Variational calculation of Helmholtz free energies with applications to the sp-type liquid metals

Thermodynamic Properties of Liquid Alkali Metals

“…The Gibbs-Bogoliubov variational approach to investigating the thermodynamic properties of liquid alkali metals using pseudopotentials theory is well established and very effectively used in the past [1][2][3][4][5][6][7][8][9][10][11][12][13]. In such type of studies, one is concerned with choosing an appropriate reference system for the structure and the pseudopotential for electron-ion interactions.…”

“…In all the above studies, people have used hard sphere (HS) [4][5][6][7][8] or one-component plasma (OCP) [9] or optimized random phase approximation [10] or charged hard sphere (CHS) [11,12] or soft sphere (SS) [13,14] as a reference system. For the electron-ion interactions they have employed either Ashcroft empty core model (AS) [15] or Heine-Abarenkov model (HA) [16] or Harmonic model potential (HMP) [17] or Generalized nonlocal model potential (GN-MP) [13] or energy independent nonlocal model potential (EINMP) [7,8]. Singh and Singh [4] have reported the thermodynamic properties of alkali metals at 373K and noticed that for the alkali metals, the results of Helmholtz free energy due to AS model deviate from the experimental data 1.55% to 4.07%.…”

Formation and Evolution Characteristics of Nano-Clusters (For Large-Scale Systems of 106 Liquid Metal Atoms)

“…The motion equations are solved using leap-frog algorithm. The interacting inter-atomic potentials adopted here are the effective pair potential function of the generalized energy independent non-local model-pseudo-potential theory developed by Wang et al (Wang S. & Lai S. K., 1980;Li D. H., Li X. R. & Wang S., 1986) …”

“…(Wang S. & Lai S. K., 1980;Li D. H., Li X. R. & Wang S., 1986). These pair potentials are cut off at 20 a.u (atom unit).…”

Theoretical Investigation of Thermodynamical and Structural Properties of 3d Liquid Transition Metals Using Different Reference Systems

“…Also it is found in our literature survey that some abinitio pseudopotentials suitable for the perturbation theory of the ionic interactions were generated. In general, the pseudopotentials like Ashcroft empty core model (AS) [16][17][18][19], Heine-Abarenkov model (HA) [17,20,21], harmonic model potential (HMP) [17,20,21], generalized nonlocal model potential (GNMP) [22][23][24], energy independent nonlocal model potential (EINMP) [25,26] and so forth. have been applied to study the structure and thermodynamics of liquids.…”