Forces and frozen phonons

FORCES AND PLANAR FORCE CONSTANTS 5.1. Forces and Frozen Phonons 

All the reasoning of Section 4 proceeded in terms of energies this is the quantity most readily accessible by the DF scheme(s). 

It is explained elsewhere in this Volume that the self-consistent charge density and ionic potential corresponding to a given configuration of atoms not only determine the system s total energy - but also provide the fo qe gacting on all atoms through the theorem of Hellmann-Feynman (HF). The details of application in the context of DF, and u jJ.n the concept of the pseudopotential, are discussed elsewhere it will be examined 

Similar calculations in terms of forces are reported in Ref. 41 for modes at F, X and L in Si. (No comparlsion with equivalent energy calculations was given.) We note that In the above calculation using forces, the self-consistent solutions corresponding to the undisplaced configuration was not needed - 

In the following Subsections, it will be shown how the HF theorem becomes a powerful tool when applied to low-symmetry displacement patterns. 

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