Electron dynamics in complex environments with real-time time dependent density functional theory in a QM-MM framework

Abstract

This article presents a time dependent density functional theory (TDDFT) implementation to propagate the Kohn-Sham equations in real time, including the effects of a molecular environment through a Quantum-Mechanics Molecular-Mechanics (QM-MM) hamiltonian. The code delivers an all-electron description employing Gaussian basis functions, and incorporates the Amber force-field in the QM-MM treatment. The most expensive parts of the computation, comprising the commutators between the hamiltonian and the density matrix-required to propagate the electron dynamics-, and the evaluation of the exchange-correlation energy, were migrated to the CUDA platform to run on graphics processing units, which remarkably accelerates the performance of the code. The method was validated by reproducing linear-response TDDFT results for the absorption spectra of several molecular species. Two different schemes were tested to propagate the quantum dynamics: (i) a leap-frog Verlet algorithm, and (ii) the Magnus expansion to first-order. These two approaches were confronted, to find that the Magnus scheme is more efficient by a factor of six in small molecules. Interestingly, the presence of iron was found to seriously limitate the length of the integration time step, due to the high frequencies associated with the core-electrons. This highlights the importance of pseudopotentials to alleviate the cost of the propagation of the inner states when heavy nuclei are present. Finally, the methodology was applied to investigate the shifts induced by the chemical environment on the most intense UV absorption bands of two model systems of general relevance: the formamide molecule in water solution, and the carboxy-heme group in Flavohemoglobin. In both cases, shifts of several nanometers are observed, consistently with the available experimental data.

Electron transport in real time from first-principles

“…In particular, although not discussed in the present work, this code offers the possibility to represent large environments through a quantummechanics molecular-mechanics approach. 22 This can be useful to model the effect of a solvent or other complex media in transport processes, which will be the subject of future work.…”

“…22,23 On the basis of GPU parallelization of the most demanding parts of the computation-which include the exchange correlation energy and the commutators between H and ρ-and other algorithmic optimizations, this scheme can handle time-dependent simulations of molecular systems above a hundred atoms, propagated for several hundreds of femtoseconds. 22 The present calculations were performed using 6-31G** basis sets in combination with the PBE exchange-correlation functional, and the equation of motion was integrated with a time step of 0.1 a.u. 22 The density matrix is propagated using a Magnus expansion to first-order,…”

“…22 The present calculations were performed using 6-31G** basis sets in combination with the PBE exchange-correlation functional, and the equation of motion was integrated with a time step of 0.1 a.u. 22 The density matrix is propagated using a Magnus expansion to first-order,…”

“…The method is implemented in an efficient real time TDDFT code developed in our group, designed for computations in graphic processing units (GPU). 22,23 The result is a powerful methodology free of adjustable parameters to accede to time-dependent electron transport properties of large molecular structures. The method is illustrated through its application to hydrocarbon polymers.…”

Real‐time time‐dependent density functional theory using density fitting and the continuous fast multipole method

“…[6,9] Due to its increasing popularity, RT-TDDFT has been implemented in several software packages like GAUSSIAN, NWCHEM, OCTOPUS, QBOX, Q-CHEM, SIESTA, etc. [4,7,8,[10][11][12][13][14][15][16][17][18][19][20][21][22] One of the limitations of RT-TDDFT is that the exchange correlation part of the Kohn-Sham (KS) matrix is generally non-local in both space and time. It is also formally a functional of the initial wave function and the entire history of the density.…”