I was thinking about basis sets used in Quantum Chemistry programs and thought of why not try to visualize them.
I started with GTO from EMSL website for $\ce{H2}$, specifically cc-pVDZ basis which is the following,
! s functions
H 5 3
13.0100000 0.0196850 0.0000000 0.0000000
1.9620000 0.1379770 0.0000000 0.0000000
0.4446000 0.4781480 0.0000000 0.0000000
0.1220000 0.0000000 1.0000000 0.0000000
0.0297400 0.0000000 0.0000000 1.0000000
! p functions
H 2 2
0.7270000 1.0000000 0.0000000
0.1410000 0.0000000 1.0000000
I framed the basis functions for $s-$orbital as following, $$0.019685\times exp(-13.01 r^2) + 0.137977\times exp(-1.962 r^2) + 0.4446\times exp(-0.478148 r^2)$$ $$1\times exp(-0.12200 r^2)$$ $$1\times exp(-0.02974 r^2) $$
This is only the radial part (the associated spherical harmonic is not here), but still I can plot the above against $r$.
The above plot is for the $s-$functions.
I am able to do the same thing for $p-$functions, and I get similar Gaussians (not shown here) with different widths, and centered at zero.
Shouldn't the lobe of $p-$ be centered larger than zero (which implies that the functional form I am using is not correct/incomplete for $p-$function). Or the lack of explicit spherical harmonic functions does not allow the $p-$functions to be similarly visualized. Could someone clarify.