We address a growing interest in trapping and cooling of mixed-species alka
li-metal atoms. Long-range coefficients that arise in the multipole expansi
on of molecular potentials for unlike alkali-metal dimers are calculated. T
he coefficients for the heteronuclear alkali-metal dimers corresponding to
different molecular symmetries that separate to nS-n'S,nS-n'P,nS-n'D, and n
P-n'P atomic levels are computed with high precision. We consider cases whe
re in the infinite separation Limit, one atom is in the ground state and th
e other is in one of the lowest S, P, and D excited states and both atoms a
re in their lowest excited P states. We find the long-range potentials for
Rb(5S)-Cs(6S), Rb(6S)-Cs(6S), K(4S)-Rb(5P) (1,3)Sigma, K(4P)-Cs(6P) (1,3)Si
gma, and Rb(5S)-Na(3D) (1,3)Sigma molecules to be the most attractive. The
K(4S)-Rb(SP) dimer represents the best candidate molecule for ultracold pho
toassociative spectroscopy. We also find the K(4P)-Cs(6P) and Rb(SS)-K(4P)
dimers to form, respectively, the most attractive and the most repulsive lo
ng-range potentials. The present calculation is in good agreement with expe
rimentally determined value for the 1/R-6 van der Waals coefficient for the
interaction between Cs(6S) and Li(2P) atoms. [S1050-2947(99)07101-2].