On the triplet instability in semiempirical <scp>RPA</scp> calculations of conjugated hydrocarbons

Niyogi, B. Guha; Sannigrahi, A. B.

doi:10.1002/qua.560140313

Cited by 4 publications

(2 citation statements)

References 9 publications

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“…(The singlet HF orbitals do not diagonalize the triplet Fock operators.) Similar behavior was seen for the PPP Hamiltonian between single-particle LCI and RPA instabilities [26].…”

Section: Model Calculationsupporting

confidence: 71%

The unitary-group formulation of the open-shell random-phase approximation

Nelin

2009

Int. J. Quantum Chem.

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Hartree-Fock stability equations for an open-shell configuration have been derived in the unitary-group formulation. These stability equations are used to compute a generalized open-shell random-phase approximation (OSRPA), where excited states are generated from the same multiplicity Hartree-Fock (HF) ground-state orbitals. This differs from conventional triplet RPA, where excited-state triplets are calculated from closed-shell singlet HF orbitals. OSRPA yields real excitation energies wherever the HF orbitals for the given multiplicity are stable, which is not the case for conventional triplet RPA. OSRPA treats excited states of any multiplicity, and for triplets yields more excited states than does conventional triplet RPA. We treat the ally1 doublet and butadiene singlet and triplet in detail using the Hiickel-Hubbard Hamiltonian and compare OSRPA with conventional triplet RPA for the butadiene triplet.

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“…(The singlet HF orbitals do not diagonalize the triplet Fock operators.) Similar behavior was seen for the PPP Hamiltonian between single-particle LCI and RPA instabilities [26].…”

Section: Model Calculationsupporting

confidence: 71%

The unitary-group formulation of the open-shell random-phase approximation

Nelin

2009

Int. J. Quantum Chem.

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“…68 Along similar lines, it has been appreciated for a long time that TDHF specifically is prone to triplet instabilities. 90,91,[118][119][120][121][122][123][124] In fact, the appearance of imaginary excitation energies at equilibrium geometries of small molecules led Furche and Ahlrichs to conclude that this method is "rather useless. .…”

Section: Tamm-dancoff Approximationmentioning

confidence: 99%

Density Functional Theory for Electronic Excited States

Herbert¹

2022

Preprint

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This chapter provides a basic introduction to excited-state extensions of density functional theory (DFT), including time-dependent (TD-)DFT in both its linear-response and its explicitly time-dependent formulations. As applied to the Kohn-Sham DFT ground state, linear-response theory affords an eigenvaluetype problem for the excitation energies in a basis of singly-excited Slater determinants, and is widely known simply as "TDDFT" despite its frequency-domain formulation. This form of TDDFT is the mostly widely-used quantum-chemical method for excited states, due to a favorable combination of low cost and reasonable accuracy. The chapter surveys the accuracy of linear-response TDDFT, which is generally more sensitive to the details of the exchange-correlation functional as compared to ground-state DFT, and also describes some known systemic problems exhibited by this approach. Some of those problems can be corrected on a case-by-case basis using orbital-optimized, excited-state self-consistent field (SCF) calculations, in what is known as excited-state Kohn-Sham theory or a "∆SCF" procedure, a class of methods that includes restricted open-shell Kohn-Sham theory. Recent successes of these approaches are highlighted, including double excitations and core-level excitations. Finally, explicitly time-dependent (or "real-time") TDDFT involves propagation of the molecular orbitals in time following an external perturbation, according to the Kohn-Sham analogue of the time-dependent Schrödinger equation. The time-dependent approach has been used to model strong-field electron dynamics, and in the weak-field limit it provides a route to broadband spectra based on the time evolution of the dipole moment function. This is useful for describing high-energy excitations (as in x-ray spectroscopy) and in systems where the density of states is high, as demonstrated by a few examples.

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Triplet instability in semiempirical RPA calculations of conjugated systems containing heteroatoms

Sannigrahi

Niyogi²

1979

Int J of Quantum Chemistry

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It is well known [l-51 that the Hartree-Fock (HF) ground state of many closed-shell molecules appears to be triplet unstable in the random-phase approximation (RPA). Recently, we have studied [6] in detail the effect of semiempirical parameters on the RPA triplet instability of conjugated hydrocarbons using a pw-type model Hamiltonian. The molecular orbitals of conjugated hydrocarbons being rather insensitive to the choice of semiempirical parameters, the triplet instability in these systems mainly stems from the possible variation of the A and B matrices with respect to such parameters. However, in conjugated systems containing heteroatoms, the molecular orbitals themselves depend to some extent on the choice of parameters as a result of which the parametric dependence of the A and B matrices will be somewhat different from that in conjugated hydrocarbons. This indicates that the nature ofthe triplet instability in conjugated systems with and without heteroatoms may not be identical. It is the purpose of this paper to verify this point taking formaldehyde, borazine, and s-triazine as test molecules. We have omitted more complicated molecules because of the involvement of too many semiempirical parameters.Exactly the same method of calculation as employed by Guha Niyogi et al.[5] has been followed here.The Roothaan-Mulliken model [7,8] is used to describe the a-bonding in borazine. The C-0, C-N.and B~-N bond lengths are taken to be 1.21, 1.34, and 1.44 A, respectively. For the one-center electron repulsion integrals, the necessary input parameters are taken from Hinze and Jaffe [9]. The two-center repulsion integrals are evaluated using the approximations due to Mataga and Nishimoto ( M N ) [ eV. and the results for the limiting value o f @ = 0 were obtained by extrapolation.In Figure 1 the p-dependence of the oxygen 2 a AO coefficients in the bonding and antibonding MOS of formaldehyde is shown. In all three cases, i.e., M I , Ohno, and MN approximations, with the decrease of 1/31, the bonding and antibonding M O~ become more and more localized on the oxygen and carbon atoms, respectively. For the M I approximation, as p -0, the ground state of formaldehyde passes on very smoothly to a separated-atom-type H F state. This is almost the situation with the Ohno approximation. In this case, however, the variation of the AO coefficients is somewhat more sensitive t o p than that in the M I approximation at small values of this parameter. The situation with the MN approximation is appreciably different from the other two cases. The variation is rather slow in this case, as a result of which the molecule maintains its symmetry throughout the variation of and no separated-atom-type H F state is obtained at the limiting value of fl = 0. These results can be qualitatively understood from a consideration of the perturbation theory.

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On the triplet instability in semiempirical RPA calculations of conjugated hydrocarbons

Cited by 4 publications

References 9 publications

The unitary-group formulation of the open-shell random-phase approximation

The unitary-group formulation of the open-shell random-phase approximation

Density Functional Theory for Electronic Excited States

Triplet instability in semiempirical RPA calculations of conjugated systems containing heteroatoms

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