Ligand-Field-Dependent Behavior of Meta-GGA Exchange in Transition-Metal Complex Spin-State Ordering

Abstract

Prediction of spin-state ordering in transition metal complexes is essential for understanding catalytic activity and designing functional materials. Semi-local approximations in density functional theory, such as the generalized-gradient approximation (GGA), suffer from several errors notably including delocalization error that give rise to systematic bias for more covalently bound low-spin electronic states. Incorporation of exact exchange is known to counteract this bias, instead favoring high-spin states, in a manner that has recently been identified to be ligand-field dependent. In this work, we introduce a tuning strategy to identify the effect of incorporating the Laplacian of the density (i.e., a meta-GGA) in exchange on spinstate ordering. We employ a diverse test set of M(II) and M(III) first-row transition metal ions from Ti to Cu as well as octahedral complexes of these ions with ligands of increasing field strength (i.e., H 2 O, NH 3 , and CO). We show that the sensitivity of spin-state ordering to meta-GGA exchange is highly ligand-field dependent, stabilizing high-spin states in strong-field (i.e., CO) cases and stabilizing low-spin states in weak-field (i.e., H 2 O, NH 3 , and isolated ions) cases. This diverging behavior leads to generally improved treatment of isolated ions and strong field complexes over a standard GGA but worsened treatment for the hexa-aqua or hexa-ammine complexes. These observations highlight the sensitivity of functional performance to subtle changes in chemical bonding.2

Spin‐State Energetics of Fe Complexes from an Optimally Tuned Range‐Separated Hybrid Functional

“…[62] Fortunately,F igure 3r eveals that the energy difference, DE,i sn ot very sensitivet ot he range-separation parameter,e specially forl arger fractionso fS Re xact exchange. Clearly, the dependence of DE on the SR exact exchange, a in Figure 4 is linear,i na greement with the work of Reiher et al for GGA hybrids [19] and the work of Ioannidis and Kulik [41] for meta-GGA hybrids, where as imilarl inear dependenceo nt he globalf raction of Fock exchange was found. Figure 3a lso reveals that the choice of a affects DE much more strongly.T his is made explicit by plotting the dependence of DE on a for the four model complexes,a sc alculated with g opt avg corresponding to each a,s hown in Figure 4.…”

“…Figure 3a lso reveals that the choice of a affects DE much more strongly.T his is made explicit by plotting the dependence of DE on a for the four model complexes,a sc alculated with g opt avg corresponding to each a,s hown in Figure 4. Clearly, the dependence of DE on the SR exact exchange, a in Figure 4 is linear,i na greement with the work of Reiher et al for GGA hybrids [19] and the work of Ioannidis and Kulik [41] for meta-GGA hybrids, where as imilarl inear dependenceo nt he globalf raction of Fock exchange was found. In some previous OT-RSH calculations, it was possible to choose an optimal value of a by plotting J 2 [Eq.…”

“…This reduction is clearly consistent with the presentr esults, as wella sw ith trends reported by Ioannidis and Kulik. [41] In particular,t he value of 12 %e xact exchange, suggested by Reiher et al [20] is au seful value for the spin-crossover complexes, with the exception of complex 8, which as mentioned above behaves differently.S wart [24] obtained the correct ground spin state (DE = 2.1 kcal mol À1 )f rom an OPBE calculation. Butt he double-hybridB 2PLYP functional .…”

“…[23,24] OPBE is ag eneralized-gradient approximation (GGA) functional with Perdew-Burke-Ernzerhof (PBE) correlation [25] and the semiempirical local exchange functional OPTX, [26] which was parametrizeda gainst static correlation. These andm any other functionals have been tested for variouss ystems [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] over the years, with mixed conclusions that are discussed in more detail below.…”

Magnetic configurations of open-shell molecules on metals: The case of CuPc and CoPc on silver

“…Specifically, in situations where the electronic potential energy surface has several local minima, the nature of the magnetic (or nonmagnetic) configuration obtained in a given calculation can depend on several factors, including the initialization of the self-consistent cycle used when solving the Kohn-Sham equations and the approximate density functional employed. A further complication arises from the fact that semilocal functionals, which are typically used for interface calculations [18,19,25,28,[36][37][38], can have difficulties with all three of the above-listed demands needed to describe magnetic properties of molecule-metal interfaces: these functionals may fail at describing charge transfer [34,[39][40][41] and the correct orbital configurations [28,[42][43][44][45][46][47][48][49][50][51][52][53], which can (in part) be traced back to errors arising from self-interaction [39,43,44,48,[54][55][56], and often do not allow for a proper description of exchange coupling [57][58][59][60][61][62][63]. A common approach to mitigate these shortcomings of semilocal DFT is the use of "higher-rung" methods, such as hybrid DFT functionals, which can partially reduce the unwanted consequences of these issues.…”