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Optimal decoupling of positive‐ and negative‐energy orbitals in relativistic electronic structure calculations beyond Hartree–Fock
Author(s) -
Bunge Carlos F.,
Jáuregui Rocio,
LeyKoo Eugenio
Publication year - 1998
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/(sici)1097-461x(1998)70:4/5<805::aid-qua27>3.0.co;2-z
Subject(s) - atomic orbital , hartree–fock method , hamiltonian (control theory) , decoupling (probability) , physics , quantum mechanics , atomic physics , basis set , fock space , molecular orbital , eigenfunction , slater type orbital , molecular orbital theory , chemistry , electron , eigenvalues and eigenvectors , density functional theory , mathematics , molecule , mathematical optimization , control engineering , engineering
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, { u j + , j =1, 2,…, m } and, more recently, with the full bases of positive‐energy and negative‐energy orbitals, { u j + , u j − , j =1, 2,…, m }. The respective eigenproblems H + C k + = E k + C k + , k =1, 2,…,( m ), and HC k = E k C k ; k =1, 2,…,(2 m ) are related through E k + ≤ E k +(2 m −( 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 E k +(2 m )−( m ) − E k + is a minimum, which amounts to maximize the energy E k + with respect to any set of m functions in the 2 m ‐dimensional space { u j + , u j − , 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 C k +(2 m )−( 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