What is the test for establishing guilt by reason of motive in a murder case?

If the challenged instruction somehow suggested that motive alone was sufficient to establish guilt, defendant's point might have merit. But in fact the instruction tells the jury that motive is not an element of the crime charged (murder) and need not be shown, which leaves little conceptual room for the idea that motive could establish all the elements of murder. When CALJIC No. 2.51 is taken together with the instruction on the concurrence of act and specific intent (CALJIC No. 3.31) and the instruction outlining the elements of murder and requiring each of them to be proved in order to prove the crime (CALJIC No. 8.10), there is no reasonable likelihood (People v. Frye, supra, 18 Cal.4th at p. 958, 77 Cal.Rptr.2d 25, 959 P.2d 183) it would be read as suggesting that proof of motive alone may establish guilt of murder.