Four-Component Damped Density Functional Response Theory Study of UV/Vis Absorption Spectra and Phosphorescence Parameters of Group 12 Metal-Substituted Porphyrins

Abstract

The influences of group 12 (Zn, Cd, Hg) metal-substitution on the valence spectra and phosphorescence parameters of porphyrins (P) have been investigated in a relativistic setting. In order to obtain valence spectra, this study reports the first application of the damped linear response function, or complex polarization propagator, in the four-component density functional theory framework [as formulated in Villaume et al. J. Chem. Phys. 2010 , 133 , 064105 ]. It is shown that the steep increase in the density of states as due to the inclusion of spin-orbit coupling yields only minor changes in overall computational costs involved with the solution of the set of linear response equations. Comparing single-frequency to multifrequency spectral calculations, it is noted that the number of iterations in the iterative linear equation solver per frequency grid-point decreases monotonously from 30 to 0.74 as the number of frequency points goes from one to 19. The main heavy-atom effect on the UV/vis-absorption spectra is indirect and attributed to the change of point group symmetry due to metal-substitution, and it is noted that substitutions using heavier atoms yield small red-shifts of the intense Soret-band. Concerning phosphorescence parameters, the adoption of a four-component relativistic setting enables the calculation of such properties at a linear order of response theory, and any higher-order response functions do not need to be considered-a real, conventional, form of linear response theory has been used for the calculation of these parameters. For the substituted porphyrins, electronic coupling between the lowest triplet states is strong and results in theoretical estimates of lifetimes that are sensitive to the wave function and electron density parametrization. With this in mind, we report our best estimates of the phosphorescence lifetimes to be 460, 13.8, 11.2, and 0.00155 s for H2P, ZnP, CdP, and HgP, respectively, with the corresponding transition energies being equal to 1.46, 1.50, 1.38, and 0.89 eV.

Behind the scenes of spin-forbidden decay pathways in transition metal complexes

“…At the four-component level of theory, the first implementation was presented by Villaume, Saue and Norman 116 and applied to, for instance, the phosphorescence of transitional metal porphyrins. 117 More recently a similar approach was implementd by Konecny et al 118 and employed on some transition metal complexes ([M(phen) 3 ] 3+ (M = Fe, Ru, Os). These developments suggests that four-component relativistic calculations of phosphorescence and ISC may soon be within reach also for transition metal complexes.…”

Photophysical properties of porphyrinic covalent cages endowed with different flexible linkers

“…This reveals a significant perturbation of the emission properties of the free-base component in the monometallated cages due to the presence of the Zn-porphyrin counterpart. A possible explanation is the close proximity of the Zn center of the metallated porphyrin to the core of the free-base partner, which can lead to a change in molecular symmetry or to an increased intersystem crossing rate [35][36][37] in the latter.…”

Application of TD-DFT Theory to Studying Porphyrinoid-Based Photosensitizers for Photodynamic Therapy: A Review

“…Theoretical calculations of porphyrinoid-based systems are usually done with Density Functional Theory (DFT)—a choice justified by the size of these systems and earlier general benchmark studies [ 43 , 44 ]. The most common is the use of the B3LYP functional [ 45 , 46 , 47 , 48 , 49 ], which is applied to predict geometries of the ground and excited states of the sensitizers [ 50 , 51 , 52 ], but other functionals, such as M06 [ 53 ], are gaining popularity as well [ 54 ].…”