Air taxi Captain reported a departure procedure navigation error during climb which resulted in an ATC altitude alert in mountainous terrain. The flight received a heading assignment and climb; then continued the flight to destination.

Narrative

*HOW THE PROBLEM AROSE*-I planned and filed the flight plan; so I received the emailed PDC; at approximately XA:30; one hour prior to our planned departure.-When loading the information from the PDC into the aircrafts navigation system; I neglected to load the RENO1 Departure.-Because I did not load the departure procedures; we did not brief the departure; as a crew; prior to takeoff.*CONTRIBUTING FACTORS*-At approximately 400' AGL I turned direct to the first fix on our flight plan (HUYJO approximate 182 mag heading).-Our initial rate of climb (ROC) was approximately 2000'/min.-When I noticed our ROC wasn't sufficient to get us over the upcoming terrain; I manually increased it (changed from flight level change to vertical speed) to approximately 2800'/min.-A few minutes after increasing our ROC; ATC stated they received a low altitude alert and instructed us to turn to a south-east heading (I do not remember the exact heading) and continue our climb to 12000'.-Upon reaching 12000' we were cleared direct to HUYJO. *HOW IT WAS DISCOVERED*-After landing at ZZZ I closely reviewed the PDC and quickly realized I missed the RENO1 departure.*CORRECTIVE ACTIONS*-I discussed my failures with my co pilot and we implemented the following internal corrective actions: -The pilot who receives the PDC; will forward the PDC to the other pilot. -The pilot who forwards the PDC will verbally confirm the other pilot received the PDC. -Before engine start; both pilots will confirm the information from the PDC is correctly inputted into the A/C's navigation systems.-Additionally; as soon as practical we will conduct remedial crew resource management training with the Chief Pilot.