Multiconfigurational g tensor calculations as a probe for the covalency of the copper-ligand bonds in copper(II) complexes: [CuCl4]2-, [Cu(NH3)4]2+, and plastocyanin

How does multi-reference computation change the catalysis chemistry? DFT and CASPT2 studies of the Cu-catalysed coupling reactions between aryl iodides and β-diketones

The molecular mechanism of a Cu-catalysed coupling reaction was theoretically studied using density functional theory (DFT) and the complete active space self-consistent field method followed by the second-order perturbation theory (CASSCF/CASPT2) to investigate the effects of the strong electron correlation of the Cu centre on the reaction profile. Both DFT and CASSCF/CASPT2 calculations showed that the catalytic cycle proceeds via an oxidative addition (OA) reaction, followed by a reductive elimination (RE) reaction, where OA is the rate-determining step. Although the DFT-calculated activation energies of the OA and RE steps are highly dependent on the choice of functionals, the CASSCF/CASPT2 results are less affected by the choice of DFT-optimised geometries. Therefore, with a careful assessment based on the CASSCF/CASPT2 single-point energy evaluation, an optimal choice of the DFT geometry is of good qualitative use for energetics at the CASPT2 level of theory. Based on the changes in the electron populations of the 3d orbitals during the OA and RE steps, the characteristic features of the DFT-calculated electronic structure were qualitatively consistent with those calculated using the CASSCF method. Further electronic structure analysis by the natural orbital occupancy of the CASSCF wavefunction showed that the ground state is almost single-reference in this system and the strong electron correlation effect of the Cu centre can be dealt with using the MP2 or CCSD method, too. However, the slightly smaller occupation numbers of the 3dπ orbital in the course of reactions suggested that the electron correlation effect of the Cu(III) centre appears through the interaction between the 3dπ orbital and the C-I antibonding σ* orbital in the OA step, and between the 3dπ orbital and the Cu-C antibonding σ* orbital in the RE step.

The π-interactions of ammonia ligands evaluated by ab initio ligand field theory

Ammonia and amine ligands are commonly assumed to be σ-only ligands in coordination chemistry, i.e. they are not expected to interact significantly with a metal via a π path. Ligand field analyses employing the Angular Overlap Model resulted in good fits to experimental data without a π parameter for ammonia ligands, thereby supporting this assumption. In this work, we challenge this assumption and suggest that it is an oversimplification. We use complete active space calculations for electronic structure analyses of copper ammine complexes that are in good agreement with the transitions observed in experimental UV-vis spectra. These findings lead to a reinterpretation of the experimental spectra that necessitates a significant π interaction of the ammonia ligands. The strength of the ammonia π interaction is evaluated by parameterizing the ligand field splittings of a series of metal hexammine complexes ([M(NH₃)₆]ⁿ⁺ with M = Cr, Mn, Fe, Co, Ni, Ru, Os and n = 2, 3) and selected tetrammine complexes ([M(NH₃)₄]ⁿ⁺ with M = Cr, Mn, Fe, Co, Ni and n = 2 or 3) with the Angular Overlap Model. The resulting π parameters show that ammonia is a π donor of similar strength as chloride.

Waste-Derived Copper-Lead Electrocatalysts for CO2 Reduction

It remains a real challenge to control the selectivity of the electrocatalytic CO₂ reduction (eCO₂R) reaction to valuable chemicals and fuels. Most of the electrocatalysts are made of non-renewable metal resources, which hampers their large-scale implementation. Here, we report the preparation of bimetallic copper-lead (CuPb) electrocatalysts from industrial metallurgical waste. The metal ions were extracted from the metallurgical waste through simple chemical treatment with ammonium chloride, and Cu_xPb_y electrocatalysts with tunable compositions were fabricated through electrodeposition at varying cathodic potentials. X-ray spectroscopy techniques showed that the pristine electrocatalysts consist of Cu⁰, Cu¹⁺ and Pb²⁺ domains, and no evidence for alloy formation was found. We found a volcano-shape relationship between eCO₂R selectivity toward two electron products, such as CO, and the elemental ratio of Cu and Pb. A maximum Faradaic efficiency towards CO was found for Cu_9.00Pb_1.00, which was four times higher than that of pure Cu, under the same electrocatalytic conditions. In situ Raman spectroscopy revealed that the optimal amount of Pb effectively improved the reducibility of the pristine Cu¹⁺ and Pb²⁺ domains to metallic Cu and Pb, which boosted the selectivity towards CO by synergistic effects. This work provides a framework of thinking to design and tune the selectivity of bimetallic electrocatalysts for CO₂ reduction through valorization of metallurgical waste.

Harnessing Colossal Magnetic Anisotropy in Sandwiched 3d2-Metallocenes

Single-molecule magnets are gaining attention in recent years with the growing focus on achieving higher barriers of magnetization reversal. Metallocenes, owing to their unique sandwiched structure, assure themselves as plausible molecular systems for the development of novel single-molecule magnets (SMMs). Here in this work, we have explicitly investigated metallocenes of first-row transition elements, along with their one-electron-oxidized (cationic) and -reduced (anionic) analogues, for their magnetic anisotropies by adopting multireference ab initio calculations. Herein, we report a high magnetic anisotropy for 3d² systems among all 3d-metallocenes.

Calculation of the Zeeman Effect for Transition-Metal Complexes by Multiconfiguration Pair-Density Functional Theory

Spin-orbit coupling is especially critical for the description of magnetic anisotropy, electron paramagnetic resonance spectroscopy of inorganic radicals and transition-metal complexes, and intersystem crossing. Here, we show how spin-orbit coupling may be included in multiconfiguration pair-density functional theory (MC-PDFT), and we apply the resulting formulation to the calculation of magnetic g tensors (which govern the Zeeman effect) of molecules containing transition metals. MC-PDFT is an efficient method for including static and dynamic electronic correlation in the quantum mechanical treatment of molecules; here, we apply it with spin-orbit coupling by using complete active space self-consistent field (CASSCF) and complete active space configuration interaction (CASCI) wave functions and on-top density functionals. We propose a systematic CASCI scheme for the g tensor calculation of the ground state of the systems under consideration, and we show its superiority over the conventional CASSCF scheme. State interaction, which is important for degenerate and nearly degenerate states, is included by extended multi-state PDFT (XMS-PDFT). Applications are reported for the ground doublet states of 25 transition-metal complexes with d¹, d⁵, d⁷, and d⁹ configurations. The MC-PDFT methods are shown to be both efficient and accurate as compared with complete active space second-order perturbation theory.

Converged Structural and Spectroscopic Properties for Refined QM/MM Models of Azurin

Blue copper proteins continue to challenge experiment and theory with their electronic structure and spectroscopic properties that respond sensitively to the coordination environment of the copper ion. In this work, we report state-of-the art electronic structure studies for geometric and spectroscopic properties of the archetypal "Type I" copper protein azurin in its Cu(II) state. A hybrid quantum mechanics/molecular mechanics (QM/MM) approach is used, employing both density functional theory (DFT) and coupled cluster with singles, doubles, and perturbative triples (CCSD(T)) methods for the QM region, the latter method making use of the domain-based local pair natural orbital (DLPNO) approach. Models of increasing QM size are employed to investigate the convergence of critical geometric parameters. It is shown that convergence is slow and that a large QM region is critical for reproducing the short experimental Cu-SCys112 distance. The study of structural convergence is followed by investigation of spectroscopic parameters using both DFT and DLPNO-CC methods and comparing these to the experimental spectrum using simulations. The results allow us to examine for the first time the distribution of spin densities and hyperfine coupling constants at the coupled cluster level, leading us to revisit the experimental assignment of the 33S hyperfine splitting. The wavefunction-based approach to obtain spin-dependent properties of open-shell systems demonstrated here for the case of azurin is transferable and applicable to a large array of bioinorganic systems.

Spin-chemical effects on intramolecular photoinduced charge transfer reactions in bisphenanthroline copper(i)-viologen dyad assemblies

Two covalently linked donor-acceptor copper phenanthroline complexes (C-A dyads) of interest for solar energy conversion/storage schemes, [Cu(i)(Rphen(OMV)2 4+)2]9+ = RC+A4 8+ with RC+ = [Cu(i)Rphen2]+ involving 2,9-methyl (R = Me) or 2,9-phenyl (R = Ph)-phenanthroline ligands that are 5,6-disubstituted by 4-(n-butoxy) linked methylviologen electron acceptor groups (A2+ = OMV2+), have been synthesized and investigated via quantum chemical calculations and nanosecond laser flash spectroscopy in 1,2-difluorobenzene/methanol (dfb/MeOH) mixtures. Upon photoexcitation, charge transfer (CT) states RC2+A+A3 6+ are formed in less than one ns and decay by charge recombination on a time scale of 6-45 ns. The CT lifetime of RC2+A+A3 6+ has a strong dependence on MeOH solvent fraction when R = Me, but is unaffected if R = Ph. This solvent effect is due to coordination of MeOH solvent in MeC+A4 8+ (i.e. exciplex formation) allowed by conformational flattening of the ligand sphere, which cannot occur in PhC+A4 8+ having bulkier Phphen ligand framework. Interestingly, the decay time of the CT state increases for both species at low magnetic fields with a maximum increase of ca. 30% at ca. 150 mT, then decreases as the field is increased up to 1500 mT, the highest field investigated. This magnetic field effect (MFE) is due to magnetic modulation of the spin dynamics interconverting 3CT and 1CT states. A quantitative modeling according to the radical pair mechanism involving ab initio multireference calculations of the complexes revealed that the spin process is dominated by the effect of Cu hyperfine coupling. The external magnetic field suppresses the hyperfine coupling induced spin state mixing thereby lengthening the CT decay time. This effect is counteracted by the field dependent processes of T0-S mixing through the Δg-mechanism and by a local mode spin-orbit mechanism. Further, the maximum MFE is limited by a finite rate of direct recombination of 3CT states and the spin-rotational mechanism of spin relaxation. This study provides a first comprehensive characterization of Cu(ii)-complex spin chemistry and highlights how spin chemistry can be used to manipulate solar energy harvesting and storage materials.

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

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 , , and/or for closed- and open-shell transition metal complexes.

Determining Key Local Vibrations in the Relaxation of Molecular Spin Qubits and Single-Molecule Magnets

To design molecular spin qubits and nanomagnets operating at high temperatures, there is an urgent need to understand the relationship between vibrations and spin relaxation processes. Herein we develop a simple first-principles methodology to determine the modulation that vibrations exert on spin energy levels. This methodology is applied to [Cu(mnt)₂]^2- (mnt^2- = 1,2-dicyanoethylene-1,2-dithiolate), a highly coherent complex. By theoretically identifying the most relevant vibrational modes, we are able to offer general strategies to chemically design more resilient magnetic molecules, where the energy of the spin states is not coupled to vibrations.

A QM/MM study of the nature of the entatic state in plastocyanin

Plastocyanin is a copper containing protein that is involved in the electron transfer process in photosynthetic organisms. The active site of plastocyanin is described as an entatic state whereby its structure represents a compromise between the structures favored by the oxidized and reduced forms. In this study, the nature of the entatic state is investigated through density functional theory‐based hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations. The strain energy is computed to be 12.8 kcal/mol and 14.5 kcal/mol for the oxidized and reduced forms of the protein, indicating that the active site has an intermediate structure. It is shown that the energy gap between the oxidized and reduced forms varies significantly with the fluctuations in the structure of the active site at room temperature. An accurate determination of the reorganization energy requires averaging over conformation and a large region of the protein around the active site to be treated at the quantum mechanical level. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Electronic Structure of a Cu(II)-Alkoxide Complex Modeling Intermediates in Copper-Catalyzed Alcohol Oxidations

In the copper-catalyzed oxidation of alcohols to aldehydes, a Cu(II)-alkoxide (Cu(II)-OR) intermediate is believed to modulate the αC-H bond strength of the deprotonated substrate to facilitate the oxidation. As a structural model for these intermediates, we characterized the electronic structure of the stable compound Tp(tBu)Cu(II)(OCH2CF3) (Tp(tBu) = hydro-tris(3-tert-butyl-pyrazolyl)borate) and investigated the influence of the trifluoroethoxide ligand on the electronic structure of the complex. The compound exhibits an electron paramagnetic resonance (EPR) spectrum with an unusually large gzz value of 2.44 and a small copper hyperfine coupling Azz of 40 × 10(-4) cm(-1) (120 MHz). Single-crystal electron nuclear double resonance (ENDOR) spectra show that the unpaired spin population is highly localized on the copper ion (≈68%), with no more than 15% on the ethoxide oxygen. Electronic absorption and magnetic circular dichroism (MCD) spectra show weak ligand-field transitions between 5000 and 12,000 cm(-1) and an intense ethoxide-to-copper charge transfer (LMCT) transition at 24,000 cm(-1), resulting in the red color of this complex. Resonance Raman (rR) spectroscopy reveals a Cu-O stretch mode at 592 cm(-1). Quantum chemical calculations support the interpretation and assignment of the experimental data. Compared to known Cu(II)-thiolate and Cu(II)-alkylperoxo complexes from the literature, we found an increased σ interaction in the Cu(II)-OR bond that results in the spectroscopic features. These insights lay the basis for further elucidating the mechanism of copper-catalyzed alcohol oxidations.

Computational study of the structure and electronic circular dichroism spectroscopy of blue copper proteins

The calculation of the electronic circular dichroism (CD) spectra of the oxidized form of the blue copper proteins plastocyanin and cucumber basic protein and the relationship between the observed spectral features and the structure of the active site of the protein is investigated. Excitation energies and transition strengths are computed using multireference configuration interaction, and it is shown that computed spectra based on coordinates from the crystal structure or a single structure optimized in quantum mechanics/molecular mechanics (QM/MM) or ligand field molecular mechanics (LFMM) are qualitatively incorrect. In particular, the rotational strength of the ligand to metal charge transfer band is predicted to be too small or have the incorrect sign. By considering calculations on active site models with modified structures, it is shown that the intensity of this band is sensitive to the nonplanarity of the histidine and cysteine ligands coordinated to copper. Calculation of the ultraviolet absorption and CD spectra based upon averaging over many structures drawn from a LFMM molecular dynamics simulation are in good agreement with experiment, and superior to analogous calculations based upon structures from a classical molecular dynamics simulation. This provides evidence that the LFMM force field provides an accurate description of the molecular dynamics of these proteins.

Fourteen-electron ring model and the anomalous magnetic circular dichroism of meso-triarylsubporphyrins

The MCD spectra of meso-triarylsubporphyrins show a sign anomaly which is correlated with the acceptor properties of the aryl substituent. From the spectra, magnetic moments of the excited states are determined. In the context of a simplified orbital model, the sign change is attributed to the quenching of the magnetic moment of the LUMO by acceptor orbitals of the substituent. The actual calculation of this moment presents a major challenge to computational methods. It is shown that wave function techniques based on CASSCF underestimate the covalency effects that are responsible for the quenching. In contrast, a CI method based on DFT orbitals yields excellent results, which fully support the orbital model.

Multiconfigurational Second-Order Perturbation Theory Restricted Active Space (RASPT2) Method for Electronic Excited States: A Benchmark Study

The recently developed second-order perturbation theory restricted active space (RASPT2) method has been benchmarked versus the well-established complete active space (CASPT2) approach. Vertical excitation energies for valence and Rydberg excited states of different groups of organic (polyenes, acenes, heterocycles, azabenzenes, nucleobases, and free base porphin) and inorganic (nickel atom and copper tetrachloride dianion) molecules have been computed at the RASPT2 and multistate (MS) RASPT2 levels using different reference spaces and compared with CASPT2, CCSD, and experimental data in order to set the accuracy of the approach, which extends the applicability of multiconfigurational perturbation theory to much larger and complex systems than previously. Relevant aspects in multiconfigurational excited state quantum chemistry such as the valence-Rydberg mixing problem in organic molecules or the double d-shell effect for first-row transition metals have also been addressed.

Predicting the ¹H and ¹³C NMR spectra of paramagnetic Ru(III) complexes by DFT

Nuclear shieldings, including the Fermi-contact and pseudocontact terms, have been calculated with density functional theory (DFT) (nonrelativistic and relativistic) methods in several Ru(III) complexes, thereby predicting (1)H and (13)C paramagnetic shifts. A fair agreement with experimental values is observed. Structural, magnetic and dynamic parameters have also been input to the Solomon-Bloembergen equation in order to predict signal lineshapes. It is shown that DFT-predicted paramagnetic shifts can greatly aid in obtaining and understanding NMR spectra of paramagnetic Ru(III) complexes.

Multireference ab initio calculations of g tensors for trinuclear copper clusters in multicopper oxidases

EPR spectroscopy has proven to be an indispensable tool in elucidating the structure of metal sites in proteins. In recent years, experimental EPR data have been complemented by theoretical calculations, which have become a standard tool of many quantum chemical packages. However, there have only been a few attempts to calculate EPR g tensors for exchange-coupled systems with more than two spins. In this work, we present a quantum chemical study of structural, electronic, and magnetic properties of intermediates in the reaction cycle of multicopper oxidases and of their inorganic models. All these systems contain three copper(II) ions bridged by hydroxide or O(2-) anions and their ground states are antiferromagnetically coupled doublets. We demonstrate that only multireference methods, such as CASSCF/CASPT2 or MRCI can yield qualitatively correct results (compared to the experimental values) and consider the accuracy of the calculated EPR g tensors as the current benchmark of quantum chemical methods. By decomposing the calculated g tensors into terms arising from interactions of the ground state with the various excited states, the origin of the zero-field splitting is explained. The results of the study demonstrate that a truly quantitative prediction of the g tensors of exchange-coupled systems is a great challenge to contemporary theory. The predictions strongly depend on small energy differences that are difficult to predict with sufficient accuracy by any quantum chemical method that is applicable to systems of the size of our target systems.

A Proton ENDOR Study of Azurin

As part of our ongoing project that aims at the optimum characterization of the electronic structure of the blue-copper site of azurin from Pseudomonas aeruginosa, we present the complete hyperfine tensors of the protons bound to the Cbeta atom of the copper-bound cysteine 112. These tensors have been obtained from a 95 GHz pulsed electron-nuclear double resonance study of a single crystal of the protein.

Density functional restricted-unrestricted approach for nonlinear properties: application to electron paramagnetic resonance parameters of square planar copper complexes

The density functional restricted-unrestricted approach for treatments of spin polarization effects in molecular properties using spin restricted Kohn-Sham theory has been extended from linear to nonlinear properties. It is shown that the spin polarization contribution to a nonlinear property has the form of a quadratic response function that includes the zero-order Kohn-Sham operator, in analogy to the lower order case where the spin polarization correction to an expectation value has the form of a linear response function. The developed approach is used to formulate new schemes for computation of electronic g-tensors and hyperfine coupling constants, which include spin polarization effects within the framework of spin restricted Kohn-Sham theory. The proposed computational schemes are in the present work employed to study the spin polarization effects on electron paramagnetic resonance spin Hamiltonian parameters of square planar copper complexes. The obtained results indicate that spin polarization gives rise to sizable contributions to the hyperfine coupling tensor of copper in all investigated complexes, while the electronic g-tensors of these complexes are only marginally affected by spin polarization and other factors, such as choice of exchange-correlation functional or molecular structures, will have more pronounced impact on the accuracy of the results.