Light Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Time Certified In Pos 1 (yrs) 24
Confusion; Distraction; Situational Awareness; Communication Breakdown
ATC Issue All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Provided Assistance; Flight Crew Returned To Clearance; Flight Crew Requested ATC Assistance / Clarification
Procedure; Human Factors
I was working Sectors 45 and 46 combined at Sector 46.  Aircraft X was on frequency and descending via the MYBAD2 arrival into RNO.  Aircraft Y was also on frequency at FL200 proceeding direct SGD. As Aircraft X descended through FL220; the pilot requested a destination change to SMF.  My first course of action was to stop Aircraft X's descent to remain in my area of jurisdiction so I stopped Aircraft X at FL200.  I then issued a clearance to SMF to Aircraft X 'direct MOEGL; Mike Oscar Echo Golf Lima; and the remainder of the SLMMR2 arrival; maintain FL200.'  The pilot garbled the readback and asked for clarification so I repeated the clearance and reinforced to maintain FL200; not to descend via.  The pilot readback MOEGL SLMMR2 arrival.  Shortly thereafter I asked the pilot for the reason for the change of destination.  As he finished; I noticed that Aircraft X had turned hard left towards Aircraft Y and that conflict alert had activated.  I immediately turned Aircraft X to a 250 heading.  Aircraft were getting closer so I climbed Aircraft X to FL210 and attempted three times to turn Aircraft Y 30 degrees left.  Apparently separation was lost; (4.97 mi).  After separation was restored I recleared both aircraft on course.I'm not really sure.  I think the aircraft; after pilot loaded the SLMMR2 in the computer; started a turn to MDOWS; the first fix on the arrival from the northeast. Direct MOEGL would've worked fine.  Also if the pilot took his 30 degree left turn immediately and not asked for clarification; separation could've been maintained.
On descent into Reno it became necessary to change our destination to SMF Sacramento International Airport due to the prevailing winds and runway in use in Reno.  We needed to use runway 34 to depart Reno and complete our passenger trip.  Reno was using runways 16 and based on performance we could not have departed.  I asked the Pilot Not Flying (PNF) to advise ATC of the destination change and he did.  We were assigned to descend and maintain FL200.  Passing FL220 we were issued our clearance to SMF. ATC claims the clearance was 'proceed direct MOEGL and the remainder of the SLAMMR2 arrival into SMF.'  We believe we heard; input; and read back proceed direct to MOGEL and then the SLMMR2 Arrival into SMF.  As the clearance was being received; written and read back to ATC by the PNF; I input MOGEL and confirmed with the PNF I heard and input it correctly.  I then followed ATC instructions and activated direct to MOGEL.  The plane began an immediate left turn.  I then proceeded to try and set up the SLMMR2 but could not find MOGEL within the first fix option for the arrival.  (There were at least 3 official option to choose from within the database).  When I couldn't find MOGEL I began to ask the PNF to query ATC; ATC got to us first and asked where we were going and turned us right.  ATC tried to get a hold of the other aircraft 3 times before he responded to turn him left. According to ATC we got to within 4.97 miles of the other aircraft.  There was no evasive action needed by either aircraft; no TCAS alert TA or RA.Factors:Pilots had a long stressful day before. By the time we clocked out and began to prepare to go to the hotel we had logged 11 hours and 30 minutes of duty. We had to circumnavigate severe weather to get into ZZZ1 for what was originally schedule for the ZZZ1-ZZZ2.  While waiting for the passengers to show (we had just over an hour to wait/plan and just over an hour to sunset. Our ops forbid us from departing ZZZ1 after sunset) the wind shifted to a tailwind. So it went from a non-stop ZZZ1-ZZZ2 to a ZZZ1-fuel stop ZZZ3-ZZZ2. My performance software wasn't working so I was relying on company dispatch/operation control to provide performance.  We had to run multiple performance calculation to determine our limits for the day out of ZZZ1. 1. Head wind no fuel stop.  Fuel for a stop if we can make it fuel last minute to go non-stop. 2. Tailwind 5 knots for departure. 3. Tailwind 10 knots for departure. Then it started to drizzle; so we ran performance to see if we could depart wet; calm; wet headwind; or wet tailwind.  We determined that we could only depart wet calm or headwind to make it to RNO we definitely couldn't go non-stop.  Then drizzle turned to rain and wind remained a tailwind so we thought it was going to have to cancel.  Then he rain stopped and the ground had time to dry; but there was a cell moving in right behind his one.  The passengers show up 20 minutes late giving us only 25 minutes to load them and their bags and takeoff.  Wind was 300 at 7 and sometimes being reported gusting to 10-15.  10 knot tailwind being limiting we may not get out.  We start up and ask ground what the delay may be for departure.  It's now XA:00 local and sunset is reported for XA:00 plus 18.  We were told we were number 3 for departure with one inbound due first; that was 8 minutes out.  So the probability was slim to make it out before sunset. I advised operational control; who stated with approval we could depart after sunset; if we were comfortable.  I said ask for approval and we will see.  We were cleared for take-off and were still waiting approval.  We got approval; it started drizzling again and the wind was reported 300 at 7.  I asked the First Officer (FO) what he thought. He said with the tailwind and the rain he wasn't comfortable.  I agreed and canceled takeoff request and taxied to the ramp.After waiting for the passenger's rental; unloading their bags and them; buttoningup the plane; securing a hotel and rental car we were finally placed into rest.  Our rest would be the minimum required followed by a short show.  Meaning; we normally get 1 hour to passenger show time and we would only get 40 minutes.  The only hotel company could find was 20 minutes away; still local in nature; but it was old; run down; with small beds; super old uncomfortable lumpy mattresses; thin walls; and no breakfast. I was awakened multiple times due to the uncomfortable beds and noise from other hotel guests.Neither of us slept great but felt fit enough to fly.  I advised mission control that neither of us had breakfast and asked for a crew meal at the fuel stop in Reno.  Flight planning begins.  Can we go non-stop or do we need a fuel stop?  Winds were again from 300; a tailwind.  Initially at 5 knots but the new AWOS would soon report 11 knots.  A no-go.  We planned on a 10 knot tailwind and would evaluate once the passengers arrived.  Then we were informed the passengers were having car trouble and may be late.  Fine; except we were hungry.  Operations said clients emailed the late notice but did not specify an ETA.  So we continued to get the plane ready and prepared for an on-time departure.  I again had to rely on operational control to provide performance as my software wasn't working. Questions:ATC claimed they needed 5 miles separation and we came to within 4.97 miles of the other aircraft.  However; AIM 4-4-11 states a 3 mile separation limit when within 40 miles of a radar antenna site.  Wasn't I within 40 miles of a radar antenna site over Reno?I'd like the tapes pulled to verify my recollection.  I believe we read MOEGL back phonetically as MOGEL.  He was busy and may have missed our read-back error.Also; the aircraft we got .03 miles too close to missed at least 2 or 3 calls to turn away from us.  If he had responded to this left turn immediately like we responded to ATC's request to immediately turn right could we have avoided getting within 5 miles of one another?Lastly; is there any requirement; expectation; or standard phraseology for ATC when issuing a new clearance from a previously assigned arrival to a newly assigned arrival.  Often you hear controllers state 'fly heading 250; when able direct MOEGL and the remainder of the SLMMR2 arrival into Sacramento'.  Asking for or being assigned a heading to initially change course and destination would have prevented all of this.
An Oakland Center (ZOA) Controller reports of a loss of separation due to an aircraft taking a different heading then they were supposed to. A Pilot reports of entering information into the FMS and then aircraft turned to continue on the routing assigned.