Keyword BATH

This keyword specifies the temperature bath for canonical BOMD simulations.
Options:
NONE / SCALING / BERENDSEN / HOOVER / NOSE

	NONE		No temperature bath. This is the default.
	SCALING		Velocity scaling thermostat [234].
	BERENDSEN		Berendsen thermostat [235].
	HOOVER		Isokinetic Hoover thermostat [236].
	NOSE		Nosé-Hoover type thermostat [237,238,239].
	T=$<$Real$>$		Temperature [K] of BOMD simulation. Default is 300 K.
	TAU=$<$Real$>$		Berendsen parameter $\tau$ in ps. Default is 0.5 ps.
	INT=$<$Integer$>$		Interval for velocity scaling. Default is 1.
	FREQ=$<$Real$>$		Nosé coupling parameter. Default is 1500.0 cm$^{-1}$.
	NHC=$<$Integer$>$		Number of Nosé-Hoover chain thermostats. Default is 3.

Description:
In experiments, it is often easier to control temperature than energy. Thus, many experiments are performed under conditions more appropriately described by the canonical (N, V, T) ensemble. On the other hand, molecular dynamics simulations are most easily performed in the microcanonical (N, V, E) ensemble. While this poses no difficulty in treating macroscopic systems, it is of critical importance in the case of microscopic systems because the transformation between different ensembles is no longer possible. Therefore, we need to perform canonical-ensemble BOMD simulations if a direct comparison to experiments under temperature control is the objective. Doing so requires a modification of the equations of motion for the nuclei [233]. In particular, thermostats must be introduced to control the temperature during the simulation. All the thermostats implemented in deMon2k work on the basis of the equipartition principle. In certain applications, e.g. the calculation of the temperature dependence of the molecular heat capacity, the thermostat must control the temperature and must also ensure a canonical phase space sampling.

The option SCALING of the BATH keyword activates a simple velocity scaling [234]. The interval for the velocity scaling can be defined with the option INT. By default, the scaling is performed in each step. Figure 11a shows the instantaneous (red) and average (blue) temperature curves for this thermostat in a BOMD run of Cu$_2$. The thermostat temperature was set to 300 K.

Figure 11: Temperature profiles of Cu$_2$ BOMD simulations with (a) velocity scaling, (b) Berendsen, (c) Hoover, and (d) Nosé-Hoover thermostats. The red curves are instantaneous temperatures and the blue ones average temperatures. The thermostat temperature is set to 300 K in all runs.

As this figure shows, velocity scaling is very efficient to adjust both instantaneous and average temperatures to the thermostat value. The freezing of the instantaneous temperature indicates that the phase space distribution is not canonical. Indeed, analysis of the phase space distribution (see 4.7.3) shows a pattern similar to a microcanonical simulation rather than a canonical one [34]. The option BERENDSEN of the BATH keyword selects the BERENDSEN thermostat [235]. This thermostat couples the physical system, namely the molecule, to an external heat bath that is fixed at the desired temperature. The coupling between the molecule and the heat bath can be modified with the TAU option of the BATH keyword. Because of this coupling, the instantaneous temperature can fluctuate around the heat bath temperature. Figure 11b shows the instantaneous (red) and average (blue) temperature curves of the Berendsen thermostat in the Cu$_2$ simulation. In contrast to the velocity scaling, the fluctuations in the instantaneous temperature remain over the full trajectory length. However, the phase space distribution of the Berendsen thermostat is similar to the one from velocity scaling [34]. Thus, the Berendsen thermostat cannot be recommended for canonical BOMD simulations of molecules. It is, however, well suited for simulated annealing due to its exponential convergence behavior. The option HOOVER of the BATH keyword specifies a thermostat for the so-called constant kinetic temperature dynamics [236]. This method generates correct configurational properties in the canonical ensemble. The instantaneous (red) and average (blue) temperature curves for this thermostat are depicted in Figure 11c, again for the Cu$_2$ simulation. The repetitive instantaneous temperature fluctuations during the full simulation are characteristic of this thermostat. As a result, it causes only a few different points in phase space to be visited during the full simulation [34].

Figure 12: Phase space distributions of N$_2$ BOMD simulations at 300 K with the Nosé-Hoover (left) and Nosé-Hoover chain (right) thermostats.

The option NOSE of the keyword BATH invokes a Nosé-Hoover (chain) thermostat [237,238,239]. The chain length is specified by the NHC option. By default, three chain links (thermostats) are used. With NHC=1 a pure Nosé-Hoover thermostat is specified. The instantaneous (red) and average (blue) temperature curves for the default Nosé-Hoover chain thermostat with three links are depicted in Figure 11d, again for the Cu$_2$ simulation. This figure shows that the instantaneous temperature exhibits stochastic fluctuations during the full simulation. Despite these fluctuations, the average temperature of 300 K is reached rather quickly and is stable along the trajectory. The coupling between the Nosé-Hoover thermostat and the real system (molecule), as well as between the thermostats in the chain, is controlled by the FREQ option of the BATH keyword. The larger the FREQ value is, the weaker the coupling is. Because the performance of the Nosé-Hoover (chain) thermostat is sensitive to this coupling frequency, test calculations are recommended. This is particularly important for sensitive properties such as temperature-dependent molecular energies and entropies. The phase space distribution for a canonical N$_2$ BOMD simulation at 300 K employing the Nosé-Hoover (NHC=1) and Nosé-Hoover chain thermostat with the default value of NHC=3 are depicted in Figure 12. The plotted reduced momenta and coordinates were obtained from a SIMULATION PHASESPACE analysis of the trajectory file. As this figure shows, the Nosé-Hoover chain thermostat yields an almost perfect canonical phase space distribution for this system (see reference [233] for a detailed discussion). For this reason the Nosé-Hoover chain thermostat is the method of choice for the calculation of molecular properties in canonical ensembles, e.g. the calculation of the temperature dependence of molecular heat capacities.