The nodeless Gaussian-type orbitals

The term spherical-harmonic is used to distinguish these orbitals from the Cartesian GTOs introduced in Section 6.6.7. Note that the GTOs of even / contain even powers of r and those of odd / contain odd powers. Thus, whereas the radial 2s and 3.s functions correspond to r exp(—ar ) and / exp(—ar ), the radial 2p and 3p functions are represented by rexp(—ar ) and r exp(—ar ). 

Completeness of the single-exponent spherical-harmonic GTOs follows from the fact that the HO functions (which constitute a complete set) may be written as finite linear combinations of GTOs, for example 

To compare the nodeless STOs and GTOs, we have in figure 6.9 plotted the first three STO and GTO functions of s symmetry with unit exponent. We note that the STOs fall off much more slowly than the GTOs, decaying exponentially that the I5 STO has a cusp at the nucleus and that the GTOs are more localized in space. 

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