NF - mysteries of a small molecule

Nitrogen fluoride (NF) seems like a very simple molecule and you would think it would very well understood, particularly as it is small enough that it is accessible to high level quantum chemistry calculations. However, the molecule exhibits some subtle properties that present a theoretical challenge. There is limited experimental data because the molecule is only found as an intermediate in some chemical reactions.

Just like oxygen (O2), to which it is isoelectronic, the ground state is a triplet due to Hund's rule, as discussed for O2 here.

I just read a nice paper
A Valence Bond Study of the Low-Lying States of the NF Molecule 
Peifeng Su, Wei Wu, Sason Shaik, and Philippe C. Hiberty

Given that F is more electronegative than N one might expect the ground state to have a large electric dipole moment and this to increase as the molecule is stretched.
However, the ground state has only a small moment, it has the opposite direction to that expected from the electronegativity, and the direction changes sign when the bond is stretched.

Furthermore, unlike most molecules, the bond length is shorter and the dissociation energy larger in the low-lying excited states [which are singlets] than in the ground state.

The ground state has one sigma bond and six electrons in two pi orbitals.

The latter form three-electron bonds, which in the Valence Bond picture, involve exchange in position of an electron pair and an unpaired electron, where one goes from T1 above to the configurations shown below.

The authors consider 9 valence bond structures for the triplet ground state and 12 singlet VB structures for the two lowest singlet states. Their calculations lead to the following picture in terms of Lewis structures.

What insights are gained by the VB approach? Key is the idea of back donation or back bonding.

In a nutshell, the three lowest-lying states of NF can be considered as primarily bonded by a polar two-electron σ bond, complemented by π-bonding contributions of the three-electron bonding type for the ground state, and of the classical two-electron type for the excited states. In all three cases, the π-bonding contributions correspond to charge transfer from F to N, thus counterbalancing the σ polarization by back-donation. The tendencies of the bond lengths in the various electronic states comply with this simple model. Thus, all the computations and experimental measurements show that the bond length decreases consistently from the ³Σ⁻ state to ¹Δ, and from ¹Δ to ¹Σ⁺. This counterintuitive tendency, which implies that the more excited the molecule is, the more strongly it is bonded, is easily explained by the weights of the π-bonding Lewis structures, that sum up to 19 % in ³Σ⁻ state, to 28 % in the ¹Δ state, and to 37 % in the ¹Σ⁺ one (Figure 1 and Table 1 and Table 3). The same increase in the π-bonding contribution accounts again for the unusual fact that the bonding energy is far larger in the first excited state than in the ground state (96.4 vs 72.0 kcal mol⁻¹ at the VBCISD level). On the other hand, the bonding energy of the second excited state is now smaller than that of the first, as expected, since both excited states dissociate to the same products.

The tendencies in the dipole moment values of the various states are also readily rationalized by the simple VB model. The polar σ bond tends to tip the electron density towards the fluorine atom, and thus to favour negative values of the dipole moment (in the direction N⁺F⁻), while backdonation from the π systems has the opposite effect. The two effects compensate for each other in the ground state, where backdonation is moderate (19 % of π charge transfer). In the ¹Δ state, as the π charge transfer is increased relative to the ground state (28 % vs 19 %), backdonation wins over σ polarization, leading to a significant positive dipole moment, in the direction F⁺N⁻. The effect is further reinforced in the ¹Σ⁺ state, in which the π-charge transfer Lewis structure has such a large weight (37 %) that it completely overwhelms the σ polarization, ending up at a positive dipole moment of 0.728 D at the BOVB level.

I would like to see a basic description of these essential features in terms of a polarised two site Hubbard model with multiple orbitals and Hund's rule coupling, generalising the unpolarised two-orbital model here.

I got interested in this paper because of thinking about improper hydrogen (and halogen) bonds and wondering whether there is an "excited" diabatic state that has a shorter and stronger X-H bond than in the ground state. A general "ionic" (X^-H+) state will not have this property but if there is the option of back donation maybe something can happen....