The carbon orbitals expanded in HO functions

Since the HO functions are the eigenfiinctions of a Hermitian operator, they form a conqilete set of functions and are therefore valid candidates for atomic basis functions. Of course, a differ question altogether is their usefulness as basis functions. Since the HO functions do not decay exponentially and do not have a cusp at the origin, we expect that more HO functions than Laguore functions are required to model the orbitals in atomic and molecular systems accurately. 

As for the Laguerre functions in Section 6.5.4, we may adjust the exponents to improve the convergence. With an exponent of 11, the Is HO expansion yields an error less than 0.1 with 3 terms included and less than 0.01 with 21 terms. Long expansions are needed for the 2s and 2p functions as well. Again, the HO functions converge much more slowly than the corresponding Laguerre functions, even with optimal exponents. 

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