## 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

Description: Set of functions of the form where and

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