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Ahn DH, Nakajima T, Hirao K, Song JW. Long-range Corrected Density Functional Theory Including a Two-Gaussian Hartree-Fock Operator for High Accuracy Core-excitation Energy Calculations of Both the Second- and Third-Row Atoms (LC2gau-core-BOP). J Chem Theory Comput 2024. [PMID: 39106473 DOI: 10.1021/acs.jctc.4c00651] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/09/2024]
Abstract
In the previous work, LCgau-core-BOP, which includes the short-range interelectronic Gaussian attenuating Hartree-Fock (HF) exchange to the long-range HF exchange, showed high accuracy core-excitation energies from 1s orbitals of the second-row atoms (1s → π*, 1s → σ*, 1s → n*, and 1s → Rydberg), but underestimates the core-excitation energies from 1s orbitals of the third-row atoms. To improve this, we added one more Gaussian attenuating HF exchange to LCgau-core-BOP. We named it LC2gau-core-BOP, which achieves a mean absolute error (MAE) of 0.6 and 0.3 eV for core excitation energies of the second- and third-row atoms of the tested small molecules, respectively. We found that the inclusion of the short-range interelectronic HF exchange at a distance ranging from 0.2 to 0.6 a.u. contributes to the increase of performances on 1s orbital energy calculations of the second-row atoms, while the inclusion of more short-range interelectronic HF exchange at a distance ranging from 0 to 0.2 a.u. does to the increase of performance on 1s orbital energy calculations of the third-row atoms. It is notable that all of these improvements were accomplished using flexible Gaussian attenuating HF exchange inclusion. LC2gau-core-BOP shows deviations of less than 0.8 eV from experimental values for all of the core-excitation energies of the tested medium-size molecules consisting of thymine, oxazole, glycine, and dibenzothiophene sulfone. Moreover, by optimizing one parameter of the OP correlation functional, LC2gau-core-BOP provides atomization energies over the G3 test set with an accuracy comparable to that of B3LYP.
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Affiliation(s)
- Dae-Hwan Ahn
- Department of Chemistry Education, Daegu University, Gyeongsan-si 113-8656, Korea
| | | | - Kimihiko Hirao
- RIKEN Center for Computational Science, Kobe 650-0047, Japan
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8501, Japan
| | - Jong-Won Song
- Department of Chemistry Education, Daegu University, Gyeongsan-si 113-8656, Korea
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2
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Fransson T, Pettersson LGM. TDDFT and the x-ray absorption spectrum of liquid water: Finding the "best" functional. J Chem Phys 2024; 160:234105. [PMID: 38884399 DOI: 10.1063/5.0209719] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2024] [Accepted: 06/03/2024] [Indexed: 06/18/2024] Open
Abstract
We investigate the performance of time-dependent density functional theory (TDDFT) for reproducing high-level reference x-ray absorption spectra of liquid water and water clusters. For this, we apply the integrated absolute difference (IAD) metric, previously used for x-ray emission spectra of liquid water [T. Fransson and L. G. M. Pettersson, J. Chem. Theory Comput. 19, 7333-7342 (2023)], in order to investigate which exchange-correlation (xc) functionals yield TDDFT spectra in best agreement to reference, as well as to investigate the suitability of IAD for x-ray absorption spectroscopy spectrum calculations. Considering highly asymmetric and symmetric six-molecule clusters, it is seen that long-range corrected xc-functionals are required to yield good agreement with the reference coupled cluster (CC) and algebraic-diagrammatic construction spectra, with 100% asymptotic Hartree-Fock exchange resulting in the lowest IADs. The xc-functionals with best agreement to reference have been adopted for larger water clusters, yielding results in line with recently published CC theory, but which still show some discrepancies in the relative intensity of the features compared to experiment.
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Affiliation(s)
- Thomas Fransson
- Department of Physics, AlbaNova University Center, Stockholm University, 10961 Stockholm, Sweden
| | - Lars G M Pettersson
- Department of Physics, AlbaNova University Center, Stockholm University, 10961 Stockholm, Sweden
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3
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Folkestad SD, Paul AC, Paul Née Matveeva R, Coriani S, Odelius M, Iannuzzi M, Koch H. Understanding X-ray absorption in liquid water using triple excitations in multilevel coupled cluster theory. Nat Commun 2024; 15:3551. [PMID: 38670938 PMCID: PMC11053016 DOI: 10.1038/s41467-024-47690-x] [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: 08/04/2023] [Accepted: 04/03/2024] [Indexed: 04/28/2024] Open
Abstract
X-ray absorption (XA) spectroscopy is an essential experimental tool to investigate the local structure of liquid water. Interpretation of the experiment poses a significant challenge and requires a quantitative theoretical description. High-quality theoretical XA spectra require reliable molecular dynamics simulations and accurate electronic structure calculations. Here, we present the first successful application of coupled cluster theory to model the XA spectrum of liquid water. We overcome the computational limitations on system size by employing a multilevel coupled cluster framework for large molecular systems. Excellent agreement with the experimental spectrum is achieved by including triple excitations in the wave function and using molecular structures from state-of-the-art path-integral molecular dynamics. We demonstrate that an accurate description of the electronic structure within the first solvation shell is sufficient to successfully model the XA spectrum of liquid water within the multilevel framework. Furthermore, we present a rigorous charge transfer analysis of the XA spectrum, which is reliable due to the accuracy and robustness of the electronic structure methodology. This analysis aligns with previous studies regarding the character of the prominent features of the XA spectrum of liquid water.
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Affiliation(s)
- Sarai Dery Folkestad
- Department of Chemistry, Norwegian University of Science and Technology, NTNU, 7491, Trondheim, Norway
| | - Alexander C Paul
- Department of Chemistry, Norwegian University of Science and Technology, NTNU, 7491, Trondheim, Norway
| | - Regina Paul Née Matveeva
- Department of Chemistry, Norwegian University of Science and Technology, NTNU, 7491, Trondheim, Norway
| | - Sonia Coriani
- Department of Chemistry, Technical University of Denmark, DTU, 2800, Kongens Lyngby, Denmark
| | - Michael Odelius
- Department of Physics, Stockholm University, 10691, Stockholm, Sweden
| | - Marcella Iannuzzi
- Department of Chemistry, University of Zurich, 8057, Zürich, Switzerland
| | - Henrik Koch
- Department of Chemistry, Norwegian University of Science and Technology, NTNU, 7491, Trondheim, Norway.
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Fransson T, Pettersson LGM. Evaluating the Impact of the Tamm-Dancoff Approximation on X-ray Spectrum Calculations. J Chem Theory Comput 2024; 20:2181-2191. [PMID: 38388006 PMCID: PMC10938498 DOI: 10.1021/acs.jctc.3c01341] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Revised: 01/29/2024] [Accepted: 02/03/2024] [Indexed: 02/24/2024]
Abstract
The impact of the Tamm-Dancoff approximation (TDA) for time-dependent density functional theory (TDDFT) calculations of X-ray absorption and X-ray emission spectra (XAS and XES) is investigated, showing small discrepancies in the excitation energies and intensities. Through explicit diagonalization of the TDDFT Hessian, XES was considered by using full TDDFT with a core-hole reference state. This has previously not been possible with most TDDFT implementations as a result of the presence of negative eigenvalues. Furthermore, a core-valence separation (CVS) scheme for XES is presented, in which only elements including the core-hole are considered, resulting in a small Hessian with the dimension of the number of remaining occupied orbitals of the same spin as the core-hole (CH). The resulting spectra are in surprisingly good agreement with the full-space counterpart, illustrating the weak coupling between the valence-valence and valence-CH transitions. Complications resulting from contributions from the discretized continuum are discussed, which can occur for TDDFT calculations of XAS and XES and for TDA calculations of XAS. In conclusion, we recommend that TDA be used when calculating X-ray emission spectra, and either CVS-TDA or CVS-TDDFT can be used for X-ray absorption spectra.
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Affiliation(s)
- Thomas Fransson
- Department of Physics, AlbaNova
University Center, Stockholm University, 109 61 Stockholm, Sweden
| | - Lars G. M. Pettersson
- Department of Physics, AlbaNova
University Center, Stockholm University, 109 61 Stockholm, Sweden
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Fransson T, Pettersson LGM. Calibrating TDDFT Calculations of the X-ray Emission Spectrum of Liquid Water: The Effects of Hartree-Fock Exchange. J Chem Theory Comput 2023; 19:7333-7342. [PMID: 37787584 PMCID: PMC10601479 DOI: 10.1021/acs.jctc.3c00728] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Indexed: 10/04/2023]
Abstract
The structure and dynamics of liquid water continue to be debated, with insight provided by, among others, X-ray emission spectroscopy (XES), which shows a split in the high-energy 1b1 feature. This split is yet to be reproduced by theory, and it remains unclear if these difficulties are related to inaccuracies in dynamics simulations, spectrum calculations, or both. We investigate the performance of different methods for calculating XES of liquid water, focusing on the ability of time-dependent density functional theory (TDDFT) to reproduce reference spectra obtained by high-level coupled cluster and algebraic-diagrammatic construction scheme calculations. A metric for evaluating the agreement between theoretical spectra termed the integrated absolute difference (IAD), which considers the integral of shifted difference spectra, is introduced and used to investigate the performance of different exchange-correlation functionals. We find that computed spectra of symmetric and asymmetric model water structures are strongly and differently influenced by the amount of Hartree-Fock exchange, with best agreement to reference spectra for ∼40-50%. Lower percentages tend to yield high density of contributing states, resulting in too broad features. The method introduced here is useful also for other spectrum calculations, in particular where the performance for ensembles of structures are evaluated.
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Affiliation(s)
- Thomas Fransson
- Department of Physics, AlbaNova
University Center, Stockholm University, 109 61 Stockholm, Sweden
| | - Lars G. M. Pettersson
- Department of Physics, AlbaNova
University Center, Stockholm University, 109 61 Stockholm, Sweden
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Langer M, Zdražil L, Medveď M, Otyepka M. Communication of molecular fluorophores with other photoluminescence centres in carbon dots. NANOSCALE 2023; 15:4022-4032. [PMID: 36728225 DOI: 10.1039/d2nr05114a] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
The establishment of structure-photoluminescence (PL) relationships remains an ultimate challenge in the field of carbon dots (CDs). It is now commonly understood that various structural domains may evolve during the preparation of CDs; nonetheless, we are still far from capturing the specific features that determine the overall PL of CDs. Although the core, surface and molecular states are usually considered the three main sources of PL, it is not known to which extent they interact and/or affect one another. Expectedly, the communication between the different PL centres depends on the mutual arrangement and the type of linking. To gain insights into such a communication, time-dependent density functional theory (TD-DFT) calculations were performed for several (N-doped/O-functionalized) polyaromatic hydrocarbons (PAHs) as representative models for the core/surfaces PL states and the prototypical molecular fluorophore (MF) 5-oxo-1,2,3,5-tetrahydroimidazo-[1,2-α]-pyridine-7-carboxylic acid (IPCA), considering different interaction modes, namely hydrogen bonded and stacked complexes as well as covalently bonded and fused structures. Our results revealed that each of the studied arrangements in some way supported the communication between the PL centres. The deactivation pathways typically involve multiple charge and energy transfer events that can promote the formation of charge separated states and/or lead to the activation of other PL centres in CDs. Depending on the arrangement, the doping pattern and surface functionalization, both the CD core and the MF can act as an electron donor or acceptor, which could help to design CDs with desirable hole-electron surface/core characteristics.
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Affiliation(s)
- Michal Langer
- Regional Centre of Advanced Technologies and Materials, Czech Advanced Technology and Research Institute (CATRIN), Palacký University Olomouc, Šlechtitelů 241/27, 783 71 Olomouc, Czech Republic.
- Chemical and Biological Systems Simulation Lab, Centre of New Technologies University of Warsaw, 2c Banacha Street, 02-097, Warszawa, Poland
| | - Lukáš Zdražil
- Regional Centre of Advanced Technologies and Materials, Czech Advanced Technology and Research Institute (CATRIN), Palacký University Olomouc, Šlechtitelů 241/27, 783 71 Olomouc, Czech Republic.
| | - Miroslav Medveď
- Regional Centre of Advanced Technologies and Materials, Czech Advanced Technology and Research Institute (CATRIN), Palacký University Olomouc, Šlechtitelů 241/27, 783 71 Olomouc, Czech Republic.
- Department of Chemistry, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovak Republic
| | - Michal Otyepka
- Regional Centre of Advanced Technologies and Materials, Czech Advanced Technology and Research Institute (CATRIN), Palacký University Olomouc, Šlechtitelů 241/27, 783 71 Olomouc, Czech Republic.
- IT4Innovations, VŠB-Technical University of Ostrava, 17. listopadu 2172/15, 708 00 Ostrava-Poruba, Czech Republic
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7
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Carter-Fenk K, Cunha LA, Arias-Martinez JE, Head-Gordon M. Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States. J Phys Chem Lett 2022; 13:9664-9672. [PMID: 36215404 DOI: 10.1021/acs.jpclett.2c02564] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
The lack of particle-hole attraction and orbital relaxation within time-dependent density functional theory (TDDFT) lead to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that uses optimized orbitals of the n - 1-electron system as the reference, building orbital relaxation and a proper hole into the initial density. Our approach is an exact generalization of the static-exchange approximation that ameliorates the particle-hole interaction error associated with the adiabatic approximation and reduces errors in TDDFT XAS by orders of magnitude. With a statistical performance of just 0.5 eV root-mean-square error and the same computational scaling as TDDFT under the core-valence separation approximation, we anticipate that this approach will be of great utility in XAS calculations of large systems.
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Affiliation(s)
- Kevin Carter-Fenk
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California94720, United States
| | - Leonardo A Cunha
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California94720, United States
| | - Juan E Arias-Martinez
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California94720, United States
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
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8
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Yao Y, Golze D, Rinke P, Blum V, Kanai Y. All-Electron BSE@ GW Method for K-Edge Core Electron Excitation Energies. J Chem Theory Comput 2022; 18:1569-1583. [PMID: 35138865 DOI: 10.1021/acs.jctc.1c01180] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
We present an accurate computational approach to calculate absolute K-edge core electron excitation energies as measured by X-ray absorption spectroscopy. Our approach employs an all-electron Bethe-Salpeter equation (BSE) formalism based on GW quasiparticle energies (BSE@GW) using numeric atom-centered orbitals (NAOs). The BSE@GW method has become an increasingly popular method for the computation of neutral valence excitation energies of molecules. However, it was so far not applied to molecular K-edge excitation energies. We discuss the influence of different numerical approximations on the BSE@GW calculation and employ in our final setup (i) exact numeric algorithms for the frequency integration of the GW self-energy, (ii) G0W0 and BSE starting points with ∼50% of exact exchange, (iii) the Tamm-Dancoff approximation and (iv) relativistic corrections. We study the basis set dependence and convergence with common Gaussian-type orbital and NAO basis sets. We identify the importance of additional spatially confined basis functions as well as of diffuse augmenting basis functions. The accuracy of our BSE@GW method is assessed for a benchmark set of small organic molecules, previously used for benchmarking the equation-of-motion coupled cluster method [Peng et al., J. Chem. Theory Comput., 2015, 11, 4146], as well as the medium-sized dibenzothiophene (DBT) molecule. Our BSE@GW results for absolute excitation energies are in excellent agreement with the experiment, with a mean average error of only 0.63 eV for the benchmark set and with errors <1 eV for the DBT molecule.
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Affiliation(s)
- Yi Yao
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
| | - Dorothea Golze
- Faculty of Chemistry and Food Chemistry, Technische Universität Dresden, 01062 Dresden, Germany.,Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
| | - Patrick Rinke
- Department of Applied Physics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland
| | | | - Yosuke Kanai
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, United States
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9
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Konecny L, Vicha J, Komorovsky S, Ruud K, Repisky M. Accurate X-ray Absorption Spectra near L- and M-Edges from Relativistic Four-Component Damped Response Time-Dependent Density Functional Theory. Inorg Chem 2022; 61:830-846. [PMID: 34958215 PMCID: PMC8767545 DOI: 10.1021/acs.inorgchem.1c02412] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2021] [Indexed: 11/27/2022]
Abstract
The simulation of X-ray absorption spectra requires both scalar and spin-orbit (SO) relativistic effects to be taken into account, particularly near L- and M-edges where the SO splitting of core p and d orbitals dominates. Four-component Dirac-Coulomb Hamiltonian-based linear damped response time-dependent density functional theory (4c-DR-TDDFT) calculates spectra directly for a selected frequency region while including the relativistic effects variationally, making the method well suited for X-ray applications. In this work, we show that accurate X-ray absorption spectra near L2,3- and M4,5-edges of closed-shell transition metal and actinide compounds with different central atoms, ligands, and oxidation states can be obtained by means of 4c-DR-TDDFT. While the main absorption lines do not change noticeably with the basis set and geometry, the exchange-correlation functional has a strong influence with hybrid functionals performing the best. The energy shift compared to the experiment is shown to depend linearly on the amount of Hartee-Fock exchange with the optimal value being 60% for spectral regions above 1000 eV, providing relative errors below 0.2% and 2% for edge energies and SO splittings, respectively. Finally, the methodology calibrated in this work is used to reproduce the experimental L2,3-edge X-ray absorption spectra of [RuCl2(DMSO)2(Im)2] and [WCl4(PMePh2)2], and resolve the broad bands into separated lines, allowing an interpretation based on ligand field theory and double point groups. These results support 4c-DR-TDDFT as a reliable method for calculating and analyzing X-ray absorption spectra of chemically interesting systems, advance the accuracy of state-of-the art relativistic DFT approaches, and provide a reference for benchmarking more approximate techniques.
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Affiliation(s)
- Lukas Konecny
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø − The Arctic University
of Norway, 9037 Tromsø, Norway
| | - Jan Vicha
- Centre
of Polymer Systems, Tomas Bata University, tř. Tomáše
Bati 5678, 760 01 Zlín, Czech Republic
| | - Stanislav Komorovsky
- Institute
of Inorganic Chemistry, Slovak Academy of
Sciences, Dúbravská cesta 9, SK-84536 Bratislava, Slovakia
| | - Kenneth Ruud
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø − The Arctic University
of Norway, 9037 Tromsø, Norway
| | - Michal Repisky
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø − The Arctic University
of Norway, 9037 Tromsø, Norway
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Carter-Fenk K, Head-Gordon M. On the choice of reference orbitals for linear-response calculations of solution-phase K-edge X-ray absorption spectra. Phys Chem Chem Phys 2022; 24:26170-26179. [DOI: 10.1039/d2cp04077h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
X-ray absorption spectra of liquids calculated with linear-response theories like TDDFT and CIS are dramatically improved with core-ion reference orbitals.
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Affiliation(s)
- Kevin Carter-Fenk
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, CA 94720, USA
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, CA 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
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