Nuclear cusp conditions and their fulfillment in molecular calculations with SLATER basis sets

• Published in: International journal of quantum chemistry Vol. 114; no. 20; pp. 1393 - 1400
• Main Authors: Fernández Rico, Jaime, López, Rafael, Ema, Ignacio, Ramírez, Guillermo
• Format: Journal Article
• Language: English
• Published: Hoboken Blackwell Publishing Ltd 15.10.2014; Wiley Subscription Services, Inc
• Subjects: Chemistry; cusp conditions; electron density; Physical chemistry; Quantum physics; Slater functions
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.24657

A short revision of the main antecedents on the nuclear cusp conditions is followed by a derivation of the general expressions of the conditions which must be accomplished by wave functions and densities. It is stressed that in case of the molecular densities, besides Kato's cusp condition, there are also simple cusp conditions for the three dipole‐type terms of the densities but not for terms of order higher than dipole. The degree of fulfillment of standard atomic and molecular calculations with Slater basis sets is tested, concluding that errors of spherical terms usually affect the third or fourth significant figures, being smaller as nuclear charges increase, and the errors of dipole‐type components are greater than those of the spherical terms. In practice, improvements in the computational method or in the basis set do not guarantee a better fulfillment of the cusp conditions. Hydrogen is a special case which can yield poor results. © 2014 Wiley Periodicals, Inc. Cusp conditions for wave function and density are examined for atoms and molecules including conditions on the dipole terms. For Slater basis sets, errors of spherical terms usually decrease with nuclear charge increases, and are smaller than errors of the dipole‐type components. In practice, improvements in the computational method or in the basis set do not automatically guarantee a better fulfillment of the cusp conditions.