Mathematical Physics - Volume II - Numerical Methods

6.2 Molecular Dynamics

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Figure 6.10: Main panels: Examples of current temperature fluctuations in time for a constant mean value of 373[K] in systems with the number of atoms: (a) 1300, and (b) 34000. Inserts: Corresponding fluctuations of the dynamic variable ξ H which ensure the constant temperature.

6.2.7 Advantages and Disadvantages of Traditional MD The main advantages of conventional MD methods are:

(i) The only model input (excluding boundary and initial conditions) is the interatomic potential. Other than that, there are no classical constitutive models that postulate the relationships between the main thermomechanical parameters of the state. (ii) No assumptions are made regarding the nature of the physical mechanisms or simulated processes that are the subject of the study. Accordingly, the possibility opens up for a well-designed virtual experiment to provide a detailed and unbiased insight into the main mechanisms of the studied physical phenomena. (iii) The above-mentioned insight into the mechanisms of the studied physical phenom ena can be achieved with extremely high spatio-temporal resolution. The main disadvantages of classical MD methods are: (i) Classical description of interatomic interactions , based on empirical potentials, greatly simplifies the rigorous quantum mechanical nature of the material. (ii) Classical description of interatomic forces in which Newton’s second law of motion replaces the Schrödinger equation of quantum mechanics. One of the indicators of the validity of this approximation is the de Broglie wavelength, which for thermal motions has the form where h is the Planck constant, m the atomic mass, k B is the Boltzmann constant and T is the absolute temperature [16]. Quantum effects are considered to be negligible if the de Broglie wavelength is less than the interatomic distance, Λ th < r 0 , or if the frequency of vibrational motion, ν , is such that h ν < k B T . In other cases, the atoms of most chemical elements (except the lightest ones like H , He , noble gases) can be considered the material points at sufficiently high temperatures and classical mechanics can be used to describe their motion. (iii) Spatio-temporal constraints which include the size of the MD model and the Λ th = h √ 2 π mk B T