Reply to Comment on "Critical analysis of a variational method used to describe molecular electron transport"

We show that the failure of the Delaney-Greer (DG) variational ansatz for transport demonstrated by us in Phys.\ Rev.\ B {\bf 80}, 165301 (2009) (I) is not related to an unsuitable constraint that prevents a broken time-reversal symmetry or to real orbitals, as DG incorrectly claim. The complex orbitals suggested by them as a way-out solution merely represent a particular case of the general case considered by us in I, which do not in the least affect our conclusion.Comment: Manuscript as submitted to Phys. Rev. B on 30 November 2010. Sections VII, VIII, and IX present significant details, which enlarge the analysis of the published versio

On a method to calculate conductance by means of the Wigner function: two critical tests

We have implemented the linear response approximation of a method proposed to compute the electron transport through correlated molecules based on the time-independent Wigner function [P. Delaney and J. C. Greer, \prl {\bf 93}, 36805 (2004)]. The results thus obtained for the zero-bias conductance through quantum dot both without and with correlations demonstrate that this method is either quantitatively nor qualitatively able to provide a correct physical escription of the electric transport through nanosystems. We present an analysis indicating that the failure is due to the manner of imposing the boundary conditions, and that it cannot be simply remedied.Comment: 22 pages, 7 figur

A physical limitation of the Wigner "distribution" function in transport

We present an example revealing that the sign of the "momentum" $P$ of the Wigner "distribution" function $f(q, P)$ is not necessarily associated with the direction of motion in the real world. This aspect, which is not related to the well known limitation of the Wigner function that traces back to the Heisenberg's uncertainty principle, is particularly relevant in transport studies, wherein it is helpful to distinguish between electrons flowing from electrodes into devices and vice versa

Applying the extended molecule approach to correlated electron transport: important insight from model calculations

Theoretical approaches of electronic transport in correlated molecules usually consider an extended molecule, which includes, in addition to the molecule itself, parts of electrodes. In the case where electron correlations remain confined within the molecule, and the extended molecule is sufficiently large, the current can be expressed by means of Laudauer-type formulae. Electron correlations are embodied into the retarded Green function of a sufficiently large but isolated extended molecule, which represents the key quantity that can be accurately determined by means of ab initio quantum chemical calculations. To exemplify these ideas, we present and analyze numerical results obtained within full CI calculations for an extended molecule described by the interacting resonant level model. Based on them, we argue that for organic electrodes the transport properties can be reliably computed, because the extended molecule can be chosen sufficiently small to be tackled within accurate ab initio methods. For metallic electrodes, larger extended molecules have to be considered in general, but a (semi-)quantitative description of the transport should still be possible particularly in the typical cases where electron transport proceeds by off-resonant tunneling. Our numerical results also demonstrate that, contrary to the usual claim, the ratio between the characteristic Coulomb strength and the level width due to molecule-electrode coupling is not the only quantity needed to assess whether electron correlation effects are strong or weak

Excitonic Splitting and Vibronic Coupling Analysis of the m -Cyanophenol Dimer

The S1/S2 splitting of the m-cyanophenol dimer, (mCP)2 and the delocalization of its excitonically coupled S1/S2 states are investigated by mass-selective two-color resonant two-photon ionization and dispersed fluorescence spectroscopy, complemented by a theoretical vibronic coupling analysis based on correlated ab initio calculations at the approximate coupled cluster CC2 and SCS-CC2 levels. The calculations predict three close-lying ground-state minima of (mCP)2: The lowest is slightly Z-shaped (Ci-symmetric); the second-lowest is <5 cm–1 higher and planar (C2h). The vibrational ground state is probably delocalized over both minima. The S0 → S1 transition of (mCP)2 is electric-dipole allowed (Ag → Au), while the S0 → S2 transition is forbidden (Ag → Ag). Breaking the inversion symmetry by 12C/13C- or H/D-substitution renders the S0 → S2 transition partially allowed; the excitonic contribution to the S1/S2 splitting is Δexc = 7.3 cm–1. Additional isotope-dependent contributions arise from the changes of the m-cyanophenol zero-point vibrational energy upon electronic excitation, which are Δiso(12C/13C) = 3.3 cm–1 and Δiso(H/D) = 6.8 cm–1. Only partial localization of the exciton occurs in the 12C/13C and H/D substituted heterodimers. The SCS-CC2 calculated excitonic splitting is Δel = 179 cm–1; when multiplying this with the vibronic quenching factor Γvibronexp = 0.043, we obtain an exciton splitting Δvibronexp = 7.7 cm–1, which agrees very well with the experimental Δexc = 7.3 cm–1. The semiclassical exciton hopping times range from 3.2 ps in (mCP)2 to 5.7 ps in the heterodimer (mCP-h)·(mCP-d). A multimode vibronic coupling analysis is performed encompassing all the vibronic levels of the coupled S1/S2 states from the v = 0 level to 600 cm–1 above. Both linear and quadratic vibronic coupling schemes were investigated to simulate the S0 → S1/S2 vibronic spectra; those calculated with the latter scheme agree better with experiment