Percentage Contour Maps of Electron Densities in Atoms

Abstract

Monte Carlo calculations are used to generate contour maps of atomic orbitals in which the contours enclose specified percentages of the total electron density. Maps for the most common atomic orbitals are presented, and recommendations for the presentation of atomic orbitals are made.

Expressions for the integrated probability density for the hydrogen 2s and 2p orbitals evaluated within isosurfaces

“…7 and 8, the sum of the two equations was plotted with values determined from Monte Carlo integration [2] (Fig. 3).…”

“…The wavefunction is also allows for the determination of the probability of finding an electron within a volume element through the integral ψ * ψ dτ . With the exception of the s orbitals, expressions for the integrated probability density ψ * ψ within an isosurface as a boundary have not been reported, and instead numerical or graphical integration [1], Monte Carlo integration [2] or approximations [3] have been employed. Even then, the expression for the 2s orbitals has not been expressed in terms of ψ.…”

Hands-On Hybridization: 3D-Printed Models of Hybrid Orbitals

“…Schrödinger wave equations, Ψ, model electron orbitals, and the squares of these wave equations, Ψ 2 , produce shapes representing the corresponding probability distributions of electron density . It is common to visualize orbitals by plotting the surface representing a specific value of Ψ 2 low enough to enclose 90–95% of the total electron density associated with that orbital. ,, The defined volume of an isosurface representation allows for the printing of the physical models. As in our previous work, we utilized the freeware CalcPlot3D to generate stereolithography (.stl) files necessary to produce 3D-printed models. ,, This paper extends our procedure to hybrid orbitals by demonstrating the linear combinations of constituent atomic orbitals necessary to generate the corresponding hybrid orbitals.…”

“…17 It is common to visualize orbitals by plotting the surface representing a specific value of Ψ 2 low enough to enclose 90−95% of the total electron density associated with that orbital. 16,17,37 The defined volume of an isosurface representation allows for the printing of the physical models. As in our previous work, we utilized the freeware CalcPlot3D to generate stereolithography (.stl) files necessary to produce 3D-printed models.…”

Energetics, structures, bonding, and kinetics of the HSCl-HClS system

“…Additionally, application of the T 1 diagnostic as an indicator of non-dynamic correlation results in a value of 0.012, smaller than the threshold of 0.02 recommended by Lee and Taylor [14], values larger than 0.02 indicate an increasing importance of nondynamical correlation. As to their dipole moments, the [12]. Tick marks are 0.5 a 0 apart.…”