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De Bruecker L, Filez M, Van Speybroeck V. On the Prediction of Spectroscopic Fingerprints of Co 2+ Complexes Relevant for the ZIF Nucleation Process. Inorg Chem 2023; 62:16304-16322. [PMID: 37753934 DOI: 10.1021/acs.inorgchem.3c01355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/28/2023]
Abstract
The nucleation process of zeolitic imidazolate frameworks (ZIFs) is to date not completely understood. Recently, it has been found that, during the formation of Co-ZIF-67, after mixing imidazole-type ligands with octahedral precursors containing oxygen-coordinated ligands, a metal-organic pool with a diversity of transition metal complexes (TMCs) is formed showing fingerprints of octahedral and tetrahedral Co2+ complexes with both types of ligands [Filez, M. Cell Rep. Phys. Sci. 2021, 2, 100680]. In order to further unravel this process, we aim to characterize the d-d transitions of the TMCs and focus on their number, intensity, and position, which change during the process and can thus serve as a fingerprint for the formed species. It was previously shown that the number of ligands and symmetry has a detrimental influence on the ground state properties of Co2+ TMCs. Herein, we investigate how far excited state properties of TMCs relevant during nanoporous formation processes can be predicted by time-dependent density functional theory (TDDFT) and ligand field density functional theory (LFDFT). As TMCs are known to be challenging systems with possibly degenerate ground states and double excitations, we first investigate the performance of both techniques on first-row octahedral aqua-complexes. With this knowledge, we then focus on tetrahedral Co2+ complexes with aqua and imidazole-type ligands in order to investigate in how far we can propose a spectroscopic fingerprint that allows us to follow the Co2+ complexes during the formation of Co-ZIF-67. The results of TDDFT and LFDFT are qualitatively in agreement and provide complementary information. We found that various features can be used to distinguish between the species. However, as LFDFT is not suited for TMCs possessing the extended imidazole-type ligands and double and spin-flip states are not included in TDDFT, both techniques need to be complemented with more advanced methods to obtain complete insight into the d-d excitations of TMCs with imidazole ligands. Therefore, we particularly explored ab initio ligand field theory, which is capable of describing double excitations and is, in contrast to LFDFT, suitable for TMCs with extended ligands.
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Affiliation(s)
- Liesbeth De Bruecker
- Center for Molecular Modeling (CMM), Ghent University, Technologiepark-Zwijnaarde 46, 9052 Zwijnaarde, Belgium
| | - Matthias Filez
- Conformal Coating of Nanomaterials (CoCooN), Ghent University, Krijgslaan 281/S1, 9000 Gent, Belgium
| | - Veronique Van Speybroeck
- Center for Molecular Modeling (CMM), Ghent University, Technologiepark-Zwijnaarde 46, 9052 Zwijnaarde, Belgium
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Ranka K, Isborn CM. Size-dependent errors in real-time electron density propagation. J Chem Phys 2023; 158:2887545. [PMID: 37125706 DOI: 10.1063/5.0142515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2023] [Accepted: 04/14/2023] [Indexed: 05/02/2023] Open
Abstract
Real-time (RT) electron density propagation with time-dependent density functional theory (TDDFT) or Hartree-Fock (TDHF) is one of the most popular methods to model the charge transfer in molecules and materials. However, both RT-TDHF and RT-TDDFT within the adiabatic approximation are known to produce inaccurate evolution of the electron density away from the ground state in model systems, leading to large errors in charge transfer and erroneous shifting of peaks in absorption spectra. Given the poor performance of these methods with small model systems and the widespread use of the methods with larger molecular and material systems, here we bridge the gap in our understanding of these methods and examine the size-dependence of errors in RT density propagation. We analyze the performance of RT density propagation for systems of increasing size during the application of a continuous resonant field to induce Rabi-like oscillations, during charge-transfer dynamics, and for peak shifting in simulated absorption spectra. We find that the errors in the electron dynamics are indeed size dependent for these phenomena, with the largest system producing the results most aligned with those expected from linear response theory. The results suggest that although the RT-TDHF and RT-TDDFT methods may produce severe errors for model systems, the errors in charge transfer and resonantly driven electron dynamics may be much less significant for more realistic, large-scale molecules and materials.
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Affiliation(s)
- Karnamohit Ranka
- Chemistry and Biochemistry, University of California Merced, Merced, California 95343, USA
| | - Christine M Isborn
- Chemistry and Biochemistry, University of California Merced, Merced, California 95343, USA
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Nazarov VU, Baer R. High-frequency limit of spectroscopy. J Chem Phys 2022; 157:084112. [DOI: 10.1063/5.0100317] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We consider an arbitrary quantum mechanical system, initially in its ground-state, exposed to a time-dependent electromagnetic pulse with a carrier frequency $\omega_0$ and a slowly varying envelope of finite duration. By working out a solution to the time-dependent Schr\"odinger equation in the high-$\omega_0$ limit, we find that, to the leading order in $\omega_0^{-1}$, a perfect self-cancellation of the system's linear response occurs as the pulse switches off. Surprisingly, the system's observables are, nonetheless, describable in terms of a combination of its linear density response function and nonlinear functions of the electric field. An analysis of jellium slab and jellium sphere models reveals a very high surface sensitivity of the considered setup, producing a richer excitation spectrum than accessible within the conventional linear response regime. On this basis, we propose a new spectroscopic technique, which we provisionally name the Nonlinear High-Frequency Pulsed Spectroscopy (NLHFPS). Combining the advantages of the extraordinary surface sensitivity, the absence of constraints by the traditional dipole selection rules, and the clarity of theoretical interpretation utilizing the linear response time-dependent density functional theory, NLHFPS has a potential to evolve into a powerful characterization method for nanoscience and nanotechnology.
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Affiliation(s)
- Vladimir U Nazarov
- Moscow Institute of Physics and Technology National Research University, Russia
| | - Roi Baer
- Department of Chemistry, Hebrew University of Jerusalem - Givat Ram Campus, Israel
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Müller C, Sharma M, Sierka M. Real-time time-dependent density functional theory using density fitting and the continuous fast multipole method. J Comput Chem 2020; 41:2573-2582. [PMID: 33464600 DOI: 10.1002/jcc.26412] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2020] [Revised: 08/17/2020] [Accepted: 08/18/2020] [Indexed: 11/07/2022]
Abstract
An implementation of real-time time-dependent density functional theory (RT-TDDFT) within the TURBOMOLE program package is reported using Gaussian-type orbitals as basis functions, second and fourth order Magnus propagator, and the self-consistent field as well as the predictor-corrector time integration schemes. The Coulomb contribution to the Kohn-Sham matrix is calculated combining density fitting approximation and the continuous fast multipole method. Performance of the implementation is benchmarked for molecular systems with different sizes and dimensionalities. For linear alkane chains, the wall time for density matrix time propagation step is comparable to the Kohn-Sham (KS) matrix construction. However, for larger two- and three-dimensional molecules, with up to about 5,000 basis functions, the computational effort of RT-TDDFT calculations is dominated by the KS matrix evaluation. In addition, the maximum time step is evaluated using a set of small molecules of different polarities. The photoabsorption spectra of several molecular systems calculated using RT-TDDFT are compared to those obtained using linear response time-dependent density functional theory and coupled cluster methods.
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Affiliation(s)
- Carolin Müller
- Otto Schott Institute of Materials Research, Friedrich Schiller University of Jena, Jena, Germany
| | - Manas Sharma
- Otto Schott Institute of Materials Research, Friedrich Schiller University of Jena, Jena, Germany
| | - Marek Sierka
- Otto Schott Institute of Materials Research, Friedrich Schiller University of Jena, Jena, Germany
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Fernando RG, Balhoff MC, Lopata K. X-ray Absorption in Insulators with Non-Hermitian Real-Time Time-Dependent Density Functional Theory. J Chem Theory Comput 2015; 11:646-54. [DOI: 10.1021/ct500943m] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Ranelka G. Fernando
- Department
of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, United States
| | - Mary C. Balhoff
- Department
of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, United States
| | - Kenneth Lopata
- Department
of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803, United States
- Center for Computation & Technology, Louisiana State University, Baton Rouge, Louisiana 70803, United States
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Wang J, Gao CZ, Calvayrac F, Zhang FS. Collision dynamics of proton with formaldehyde: fragmentation and ionization. J Chem Phys 2014; 140:124306. [PMID: 24697440 DOI: 10.1063/1.4868985] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using time-dependent density functional theory, applied to the valence electrons and coupled non-adiabatically to molecular dynamics of the ions, we study the ionization and fragmentation of formaldehyde in collision with a proton. Four different impact energies: 35 eV, 85 eV, 135 eV, and 300 eV are chosen in order to study the energy effect in the low energy region, and ten different incident orientations at 85 eV are considered for investigating the steric effect. Fragmentation ratios, single, double, and total electron ionization cross sections are calculated. For large impact parameters, these results are close to zero irrespective of the incident orientations due to a weak projectile-target interaction. For small impact parameters, the results strongly depend on the collision energy and orientation. We also give the kinetic energy releases and scattering angles of protons, as well as the cross section of different ion fragments and the corresponding reaction channels.
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Affiliation(s)
- Jing Wang
- The Key Laboratory of Beam Technology and Material Modification of Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China
| | - Cong-Zhang Gao
- The Key Laboratory of Beam Technology and Material Modification of Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China
| | - Florent Calvayrac
- Institut des Molecules et Matériaux du Mans UMR 6283, Université du Maine, LUNAM 72085 Le Mans Cedex 9, France
| | - Feng-Shou Zhang
- The Key Laboratory of Beam Technology and Material Modification of Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China
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Gao CZ, Wang J, Wang F, Zhang FS. Theoretical study on collision dynamics of H+ + CH4 at low energies. J Chem Phys 2014; 140:054308. [DOI: 10.1063/1.4863635] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
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Yuen-Zhou J, Aspuru-Guzik A. Remarks on time-dependent [current]-density functional theory for open quantum systems. Phys Chem Chem Phys 2013; 15:12626-36. [DOI: 10.1039/c3cp51127h] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Verdozzi C, Karlsson D, Puig von Friesen M, Almbladh CO, von Barth U. Some open questions in TDDFT: Clues from lattice models and Kadanoff–Baym dynamics. Chem Phys 2011. [DOI: 10.1016/j.chemphys.2011.04.035] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Lopata K, Govind N. Modeling Fast Electron Dynamics with Real-Time Time-Dependent Density Functional Theory: Application to Small Molecules and Chromophores. J Chem Theory Comput 2011; 7:1344-55. [DOI: 10.1021/ct200137z] [Citation(s) in RCA: 182] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Kenneth Lopata
- William R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory
| | - Niranjan Govind
- William R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory
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Hess BC, Jensen DS, Okhrimenko IG. Spatial distribution of electron densities during optical excitation of C60. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:445502. [PMID: 21403349 DOI: 10.1088/0953-8984/22/44/445502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We calculate the spatial distribution of the oscillating electron density for the low energy optical excitations in C(60), using ab initio time-dependent density functional theory. We contrast this with the unscreened free response of the Kohn-Sham eigenfunctions, in which the charge transfer is between hemispheres and the simple density oscillation patterns are very similar for electrons outside and inside the C(60) radius. In the screened case, the oscillation patterns involve charge transfer on the scale of interatomic distances. The exterior and interior densities play different roles in the oscillator strength and screening. Almost all of the dipole oscillation for optical absorption strength is from exterior electrons, a consequence of the superposition of π and σ electron oscillations. The lowest transition with appreciable strength is dominated by screening from π electrons.
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Affiliation(s)
- Bret C Hess
- Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, USA.
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Affiliation(s)
- Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 Israel;
| | - Ester Livshits
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904 Israel;
| | - Ulrike Salzner
- Department of Chemistry, Bilkent University, 06800 Bilkent, Ankara, Turkey
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Yuen-Zhou J, Tempel DG, Rodríguez-Rosario CA, Aspuru-Guzik A. Time-dependent density functional theory for open quantum systems with unitary propagation. PHYSICAL REVIEW LETTERS 2010; 104:043001. [PMID: 20366703 DOI: 10.1103/physrevlett.104.043001] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2009] [Indexed: 05/29/2023]
Abstract
We extend the Runge-Gross theorem for a very general class of open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS) time-dependent density functional theory, it is possible to rigorously include the effects of the environment within a bath functional in the KS potential. A Markovian bath functional inspired by the theory of nonlinear Schrödinger equations is suggested, which can be readily implemented in currently existing real-time codes. Finally, calculations on a helium model system are presented.
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Affiliation(s)
- Joel Yuen-Zhou
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, 02138, Cambridge, Massachusetts, USA
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