A Hirshfeld interpretation of the charge, spin distribution and polarity of the dipole moment of the open shell $\left( {^{3} \Sigma^{ - } } \right)$ phosphorus halides: PF and PCl

Abstract

The charge, spin distribution and dipole moments of the open shell molecules PF and PCl have been analyzed using two variants of the Hirshfeld partitioning of the electronic density. In the HI or iterative Hirshfeld approach, one keeps the number of electrons on a given atom in the molecule and proto molecule equal and does not constrain the spin distribution in any way. In the spin-adapted approach, one constrains both the charges and spins on the in situ and proatoms to be equal. We find that while allowing for both spin and charge equalization results in a spin distribution that is different from that of the conventional HI method, the behavior of the atomic spin populations as a function of internuclear separation is similar. Both methods predict that as the bond is formed, the halogen gains α and looses β electrons with the converse for P. These electron shifts are further broken down into their σ and π components and we find that while the α electrons gained by the halogen are essentially all in the σ system, they come from both the σ and π system of P. The β electrons gained by P occupy both σ and π densities, but come essentially from the π system on the halogen. The dipole moment curves are partitioned into their α and β components and showing that the dipole due to the σ spin density has the polarity P ⁺ X ⁻ while that due to the β spin density has the polarity P ⁻ X ⁺, while the net dipole polarity at equilibrium is P ⁺ X ⁻, consistent with the spin-dependent charge shifts described above.