Complex basis functions are not used in electronic structure calculations
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REFUTED
the evidence says no
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Scientific literature explicitly documents the use of complex Gaussian functions and complex-plane transformations of basis functions in electronic structure and quantum dynamics calculations.
Abstract Frozen Gaussian wavepackets for simulations of molecular dynamics including quantum effects require specification of the widths of the complex Gaussian functions, which may be viewed as parameters. Motivated by the standardized basis sets used in electronic structure theory, we develop a scheme for optimizing the width parameters for frozen Gaussian nuclear basis functions. The optimization approach maximizes the overlap between a reference ground state vibrational wavefunction in internal coordinates and a wavefunction determined by the product of complex Gaussians in Cartesian coordinates. After optimizing the parameters using a test set of over 100 molecules, the average width parameters are determined for a set of common atoms (H, C, O, N, F, S and Cl). The parameters are tested for excited state dynamics of ethylene and benzene using the ab initio multiple spawning (AIMS) method.
Abstract A numerical method for the calculation of spherical Bessel transforms via Gaussian quadrature in the complex plane is presented. The method is evaluated by transforming Slater and Gaussian-type spherical coordinate basis functions, used in electronic structure calculations, from position space to momentum space. The feasibility and efficiency of the method is explored for different regions of momenta and different orders of the spherical Bessel transform. The results illustrate that in general the method performs very well in the large p regions when applied to the Slater-type functions. On the other hand, a parameter has to be introduced for the application to Gaussian-type functions in order to avoid cancellation. In this case, the method performs well but accuracy is lost at larger p. Use of the parameter in application to Slater functions yields accurate results for all regions of p.
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