Metadynamics Keywords

Now let's start with the explanation of the keywords. First, the definition of the CV is required. The selected CV are read from the input subsection enclosed between the initial and final lines:
$DEFINE$ $VARIABLES$
$\cdots$
$END$ $DEFINE$
Between these two lines the first input line states how many CV are used, $NCOLVAR$ . In the following, each variable is described by one or more lines, according to its type. In general, each line must start with the name of the CV, $type-name$ , followed by some indexes or parameters that are needed to specify its analytical function and the kind of atoms or species that are involved. At the end, always on the same line of the $type-name$ , the scaling factor $scf$ and, if the extended Lagrangian is used, $k$ and $M$ can be given. If not specified $scf$ , $k$ and $M$ take some default values.
scf: by default, $scf=1$ and it is fixed during the whole run. Otherwise, you can write $\mathbf{SCF}$ followed by the value, or $\mathbf{SCA}$ followed by the value, a lower bound and an upper bound. In the latter case, the $scf$ is tuned along the MTD run. In practice, the average amplitude of the CV fluctuation is checked every time to time, and, if $scf_{\alpha}\cdot\delta s_{\alpha}$ is far from $\Delta s^{\perp}$ , the $scf_{\alpha}$ is changed accordingly.
M: it determines how fast the $s$ variable spans the entire well. Given the width of the well $scf\cdot\Delta s^{\perp}$ and the temperature $T_s$ , it is possible to choose $M$ by stating the number of complete fluctuations per ps. The default value is taken for 10 fluctuation per ps. Otherwise, you can write $\mathbf{MCV}$ followed by the desired value for $M$ in $Hartree ((t)/(u.s.))^2/1822 = a.m.u. (a.u./a.s.)^2$ .
k: it determines the dynamics of $s$ with respect to the dynamics of the physical CV. If $S(\cdots)$ is dominated by fast modes, it is recommended that $s$ be slower and its fluctuations span the entire well. Given the characteristic frequencies of the normal modes $\omega_{0}$ , $k$ can be chosen such that $\sqrt{k/M}< \omega_{0}$ . On the other hand, we want $k$ big enough, so that $s$ and $S$ stay close, and $S$ fluctuates many times at each position in the configuration space. By satisfying the latter condition, the average forces due to the underlying potential can be accurately estimated, and the trajectory lays on the minimum energy path. Therefore, also for $k$ , the default value is chosen in terms of $T_s$ and $scf_{\alpha}\cdot\delta s_{\alpha}$ Otherwise, you can write $\mathbf{KCV}$ followed by the desired value.

On the same line, by writing WALL+ or WALL-, some fixed upper and lower boundaries for the CV can be determined. After the keyword the position of the boundary and the value of the constant repulsive force have to be specified.

Warning: if even only one $k$ or one $M$ is read from input, the Lagrangian formulation of the MTD is initialized.