An Attempt to Construct an Isosurface Having Symmetry Elements

Abstract

Symmetry elements in various hydrogen atomic orbitals are summarized with respect to quantum numbers n, l and m. The results are useful to improve the efficiency of drawing the isosurfaces of these orbitals.

Multiscale simulation of fluids: coupling molecular and continuum

“…111 In this regard, this extraction of continuum models from the molecular mirrors the use of generalized neural-network representations of high-dimensional potentialenergy surfaces, 112 which are used to obtain machine learning potentials for atomistic and coarse-grained simulations, emerging from first principles approaches, such as quantum DFT. [113][114][115] Embedded coupling shown in Fig. 2b and described in Ren, 116 is also known as the heterogeneous multi-scale method (HMM).…”

An overview about neural networks potentials in molecular dynamics simulation

“…There is no detailed tutorial or summary explaining how to train a neural network. A recently publication [167] describe the necessary steps for training dependable MLPs, from data creation to training and eventual validation. The process, exemplified by a high‐dimensional neural network potential, is universal and relevant to various kinds of MLP.…”

Visualization of a Large Set of Hydrogen Atomic Orbital Contours Using New and Expanded Sets of Parametric Equations

“…Atomic orbitals are a theme throughout the undergraduate chemistry curriculum, and visualizing them has been a theme in this journal. Contour plots as isosurfaces or contour lines in a plane are the most familiar representations of the hydrogen wave functions. − In these representations, a surface of a fixed value of the wave function ψ is plotted in analogy to a contour map. The values of ψ and ψ*ψ, the probability density, are closely related.…”

“…The alternative to these equations is to generate the isosurfaces or contour lines implicitly through an algorithm that may require programming or software with the ability to implement them. (The marching cubes algorithm is a common algorithm for isosurfaces, and other algorithms have been used for computerized plotting of orbitals. ,,, ) The use of software has allowed for orbital plotting for pedagogical purposes, with varying levels of complexity and success. ,,− ,, …”

“…(The marching cubes algorithm is a common algorithm for isosurfaces, 25 and other algorithms have been used for computerized plotting of orbitals. 8,12,13,21 ) The use of software has allowed for orbital plotting for pedagogical purposes, with varying levels of complexity and success. 7,9,[15][16][17][18][19][20]22,24 Here we generate vector graphic images for a large set of orbitals using parametric equations, many of which are newly described.…”