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de Wergifosse M, Grimme S. The eXact integral simplified time-dependent density functional theory (XsTD-DFT). J Chem Phys 2024; 160:204110. [PMID: 38805556 DOI: 10.1063/5.0206380] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2024] [Accepted: 05/05/2024] [Indexed: 05/30/2024] Open
Abstract
In the framework of simplified quantum chemistry methods, we introduce the eXact integral simplified time-dependent density functional theory (XsTD-DFT). This method is based on the simplified time-dependent density functional theory (sTD-DFT), where all semi-empirical two-electron integrals are replaced by exact one- and two-center two-electron integrals, while other approximations from sTD-DFT are kept. The performance of this new parameter-free XsTD-DFT method was benchmarked on excited state and (non)linear response properties, including ultra-violet/visible absorption, first hyperpolarizability, and two-photon absorption (2PA). For a set of 77 molecules, the results from the XsTDA approach were compared to the TDA data. XsTDA/B3LYP excitation energies only deviate on average by 0.14 eV from TDA while drastically cutting computational costs by a factor of 20 or more depending on the energy threshold chosen. The absolute deviations of excitation energies with respect to the full scheme are decreasing with increasing system size, showing the suitability of XsTDA/XsTD-DFT to treat large systems. Comparing XsTDA and its predecessor sTDA, the new scheme generally improves excitation energies and oscillator strengths, in particular, for charge transfer states. TD-DFT first hyperpolarizability frequency dispersions for a set of push-pull π-conjugated molecules are faithfully reproduced by XsTD-DFT, while the previous sTD-DFT method provides redshifted resonance energy positions. Excellent performance with respect to the experiment is observed for the 2PA spectrum of the enhanced green fluorescent protein. The obtained robust accuracy similar to TD-DFT at a fraction of the computational cost opens the way for a plethora of applications for large systems and in high throughput screening studies.
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Affiliation(s)
- Marc de Wergifosse
- Theoretical Chemistry Group, Molecular Chemistry, Materials and Catalysis Division (MOST), Institute of Condensed Matter and Nanosciences, Université Catholique de Louvain, Place Louis Pasteur 1, B-1348 Louvain-la-Neuve, Belgium
- Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Beringstr. 4, 53115 Bonn, Germany
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Beringstr. 4, 53115 Bonn, Germany
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Madden E, Zwijnenburg MA. The effect of particle size on the optical and electronic properties of hydrogenated silicon nanoparticles. Phys Chem Chem Phys 2024; 26:11695-11707. [PMID: 38563473 DOI: 10.1039/d4cp00119b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/04/2024]
Abstract
We use a combination of many-body perturbation theory and time-dependent density functional theory to study the optical and electronic properties of hydrogen terminated silicon nanoparticles. We predict that the lowest excited states of these silicon nanoparticles are excitonic in character and that the corresponding excitons are completely delocalised over the volume of the particle. The size of the excitons is predicted to increase proportionally with the particle size. Conversely, we predict that the fundamental gap, the optical gap, and the exciton binding energy increase with decreasing particle size. The exciton binding energy is predicted to counter-act the variation in the fundamental gap and hence to reduce the variation of the optical gap with particle size. The variation in the exciton binding energy itself is probably caused by a reduction in the dielectric screening with decreasing particle size. The intensity of the excited state corresponding to the optical gap and other low energy excitations are predicted to increase with decreasing particle size. We explain this increase in terms of the 'band structure' becoming smeared out in reciprocal space with decreasing particle size, increasing the 'overlap' between the occupied and unoccupied quasiparticle states and thus, the oscillator strength. Fourier transforms of the lowest excitons show that they inherit the periodicity of the frontier quasiparticle states. This, combined with the delocalisation of the exciton and the large exciton binding energy, means that the excitons in silicon nanoparticles combine aspects of Wannier-Mott, delocalisation and effect of periodicity of the underlying structure, and Frenkel, large exciton binding energy, excitons.
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Affiliation(s)
- Eimear Madden
- Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK.
| | - Martijn A Zwijnenburg
- Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK.
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Tölle J, Niemeyer N, Neugebauer J. Accelerating Analytic-Continuation GW Calculations with a Laplace Transform and Natural Auxiliary Functions. J Chem Theory Comput 2024; 20:2022-2032. [PMID: 38469629 DOI: 10.1021/acs.jctc.3c01264] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/13/2024]
Abstract
We present a simple and accurate GW implementation based on a combination of a Laplace transform (LT) and other acceleration techniques used in post-self-consistent field quantum chemistry, namely, natural auxiliary functions and the frozen-core approximation. The LT-GW approach combines three major benefits: (a) a small prefactor for computational scaling, (b) easy integration into existing molecular GW implementations, and (c) significant performance improvements for a wide range of possible applications. Illustrating these advantages for systems consisting of up to 352 atoms and 7412 basis functions, we further demonstrate the benefits of this approach combined with an efficient implementation of the Bethe-Salpeter equation.
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Affiliation(s)
- Johannes Tölle
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Niklas Niemeyer
- University of Münster, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Corrensstraße 36, Münster 48149, Germany
| | - Johannes Neugebauer
- University of Münster, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Corrensstraße 36, Münster 48149, Germany
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Rauwolf N, Klopper W, Holzer C. Non-linear light-matter interactions from the Bethe-Salpeter equation. J Chem Phys 2024; 160:061101. [PMID: 38341783 DOI: 10.1063/5.0191499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2023] [Accepted: 01/15/2024] [Indexed: 02/13/2024] Open
Abstract
A route to assess non-linear light-matter interactions from the increasingly popular GW-Bethe-Salpeter equation (GW-BSE) method is outlined. In the present work, the necessary analytic expressions within the static-screened exchange approximation of the BSE are derived. This enables a straightforward implementation of the computation of the first hyperpolarizability as well as two-photon absorption processes for molecular systems. Benchmark calculations on small molecular systems reveal that the GW-BSE method is intriguingly accurate for predicting both first hyperpolarizabilities and two-photon absorption strengths. Using state-of-the-art Kohn-Sham references as a starting point, the accuracy of the GW-BSE method rivals that of the coupled-cluster singles-and-doubles method, outperforming both second-order coupled-cluster and time-dependent density-functional theory.
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Affiliation(s)
- Nina Rauwolf
- Institute of Physical Chemistry, Karlsruhe Institute of Technology, Kaiserstraße 12, 76131 Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology, Kaiserstraße 12, 76131 Karlsruhe, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, Kaiserstraße 12, 76131 Karlsruhe, Germany
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Austin R, Farah Y, Sayer T, Luther B, Montoya-Castillo A, Krummel A, Sambur J. Hot carrier extraction from 2D semiconductor photoelectrodes. Proc Natl Acad Sci U S A 2023; 120:e2220333120. [PMID: 37011201 PMCID: PMC10104502 DOI: 10.1073/pnas.2220333120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 03/07/2023] [Indexed: 04/05/2023] Open
Abstract
Hot carrier-based energy conversion systems could double the efficiency of conventional solar energy technology or drive photochemical reactions that would not be possible using fully thermalized, "cool" carriers, but current strategies require expensive multijunction architectures. Using an unprecedented combination of photoelectrochemical and in situ transient absorption spectroscopy measurements, we demonstrate ultrafast (<50 fs) hot exciton and free carrier extraction under applied bias in a proof-of-concept photoelectrochemical solar cell made from earth-abundant and potentially inexpensive monolayer (ML) MoS2. Our approach facilitates ultrathin 7 Å charge transport distances over 1 cm2 areas by intimately coupling ML-MoS2 to an electron-selective solid contact and a hole-selective electrolyte contact. Our theoretical investigations of the spatial distribution of exciton states suggest greater electronic coupling between hot exciton states located on peripheral S atoms and neighboring contacts likely facilitates ultrafast charge transfer. Our work delineates future two-dimensional (2D) semiconductor design strategies for practical implementation in ultrathin photovoltaic and solar fuel applications.
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Affiliation(s)
- Rachelle Austin
- Department of Chemistry, Colorado State University, Fort Collins, CO80523
| | - Yusef R. Farah
- Department of Chemistry, Colorado State University, Fort Collins, CO80523
| | - Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, CO80309
| | - Bradley M. Luther
- Department of Chemistry, Colorado State University, Fort Collins, CO80523
| | | | - Amber T. Krummel
- Department of Chemistry, Colorado State University, Fort Collins, CO80523
| | - Justin B. Sambur
- Department of Chemistry, Colorado State University, Fort Collins, CO80523
- School of Advanced Materials Discovery, Colorado State University, Fort Collins, CO80523
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Zhou Z, Della Sala F, Parker SM. Minimal Auxiliary Basis Set Approach for the Electronic Excitation Spectra of Organic Molecules. J Phys Chem Lett 2023; 14:1968-1976. [PMID: 36787711 DOI: 10.1021/acs.jpclett.2c03698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
We report a minimal auxiliary basis model for time-dependent density functional theory (TDDFT) with hybrid density functionals that can accurately reproduce excitation energies and absorption spectra from TDDFT while reducing cost by about 2 orders of magnitude. Our method, dubbed TDDFT-ris, employs the resolution-of-the-identity technique with just one s-type auxiliary basis function per atom for the linear response operator, where the Gaussian exponents are parametrized across the periodic table using tabulated atomic radii with a single global scaling factor. By tuning on a small test set, we determine a single functional-independent scale factor that balances errors in excitation energies and absorption spectra. Benchmarked on organic molecules and compared to standard TDDFT, TDDFT-ris has an average energy error of only 0.06 eV and yields absorption spectra in close agreement with TDDFT. Thus, TDDFT-ris enables simulation of realistic absorption spectra in large molecules that would be inaccessible from standard TDDFT.
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Affiliation(s)
- Zehao Zhou
- Department of Chemistry, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106, United States
| | - Fabio Della Sala
- Center for Biomolecular Nanotechnologies, Istituto Italiano di Tecnologia, Via Barsanti 14, 73010 Arnesano (LE), Italy
- Institute for Microelectronics and Microsystems (CNR-IMM), Via Monteroni, Campus Unisalento, 73100 Lecce, Italy
| | - Shane M Parker
- Department of Chemistry, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106, United States
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Feighan O, Manby FR, Bourne-Worster S. An efficient protocol for excited states of large biochromophores. J Chem Phys 2023; 158:024107. [PMID: 36641400 DOI: 10.1063/5.0132417] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
Efficient energy transport in photosynthetic antenna is a long-standing source of inspiration for artificial light harvesting materials. However, characterizing the excited states of the constituent chromophores poses a considerable challenge to mainstream quantum chemical and semiempirical excited state methods due to their size and complexity and the accuracy required to describe small but functionally important changes in their properties. In this paper, we explore an alternative approach to calculating the excited states of large biochromophores, exemplified by a specific method for calculating the Qy transition of bacteriochlorophyll a, which we name Chl-xTB. Using a diagonally dominant approximation to the Casida equation and a bespoke parameterization scheme, Chl-xTB can match time-dependent density functional theory's accuracy and semiempirical speed for calculating the potential energy surfaces and absorption spectra of chlorophylls. We demonstrate that Chl-xTB (and other prospective realizations of our protocol) can be integrated into multiscale models, including concurrent excitonic and point-charge embedding frameworks, enabling the analysis of biochromophore networks in a native environment. We exploit this capability to probe the low-frequency spectral densities of excitonic energies and interchromophore interactions in the light harvesting antenna protein LH2 (light harvesting complex 2). The impact of low-frequency protein motion on interchromophore coupling and exciton transport has routinely been ignored due to the prohibitive costs of including it in simulations. Our results provide a more rigorous basis for continued use of this approximation by demonstrating that exciton transition energies are unaffected by low-frequency vibrational coupling to exciton interaction energies.
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Affiliation(s)
- Oliver Feighan
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - Frederick R Manby
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - Susannah Bourne-Worster
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
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Förster A, Visscher L. Quasiparticle Self-Consistent GW-Bethe-Salpeter Equation Calculations for Large Chromophoric Systems. J Chem Theory Comput 2022; 18:6779-6793. [PMID: 36201788 PMCID: PMC9648197 DOI: 10.1021/acs.jctc.2c00531] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
The GW-Bethe–Salpeter equation
(BSE) method
is promising for calculating the low-lying excitonic states of molecular
systems. However, so far it has only been applied to rather small
molecules and in the commonly implemented diagonal approximations
to the electronic self-energy, it depends on a mean-field starting
point. We describe here an implementation of the self-consistent and
starting-point-independent quasiparticle self-consistent (qsGW)-BSE approach, which is suitable for calculations on
large molecules. We herein show that eigenvalue-only self-consistency
can lead to an unfaithful description of some excitonic states for
chlorophyll dimers while the qsGW-BSE vertical excitation
energies (VEEs) are in excellent agreement with spectroscopic experiments
for chlorophyll monomers and dimers measured in the gas phase. Furthermore,
VEEs from time-dependent density functional theory calculations tend
to disagree with experimental values and using different range-separated
hybrid (RSH) kernels does change the VEEs by up to 0.5 eV. We use
the new qsGW-BSE implementation to calculate the
lowest excitation energies of the six chromophores of the photosystem
II (PSII) reaction center (RC) with nearly 2000 correlated electrons.
Using more than 11,000 (6000) basis functions, the calculation could
be completed in less than 5 (2) days on a single modern compute node.
In agreement with previous TD-DFT calculations using RSH kernels on
models that also do not include environmental effects, our qsGW-BSE calculations only yield states with local characters
in the low-energy spectrum of the hexameric complex. Earlier works
with RSH kernels have demonstrated that the protein environment facilitates
the experimentally observed interchromophoric charge transfer. Therefore,
future research will need to combine correlation effects beyond TD-DFT
with an explicit treatment of environmental electrostatics.
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Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HVAmsterdam, The Netherlands
| | - Lucas Visscher
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HVAmsterdam, The Netherlands
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