	This is part of the ves module
	It is only available if you configure PLUMED with ./configure –enable-modules=ves . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list.

Polynomial power basis functions.

Attention: These basis functions should not be used in conventional biasing simulations. Instead you should use orthogonal basis functions like Legendre or Chebyshev polynomials. They are only included for usage in ves_md_linearexpansion and some special cases.

Basis functions given by polynomial powers defined on a bounded interval. You need to provide the interval \([a,b]\) on which the basis functions are to be used, and the order of the expansion \(N\) (i.e. the highest power used). The total number of basis functions is \(N+1\) as the constant \(f_{0}(x)=1\) is also included. These basis functions should not be used for periodic CVs.

The basis functions are given by

\begin{align} f_{0}(x) &= 1 \\ f_{1}(x) &= x \\ f_{2}(x) &= x^2 \\ & \vdots \\ f_{n}(x) &= x^n \\ & \vdots \\ f_{N}(x) &= x^N \\ \end{align}

Note that these basis functions are not orthogonal. In fact the integral over the uniform target distribution blows up as the interval is increased. Therefore they should not be used in conventional biasing simulations. However, they can be useful for usage with ves_md_linearexpansion.

Compulsory keywords

ORDER	The order of the basis function expansion.
MINIMUM	The minimum of the interval on which the basis functions are defined.
MAXIMUM	The maximum of the interval on which the basis functions are defined.

Options

DEBUG_INFO

( default=off ) Print out more detailed information about the basis set. Useful for debugging.

NORMALIZATION

The normalization factor that is used to normalize the basis functions. By default it is 1.0.

Examples

Here we employ a polynomial power expansion of order 5 over the interval -2.0 to 2.0. This results in a total number of 6 basis functions. The label used to identify the basis function action can then be referenced later on in the input file.

BF_POWERS MINIMUM=-2.0 MAXIMUM=2.0 ORDER=5 LABEL=bf_pow