See examples in AO.mw
AO::[center,angular,radial,C,label] encoded form of atomic orbital (AO), wherecenter::{0,atomindex,<X,Y,Z>} AO center (coordinates are in bohr),angular::{[px,py,pz],[-l,m,0],[-l,k],[l,k],AOsym} angular part of monomial "m", trigonometric "t", or cubic "c" type, where[px,py,pz] powers at x,y,z of monomial angular part,[-l,m,0] orbital quantum numbers (l,m) of trigonometric angular part
(real spherical harmonics Ylm, the last number is ignored but 0 guarantees correct interpretation of 00 harmonics),[-l,k] orbital main quantum number (l) and order number (k) of trigonometric harmonics ordered as 0,1,-1,2,-2,...,[l,k] orbital main quantum number (l) and order number (k) of monomial functions ordered according to pqr table,AOsym either a monomial "X..XY..YZ..Z" or one of cubic harmonics recognized by Yxyz command (e.g. X2,Y3,Z3,XY2,S4),radial::{[n2,zeta],list([a,c])} radial part of Gaussian (GTO) or Slater (STO) type, wheren,n2,zeta principal quantum number (n=n2+l) and exponent of STO,a,c exponent and coefficient of a primitive gaussian constituting the contracted gaussian,C::numeric:=1 optional precomputed normalization constant (or a multiplicative factor),label::string:="" optional label.AOangular(angular,x,y,z)::expression normalized angular part,AOl(angular)::nonnegint angular quantum number,AOt(angular)::{"m","t","c"} type of angular function,AOr(AO,r)::expression radial part,AOxyz(AO,x,y,z)::expression explicit form,AOnormalize(AO,{function})::AO normalize AO by recalculating C,
if function then it normalizes only radial part (constants c for GTO, error for STO)
and recalculates C to keep the entire norm unchanged.