NDLI: Dominance and separability in posets, their application to isoelectronic species with equal total nuclear charge

Content Provider	Springer Nature Link
Author	Restrepo, Guillermo Brüggemann, Rainer
Copyright Year	2007
Abstract	We developed the dominance and separability degrees as two new mathematical tools measuring the amount of comparabilities and incomparabilities among pairs of disjoint subposets in a parent poset and we have related them through a theorem. Their mathematical properties when these measures are constrained to be higher than 0.5 have been studied. We have shown that variations of dominance and separability degrees from values in the real interval (0.5, 1] permit to “tune” the level of detail on the comparabilites and incomparabilities among the subsets studied. The lack of transitivity of dominance and separability degrees is established, along with the special requirement, needed on the poset, to have a transitivity of these measures. As a chemical application, the Hasse diagram of Born-Oppenheimer molecular total energies of the complete set of isoelectronic species with total nuclear charge 10 in their minimum energy configurations has been studied. We partition this set into 10 subsets, each one containing all the species with the same number of nuclei. By the calculation of the dominance and separability degrees a relation between the number of atoms in any ensemble and the Born-Oppenheimer energies is established.
Starting Page	577
Ending Page	602
Page Count	26
File Format	PDF
ISSN	02599791
Journal	Journal of Mathematical Chemistry
Volume Number	44
Issue Number	2
e-ISSN	15728897
Language	English
Publisher	Springer Netherlands
Publisher Date	2007-12-08
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Partially ordered sets Posets Ranking Born-Oppenheimer energies Math. Applications in Chemistry Theoretical and Computational Chemistry Physical Chemistry
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Chemistry

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

A Non-Born–Oppenheimer Self-consistent Field Method

Energy bounds for isoelectronic molecular sets and the implicated order

Exactly Solvable Model Mimicking the H$_{2}$ Molecule in the Limit of Large Nuclear Masses

Particle correlation from uncorrelated non Born–Oppenheimer SCF wavefunctions

Comparison Between a Generalized Electronic Diabatic Approach and the Born–Oppenheimer Separation Scheme in Inertial Frames

Non-adiabatic transitions near avoided crossings: theory and numerics

Enfolded conformational spaces: definition of the chemical quantum mechanical multiverse under Born–Oppenheimer approximation

The $m$-Cover Posets and Their Applications

Applications of Quotient Posets

Dominance and separability in posets, their application to isoelectronic species with equal total nuclear charge

Similar Documents

A Non-Born–Oppenheimer Self-consistent Field Method

Energy bounds for isoelectronic molecular sets and the implicated order

Exactly Solvable Model Mimicking the H$_{2}$ Molecule in the Limit of Large Nuclear Masses

Particle correlation from uncorrelated non Born–Oppenheimer SCF wavefunctions

Comparison Between a Generalized Electronic Diabatic Approach and the Born–Oppenheimer Separation Scheme in Inertial Frames

Non-adiabatic transitions near avoided crossings: theory and numerics

Enfolded conformational spaces: definition of the chemical quantum mechanical multiverse under Born–Oppenheimer approximation

The $m$-Cover Posets and Their Applications

Applications of Quotient Posets

Dominance and separability in posets, their application to isoelectronic species with equal total nuclear charge