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О Выборе Дистрибутивного Базиса В Расчетах Дипольных Моментов Перехода В Однодетерминантном Приближении

“…В соответствии с методологией асимп-тотического проектирования [22,[24][25][26][27] слагаемые при множителе λ s обеспечивают спиновую чистоту, тогда как слагаемые при λ 0 ведут к ортогональности функ-ций (6) и (7), т. е. 0 |ϕ 1 = 0.…”

Orthogonality of determinant functions in the Hartree-Fock method for highly excited electronic states

“…For a Nth excited state, we proceed from the stationarity condition for the functional where E UHF is the total energy of a system in the UHF formalism; Q α is the orthoprojector on the subspace of virtual orbitals; and λ s and λ o are the Lagrange multipliers, which, in accordance with the AP-method [12,13], ensure, in the limit λ s , λ o → ∞, the fulfillment of conditions for the spin purity and orthogonality of states, respectively (in practice, values λ s = 100 au and λ o = 1000 au ensure the required accuracy). Finally, variations of orbitals in δL (N) = 0, their independence and arbitrariness yield the equations sought for the MOs of α-and β-clusters: (13) Here, f α and f β are the standard Fock operators in the UHF formalism and P β is the orthoprojector on the subspace of occupied orbitals of the β-cluster. Equations (13) , P β = is the β-spin density matrix from occupied orbitals of the α-cluster, Q α = is the density matrix from virtual orbitals of the α-cluster, and P HOMO, k = .…”

“…In this case, the method of asymptotic projection proposed in our earlier papers [11][12][13] to solve eigenvalue problems with restrictions of the orthogonality of eigenvectors to an arbitrary coupling vector can be applied.…”

The Coulson–Fischer wave functions for the ground and excited states of H2and HeH+: parametrisation using distributed Gaussian basis sets

“…where λ 0 is a Lagrange multiplier which, according to the asymptotic projection method [79][80][81], ensures rigorous orthogonality in the limit λ 0 → ∞. Variation of the energy expectation value, subject only to the normalisation of the orbitals: ϕ 11 |ϕ 11 = 1 and ϕ 12 |ϕ 12 = 1, gives…”