Variational thermodynamic calculations for liquid transition metals

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Abstract
We present calculations of the Helmholtz free energy of three series of liquid transition metals performed by using the Gibbs-Bogoliubov variational method with a hard-sphere reference system. In order to observe the role of the s- and d-like electrons, the interaction is evaluated by extending the nearly-free-electron theory of simple metals to include the effects of transition-metal d states. For the 3d series, our results for the free energy compare fairly well with those given in the literature, and the packing fraction lies in the same range as that of simple metals, for all transition metals.