Accurate Spin-State Energetics of Transition Metal Complexes. 1. CCSD(T), CASPT2, and DFT Study of [M(NCH) 6 ] 2+ (M = Fe, Co) Late ́ vi Max Lawson Daku,* ,† Francesco Aquilante, ‡ Timothy W. Robinson, § and Andreas Hauser † † Universite ́ de Gene ̀ ve, Faculte ́ des Sciences, Quai E. Ansermet 30, CH-1211 Genè ve 4, Switzerland ‡ Department of Chemistry - Ångströ m, The Theoretical Chemistry Programme, Uppsala University, P.O. Box 518, SE-751 20 Uppsala, Sweden § CSCS Swiss National Supercomputing Centre, Via Trevano 131, CH-6900 Lugano, Switzerland * S Supporting Information ABSTRACT: Highly accurate estimates of the high-spin/low-spin energy difference ΔE HL el in the high-spin complexes [Fe(NCH) 6 ] 2+ and [Co(NCH) 6 ] 2+ have been obtained from the results of CCSD(T) calculations extrapolated to the complete basis set limit. These estimates are shown to be strongly influenced by scalar relativistic effects. They have been used to assess the performances of the CASPT2 method and 30 density functionals of the GGA, meta-GGA, global hybrid, RSH, and double-hybrid types. For the CASPT2 method, the results of the assessment support the proposal [Kepenekian, M.; Robert, V.; Le Guennic, B. J. Chem. Phys. 2009, 131, 114702] that the ionization potential−electron affinity (IPEA) shift defining the zeroth-order Hamiltonian be raised from its standard value of 0.25 au to 0.50−0.70 au for the determination of ΔE HL el in Fe(II) complexes with a [FeN 6 ] core. At the DFT level, some of the assessed functionals proved to perform within chemical accuracy (±350 cm −1 ) for the spin-state energetics of [Fe(NCH) 6 ] 2+ , others for that of [Co(NCH) 6 ] 2+ , but none of them simultaneously for both complexes. As demonstrated through a reparametrization of the CAM-PBE0 range-separated hybrid, which led to a functional that performs within chemical accuracy for the spin-state energetics of both complexes, performing density functionals of broad applicability may be devised by including in their training sets highly accurate data like those reported here for [Fe(NCH) 6 ] 2+ and [Co(NCH) 6 ] 2+ . 1. INTRODUCTION Transition metal (TM) complexes exhibit many interesting physical and chemical properties, which are dictated by the shapes and relative positions of the potential energy surfaces (PESs) of their low-lying spin states. For instance, (pseudo)- octahedral 3d 4 −3d 7 TM complexes can exhibit spin crossover (SCO), that is, the entropy-driven thermal depopulation of their electronic low-spin (LS) ground state in favor of the close- lying high-spin (HS) state. SCO is accompanied by a change of the optical, magnetic, and structural properties of the complexes. Furthermore, light irradiation can also be used to control the SCO equilibrium. The SCO complexes are therefore likely to be used in the design of optical devices for the storage and display of information at the molecular level. As such, they are the subject of numerous multidisciplinary studies. 1−3 A change of spin states also takes place in many reactions of TM complexes, as well as in the chemistry of many metalloproteins and metalloenzymes. 4−6 The in-depth understanding of SCO and related phenomena or of spin-nonconserving reactions of TM systems relies on the accurate description of the PESs of the corresponding spin- states, at given critical points or along given relevant coordinates. Theoretical methods can in principle be used to obtain an accurate description of these PESs. However, such theoretical studies are seriously undermined by the issues tied to the accurate determination of the energy difference between states of different spin multiplicities. In the framework of density functional theory (DFT), 7,8 the results are strongly dependent on the exchange-correlation (XC) functional used. Although considerable attention has been paid to this issue, 4,5,9−42 no XC functional has emerged so far as the functional of choice for the evaluation of TM spin- state energetics. Furthermore, there is no guarantee that the accuracy of the DFT results shall improve with the degree of sophistication of the functional. In contrast, in wave function theory (WFT), the accuracy of the results can be systematically improved by resorting to methods that improve the treatment of both static and dynamic correlation effects. However, such methods are limited to systems of small to medium size (∼100 atoms at most). And, even in the case of the well-established CASPT2 multireference perturbation (MRPT) method, 43,44 some empiricism turns out to be needed in the definition of the zeroth-order Hamiltonian. 45−47 Such limitations can be over- come by resorting to high-level coupled-cluster (CC) methods. 48,49 CC methods are the most accurate methods for treating electronic correlation in single-reference systems, and even in their standard formulation, they can also be used to reliably cope with situations of multireference character. 48−50 However, CC calculations are unquestionably computationally very demanding. For instance, the CCSD and CCSDT methods have canonical scalings of N ( ) 6 U and N ( ) 8 U , respectively, where N is the number of basis functions. Consequently, given that sufficiently large basis sets must be used to obtain accurate Received: July 11, 2012 Published: September 26, 2012 Article pubs.acs.org/JCTC © 2012 American Chemical Society 4216 dx.doi.org/10.1021/ct300592w | J. Chem. Theory Comput. 2012, 8, 4216−4231