electron relative to a set of axes attached to the nucleus on which the basis orbital is located. Note that Slater-type orbitals(STOS) are similar to hydrogenic orbitals in the region close to the nucleus. Specifically, they have a non-zero slope near the nucleus (i.e d/dr(exp(-Cr))=0=-s). In contrast, GTOS, have zero slope near r=0 because d/dr(exp(-ar))20=0. We say that STOs display a cusp"at r=0 that is characteristic of the hydrogenic solutions, whereas GtOs do not Although STOs have the proper'cusp' behavior near nuclei, they are used primarily for atomic and linear-molecule calculations because the multi-center integrals <X(1)X(2)e/rr-r2llx(1)x( 2)> which arise in polyatomic-molecule calculations(we will discuss these intergrals later in this Chapter) can not efficiently be evalusted when STOs are employed. In contrast, such integrals can routinely be computed when GTOs are used. This fundamental advantage of gtos has lead to the dominance of these functions in molecular quantum chemistry To overcome the primary weakness of GTO functions(i.e, their radial derivatives vanish at the nucleus), it is common to combine two, three or more gtOs, with combination coefficients which are fixed and not treated as lcao parameters, into new functions called contracted GTOs or CGTOs. Typically, a series of radially tight medium, and loose GTOs are multiplied by contraction coefficients and summed to produce a CGto which approximates the proper'cusp' at the nuclear center(although no such combination of GTOs can exactly produce such a cusp because each Gto has zero slope at r=0) Although most calculations on molecules are now performed using Gaussian orbitals, it should be noted that other basis sets can be used as long as they span enough 99 electron relative to a set of axes attached to the nucleus on which the basis orbital is located. Note that Slater-type orbitals (STO's) are similar to hydrogenic orbitals in the region close to the nucleus. Specifically, they have a non-zero slope near the nucleus (i.e., d/dr(exp(-zr))r=0 = -z). In contrast, GTOs, have zero slope near r=0 because d/dr(exp(-ar 2 ))r=0 = 0. We say that STOs display a “cusp” at r=0 that is characteristic of the hydrogenic solutions, whereas GTOs do not. Although STOs have the proper 'cusp' behavior near nuclei, they are used primarily for atomic and linear-molecule calculations because the multi-center integrals <cm (1) ck (2)|e2 /|r1 -r2 || cn (1) cg (2)> which arise in polyatomic-molecule calculations (we will discuss these intergrals later in this Chapter) can not efficiently be evalusted when STOs are employed. In contrast, such integrals can routinely be computed when GTOs are used. This fundamental advantage of GTOs has lead to the dominance of these functions in molecular quantum chemistry. To overcome the primary weakness of GTO functions (i.e., their radial derivatives vanish at the nucleus), it is common to combine two, three, or more GTOs, with combination coefficients which are fixed and not treated as LCAO parameters, into new functions called contracted GTOs or CGTOs. Typically, a series of radially tight, medium, and loose GTOs are multiplied by contraction coefficients and summed to produce a CGTO which approximates the proper 'cusp' at the nuclear center (although no such combination of GTOs can exactly produce such a cusp because each GTO has zero slope at r = 0). Although most calculations on molecules are now performed using Gaussian orbitals, it should be noted that other basis sets can be used as long as they span enough