The STO-xG Basis Set

The true value of tk for a many-electron atom or a molecule is unknown. If we could set it equal ( expand it) to a linear combination of an infinite number of basis functions, each defined in a space of infinite dimensions, we could carry out an exact calculation of (k. Such a set of basis functions would be a complete set. 

The various basis sets used in a calculation of the H and S integrals for a system are attempts to obtain a basis set that is as close as possible to a complete set but to stay within practical limits set by the speed and memory of contemporary computers. One immediately notices that the enterprise is directly dependent on the capabilities of available computers, which have become more powerful over the past several decades. The size and complexity of basis sets in common use have increased accordingly. Whatever basis set we choose, however, we are attempting to strike a balance. If the basis set is too small, it is inaeeurate if it is too large, it exceeds the capabilities of our computer. Whether our basis set is large or small, if we attempt to calculate all the H and S integrals in the secular matrix without any infusion of empirical information, the procedure is described as ab initio. 

The Slater-type orbitals are a family of functions that give us an economical way of approximating various atomic orbitals (which, for atoms other than hydrogen, we don t know anyway) in a single relatively simple form. For the general case, STOs are written 

Input File 8-1. The General Basis Input for an STO-IG Calculation of the Ground State Energy of the Hydrogen Atom. 

The first line gen (route section) tells the system that we want to define our own function. The lines 2, 3, and 4 are a blank line, program label (for human readers), and a blank line. The next line that is read by the system is 0 2, specifying that the ground state of H has a 0 charge and is a spin doublet (one unpaired election). The next line, h, specifies hydrogen, followed by a blank. 

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Th e con traction expon en ts and cocfTicien ts of th e d-type functions were optinii/ed using five d-primitives (the first set of d-type functions) for the STO-XG basis sets and six d-primitives (the second set of d-type functions ) for the split-valence basis sets. Thus, five d orbitals are recommended for the STO-XG basis sets and six d orhitals for the split-valence basis sets. 

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