Nose-Hoover-chain thermostat

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The standard Nosé-Hoover thermostat suffers from well-known issues, such as the ergodicity violation in the case of simple harmonic oscillator[1]. As proposed by Martyna and Klein[1], these problems can be solved by using multiple Nose Hoover thermostats connected in a chain. Although the underlining dynamics is non-Hamiltonian, the corresponding equations of motion conserve the following energy term:

where is the Hamiltonian of the physical system, , and are the numbers of thermostats, atoms in the cell, and geometric constraints, respectively, and , , and are the position, momentum, and mass-like parameter associated with the thermostat . Just like the total energy in NVE ensemble, is valuable for diagnostics purposes. Indeed, a significant drift in indicates that the corresponding computational setting is suboptimal. Typical reasons for this behavior involve noisy forces (e.g., because of a poor SCF convergence) and/or a too large integration step (defined via POTIM).

The number of thermostats is controlled by the flag NHC_NCHAINS. Typically, this flag is set to a value between 1 and 5, the maximal allowed value is 20. In the special case of NHC_NCHAINS=0, the thermostat is switched off, leading to a MD in microcanonical ensemble. Another special case of NHC_NCHAINS=1 corresponds to the standard Nose-Hoover thermostat.

The only parameter of this thermostat is the characteristic time scale (), defined via flag NHC_PERIOD. This parameter is used to setup the mass-like variables via the relations:

Furthermore, due to rapidly varying forces in thermostat variables propagators, the standard velocity Verlet algorithm with fixed integration step might be insufficiently accurate. As proposed by Tuckerman et al., the RESPA[2] methodology can be used to overcome this problem, in which the integration step used in thermostat variables propagation is split into NHC_NRESPA equal parts, each of which may be further divided into NHC_NS smaller parts treated by Suzuki-Yoshida scheme of fourth or sixth order.


References