E145 Captain reported a number 2 engine failure at cruise followed by a diversion with a single engine landing.

Narrative

Normal flights from ZZZ3 - ZZZ2 - ZZZ1. No indications of any anomalies. Normal engine starts in ZZZ1 for flight to ZZZ4. Oil quantity at start in ZZZ1 - Eng 1 10 QTS; Eng 2 12 QTS. First Officer (FO) pilot flying (PF) on this leg; Captain was pilot monitoring (PM). Normal departure off Runway XL in ZZZ1 with routing as filed: ZZZZZ 2 ZZZZZ1 ZZZZZ2 ARXX ZZZ5 JXXX ZZZ6 JXXY ZZZ7 ZZZZZ3 4. Filed for FL370. Flying assigned route. Leveled at FL350 for several minutes where we accomplished the cruise checklist; then given the climb to FL370. FO made the 2;000 foot climb at cruise power in a cruise climb which was fine by me. Upon reaching FL370; rechecked the cruise checklist items. Soon after reaching FL370; PM noted engine #2 ITT began a fluctuating climb rapidly reaching toward redline. Captain verbalized issue to FO. Both pilots saw ITT (Interstage Turbine Temperature) passing redline; noted 979 degrees C. FO began retarding #2 engine thrust lever and both pilots noted continued ITT rise; and Captain noted oil pressure at 0; and ITT at 1;000 degrees C. Now; remember it takes longer to read these last sentences than it took in actual time; as the Captain directed and assisted the #2 thrust lever to idle and turned the #2 Start/Stop Selector to STOP. Proper confirmation techniques were used. FO disconnected the Autopilot; trimmed the aircraft and verbalized the need for a descent as Captain notified ATC of the loss of an engine and requested a descent. Flight initially given a descent to FL240 which the FO hand flew. ATC also provided a turn to the southwest. At about this point; the FA (Flight Attendant) called on the intercom. Captain responded and advised we had lost an engine and were beginning a descent. Advised flight attendant (FA) quite busy at the moment and would call her back; adding a question of there was something urgent. Nothing immediately urgent and a return call was made to the FA within a minute when she advised she noted smoke in the cabin. Questioning indicated that the smoke was almost undetectable except in the sunlight coming through the windows; was maintaining or dissipating. Captain asked for updates and advised he would have more information shortly and would make a cabin announcement when able. FA advised to interact with and calm the passengers as necessary to answer any questions and advise the Captain would be making an announcement shortly. ATC requested intentions and Captain advised they wanted to land at the nearest suitable airport and requested ATC provide airport options. ATC advised ZZZ8 and ZZZ9 closest (later investigation revealed distances nearly the same). Captain elected ZZZ8 and flight was given a direct to ZZZ8 clearance. Flight did not declare; however; ATC advised they were prioritizing the flight. In the Captain's judgment; the flight was stable; under control; the smoke report was noted yet not an issue at the time; and there was no need for drastic actions beyond the normal descent and turn toward a suitable airport. The QRH was consulted; memory items having been performed appropriately for an engine out. The fire handle was not actuated as there was no indication of fire. QRH was completed for engine out item and the APU was started; the APU bleed turned on and the crossbleed turned on. The single engine landing checklist was reviewed. Once secured; the Captain confirmed with the FA the smoke status had dissipated and then she reported hearing a 'pop' sound just before it appeared; and then the Captain made a PA to advise the passengers they were diverting to ZZZ8; the issue was under control; there was no immediate reason for concern; and that he'd update them as able. The FA was asked to prepare the cabin for landing. ATC requested and was provided SOBs and FOB information. Descent was further cleared to 12;000. FO at some point asked to and was granted permission to reengage the Autopilot; which then remained on until the Captain took control at 3;000 ft. on the visual approach and landing at ZZZ8. The crew completed the Single Engine Landing checklist and set the speeds. During the descent; EICAS message ENG 1 FIRE DET FAIL. Obviously; this created further discussion on a possible issue with engine #1; but by the time the QRH was accessed; the EICAS message cleared and did not return. Discussion of altitude control was initiated just in case something developed in the remaining engine. FO utilized good judgment in minimizing thrust on engine #1 during descent and leveling at 12;000. Engine 1 indications remained stable and normal. Flight transitioned to a normal approach using flaps 22 and Vref of flaps 45 (based on emergency return numbers based on takeoff weight for conservative position) plus 10 kts. A landing was made on Runway XXL in ZZZ8. Tower had mobilized the rescue vehicles. Captain determined the flight could exit the runway and pulled clear; stopped and made contact with the rescue vehicles. The FO was asked to request an inspection of the aircraft and engine #2 for indications of damage or fire while the Captain made a short PA to advise the passengers to remain seated and they were going to taxi to the gate after the inspection. FA reported some passenger agitation when they observed the rescue vehicles; but they remained in control. Rescue crews reported no visible damage or evidence of fire. The flight had advised ATC on the approach they would like to go to FBO upon arrival and was subsequently cleared to taxi to FBO; which had personnel deployed to the ramp to guide the aircraft to parking and then secured with chocks. Captain shut down the #1 engine and the parking checklist was performed. Communication was established with FBO to obtain a ramp which they eventually obtained from another FBO. While we waited Captain took a call from Name at [operations] just as he was picking up the phone to call [them]. It should be noted that once established toward ZZZ8; the Captain attempted to contact ARINC on both radio frequencies with no response. It was my intention to communicate with [operations] our condition and intention and seek any guidance which they could provide. Additionally; to make pre-arrangements for service and passenger handling upon arrival. Captain left the cockpit with the FO in control to personally address the passengers. They were calm and attentive with much of their concern being 'What now?'. The Captain advised them he had communicated with Operations and that passenger arrangements were being made as they spoke and he'd coordinate updated information as it was received. During the wait for the ramp the Captain communicated the events to Maintenance and made additional briefings to the passengers. Eventually the ramp was obtained; stationed by the FO and the crew performed a briefing on how to deplane the passengers. FBO provided vans on the ramp to take the passengers and their luggage to the FBO lounge. FBO unloaded the baggage compartment with the assistance of the Captain. The FA controlled the exit to one passenger at a time; the FO stationed on the ramp at the aircraft door to assist each passenger's transition from the aircraft to the ramp; the Captain positioned on the ramp stairs to further assist to the ground; where FBO personnel directed each passenger to the vans. The crew secured the aircraft with gear pins; ensured chocks were properly installed; closed the cargo door; shut down the APU and the leaving the aircraft checklist was completed. The Captain did a final check and went to the FBO along with the FA and FO. Captain checked in with the passengers. Additional phone calls with Name; and [operations]. Maintenance contacted the Captain and asked he return to the aircraft to power up the avionics and APU to pull up maintenance pages on the MFD. Captain re-secured the aircraft and returned to the FBO to communicate with the passengers. Once all the passengers were accommodated by Customer Service; Captain; FO and FA took a van to the main terminal where they were to catch a carrier flight to ZZZ4 to pick up the schedule on Day 1 with a repositioned aircraft being delivered to ZZZ4 on the morning of date. It should be noted that the FO and FA performed their jobs with exceptional professionalism and calm demeanor. They were both assessed by the Captain as well as self-assessed for fitness to continue duty and pick up the schedule the following day. Captain's assessment of the passengers was they were all calm; uninjured; unstressed; and comfortable and happy with the service options provided by Customer Service. Aside from the ARINC failure; the crew and support staff performed admirably and with true courtesy; customer-centric attention; and professionalism.