# Units

IMD does not need a particular system of units. It can work with any system. The units used by IMD are implicitly defined in the configuration and potential files, and possibly by certain parameters specifying the potential. The configuration file contains atom positions and atom masses, which implicitly defines a length unit and a mass unit, respectively. The interaction potential implicitly makes use of a length unit and an energy unit. Of course, this length unit must be the same as for the configuration file. The three units of length, mass, and energy determine all other units, which are derived from them. The temperature is always given in energy units.

### Example

If the length unit is 1 Angstrom = 1e-10 m, the energy unit 1 eV = 1.6022e-19 J (which corresponds to 11605 K), and the mass unit is 1 amu = 1.6605e-27 kg, we have for the unit of time 1.018e-14 s = 10.18 fs. The unit of pressure then is 160.2 GPa = 1602 kbar.

### Time step

For simulating a solid, a time step of 1 femtosecond is usually a good starting point. Whether a certain time step is a reasonable choice can be checked by making an NVE simulation for some 10000 time steps, with eng_int set to 1 (writing the energy at every time step). The resulting .eng file can then be Fourier transformed with the utility program imd_power, revealing the frequency spectrum of the fluctuations of the kinetic energy and other quantities. If the mode with the highest essential frequency omega_max in that spectrum shall be tracked with, say, 30 time steps, then the time step must be roughly equal to 2*pi/(30*omega_max). If the initial time step was too small, this procedure should be repeated.

### Time constant for temperature control

The integrators nvt, npt_iso, and npt_axial offer a Nose-Hoover thermostat, which requires a time constant inv_tau_eta to be set appropriately. This time constant defines another frequency in the system; in order for the thermostat to work well, it must couple effectively to the native freqency spectrum of the system. A good estimate for a suitable value of inv_tau_eta can be obtained in an NVE simulation with the compile option einstein switched on. The Einstein frequency is then written to the .eng file, whose average (or two thirds thereof) can be used as an initial value of inv_tau_eta. With that value, an NVT simulation should then be performed, and the frequency spectrum analysed with the utility program imd_power. With a bad choice of inv_tau_eta, an extra peak outside the native frequency spectrum is visible, whose position is proportional to inv_tau_eta, which can then be corrected accordingly. For a good choice of inv_tau_eta, the frequency spectrum is only slighly distorted. The optimal value of inv_tau_eta is usually not very critical, and changes only slowly with temperature and pressure.

### Time constant for pressure control

Besides a time constant for temperature control (which should be determined first and then kept fixed), the ensembles npt_iso and npt_axial also require a time constant for pressure control, inv_tau_xi. Its determination is analoguous to the determination of inv_tau_eta, except that here one looks at pressure fluctuations. Also, there is no analogue of the Einstein frequency as initial guess, so that some experimentation is necessary. One usually obtains a very large and sharp peak in the fluctuation spectrum, which suggests how to change inv_tau_xi. It is in fact not so easy to find a value for which there is no large extra peak in the spectrum. The value of inv_tau_xi needs to be determined much more precisely than inv_tau_eta.