Robust <b>Δ</b>SCF calculations with direct energy functional minimization methods and STEP for molecules and materials

Kumar, Chandan; Luber, Sandra

doi:10.1063/5.0075927

Cited by 6 publications

(4 citation statements)

References 94 publications

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“…There has also been some preliminary work on the description of conical intersections and nonadiabatic dynamics using ∆SCF methods. 339,393 States with double-excitation character represent another categorical failure of LR-TDDFT within the adiabatic approximation, 99 with the most famous example being the optically-dark S 1 (2 1 A − g ) state in carotenoids, [395][396][397] or the analogous 2 1 A − g state in butadiene and other conjugated polyenes. [398][399][400][401][402] Doublyexcited states can be captured accurately using ∆SCF methods, 338,347,348 as shown for a few examples in Fig.…”

Section: Examplesmentioning

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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Section: Examplesmentioning

confidence: 99%

Density Functional Theory for Electronic Excited States

Herbert¹

2022

Preprint

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“…Compared to TD-DFT, orbital-optimized density functional calculations have been shown to produce better results for long-range intermolecular charge transfer excitations. ,,,, First, they provide the correct 1/ R asymptote of the energy, and second, they typically yield a more accurate excitation energy, even when local and semilocal functionals are used. Fewer studies address intramolecular charge transfer states, where the separation between the donor and acceptor is smaller, with the preliminary results indicating that the time-independent approach can also give an improvement in these cases. − …”

Section: Introductionmentioning

confidence: 99%

Orbital-Optimized Versus Time-Dependent Density Functional Calculations of Intramolecular Charge Transfer Excited States

Selenius,

Sigurdarson,

Schmerwitz

et al. 2024

J. Chem. Theory Comput.

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The performance of time-independent, orbital-optimized calculations of excited states is assessed with respect to charge transfer excitations in organic molecules in comparison to the linear-response time-dependent density functional theory (TD-DFT) approach. A direct optimization method to converge on saddle points of the electronic energy surface is used to carry out calculations with the local density approximation (LDA) and the generalized gradient approximation (GGA) functionals PBE and BLYP for a set of 27 excitations in 15 molecules. The time-independent approach is fully variational and provides a relaxed excited state electron density from which the extent of charge transfer is quantified. The TD-DFT calculations are generally found to provide larger charge transfer distances compared to the orbital-optimized calculations, even when including orbital relaxation effects with the Z-vector method. While the error on the excitation energy relative to theoretical best estimates is found to increase with the extent of charge transfer up to ca. −2 eV for TD-DFT, no correlation is observed for the orbital-optimized approach. The orbital-optimized calculations with the LDA and the GGA functionals provide a mean absolute error of ∼0.7 eV, outperforming TD-DFT with both local and global hybrid functionals for excitations with a long-range charge transfer character. Orbital-optimized calculations with the global hybrid functional B3LYP and the range-separated hybrid functional CAM-B3LYP on a selection of states with short-and long-range charge transfer indicate that inclusion of exact exchange has a small effect on the charge transfer distance, while it significantly improves the excitation energy, with the best-performing functional CAM-B3LYP providing an absolute error typically around 0.15 eV.

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“…The delta self-consistent field (ΔSCF) method is an extension of density functional theory (DFT) concepts for the description of any stationary excited electronic state. − As a variational method, unlike its perturbative time-dependent (TD) DFT counterpart, the ΔSCF method optimizes a guess electronic density which approximates an excited electronic state. However, the low computational cost of the ground state energy calculation and the ability to selectively model excited electronic states of interest in a dense manifold of various electronic excitations make the ΔSCF method attractive for simulating NA mechanisms in condensed phase systems. − Because the ΔSCF method just optimizes a guess electron density, it has to be provided, either by an educated guess or, for instance, TD-DFT can provide the initial guess excited electronic state density, , whereas a number of optimization procedures can be chosen for its successful convergence. ,− ,,− In ΔSCF NA-MD, a converged density from a previous step can be used for the guess electron density in the next step. As the method is ignorant to the presence of other electronic states, it is advised to check the ordering and characters of electronic states along the ΔSCF trajectory with another electronic structure method which can directly generate a set of electronic states, for example with TD-DFT, especially when conducting the NA-MD for the first time.…”

Section: Introductionmentioning

confidence: 99%

Spin–Orbit Couplings for Nonadiabatic Molecular Dynamics at the ΔSCF Level

Mališ

Vandaele

Luber

2022

J. Chem. Theory Comput.

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A procedure for the calculation of spin–orbit coupling (SOC) at the delta self-consistent field (ΔSCF) level of theory is presented. Singlet and triplet excited electronic states obtained with the ΔSCF method are expanded into a linear combination of singly excited Slater determinants composed of ground electronic state Kohn–Sham orbitals. This alleviates the nonorthogonality between excited and ground electronic states and introduces a framework, similar to the auxiliary wave function at the time-dependent density functional theory (TD-DFT) level, for the calculation of observables. The ΔSCF observables of the formaldehyde system were compared to reference TD-DFT values. Our procedure gives all components (energies, gradients, nonadiabatic couplings, and SOC terms) at the ΔSCF level of theory for conducting efficient, full-atomistic nonadiabatic molecular dynamics with intersystem crossing, particularly in condensed phase systems.

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Robust ΔSCF calculations with direct energy functional minimization methods and STEP for molecules and materials

Cited by 6 publications

References 94 publications

Density Functional Theory for Electronic Excited States

Density Functional Theory for Electronic Excited States

Orbital-Optimized Versus Time-Dependent Density Functional Calculations of Intramolecular Charge Transfer Excited States

Spin–Orbit Couplings for Nonadiabatic Molecular Dynamics at the ΔSCF Level

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