Energy minimization, molecular mechanics and lattice statics

Energy minimization, molecular mechanics and lattice statics 

In lattice statics simulations all vibrational effects are neglected2 and the internal energy of the solid U is simply equal to , and the entropy is zero. Such minimizations give the crystal structure and internal energy (often referred to as the lattice energy) of the low-temperature phase. In the static limit at 0 K and zero pressure3 the crystal structure is thus determined by the equation 

2 The inclusion of vibrational terms is dealt with later. We note in passing the fascinating example of solid He, where lattice statics is completely inappropriate. The binding forces are so weak that even at the lowest temperatures solidification occurs only at pressures of at least 2.5 MPa, and it is the zero-point vibrational energy that stabilizes the structure. 

3 For all practical purposes in modelling condensed phases the difference between zero pressure and one atmosphere can be ignored. At zero pressure, also, U and H are equal. 

Considerable effort has been made to develop efficient algorithms for quick and efficient minimization there is a vast literature on the subject. Minimization methods are divided into two classes - those that use derivatives of the energy with respect to the variables defining the structure (useful for providing information about the shape of the energy surface and thus enhancing the efficiency of the minimization), and those that do not. Considerable care is often needed in the choice of minimizes 

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