Action: BF_POWERS

Module	ves
Description	Usage
Polynomial power basis functions.

Details and examples

Polynomial power basis functions.

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

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

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.

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.

Click on the labels of the actions for more information on what each action computes

BF_POWERSPolynomial power basis functions. More details MINIMUMThe minimum of the interval on which the basis functions are defined=-2.0 MAXIMUMThe maximum of the interval on which the basis functions are defined=2.0 ORDERThe order of the basis function expansion=5 LABELa label for the action so that its output can be referenced in the input to other actions=bf_pow
The BF_POWERS action with label bf_pow calculates something

Full list of keywords

The following table describes the keywords and options that can be used with this action

Keyword	Type	Default	Description
ORDER	compulsory	none	The order of the basis function expansion
MINIMUM	compulsory	none	The minimum of the interval on which the basis functions are defined
MAXIMUM	compulsory	none	The maximum of the interval on which the basis functions are defined
DEBUG_INFOThis keyword do not have examples	optional	false	Print out more detailed information about the basis set
NORMALIZATIONThis keyword do not have examples	optional	not used	The normalization factor that is used to normalize the basis functions