After my previous question (here), I'm now studying the orbitals actually used in Gaussian through calculating them myself using Basis Set Exchange data. However, I found that some orbital exponents of s-orbital are too large and correspondingly their normalization terms become too large. As a result, the scale of s-orbital and other orbitals (e.g., p- and d-orbitals) is very different.
For example, the following figure shows the orbital shapes on O-H bond of H2O molecule (note that the direction of spherical harmonic is along O-H bond, that is, O-H is the x-axis).
Of course, each primitive Gaussian function is normalized (e.g., six primitives for O_1s) so that the integral is one. Actually, Basis Set Exchange provides the following orbital exponent and contraction coefficient values for the primitive functions as follows.
SHELL TYPE PRIMITIVE EXPONENT CONTRACTION COEFFICIENT(S)
S 6 1.00
SP 3 1.00
0.1553961625D+02 -0.1107775495D+00 0.7087426823D-01
0.3599933586D+01 -0.1480262627D+00 0.3397528391D+00
0.1013761750D+01 0.1130767015D+01 0.7271585773D+00
SP 1 1.00
0.2700058226D+00 0.1000000000D+01 0.1000000000D+01
D 1 1.00
Comparing p- and d-orbitals, the extreme value of s-orbital near O atom seems strange to me. Is this because the orbital exponent is too large (e.g., 0.5484671660D+04 and 0.8252349460D+03)? Or is this because multiple primitive Gaussian functions with large exponents actually represent a real Slater function? (Or this may be just a mistake of my implementation.)