Efficient Semi-numerical Implementation of Global and Local Hybrid Functionals for Time-Dependent Density Functional Theory

Maier, Toni M.; Bahmann, Hilke; Kaupp, Martin

doi:10.1021/acs.jctc.5b00624

Cited by 67 publications

(136 citation statements)

References 72 publications

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“…In order to provide a better description of the spin-density distribution, and in particular better electronic excitation spectra in TDDFT calculations (see below), single point calculations using the local hybrid functional Lh-SsirPW92-D3 44 were performed (with D3-type dispersion corrections), using a recent efficient implementation. [45][46] Related local hybrids, which in contrast to BLYP35 or B3LYP exhibit position-dependent rather than constant exact-exchange admixture, have recently been shown to provide a good description of both localized and delocalized mixed-valence systems, 47 while reducing the spin contamination compared to "global" hybrids with high exact exchange, such as BLYP35. The structures were not optimized with local hybrids, as the higher computational demand of the current gradient implementation for local hybrids was not warranted by the expected small structural improvements.…”

Section: Resultsmentioning

confidence: 99%

“…BLYP35 has been found to perform well for mixed-valence (MV) systems near the Class II/III borderline in the Robin-Day scheme. 14, 41-42, 51, 66 Additional structure optimizations and vibrational frequency calculations were performed with the well-known global hybrid functional B3LYP, 65,[67][68][69] for ground- 45 and TDDFT excited-state 46 calculations (in the latter case extending the available Turbomole TDDFT implementation 71 ).…”

Section: Computational Detailsmentioning

confidence: 99%

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Iron versus Ruthenium: Clarifying the Electronic Differences between Prototypical Mixed-Valence Organometallic Butadiyndiyl Bridged Molecular Wires

et al. 2018

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The electronic structures of the prototypical bimetallic buta-1,3-diyn-1,4-diylbridged radical cation complexes [{M(dppe)Cp´} 2 (µ-C≡CC≡C)] + (M= Fe, Cp´ = Cp* (1a), Cp (1b); M = Ru, Cp´ = Cp* (2a), Cp (2b)) have been (re-)investigated using a combination of UV-vis-NIR and IR spectroelectrochemistry, and quantum chemical calculations based on both dispersion-corrected global (BLYP35-D3) and local (Lh-SsirPW92-D3) hybrid functionals. Following analysis of new and existing data, including the IR-active ν(C≡C) bands, the iron compounds [1] + are reclassified as valence-trapped (Robin and Day Class II) mixed-valence complexes, in contrast to the ruthenium complexes [2] + , which are delocalized (Robin and Day Class III) systems. All members of the series exist as a thermally populated distribution of conformers in solution, and the overlapping spectroscopic profiles make the accurate extraction of the parameters necessary for the analysis of [1] + and [2] + within the framework of the Marcus-Hush model extremely challenging. Analysis of the spin-density distributions from a range of conformational minima provides an alternative representation of

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Section: Resultsmentioning

confidence: 99%

Section: Computational Detailsmentioning

confidence: 99%

Iron versus Ruthenium: Clarifying the Electronic Differences between Prototypical Mixed-Valence Organometallic Butadiyndiyl Bridged Molecular Wires

et al. 2018

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“…137,144 In case of TDDFT computations of excitations to Rydberg states, we recently noted the requirement of sufficiently diffuse grids when diffuse basis sets are used. 124 This was found to be more pronounced for local compared to global hybrids. Numerical errors could be reduced appreciably by simply using more diffuse grids and a moderate number of additional radial grid points.…”

Section: Evaluation Of Nonstandard Integralsmentioning

confidence: 95%

“…125 For details on the computational performance of local hybrid functionals using semi-numerical integration techniques, we refer to the implementation works. 124,125,135 With the current exception of linear-response TDDFT (cf., Reference 121), semi-numerical integration for local hybrids also does not require significantly more main memory compared to conventional global hybrid calculations.…”

Section: Evaluation Of Nonstandard Integralsmentioning

confidence: 99%

Local hybrid functionals: Theory, implementation, and performance of an emerging new tool in quantum chemistry and beyond

Maier

Arbuznikov

Kaupp

2018

WIREs Comput Mol Sci

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The state of the art in the development, implementation, validation, and application of local hybrid functionals with position‐dependent exact‐exchange admixture is reviewed comprehensively. Starting from the general formulation of a local hybrid functional, possible constructions of local mixing functions to determine the position dependence are scrutinized in terms of their exact properties as well as their desirable features. The gauge problem pertaining to the ambiguity of exchange‐energy densities is discussed. “Smoking guns” for the gauge problem are identified, and the first calibration functions to improve the match of the exact and semi‐local exchange‐energy densities are compared. In view of the appearance of nonstandard exact‐exchange integrals, a crucial aspect is the efficient implementation of local hybrid functionals. This has been achieved recently using a resolution of the identity and/or semi‐numerical techniques, both for ground‐state energies and gradients, and for linear‐response time‐dependent density functional theory. The validation and early applications of local hybrids are reviewed, including thermochemistry, reaction barriers, structures and vibrational frequencies, electric and magnetic properties, as well as electronic excitation spectra. This article is categorized under: Electronic Structure Theory > Density Functional Theory Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry

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“…Applying the substitution rg ss 1=2 ¼ rr T r s rr s g ss 1=2 (50) results in the alternative formulation…”

Section: Appendixmentioning

confidence: 99%

New approaches for the calibration of exchange-energy densities in local hybrid functionals

Maier

Haasler

Arbuznikov

et al. 2016

Phys. Chem. Chem. Phys.

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123

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The ambiguity of exchange-energy densities is a fundamental challenge for the development of local hybrid functionals, or of other functionals based on a local mixing of exchange-energy densities. In this work, a systematic construction of semi-local calibration functions (CFs) for adjusting the exchangeenergy densities in local hybrid functionals is provided, which directly links a given CF to an underlying semi-local exchange functional, as well as to the second-order gradient expansion of the exchange hole. Using successive steps of integration by parts allows the derivation of correction terms of increasing order, resulting in more and more complicated but also more flexible CFs. We derive explicit first-and second-order CFs (pig1 and pig2) based on B88 generalized-gradient approximation (GGA) exchange, and a first-order CF (tpig1) based on t-dependent B98 meta-GGA exchange. We combine these CFs with different long-range damping functions and evaluate them for calibration of LDA, B88 GGA, and TPSS meta-GGA exchange-energy densities. Based on a minimization of unphysical nondynamical correlation contributions in three noble-gas dimer potential-energy curves, free parameters in the CFs are optimized, and performance of various approaches in the calibration of different exchangeenergy densities is compared. Most notably, the second-order pig2 CF provides the largest flexibility with respect to the diffuseness of the damping function. This suggests that higher-order CFs based on the present integration-by-parts scheme may be particularly suitable for the flexible construction of local hybrid functionals.

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Efficient Semi-numerical Implementation of Global and Local Hybrid Functionals for Time-Dependent Density Functional Theory

Cited by 67 publications

References 72 publications

Iron versus Ruthenium: Clarifying the Electronic Differences between Prototypical Mixed-Valence Organometallic Butadiyndiyl Bridged Molecular Wires

Iron versus Ruthenium: Clarifying the Electronic Differences between Prototypical Mixed-Valence Organometallic Butadiyndiyl Bridged Molecular Wires

Local hybrid functionals: Theory, implementation, and performance of an emerging new tool in quantum chemistry and beyond

New approaches for the calibration of exchange-energy densities in local hybrid functionals

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