Possible criterion for the balance of basis sets in quantum-chemical calculations

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.