Topological analyses of time-dependent electronic structures: application to electron-transfers in methionine enkephalin

Abstract

We have studied electron transfers (ET) between electron donors and acceptors, taking as illustrative example the case of ET in methionine enkephalin. Recent pulse and gamma radiolysis experiments suggested that an ultrafast ET takes place from the C-terminal tyrosine residue to the N-terminal, oxidized, methionine residue. According to standard theoretical frameworks like the Marcus theory, ET can be decomposed into two successive steps: i) the achievement through thermal fluctuations, of a set of nuclear coordinates associated with degeneracy of the two electronic states, ii) the electron tunneling from the donor molecular orbital to the acceptor molecular orbital. Here, we focus on the analysis of the time-dependent electronic dynamics during the tunneling event. This is done by extending the approaches based on the topological analyses of stationary electronic density and of the electron localization function (ELF) to the time-dependent domain. Furthermore, we analyzed isosurfaces of the divergence of the current density, showing the paths that are followed by the tunneling electron from the donor to the acceptor. We show how these functions can be calculated with constrained density functional theory. Beyond this work, the topological tools used here can open up new opportunities for the electronic description in the time-dependent domain.

Progress and challenges in simulating and understanding electron transfer in proteins

“…They showed extremely complex flows with vortices and nodes [164,165]. More recently we proposed to consider the divergence of the density current, which is related to the derivative with respect to time of the time-dependent electronic density [166]. The method was applied to an ET within a small peptide.…”

“…The complexity of the electron flow may discourage the establishment of high-resolution models, however we believe that original tools for analyzing these functions should be devised. One may think for example of the identification of the topology of these functions [166]: @ @t qðr; tÞ ¼ Àdiv jðr; tÞ: …”

Methionine one-electron oxidation: Coherent contributions from radiolysis, IRMPD spectroscopy, DFT calculations and electrochemistry

“…Details on the performance of our modified Bruker Esquire 3000+ were already published [14]. Different electron energies were used (40)(41)(42)(43)(44) We used the relatively small basis set 6-31G(d) (SB) and the greater basis set 6-311+G(2d,2p) (GB) considering the experimental and the theoretical difficulties linked to measurements of redox potentials.…”

“…Recently, a study of the IET in one conformation of Met-enkephalin was performed by DFT and MD methods [44]. The most effective ET pathway connects an aromatic hydrogen atom on the tyrosine residue to a CH 2 group of the methionine residue.…”

Electron localisation function in current-density-functional theory

“…This generalisation has previously been used to compute time-dependent ELFs [35,36] and in the generalisation of meta-GGA functionals to calculate response properties perturbatively [27] and magnetic properties non-perturbatively [25]. The latter implementation allows for the self-consistent determination of molecular energies and orbitals in a magnetic field using London atomic orbitals [37][38][39] (also known as gauge-including atomic orbitals (GIAOs)).…”