  We present an embedded-atom-method (EAM) model that is specifically designed
to accurately describe vibrations in bcc alkali metals. Using this model, we
study bulk vibrational structure of Li, Na, K, and Rb when configured in bcc
and the closed-packed (cp) fcc, hcp, and 9$R$ phases. From the vibrational
density of states for each phase we thence find the corresponding vibrational
contribution $A_{\rm vib}(T)$ to the Helmholtz free energy $A(T)$. Utilizing
(i) differences in $A_{\rm vib}(T)$ between the bcc and cp structures and (ii)
experimentally inferred thermodynamic transition temperatures for Li and Na
(which martensitically transform from bcc to cp phases upon cooling), we
extract values for zero-temperature energy differences between the bcc and
relevant cp phases. We also put constraints on zero-temperature cp-bcc energy
differences for K and Rb, which do not exhibit temperature induced transitions.
