Comparison of density functionals for energy and structural differences between the high- [5T2g: (t2g)4(eg)2] and low- [1A1g: (t2g)6(eg)] spin states of the hexaquoferrous cation [Fe(H2O)6]2+

Abstract

Comparison of density functionals for energy and structural differences between the high- † 5 T 2g : "t 2g … 2ϩ . Since very little experimental results are available ͑except for crystal structures involving the cation in its high-spin state͒, the primary comparison is with our own complete active-space self-consistent field ͑CASSCF͒, second-order perturbation theory-corrected complete active-space self-consistent field ͑CASPT2͒, and spectroscopy-oriented configuration interaction ͑SORCI͒ calculations. We find that generalized gradient approximations ͑GGAs͒ and the B3LYP hybrid functional provide geometries in good agreement with experiment and with our CASSCF calculations provided sufficiently extended basis sets are used ͑i.e., polarization functions on the iron and polarization and diffuse functions on the water molecules͒. In contrast, CASPT2 calculations of the low-spin-high-spin energy difference ⌬E LH ϭE LS ϪE HS appear to be significantly overestimated due to basis set limitations in the sense that the energy difference of the atomic asymptotes ( 5 D→ 1 I excitation of Fe 2ϩ ) are overestimated by about 3000 cm Ϫ1 . An empirical shift of the molecular ⌬E LH based upon atomic calculations provides a best estimate of 12 000-13 000 cm Ϫ1 . Our unshifted SORCI result is 13 300 cm Ϫ1, consistent with previous comparisons between SORCI and experimental excitation energies which suggest that no such empirical shift is needed in conjunction with this method. In contrast, after estimation of incomplete basis set effects, GGAs with one exception underestimate this value by 3000-4000 cm Ϫ1 while the B3LYP functional underestimates it by only about 1000 cm Ϫ1 . The exception is the GGA functional RPBE which appears to perform as well as or better than the B3LYP functional for the properties studied here. In order to obtain a best estimate of the molecular ⌬E LH within the context of density functional theory ͑DFT͒ calculations we have also performed atomic excitation energy calculations using the multiplet sum method. These atomic DFT calculations suggest that no empirical correction is needed for the DFT calculations. © 2004 American Institute of Physics. ͓DOI: 10.1063/1.1710046͔ I. INTRODUCTIONA well-known feature of d 6 Tanabe-Sugano ligand field theory ͑LFT͒ diagrams for octahedral complexes is the reversal of the ordering of the low-spin 1 A and high-spin 5 T in the spin-crossover region of ligand field strength.1 For compounds in this region, spin crossover may be either thermally or optically induced, 2 leading to possible applications in storage and display devices. [3][4][5] We are particularly interested in the phenomenon of light-induced excited spin-state trapping ͑LIESST͒ in octahedral iron II compounds, which involves the optical interconversion of the high-spin ͑HS͒ 5 T 2g and low-spin ͑LS͒ 1 A g electronic states. While this can be understood at a qualitative level using LFT, 1,2 it is also known that the e g orbitals, populated in going from the LS to the HS state, are antibonding, so that b...

Spin states of (bio)inorganic systems: Successes and pitfalls

“…More reliable data were obtained with CASPT2, [5,6] but this method is computationally expensive as well, needs specific expertise and much depends on the choice of orbitals to be included in the active space and the basis set used. For instance, for Fe(H 2 O) 6 2þ , CASPT2 with six electrons in five orbitals [6,5] complete active space (CAS) space with the small 6-31G** basis set gives a [7] which goes down by about 16 kcal mol À1 (to give 46.3 kcal mol) À1 with 12 electrons in 10 orbitals [12,10]. Using larger basis sets, Pierloot and Vancoillie [6] [8] on Mn-oxo corrole and corrolazine shows differences of up to 5 kcal mol À1 between CASPT2 and RASPT2 for low-lying states (8-15 kcal mol À1 above the ground state), and up to 10 kcal mol À1 for higher ones (31-42 kcal mol À1 above the ground state).…”

Assessment of Density Functionals for the High‐Spin/Low‐Spin Energy Difference in the Low‐Spin Iron(II) Tris(2,2′‐bipyridine) Complex

“…HL of the [Fe(bpy) 3 ] 2 + complex points to the inherent difficulty of XC functionals to predict the relative energies of states of different spin multiplicities correctly, particularly for spin-crossover systems [27,49,[60][61][62] but also for spin-forbidden chemical reactions. [88] This is emphasised by the fact that for the TZP basis set the 5 E and the 5 A 1 components of the quintet state are consistently predicted to be nearly degenerate, that is within the chemical accuracy of 350 cm À1 , by functionals which behave quite differently when it comes to evaluating the HS--LS energy gap.…”

“…[41,43] As a cautious note, we believe at this point that it is worth insisting that the success met with the RPBE functional for the evaluation of the HS--LS energy difference in [Fe(bpy) 3 ] 2 + , or even in [Fe(H 2 O) 6 ] 2 + as in ref. [27], does not imply that this GGA is the functional of choice for the description of iron(II) complexes. For instance, for the [Fe(NH 3 ) 6 ] 2 + complex investigated in ref.…”

“…[27] We used the BP86, BLYP, PW91 GGAs, the recent exchange-correlation GGA of Perdew-Burke-Ernzerhof (PBE) [63,64] and the revised PBE (RPBE) functional of Hammer, Hansen and Nørskov [65] as well as the B3LYP hybrid, and compared the DFT results with results obtained at the complete active space SCF (CASSCF), secondorder-perturbation-theory-corrected CASSCF (CASPT2), and spectroscopy-oriented configuration interaction (SORCI [66] ) levels. Whatever the theoretical method, the HS state was correctly reproduced as the ground state for this HS system, (DE el: HL < 0).…”

“…In two previous papers, [27,28] 6 ] 2 + complexes in the LS and HS states. In this paper, we extend our investigation of iron(II) complexes to the analysis of the low-temperature tunnelling process in the HS!LS relaxation dynamics for a LS complex.…”