Effect of density functional approximations on the calculated Jahn–Teller distortion in bis(terpyridine)manganese(III) and related compounds
Authors: Conradie Jeanet 
Published: January 2024

Abstract
Context
Bis(terpyridine)manganese(III) exhibits Jahn–Teller distortion due to the inequivalent occupation of the degenerate eg orbitals of this high-spin d4 pseudo octahedral complex. Due to the spatially constrained nature of the terpyridine ligand, the central Mn-N bonds will always be shorter than the Mn-N terminal bonds, making it more difficult to distinguish between compression and elongation Jahn–Teller structures for bis(terpyridine)manganese(III). Density functional theory (DFT) calculations were utilized as a tool to evaluate the type of Jahn–Teller distortion in the high-spin d4 bis(terpyridine)manganese(III). The nature of the Jahn–Teller distortion calculated does depend upon the choice of density functional approximation (DFA) with the B3LYP, M06, and OLYP-D3 DFAs giving compression and the PW6B95D3, MN15, and MN15-D3 DFAs giving elongation in gas-phase calculations. All solvent-phase calculations yield an elongated structure for the bis(terpyridine)manganese(III) compound, which is yet to be structurally characterized experimentally. However, both gas and solvent OLYP-D3 calculations result in a compressed structure for the only experimentally isolated and characterized bis(terpyridine)manganese(III) complex, specifically the complex with terpyridine = 4′-(4-methylphenyl)-2,2′:6′,2′′-terpyridine. This alignment with the experimentally observed compression Jahn–Teller structure enhances the credibility of OLYP-D3 calculations in reproducing the observed geometries. The compressed Jahn–Teller geometries were near D2d symmetry with the z-axis for compression defined along the Mn-N central bonds. Elongation Jahn–Teller distortion is not possible along the Mn-N central bonds, due to their spatially constrained nature. Thus, elongation occur along one pair of opposite Mn-N terminal bonds that are longer than the other pair of opposite terminal bonds, with shorter central bonds. The highest symmetry of the elongation Jahn–Teller distortion geometry of bis(terpyridine)manganese(III) is C2v. Criteria to distinguish between a compression and elongation Jahn–Teller geometry for bis(terpyridine)manganese(III) are identified. The nature of the singly occupied eg molecular orbital, exhibiting anti-bonding interaction with the nitrogen-p MOs involved, dictates the type of Jahn–Teller distortion that occurs. The low-energy occupied bonding t2g molecular orbitals establish bonds with and undergo mixing with the ligand molecular orbitals. The OLYP-D3 functional is recommended for calculating bis(terpyridine)manganese(III) and related compounds due to its consistent generation of metal–ligand bonds slightly longer than observed in experiments, in line with the required behavior. Additionally, OLYP-D3 offers a realistic electronic structure for Jahn–Teller distorted bis(terpyridine)manganese(III), correctly identifying alpha eg molecular orbitals as the highest occupied molecular orbital and lowest unoccupied molecular orbital in agreement with experimental electrochemical studies. Furthermore, OLYP-D3 accurately reproduces the experimental compression geometry for the only structurally known bis(terpyridine)manganese(III) compound, instilling confidence in its reliability for such calculations.

Methods
DFT geometry optimization and frequency calculations were done on the two different modes of Jahn–Teller distortion of bis(terpyridine)manganese(III), using the OLYP, B3LYP, M06, PW6B95D3, and MN15 functionals, with and without the Grimme’s D3 dispersion correction, and the 6-311G(d,p) or def2TZVPP basis set, as implemented in Gaussian 16. All optimizations were in the gas phase and also in the solvent phase with CH3CN as implicit solvent using IEFPCM.

Graphical Abstract
DFT calculations were utilized to determine the Jahn–Teller effect on the geometry of high-spin d4 bis(terpyridine)manganese(III) complex containing two structurally constrained tridentate ligands.