Abstract
We analyze the electron densities n(r) of atoms, molecules, solids, and surfaces. The distributions of values of the Seitz radius rs=(3/4πn)1/3 and the reduced density gradient s=|∇n|/(2(3π2)1/3n4/3) in an electron density indicate which ranges of these variables are significant for physical processes. We also define energy-weighted averages of these variables, 〈rs〉 and 〈s〉, from which local spin density (LSD) and generalized gradient approximation (GGA) exchange-correlation energies may be estimated. The changes in these averages upon rearrangement of the nuclei (atomization of molecules or solids, stretching of bond lengths or lattice parameters, change of crystal structure, etc.) are used to explain why GGA corrects LSD in the way it does. A thermodynamic-like inequality (essentially d〈s〉/〈s〉>d〈rs〉/2〈rs〉) determines whether the gradient corrections drive a process forward. We use this analysis to explain why gradient corrections usually stretch bonds (but not for example H–H bonds), reduce atomization and surface energies, and raise energy barriers to formation at transition states.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.