The role of the magnetic orbitals in the calculation of the magnetic coupling constants from multireference perturbation theory methods

Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive

We present a self-consistent field (SCF) approach within the adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression that is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition-metal complex ferrocene [Fe (C5H5)2], indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to the complete active space SCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way toward a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.

Voltage-induced modulation of the magnetic exchange in binuclear Fe(III) complex deposited on Au(111) surface

We present a complete computational study devoted to the deposition of a magnetic binuclear complex on a metallic surface, aimed to obtain insight into the interaction of magnetically coupled complexes with their supporting substrates, as well as their response to external electrical stimuli applied through a surface-molecule-STM molecular junction-like architecture. Our results not only show that the deposition is favorable in two of the four studied orientations, but also, that the magnetic coupling is only slightly perturbed once the complex is adsorbed. We observe that the effects of the applied bias voltage on the magnetic coupling strongly depend on the molecule orientation with respect to the surface and the voltage polarity. Further analysis shows that this behavior is attributable to the stabilization/destabilization of the d-type singly occupied orbitals of the iron centers, reinforced by the strong local electric fields and induced charge densities only present in certain orientations of the deposited molecule and applied voltage polarity.

Toward a Stochastic Complete Active Space Second-Order Perturbation Theory

In this work, an internally contracted stochastic complete active space second-order perturbation theory, stochastic-CASPT2, is reported. The method relies on stochastically sampled reduced density matrices (RDMs) up to rank four and contractions thereof with the generalized Fock matrix. A new protocol for calculating higher-order RDMs in full configuration interaction quantum Monte Carlo (FCIQMC) has been designed based on (1) restricting sampling of the corresponding excitations to a deterministic subspace, (2) averaging the RDMs from independent dynamics and (3) projecting them onto the closest positive semi-definite matrix. Our protocol avoids previously encountered numerical conditioning problems in the orthogonalization of the perturber overlap matrix stemming from numerical noise. The chromium dimer CASSCF(12,12)/CASPT2 binding curve is computed as a proof of concept.

Theoretical Perspective for the Relationship Between Structures and Luminescent Properties of Red Thermally Activated Delayed Fluorescence Molecules

Orange and red thermally activated delayed fluorescence (TADF) emitters have shown promising applications in organic light emitting diodes (OLEDs) and bio-medical field. However, both the species and amounts of orange...

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.

Orbital Entanglement Analysis of Exchange-Coupled Systems

A new tool for the interpretation of multiconfigurational wave functions representing the spin states of exchange-coupled transition metal complexes is introduced. Based on orbital entanglement measures, herein derived from multiconfigurational density matrix renormalization group calculations, the complexity of the wave function is reduced, thus facilitating a connection with established concepts for the interpretation of magnetically coupled systems. We show that the entanglement of localized orbitals with a small basis set is a good representation of the magnetic coupling topology and that it is sensitive to chemical changes in homologous complexes. Furthermore, we introduce a measure for the magnetic relevance of orbitals in the active subspace and a concept for the quantitative comparison of different chemical species. The approach presented here will be easily applicable to higher nuclearity clusters, providing a direct insight into all states of the Heisenberg spin ladder for systems previously accessible only by single-configurational methods.

A theoretical study of the super exchange mechanism and magneto-structural relationships in the [Mn(iii)2(μ-F)F4(Me3tacn)2](PF6) coordination compound

A detailed theoretical study of the electronic structure and magnetic properties of the dinuclear Mn(iii) complex, [Mn(iii)₂(μ-F)F₄(Me₃tacn)₂] (complex 1), with a single fluoride bridge is reported.

The role of the multiconfigurational character of nitronyl-nitroxide in the singlet–triplet energy gap of its diradicals

CAS(2,2) reference may not be sufficient for the computation of singlet–triplet energy gap by DDCI.

Exchange Coupling Interactions from the Density Matrix Renormalization Group and N-Electron Valence Perturbation Theory: Application to a Biomimetic Mixed-Valence Manganese Complex

The accurate description of magnetic level energetics in oligonuclear exchange-coupled transition-metal complexes remains a formidable challenge for quantum chemistry. The density matrix renormalization group (DMRG) brings such systems for the first time easily within reach of multireference wave function methods by enabling the use of unprecedentedly large active spaces. But does this guarantee systematic improvement in predictive ability and, if so, under which conditions? We identify operational parameters in the use of DMRG using as a test system an experimentally characterized mixed-valence bis-μ-oxo/μ-acetato Mn(III,IV) dimer, a model for the oxygen-evolving complex of photosystem II. A complete active space of all metal 3d and bridge 2p orbitals proved to be the smallest meaningful starting point; this is readily accessible with DMRG and greatly improves on the unrealistic metal-only configuration interaction or complete active space self-consistent field (CASSCF) values. Orbital optimization is critical for stabilizing the antiferromagnetic state, while a state-averaged approach over all spin states involved is required to avoid artificial deviations from isotropic behavior that are associated with state-specific calculations. Selective inclusion of localized orbital subspaces enables probing the relative contributions of different ligands and distinct superexchange pathways. Overall, however, full-valence DMRG-CASSCF calculations fall short of providing a quantitative description of the exchange coupling owing to insufficient recovery of dynamic correlation. Quantitatively accurate results can be achieved through a DMRG implementation of second order N-electron valence perturbation theory (NEVPT2) in conjunction with a full-valence metal and ligand active space. Perspectives for future applications of DMRG-CASSCF/NEVPT2 to exchange coupling in oligonuclear clusters are discussed.

Quantitative prediction and interpretation of spin energy gaps in polyradicals: the virtual magnetic balance

Open-shell organic molecules possessing more than two unpaired electrons and sufficient stability at room temperature are very unusual, but some of them were recently synthesized and promise a number of fascinating applications.

Electronic Structures of Anti-Ferromagnetic Tetraradicals: Ab Initio and Semi-Empirical Studies

The energy relationships and electronic structures of the lowest-lying spin states in several anti-ferromagnetic tetraradical model systems are studied with high-level ab initio and semi-empirical methods. The Full-CI method (FCI), the complete active space second-order perturbation theory (CASPT2), and the n-electron valence state perturbation theory (NEVPT2) are employed to obtain reference results. By comparing the energy relationships predicted from the Heisenberg and Hubbard models with ab initio benchmarks, the accuracy of the widely used Heisenberg model for anti-ferromagnetic spin-coupling in low-spin polyradicals is cautiously tested in this work. It is found that the strength of electron correlation (|U/t|) concerning anti-ferromagnetically coupled radical centers could range widely from strong to moderate correlation regimes and could become another degree of freedom besides the spin multiplicity. Accordingly, the Heisenberg-type model works well in the regime of strong correlation, which reproduces well the energy relationships along with the wave functions of all the spin states. In moderately spin-correlated tetraradicals, the results of the prototype Heisenberg model deviate severely from those of multi-reference electron correlation ab initio methods, while the extended Heisenberg model, containing four-body terms, can introduce reasonable corrections and maintains its accuracy in this condition. In the weak correlation regime, both the prototype Heisenberg model and its extended forms containing higher-order correction terms will encounter difficulties. Meanwhile, the Hubbard model shows balanced accuracy from strong to weak correlation cases and can reproduce qualitatively correct electronic structures, which makes it more suitable for the study of anti-ferromagnetic coupling in polyradical systems.

Highly efficient perturbative + variational strategy based on orthogonal valence bond theory for the evaluation of magnetic coupling constants. Application to the trinuclear Cu(ii) site of multicopper oxidases

A new perturbative + variational strategy: a low-cost, quantitative and rational evaluation of the magnetic coupling constant in complex systems.

Partly saturated polyacene structures: a theoretical study

Planar molecular edifices obtained by joining polyacene fragments (polyacene stripes) are investigated at tight-binding (i.e., with a Hückel Hamiltonian) and ab initio level. For this kind of system, it is known that the presence of 60-degree angles between two stripes of the polyacene molecular skeleton induces the formation of singly occupied molecular orbitals, whose combination gives rise to quasi-degenerate electronic states. In particular, two types of convex polygons having a unique side length (rhombuses and triangles) are considered in this work. It is shown that the saturation via hydrogen atoms of the apical carbons located on outer borders of the 60-degree angles increases the number of quasi-degenerate orbitals, and hence the maximal multiplicity of the low-lying states of the system. Our tight-binding and ab initio (CAS-CI, NEVPT2) calculations indicate that the spin multiplicity of these molecular structures is in systematical accord with the Ovchinnikov rule.

Switching magnetic interactions in the NiFe Prussian Blue Analogue: an ab initio inspection

Wave function embedded cluster calculations are performed to stress a cation-coupled electron transfer process in the NiFe Prussian Blue Analogue.