Complementing Adiabatic and Nonadiabatic Methods To Understand Internal Conversion Dynamics in Porphyrin Derivatives

Abstract

We analyze the internal conversion dynamics within the Q_y and Q_x excited states of both bare and functionalized porphyrins, which are known to exhibit significantly different time constants experimentally. Through the integration of two complementary approaches, static calculation of per-mode reorganization energies and nonadiabatic molecular dynamics, we achieve a comprehensive understanding of the factors determining the different behavior of the two molecules. We identify the key normal and essential modes responsible for the population transfer between excited states and discuss the efficacy of different statistical and nonstatistical analyses in providing a full physics-based description of the phenomenon.

Figure 1

Molecular structures of bare (a) and functionalized (b) porphyrin.

Figure 2

Schematic workflow of the calculations. In the adiabatic part (light red) of our approach, the excited states and the corresponding REs are calculated to define the relevant (i.e., most vibronically active) normal modes (μ) of the system. The nonadiabatic part (light green) consists of NAMD simulations and essential mode (ν) analysis. The analysis of essential and normal modes (light blue) comprises: (1) PES scans along these modes to find crossing points and access energy barriers (E_acc); (2) projections of essential modes on normal ones to correlate adiabatic and nonadiabatic analyses.

Figure 3

(a, c) Q_x/Q_y REs for BP (a) and FP (c), respectively. (b, d) Section of the PES along the most active Q_x mode in the range [900, 1700] cm^–1 for BP (b) and FP (d), respectively. Here, q = 0 corresponds to the ground state geometry. Red color is used for Q_x PES, and blue for Q_y. The size of the circles is proportional to their relative oscillator strength. E_acc indicates the maximum energy barrier from the Q_y minimum to the Q_x–Q_y crossing point.

Figure 4

Time evolution of the ensemble-averaged populations (a, b) and electronic energy levels (c, d) of Q_x (red) and Q_y (blue) states for bare (a, c) and functionalized (b, d) porphyrin. The shaded bands indicate 99% confidence intervals.

Figure 5

Sorted weights w_ν (eq 8) showing the percentages of the total variance explained by each essential mode, calculated on a 20 fs (a, c) and 100 fs time frame (b, d), for both BP (a, b) and FP (c, d).

Figure 6

Time-dependent standard deviation of the displacements for the first six essential modes of T₂₀, normalized at each time step and expressed as percentages for BP (a) and FP (b).

Figure 7

Atomic displacements corresponding to the six most essential modes within the 20 fs time frame for BP (a) and FP (b). Each displacement is accompanied by the PES of the Q_x (red) and Q_y (blue) states along the mode. Here, q = 0 corresponds to the ground state geometry. The sizes of the circles depict the oscillator strengths of the transitions for each single-point TDDFT calculation.

Figure 8

Projections (see eqs 11 and 12) of the essential modes within the 20 fs time frame on the Q_x normal modes of BP (a) and FP (b). Atomic displacements of the Q_x normal modes mostly contributing to each essential mode are depicted in the plots, and their frequencies are indicated in green.