A general aviation pilot reported that their passenger saw a UAS pass near by their aircraft at 4;000 ft. The reporting pilot advised ATC and they attempted to provide assistance.

Narrative

On IFR departure from HEF to ZZZ via ARSNL 5 MOL transition. Cleared direct to destination with climb to 3000 ft. A large jet passed overhead at 5000 ft. Cleared to climb to 6000 ft. Passing 4000 ft my passenger saw what she thought was an airplane far away and low. After staring at it for a second; she realized she didn't know what it was. As it passed; she realized it was a drone and it was very close. Estimated within 50 feet and perhaps 4-8 feet below us. In this 2.5 seconds; she did not say anything. After it passed; she said 'I think we almost hit a drone' and pointed it out to me.She estimated the drone was fairly large with a black bent pipe structure below it and a gray and white body. It was perhaps 2 to 3 feet across. She did not think it was a quad rotor; but she is not an expert in drones either. She thought it had a large single mast. I only caught a glance at the drone after we past it and did not maneuver. Needless to say; this could have been a fatal accident but for the 'big sky theory.'I notified Potomac Approach immediately and provided 5 'Ws'. They asked me to call on landing. I did about XA:00 EDT. They informed me FAA had dispatched local authorities to the location; but no drone operators were found.