Citationjet (C525/C526) - CJ I / II / III / IV
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 60; Flight Crew Total 18000; Flight Crew Type 500
Confusion; Other / Unknown
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Procedure; Human Factors; Aircraft
OPF departure [with this clearance : MIA1] RDV Vally AF M2000/E410 in 10 departure on  119.45/swk XXXX.  Upon departure from OPF we were handed off to Miami departure and subsequently cleared to 7000.  Shortly thereafter; we were cleared to intercept the VALLY transition.  This was not filed in our flight plan nor was it depicted on the published MIA One SID departure chart.  We advised ATC that the VALLY transition was not in our clearance. MIA departure then instructed us to intercept the Virginia Key 058R to VALLY.  We programmed the FMS to reflect the clearance and ARMED the auto pilot NAV mode.  Both of us verified the ARMED condition and that the correct radial was displayed on the PFD.  However; as we approached the radial the AP did not capture the NAV mode and remained in HDG taking us west of the radial.  Simultaneously; I was confirming fixes; radials and FMS programming.  This momentary distraction caused me to miss the fact that we flew through the radial.  At about the same time I picked up the off track condition and was correcting MIA departure called an instructed us to turn to a 090 heading; now.  I advised that we were already turning in that direction an apologized for the over shoot.  I asked if this caused any problem and was advised that it did not; she further stated her concern was that we might continue further west and interfere with MIA arrivals.I have recently experienced a number of clearances like the one described above where ATC issues instructions that differ from the filed routing and the accepted clearance.  This increases cockpit workload and sets all of us up for a potential conflict.  It appears to me that MIA departure is running together old departures fixes and SIDs with new ones; which is confusing.  As I pointed out earlier; VALLY is not a fix published on the OPA LOCKA; Miami One departure; but there used to be?  It is rather an enroute fix thus the verbiage; join the Vally Transition; caused some momentary confusion at a crucial time.
CE525 Captain reports departing OPF with a clearance of Radar vectors to VALLY and upon contact with MIA Departure is instructed to join the VALLY transition.  There is no VALLY transition on the MIA1 SID (the only SID available from OPF) and a clarification request leads to instructions to intercept the VKZ 058 degree Radial.  This Radial is inadvertently overshoot due to FMC programing error or autopilot malfunction.