Intruder state
In quantum and theoretical chemistry, an intruder state is a particular situation arising in perturbative evaluations, where the energy of the perturbers is comparable in magnitude to the energy associated to the zero order wavefunction. In this case, a divergent behavior occurs, due to the nearly zero denominator in the expression of the perturbative correction.
Multi-reference wavefunction methods are not immune.{{cite journal|doi=10.1039/a808518h|title=A study of FeCO+ with correlated wavefunctions|journal=Physical Chemistry Chemical Physics|volume=1|issue=6|pages=967–975|year=1999|last1=Glaesemann|first1=Kurt R.|last2=Gordon|first2=Mark S.|last3=Nakano|first3=Haruyuki|s2cid=55761535|url=http://ccl.scc.kyushu-u.ac.jp/~nakano/papers/pccp-1-967.pdf|bibcode=1999PCCP....1..967G|access-date=2024-01-22|archive-date=2017-08-08|archive-url=https://web.archive.org/web/20170808050918/http://ccl.scc.kyushu-u.ac.jp/~nakano/papers/pccp-1-967.pdf|url-status=bot: unknown}}{{cite journal|doi=10.1021/jp101761d|pmid=20540550|title=EOMCC, MRPT, and TDDFT Studies of Charge Transfer Processes in Mixed-Valence Compounds: Application to the Spiro Molecule†|journal=The Journal of Physical Chemistry A|volume=114|issue=33|pages=8764–8771|year=2010|last1=Glaesemann|first1=Kurt R.|last2=Govind|first2=Niranjan|last3=Krishnamoorthy|first3=Sriram|last4=Kowalski|first4=Karol|bibcode=2010JPCA..114.8764G|s2cid=30757230}} There are ways to identity them.{{cite journal|doi=10.1063/1.1345510|title=Identifying and removing intruder states in multireference Mo̸ller–Plesset perturbation theory|journal=The Journal of Chemical Physics|volume=114|issue=9|pages=3913–3918|year=2001|last1=Choe|first1=Yoong-Kee|last2=Witek|first2=Henryk A.|last3=Finley|first3=James P.|last4=Hirao|first4=Kimihiko|bibcode=2001JChPh.114.3913C}}{{cite journal|doi=10.1002/jcc.21074|pmid=18680217|title=Intruder states in multireference perturbation theory: The ground state of manganese dimer|journal=Journal of Computational Chemistry|volume=30|issue=3|pages=468–478|year=2009|last1=Camacho|first1=Cristopher|last2=Witek|first2=Henryk A.|last3=Yamamoto|first3=Shigeyoshi|citeseerx=10.1.1.1010.7287|s2cid=5649816|hdl=11536/7682}} The natural orbitals of the perturbation expansion are a useful diagnostic for detecting intruder state effects.{{cite journal|doi=10.1063/1.478301|title=A natural orbital diagnostic for multiconfigurational character in correlated wave functions|journal=The Journal of Chemical Physics|volume=110|issue=9|pages=4199–4207|year=1999|last1=Gordon|first1=Mark S.|last2=Schmidt|first2=Michael W.|last3=Chaban|first3=Galina M.|last4=Glaesemann|first4=Kurt R.|last5=Stevens|first5=Walter J.|last6=Gonzalez|first6=Carlos|bibcode=1999JChPh.110.4199G|url=https://dr.lib.iastate.edu/handle/20.500.12876/14794 |hdl=20.500.12876/14794 |s2cid=480255 }} Sometimes what appears to be an intruder state is simply a change in basis.{{cite journal|doi=10.1021/jp101758y|pmid=20443582|title=On the Ordering of Orbital Energies in High-Spin ROHF†|journal=The Journal of Physical Chemistry A|volume=114|issue=33|pages=8772–8777|year=2010|last1=Glaesemann|first1=Kurt R.|last2=Schmidt|first2=Michael W.|bibcode=2010JPCA..114.8772G|s2cid=12313638|osti=988621}}