Air taxi Captain reported a ground conflict and wingtip collision with a parked aircraft. The flight crew shut down the aircraft to assess the situation.

Narrative

Taxied in to the FBO In ZZZ on Day 0; at XA:58. The follow me cart led Aircraft X into a parking spot on the first row between a service lane and Aircraft Y. There were 2 marshals; one on the nose and the other was a wing walker on the right side in between the two aircraft. I squared up the approach to make sure the aft section of the aircraft would not cut across and track straight into the parking spot. The centerline nose marshals signaled clear and to track directly to him; with no indication of risk and didn't signal to slow down which we did anyway. I stated to my crew member that the brakes were his if he needed them. Our proximity to the other aircraft made me slow but I was still getting positive signals from the centerline marshal. At this point we were moving very slowly and anticipating crossed batons for final stop; the aircraft lurched to the right; un commanded by me and I applied the brakes and set the parking brake because whatever had just happened; I didn't want the aircraft to move any further. At that time my pilot in the right seat said that we had hit the other aircraft's wing tip. I think he applied the brakes and I applied them after I felt the initial contact. At this point we initiated the shut down and shutdown flows and checklist. We opened the aircraft door and I exited to the bottom of the stairs to assist the passengers exit. The passengers were unharmed and exited the aircraft without assistance or incident. We unloaded the baggage and once the passengers were on their way to the FBO; then we assessed the situation and observed the damage. The passengers were aware of the incident. The crew of the other aircraft were present and I think; witnessed the event. Suggestions: Logic training for line personnel; what and how they do the job and where they should be looking to get information. Don't be in a hurry.