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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.
3D views of some hydrogen-like atomic orbitals showing probability density and phase (g orbitals and higher not shown) Atomic orbitals can be the hydrogen-like "orbitals" which are exact solutions to the Schrödinger equation for a hydrogen-like "atom" (i.e., atom with one electron). Alternatively, atomic orbitals refer to functions that depend ...
The oxygen atomic orbitals are labeled according to their symmetry as a 1 for the 2s orbital and b 1 (2p x), b 2 (2p y) and a 1 (2p z) for the three 2p orbitals. The two hydrogen 1s orbitals are premixed to form a 1 (σ) and b 2 (σ*) MO. Mixing takes place between same-symmetry orbitals of comparable energy resulting a new set of MO's for water:
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.
In hydrogen fluoride HF overlap between the H 1s and F 2s orbitals is allowed by symmetry but the difference in energy between the two atomic orbitals prevents them from interacting to create a molecular orbital. Overlap between the H 1s and F 2p z orbitals is also symmetry allowed, and these two atomic orbitals have a small energy separation ...
A hydrogen-like atom (or hydrogenic atom) is any atom or ion with a single valence electron.These atoms are isoelectronic with hydrogen.Examples of hydrogen-like atoms include, but are not limited to, hydrogen itself, all alkali metals such as Rb and Cs, singly ionized alkaline earth metals such as Ca + and Sr + and other ions such as He +, Li 2+, and Be 3+ and isotopes of any of the above.
For example, hydrogen has one electron in the s-orbital of the first shell, so its configuration is written 1s 1. Lithium has two electrons in the 1s-subshell and one in the (higher-energy) 2s-subshell, so its configuration is written 1s 2 2s 1 (pronounced "one-s-two, two-s-one"). Phosphorus (atomic number 15) is as follows: 1s 2 2s 2 2p 6 3s 2 ...
Thus for the hydrogen atom, only a single 1s orbital is needed, while for a carbon atom, 1s, 2s and three 2p orbitals are needed. The core and valence orbitals are represented by the same number of primitive Gaussian functions . For example, an STO-3G basis set for the 1s, 2s and 2p orbital of the carbon atom are all linear combination of 3 ...