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X-ray spectroscopies through damped linear response theory
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Chemistry. Linköping University, Faculty of Science & Engineering.
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In order to reach a fundamental understanding of interactions between electromagnetic radiation and molecular materials, experimental measurements need to be supplemented with theoretical models and simulations. With the use of this combination, it is possible to characterize materials in terms of, e.g., chemical composition and molecular structure, as well as achieve time-resolution in studies of chemical reactions. This doctoral thesis focuses on the development and evaluation of theoretical methods with which, amongst others, X-ray absorption and X-ray emission spectroscopies can be interpreted and predicted.  In X-ray absorption spectroscopy the photon energy is tuned such that core electrons are targeted and excited to either bound or continuum states, and X-ray emission spectroscopy measures the subsequent decay from such an excited state. These core excitations/de-excitations exhibit strong relaxation effects, making theoretical considerations of the processes particularly challenging. While the removal of a valence electron leaves the remaining electrons relatively unaffected, removing core electrons has a substantial effect on the other electrons due to the significant change in the screening of the nucleus. Additionally, the core-excited states are embedded in a manifold of valence-excited states that needs to be considered by some computationally feasible method. In this thesis, a damped formalism of linear response theory, which is a perturbative manner of considering the interactions of (weak) external or internal fields with molecular systems, has been utilized to investigate mainly the X-ray absorption spectra of small- to medium-sized molecular systems.

Amongst the standard quantum chemical methods available, coupled cluster is perhaps the most accurate, with a well-defined, hierarchical manner of approaching the correct electronic wave function. Combined with response theory, it provides a reliable theoretical method in which relaxation effects are addressed by means of an accurate treatment of electron correlation. The first part of this thesis deals with the development and evaluation of such an approach, and it is shown that the relaxation effects can be addressed by the inclusion of double excitations in the coupled cluster manifold.  However, these calculations are computationally very demanding, and in order to treat larger systems the performance of the coupled cluster approach has been compared to that of the less demanding method of time-density dependent functional theory (TDDFT). Both methods have been used to investigate the X-ray absorption spectrum of water, which has been extensively debated in the scientific community following a relatively recent hypothesis concerning the underlying structure of liquid water. Water exhibits a great number of anomalous properties that stand out from those of most compounds, and the importance of reaching a fundamental understanding of this substance cannot be overstated. It has been demonstrated that TDDFT yields excellent results for liquid water, opening up possibilities of investigating the correlation between spectral features and local structures.

Furthermore, recent developments in damped linear response TDDFT in the four-component relativistic regime have enabled the inclusion of spin-orbit coupling in damped linear response calculations, making black-box calculations of absorption spectra in a relativistic setting practical. With this approach, it is possible to address the spin-orbit splitting in L2,3-edge X-ray absorption spectra, and the performance of such a method has been demonstrated for a set of small molecules. Excellent agreement with experiment is obtained in terms of relative features, but an anomalous error in absolute energy has been observed for silane derivatives featuring fluorine-substitutions. This is likely a result of the strong influence of the very electronegative fluorine atoms on the electron density of the core-excited atom.

Finally, the treatment of non-resonant X-ray emission spectroscopy using damped linear response theory is discussed. The expansion needed for the development of a simple method by which this spectroscopy can be treated using damped linear response theory at the TDDFT level of theory has been identified, and proof of principle calculations at the time-dependent Hartree-Fock level of theory are presented.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016. , 122 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1719
National Category
Chemical Sciences
Identifiers
URN: urn:nbn:se:liu:diva-124272DOI: 10.3384/diss.diva-124272ISBN: 978-91-7685-908-7 (print)OAI: oai:DiVA.org:liu-124272DiVA: diva2:897235
Public defence
2016-02-19, Planck, Fysikhuset, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2016-01-25 Created: 2016-01-25 Last updated: 2016-01-26Bibliographically approved
List of papers
1. Coupled-cluster response theory for near-edge x-ray-absorption fine structure of atoms and molecules
Open this publication in new window or tab >>Coupled-cluster response theory for near-edge x-ray-absorption fine structure of atoms and molecules
2012 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 85, no 2, 022507- p.Article in journal (Refereed) Published
Abstract [en]

Based on an asymmetric Lanczos-chain subspace algorithm, damped coupled cluster linear response functions have been implemented for the hierarchy of coupled cluster (CC) models including CC with single excitations (CCS), CC2, CC with single and double excitations (CCSD), and CCSD with noniterative triple corrected excitation energies CCSDR(3). This work is a first step toward the extension of these theoretical electronic structure methods of well-established high accuracy in UV-vis absorption spectroscopies to applications concerned with x-ray radiation. From the imaginary part of the linear response function, the near K-edge x-ray absorption spectra of neon, water, and carbon monoxide are determined and compared with experiment. Results at the CCSD level show relative peak intensities in good agreement with experiment with discrepancies in transition energies due to incomplete treatment of electronic relaxation and correlation that amount to 1-2 eV. With inclusion of triple excitations, errors in energetics are less than 0.9 eV and thereby capturing 90%, 95%, and 98% of the relaxation-correlation energies for C, O, and Ne, respectively.

Place, publisher, year, edition, pages
American Physical Society, 2012
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-75466 (URN)10.1103/PhysRevA.85.022507 (DOI)000300081800005 ()
Note
Funding Agencies|EU|254326|Swedish Research Council|621-2010-5014|National Supercomputer Centre (NSC), Sweden||Available from: 2012-03-02 Created: 2012-03-02 Last updated: 2017-12-07
2. Asymmetric-Lanczos-Chain-Driven Implementation of Electronic Resonance Convergent Coupled-Cluster Linear Response Theory
Open this publication in new window or tab >>Asymmetric-Lanczos-Chain-Driven Implementation of Electronic Resonance Convergent Coupled-Cluster Linear Response Theory
2012 (English)In: Journal of Chemical Theory and Computation, ISSN 1549-9618, E-ISSN 1549-9626, Vol. 8, no 5, 1616-1628 p.Article in journal (Refereed) Published
Abstract [en]

We present an implementation of the damped coupled-cluster linear response function based on an asymmetric Lanczos chain algorithm for the hierarchy of coupled-cluster approximations CCS (coupled-cluster singles), CC2 (coupled. cluster singles and approximate doubles), and CCSD (coupled-cluster singles and doubles). Triple corrections to the excitation energies can be included via the CCSDR(3) (coupled-cluster singles and doubles with noniterative-triples-corrected excitation energies) approximation. The performance and some of the potentialities of the approach are investigated in calculations of the visible/ultraviolet absorption spectrum and the dispersion of the real polarizability in near-resonant regions of pyrimidine, the near-edge absorption fine structure (NEXAFS) of ammonia, and the direct determination of the C-6 dipole-dipole dispersion coefficient of the benzene dimer.

Place, publisher, year, edition, pages
American Chemical Society, 2012
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-77865 (URN)10.1021/ct200919e (DOI)000303628400011 ()
Note
Funding Agencies|FP7-PEOPLE-2009-IEF|254326|Swedish Research Council|621-2010-S014|National Supercomputer Centre (NSC), Sweden||Available from: 2012-05-31 Created: 2012-05-31 Last updated: 2017-12-07
3. Carbon X-ray absorption spectra of fluoroethenes and acetone: A study at the coupled cluster, density functional, and static-exchange levels of theory
Open this publication in new window or tab >>Carbon X-ray absorption spectra of fluoroethenes and acetone: A study at the coupled cluster, density functional, and static-exchange levels of theory
2013 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 138, no 12Article in journal (Refereed) Published
Abstract [en]

Near carbon K-edge X-ray absorption fine structure spectra of a series of fluorine-substituted ethenes and acetone have been studied using coupled cluster and density functional theory (DFT) polarization propagator methods, as well as the static-exchange (STEX) approach. With the complex polarization propagator (CPP) implemented in coupled cluster theory, relaxation effects following the excitation of core electrons are accounted for in terms of electron correlation, enabling a systematic convergence of these effects with respect to electron excitations in the cluster operator. Coupled cluster results have been used as benchmarks for the assessment of propagator methods in DFT as well as the state-specific static-exchange approach. Calculations on ethene and 1,1-difluoroethene illustrate the possibility of using nonrelativistic coupled cluster singles and doubles (CCSD) with additional effects of electron correlation and relativity added as scalar shifts in energetics. It has been demonstrated that CPP spectra obtained with coupled cluster singles and approximate doubles (CC2), CCSD, and DFT (with a Coulomb attenuated exchange-correlation functional) yield excellent predictions of chemical shifts for vinylfluoride, 1,1-difluoroethene, trifluoroethene, as well as good spectral features for acetone in the case of CCSD and DFT. Following this, CPP-DFT is considered to be a viable option for the calculation of X-ray absorption spectra of larger pi-conjugated systems, and CC2 is deemed applicable for chemical shifts but not for studies of fine structure features. The CCSD method as well as the more approximate CC2 method are shown to yield spectral features relating to pi*-resonances in good agreement with experiment, not only for the aforementioned molecules but also for ethene, cis-1,2-difluoroethene, and tetrafluoroethene. The STEX approach is shown to underestimate pi*-peak separations due to spectral compressions, a characteristic which is inherent to this method.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2013
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-92613 (URN)10.1063/1.4795835 (DOI)000316969500078 ()
Note

Funding Agencies|Swedish Research Council|621-2010-5014|EU|254326|Supercomputer Centre (NSC), Sweden||

Available from: 2013-05-16 Created: 2013-05-14 Last updated: 2017-12-06
4. Requirements of first-principles calculations of X-ray absorption spectra of liquid water
Open this publication in new window or tab >>Requirements of first-principles calculations of X-ray absorption spectra of liquid water
Show others...
2016 (English)In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, Vol. 18, no 1, 566-583 p.Article in journal (Refereed) Published
Abstract [en]

A computational benchmark study on X-ray absorption spectra of water has been performed by means of transition-potential density functional theory (TP-DFT), damped time-dependent density functional theory (TDDFT), and damped coupled cluster (CC) linear response theory. For liquid water, using TDDFT with a tailored CAM-B3LYP functional and a polarizable embedding, we find that an embedding with over 2000 water molecules is required to fully converge spectral features for individual molecules, but a substantially smaller embedding can be used within averaging schemes. TP-DFT and TDDFT calculations on 100 MD structures demonstrate that TDDFT produces a spectrum with spectral features in good agreement with experiment, while it is more difficult to fully resolve the spectral features in the TP-DFT spectrum. Similar trends were also observed for calculations of bulk ice. In order to further establish the performance of these methods, small water clusters have been considered also at the CC2 and CCSD levels of theory. Issues regarding the basis set requirements for spectrum simulations of liquid water and the determination of gas-phase ionization potentials are also discussed.

Place, publisher, year, edition, pages
Royal Society of Chemistry, 2016
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:liu:diva-124266 (URN)10.1039/C5CP03919C (DOI)000368755500059 ()26619162 (PubMedID)
Note

Funding agencies: Swedish Research Council [621-2014-4646, 621-2011-4223]; Knut and Alice Wallenberg Foundation [KAW-2013.0020]

Available from: 2016-01-25 Created: 2016-01-25 Last updated: 2017-11-30Bibliographically approved
5. Four-component damped density functional response theory study of UV/vis absorption spectra and phosphorescence parameters of group 12 metal-substituted porphyrins
Open this publication in new window or tab >>Four-component damped density functional response theory study of UV/vis absorption spectra and phosphorescence parameters of group 12 metal-substituted porphyrins
2016 (English)In: Journal of Chemical Theory and Computation, ISSN 1549-9618, E-ISSN 1549-9626, Vol. 12, no 5, 2324-2334 p.Article in journal (Refereed) Published
Abstract [en]

The influences of group 12 (Zn, Cd, Hg) metal-substitution on the valence spectra and phosphorescence parameters of porphyrins (P) have been investigated in a relativistic setting. In order to obtain valence spectra, this study reports the first application of the damped linear response function, or complex polarization propagator, in the four-component density functional theory framework [as formulated in J. Chem. Phys. 133, 064105 (2010)]. It is shown that the steep increase in the density of states as due to the inclusion of spin-orbit coupling yields only minor changes in overall computational costs involved with the solution of the set of linear response equations. Comparing single-frequency to multi-frequency spectral calculations, it is noted that the number of iterations in the iterative linear equation solver per frequency grid-point decreases monotonously from 30 to 0.74 as the number of frequency points goes from one to 19. The main heavy-atom effect on the UV/vis-absorption spectra is indirect and attributed to the change of point group symmetry due to metal-substitution, and it is noted that substitutions using heavier atoms yield small red-shifts of the intense Soret-band. Concerning phosphorescence parameters, the adoption of a four-component relativistic setting enables the calculation of such properties at a linear order of response theory, and any higher-order response functions does not need to be considered. For the substituted porphyrins, electronic coupling between the lowest triplet states is strong and results in theoretical estimates of lifetimes that are sensitive to the wave function and electron density parametrization. With this in mind, we report our best estimates of the phosphorescence lifetimes to be 460, 13.8, 11.2, and 0.00155 s for H2P, ZnP, CdP, and HgP, respectively, with the corresponding transition energies being equal to 1.46, 1.50, 1.38, and 0.89 eV.

Place, publisher, year, edition, pages
American Chemical Society (ACS), 2016
National Category
Chemical Sciences
Identifiers
urn:nbn:se:liu:diva-124270 (URN)10.1021/acs.jctc.6b00030 (DOI)000375810000020 ()
Note

Funding agencies: Swedish Research Council [621-2014-4646]

Vid tiden för disputation förelåg publikationen som manuskript

Available from: 2016-01-25 Created: 2016-01-25 Last updated: 2017-11-30Bibliographically approved
6. K- and L-edge X-ray absorption spectrum calculations of closed-shell carbon, silicon, germanium, and sulfur compounds using damped four-component density functional response theory
Open this publication in new window or tab >>K- and L-edge X-ray absorption spectrum calculations of closed-shell carbon, silicon, germanium, and sulfur compounds using damped four-component density functional response theory
2016 (English)In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, Vol. 18, no 19, 13591-13603 p.Article in journal (Other academic) Published
Abstract [en]

X-ray absorption spectra of carbon, silicon, germanium, and sulfur compounds have been investigated by means of damped four-component density functional response theory. It is demonstrated that a reliable description of relativistic effects is obtained at both K- and L-edges. Notably, an excellent agreement with experimental results is obtained for L2,3-spectra—with spin-orbit effects well accounted for—also in cases when the experimental intensity ratio deviate from the statistical one of 1:2. The theoretical results are consistent with calculations using standard response theory as well as recently reported real-time propagation methods in time-dependent density functional theory, and the virtues of different approaches are discussed. As compared to silane and silicon tetrachloride, an anomalous error in the absolute energy is reported for the L2,3-spectrum of silicon tetrafluoride, amounting to an additional spectral shift of ~ 1 eV. This anomaly is observed also for other exchange-correlation functionals, but it is seen neither at other silicon edges nor at the carbon K-edge of fluorine derivatives of ethene. Considering the series of molecules SiH4−XFX with X = 1, 2, 3, 4, a gradual divergence from interpolated experimental ionization potentials is observed at the level of Kohn–Sham density functional theory (DFT), and to a smaller extent with use of Hartree–Fock. This anomalous error is thus attributed partly to difficulties in correctly emulating the electronic structure effects imposed by the very electronegative fluorines, and partly due to inconsistencies in the spurious electron self-repulsion in DFT. Substitution with one, or possibly two, fluorine atoms is estimated to yield small enough errors to allow for reliable interpretations and predictions of L2,3-spectra of more complex and extended silicon-based systems.

Place, publisher, year, edition, pages
Royal Society of Chemistry, 2016
National Category
Chemical Sciences
Identifiers
urn:nbn:se:liu:diva-124271 (URN)10.1039/c6cp00561f (DOI)000376138000050 ()
Note

Funding agencies. Knut and Alice Wallenberg Foundation [KAW-2013.0020]; Swedish Research Council [621-2014-4646]

Available from: 2016-01-25 Created: 2016-01-25 Last updated: 2017-11-30Bibliographically approved

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