Restricted Active Space Self-consistent Field Research Articles

Photoionization cross sections and photoelectron angular distributions of molecules with XCHEM-2.0

The XCHEM code was introduced in 2017 [1] to provide an accurate description of electron correlation and exchange in the electronic continuum of molecules at the same level as complete or restricted active-space self-consistent field (CASSCF or RASSCF) methods. This has allowed for an accurate description of molecular photoionization in the region of Feshbach resonances, shake up processes in which ionization is accompanied by excitation of one or several of the remaining electrons, and interchannel couplings. The success of XCHEM for small molecules has led us to improve its performance in several aspects, which now allows for the description of resonant molecular photoionization in larger systems. In addition, we have incorporated the possibility to calculate photoelectron angular distributions in the laboratory and molecular frames, which are essential to interpret angularly resolved photoionization experiments. Here we show its performance in the N2 and pyrazine molecules. The new version of the code, XCHEM-2.0, is freely available at https://gitlab.com/xchem/xchem_public. Program summaryProgram Title: XCHEM-2.0CPC Library link to program files:https://doi.org/10.17632/t8tbk9gdt2.1Developer's repository link:https://gitlab.com/xchem/xchem_public/-/archive/2.0.0/xchem_public-2.0.0.tar.gzLicensing provisions: LGPLProgramming language: Fortran, pythonNature of problem: Understanding photoionization of molecules is a recurrent goal in Atomic, Molecular and Optical physics, even more nowadays with the advent of XUV and X-ray high-harmonic generation sources and free electron lasers. Photoionization can be employed to induce electron dynamics in molecules, e.g., by using ultrashort XUV or X-ray pulses, or as a probe of these dynamics by recording time-resolved photoelectron spectra. At low photoelectron energies, photoionization may result from various competing processes, such as direct ionization, autoionization of Feshbach and shape resonances, shake up, etc., each of these leaving its trace in the measured spectra. So, interpretation of these spectra can be a difficult task and theoretical simulations are often required to separate the different contributions. However, a method able to do so must be able to describe electron correlation in the electronic continuum beyond the Hartree-Fock (HF) and configuration interaction singles (CIS) approximations. XCHEM-2.0 has been designed to account for all these processes by providing an accurate description of electron correlation in the ionization continuum of molecules.Solution method: XCHEM-2.0 employs a close coupling formalism to describe the electronic continuum of molecules at the level of multiference configuration interaction (MRCI) methods in combination with a hybrid Gaussian-Bspline basis set (the so-called GABs basis). In particular, it makes use of a restricted active space self-consistent field (RASSCF) approximation to evaluate the bound electronic states of the remaining molecular cation using localized Gaussian functions. These localized Gaussians are then supplemented with a single centered Gaussian expansion to allow the electron to leave the nuclear environment. Finally, the basis set includes a set of B-spline functions, centered at the same position as the single-centered Gaussians, which reach the asymptotic region. Thanks to the last B-spline function, which does not vanish at the box boundary, XCHEM-2.0 can determine continuum states fulfilling any required asymptotic behavior. The present version of the code improves on the original version by incorporating a more efficient augmentation procedure to build Ne-electron configurations from (Ne−1) ones, reducing the space to store data, providing a more efficient removal of linear dependencies resulting from the over-completeness of the polycentric+GABS basis and a more efficient solution of the scattering equations, and including new routines to calculate photoelectron angular distributions in the laboratory and molecular frames.Additional comments including restrictions and unusual features: The proposed method focuses on RASSCF methodology, so part of electron correlation is still not included. Also, one- and two electron integrals involving exclusively Gaussian functions are done using a modified version of the OpenMOLCAS software, so the installation of this code is also required and limitation associated with the latter is applicable. The code is limited to include a few ionization channels (around 20) with medium angular momentum (limited to ℓ = 15 as in OpenMOLCAS).

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.

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.

Electron and ion spectroscopy of azobenzene in the valence and core shells.

Azobenzene is a prototype and a building block of a class of molecules of extreme technological interest as molecular photo-switches. We present a joint experimental and theoretical study of its response to irradiation with light across the UV to x-ray spectrum. The study of valence and inner shell photo-ionization and excitation processes combined with measurement of valence photoelectron-photoion coincidence and mass spectra across the core thresholds provides a detailed insight into the site- and state-selected photo-induced processes. Photo-ionization and excitation measurements are interpreted via the multi-configurational restricted active space self-consistent field method corrected by second order perturbation theory. Using static modeling, we demonstrate that the carbon and nitrogen K edges of azobenzene are suitable candidates for exploring its photoinduced dynamics thanks to the transient signals appearing in background-free regions of the NEXAFS and XPS.

Compact and accurate ab initio valence bond wave functions for electron transfer: The classic but challenging covalent-ionic interaction in LiF

This paper combines the valence bond block diabatization approach with the idea of orbital breathing. With highly compact wave functions, the breathing orbital valence bond (BOVB) method is applied to investigate several atomic and molecular properties, including the electron affinity of F, the adiabatic and diabatic potential energy curves and the dipole moment curves of the two lowest-lying 1Σ+ states, the electronic coupling curve and the crossing distance of the two diabatic states, and the spectroscopic constants of the ground states for LiF. The configuration selection scheme proposed in this work is quite general, requiring only the selection of several de-excitation and excitation orbitals in a sense like the restricted active space self-consistent field method. Practically, this is also the first time that BOVB results are extrapolated to complete basis set limit. Armed with the chemical intuition provided by valence bond theory, the classic but challenging covalent-ionic interaction in the title molecule is not only conceptually interpreted but also accurately computed.

Multireference Approach to Normal and Resonant Auger Spectra Based on the One-Center Approximation.

A methodology to calculate the decay rates of normal and resonant Auger processes in atoms and molecules based on the One-Center Approximation (OCA), using atomic radial Auger integrals, is implemented within the restricted-active-space self-consistent-field (RASSCF) and the multistate restricted-active-space perturbation theory of second order (MS-RASPT2) frameworks, as part of the OpenMolcas project. To ensure an unbiased description of the correlation and relaxation effects on the initial core excited/ionized states and the final cationic states, their wave functions are optimized independently, whereas the Auger matrix elements are computed with a biorthonormalized set of molecular orbitals within the state-interaction (SI) approach. As a decay of an isolated resonance, the computation of Auger intensities involves matrix elements with one electron in the continuum. However, treating ionization and autoionization problems can be overwhelmingly complicated for nonexperts, because of many peculiarities, in comparison to bound-state electronic structure theory. One of the advantages of our approach is that by projecting the intensities on the atomic center bearing the core hole and using precalculated atomic radial two-electron integrals, the Auger decay rates can be easily obtained directly with OpenMolcas, avoiding the need to interface it with external programs to compute matrix elements with the photoelectron wave function. The implementation is tested on the Ne atom, for which numerous theoretical and experimental results are available for comparison, as well as on a set of prototype closed- and open-shell molecules, namely, CO, N2, HNCO, H2O, NO2, and C4N2H4 (pyrimidine).

Soft X-ray Spectroscopy Simulations with Multiconfigurational Wave Function Theory: Spectrum Completeness, Sub-eV Accuracy, and Quantitative Reproduction of Line Shapes.

Multireference methods are known for their ability to accurately treat states of very different nature in many molecular systems, facilitating high-quality simulations of a large variety of spectroscopic techniques. Here, we couple the multiconfigurational restricted active space self-consistent field RASSCF/RASPT2 method (of the CASSCF/CASPT2 methods family) to the displaced harmonic oscillator (DHO) model, to simulate soft X-ray spectroscopy. We applied such an RASSCF/RASPT2+DHO approach at the K-edges of various second-row elements for a set of small organic molecules that have been recently investigated at other levels of theory. X-ray absorption near-edge structure (XANES) and X-ray photoelectron spectroscopy (XPS) are simulated with a sub-eV accuracy and a correct description of the spectral line shapes. The method is extremely sensitive to the observed spectral shifts on a series of differently fluorinated ethylene systems, provides spectral fingerprints to distinguish between stable conformers of the glycine molecule, and accurately captures the vibrationally resolved carbon K-edge spectrum of formaldehyde. Differences with other theoretical methods are demonstrated, which show the advantages of employing a multireference/multiconfigurational approach. A protocol to systematically increase the number of core-excited states considered while maintaining a contained computational cost is presented. Insight is eventually provided for the effects caused by removing core–electrons from a given atom in terms of bond rearrangement and influence on the resulting spectral shapes within a unitary orbital-based framework for both XPS and XANES spectra.

Spin-Orbit Natural Transition Orbitals and Spin-Forbidden Transitions.

Natural transition orbitals (NTOs) are in widespread use for visualizing and analyzing electronic transitions. The present work introduces the analysis of formally spin-forbidden transitions with the help of complex-valued spin-orbit (SO) NTOs. The analysis specifically focuses on the components in such transitions that cause their intensity to be nonzero because of SO coupling. Transition properties such as transition dipole moments are partitioned into SO-NTO hole-particle pairs, such that contributions to the intensity from specific occupied and unoccupied orbitals are obtained. The method has been implemented within the restricted active space (RAS) self-consistent field wave function theory framework, with SO coupling treated by RAS state interaction. SO-NTOs have a broad range of potential applications, which is illustrated by the T2-S1 state mixing in pyrazine, spin-forbidden versus spin-allowed 4f-5d transitions in the Tb3+ ion, and the phosphorescence of tris(2-phenylpyridine) iridium [Ir(ppy)3].

Computational Study for CO2-to-CO Conversion over Proton Reduction Using [Re[bpyMe(Im-R)](CO)3Cl]+ (R = Me, Me2, and Me4) Electrocatalysts and Comparison with Manganese Analogues

The Nippe group has previously reported a series of imidazolium-functionalized rhenium bipyridyl tricarbonyl electrocatalysts, [Re[bpyMe(Im-R)](CO)3Cl]+ (R = Me and Me2), for CO2-to-CO conversion using H2O as the proton source [Sung, S.; Kumar, D., Electrocatalytic CO2 Reduction by Imidazolium-Functionalized Molecular Catalysts. J. Am. Chem. Soc. 2017, 139, 40, 13993−13996. 10.1021/jacs.7b07709]. These compounds feature charged imidazolium ligands in the secondary coordination sphere and exhibit higher catalytic activities as compared to the Lehn catalyst [Re(bpy)(CO)3Cl] (where bpy = 2,2′-bipyridine). However, the reaction mechanism for the CO2 reduction reaction (CO2RR) over the competing hydrogen evolution reaction (HER) is unclear. Here, we employ density functional theory (DFT) and restricted active space self-consistent field (RASSCF) methods to study the selectivity for CO2 fixation using [Re[bpyMe(ImMe)](CO)3Cl]+ (1+) in water and compare its reactivity to [Re[bpyMe(ImMe2)](CO)3Cl]+ (2+) and [Re[bpyMe(ImMe4)](CO)3Cl]+ (3+). Our results reveal that the turnover frequency (TOF) for CO2RR using 1+ is 4 orders of magnitude higher than for proton reduction, consistent with controlled potential electrolysis (CPE) experiments in which CO was the only detectable reduction product. The imidazolium moiety in the secondary coordination sphere stabilizes the metallocarboxylate species and assists the C–O cleavage through intermolecular hydrogen-bonding stabilizations. Furthermore, our calculations imply that the strongest hydrogen-bonding interactions at the C2 position in 1+ contribute to the faster reaction rate observed experimentally with respect to 2+. More significantly, the use of the energy span model demonstrates that the turnover frequency-determining transition state (TDTS) corresponds to the formation of the Re–CO2 adduct, contrasting with manganese analogues in which the C–O bond cleavage step is the TDTS. We attribute this distinction based on the electronic structures of doubly reduced active catalysts. Indeed, RASSCF calculations indicate that rhenium compounds are best described as a rhenium(I) coupled with a doubly reduced bipyridine ligand, [ReI[bpyMe(ImMe)2–](CO)3]0. In contrast, manganese analogues feature a metal center in a formal zero oxidation state antiferromagnetically coupled with an unpaired electron on the bpy, [Mn0[bpyMe(ImMe)•–](CO)3]0.

Multi-reference approach to the computation of double core-hole spectra.

Double Core-Hole (DCH) states of small molecules are assessed with the restricted active space self-consistent field and multi-state restricted active space perturbation theory of second order approximations. To ensure an unbiased description of the relaxation and correlation effects on the DCH states, the neutral ground-state and DCH wave functions are optimized separately, whereas the spectral intensities are computed with a biorthonormalized set of molecular orbitals within the state-interaction approximation. Accurate shake-up satellite binding energies and intensities of double-core-ionized states (K-2) are obtained for H2O, N2, CO, and C2H2n (n = 1-3). The results are analyzed in detail and show excellent agreement with recent theoretical and experimental data. The K-2 shake-up spectra of H2O and C2H2n molecules are here completely characterized for the first time.

Model protein excited states: MRCI calculations with large active spaces vs CC2 method.

Benchmarking calculations on excited states of models of phenylalanine protein chains are presented to assess the ability of alternative methods to the standard and most commonly used multiconfigurational wave function-based method, the complete active space self-consistent field (CASSCF), in recovering the non-dynamical correlation for systems that become not affordable by the CASSCF. The exploration of larger active spaces beyond the CASSCF limit is benchmarked through three strategies based on the reduction in the number of determinants: the restricted active space self-consistent field, the generalized active space self-consistent field (GASSCF), and the occupation-restricted multiple active space (ORMAS) schemes. The remaining dynamic correlation effects are then added by the complete active space second-order perturbation theory and by the multireference difference dedicated configuration interaction methods. In parallel, the approximate second-order coupled cluster (CC2), already proven to be successful for small building blocks of model proteins in one of our previous works [Ben Amor et al., J. Chem. Phys. 148, 184105 (2018)], is investigated to assess its performances for larger systems. Among the different alternative strategies to CASSCF, our results highlight the greatest efficiency of the GASSCF and ORMAS schemes in the systematic reduction of the configuration interaction expansion without loss of accuracy in both nature and excitation energies of both singlet ππ* and nπ* CO excited states with respect to the equivalent CASSCF calculations. Guidelines for an optimum applicability of this scheme to systems requiring active spaces beyond the complete active space limit are then proposed. Finally, the extension of the CC2 method to such large systems without loss of accuracy is demonstrated, highlighting the great potential of this method to treat accurately excited states, mainly single reference, of very large systems.

Site‐Selective Real‐Time Observation of Bimolecular Electron Transfer in a Photocatalytic System Using L‐Edge X‐Ray Absorption Spectroscopy**

Time‐resolved X‐ray absorption spectroscopy has been utilized to monitor the bimolecular electron transfer in a photocatalytic water splitting system. This has been possible by uniting the local probe and element specific character of X‐ray transitions with insights from high‐level ab initio calculations. The specific target has been a heteroleptic [IrIII(ppy)2(bpy)]+ photosensitizer, in combination with triethylamine as a sacrificial reductant and Fe3(CO)12 as a water reduction catalyst. The relevant molecular transitions have been characterized via high‐resolution Ir L‐edge X‐ray absorption spectroscopy on the picosecond time scale and restricted active space self‐consistent field calculations. The presented methods and results will enhance our understanding of functionally relevant bimolecular electron transfer reactions and thus will pave the road to rational optimization of photocatalytic performance.

Intramolecular Magnetic Interaction in a Photogenerated Dual Angular Momentum System in a Terbium-Phthalocyaninato 1:1 Complex.

Intramolecular magnetic interaction between a localized open-shell 4f-electronic system and a photoexcited macrocyclic π-conjugate system in terbium-phthalocyaninnato (Tb-Pc) 1:1 complex was investigated using variable-temperature variable-field magnetic circular dichroism (VTVH MCD) spectroscopy. The 1:1 complex [Tb(Pc)(cyclen)]Cl (Pc2- = phthalocyaninato dianion, cyclen = 1,4,7,10-tetraazacyclododecane) with the capping ligand providing an exact fourfold symmetry showed a significant temperature dependence and a nonlinear field dependence in the MCD intensity of the Pc-centered highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) π-π* transition, while a diamagnetic congener [Y(Pc)(cyclen)]Cl showed a temperature-independent MCD with a linear-field dependence. This indicates that the (4f)8 system of the Tb ion with a total angular momentum J and the photoexcited π-system of the Pc macrocycle with an orbital angular momentum L are magnetically coupled. By numerical simulation using a model where ground doublet state |Jz⟩ = |±6⟩ and excited quartet state |Jz, Lz⟩ = |±6, ±|Lz|⟩ are included, the J-L interaction magnitude ΔJL and the Pc-centered orbital angular momentum |Lz|ℏ were determined to be 1.1 cm-1 and 2.0 ℏ, respectively. From ab initio restricted active space self-consistent field (RASSCF)-restricted active space state interaction (RASSI) calculations on the π-π* excited states of the Tb complex, the magnitude of the J-L interaction was estimated. The comparison between the calculations on the Y and Tb complexes revealed that the ferromagnetic-type coupling occurs between the orbital component in the J of Tb and the L on Pc, supporting the model that we employed for the analysis of the experimental data.

Description of Two-Particle One-Hole Electronic Resonances Using Orbital Stabilization Methods.

Two-particle one-hole (2p-1h) resonances are elusive to accurate characterization, their decay to the neutral state being a two-electron process. Although in limited cases, single reference methods can be used, a proper description of a 2p-1h resonant state entails a multiconfigurational treatment of the reference wavefunction. In this work, we test the performance of the orbital stabilization method to characterize the 2p-1h resonances found in water and benzene. We employ a set of two multireference approaches, namely, the restricted active space self-consistent field and the multireference configuration interaction, as well as the single reference method equation of motion for electron attachment coupled-cluster with singles and doubles, in the case of benzene. We further explore the resonant channel mixing in benzene between the B2g shape resonance and 2p-1h resonance, a phenomenon which has been explored quite often in experimental studies.

Multireference quantum chemistry protocol for simulating autoionization spectra: Test of ionization continuum models for the neon atom

In this contribution we present a protocol to evaluate partial and total Auger decay rates combining the restricted active space self-consistent field electronic structure method for the bound part of the spectrum and numerically obtained continuum orbitals in the single-channel scattering theory framework. On top of that, the two-step picture is employed to evaluate the partial rates. The performance of the method is exemplified for the prototypical Auger decay of the neon $1s^{-1}3p$ resonance. Different approximations to obtain the continuum orbitals, the partial rate matrix elements, and the electronic structure of the bound part are tested against theoretical and experimental reference data. It is demonstrated that the partial and total rates are most sensitive to the accuracy of the continuum orbitals. For instance, it is necessary to account for the direct Coulomb potential of the ion for the determination of the continuum wave functions. The Auger energies can be reproduced quite well already with a rather small active space. Finally, perspectives of the application of the proposed protocol to molecular systems are discussed.

Automatic Active Space Selection for Calculating Electronic Excitation Energies Based on High-Spin Unrestricted Hartree–Fock Orbitals

Multireference perturbation theory (MR-PT2, e.g., MS-CASPT2) and multiconfiguration pair-density functional theory (MC-PDFT) use a multiconfigurational wave function as the reference wave function, and this can be generated, for example, by the complete active space self-consistent field (CASSCF) method or restricted active space self-consistent field (RASSCF) method. The MR-PT2 and MC-PDFT methods have proved successful in many previous studies, but their performance depends on the quality of the reference wave function, and the quality of a CASSCF or RASSCF wave function depends on the active space. Even for a given number of active electrons and active orbitals, the orbitals obtained at the end of the self-consistent field iterations of the CASSCF calculation may be different for different sets of initial guess orbitals. Consequently, it is a worthwhile goal to automate active space selection, including the choice of orbitals to start the iterations, and here we examine the question of whether we can devise a broadly applicable automatic scheme for producing guess orbitals that lead to an active space that gives accurate excitation energies. Such a scheme depends on the target number of excitation energies that one is trying to calculate, and here our target is the first two spin-conserving excited electronic states of a closed-shell molecule or a doublet radical. For this target, we propose a scheme called ABC2 to automatically select an active space for MC-PDFT calculations and MS-CASPT2 calculations; the scheme uses high-spin-state unrestricted Hartree-Fock (UHF) natural orbitals as guess orbitals. A novel feature of the ABC2 scheme is that it contains a reliability test that should be passed for the results to be considered reliable. This test requires that the MC-PDFT or CASPT2 excitation energy be within 1.1 eV of the CASSCF excitation energy for the result to be considered reliable. We evaluated the performance of ABC2 for the two lowest excitation energies (or only the lowest when an accurate value of the second lowest state is not available) of 16 singlet systems and 10 doublet systems. We compared the performance of ABC2 to that of our previous ABC scheme, which finds active orbitals through a more expensive (multiconfigurational) excited-state calculation, to the use of ground-state UHF natural orbitals, and to the default scheme in OpenMolcas. We found that the new scheme is more robust than previous methods for a variety of systems.

Ab Initio Study of Circular Dichroism and Circularly Polarized Luminescence of Spin-Allowed and Spin-Forbidden Transitions: From Organic Ketones to Lanthanide Complexes.

Complete and restricted active space self-consistent field (CAS-/RAS-SCF) wave function methods are applied for the calculation of circular dichroism (CD) and circularly polarized luminescence (CPL) of a series of molecules comprising four organic ketones, the chiral cobalt(III) complex [Co(en)3]3+, and the europium(III) complex [Eu(DPA)3]3-. The ab initio results are in good agreement with the experimental data and previous results obtained with Kohn-Sham density functional theory in the case of the spin-allowed transitions. CD and CPL properties are calculated ab initio for the spin-forbidden transitions of both a transition metal and a lanthanide complex.

The multiplet electronic structure of UO+ ion: Relativistic two-component ab initio approach

The relativistic two-component ab initio calculations have been carried out to calculate the electronic structure and spectroscopic properties of UO+ ion. The State-Averaged Restricted Active Space Self-Consistent Field (SA-RASSCF) calculations have been performed with spin-orbit effects. The ground state along with a manifold of low-lying spin-orbit states below 12 600 cm−1 have been reported and compared with available results from experiment, Ligand Field Theory (LFT) and previous theoretical results. The configurational assignments along with spectroscopic properties at equilibrium bond distances and also the nature of the potential energy curves have been reported. The ground state Ω = 9/2 at R = 1.790 Å is found to be ionic in nature, U3+(5f3(4I))O2−(1S), with a vibrational frequency of 962 cm−1. The computed excitation energies compare reasonably well with the available experimental counterpart.

Single-ion anisotropy and exchange coupling in cobalt(ii)-radical complexes: insights from magnetic and ab initio studies.

The concurrent effects of single-ion anisotropy and exchange interactions on the electronic structure and magnetization dynamics have been analyzed for a cobalt(ii)-semiquinonate complex. Analogs containing diamagnetic catecholate and tropolonate ligands were employed for comparison of the magnetic behavior and zinc congeners assisted with the spectroscopic characterization and assessment of intermolecular interactions in the cobalt(ii) compounds. Low temperature X-band (ν ≈ 9.4 GHz) and W-Band (ν ≈ 94 GHz) electron paramagnetic resonance spectroscopy and static and dynamic magnetic measurements have been used to elucidate the electronic structure of the high spin cobalt(ii) ion in [Co(Me3tpa)(Br4cat)] (1; Me3tpa = tris[(6-methyl-2-pyridyl)methyl]amine, Br4cat2- = tetrabromocatecholate) and [Co(Me3tpa)(trop)](PF6) (2(PF6); trop- = tropolonate), which show slow relaxation of the magnetization in applied field. The cobalt(ii)-semiquinonate exchange interaction in [Co(Me3tpa)(dbsq)](PF6)·tol (3(PF6)·tol; dbsq- = 3,5-di-tert-butylsemiquinonate, tol = toluene) has been determined using an anisotropic exchange Hamiltonian in conjunction with multistate restricted active space self-consistent field ab initio modeling and wavefunction analysis, with comparison to magnetic and inelastic neutron scattering data. Our results demonstrate dominant ferromagnetic exchange for 3+ that is of similar magnitude to the anisotropy parameters of the cobalt(ii) ion and contains a significant contribution from spin-orbit coupling. The nature of the exchange coupling between octahedral high spin cobalt(ii) and semiquinonate ligands is a longstanding question; answering this question for the specific case of 3+ has confirmed the considerable sensitivity of the exchange to the molecular structure. The methodology employed will be generally applicable for elucidating exchange coupling between orbitally-degenerate metal ions and radical ligands and relevant to the development of bistable molecules and their integration into devices.

Magnetic circular dichroism spectra of transition metal complexes calculated from restricted active space wavefunctions.

First principles multiconfigurational restricted active space (RAS) self-consistent field (SCF) or configuration interaction (CI) approaches, augmented with a treatment of spin-orbit coupling by state interaction, were used to calculate the magnetic circular dichroism (MCD) , , and/or for closed- and open-shell transition metal complexes: PdCl42-, PdBr42-, AuCl4-, AuBr4-, MnO4-, CuCl42-, CuBr42-, and Fe(CN)63-. The were determined with a sum-over-states approach. It is shown that reasonably accurate MCD spectra can be obtained directly at a RAS level or at a RAS level augmented with corrections for the dynamic correlation. The sign and magnitude of the individual MCD terms can be unambiguously determined and assigned to particular electronic transitions.