Current methods for assessing safety pharmacology in the context of cardiac arrhythmia risk are unable to distinguish between drugs that cause cardiac rhythm disturbances and benign drugs. Drugs deemed likely to be unsafe share the common property of blocking the human Ether-à-go-go-Related Gene (hERG) encoded cardiac potassium channel and consequent prolongation of QT interval on the ECG. However, hERG block and QT prolongation alone are not selective indicators for cardiac arrhythmia. Here we present a prototype computational framework to distinguish between safe and unsafe hERG blockers. We used recent cryo-EM hERG structure to build and validate an atomistic structural model of the channel open conducting state. We also developed structural atomistic models of dofetilide, a hERG blocking drug with high pro-arrhythmia risk, in both charged and neutral ionization states. Next, we employed unbiased and enhanced sampling all-atom molecular dynamics (MD) simulations to probe atomic-scale mechanisms of dofetilide interaction with openstate hERG. Multi-microsecond drug "flooding" simulations revealed spontaneous dofetilide binding to the channel pore through the intracellular gate. Umbrella sampling MD was used to compute dofetilide affinity to hERG, in good agreement with experiment, as well as ingress and egress rates, which in a novel linkage between the atomistic and functional scale are utilized in our companion paper (Yang P-C et al. 2019 bioRxiv:635433) to parameterize functional kinetic models of dofetilide -hERG interactions used to predict emergent drug effects on the cardiac rhythm. This study represents the first necessary components of a computational framework for virtual cardiac safety pharmacology screening from the atom to the rhythm.