Reaction-Coordinate Mapping for Vibronic Molecular Transport

We present a continuum reaction-coordinate (RC) mapping for reduced descriptions of single-channel vibronic electron transport through a molecular junction coupled to an Ohmic bath with an exponential cutoff. The parameters are taken from earlier multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) benchmark calculations that reveal a phonon blockade phenomenon. For this bath, the analytic one-RC mapping gives ΩRC2=12ωc2, while the secondary bath reduces the static response to Ωeff2=2ωc2 and keeps Ohmic at low frequency, Jsec(ω)→πωcω. The bare-frequency ratio ΩRC/Jsec(ΩRC)≃1.72 provides a useful damping diagnostic and shows that the secondary bath is an essential part of both the static and dynamical response. A finite Householder construction produces the same mapping and provides direct correlation-function and discretization tests. The orthogonal transformation can be continued to a multi-RC chain, but successive extraction shifts the residual spectral density to higher characteristic frequency while its absolute strength grows rather than weakens, so the number of explicit RCs is not itself a measure of accuracy; i.e., the truncated approximations examined here do not yield a systematically improving transport current. Among the reduced descriptions examined here, a single statically renormalized RC captures much of the strong-coupling current suppression, while the finite-hybridization tests show that accurate transport additionally requires a consistent treatment of lead broadening and residual-bath dynamics. The analysis therefore separates the exact mapping, its numerical representation, and the subsequent dynamical approximation, and develops practical tests based on static response, charge-transfer correlations, correlated preparation, passivity, and the finite-hybridization spectral response. RC-based sequential kinetic calculations reproduce the qualitative strong-coupling blockade trend, with semiquantitative agreement at selected parameters that can arise in part from cancellation of distinct approximation errors.