Previous work testing density functionals for use in calculating high-spin-low-spin energy differences, deltaE(HL), for iron(II) spin-crossover transitions has tended to conclude that only properly reparametrized hybrid functionals can predict deltaE(HL) since it seems to depend critically on a correct description of the electron pairing energy governed by the exchange term. Exceptions to this rule are the previous three papers (I, II, and III in the present series of papers) where it was found that modern generalized gradient approximations (GGAs) and meta-GGAs could do as well as hybrid functionals, if not better, for this type of problem. In the present paper, we extend these previous studies to five more molecules which are too large to treat with high-quality ab initio calculations, namely, the series [Fe(L)('NHS(4)')], where NHS(4)=2.2'-bis(2-mercaptophenylthio)diethylamine dianion, and L=NH(3), N(2)H(4), PMe(3), CO, and NO(+). Since we know of no reliable experimental estimate of deltaE(HL), we content ourselves with a comparison against the experimentally determined ground-state spin symmetry including, in so far as possible, finite-temperature effects. Together with the results of Papers I, II, and III, this paper provides a test of a large number of functionals against the high-spin/low-spin properties of a diverse set of Fe(II) compounds, making it possible to draw some particularly interesting conclusions. Trends among different classes of functionals are discussed and it is pointed out that there is at least one functional, namely, the OLYP generalized gradient approximation, which is able to give a reasonably good description of the delicate spin energetics of Fe(II) coordination compounds without resorting to hybrid functionals which require the relatively more expensive calculation of a Hartree-Fock-type exchange term.

Comparison of density functionals for energy and structural differences between the high- † 5 T 2g :"t 2g … The ability of different density functionals to describe the structural and energy differences between the high-͓ 5 T 2g :(t 2g ) 4 (e g ) 2 ͔ and low-͓ 1 A 1g :(t 2g ) 6 (e g ) 0 ͔ spin states of small octahedral ferrous compounds is studied. This work is an extension of our previous study of the hexaquoferrous cation, ͓Fe(H 2 O) 6 ͔ 2ϩ , ͓J. Chem. Phys. 120, 9473 ͑2004͔͒ to include a second compound-namely, the hexaminoferrous cation, ͓Fe(NH 3 ) 6 ͔ 2ϩ -and several additional functionals. In particular, the present study includes the highly parametrized generalized gradient approximations ͑GGAs͒ known as HCTH and the meta-GGA VSXC ͓which together we refer to as highly parametrized density functionals ͑HPDFs͔͒, now readily available in the GAUSSIAN03 program, as well as the hybrid functional PBE0. Since there are very few experimental results for these molecules with which to compare, comparison is made with best estimates obtained from second-order perturbation theory-corrected complete active space self-consistent field ͑CASPT2͒ calculations, with spectroscopy oriented configuration interaction ͑SORCI͒ calculations, and with ligand field theory ͑LFT͒ estimations. While CASPT2 and SORCI are among the most reliable ab initio methods available for this type of problem, LFT embodies many decades of empirical experience. These three methods are found to give coherent results and provide best estimates of the adiabatic low-spin-high-spin energy difference, ⌬E LH adia , of 12 000-13 000 cm Ϫ1 for ͓Fe(H 2 O) 6 ͔ 2ϩ and 9 000-11 000 cm Ϫ1 for ͓Fe(NH 3 ) 6 ͔ 2ϩ . All functionals beyond the purely local approximation produce reasonably good geometries, so long as adequate basis sets are used. In contrast, the energy splitting, ⌬E LH adia , is much more sensitive to the choice of functional. The local density approximation severely over stabilizes the low-spin state with respect to the high-spin state. This ''density functional theory ͑DFT͒ spin pairing-energy problem'' persists, but is reduced, for traditional GGAs. In contrast the hybrid functional B3LYP underestimates ⌬E LH adia by a few thousands of wave numbers. The RPBE GGA of Hammer, Hansen, and Nørskov gives good results for ⌬E LH adia as do the HPDFs, especially the VSXC functional. Surprisingly the HCTH functionals actually over correct the DFT spin pairing-energy problem, destabilizing the low-spin state relative to the high-spin state. Best agreement is found for the hybrid functional PBE0. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1839854͔ I. INTRODUCTIONThe identification of the spin symmetry of the ground and low-lying excited states is important for the comprehension of chemical reactivity. However, many interesting cases occur, especially among transition metal coordination compounds, where the competition between the splitting of nearly degenerate orbitals with the electron pairing energy makes the prediction of relative spin-s...

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...