Gaussian-Type Orbitals versus Slater-Type Orbitals: A Comparison

Abstract

The advantages of Gaussian-type orbitals (GTO) over Slater-type orbitals (STO) in quantum chemistry calculations are clarified here by means of a holistic approach. The popular Microsoft Office Excel program was used to create an interactive application with which students are able to explore the features of GTO, including automatic calculations and graphical displays. The simple case of the ground state wave function of the hydrogen atom is analyzed, for which the mathematical expressions are easily obtained by the students. The present work can be used also as a classroom guide for the particular topic of GTO, usually taught in introductory courses to atomic and molecular structure.

Crossover from weakly indirect to direct excitons in atomically thin films of InSe

“…The higher excited states with l = 0 required a very large basis size in order to accurately calculate the binding energy due to the very sharp singularity of the wave function appearing at r = 0 (Kato cusp). This situation is similar to the well-known problem in the Slater-type versus Gaussian-type orbitals in quantum chemistry [76], since the harmonic oscillator is essentially a Gaussian basis. Such a sharp feature in the excitonic wave function is mitigated in the Keldysh potential as the 1/r divergence becomes logarithmic.…”

Crossover from weakly indirect to direct excitons in atomically thin films of InSe

“…The higher excited states with l = 0 required a very large basis size in order to accurately calculate the binding energy due to the very sharp singularity of the wavefunction appearing at r = 0 (Kato cusp). This situation is similar to the well-known problem in the Slater-type versus Gaussian-type orbitals in quantum chemistry 57 , since harmonic oscillator (Hermite function) is essentially a Gaussian basis. Such a sharp feature in the excitonic wavefunction is mitigated in the Keldysh potential as the 1/r-divergence becomes logarithmic.…”

Electron and positron elastic scattering by non‐central potentials: Matrix elements and symmetry properties in the first Born approximation

“…In quantum chemistry research, the mathematical description of atomic orbitals have been studied mainly with the use of Slater [25, 26] and Gaussian functions [27–29]. The Slater function has the correct cusp at the origin and the physical exponential decay at long range [30, 31], expected by the orbital representation, nevertheless, when a many‐electron system is taken into account, the matrix elements become very hard to calculate in the coordinate space [32].…”

“…In quantum chemistry research, the mathematical description of atomic orbitals have been studied mainly with the use of Slater [25,26] and Gaussian functions [27][28][29]. The Slater function has the correct cusp at the origin and the physical exponential decay at long range [30,31],…”