A comparative study of the convergence characteristics of modified virtual orbitals within an orbitally ordered CI expansion

Cooper, Ian L.; Pounder, Christopher N. M.

doi:10.1063/1.443677

Cited by 28 publications

(6 citation statements)

References 12 publications

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“…This deficiency of the HF orbitals has been known for a long time and it has led over time to many attempts to improve these orbitals, the so-called improved virtual orbital (IVO) methods. [106][107][108][109][110][111] These methods have been used to improve the HF virtual orbitals for excited state and correlation calculations, e.g. by Davidson and collaborators 106,108,109 and Cooper and Pounder.…”

Section: Solidsmentioning

confidence: 99%

See 1 more Smart Citation

The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham orbital energies

Baerends¹,

Gritsenko²,

Meer³

2013

Phys. Chem. Chem. Phys.

400

387

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A number of consequences of the presence of the exchange-correlation hole potential in the Kohn-Sham potential are elucidated. One consequence is that the HOMO-LUMO orbital energy difference in the KS-DFT model (the KS gap) is not "underestimated" or even "wrong", but that it is physically expected to be an approximation to the excitation energy if electrons and holes are close, and numerically proves to be so rather accurately. It is physically not an approximation to the difference between ionization energy and electron affinity I-A (fundamental gap or chemical hardness) and also numerically differs considerably from this quantity. The KS virtual orbitals do not possess the notorious diffuseness of the Hartree-Fock virtual orbitals, they often describe excited states much more closely as simple orbital transitions. The Hartree-Fock model does yield an approximation to I-A as the HOMO-LUMO orbital energy difference (in Koopmans' frozen orbital approximation), if the anion is bound, which is often not the case. We stress the spurious nature of HF LUMOs if the orbital energy is positive. One may prefer Hartree-Fock, or mix Hartree-Fock and (approximate) KS operators to obtain a HOMO-LUMO gap as a Koopmans' approximation to I-A (in cases where A exists). That is a different one-electron model, which exists in its own right. But it is not an "improvement" of the KS model, it necessarily deteriorates the (approximate) excitation energy property of the KS gap in molecules, and deteriorates the good shape of the KS virtual orbitals.

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Section: Solidsmentioning

confidence: 99%

“…by Davidson and collaborators 106,108,109 and Cooper and Pounder. 110 The IVO methods have as common rationale that they try to ''pull'' orbitals from the HF virtual space into the molecular valence region by applying additional attractive operators, such as can be provided by an exchange hole. The analogy with the KS potential is evident.…”

Section: Solidsmentioning

confidence: 99%

The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham orbital energies

Baerends¹,

Gritsenko²,

Meer³

2013

Phys. Chem. Chem. Phys.

400

387

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“…One can, therefore, reduce the computational cost by identifying and removing these irrelevant functions from the basis set. There is a long history of trying to generate such spaces for configuration interaction [4][5][6][7][8][9][10][11] and many-body perturbation theory [12][13][14] ͑MBPT͒ and, more recently for coupled-cluster theory. [15][16][17][18][19][20][21][22] Perhaps the most powerful method of doing so is to use frozen natural orbitals ͑FNOs͒.…”

Section: Introductionmentioning

confidence: 99%

Frozen natural orbital coupled-cluster theory: Forces and application to decomposition of nitroethane

Taube

Bartlett

2008

The Journal of Chemical Physics

113

128

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The frozen natural orbital ͑FNO͒ coupled-cluster method increases the speed of coupled-cluster ͑CC͒ calculations by an order of magnitude with no consequential error along a potential energy surface. This method allows the virtual space of a correlated calculation to be reduced by about half, significantly reducing the time spent performing the coupled-cluster ͑CC͒ calculation. This paper reports the derivation and implementation of analytical gradients for FNO-CC, including all orbital relaxation for both noncanonical and semicanonical perturbed orbitals. These derivatives introduce several new orbital relaxation contributions to the CC density matrices. FNO-CCSD͑T͒ and FNO-⌳CCSD͑T͒ are applied to a test set of equilibrium structures, verifying that these methods are capable of reproducing geometries and vibrational frequencies accurately, as well as energies. Several decomposition pathways of nitroethane are investigated using CCSD͑T͒ and ⌳CCSD͑T͒ with 60% of the FNO virtual orbitals in a cc-pVTZ basis, and find differences on the order of 5 kcal/ mol with reordering of the transition state energies when compared to B3LYP 6-311 +G͑3df ,2p͒.

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“…The HF virtual orbitals are indeed known to be unduly diffuse (often not even bound) due to the lack of an exchange hole in the Fock operator for the virtual orbitals (i.e., the Fock operator has a repulsive N-electron field). [53][54][55][56][57] That is the reason that in the TDHF case the response vectors F α have many nonzero elements F α ai , indicating involvement of many transitions i → a in a single excitation. 41 A natural way to improve the orbital character would be to diagonalize the submatrix A TDHF+ ai,ib with constant index i.…”

Section: B Tdhfmentioning

confidence: 99%

Natural excitation orbitals from linear response theories: Time-dependent density functional theory, time-dependent Hartree-Fock, and time-dependent natural orbital functional theory

Meer

Gritsenko²,

Baerends³

2017

The Journal of Chemical Physics

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Straightforward interpretation of excitations is possible if they can be described as simple single orbital-to-orbital (or double, etc.) transitions. In linear response time-dependent density functional theory (LR-TDDFT), the (ground state) Kohn-Sham orbitals prove to be such an orbital basis. In contrast, in a basis of natural orbitals (NOs) or Hartree-Fock orbitals, excitations often employ many orbitals and are accordingly hard to characterize. We demonstrate that it is possible in these cases to transform to natural excitation orbitals (NEOs) which resemble very closely the KS orbitals and afford the same simple description of excitations. The desired transformation has been obtained by diagonalization of a submatrix in the equations of linear response time-dependent 1-particle reduced density matrix functional theory (LR-TDDMFT) for the NO transformation, and that of a submatrix in the linear response time-dependent Hartree-Fock (LR-TDHF) equations for the transformation of HF orbitals. The corresponding submatrix is already diagonal in the KS basis in the LR-TDDFT equations. While the orbital shapes of the NEOs afford the characterization of the excitations as (mostly) simple orbital-to-orbital transitions, the orbital energies provide a fair estimate of excitation energies.

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A comparative study of the convergence characteristics of modified virtual orbitals within an orbitally ordered CI expansion

Cited by 28 publications

References 12 publications

The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham orbital energies

The Kohn–Sham gap, the fundamental gap and the optical gap: the physical meaning of occupied and virtual Kohn–Sham orbital energies

Frozen natural orbital coupled-cluster theory: Forces and application to decomposition of nitroethane

Natural excitation orbitals from linear response theories: Time-dependent density functional theory, time-dependent Hartree-Fock, and time-dependent natural orbital functional theory

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