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Experimental methods based on magnetic resonance are among the most used techniques for investigating molecular and electronic structure. Nuclear magnetic resonance (NMR) is mostly applied to closed-shell molecules and can be used for structural research of matter in solid, liquid and gaseous form. The computation of NMR parameters, which are of a great interest not only in chemistry but also in biology and solid-state physics, presents severe analytical and numerical difficulties [Dickson & Ziegler (1996); Ditchfield (1974); Fukui et al. (2004); Helgaker et al. (1999); Ishida (2003); London (1937); Pople et al. (1968); Pyykko (1988); Schreckenbach & Ziegler (1995); Vaara (2007); Watson et al. (2004)]. The computation of NMR parameters for any of the standard models of quantum chemistry constitute an important challenge [Helgaker et al. (1999)]. Calculations involving a magnetic field should preserve gauge invariance. This is conveniently accomplished by using a gauge including atomic orbitals (GIAO) [London (1937)], which is based on atom-centered basis functions with an explicit field dependence. Magnetic properties are sensitive to the quality of the basis sets due to many contributing physical phenomena arising from both the vicinity of the nucleus and from the valence region. A good atomic orbital basis should decay exponentially for large distances [Agmon (1985)] and should also satisfy Kato’s conditions for exact solutions of the appropriate Schrodinger equation [Kato (1957)]. Exponential type functions (ETFs) are better suited than Gaussian functions (GTFs) [Boys (1950a;b)] to represent electron wave functions near the nucleus and at long range. Among the ETFs, Slater type functions (STFs) [Slater (1932)], have a dominating position due to their simple analytic expression, but their multi-center integrals are extremely difficult to evaluate for polyatomic molecules, particularly bi-electronic terms. We note that many researchers hope that the next generation of ab initio programs will be based on the usage of ETFs. Indeed much effort is being made to develop efficient molecular algorithms for integrals over conventional ETFs (STFs or B functions) [Barnett (1990); Fernandez et al. (2001); Kutzelnigg (1988); Niehaus et al. (2008); Ozdogan & (Editors); Rico et al. (1998; 1999; 2001); Steinborn et al. (2000); Weatherford & Jones (1982)].

Fourier Transformation Method for Computing NMR Integrals over Exponential Type Functions