An empty leg is a one-way repositioning flight: the aircraft — a Pilatus PC 12 — has to fly Raleigh/Durham to New Orleans anyway, so the whole cabin is offered as a single one-way charter at the operator's repositioning rate rather than a round-trip one. You charter the aircraft, not a seat, and the date and route are fixed by the operator's own schedule. This leg covers 766 miles, about 2h 23m in the air. The cabin seats 8.
Empty-leg inventory turns over continuously — a leg is live until the operator sells or cancels it. If this one is gone by the time you call, the links below show what is live on the same route and at the same airports right now.