Local spin

Radical revelations: the pnictogen effect in linear acetylenes

Acetylenes are essential building blocks in modern chemistry due to their remarkable modularity. The introduction of heteroatoms, such as pnictogens (X), is one of the simplest approaches to altering the C≡C bond. However, the chemistry of the resultant dipnictogenoacetylenes (DXAs) is strongly dependent on the nature of X. In this work, rigorous theoretical chemistry tools are employed to shed light on the origin of these differences, providing a detailed evaluation of the impact of X on the geometrical and electronic features of DXAs. Special emphasis is made on the study of the carbene character of the systems through the analysis of the interconversion mechanism between the linear and zigzag isomers. Our results show that second-period atoms behave drastically differently to the remaining X: down the group, a zwitterionic resonance form emerges at the expense of decreasing the carbenoid role, eventually resulting in an electrostatically driven ring closure. Furthermore, our findings pave the way to potentially unveiling novel routes for the promotion of free-radical chemistry.

Natural orbitals and two-particle correlators as tools for the analysis of effective exchange couplings in solids

Using generalizations of spin-averaged natural orbitals and two-particle charge correlators for solids, we investigate the electronic structure of antiferromagnetic transition-metal oxides with a fully self-consistent, imaginary-time GW method. Our findings disagree with the Goodenough-Kanamori (GK) rules that are commonly used for the qualitative interpretation of such solids. First, we found a strong dependence of the natural orbital occupancies on momenta, contradicting GK assumptions. Second, along the momentum path, the character of natural orbitals changes. In particular, the contributions of oxygen 2s orbitals are important, which has not been considered in the GK rules. To analyze the influence of the electronic correlation on the values of effective exchange coupling constants, we use both natural orbitals and two-particle correlators and show that electronic screening modulates the degree of superexchange by stabilizing the charge-transfer contributions, which greatly affects these coupling constants. Finally, we give a set of predictions and recommendations regarding the use of density functional, Green's function, and wave-function methods for evaluating effective magnetic couplings in molecules and solids.

Validation of the Green's Function Approximation for the Calculation of Magnetic Exchange Couplings

In this work, we assess the potential of the Green's function approximation to predict isotropic magnetic exchange couplings and to reproduce the standard broken-symmetry energy difference approach for transition metal complexes. To this end, we have selected a variety of heterodinuclear, homodinuclear, and polynuclear systems containing 3d transition metal centers and computed the couplings using both the Green's function and energy difference methods. The Green's function approach is shown to have mixed results for the cases tested. For dinuclear complexes with large strength couplings (≳50 cm^-1), the Green's function method is unable to reliably reproduce the energy difference values. However, for weaker dinuclear couplings, the Green's function approach acceptably reproduces broken-symmetry energy difference couplings. In polynuclear cases, the Green's function approximation worked remarkably well, especially for Fe^III complexes. On the other hand, for a Ni^II polynuclear complex, qualitatively wrong couplings are predicted. Overall, the evaluation of exchange couplings from local rigid magnetization rotations offers a powerful alternative to time-consuming energy differences methods for large polynuclear transition metal complexes, but to achieve a quantitative agreement, some improvements to the method are needed.

Exchange Spin Coupling in Optically Excited States

In optically excited states in molecules and materials, coupling between local electron spins plays an important role for their photoemission properties and is interesting for potential applications in quantum information processing. Recently, it was experimentally demonstrated that the photogenerated local spins in donor-acceptor metal complexes can interact with the spin of an attached radical, resulting in a spin-coupling-dependent mixing of excited doublet states, which controls the local spin density distributions on donor, acceptor, and radical subunits in optically excited states. In this work, we propose an energy-difference scheme to evaluate spin coupling in optically excited states, using unrestricted and spin-flip simplified time-dependent density functional theory. We apply it to three platinum complexes which have been studied experimentally to validate our methodology. We find that all computed coupling constants are in excellent agreement with the experimental data. In addition, we show that the spin coupling between donor and acceptor in the optically excited state can be fine-tuned by replacing platinum with palladium and zinc in the structure. Besides the two previously discussed excited doublet states (one bright and one dark), our calculations reveal a third, bright excited doublet state which was not considered previously. This third state possesses the inverse spin polarization on donor and acceptor with respect to the previously studied bright doublet state and is by an order of magnitude brighter, which might be interesting for optically controlling local spin polarizations with potential applications in spin-only information transfer and manipulation of connected qubits.

Extraction of local spin-coupled states by second quantized operators

We present a methodology for analyzing chemical bonds embedded in the electronic wave function of molecules, especially in terms of spin correlations or so-called "local spin." In this paper, based on biorthogonal second quantization, the spin correlation functions of molecules are naturally introduced, which enables us to extract local singlet and local triplet elements from the wave function. We also clarify the relationship between these spin correlations and traditional chemical concepts, i.e., resonance structures. Several chemical reactions, including the intramolecular radical cyclization and the formation of preoxetane, are demonstrated to verify the analysis method numerically.

A Combined Spectroscopic and Computational Study on the Mechanism of Iron-Catalyzed Aminofunctionalization of Olefins Using Hydroxylamine Derived N-O Reagent as the "Amino" Source and "Oxidant"

Herein, we study the mechanism of iron-catalyzed direct synthesis of unprotected aminoethers from olefins by a hydroxyl amine derived reagent using a wide range of analytical and spectroscopic techniques (Mössbauer, Electron Paramagnetic Resonance, Ultra-Violet Visible Spectroscopy, X-ray Absorption, Nuclear Resonance Vibrational Spectroscopy, and resonance Raman) along with high-level quantum chemical calculations. The hydroxyl amine derived triflic acid salt acts as the “oxidant” as well as “amino” group donor. It activates the high-spin Fe(II) (S_t = 2) catalyst [Fe(acac)₂(H₂O)₂] (1) to generate a high-spin (S_t = 5/2) intermediate (Int I), which decays to a second intermediate (Int II) with S_t = 2. The analysis of spectroscopic and computational data leads to the formulation of Int I as [Fe(III)(acac)₂-N-acyloxy] (an alkyl-peroxo-Fe(III) analogue). Furthermore, Int II is formed by N–O bond homolysis. However, it does not generate a high-valent Fe(IV)(NH) species (a Fe(IV)(O) analogue), but instead a high-spin Fe(III) center which is strongly antiferromagnetically coupled (J = −524 cm^–1) to an iminyl radical, [Fe(III)(acac)₂-NH·], giving S_t = 2. Though Fe(NH) complexes as isoelectronic surrogates to Fe(O) functionalities are known, detection of a high-spin Fe(III)-N-acyloxy intermediate (Int I), which undergoes N–O bond cleavage to generate the active iron–nitrogen intermediate (Int II), is unprecedented. Relative to Fe(IV)(O) centers, Int II features a weak elongated Fe–N bond which, together with the unpaired electron density along the Fe–N bond vector, helps to rationalize its propensity for N-transfer reactions onto styrenyl olefins, resulting in the overall formation of aminoethers. This study thus demonstrates the potential of utilizing the iron-coordinated nitrogen-centered radicals as powerful reactive intermediates in catalysis.

Towards multistate multimode landscapes in singlet fission of pentacene: the dual role of charge-transfer states

Singlet fission duplicates triplet excitons for improving light harvesting efficiency. The presence of the interaction between electronic and nuclear degrees of freedom complicates the interpretation of correlated triplet pairs. We report a quantum chemistry study on the significance and subtleties of multistate and multimode pathways in forming triplet pair states of the pentacene dimer through a six-state vibronic-coupling Hamiltonian derived from many-electron adiabatic wavefunctions of an ab initio density matrix renormalization group. The resulting spin values of the singlet manifolds on each pentacene center are computed, and the varying spin nature can be distinguished clearly with respect to dimer stacking and vibronic progression. Our monomer spin assignments reveal the coexistence of both lower-lying weak and higher-lying strong charge transfer states which interact vibronically with the triplet pair state, providing important implications for its generation and separation occurring in vibronic regions. This work conveys the importance of the many-electron process requiring close low-lying singlet manifolds to determine the subtle fission details, and represents an important step for understanding vibronically resolved spin states and conversions underlying efficient singlet fission.

Questioning the orbital picture of magnetic spin coupling: a real space alternative

The prevailing magnetic spin coupling paradigm is based on a one-electron picture, and is therefore orbital dependent and unsatisfactory from a physical point of view. We examine it under a truly invariant real space perspective, focusing on the role of electron delocalization. We show that this view, compatible with orbital thinking, overcomes its limitations. By examining simple model systems we show that it is electron delocalization that drives any singlet-triplet gap, and that delocalization and ionic mixing are two sides of the same reality. It is in the end delocalization, fostered or hindered by the specific structure of a system, that lies behind its preferred magnetic coupling mode. In the case of superexchange-mediated coupling through atomic bridges, we also point out the non-essential role of the bridge's electrons in setting up singlet-triplet preferences. We show that the use of real space thinking allows for tuning singlet-triplet gaps using knobs that are not easily grasped from the orbital standpoint, opening new avenues in the design and control of molecular magnets.

Spin-Pure Stochastic-CASSCF via GUGA-FCIQMC Applied to Iron-Sulfur Clusters

In this work, we demonstrate how to efficiently compute the one- and two-body reduced density matrices within the spin-adapted full configuration interaction quantum Monte Carlo (FCIQMC) method, which is based on the graphical unitary group approach (GUGA). This allows us to use GUGA-FCIQMC as a spin-pure configuration interaction (CI) eigensolver within the complete active space self-consistent field (CASSCF) procedure and hence to stochastically treat active spaces far larger than conventional CI solvers while variationally relaxing orbitals for specific spin-pure states. We apply the method to investigate the spin ladder in iron-sulfur dimer and tetramer model systems. We demonstrate the importance of the orbital relaxation by comparing the Heisenberg model magnetic coupling parameters from the CASSCF procedure to those from a CI-only (CASCI) procedure based on restricted open-shell Hartree-Fock orbitals. We show that the orbital relaxation differentially stabilizes the lower-spin states, thus enlarging the coupling parameters with respect to the values predicted by ignoring orbital relaxation effects. Moreover, we find that, while CASCI results are well fit by a simple bilinear Heisenberg Hamiltonian, the CASSCF eigenvalues exhibit deviations that necessitate the inclusion of biquadratic terms in the model Hamiltonian.

Spin-Orbit Coupling Changes the Identity of the Hyper-Open-Shell Ground State of Ce+, and the Bond Dissociation Energy of CeH+ Proves to Be Challenging for Theory

Cerium (Ce) plays important roles in catalysis. Its position in the sixth period of the periodic table leads to spin-orbit coupling (SOC) and other open-shell effects that make the quantum mechanical calculation of cerium compounds challenging. In this work, we investigated the low-lying spin states of Ce⁺ and the bond energy of CeH⁺, both by multiconfigurational methods, in particular, SA-CASSCF, MC-PDFT, CASPT2, XMS-PDFT, and XMS-CASPT2, and by single-configurational methods, namely, Hartree-Fock theory and unrestricted Kohn-Sham density functional theory with 34 choices of the exchange-correlation functional. We found that only CASPT2, XMS-CASPT2, and SA-CASSCF (among the five multiconfigurational methods) and GAM, HCTH, SOGGA11, and OreLYP (among the 35 single-configuration methods) successfully predict that the SOC-free ground spin state of Ce⁺ is a doublet state, and CASPT2 and GAM give the most accurate multireference and single-reference calculations, respectively, of the excitation energy of the first SOC-free excited state for Ce⁺. We calculated that the ground doublet state of Ce⁺ is an intra-atomic hyper-open-shell state. We calculated the spin-orbit energy (E^SO) of Ce⁺ by the five multiconfigurational methods and found that E^SO calculated by CASPT2 is the closest to the experimental value. Taking advantage of the availability of an experimental D₀ for CeH⁺ as a way to provide a unique test of theory, we showed that all the multiconfigurational methods overestimate D₀ by at least 246 meV (5.7 kcal/mol), and only three functionals, namely, SOGGA, MN15, and GAM, have an error of D₀ that is less than 200 meV (5 kcal/mol).

Local spin and open quantum systems: clarifying misconceptions, unifying approaches

The theory of open quantum systems (OQSs) is applied to partition the squared spin operator into fragment (local spin) and interfragment (spin-coupling) contributions in a molecular system.

Partitioning a Molecule into the Atomic Basins and the Resultant Atomic Charges from Quantum Chemical Topology Analysis of the Kohn-Sham Potential

Quantum chemical topology (QCT) solidifies the chemical basic concepts demonstrating how a molecular system is intrinsically partitioned into its components and what the interaction lines between them are. Here, QCT analysis using a Kohn-Sham one-electron potential (KSpot) in KS equation as a scalar function is initiated and explored, showing KSpot and its resultant electron force lines have novel spatial features which reveal that an atom in a molecule is a spatial basin governed by its nucleus as a 3D-attractor that terminates all the electron force lines defined by the negative gradient of KSpot and that a chemical bond line is just a minimum path of KSpot for the electron motion. Particularly, the atomic charges from this KSpot QCT analysis are moderate and good, having much lower dependence on basis sets chosen for computation. This may provide a platform for the study of molecular structures and properties, intra- and intermolecular electrostatic interaction, energy decomposition, and construction of force field.

The Right Answer for the Right Reason: My Personal Goal for Quantum Chemistry

A brief history of quantum theory is given to illustrate the barriers to progress caused by preconceived ideas. The biases in my own thinking which I had to overcome to approach the right answer for the right reason are discussed. This is followed by a personal autobiography illustrating how I have led a life of serendipity with no real sense of purpose. Chance events have shaped my life. The algorithms for which I am best known are briefly discussed. Then highlights from the many applications of theory to excited states, bonding in ice, spin properties and magnetism, (e,2e) shake-up spectra, and organic reactions are mentioned. This wide range of applications is mostly due to accidental collaboration with colleagues who sought my help. My real interest was in developing methods which could address these problems.

Theoretical Modeling of Singlet Fission

Singlet fission is a photophysical reaction in which a singlet excited electronic state splits into two spin-triplet states. Singlet fission was discovered more than 50 years ago, but the interest in this process has gained a lot of momentum in the past decade due to its potential as a way to boost solar cell efficiencies. This review presents and discusses the most recent advances with respect to the theoretical and computational studies on the singlet fission phenomenon. The work revisits important aspects regarding electronic states involved in the process, the evaluation of fission rates and interstate couplings, the study of the excited state dynamics in singlet fission, and the advances in the design and characterization of singlet fission compounds and materials such as molecular dimers, polymers, or extended structures. Finally, the review tries to pinpoint some aspects that need further improvement and proposes future lines of research for theoretical and computational chemists and physicists in order to further push the understanding and applicability of singlet fission.

Maximum bonding fragment orbitals for deciphering complex chemical interactions

An optimal set of fragment orbitals is proposed as a simple and powerful tool for analyzing complex bonding interactions.

Role of the Dark 2Ag State in Donor-Acceptor Copolymers as a Pathway for Singlet Fission: A DMRG Study

The mechanism of intramolecular singlet fission in donor-acceptor-type copolymers, especially the role of the dark 2A_g state, is not so clear. In this Letter, the electronic structure of the benzodithiophene (B)-thiophene-1,1-dioxide (TDO) copolymer is calculated by density matrix renormalization group theory with the Pariser-Parr-Pople model. We find that the dark 2A_g state is the lowest singlet excited state and is nearly degenerate with the 1B_u state. So, a fast internal conversion from 1B_u to 2A_g state is highly possible. The 2A_g state has a strong triplet pair character, localized on two neighboring acceptor units, which indicates that it is an intermediate state for the intramolecular singlet fission process. With the increase of the donor-acceptor push-pull strength in our model, this triplet pair character of the 2A_g state becomes more prominent, and meanwhile the binding energy of this coupled triplet pair state decreases, which favors the separation into two uncoupled triplet states. We propose a model in which the competition between the singlet fission process and the nonradiative decay process from the 2A_g state would determine the final quantum yield.

Local electric dipole moments: A generalized approach

We present an approach for calculating local electric dipole moments for fragments of molecular or supramolecular systems. This is important for understanding chemical gating and solvent effects in nanoelectronics, atomic force microscopy, and intensities in infrared spectroscopy. Owing to the nonzero partial charge of most fragments, "naively" defined local dipole moments are origin-dependent. Inspired by previous work based on Bader's atoms-in-molecules (AIM) partitioning, we derive a definition of fragment dipole moments which achieves origin-independence by relying on internal reference points. Instead of bond critical points (BCPs) as in existing approaches, we use as few reference points as possible, which are located between the fragment and the remainder(s) of the system and may be chosen based on chemical intuition. This allows our approach to be used with AIM implementations that circumvent the calculation of critical points for reasons of computational efficiency, for cases where no BCPs are found due to large interfragment distances, and with local partitioning schemes other than AIM which do not provide BCPs. It is applicable to both covalently and noncovalently bound systems. © 2016 Wiley Periodicals, Inc.

Effective Hamiltonians for correlated narrow energy band systems and magnetic insulators: Role of spin-orbit interactions in metal-insulator transitions and magnetic phase transitions

Using a second-quantized many-electron Hamiltonian, we obtain (a) an effective Hamiltonian suitable for materials whose electronic properties are governed by a set of strongly correlated bands in a narrow energy range and (b) an effective spin-only Hamiltonian for magnetic materials. The present Hamiltonians faithfully include phonon and spin-related interactions as well as the external fields to study the electromagnetic response properties of complex materials and they, in appropriate limits, reduce to the model Hamiltonians due to Hubbard and Heisenberg. With the Hamiltonian for narrow-band strongly correlated materials, we show that the spin-orbit interaction provides a mechanism for metal-insulator transition, which is distinct from the Mott-Hubbard (driven by the electron correlation) and the Anderson mechanism (driven by the disorder). Next, with the spin-only Hamiltonian, we demonstrate the spin-orbit interaction to be a reason for the existence of antiferromagnetic phase in materials which are characterized by a positive isotropic spin-exchange energy. This is distinct from the Néel-VanVleck-Anderson paradigm which posits a negative spin-exchange for the existence of antiferromagnetism. We also find that the Néel temperature increases as the absolute value of the spin-orbit coupling increases.

Puzzles in bonding and spectroscopy: the case of dicarbon

The unstable molecule C₂ has been of interest since its identification as the source of the "Swan band" features observable in the spectra offlames, carbon arcs, white dwarf stars, and comets, and it continues to serve as a focal point for experimental and theoretical discovery. Recent spectroscopic work has identified a quintet state of the molecule for the first time, while new insights into the bond order of C₂ in its ground state have been provided by sophisticated computational methods based on valence bond theory. This article gives a review of spectroscopic and computational work on C₂ including both historical background and the most recent discoveries.

A novel 1,3,5-triaminocyclohexane-based tripodal ligand forms a unique tetra(pyrazolate)-bridged tricopper(ii) core: solution equilibrium, structure and catecholase activity

A polydentate tripodal ligand forms a series of tricopper(ii) complexes, that feature unique pyrazolate-bridged linear core. The Cu₃H₋₃L₂ complex is an efficient catecholase mimic with a surprisingly low pH optimum at pH = 5.6.

Rethinking first-principles electron transport theories with projection operators: the problems caused by partitioning the basis set

We revisit the derivation of electron transport theories with a focus on the projection operators chosen to partition the system. The prevailing choice of assigning each computational basis function to a region causes two problems. First, this choice generally results in oblique projection operators, which are non-Hermitian and violate implicit assumptions in the derivation. Second, these operators are defined with the physically insignificant basis set and, as such, preclude a well-defined basis set limit. We thus advocate for the selection of physically motivated, orthogonal projection operators (which are Hermitian) and present an operator-based derivation of electron transport theories. Unlike the conventional, matrix-based approaches, this derivation requires no knowledge of the computational basis set. In this process, we also find that common transport formalisms for nonorthogonal basis sets improperly decouple the exterior regions, leading to a short circuit through the system. We finally discuss the implications of these results for first-principles calculations of electron transport.

Quantum entanglement in carbon–carbon, carbon–phosphorus and silicon–silicon bonds

We present a quantum entanglement analysis to dissect the bond orders in polyatomic molecules.