%0 Journal Article %1 springerlink:10.1007/s10910-011-9819-2 %A Marquardt, Roberto %D 2012 %I Springer Netherlands %J Journal of Mathematical Chemistry %K analysis data fit least mathematics squares %N 3 %P 577-587 %R 10.1007/s10910-011-9819-2 %T Non linear adjustments with external conditions %U http://dx.doi.org/10.1007/s10910-011-9819-2 %V 50 %X A new non linear adjustment algorithm is proposed that includes the possibility to satisfy conditions involving non linear analytical functions of the adjustment parameters. It is based on the Levenberg-Marquardt algorithm and makes use of Lagrange multipliers to fulfill external conditions. As an application, the method is used to derive a modified Morse potential to represent the potential energy function of the 2 Π 1/2 ground state of nitric oxide (NO), while having both an acceptable description of the equilibrium bond length, the vibrational overtone spectrum to up to the 6th overtone, the energy and the dispersion coefficient at dissociation NO → N + O.

@article{springerlink:10.1007/s10910-011-9819-2, abstract = {A new non linear adjustment algorithm is proposed that includes the possibility to satisfy conditions involving non linear analytical functions of the adjustment parameters. It is based on the Levenberg-Marquardt algorithm and makes use of Lagrange multipliers to fulfill external conditions. As an application, the method is used to derive a modified Morse potential to represent the potential energy function of the 2 Π 1/2 ground state of nitric oxide (NO), while having both an acceptable description of the equilibrium bond length, the vibrational overtone spectrum to up to the 6th overtone, the energy and the dispersion coefficient at dissociation NO → N + O.}, added-at = {2012-03-09T03:03:43.000+0100}, affiliation = {Laboratoire de Chimie Quantique - Institut de Chimie, UMR 7177 CNRS/UdS Université de Strasbourg, 4, rue Blaise Pascal CS90032, 67081 Strasbourg Cedex, France}, author = {Marquardt, Roberto}, biburl = {https://www.bibsonomy.org/bibtex/215386458df99fe2f518660ff1aa94108/drmatusek}, doi = {10.1007/s10910-011-9819-2}, interhash = {855c625c2ef279eaeb5a1b3c9e8a57f2}, intrahash = {15386458df99fe2f518660ff1aa94108}, issn = {0259-9791}, issue = {3}, journal = {Journal of Mathematical Chemistry}, keyword = {Chemistry and Materials Science}, keywords = {analysis data fit least mathematics squares}, month = {March}, number = 3, pages = {577-587}, publisher = {Springer Netherlands}, timestamp = {2012-10-30T15:30:41.000+0100}, title = {Non linear adjustments with external conditions}, url = {http://dx.doi.org/10.1007/s10910-011-9819-2}, volume = 50, year = 2012 }