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Effective hamiltonians and the quasidegeneracy problem: Calculations on ethylene
Author(s) -
Westhaus Paul A.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560160824
Subject(s) - hamiltonian (control theory) , atomic orbital , valence (chemistry) , excited state , coupled cluster , atomic physics , physics , cluster expansion , valence electron , quantum mechanics , open shell , electron , chemistry , mathematics , molecule , mathematical optimization
We report calculations on the electronic states of ethylene using the canonical transformation cluster expansion formalism to generate an effective valence shell Hamiltonian. The approximate formulas are very sensitive to the partition of one‐electron space into core, valence, and excited Orbitals. Consequently, although the formalism in principle should yield the “true” effective valence space Hamiltonian H H for any partition of one‐electron space, we find in practice excellent agreement with experiment for the N → T,N → V , and T → V transition energies only when certain potentially catastrophic problems are avoided. Chief among our problems is the “quasidegeneracy” between certain two‐particle states. The working formulas for the corrections to the Coulomb interaction resemble those of second‐order perturbation theory, with either single‐particle or modified energy denominators. If the denominator of just one term becomes very small, the corresponding correction “blows up” leading directly to spurious results for H v . Besides being extremely cautious about the partition of core, valence, and excited orbitals so as to avoid the problem completely, other suggested solutions range from the inclusion of higher‐order terms in the cluster expansion to carrying out the calculation in a localized basis.