The GTOs with variable exponents

Equipped with a complete set of simple spherical-harmonic GTOs of the form (6.6.6), we now turn our attention to the description of the radial space by means of variable exponents. We begin by comparing the expansion of the radial part of the one-electron space by means of variable exponents and by means of the principal quantum number n. 

In Eigure 6.10, we have plotted the the first three l.v GTOs with exponent 

2s and 3s GTOs (6.6.6) with unit exponent as well as 1/n. The fixed-exponent functions are more localized in 

The radial forms R J°(r) of the STOs (left) and R J°(r) of the GTOs (right) with unit exponents (atomic units). 

Complex algebra is avoided by rewriting the spherical harmonics in terms of the real solid harmonics of Section 6.4.2 (which then absorb the monomials in r), leaving us with the following simple set of real-valued spherical-harmonic GTOs 

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