Excited states from range-separated density-functional perturbation theory

Rebolini, Elisa; Toulouse, Julien; Teale, Andrew M.; Helgaker, Trygve; Savin, Andreas

doi:10.1080/00268976.2015.1011248

Cited by 14 publications

(19 citation statements)

References 79 publications

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“…In a series of papers, Rebolini et al 171–174 considered approximate RS MC‐DFT approaches aiming at correcting excited‐state energies of the LR Hamiltonian

{\overset{true^}{H}}^{LR}

. Corrections can be derived either by considering the exact expansion in orders of μ along a range separated adiabatic connection, 172 or from the perturbation theory 173,174 . In the latter case, the

{\overset{true^}{H}}^{LR}

Hamiltonian is chosen as the unperturbed operator and the perturbation is defined as

{\overset{true^}{V}}_{ee}^{SR} - {\overset{true^}{V}}^{SR} ([], ρ_{0})

, cf.…”

Section: Excited States From Rs Mc‐dftmentioning

confidence: 99%

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Range‐separated multiconfigurational density functional theory methods

Pernal

Hapka

2021

WIREs Comput Mol Sci

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Range-separated multiconfigurational density functional theory (RS MC-DFT) rigorously combines density functional (DFT) and wavefunction (WFT) theories. This is achieved by partitioning of the electron interaction operator into long-and short-range components and modeling them with WFT and DFT, respectively. In contrast to other methods, mixing wavefunctions with density functionals, RS MC-DFT is free from electron correlation double counting. The general formulation of RS MC-DFT allows for merging any ab initio approximation with density functionals. Implementations of RS MC-DFT aim at increasing both versatility and accuracy of the underlying methods, while reducing the computational cost of the ab initio problem. Variants of the RS MC-DFT approach can be divided into single-determinant-based range-separated methods and range-separated multideterminantal WFT methods. In these approaches the electron correlation energy is described both by a pertinent short-range density functional and by the wavefunction theory. We review the short-range functionals and correlated wavefunction theories employed in the framework of RS MC-DFT. We discuss applications of the RS MC-DFT methods to ground-state properties of molecules and to noncovalent interactions. Time-dependent linear-response theory and direct approaches to excited states are also presented. For each area of applications, we assess advantages of RS MC-DFT over conventional DFT and ab initio methods.

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“…In a series of papers, Rebolini et al 171–174 considered approximate RS MC‐DFT approaches aiming at correcting excited‐state energies of the LR Hamiltonian

{\overset{true^}{H}}^{LR}

{\overset{true^}{H}}^{LR}

Hamiltonian is chosen as the unperturbed operator and the perturbation is defined as

{\overset{true^}{V}}_{ee}^{SR} - {\overset{true^}{V}}^{SR} ([], ρ_{0})

, cf.…”

Section: Excited States From Rs Mc‐dftmentioning

confidence: 99%

“…Equations () and (). Both Rayleigh–Schrödinger 173 and Görling–Levy 174 perturbation theories have been applied. For the i th eigenstate of

{\overset{true^}{H}}^{LR}

one recovers the pertinent eigenvalue in the 0th order.…”

Section: Excited States From Rs Mc‐dftmentioning

confidence: 99%

Range‐separated multiconfigurational density functional theory methods

Pernal

Hapka

2021

WIREs Comput Mol Sci

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“…can be used as starting points for reaching the physical excitation energies by means of extrapolation techniques [36][37][38], perturbation theory [39], time-dependent linear response theory [4,5] or ensemble range-separated DFT [13,14], as discussed further in the following.…”

Section: Theorymentioning

confidence: 99%

Linear interpolation method in ensemble Kohn-Sham and range-separated density-functional approximations for excited states

et al. 2015

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Gross-Oliveira-Kohn density functional theory (GOK-DFT) for ensembles is in principle very attractive, but has been hard to use in practice. A novel, practical model based on GOK-DFT for the calculation of electronic excitation energies is discussed. The new model relies on two modifications of GOK-DFT: use of range separation and use of the slope of the linearly-interpolated ensemble energy, rather than orbital energies. The range-separated approach is appealing as it enables the rigorous formulation of a multi-determinant state-averaged DFT method. In the exact theory, the short-range density functional, that complements the long-range wavefunction-based ensemble energy contribution, should vary with the ensemble weights even when the density is held fixed. This weight dependence ensures that the range-separated ensemble energy varies linearly with the ensemble weights. When the (weight-independent) ground-state short-range exchangecorrelation functional is used in this context, curvature appears thus leading to an approximate weight-dependent excitation energy. In order to obtain unambiguous approximate excitation energies, we propose to interpolate linearly the ensemble energy between equiensembles. It is shown that such a linear interpolation method (LIM) can be rationalized and that it effectively introduces weight dependence effects. As proof of principle, LIM has been applied to He, Be, H2 in both equilibrium and stretched geometries as well as the stretched HeH + molecule. Very promising results have been obtained for both single (including charge transfer) and double excitations with spin-independent short-range local and semi-local functionals. Even at the Kohn-Sham ensemble DFT level, that is recovered when the range-separation parameter is set to zero, LIM performs better than standard time-dependent DFT. arXiv:1504.06477v2 [physics.chem-ph]

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“…In this previous work [50], a Rayleigh-Schrödinger (RS)-based perturbation theory was tested on a few atoms and molecules and it was found that the first-order excitation energies are not overall improved in comparison with the zeroth-order excitation energies. This finding was rationalized by the fact that this perturbation theory does not keep the ground-state density constant at each order.…”

Section: Introductionmentioning

confidence: 99%

“…Zeroth-order excitation energies ∆E µ k = E µ k − E µ 0 (plain line) and zeroth+first order excitation energies ∆E dashed line) in the GL-based perturbation theory for the hydrogen molecule at the equilibrium distance (top) and three times the equilibrium distance (bottom) as a function of µ. For comparison, the zeroth+first order excitation energies ∆E ) in the RS-based perturbation theory of Ref [50]. are also shown.…”

mentioning

confidence: 98%

Excitation energies from Görling–Levy perturbation theory along the range-separated adiabatic connection

Rebolini¹,

Teale

Helgaker

et al. 2018

Molecular Physics

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A Görling-Levy (GL)-based perturbation theory along the range-separated adiabatic connection is assessed for the calculation of electronic excitation energies. In comparison with the Rayleigh-Schrödinger (RS)-based perturbation theory introduced in a previous work [E. Rebolini, J. Toulouse, A. M. Teale, T. Helgaker, A. Savin, Mol. Phys. 113, 1740(2015], this GL-based perturbation theory keeps the ground-state density constant at each order and thus gives the correct ionization energy at each order. Excitation energies up to first order in the perturbation have been calculated numerically for the helium and beryllium atoms and the hydrogen molecule without introducing any density-functional approximations. In comparison with the RS-based perturbation theory, the present GL-based perturbation theory gives much more accurate excitation energies for Rydberg states but similar excitation energies for valence states.

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Excited states from range-separated density-functional perturbation theory

Cited by 14 publications

References 79 publications

Range‐separated multiconfigurational density functional theory methods

Range‐separated multiconfigurational density functional theory methods

Linear interpolation method in ensemble Kohn-Sham and range-separated density-functional approximations for excited states

Excitation energies from Görling–Levy perturbation theory along the range-separated adiabatic connection

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