Multireference Approaches to Spin‐State Energetics of Transition Metal Complexes Utilizing the Density Matrix Renormalization Group

Abstract

The accurate and reliable calculation of different electronic states in transition metal systems is a persistent challenge for theoretical chemistry. The widespread use of density functional theory for computing the relative energies of states with different spin in transition metal complexes not only has not discouraged, but often, owing to its limitations, has motivated the development and refinement of first-principles wavefunction-based methods, including both single-reference and multireference approaches. A significant boost for the latter has been the emergence of the density matrix renormalization group (DMRG) as a reliable tool in applied quantum chemistry. By enabling the use of larger active spaces than conventionally possible, DMRG has opened up areas of transition metal chemistry that were previously inaccessible to multireference approaches. The present perspective provides an overview of representative studies that make use of DMRG methods and discusses recent applications to spin-state energetics of transition metal systems. These range from mononuclear to exchange-coupled systems that define an important emerging field of DMRG applications. Major achievements are highlighted and potential pitfalls are identified with a view toward future methodological developments as well as extensions in the applicability of DMRG-based approaches to problems of spin-state energetics and exchange-coupling in transition metal chemistry.

The S3 State of the Oxygen-Evolving Complex: Overview of Spectroscopy and XFEL Crystallography with a Critical Evaluation of Early-Onset Models for O–O Bond Formation

“…Multireference methods are appropriate for the description of strongly correlated open-shell transition metal systems, but conventional approaches are limited to systems considerably smaller than the OEC. The density matrix renormalization group , extends the applicability of such methods and can be used for relative energies and spin state energetics of transition metal systems [160,161]. DMRG-based complete active space self-consistent field (DMRG-CASSCF) calculations have been used [162] to compare the relative stabilities of isomeric forms in the case of a synthetic tetramanganese complex [163] of similar size as typical quantum chemical models of the OEC.…”

Assessment of Double-Hybrid Density Functional Theory for Magnetic Exchange Coupling in Manganese Complexes

“…Complex 3 is a mixed-valence system with asymmetric ligation [65] that facilitates spin localization. This complex has a moderate antiferromagnetic coupling resulting in a spin doublet (S = 1/2) ground state and has been the subject of a recent study [20] that evaluated the use of the density matrix renormalization group [66] in the multireference treatment of exchange coupling [18,22]. Complex 4 is a classic example of a strongly coupled bis-µ-oxo Mn(IV,IV) system [67].…”

“…This forms the basis for obtaining the full range of spin-dependent observables for a given system. By definition, this is a genuine multireference problem and in principle should be addressed with appropriate multireference quantum chemical methods [16][17][18][19][20][21][22]. However, the challenge of directly computing the full spectrum of energy states often can or has to be reduced for practical purposes to the more modest target of extracting pairwise exchange coupling constants that parameterize the magnetic energy levels in the framework of an effective spin Hamiltonian.…”

Exchange Spin Coupling from Gaussian Process Regression

“…Our goal is to predict J for transition metal complexes. This is most often done by combining Kohn-Sham (KS) density functional theory (DFT) with a broken-symmetry approach to model the AF state [15][16][17][18][19][20][21] , or by employing multireference wave function methods 18,[22][23][24][25][26] . The latter is computationally demanding, and requires efforts towards avoiding artefacts resulting from too inflexible wave function expressions [27][28][29][30] .…”