Classical or Quantum? A Computational Study of Small Ion Diffusion in II–VI Semiconductor Quantum Dots

Abstract

Ion diffusion in semiconductor nanocrystals, or quantum dots (QDs), has gained recognition in recent years as a crucial process for advancing both energy storage and, more generally, the postsynthetic p-type doping chemistry of these materials. In this report, we present first an energetic analysis of group I cations (H+, Li+, and Na+) diffusion in (MX)84 – QDs, with M = Zn, Cd and X = S, Se. The bound solutions to the corresponding one-dimensional nuclear Schrödinger equation were solved for these systems, relying on the discrete variable representation method. From this vantage, the quantum nature of the intercalating ion can be revealed. Evidence for the importance of including quantum effects in the treatment of these diffusion processes is presented, both with the density of energy eigenstates of the intercalating ion and from a comparison of the standard deviation in the population distribution of the intercalating ion to the lattice spacings of its host material. Results suggest that the use of classical mechanics for simulations of the ion diffusion processes in these and other related materials can be a questionable practice for the smallest group I cations. Trends devised herein can be useful to help guide the development of new experimental approaches to postsynthetic doping of semiconductor nanocrystals, and in designing electrode materials for next generation electrochemical energy storage devices.

A Hybrid Quantum-Classical Model of Electrostatics in Multiply Charged Quantum Dots

“…Whereas analytical solutions of the Schrödinger equation using the “Square Well” model (eq ) can be obtained (eqs and ), the Schrödinger equation using the “Charged Sphere” model (eq ) does not have analytical solutions. Instead, the discrete variable representation (DVR) approach , is used to numerically solve the Schrödinger equation for e CB – , with the potential as defined in eq . To compare eqs – and Figure against undoped ZnO ( q – = q + = 0), an additional uncompensated probe electron was used to evaluate V ( r ).…”

“…As electrons populate the CB, interelectronic and electron–countercation interactions significantly perturb the effective potential acting upon an e CB – . In first-principles methods, interelectronic interactions produce Coulomb and exchange contributions to the Fermi-level energy ( E F ), but such calculations are only tractable for small clusters of atoms. − Here, we present a model of interelectronic and electron–cation interactions in multiply charged QDs that, through comparison with ab initio calculations and experimental results, accurately approximates E F of charged QDs. By treating key experimental parameters as explicit variables in the model, their impact on the energetics of excess electrons can be investigated systematically for any QD material.…”

First-principles calculations of hybrid inorganic–organic interfaces: from state-of-the-art to best practice

“…This can be done either by artificially saturating them, e.g. with (pseudo)hydrogen atoms, [38][39][40][41][42][43][44] or by employing density embedding methods. 45,16,31,[46][47][48][49][50] In the latter case, the cluster, which is computed using an expensive method, is embedded into a surrounding material that is significantly more extended, but described by a computationally less demanding method (often, specially designed pseudopotentials).…”

A Not Obvious Correlation Between the Structure of Green Fluorescent Protein Chromophore Pocket and Hydrogen Bond Dynamics: A Choreography From ab initio Molecular Dynamics

“…AIMD trajectories are collected according to a hybrid Quantum mechanical (QM)/molecular mechanic (MM) scheme and the energy potential ruling AIMD simulations including QM and MM regions is combined according to the hybrid Nlayered integrated molecular orbital and molecular mechanics (ONIOM) extrapolation scheme; more details on the simulations are provided in the Materials and Methods section (Svensson et al, 1996;Morokuma et al, 2006;. Density functional theory (DFT) is employed for the ab initio treatment of the QM part, since it has an optimal balance between accuracy and computational cost and DFT, in its hybrid version, has been vastly used for the theoretical characterization of both vibrational and dynamical properties of molecules (Wong, 1996;Adamo et al, 2001;Barone et al, 2010;Branduardi et al, 2011;Petrone et al, 2013;Cimino et al, 2016;Lingerfelt et al, 2016;Pepin et al, 2016;Wildman et al, 2019) and the description of the electronic structure of both ground and excited electronic states in macromolecular systems of material (Hafner et al, 2006;Beaulac et al, 2011;Guido et al, 2013;Lestrange et al, 2015;Aarons et al, 2016;Chong et al, 2016;Petrone et al, 2016bPetrone et al, , 2018Donati et al, 2017Donati et al, , 2018aGary et al, 2017;Stein et al, 2017;Crane et al, 2019) or biological interest (Langella et al, 2002;Improta et al, 2005;Lever et al, 2014;Savarese et al, 2014;Battista et al, 2018). An abinitio treatment of the HBDI chromophore and the surrounding residues is mandatory for an accurate modeling not only of their structure, but also of the non-covalent interactions among them.…”