# Too large value of s-orbital in near nucleus

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)
O     0
S    6   1.00
0.5484671660D+04       0.1831074430D-02
0.8252349460D+03       0.1395017220D-01
0.1880469580D+03       0.6844507810D-01
0.5296450000D+02       0.2327143360D+00
0.1689757040D+02       0.4701928980D+00
0.5799635340D+01       0.3585208530D+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
0.8000000000D+00       1.0000000


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.)

• I'm very confused. Are you asking why an s type orbital has a large value near the nucleus at which it is sited, while all other angular momenta do not? Commented Feb 6, 2022 at 11:05
• @IanBush Yes. After normalizing all orbitals, the scale or "max value" of the s-orbital and other orbitals is very different and this is strange to me, but is this not strange? If so, the electron density on the O-H bond will be very thin, but is this not strange? If this is normal, there is no problem.
– neco
Commented Feb 6, 2022 at 11:58