ISSN:
0020-7608
Keywords:
negative-energy orbitals
;
Dirac equation
;
relativistic configuration interaction
;
Breit-Dirac-Hartree-Fock
;
minimax theorem
;
best orbitals
;
natural orbitals
;
Chemistry
;
Theoretical, Physical and Computational Chemistry
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
When the one-body part of the relativistic Hamiltonian H is a sum of one-electron Dirac Hamiltonians, relativistic configuration interaction (CI) calculations are carried out with an ad hoc basis of positive-energy orbitals, {uj+, j=1, 2,…,m} and, more recently, with the full bases of positive-energy and negative-energy orbitals, {uj+, uj-, j=1, 2,…,m}. The respective eigenproblems H+Ck+=Ek+Ck+, k=1, 2,…,N(m), and HCk=EkCk; k=1, 2,…,N(2m) are related through Ek+≤Ek+N(2m-N(m) [R. Jáuregui et al., Phys. Rev. A 55, 1781 (1997)]. This inequality becomes an equality for the independent-particle Hartree-Fock model and some other simple multiconfiguration models, leading to an exact decoupling of positive-energy and negative-energy orbitals. Beyond Hartree-Fock, however, it is generally impossible to achieve an equality. By definition, optimal decoupling is obtained when the difference Ek+N(2m)-N(m)-Ek+ is a minimum, which amounts to maximize the energy Ek+ with respect to any set of m functions in the 2m-dimensional space {uj+, uj-, j=1, 2,…,m}. Straight maximization is a slowly convergent process. Fortunately, numerical calculations on high-Z atomic states show that optimally decoupled, or best positive-energy orbitals are given, to within 6 decimals in atomic units by the positive-energy natural orbitals of the full eigenfunction Ck+N(2m)-N(m). Best orbitals can accurately be obtained through CI-by-parts treatments for later use in large-scale relativistic CI, as illustrated with Ne ground-state calculations. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 805-812, 1998
Additional Material:
5 Tab.
Type of Medium:
Electronic Resource
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