NOTE On the Electronic Structure of FeF and Its Cations
Recently, iron monofluoride has been investigated both theoretically (1) and experimentally (2). In a high level ab initio study, Bauschlicher (1) confirmed that the ground state of the molecule should be a 6 D (rr[1d 3 4p 2 9s]10s) electronic state (all the orbitals are essentially metallic and those in brackets arise from Fe / 3d). He found that the 4 D state of the same configuration lies 5210 cm 01 above the ground state at the MCPF level of calculations. The 4 F(rr[1d 3 4p 3 9s]) state is calculated to be at 11 073 cm 01 . Simultaneously, Ram et al. (2) observed, by Fourier transform emission spectroscopy, the g 4 D-a 4 D system and, assuming a complete similarity between the FeF and FeH (3) spectra, they assigned it to a transition between the 4 D states arising from the Fe / 3d 6 4s( 4 D) and 3d 7 ( 4 F) configurations. However, the derivation of the 3d-halides spectra from those of the corresponding hydrides is often deceptive because the ligand charge could be either H / or H 0 . A very instructive and pedagogical case is the NiH molecule: the ligand charge z H is calculated to be /0.538 in the d 9 ( 2 D)s 2 supermultiplet and 00.442 in the d 8 ( 3 F)s 2 s* 1 manifold of states (4). In this note we reinvestigate the ordering of the low-lying electronic states of FeF on the basis of combined ab initio and ligand field theory (LFT) calculations ( 5).
The ab initio calculations are based on density functional theory as implemented in the deMon program (6, 7). They were performed on the sextet 6 D (rr[1d 3 4p 2 9s]10s), 6 P(rr[1d 2 4p 3 9s]10s), and 6 S / (rr[1d 2 4p 2 9s 2 ]10s) states since the lowest energy terms of Fe / (a 6 D, a 4 F, and a 4 D) are expected to give rise to all the low-lying electronic states of FeF. All internal molecular orbitals are fully occupied and keep their atomic character. The valence orbitals are essentially metallic even though they exhibit some mixing with 2p(F). This causes a polarization of the electronic cloud toward fluorine which leads to a lack of negative charge on the iron atom (about 0.47 from Mulliken population analysis). Similarly to Bauschlicher's results on the ground state, the two remaining sextet states present a nearly Fe d 6 s 1 occupation. The energy ordering is consistent with a negatively charged ligand: T e ( 6 P) Γ
5960 cm 01 and T e ( 6 S / ) Γ
8232 cm 01 . Note that these values deviate from Pouilly et al. 's SCF values (8) by /1460 and /1812 cm 01 , respectively. The quartet states, except the 4 F, have not been calculated because they could not be well described by a single Slater determinant. The calculated energy of the 4 F state is found to lie at 3540 cm 01 , 7533 cm 01 below the Bauschlicher's value. This probably results, in a large extent, from the usual energy lowering of the d n configuration with respect to the d n 01 s one (1).
The ligand field calculations were carried out in Hund's case (a) for both d 6 s( 4,6 D) and d 7 ( 4 F) configurations, separately. First, the matrix of the d 6 s configuration was diagonalized and its eigenvalues fitted on the transition energies of our 6 P and Bauschlicher's a 4 D states. Then the d 7 matrix was diagonalized by fitting the 4 D state on the observed g 4 D one (2). The LFT parameters were: d 6 s (B 2 0 Γ
15 612 cm 01 , B 4 0 Γ
4788 cm 01 , G 2 Γ
962 cm 01 , z d Γ
0413 cm 01 ) and d 7 (B 2 0 Γ
15 202 cm 01 , B 4 0 Γ
4580 cm 01 , z d Γ
0298 cm 01 ). The resulting averaged levels are depicted in Fig. 1. The lowest spin-orbit component of the 4 F state is found to lie at 10 728 cm 01 , in very good agreement with the Bauschlicher's value (11 073 cm 01 ). The 6 S / state lies at about 10 520 cm 01 , 2288 cm 01 above our FIG. 1. Low-lying energy levels of FeF from combined LFT and ab density functional value. This downward displacement could probably be initio calculations. Only the 3d 6 4s ( 6 D), 3d 6 4s ( 4 D), and 3d 7 ( 4 F) configurations are considered. due to a crystal-field-induced interaction (9) between the zero-order