DA50 Captain reported a leading edge slat malfunction after dealing with a communication problem just after departure. Captain elected to do a no flap landing at the diversion airport and made a normal landing.

Narrative

On Day 0 at XA55z my First Officer (FO) and I departed from Runway XX in ZZZ.Prior to departure; our clearance was rerouted due to active military airspace. I delayed our startup and recalculated a new flight plan with our assigned routing and new ETPs for the route. After printing a new flight plan we started up. On takeoff; after positive rate of climb was established; we retracted the gear. At 400ft AGL and above flap retraction speed; began to clean the wing on schedule. Not long after; we were instructed to switch from tower to departure. FO switched over on com 2 but did not receive a reply. At that point I tried my mic and received no reply. I reached over and switched it back to tower to confirm the frequency but no reply from tower. We noticed there was 'ACT' flashing on the radio. Assuming something was wrong with #2 I tuned the com 1 to the departure frequency and made a transmission after leveling the aircraft off at 3000ft. Right away; ATC gave us a new heading and altitude to climb to. While doing so I turned off and then on the #2 radio to reset it. After several hand offs; vectors and step climbs; I was given a clearance to proceed direct to ZZZ [VOR]. I then turned on the autopilot and began to accelerate above 200kts in Nav mode direct to ZZZ [VOR]. After reducing the workload of taking handoffs; step climbing; and being vectored; I started to use VS mode to lower the nose and accelerate. I noticed a rumble from the aircraft; looked over to the right at the flap / slat indicator; and saw that the slats were never retracted. Right away we brought them up. That's when there was a strong pull on the yoke and the aircraft began to roll. We immediately re-extended the slats. The rolling force stopped. I [advised ATC] and requested the longest runway in the area. ATC gave us a descent clearance and vectors for a visual approach to Runway XX at ZZZ1. Prior to landing we completed the slat system malfunction checklist except I elected not to use flaps and change the configuration of the aircraft. Without knowledge regarding the extent of damage to the slats; I did not want to wait to burn fuel down to landing weight and risk a slat departing the aircraft. An emergency landing was accomplished with a very shallow final approach and minimum sink rate upon touch down. We used air brakes and TRs (Thrust Reversers) to slow the aircraft. Minimum braking was applied around 110kts without excessive pressure on the brakes.In hind sight; it is SOP for first officers to complete a checklist during the gaze of flight that it should be accomplished before the captain calls for it. It has become a culture for FOs to want to do it before told or requested. I believe that because of that; when he forgot to retract the slats; I assumed he had done so and completed the checklist and did not double check.