Multideterminant assessment of mean-field methods for the description of electron transfer in the weak-coupling regime

Abstract

Multideterminant calculations have been performed on model systems to emphasize the role of many-body effects in the general description of charge quantization experiments. We show numerically and derive analytically that a closed-shell ansatz, the usual ingredient of mean-field methods, does not properly describe the step-like electron transfer characteristic in weakly coupled systems. With the multideterminant results as a benchmark, we have evaluated the performance of common ab initio mean field techniques, such as Hartree Fock (HF) and Density Functional Theory (DFT) with local and hybrid exchange correlation functionals, with a special focus on spin-polarization effects. For HF and hybrid DFT, a qualitatively correct open-shell solution with distinct steps in the electron transfer behaviour can be obtained with a spin-unrestricted (i.e., spin-polarized) ansatz though this solution differs quantitatively from the multideterminant reference. We also discuss the relationship between the electronic eigenvalue gap and the onset of charge transfer for both HF and DFT and relate our findings to recently proposed practical schemes for calculating the addition energies in the Coulomb blockade regime for single molecule junctions from closed-shell DFT within the local density approximation.

High-Conductive Organometallic Molecular Wires with Delocalized Electron Systems Strongly Coupled to Metal Electrodes

“…3B which is due to the mean field character of DFT with semi-local exchange correlation functionals which do not capture many body effects. 33,34 Compared with trimethylsilyl-14 or trimethyltin-capped oligophenyls with a direct Au-benzene attachment, 35 the conductance of compound 4 is more than ten-fold higher if similar wire lengths, l, (approx. 2 nm) are taken into account.…”

Partial vs. integer electron transfer in molecular assemblies: On the importance of multideterminant theoretical description and the necessity to find a solution within DFT

“…Let us replace infinite metal electrodes of an electrode-molecule-electrode system by closed-shell molecules and focus on a molecular triad as a model for electron-transfer processes triggered by an external electric field [1,2]. This approach does not allow for the definition of a conductance or current and relates rather to e.g.…”

“…The RHF calculations show that charge transfer in weakly Sparkle charge (|e|) Wave-function theory provides a general solution for charge-transfer situations, namely, with its multideterminant methods. For practical reasons, we have explored [1] the open-shell (spin-polarized) solutions of DFT with hybrid functionals and found that qualitatively correct step like behavior of charging curves can be obtained, although the quantitative values for the onsets still differ from the multideterminant benchmarks. There is a complication in obtaining these solutions: the spin symmetry of the initial guess, closed-shell by default for even number of electrons in the absence of degenerate HOMOs, has to be broken in some way in order to reach the energetically lowered and correct open-shell solution for systems where such a solution is likely to exist.…”

“…This deep correspondence suggests that an RHF result might probably be useful even beyond the domain of the strict applicability of the method, if properly assessed, and motivates a deeper analysis by means of an analytical model. The basic features of the RHF solution behavior are captured already within a model for charge transfer under Zero differential overlap between 2 MOs (one on the donor, one on the acceptor) bearing a total of 2 electrons (Z22) [1]. This model explains (i) the sharp onset of continuous charge transfer in RHF as a function of the external field, (ii) the reason for the unphysical linearity of the field dependence of the charges on the donor and the acceptor units in RHF, (iii) the origin of the HOMO-LUMO gap in the RHF mixing region, (iv) why the RHF charge-transfer onset coincides with the full one-electron transfer in CI, and finally (v) how CI corrects for the described artifacts of RHF.…”

“…However, the behavior, or rather misbehavior, of a closedshell solution merits analysis as a usual ingredient of mean-field methods in electron-transport calculations, and this is the first goal of our work. We show numerically and derive analytically using molecular models [1,2] how a closed-shell ansatz always predicts partial electron transfer, which can lead to qualitatively erroneous assessments. The partial and integer electron transfer (equivalent to CT and CB situations) are automatically discerned, and the spin purity is assured, by application of a multideterminant wave function ansatz that serves as a benchmark.…”