Retrieving "Internal Coordinates" from the archives
Cross-reference notes under review
While the archivists retrieve your requested volume, browse these clippings from nearby entries.
-
Molecular Coordinates
Linked via "internal coordinates"
Molecular coordinates are the fundamental set of parameters used in computational chemistry and molecular physics to define the instantaneous spatial arrangement of the constituent atoms within a chemical system. These coordinates are essential for defining the Potential Energy Surface (PES)/) and calculating molecular properties such as dipole moments, [polarizabilities](/entries/polarizabiliti…
-
Molecular Coordinates
Linked via "Internal coordinates"
Internal Coordinates
Internal coordinates describe the geometry based on the intrinsic geometric features of the molecule, primarily bond lengths, bond angles, and dihedral (torsion) angles. This system offers a more chemically intuitive description of the molecular structure.
Bond Lengths ($s_i$) -
Molecular Coordinates
Linked via "internal coordinates"
Redundant and Tortional Coordinates
While a minimal set of $3N-6$ internal coordinates is sufficient to define the structure, many more chemically meaningful internal coordinates (such as those describing ring strain or angle distortions not directly involving central atoms) can be defined. These additional coordinates are termed redundant coordinates. Calculations must account for these redundancies, typically by projecting… -
Molecular Coordinates
Linked via "internal coordinates"
The $Z$-Matrix Convention
The $Z$-Matrix (or internal coordinate matrix) is a specific convention for arranging internal coordinates. It defines the position of each atom sequentially based on its relationship (distance, angle, dihedral) to one or two previously defined atoms. While highly useful for inputting molecular geometries, the $Z$-Matrix is inherently less suited for calculating [dynamic proper…