Automatized protocol and interface to simulate QM/MM time-resolved transient absorption at TD-DFT level with COBRAMM

Abstract

We present a series of new implementations that we recently introduced in COBRAMM, the open-source academic software developed in our group. The goal of these implementations is to offer an automatized workflow and interface to simulate time-resolved transient absorption (TA) spectra of medium-to-big chromophore embedded in a complex environment. Therefore, the excited states absorption and the stimulated emission are simulated along nonadiabatic dynamics performed with trajectory surface hopping. The possibility of treating systems from medium to big size is given by the use of time-dependent density functional theory (TD-DFT) and the presence of the environment is taken into account employing a hybrid quantum mechanics/molecular mechanics (QM/MM) scheme. The full implementation includes a series of auxiliary scripts to properly setup the QM/MM system, the calculation of the wavefunction overlap along the dynamics for the propagation, the evaluation of the transition dipole moment at linear response TD-DFT level, and scripts to setup, run and analyze the TA from an ensemble of trajectories. Altogether, we believe that our implementation will open the door to the easily simulate the time-resolved TA of systems so far computationally inaccessible.

Keywords: QM/MM; TD-DFT; trajectory surface hopping; transient absorption; ultrafast spectroscopy.

FIGURE 1

Schematic representation of a transient absorption experiment and of the signals simulated in this work: (A) a pump prob λ ₁ excited the system to an excited state and the created wavepacket starts propagating along this potential energy surface (PES); (B) during a certain delay time the wavepacket can split and decay to a low‐lying electronic state; (C) after that delay time a second probe pulse λ ₂ can promote the system to a different excited states or induce the relaxation to the ground states and stimulate the emission.

FIGURE 2

Schematic representation of the workflow to simulate TA spectrum. A trajectory (orange circle) is propagated along the potential energy surface of the active state (S _n) and can hop (pink arrows) between states. For each step (each circle) vertical excitations are run. The SE is convoluted according to the energy and oscillator strength of the S ₀ ‐ > Sn transition (yellow arrows and convoluted signal on the right) and the ESA from transitions from Sn to higher states (purple arrows and convoluted signal). ESA, excited state absorption; TA, transient absorption

FIGURE 3

Relative population profile for S ₂ (red line) and S ₁ (orange line) states averaged over the 150 propagated trajectories

FIGURE 4

Time‐derivative coupling between S ₂ and S ₁ along the same adiabatic (no hops allowed) trajectory, starting from the same DMABN/MeCN geometries and momenta, calculated with rigorous formula (bold orange line) and with the routine based on sub‐matrices transformations (thin black line). Time step employed in the simulation was 0.5 fs in both cases.

FIGURE 5

Simulated transient absorption spectrum of DMABN. The signal a lower energy and positive (normalized) intensity is assigned to the excited state absorption (ESA) of the populated states. While the signal rising from 5 eV at negative (normalized) intensity is assigned to the stimulated emission from the populated state to the ground state

FIGURE 6

Spectra obtained at different delay times of the probe pulse (interval of 20 fs)

FIGURE 7

Transient absorption spectra for parallel (left), magic angle (center), and orthogonal (right) orientation of the pump and probe pulses

FIGURE 8

Excited state absorption band decomposition in single contributions of transition from active state S ₁ (top half) and S ₂ (bottom half) to single S _n and full signal (bottom right square). Each box represents a single excite state absorption band and the letters indicates individual bands to whose single state absorptions contribute to