Analytic derivative calculation of electronicg-tensors based on multireference configuration interaction wavefunctions

State-Interaction Approach for Evaluating g-Tensors within EOM-CC and RAS-CI Frameworks: Theory and Benchmarks

Among various techniques designed for studying open-shell species, electron paramagnetic resonance (EPR) spectroscopy plays an important role. The key quantity measured by EPR is the g-tensor, describing the coupling between an external magnetic field and molecular electronic spin. One theoretical framework for quantum chemistry calculations of g-tensors is based on response theory, which involves substantial developments that are specific to the underlying electronic structure models. A simplified and easier-to-implement approach is based on the state-interaction scheme, in which perturbation is included by considering a small number of states. We describe and benchmark the state-interaction approach using equation-of-motion coupled-cluster and restricted-active-space configuration interaction wave functions. The analysis confirms that this approach can deliver accurate results and highlights caveats of applying it, such as a choice of the reference state, convergence with respect to the number of states used in calculations, etc. The analysis also contributes toward a better understanding of challenges in calculations of higher-order properties using approximate wave functions.

Solution of a Puzzle: High-Level Quantum-Chemical Treatment of Pseudocontact Chemical Shifts Confirms Classic Semiempirical Theory

A recently popularized approach for the calculation of pseudocontact shifts (PCSs) based on first-principles quantum chemistry (QC) leads to different results than the classic "semiempirical" equation involving the susceptibility tensor. Studies that attempted a comparison of theory and experiment led to conflicting conclusions with respect to the preferred theoretical approach. In this Letter, we show that after inclusion of previously neglected terms in the full Hamiltonian, one can deduce the semiempirical equations from a rigorous QC-based treatment. It also turns out that in the long-distance limit, one can approximate the complete A tensor in terms of the g tensor. By means of Kohn-Sham density functional theory calculations, we numerically confirm the long-distance expression for the A tensor and the theoretically predicted scaling behavior of the different terms. Our derivation suggests a computational strategy in which one calculates the susceptibility tensor and inserts it into the classic equation for the PCS.

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] (1_Mn) 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 1_Mn in detail, a combination of experimental and computational studies is presented herein. Alternating-current magnetometry on magnetically diluted samples (1_Mn/1_Ga) of 1_Mn in the diamagnetic gallium analogue, [Ga{(OPPh₂)₂N}₃], indicates that the slow relaxation behavior of 1_Mn is due to the intrinsic properties of the individual molecules of 1_Mn. Investigation of the single-crystal magnetization of both 1_Mn and 1_Mn/1_Ga 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 (B₄^m) are required in order to appropriately describe the magnetic properties of 1_Mn. These studies provide accurate spin-Hamiltonian (sH) parameters of 1_Mn, 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 1_Mn/1_Ga and CH₂Cl₂ solutions of 1_Mn probe the electronic-nuclear hyperfine interactions in the solid state and solution. The electronic structure of 1_Mn 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 B₄^m, 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 1_Mn are rationalized on the basis of the composition of the ground-state wave functions in the absence or presence of an external magnetic field.

Accurate spin-densities based on the domain-based local pair-natural orbital coupled-cluster theory

Exploiting locality in the electron correlation reduces the computational cost for solving the Coupled-Cluster (CC) equations. This is important for making CC theory applicable to routine computational chemistry applications where it promises to deliver results of "gold-standard" quality. Recently, we have proposed a series of CC formulations in the domain-based local pair-natural orbital framework [DLPNO-coupled-cluster with singles and doubles (CCSD) and DLPNO-coupled-cluster singles and doubles with perturbative triples] which are designed to reproduce approximately 99.9% of the canonical correlation energy. In our previous work, the DLPNO-CCSD method has been extended to the high-spin open-shell reference and shown to possess comparable accuracy to the closed-shell counterpart [M. Saitow et al., J. Chem. Phys. 146, 164105 (2017)]. The so-called Λ-equations have been formulated in the DLPNO framework for the closed-shell species as an exact derivative of the DLPNO-CCSD Lagrangian with respect to the PNO-based cluster amplitudes [D. Datta et al., J. Chem. Phys. 145, 114101 (2016)]. In this paper, we extend the DLPNO-based Lagrangian scheme to the high-spin open-shell reference cases, thus enabling the accurate computation of the electron- and spin-densities for large open-shell species. We apply this newly developed approach to various first-order electronic and magnetic properties such as isotropic and anisotropic components in the hyperfine coupling interactions and the electric field gradient. We demonstrate that the DLPNO-CCSD results converge toward the respective canonical CC density and also that the DLPNO-CCSD-based properties are more accurate than the conventional density functional theory (DFT) results in real-life applications. The additional computational cost is not more than one energy evaluation in the DLPNO-CCSD framework.

cis-Tetrachlorido-bis(indazole)osmium(iv) and its osmium(iii) analogues: paving the way towards the cis-isomer of the ruthenium anticancer drugs KP1019 and/or NKP1339

The relationship between cis-trans isomerism and anticancer activity has been mainly addressed for square-planar metal complexes, in particular, for platinum(ii), e.g., cis- and trans-[PtCl2(NH3)2], and a number of related compounds, of which, however, only cis-counterparts are in clinical use today. For octahedral metal complexes, this effect of geometrical isomerism on anticancer activity has not been investigated systematically, mainly because the relevant isomers are still unavailable. An example of such an octahedral complex is trans-[RuCl4(Hind)2]-, which is in clinical trials now as its indazolium (KP1019) or sodium salt (NKP1339), but the corresponding cis-isomers remain inaccessible. We report the synthesis of Na[cis-OsIIICl4(κN2-1H-ind)2]·(Na[1]) suggesting a route to the cis-isomer of NKP1339. The procedure involves heating (H2ind)[OsIVCl5(κN1-2H-ind)] in a high boiling point organic solvent resulting in an Anderson rearrangement with the formation of cis-[OsIVCl4(κN2-1H-ind)2] ([1]) in high yield. The transformation is accompanied by an indazole coordination mode switch from κN1 to κN2 and stabilization of the 1H-indazole tautomer. Fully reversible spectroelectrochemical reduction of [1] in acetonitrile at 0.46 V vs. NHE is accompanied by a change in electronic absorption bands indicating the formation of cis-[OsIIICl4(κN2-1H-ind)2]- ([1]-). Chemical reduction of [1] in methanol with NaBH4 followed by addition of nBu4NCl afforded the osmium(iii) complex nBu4N[cis-OsIIICl4(κN2-1H-ind)2] (nBu4N[1]). A metathesis reaction of nBu4N[1] with an ion exchange resin led to the isolation of the water-soluble salt Na[1]. The X-ray diffraction crystal structure of [1]·Me2CO was determined and compared with that of trans-[OsIVCl4(κN2-1H-ind)2]·2Me2SO (2·2Me2SO), also prepared in this work. EPR spectroscopy was performed on the OsIII complexes and the results were analyzed by ligand-field and quantum chemical theories. We furthermore assayed effects of [1] and Na[1] on cell viability and proliferation in comparison with trans-[OsIVCl4(κN1-2H-ind)2] [3] and cisplatin and found a strong reduction of cell viability at concentrations between 30 and 300 μM in different cancer cell lines (HT29, H446, 4T1 and HEK293). HT-29 cells are less sensitive to cisplatin than 4T1 cells, but more sensitive to [1] and Na[1], as shown by decreased proliferation and viability as well as an increased late apoptotic/necrotic cell population.

A Nonorthogonal State-Interaction Approach for Matrix Product State Wave Functions

We present a state-interaction approach for matrix product state (MPS) wave functions in a nonorthogonal molecular orbital basis. Our approach allows us to calculate, for example, transition and spin-orbit coupling matrix elements between arbitrary electronic states, provided that they share the same one-electron basis functions and size of the active orbital space, respectively. The key element is the transformation of the MPS wave functions of different states from a nonorthogonal to a biorthonormal molecular orbital basis representation, by exploiting a sequence of nonunitary transformations, following a proposal by Malmqvist [Int. J. Quantum Chem. 1986, 30, 479]. This is well-known for traditional wave function parametrizations but has not yet been exploited for MPS wave functions.

Theoretical Characterisation of Phosphinyl Radicals and Their Magnetic Properties: g Matrix

The g matrices (g tensors) of various phosphinyl radicals (R2 P(.) ) were calculated using the DFT and multireference configuration interaction (MRCI) methods. The g matrices were distinctly dependent on the molecular structure of the radical. To thoroughly examine this dependence, the contributions from individual atoms and excited states were calculated. The former revealed the gain from the phosphorus atom to be preeminent unless PO or PS bonds are present in the radical molecule. The contributions owing to excited states arising from electronic transitions between doubly occupied molecular orbitals and the SOMO were clearly positive, as in the case of semiquinone and niroxide radicals. The transitions from the phosphorus lone pair were of paramount importance. Surprisingly, unlike for semiquinones and nitroxides, a significant negative contribution was observed from excitations from the SOMO to unoccupied molecular orbitals. For radicals with PO bonds, this contribution to the g2 component was dominant.

Basis set error estimation for DFT calculations of electronic g-tensors for transition metal complexes

We present a detailed study of the basis set dependence of electronic g-tensors for transition metal complexes calculated using Kohn-Sham density functional theory. Focus is on the use of locally dense basis set schemes where the metal is treated using either the same or a more flexible basis set than used for the ligand sphere. The performance of all basis set schemes is compared to the extrapolated complete basis set limit results. Furthermore, we test the performance of the aug-cc-pVTZ-J basis set developed for calculations of NMR spin-spin and electron paramagnetic resonance hyperfine coupling constants. Our results show that reasonable results can be obtain when using small basis sets for the ligand sphere, and very accurate results are obtained when an aug-cc-pVTZ basis set or similar is used for all atoms in the complex.

QM/MM investigations of organic chemistry oriented questions

About 35 years after its first suggestion, QM/MM became the standard theoretical approach to investigate enzymatic structures and processes. The success is due to the ability of QM/MM to provide an accurate atomistic picture of enzymes and related processes. This picture can even be turned into a movie if nuclei-dynamics is taken into account to describe enzymatic processes. In the field of organic chemistry, QM/MM methods are used to a much lesser extent although almost all relevant processes happen in condensed matter or are influenced by complicated interactions between substrate and catalyst. There is less importance for theoretical organic chemistry since the influence of nonpolar solvents is rather weak and the effect of polar solvents can often be accurately described by continuum approaches. Catalytic processes (homogeneous and heterogeneous) can often be reduced to truncated model systems, which are so small that pure quantum-mechanical approaches can be employed. However, since QM/MM becomes more and more efficient due to the success in software and hardware developments, it is more and more used in theoretical organic chemistry to study effects which result from the molecular nature of the environment. It is shown by many examples discussed in this review that the influence can be tremendous, even for nonpolar reactions. The importance of environmental effects in theoretical spectroscopy was already known. Due to its benefits, QM/MM can be expected to experience ongoing growth for the next decade.In the present chapter we give an overview of QM/MM developments and their importance in theoretical organic chemistry, and review applications which give impressions of the possibilities and the importance of the relevant effects. Since there is already a bunch of excellent reviews dealing with QM/MM, we will discuss fundamental ingredients and developments of QM/MM very briefly with a focus on very recent progress. For the applications we follow a similar strategy.

Electrochemical and photochemical cyclization and cycloreversion of diarylethenes and diarylethene-capped sexithiophene wires

A combined theoretical and experimental study was performed on diarylethenes and diarylethene-capped sexithiophenes aiming at an improved understanding of the electrochemical and photochemical ring-opening and ring-closing mechanisms. Theoretical calculations, based on DFT and TDDFT, suggested that the spatial distribution and the occupancy of the frontier orbitals determine and control the diarylethenes' ring-opening and ring-closing upon photoirradiation and electrochemical oxidation. Optimized geometries, potential energy surfaces, and activation energies between the open-ring and closed-ring forms were calculated for diarylethenes in the neutral ground state, excited states, and mono- and dicationic states. Analysis of the frontier orbitals was employed to understand the cyclization and cycloreversion of diarylethenes and to predict and explain the switching properties of diarylethene-capped sexithiophene molecular wires. The TDDFT data were verified with experimentally measured UV/vis spectra. The DFT calculations estimated open-shell ground states of diarylethene-capped sexithiophene dications, which were verified with EPR spectroscopy, and the broadening of the peaks in the EPR spectra were explained with the calculated singlet-triplet splitting. The good agreement of experiment and theory allows for the understanding of switching behavior of diarylethenes in solutions, in metal break junctions, in monolayers on metal surfaces, and as a part of complex organic molecular wires.

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.