Other Keywords

• ANALYSIS: A standard MD run is performed, where the equations of motions are not affected by the hills-potential or the coupling potential. The selected CV are monitored and the values are reported in the output file, after every 10 MD steps. This option is useful in order to observe the behavior of the selected CV in equilibrium conditions. With this option only two output files are written: istvar_mtd, and enevar_mtd (see section 9.11.6). The former file contains the values of the $S_{\alpha}$ and their averages in time.

• METASTEPNUM: The maximum number of MTD steps is read from the next line,
  $I\_META\_MAX$ (default: 100).

• META_RESTART: To restart a metadynamic's run from where the former run has stopprd, one can use this keyword, and write in the following line, the number of meta-steps completed already $I\_META\_RES$ (default: 0). Beware that for restarting the MTD in this way, the output files of the previous run are to be available in the run's directory and must contain a number of lines at least equal to the $I\_META\_RES$ . From this files the previous history of the MTD is read and the MTD is initialized accordingly.
  Otherwise, it is possible to restart from the restart file of the MTD, $MTD\_RESTART$ . This is an unformatted file, which is written whenever the standard CPMD restart file, $RESTART.1$ , is also written. It contains the number of meta-steps already performed, the number of CV used in the previous run and the information about the position and the size of the hills which have been already located. To restart the MTD from this file, the same keyword is used, and the keyword $RFILE$ is added in the same line, providing that the unformatted restart file is available in the run's directory. In this second case the number of performed meta-step is not read from the input file but from the restart file
  . Obviously, when a run is restarted, the same number and the same kinds of CV must be used. However masses, force constants, scaling factors, and the width and height of the hills can be changed.

• MINSTEPNUM INTERMETA: The minimum number of MD steps between two MTD steps (in general, the MTD step is characterized by the positioning of a new hill in the CV-space) is read from the next line, $INTER\_HILL$ (default: 100). This is a lower bound because, before the construction of a new hill, the displacement in the CV-space is checked, and the new step is accepted only if the calculated displacement is above a given tolerance.

• MOVEMENT CHECK: The tolerance for the acceptance of a new MTD step is read from the next line (default: 0.001D0)

• CHECK DELAY: The number of MD steps to be run, before a new check of the displacement is done, is read from the following line (default: 20).

• MAXSTEPNUM INTERMETA: The maximum number of MD steps that can be run, before a new MTD step is accepted anyway, is read from the following line (default: 300).

• METASTORE [NO TRAJECTORY]: In the following line, three integer numbers are given, which indicate respectively how often (in terms of MTD steps) the $RESTART.1$ and the $MTD\_RESTART$ files are over-written (default: 50), how often the trajectory files are appended (default: 1), and how often a quench of the electronic wavefunctions onto the BO surface is performed (default: 10000). With the additional flag NO TRAJECTORY, the trajectories are still written according to the settings as indicated by the TRAJECTORY keyword in the &CPMD section. The selection of the files (e.g. turning on TRAJEC.xyz via the XYZ flag and turning TRAJECOTORY off via a negative value of NTRAJ in combination with the SAMPLE flag) is always honored.

• MAXKINEN: From the following line, the maximum electronic kinetic energy is given, above which a quench of the electronic wavefunctions onto the BO surface is performed anyway (by default no quench is done whatever is the kinetic energy).

• LAGRANGE TEMPERATURE: The temperature $T_s$ used to initialize the velocities of the $\mathbf{s}$ CV is read from the next line. By default $T_s$ is chosen equal to the temperature of the ions, the units are Kelvin. Notice that this keyword causes the initialization of the Lagrangian formulation of MTD.

• LAGRANGE TEMPCONTROL: The control of the $T_s$ is activated, and the rescaling velocities algorithm is used. The average temperature and the permitted range of variation are read from the next line. By default $T_s$ is not controlled. Notice that this keyword causes the initialization of the extended degrees of freedom of the Lagrangian formulation of MTD.

• LAGRANGE LANGEVIN: Performs Langevin dynamics for the Lagrangian formulation of MTD. In the next line the Temperature (Kelvin) and the friction $\gamma$ (a.u.) are read. The Langevin equation in its standard form writes ($z$ is a CV):
  

  $$M\ddot z=F(z)-\gamma M \dot z+\sqrt{2k_BT\gamma M}\eta(t)$$ (272)

  
  where $M$ is the CV mass, $F$ a generic force field, $\gamma$ the friction coefficient, $T$ the temperature and $\eta$ is a white noise. The integration algorithm is a Velocity-Verlet which can be written as:
  

  $$\dot z_{n+1/2}=\dot z_n+{1\over 2}dt\Big[{F(z_n)\over M}-\gamma\dot z_n\Big]+{1\over2}\sqrt{2k_BT\gamma dt\over M}\xi_n$$

  $$z_{n+1}=z_n+\dot z_{n+1}dt$$

  $$\dot z_{n+1}=\dot z_{n+1/2}+{1\over 2}dt\Big[{F(z_{n+1})\over M}-\gamma\dot z_{n+1/2}\Big]+{1\over2}\sqrt{2k_BT\gamma dt\over M}\xi_n$$ (273)

  
  the $\xi_n$ are independent Gaussian random numbers with mean zero and variance one.

• HILLS: With this keyword it is defined the shape of $V(t)$ . If $OFF$ is read in the same line, no hill potential is used. The default hills' shape is the Gaussian-like one described above. If $SPHERE$ is read from the same line, the second exponential term in equation 263 is not applied. i.e., a normal Gaussian function rather than a Gaussian tube formalism is used. If, instead, $LORENZIAN$ is read in the same line as $HILLS$ , Lorentzian functions are used in place of Gaussians. If, instead, $RATIONAL$ is read in the same line as $HILLS$ , the rational function described in the previous section is used; in this case, if $POWER$ is read, the exponents $n$ and $m$ , and the boosting factor $f_b$ are also read immediately after (defaults: $n=2$ , $m=16$ , $f_b=1$ ). If, instead, $SHIFT$ is read on the same line as $HILLS$ , the shifted Gaussians are used, where the tails after a given cutoff are set equal to zero; in this case, if $RCUT$ is read, the cutoff $rshift$ and the boosting factor $f_b$ are also read immediately after (defaults: $rshift = 2$ ,$f_b=1$ ).
  In all this cases, if the symbol $=$ is read in the same line as $HILLS$ , the perpendicular width $\Delta s^{\perp}$ and the height $W$ are read immediately after (defaults: $\Delta s^{\perp} = 0.1 u.s.$ , $W = 0.001 Hartree$ ).

• TUNING HHEIGHT: With this keyword the height of the hills is tuned according to the curvature of the underlying potential. If the symbol $=$ is read in the same line as $TUNING$ $HHEIGHT$ , the lower and upper bounds of $W$ are read immediately after (defaults: $W_{min}=0.0001 Hartree$ , $W_{max}=0.016 Hartree$ ).

• HILLVOLUME: With this keyword the volume of the hills, $\sim W\cdot (\Delta s^{\perp})^{NCOLVAR}$ , is kept constant during the MTD run, i.e. when the height changes due to the tuning (see the previous keyword), the width is changed accordingly. This option is can be used only if the tuning of the hills' height is active.

• CVSPACE BOUNDARIES: With this keyword the confinement of the CV-space is required, in the direction of a selected group of CV. The number of dimensions of the CV-space, in which the confinement is applied, is read from the next line, $NUMB$ (default: 0). The following $NUMB$ lines describe the type of confinement. For each line the following parameters are required: index of the CV (as from the list given in the definition of the CV), the strength of the confinement potential $V_{0}$ in Hartree, two real numbers, $C1$ and $C2$ , that determine from which value of the CV the confining potential is active. Finally, if the keyword $EPS$ is read in the same line, the real number, which is read immediately after, determines how smoothly the confining potential is switched on (default $\varepsilon = 0.01$ ). The confining potential can be used with the following CV:
  DIST: $V_{conf} = V_{0}\left(\frac{s_{\alpha}}{C1}\right)^{4}$ and it becomes active only if $s_{\alpha} > C2$ .
  DIFFER: $V_{conf} = V_{0}\left(\frac{\vert s_{\alpha}\vert}{C1}\right)^{4}$ and it becomes active only if $s_{\alpha} > C2$ or $s_{\alpha} < -C2$ .
  Coordination numbers: if $(CN-\varepsilon) < C1$ , $V_{conf} = V_{0} (\frac{C1}{CN})^{10}$ , if $(CN+\varepsilon) > C2$ , $V_{conf} = V_{0} (\frac{CN}{C2})^{10}$ .

• RESTRAIN VOLUME: With this keyword a confining potential is applied to the volume variations. The option can be used only in combination with the NPE/NPT MD. From the next line, the following parameters are required: $f_{min}$ , $f_{max}$ , and $V_0$ . The factors $f_{min}$ and $f_{max}$ multiplied by the initial volume of the cell, give, respectively, the lower and upper bounds for the volume, whereas $V_0$ gives the strength of the confining potential.

• MULTI NUM: his keyword should be used when a multiple set of MTD runs are performed simultaneously on the same system. Here the number of separated sets CV for each subsystem has to be given in the following line, $NCVSYS_1 \cdots NCVSTS_{NSUBSYS}$ . This means that the first $NCVSYS_1$ CV, in the list of those defined in the $DEFINE$ $VARIABLES$ section, will belong to the first subset, the next $NCVSYS_2$ to the second, and so on. This option is implemented only together with the extended Lagrangian formulation.

• MONITOR: This keyword requires that an additional monitoring of the values of the CV is performed along the MD trajectory. This means that the values are written on an output file every WCV_FREQ MD steps, even if no hill is added at that step. The frequency for updating the file is read from the following line, the file name is cvmdck_mtd, and it is not created if this option is not activated.