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A normalized 1s Slater-type function is a function which is used in the descriptions of atoms and in a broader way in the description of atoms in molecules. It is particularly important as the accurate quantum theory description of the smallest free atom, hydrogen. It has the form
Given that the hydrogen atom contains a nucleus and an electron, quantum mechanics allows one to predict the probability of finding the electron at any given radial distance . It is given by the square of a mathematical function known as the "wavefunction", which is a solution of the Schrödinger equation. The lowest energy equilibrium state of ...
STO-nG basis sets are minimal basis sets, where primitive Gaussian orbitals are fitted to a single Slater-type orbital (STO).originally took the values 2 – 6. They were first proposed by John Pople. A minimum basis set is where only sufficient orbitals are used to contain all the electrons in the neutral atom. Thus for the hydrogen atom, only a single 1s orbital is needed, while for a carbon ...
In theoretical and computational chemistry, a basis set is a set of functions (called basis functions) that is used to represent the electronic wave function in the Hartree–Fock method or density-functional theory in order to turn the partial differential equations of the model into algebraic equations suitable for efficient implementation on a computer.
Slater-type orbitals (STOs) are functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method.They are named after the physicist John C. Slater, who introduced them in 1930.
Using the orthonormality properties of the real unit-power spherical harmonic functions, it is straightforward to verify that the total power of a function defined on the unit sphere is related to its spectral coefficients by a generalization of Parseval's theorem (here, the theorem is stated for Schmidt semi-normalized harmonics, the ...
The use of Gaussian orbitals in electronic structure theory (instead of the more physical Slater-type orbitals) was first proposed by Boys [2] in 1950. The principal reason for the use of Gaussian basis functions in molecular quantum chemical calculations is the 'Gaussian Product Theorem', which guarantees that the product of two GTOs centered on two different atoms is a finite sum of ...
Quantum chemistry and Physics textbooks usually treat the binding of the molecule in the electronic ground state by the simplest possible ansatz for the wave function: the (normalized) sum of two 1s hydrogen wave functions centered on each nucleus. This ansatz correctly reproduces the binding but is numerically unsatisfactory.