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We apply Löwdin's canonical orthogonalization method to investigate the linearly dependent problem arising from the variational calculation of atomic systems using Slater‐type orbital configuration‐interaction (STO‐CI) basis functions. With a specific arithmetic precision used in numerical computations, the nonorthogonal STO‐CI basis is easily linearly dependent when the number of basis functions is sufficiently large. We show that Löwdin's canonical orthogonalization method can successfully overcome such problem and simultaneously reduce the dimension of basis set. This is illustrated first through an S‐wave model He atom, and then the real two‐electron atoms in both the ground and excited states. In all of these calculations, the variational bound state energies of the two‐electron systems are obtained in reasonably high accuracy using over‐redundant STO‐CI bases, however, without using extended high‐precision technique. © 2015 Wiley Periodicals, Inc.  相似文献   

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We propose to characterize the width of a basis set (BS) by the number of basis functions falling within one electron of the considered atomic or molecular systems. It is established that for atoms, this value (the electron function endowment, or EFE) undergoes drastic changes as the atomic number of a periodic system element increases. It is shown that widening the BS through the addition of valence and polarizational functions increases the imbalance of the basis sets of various atoms in terms of EFE. A scheme of construction is proposed and an example of a BS balanced according to the EFE value is given. The properties of LiH and HF molecules are calculated by the density functional UB3LYP method with the use of standard and molecular-optimized (relaxed) BSes with segmented and general contraction of the Gaussian functions. It is established that there are uniform dependences for the error of calculating the properties of both molecules from the EFE. We conclude that the accuracy of calculating the equilibrium distance, ionization energy, electron affinity, atomization energy, dipole moment, and frequency of normal vibration increases steadily as the EFE value of a molecule rises.  相似文献   

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Analysis of various optimum and non-optimum Gaussian basis sets for firstrow elements have indicated that with a minimum increase of the basis set size and without loss of accuracy of the calculated total energy, a single universal Gaussian basis set may replace individually optimized Gaussian basis sets for a series of atoms. Such a universal Gaussian basis set may substantially reduce the computational work required for the calculation of molecular integrals in ab initio MO calculations.  相似文献   

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New segmented all-electron relativistically contracted (SARC) basis sets have been developed for the elements 81Tl–86Rn, thus extending the SARC family of all-electron basis sets to include the 6p block. The SARC basis sets are separately contracted for the second-order Douglas–Kroll–Hess and the zeroth-order regular approximation scalar relativistic Hamiltonians. Their compact size and segmented construction are best suited to the requirements of routine density functional theory (DFT) applications. Evaluation of the basis sets is performed in terms of incompleteness and contraction errors, orbital properties, ionization energies, electron affinities, and atomic polarizabilities. From these atomic metrics and from computed basis set superposition errors for a series of homonuclear dimers, it is shown that the SARC basis sets achieve a good balance between accuracy and size for efficient all-electron scalar relativistic DFT applications.  相似文献   

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