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The existing techniques of account for the phonon dispersion arecomputationally costly, while its impact on a variety of thermodynamicproperties appears negligible. We develop a mathematical formalism, whichallows for clear understanding of the effect. The theoretical elaborations arethen confronted with a widely used phenomenological model of the dispersionrelation. The results show that accuracy of the models, which neglect thephonon dispersion, allows for calculation of many thermodynamic quantities upto an admissible precision. Although the context refers mainly to the Helmholtzenergy , other properties are concerned as well with less details.Time-efficient schemes of control over the accuracy loss due to the neglectedphonon dispersion are discussed.

The impact of phonon dispersion on thermodynamical properties in computational models of crystalline solids