CASSCF Calculations Research Articles

Tolane-Based Phosphino- and Arsino-Ruthenium Complexes in Three Different Oxidation States: Ru(I), Ru(II) and Ru(III).

Targeting Ru(III) and Ru(I) η2-alkyne species, 2,2'-(iPr2E)2-substituted diphenylacetylenes (1-E, E = P, As) were em-ployed for the pre-paration of [ECCE]-coordinated ruthenium com-plexes. The re-actions between 1-E and cis-(MeCN)2(COD)RuCl2 led to the required Ru(II) starting materials cis-[ECCE]RuCl2(MeCN) (3-E). Upon oxi-dation of 3-E with PhICl2, the Ru(III) target com-plexes [ECCE]RuCl3 (7-E) were detectable for E = P and E = As, but only the arsa-deriva-tive 7-As was obtained in a pure form, namely via oxi-da-tion of cis-[AsCCAs]RuCl2(THT) (THT = tetrahydrothiophene). Upon re-duction of compounds 3-E, a hitherto unprecedented Ru(I) η2-alkyne complex, [PCCP]RuCl (9), was obtained for E = P. The former square planar Ru(I) complex (9) was characterized com-prehensively and examined in detail by means of DFT and CASSCF calculation. Upon treatment of 9 with TlPF6, a diamagnetic µ-Tl-bridged compound (10) with a nearly linear Ru-Tl-Ru array was formed and isolated in high yields. Careful analysis of the bonding situation suggested that the Ru-Tl-Ru moiety in 10 is best interpreted in terms of a 3c-4e- bond.

Dinuclear Rare-Earth β-Diketiminates with Bridging 3,5-Ditert-butyl-catecholates: Synthesis, Structure, and Single-Molecule Magnet Properties.

The dinuclear β-diketiminato complex [L1ClDy(μ-Cl)3DyL1(THF)] (1) (L1 = {2,6-iPr2C6H3-NC(Me)CHC(Me)N-2,6-iPr2C6H3}-) was obtained by reaction of DyCl3 with KL1 in a molar ratio of 1:1 and used for the preparation of the mixed-ligand complex [L1Dy(μ-3,5-Cat)]2 (2) by salt metathesis reaction with 3,5-CatK2 (3,5-Cat -3,5-di-tert-butyl-catecholate). Reactions of 3,5-CatNa2 with [L2LnCl2(THF)2] (Ln3+ = Dy, Y) ligated with the less bulky ligand L2 = {2,4,6-Me3C6H2-NC(Me)CHC(Me)N-2,4,6-Me3C6H2}- afforded the mixed-ligand THF-containing complexes [L2Ln(μ-3,5-Cat)(THF)]2 (Ln3+ = Dy (3a), Y (3b)). All new complexes were fully characterized, and the solid-state structures were determined by single-crystal X-ray diffraction. Magnetic measurements revealed single-molecule magnet behavior for the dysprosium complexes. Sub-Kelvin μSQUID studies confirm the SMM character of the systems, while CASSCF calculation along with simulation of the experimental data yields an antiferromagnetic interaction operating between the Dy3+ ions.

A Constrained CASSCF(2,2) Approach to Study Electron Transfer between a Molecule and Metal Cluster.

We have implemented a constrained CASSCF(2,2) calculation so as to study thermal electron transfer between a chlorine ion and a cluster of lithium atoms of variable size (from 1 to 17). Our calculations illustrate how the geometry of the ground state-charge transfer state crossing point (as well as the strength of a diabatic coupling) can depend sensitively on the number of metal ions (i.e., the size of the cluster) and the relative positioning of the donor and acceptor. Thus, this set of calculations is an initial step toward understanding the transition from homogeneous to heterogeneous electron transfer. In the future, these constrained calculations should allow us to model still far larger systems, ideally opening up a pathway to study meaningful electrochemical phenomena.

The Role of a Redox‐Active Ligand in Cu(II)‐Nitrenoid Formation and Its Aziridination Reactivity

AbstractMetal‐nitrenoid species are the key intermediate in nitrene transfer reactions. The bond formation between the open‐shell transition metal and the nitrene species dictates their overall reactivity. Herein, we present an in‐depth electronic structure investigation to uncover how the formation of a Cu(II)‐nitrenoid species is assisted by redox‐active iminosemiquinone (ISQ) ligand in the [CuII(LISQ)2] complex and impacts the nitrene transfer reactivity. The reaction energetics of the aziridination reaction between N‐tosyliminophenyliodinane and 4‐chlorostyrene is established by DFT calculations, where the formation of the Cu(II)‐nitrenoid intermediate (Int1) is found to be the rate‐determining step. Based on the natural orbital and spin populations obtained from the ab initio multiconfigurational CASSCF(13,13) calculation, the electronic nature of the elusive Cu(II)‐nitrenoid intermediate (Int1) could be formulated as “imidyl” [(LISQ)(LIBQ)CuII─•NTos] (Tos = Tosyl) species. A weak σ interaction between the Cu(II) center and the N‐atom of the nitrene moiety (Cu 20% + N 29%) involving a Cu─N distance of 1.92 Å defines the Cu‐nitrenoid bonding. The interplay between elongated Cu─N bond and high‐spin population on N‐atom (+0.96) corroborates its high nitrene transfer ability. Furthermore, the intrinsic bond orbital (IBO) analysis unravels a ligand‐to‐substrate electron transfer mechanism that facilitates the formation of the crucial Cu(II)‐nitrenoid species.

Structure, Covalency, and Paramagnetism of Homoleptic Actinide and Lanthanide Amidinate Complexes.

Isostructural trivalent lanthanide and actinide amidinates bearing the N,N'-bis(isopropyl)benzamidinate (iPr2BA) ligand [LnIII/AnIII(iPr2BA)3] (Ln = La, Nd, Sm, Eu, Yb, Lu; An = U, Np) have been synthesized and characterized in both solid and solution states. All compounds were examined in the solid state utilizing single crystal X-ray diffraction (SC-XRD), revealing a notable deviation in the actinide series with shortened bond lengths compared to the trend in the lanthanide series, suggesting a nonionic contribution to the actinide-ligand bonding. Quantum-chemical bonding analysis further elucidated the nature of these interactions, highlighting increased covalency within the actinide series, as evidenced by higher delocalization indices and greater 5f orbital occupation, except for Th(III) and Pa(III), which demonstrated substantial 6d orbital occupancies. An in-depth paramagnetic NMR study in solution also sheds light on the covalent character of actinide-ligand bonding, with the separation of pseudocontact (PCS) and contact shift (FCS) contributions employing the Bleaney and Reilley method. This analysis unveiled significant contact contributions in the actinide complexes, indicating enhanced covalency in actinide-ligand bonding. To corroborate these observations, an accurate PCS calculation method based on the Kuprov equation, incorporating both the distribution of electronic spin density and magnetic susceptibility obtained from CASSCF calculations, was applied and compared with experimental values.

Theoretical Study of an Authentic Hydrocarbon Ion Pair.

For many years researchers believed that hydrocarbons only contain covalent bonds. However, since 1985 Okamoto et al. demonstrated the formation of hydrocarbon salts in several systems, demolishing the structural principle that hydrocarbons only contain covalent bonds. Despite the great importance of this outcome to the study of chemical bonds, quantum chemical calculations on these systems are essentially nonexistent. The stability of the hydrocarbon ions along with the steric hindrance associated with the formation of the covalent bond contribute to their occurrence either in solution (dissociated) or in the solid state. These facts along with the common formation of ion pairs in solvents of low polarity motivated us to search for hydrocarbon ion pairs in the gas phase. Its energetics has also been studied in four nonprotic solvents, through a continuum solvation model (CPCM). DFT and CASSCF calculations indicate a metastable and highly polar ion pair between the tricyclopropylcyclopropenylium cation and a simplified Kuhn's anion. The barrier to the covalent structure varies from ∼4.8 to 14.4 kcal/mol, while the energy difference between the ion pair and the covalent form varies from ∼4.3 to 25.4 kcal/mol. The obtained theoretical results along with previous experimental results suggest the following strategy to obtain kinetically and thermodynamically stable hydrocarbon ion pairs: choose very stable hydrocarbon ions and systematically increase the steric hindrance between them.

Divergent Interaction of (Iso)nitriles with a Linear Iron(I) Silylamide─A Combined Structural, Spectroscopic, and Computational Study.

Nitriles and isonitriles are important σ-donor ligands in coordination chemistry. Isonitriles also function in low-valent complexes as π-acceptor ligands similar to CO. Herein we present the unusual behavior of the highly reducing, high-spin iron(I) complex [Fe(hmds)2]- toward these compound classes. Rare examples of side-on coordination of nitriles to the metal center are observed. Insights gained by 57Fe Mössbauer spectroscopy as well as DFT and CASSCF calculations give an interplay between the resonance structures of not only an iron(I) π-complex and an iron(III) metallacycle but also point to the importance of an iron(II) nitrile radical anion. For an aromatic isonitrile end-on coordination is observed, which is best described as an iron(I) complex with only minor unpaired spin transfer onto the isonitrile. For aliphatic isonitriles, the selective R-CN bond cleavage occurs and yields stoichiometric mixtures of alkyl iron(II) and cyanido iron(II) complexes. Attempts to isolate presumed (iso)nitrile radical anions void of 3d-metal coordination give for the reaction of an aromatic isonitrile with KC8 facile reductive coupling to the corresponding diamido acetylene.

Wavelength-dependent photoisomerization of trans-4,4′-azopyridine: Nonadiabatic dynamics simulation

The trans–cis photoisomerization processes of 4,4′-azopyridine upon S1 and S2 excitations have been investigated by nonadiabatic dynamics simulations based on multi-reference CASSCF calculations. 119 sampling trajectories were simulated starting from the trans form excited to the S1 (S2) state and the cis-isomer quantum yield is evaluated to be (3 ± 2)% ((18 ± 4)%), which is qualitatively in agreement with the recent experimental results in ethanol. We found that rotation around the central N-N bond accompanied by the N-N-C symmetrical bending vibrations is the main mechanism in photoisomerization of the target molecule excited to the S1 and S2 states. Upon S1 excitation, S1-S0 transition occurs earlier along the C-N-N-C torsional coordinate, leading to a low cis-isomer quantum yield. Upon S2 excitation, half of the simulated trajectories are trapped in a potential well on the S2 state, from which the twisted conical intersections are more easily reached in the internal conversion, resulting in a higher cis-isomer quantum yield.

Linear, Electron-Rich Erbium Single-Molecule Magnet with Dibenzocyclooctatetraene Ligands.

Judicious design of ligand scaffolds to highly anisotropic lanthanide ions led to substantial advances in molecular spintronics and single-molecule magnetism. Erbium-based single-molecule magnets (SMMs) are rare, which is attributed to the prolate-shaped ErIII ion requiring an equatorial ligand field for enhancing its single-ion magnetic anisotropy. Here, we present an electron-rich mononuclear Er SMM, [K(crypt-222)][Er(dbCOT)2], 1 (where dbCOT = dibenzocyclooctatetraene), that was obtained from a salt metathesis reaction of ErCl3 and K2dbCOT. The dipotassium salt, K2dbCOT, was generated through a two-electron reduction of the bare dbCOT0 ligand employing potassium graphite and was crystallized from DME to give the new solvated complex, [K(DME)]2[dbCOT]n, 2. 1 was analyzed through crystallography, electrochemistry, spectroscopy, magnetometry, and CASSCF calculations. The structure of 1 consists of an anionic metallocene complex featuring a linear (180.0°) geometry with an ErIII ion sandwiched between dianionic dbCOT ligands and an outer-sphere K+ ion encapsulated in 2.2.2-cryptand. Two pronounced redox events at negative potentials allude to the formation of a trianionic erbocene complex, [Er(dbCOT)2]3-, on the electrochemical time scale. 1 shows slow magnetic relaxation with an effective spin-reversal barrier of Ueff = 114(2) cm-1, which is close in magnitude to the calculated energies of the first and second excited states of 96.9 and 109.13 cm-1, respectively. 1 exhibits waist-constricted hysteresis loops below 4 K and constitutes the first example of an erbocene-SMM bearing fused aromatic rings to the central COT ligand. Notably, 1 comprises the largest COT scaffold implemented in erbocene SMMs, yielding the most electron-rich homoleptic erbium metallocene SMM.

Selective Transition Enhancement in a g-Engineered Diradical.

A diradical with engineered g-asymmetry was synthesized by grafting a nitroxide radical onto the [Y(Pc)2]⋅ radical platform. Various spectroscopic techniques and computational studies revealed that the electronic structures of the two spin systems remained minimally affected within the diradical system. Fluid-solution Electron Paramagnetic Resonance (EPR) experiments revealed a weak exchange coupling with |J| ~ 0.014 cm-1, subsequently rationalized by CAS-SCF calculations. Frozen solution continuous-wave (CW) EPR experiments showed a complicated and power-dependent spectrum that eluded analysis using the point-dipole model. Pulse EPR manipulations with varying microwave powers, or under varying magnetic fields, demonstrated that different resonances could be selectively enhanced or suppressed, based on their different tipping angles. In particular, Field-Swept Echo-Detected (FSED) spectra revealed absorptions of MW power-dependent intensities, while Field-Swept Spin Nutation (FSSN) experiments revealed two distinct Rabi frequencies. This study introduces a methodology to synthesize and characterize g-asymmetric two-spin systems, of interest in the implementation of spin-based CNOT gates.

Quantum Equation of Motion with Orbital Optimization for Computing Molecular Properties in Near-Term Quantum Computing.

Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is how to use imperfect near-term quantum computers to solve problems of practical value. Inspired by the recently developed variants of the quantum counterpart of the equation-of-motion (qEOM) approach and the orbital-optimized variational quantum eigensolver (oo-VQE), we present a quantum algorithm (oo-VQE-qEOM) for the calculation of molecular properties by computing expectation values on a quantum computer. We perform noise-free quantum simulations of BeH2 in the series of STO-3G/6-31G/6-31G* basis sets and of H4 and H2O in 6-31G using an active space of four electrons and four spatial orbitals (8 qubits) to evaluate excitation energies, electronic absorption, and, for twisted H4, circular dichroism spectra. We demonstrate that the proposed algorithm can reproduce the results of conventional classical CASSCF calculations for these molecular systems.

How electrons still guard the space: Electron number distribution functions based on QTAIM∩ELF intersections.

Despite the importance of the one-particle picture provided by the orbital paradigm, a rigorous understanding of the spatial distribution of electrons in molecules is still of paramount importance to chemistry. Considerable progress has been made following the introduction of topological approaches, capable of partitioning space into chemically meaningful regions. They usually provide atomic partitions, for example, through the attraction basins of the electron density in the quantum theory of atoms in molecules (QTAIM) or electron-pair decompositions, as in the case of the electron localization function (ELF). In both cases, the so-called electron distribution functions (EDFs) provide a rich statistical description of the electron distribution in these spatial domains. Here, we take the EDF concept to a new fine-grained limit by calculating EDFs in the QTAIM ∩ ELF intersection domains. As shown in AHn systems based on main group elements, as well as in the CO, NO, and BeO molecules, this approach provides an exquisitely detailed picture of the electron distribution in molecules, allowing for an insightful combination of the distribution of electrons between Lewis entities (such as bonds and lone pairs) and atoms at the same time. Besides mean-field calculations, we also explore the impact of electron correlation through Hartree-Fock (HF), density functional theory (DFT) (B3LYP), and CASSCF calculations.

Alkoxy-Bridged Dicopper(II) Cores Meet Tetracyanonickelate Linkers: Structural, Magnetic, and Theoretical Investigation of Cu/Ni Coordination Polymers.

Two heterometallic Cu(II)/Ni(II) coordination polymers, [Cu2(Hbdea)2Ni(CN)4]n (1) and [Cu2(dmea)2Ni(CN)4]n·nH2O (2), were successfully self-assembled in water by reacting Cu(II) nitrate with H2bdea (N-butyldiethanolamine) and Hdmea (N,N-dimethylethanolamine) in the presence of sodium hydroxide and [Ni(CN)4]2-. These new coordination polymers were investigated by single-crystal and powder X-ray diffraction and fully characterized by FT-IR spectroscopy, thermogravimetry, elemental analysis, variable-temperature magnetic susceptibility measurements, and theoretical DFT and CASSCF calculations. Despite differences in crystal systems, in both compounds, each dinuclear building block [Cu2(μ-aminopolyalcoholate)2]2+ is bridged by diamagnetic [Ni(CN)4]2- linkers, resulting in 1D (1) or 2D (2) metal-organic architectures. Experimental magnetic studies show that both compounds display strong antiferromagnetic coupling (J = -602.1 cm-1 for 1 and -151 cm-1 for 2) between Cu(II) ions within the dimers mediated by the μ-O-alkoxo bridges. These results are corroborated by the broken symmetry DFT studies, which also provide further insight into the electronic structures of copper dimeric units. By reporting a facile self-assembly synthetic protocol, this study can be a model to widen a still limited family of heterometallic Cu/Ni coordination polymer materials with different functional properties.

A Simulation of Hydrazine Molecule’s Potential Energy Surface using Variational Quantum Eigensolver Algorithm

Quantum computing is a technology that utilizes the principles of quantum mechanics to perform complex computational processes. In this work, we use Qiskit Module from IBM to do quantum computational calculation using Variational Quantum Eigensolver (VQE) algorithm. VQE is a hybrid quantum-classical method that combines a quantum computer to measure energies and a classical computer to process the measurement results and update the parameters of the quantum computer. The purpose of VQE is to find the ground state energy of a chemical system. In the previous study, many of the VQE calculations have been done on simple molecules. So, in this study, we would like to use Hydrazine molecule as our object of VQE calculation. Furthermore, these results will be compared with the results from the classical calculation (MP2, CCSD(T), QCISD(T), and CASSCF) methods for testing the effectiveness of VQE using Unitary Coupled-Cluster Single and Double excitations (UCCSD) Ansatz. The quantum algorithm based on the UCCSD Ansatz led to a simplification of the algorithm by reducing the circuit depth. Then, the possibility to use active space approximation, can be used to reduce the quantum gates while trying to keep a good level of accuracy. In this study, we chose (2,2) and (4,4) active spaces. Based on the results, as we increase the size of the active space during the evaluation of the single-point energy, the estimated ground states obtained from the VQE algorithm yield nearly identical values. Conversely, in CASSCF calculations, expanding the active space introduces more energy corrections, thus making it more sensitive. Additionally, when examining potential energy surfaces, VQE demonstrates results that gradually align with CCSD(T) and QCISD(T) methods.

A First Proposal on the Nitrobenzene Photorelease Mechanism of NO2 and Its Relation to NO Formation through a Roaming Mechanism.

Despite the fact that NO2 is considered to be the main photoproduct of nitrobenzene photochemistry, no mechanism has ever been proposed to rationalize its formation. NO photorelease is instead a more studied process, probably due to its application in the drug delivery sector and the study of roaming mechanisms. In this contribution, a photoinduced mechanism accounting for the formation of NO2 in nitrobenzene is theorized based on CASPT2, CASSCF, and DFT electronic structure calculations and CASSCF classical dynamics. A triplet nπ* state is shown to evolve toward C-NO2 dissociation, being, in fact, the only low-lying excited state favoring such a deformation. Along the triplet dissociation path, the possibility to decay to the singlet ground state results in the frustration of the dissociation and in the recombination of the fragments, either back to the nitro or the nitrite isomer. The thermal decomposition of the latter to NO constitutes globally a roaming mechanism of NO formation.

Dysprosium‐Radical Based Single‐Molecule Magnet Containing a Seven Coordinate Dy(III) Ion: A System for ab initio Study

AbstractSingle–ion magnets (SIMs) possessing a Dy(III) ion have recently attracted huge scientific attention. Herein, we report on a Dy(III)‐radical single–molecule magnet containing a seven‐coordinate Dy(III) ion with an O3N3Cl donor set. The frequency–dependent slow relaxation of magnetization has been observed below 8 K. DC magnetic studies have shown the presence of weak antiferromagnetic coupling between the Kramers ion (Dy(III), J = 15/2) and the ligand‐centered radical electron (S = 1/2) which was confirmed by multifunctional CASSCF calculations.

Phosphonium-substituted Diphosphaindenylide (PPI): Exploration of Biradical Character and Ligand Properties.

Starting from C6 H4 (PCl2 )2 and the TMS-substituted ylide (TMS)2 C=PR3 (TMS=trimethylsilyl, R=p-tolyl), the phosphonium-substituted diphosphaindenylide PPI was prepared in two steps. CASSCF calculations as well as the reactivity toward diphenyl acetylene suggest a notable biradical character in PPI. Reaction with [Cr(CO)3 (MeCN)3 ] affords the complex [Cr(CO)3 (η5 -PPI)] (5). This complex was employed to explore the ligand properties of PPI, which demonstrates considerable potential through the combination of strong metal-ligand interactions and the possibility of a pronounced indenyl effect.

Magnetic behaviour of a spin-canted asymmetric lanthanide quinolate trimer.

An asymmetrical dysprosium trimer with a molecular formula of [Dy3(hq)7(hqH)(NO3)2(H2O)] was obtained through a reflux reaction employing as starting material Dy(NO3)3·nH2O and 8-quinolinoline as ligand. Magnetic susceptibility investigations show the system to be an SMM, which was corroborated by sub-Kelvin μSQUID studies. Upon cooling, the magnetic susceptibility also exhibits a decrease in the χMT product, which was confirmed to be due to intramolecular antiferromagnetic interactions. μSQUID measurements, moreover, reveal a marked magnetic behaviour in the angular dependence of the hysteresis loops. The latter is a direct consequence of the non-colinear spin arrangement of the anisotropy axes of each Dy(III) ion in [Dy3(hq)7(hqH)(NO3)2(H2O)] and the interaction between the ions, as also evidenced by CASSCF calculations. Our results evidence the effect of spin canting along with the intramolecular interactions, which can induce non-trivial magnetic behaviour in SMMs.

Insight into ferromagnetic interactions in CuII-LnIII dimers with a compartmental ligand.

In the last two decades, efforts have been devoted to obtaining insight into the magnetic interactions between CuII and LnIII utilizing experimental and theoretical means. Experimentally, it has been observed that the exchange coupling (J) in CuII-LnIII systems is often found to be ferromagnetic for ≥4f7 metal ions. However, exchange interactions at sub-Kelvin temperatures between CuII and the anisotropic/isotropic LnIII ions are not often explored. In this report, we have synthesized a series of heterobimetallic [CuLn(HL)(μ-piv)(piv)2] complexes (LnIII = Gd (1), Tb (2), Dy (3) and Er (4)) from a new compartmental Schiff base ligand, N,N'-bis(3-methoxy-5-methylsalicylidene)-1,3-diamino-2-propanol (H3L). X-ray crystallographic analysis reveals that all four complexes are isostructural and isomorphous. Magnetic susceptibility measurements reveal a ferromagnetic coupling between the CuII ion and its respective LnIII ion for all the complexes, as often observed. Moreover, μ-SQUID studies, at sub-Kelvin temperatures, show S-shaped hysteresis loops indicating the presence of antiferromagnetic coupling in complexes 1-3. The antiferromagnetic interaction is explained by considering the shortest Cu⋯Cu distance in the crystal structure. The nearly closed loops for 1-3 highlight their fast relaxation characteristics, while the opened loops for 4 might arise from intermolecular ordering. CASSCF calculations allow the quantitative assessment of the interactions, which are further supported by BS-DFT calculations.

Magnetic anisotropy in octahedral Dy(III) and Yb(III) complexes.

New organophosphate complexes [Ln(dippH)3(dippH2)3]·(H2O)6, (Ln = Dy, Yb and Y; dippH2 = 2,6-diisopropylphenyl phosphate), displaying octahedral coordination geometry around the metal ion, exhibit unusual slow relaxation of magnetisation, which is investigated through experimental studies and ab initio CASSCF calculations.