined experimental and theoretical spectroscopic protocol for determination of the structure of heterogeneous catalysts: developing the information content of the resonance Raman spectra of M1 MoVO x.

Absorption and multiwavelength resonance Raman spectroscopy are widely used to investigate the electronic structure of transition metal centers in coordination compounds and extended solid systems. In combination with computational methodologies that have predictive accuracy, they define powerful protocols to study the spectroscopic response of catalytic materials. In this work, we study the absorption and resonance Raman spectra of the M1 MoVO x catalyst. The spectra were calculated by time-dependent density functional theory (TD-DFT) in conjunction with the independent mode displaced harmonic oscillator model (IMDHO), which allows for detailed bandshape predictions. For this purpose cluster models with up to 9 Mo and V metallic centers are considered to represent the bulk structure of MoVO x . Capping hydrogens were used to achieve valence saturation at the edges of the cluster models. The construction of model structures was based on a thorough bonding analysis which involved conventional DFT and local coupled cluster (DLPNO-CCSD(T)) methods. Furthermore the relationship of cluster topology to the computed spectral features is discussed in detail. It is shown that due to the local nature of the involved electronic transitions, band assignment protocols developed for molecular systems can be applied to describe the calculated spectral features of the cluster models as well. The present study serves as a reference for future applications of combined experimental and computational protocols in the field of solid-state heterogeneous catalysis.

A Restricted Open Configuration Interaction with Singles Method To Calculate Valence-to-Core Resonant X-ray Emission Spectra: A Case Study.

In this work, a new protocol for the calculation of valence-to-core resonant X-ray emission (VtC RXES) spectra is introduced. The approach is based on the previously developed restricted open configuration interaction with singles (ROCIS) method and its parametrized version, based on a ground-state Kohn-Sham determinant (DFT/ROCIS) method. The ROCIS approach has the following features: (1) In the first step approximation, many-particle eigenstates are calculated in which the total spin is retained as a good quantum number. (2) The ground state with total spin S and excited states with spin S' = S, S ± 1, are obtained. (3) These states have a qualitatively correct multiplet structure. (4) Quasi-degenerate perturbation theory is used to treat the spin-orbit coupling operator variationally at the many-particle level. (5) Transition moments are obtained between the relativistic many-particle states. The method has shown great potential in the field of X-ray spectroscopy, in particular in the field of transition-metal L-edge, which cannot be described correctly with particle-hole theories. In this work, the method is extended to the calculation of resonant VtC RXES [alternatively referred to as 1s-VtC resonant inelastic X-ray scattering (RIXS)] spectra. The complete Kramers-Dirac-Heisenerg equation is taken into account. Thus, state interference effects are treated naturally within this protocol. As a first application of this protocol, a computational study on the previously reported VtC RXES plane on a molecular managanese(V) complex is performed. Starting from conventional X-ray absorption spectra (XAS), we present a systematic study that involves calculations and electronic structure analysis of both the XAS and non-resonant and resonant VtC XES spectra. The very good agreement between theory and experiment, observed in all cases, allows us to unravel the complicated intensity mechanism of these spectroscopic techniques as a synergic function of state polarization and interference effects. In general, intense features in the RIXS spectra originate from absorption and emission processes that involve nonorthogonal transition moments. We also present a graphical method to determine the sign of the interference contributions.