Constraints during Molecular Dynamics

An initial and desired final configuration of a system can be used by the targeted molecular dynamics (TMD) method (Schlitter et al., 1993) to establish a suitable pathway between the given configurations. The resulting pathway, can then be employed during further SMD simulations for choosing the direction of the applied force. TMD imposes time-dependent holonomic constraints which drive the system from one known state to another. This method is also discussed in the chapter by Helms and McCammon in this volume. 

In addition to the study of atomic motion during chemical reactions, the molecular dynamics technique has been widely used to study the classical statistical mechanics of well-defined systems. Within this application considerable progress has been made in introducing constraints into the equations of motion so that a variety of ensembles may be studied. For example, classical equations of motion generate constant energy trajectories. By adding additional terms to the forces which arise from properties of the system such as the pressure and temperature, other constants of motion have been introduced. 

The SHAKE method has been extended by Tobias and Brooks [Tobias and Brooks 1988] to enable constraints to be applied to arbitrary internal coordinates. This enables the torsion angle of a rotatable bond to be constrained to a particular value during a molecular dynamics simulation, which is particularly useful when used in conjunction with methods for calculating free energies (see Section 11.7)... 

Molecular dynamics simulations may be performed under a variety of conditions and constraints, corresponding to different ensembles in statistical mechanics. Most commonly the microcanonical (NVE) ensemble is used, i.e., the number of particles, the volume, and the total energy of the system remain constant during the simulation. The relationships in Equations (l)-(3) are valid for this case. 

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