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Abstract

A comparison of density functionals is made for the calculation of energy and geometry differences for the high- [⁵T_2g: (t_2g)⁴(e_g)²] and low- [¹A_1g: (t_2g)⁶(e_g)⁰] spin states of the hexaquoferrous cation [Fe(H₂O)₆]²⁺. Since very little experimental results are available (except for crystal structures involving the cation in its high-spin state), the primary comparison is with our own complete active-space self-consistent field (CASSCF), second-order perturbation theory-corrected complete active-space self-consistent field (CASPT2), and spectroscopy-oriented configuration interaction (SORCI) calculations. We find that generalized gradient approximations (GGAs) 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 molecules). In contrast, CASPT2 calculations of the low-spin–high-spin energy difference ΔE_LH=E_LS−E_HS appear to be significantly overestimated due to basis set limitations in the sense that the energy difference of the atomic asymptotes (⁵D→¹I excitation of Fe²⁺) are overestimated by about 3000 cm⁻¹. An empirical shift of the molecular ΔE_LH based upon atomic calculations provides a best estimate of 12 000–13 000 cm⁻¹. Our unshifted SORCI result is 13 300 cm⁻¹, 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⁻¹ while the B3LYP functional underestimates it by only about 1000 cm⁻¹. 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 ΔE_LH
within the context of density functional theory (DFT) 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.