  We study an intermediate quantum coherent-incoherent charge transport
mechanism in metal-molecule-metal junctions using B\"uttiker's probe technique.
This tool allows us to include incoherent effects in a controlled manner, and
thus to study situations in which partial decoherence affects charge transfer
dynamics. Motivated by recent experiments on intermediate coherent-incoherent
charge conduction in DNA molecules [L. Xiang {\it et al.}, Nature Chem. 7,
221-226 (2015)], we focus on two representative structures: alternating
(GC)$_n$ and stacked G$_n$C$_n$ sequences; the latter structure is argued to
support charge delocalization within G segments, and thus an intermediate
coherent-incoherent conduction. We begin our analysis with a highly simplified
1-dimensional tight-binding model, while introducing environmental effects
through B\"uttiker's probes. This minimal model allows us to gain fundamental
understanding of transport mechanisms and derive analytic results for molecular
resistance in different limits. We then use a more detailed ladder-model
Hamiltonian to represent double-stranded DNA structures---with environmental
effects captured by B\"uttiker's probes. We find that hopping conduction
dominates in alternating sequences, while in stacked sequences charge
delocalization (visualized directly through the electronic density matrix)
supports significant resonant-ballistic charge dynamics reflected by an
even-odd effect and a weak distance dependence for resistance. Our analysis
illustrates that lessons learned from minimal models are helpful for
interpreting charge dynamics in DNA.
