Basis function

Cosine basis function

Keyword: COSINE

Description: The function $f(r)=\cos(g\cdot r)$ , where

Required keywords

Keyword	Type	Description
GVECTOR	section	A list of the $g$ vectors this function represents.

Optional keywords

None

Cubic spline representation of an atomic orbital

Keyword: AOSPLINE

Description: This function represents $f({\mathbf r}) = f(r) Y_{lm}(\theta,\phi)$ Several different representations of the $Y_{lm}$ spherical harmonics are available.

Keyword	$Y_{lm}$
S	1
P	$x,y,z$
5D	$3z^2-r^2,xz,yz,x^2-y^2,xy$
6D	$xx,yy,zz,xy,xz,yz$
7F_crystal	$F0,Fp1,Fm1,Fp2,Fxyz,Fp3mod,Fm3$
7F	$F0,Fm3,Fp3mod,Fp2,Fxyz,Fm1,Fp1$
10F	$xxx,yyy,zzz,xxy,xxz,yyx,yyz,zzx,zzy,xyz$
9G	$G0-9$
15G	$xxxx,yyyy,zzzz,xxxy,xxxz,yyyx,yyyz,zzzx,zzzy,xxyy,xxzz,yyzz,xxyz,yyxz,zzxy$

One of GAMESS or SPLINE is required.

Required keywords

Keyword	Type	Description
GAMESS	section	A Gaussian basis set in roughly GAMESS format, although any of the spherical harmonic keywords from the description can be used.
SPLINE	section	Fit to a 1-D spline multiplied by spherical harmonics. The first value in the section should be one of the spherical harmonics, followed by x,y pairs in atomic units.

Optional keywords

Keyword	Type	Default	Description
CUSP	float	none	For a SPLINE input, enforce a cusp at r=0 with the derivative given. For example, for H, CUSP should be -1, for Ne -10, etc.
ZERO_DERIVATIVE	flag	False	For a GAMESS input, strictly enforces derivative at r=0 (i.e. cusp) to be zero. To be used when electron-nucleus cusp conditions on all-electron atoms are treated in the Jastrow factor
SPACING	float	0.02	For GAMESS input. Spacing with which the independent variable is discretized. The default value is a safe choice for pseudoatoms, heavier all-electron atoms might require reduced value corresponding to a finer grid.
NORENORMALIZE	flag	False	Do not renormalize the basis functions
CUTOFF	float	infinity	Forces a smooth cutoff at a specified distance. Otherwise, a safe cutoff is calculated automatically.
NORMTYPE	string	GAMESSNORM	Specify the normalization type. GAMESSNORM or CRYSTAL

Cutoff cusp function

Keyword: CUTOFF_CUSP

Description: The function $f(r)=c*p/(1+\gamma*p)$ , where $p=z-z^2+z^3/3$ , $z=r/{rcut}$ , $\gamma$ is the curvature, and c is the cusp. $\gamma$ can be optimized.

Required keywords

Keyword	Type	Description
CUSP	float	The value of c
GAMMA	float	The value of $\gamma$
RCUT	float	The value of $rcut$

Optional keywords

None

Polynomial Pade function

Keyword: POLYPADE

Description: Set of functions of the form $a_n(r) = \frac{1-z(r/b_0)}{1+\beta_n z(r/b_0)}$ where $z(x)=x^2(6-8x+3x^2)$ and $\beta_n=\exp(\beta_0+1.6*n)-1$

This creates a set of monotonically functions that have zero derivative and value equal to 1 at r=0, as well as zero derivative and zero value at $r= b_0$ . $\beta_0$ can be optimized and sets the longest distance function.

Required keywords

Keyword	Type	Description
NFUNC	integer	The number of functions.
BETA	float	The value of $\beta_0$
RCUT	float	The value of $b_0$

Optional keywords

None