Metadynamics

These are some notes about the use of the metadynamics (MTD) machinery within CPMD.

The metadynamics can run in a standard NVE/NVT MD run or in a NPE/NPT run (variable cell). In order to apply the MTD algorithms in CPMD some (not few) lines have to be added in the input file. These lines have to be in the &ATOMS section and they provide information about the kind of MTD to be performed, the choice of collective variables (CV), some parameters required to determine the time dependent potential and some other options. All the MTD input must be between an initial and a final line which are:
METADYNAMICS
$\cdots$
END METADYNAMICS
If the initial line contains also the keyword $COLLECTIVE$ $VARIABLES$ , the standard MTD, with one single set of CV, is initialized. If, instead, the keyword $MULTI$ is found, more than one MTD are performed simultaneously on the same system; therefore, the whole set of CV is constituted by $NSUBSYS$ subsets, which are independent one from each other. The number of subsystems is given on the same line by writing $NS=$ followed by an integer number (default: 1). Instead, if $CELL FULL$ is the keyword, the CV are the 6 cell parameters (3 side lengths and 3 angles), and the MTD is performed without extended Lagrangian, i.e. the contribution coming from $V(t)$ is directly added into the stress tensor (see below in MTD Algorithm).

For almost all the input parameters there is a reasonable default value, but, since the range of applications of MTD is quite wide, it is likely that the default values do not fit your problem. Therefore some effort is required to choose the optimal conditions for your run.

Of course, it is important to know something about MTD before using it. References [112] and [113] are recommended to start with. There also is original literature about the method [114,115,116], and about successful applications, e.g. [117,118,119,120,121,122]. It can be of great help to read about the choices and results obtained by other users. But there are very few general rules that can be held valid for different problems and systems.

The method is based on the definition of a manifold of CVs as functions of the degrees of freedom characterizing your system, $\mathbf{S} = \{S_{\alpha}(\mathbf{R},\mathbf{\phi},\mathbf{h})\}$ , where $\mathbf{R}$ are the ionic degrees of freedom, $\mathbf{\phi}$ are the electronic wavefunctions, and $\mathbf{h}$ defines the cell box. The CV which are implemented in the code, have been chosen according to the needs of those who used the method up to now. Of course they do not exhaust all the problems, and many more CV might be needed in the future. To implement them, once the analytical formula and its derivatives are available, is not complicated at all. In principle, the implementation should be easy for anybody who knows a bit the CPMD code.