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Zhang Q, Shao X, Li W, Mi W, Pavanello M, Akimov AV. Nonadiabatic molecular dynamics with subsystem density functional theory: application to crystalline pentacene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:385901. [PMID: 38866023 DOI: 10.1088/1361-648x/ad577d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2024] [Accepted: 06/12/2024] [Indexed: 06/14/2024]
Abstract
In this work, we report the development and assessment of the nonadiabatic molecular dynamics approach with the electronic structure calculations based on the linearly scaling subsystem density functional method. The approach is implemented in an open-source embedded Quantum Espresso/Libra software specially designed for nonadiabatic dynamics simulations in extended systems. As proof of the applicability of this method to large condensed-matter systems, we examine the dynamics of nonradiative relaxation of excess excitation energy in pentacene crystals with the simulation supercells containing more than 600 atoms. We find that increased structural disorder observed in larger supercell models induces larger nonadiabatic couplings of electronic states and accelerates the relaxation dynamics of excited states. We conduct a comparative analysis of several quantum-classical trajectory surface hopping schemes, including two new methods proposed in this work (revised decoherence-induced surface hopping and instantaneous decoherence at frustrated hops). Most of the tested schemes suggest fast energy relaxation occurring with the timescales in the 0.7-2.0 ps range, but they significantly overestimate the ground state recovery rates. Only the modified simplified decay of mixing approach yields a notably slower relaxation timescales of 8-14 ps, with a significantly inhibited ground state recovery.
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Affiliation(s)
- Qingxin Zhang
- Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, NY 14260, United States of America
| | - Xuecheng Shao
- Department of Physics, Rutgers University, The State University of New Jersey, Newark, NJ 07102, United States of America
| | - Wei Li
- School of Chemistry and Materials Science, Hunan Agricultural University, Changsha 410128, People's Republic of China
| | - Wenhui Mi
- Key Laboratory of Material Simulation Methods & Software of Ministry of Education, College of Physics, Jilin University, Changchun 130012, People's Republic of China
- State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, People's Republic of China
| | - Michele Pavanello
- Department of Physics, Rutgers University, The State University of New Jersey, Newark, NJ 07102, United States of America
| | - Alexey V Akimov
- Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, NY 14260, United States of America
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Schreder L, Luber S. Propagated (fragment) Pipek-Mezey Wannier functions in real-time time-dependent density functional theory. J Chem Phys 2024; 160:214117. [PMID: 38832736 DOI: 10.1063/5.0203442] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2024] [Accepted: 05/14/2024] [Indexed: 06/05/2024] Open
Abstract
Localization procedures are an important tool for analysis of complex systems in quantum chemistry, since canonical molecular orbitals are delocalized and can, therefore, be difficult to align with chemical intuition and obscure information at the local level of the system. This especially applies to calculations obeying periodic boundary conditions. The most commonly used approach to localization is Foster-Boys Wannier functions, which use a unitary transformation to jointly minimize the second moment of the orbitals. This procedure has proven to be robust and fast but has a side effect of often mixing σ- and π-type orbitals. σ/π-separation is achieved by the Pipek-Mezey Wannier function (PMWF) approach [Lehtola and Jónsson, J. Chem. Theory Comput. 10, 642 (2014) and Jónsson et al., J. Chem. Theory Comput. 13, 460 (2017)], which defines the spread functional in terms of partial charges instead. We have implemented a PMWF algorithm in the CP2K software package using the Cardoso-Souloumiac algorithm to enable their application to real-time time-dependent density functional theory. The method is demonstrated on stacked CO2 molecules, linear acetylenic carbon, boron and nitrogen co-doped graphene, and nitrogen-vacancy doped diamond. Finally, we discuss its computational scaling and recent efforts to improve it with fragment approaches.
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Affiliation(s)
- Lukas Schreder
- University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Sandra Luber
- University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
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Selenius E, Sigurdarson AE, Schmerwitz YLA, Levi G. Orbital-Optimized Versus Time-Dependent Density Functional Calculations of Intramolecular Charge Transfer Excited States. J Chem Theory Comput 2024; 20:3809-3822. [PMID: 38695313 DOI: 10.1021/acs.jctc.3c01319] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/15/2024]
Abstract
The performance of time-independent, orbital-optimized calculations of excited states is assessed with respect to charge transfer excitations in organic molecules in comparison to the linear-response time-dependent density functional theory (TD-DFT) approach. A direct optimization method to converge on saddle points of the electronic energy surface is used to carry out calculations with the local density approximation (LDA) and the generalized gradient approximation (GGA) functionals PBE and BLYP for a set of 27 excitations in 15 molecules. The time-independent approach is fully variational and provides a relaxed excited state electron density from which the extent of charge transfer is quantified. The TD-DFT calculations are generally found to provide larger charge transfer distances compared to the orbital-optimized calculations, even when including orbital relaxation effects with the Z-vector method. While the error on the excitation energy relative to theoretical best estimates is found to increase with the extent of charge transfer up to ca. -2 eV for TD-DFT, no correlation is observed for the orbital-optimized approach. The orbital-optimized calculations with the LDA and the GGA functionals provide a mean absolute error of ∼0.7 eV, outperforming TD-DFT with both local and global hybrid functionals for excitations with a long-range charge transfer character. Orbital-optimized calculations with the global hybrid functional B3LYP and the range-separated hybrid functional CAM-B3LYP on a selection of states with short- and long-range charge transfer indicate that inclusion of exact exchange has a small effect on the charge transfer distance, while it significantly improves the excitation energy, with the best-performing functional CAM-B3LYP providing an absolute error typically around 0.15 eV.
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Affiliation(s)
- Elli Selenius
- Science Institute of the University of Iceland, Reykjavík 107, Iceland
| | | | | | - Gianluca Levi
- Science Institute of the University of Iceland, Reykjavík 107, Iceland
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Eschenbach P, Neugebauer J. Subsystem density-functional theory: A reliable tool for spin-density based properties. J Chem Phys 2022; 157:130902. [PMID: 36209003 DOI: 10.1063/5.0103091] [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
Subsystem density-functional theory compiles a set of features that allow for efficiently calculating properties of very large open-shell radical systems such as organic radical crystals, proteins, or deoxyribonucleic acid stacks. It is computationally less costly than correlated ab initio wave function approaches and can pragmatically avoid the overdelocalization problem of Kohn-Sham density-functional theory without employing hard constraints on the electron-density. Additionally, subsystem density-functional theory calculations commonly start from isolated fragment electron densities, pragmatically preserving a priori specified subsystem spin-patterns throughout the calculation. Methods based on subsystem density-functional theory have seen a rapid development over the past years and have become important tools for describing open-shell properties. In this Perspective, we address open questions and possible developments toward challenging future applications in connection with subsystem density-functional theory for spin-dependent properties.
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Affiliation(s)
- Patrick Eschenbach
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Simulation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Simulation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany
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Mališ M, Vandaele E, Luber S. Spin-Orbit Couplings for Nonadiabatic Molecular Dynamics at the ΔSCF Level. J Chem Theory Comput 2022; 18:4082-4094. [PMID: 35666703 DOI: 10.1021/acs.jctc.1c01046] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A procedure for the calculation of spin-orbit coupling (SOC) at the delta self-consistent field (ΔSCF) level of theory is presented. Singlet and triplet excited electronic states obtained with the ΔSCF method are expanded into a linear combination of singly excited Slater determinants composed of ground electronic state Kohn-Sham orbitals. This alleviates the nonorthogonality between excited and ground electronic states and introduces a framework, similar to the auxiliary wave function at the time-dependent density functional theory (TD-DFT) level, for the calculation of observables. The ΔSCF observables of the formaldehyde system were compared to reference TD-DFT values. Our procedure gives all components (energies, gradients, nonadiabatic couplings, and SOC terms) at the ΔSCF level of theory for conducting efficient, full-atomistic nonadiabatic molecular dynamics with intersystem crossing, particularly in condensed phase systems.
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Affiliation(s)
- Momir Mališ
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Eva Vandaele
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Sandra Luber
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
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Schmerwitz YLA, Ivanov AV, Jónsson EÖ, Jónsson H, Levi G. Variational Density Functional Calculations of Excited States: Conical Intersection and Avoided Crossing in Ethylene Bond Twisting. J Phys Chem Lett 2022; 13:3990-3999. [PMID: 35481754 DOI: 10.1021/acs.jpclett.2c00741] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Theoretical studies of photochemical processes require a description of the energy surfaces of excited electronic states, especially near degeneracies, where transitions between states are most likely. Systems relevant to photochemical applications are typically too large for high-level multireference methods, and while time-dependent density functional theory (TDDFT) is efficient, it can fail to provide the required accuracy. A variational, time-independent density functional approach is applied to the twisting of the double bond and pyramidal distortion in ethylene, the quintessential model for photochemical studies. By allowing for symmetry breaking, the calculated energy surfaces exhibit the correct topology around the twisted-pyramidalized conical intersection even when using a semilocal functional approximation, and by including explicit self-interaction correction, the torsional energy curves are in close agreement with published multireference results. The findings of the present work point to the possibility of using a single determinant time-independent density functional approach to simulate nonadiabatic dynamics, even for large systems where multireference methods are impractical and TDDFT is often not accurate enough.
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Affiliation(s)
| | - Aleksei V Ivanov
- Science Institute of the University of Iceland, VR-III, 107 Reykjavík, Iceland
| | - Elvar Ö Jónsson
- Science Institute of the University of Iceland, VR-III, 107 Reykjavík, Iceland
| | - Hannes Jónsson
- Faculty of Physical Sciences, University of Iceland, VR-III, 107 Reykjavík, Iceland
- Department of Applied Physics, Aalto University, FI-00076 Espoo, Finland
| | - Gianluca Levi
- Science Institute of the University of Iceland, VR-III, 107 Reykjavík, Iceland
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Kumar C, Luber S. Robust ΔSCF calculations with direct energy functional minimization methods and STEP for molecules and materials. J Chem Phys 2022; 156:154104. [PMID: 35459303 DOI: 10.1063/5.0075927] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The direct energy functional minimization method using the orbital transformation (OT) scheme in the program package CP2K has been employed for Δ self-consistent field (ΔSCF) calculations. The OT method for non-uniform molecular orbitals occupations allows us to apply the ΔSCF method for various kinds of molecules and periodic systems. Vertical excitation energies of heteroaromatic molecules and condensed phase systems, such as solvated ethylene and solvated uracil obeying periodic boundary conditions, are reported using the ΔSCF method. In addition, a Re-phosphate molecule attached to the surface of anatase (TiO2) has been investigated. Additionally, we have implemented a recently proposed state-targeted energy projection ΔSCF algorithm [K. Carter-Fenk and J. M. Herbert, J. Chem. Theory Comput. 16(8), 5067-5082 (2020)] for diagonalization based SCF in CP2K. It is found that the OT scheme provides a smooth and robust SCF convergence for all investigated excitation energies and (non-)periodic systems.
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Affiliation(s)
- Chandan Kumar
- Department of Chemistry, University of Zurich, Zurich, Switzerland
| | - Sandra Luber
- Department of Chemistry, University of Zurich, Zurich, Switzerland
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Vandaele E, Mališ M, Luber S. The ΔSCF method for non-adiabatic dynamics of systems in the liquid phase. J Chem Phys 2022; 156:130901. [PMID: 35395890 DOI: 10.1063/5.0083340] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
Computational studies of ultrafast photoinduced processes give valuable insights into the photochemical mechanisms of a broad range of compounds. In order to accurately reproduce, interpret, and predict experimental results, which are typically obtained in a condensed phase, it is indispensable to include the condensed phase environment in the computational model. However, most studies are still performed in vacuum due to the high computational cost of state-of-the-art non-adiabatic molecular dynamics (NAMD) simulations. The quantum mechanical/molecular mechanical (QM/MM) solvation method has been a popular model to perform photodynamics in the liquid phase. Nevertheless, the currently used QM/MM embedding techniques cannot sufficiently capture all solute-solvent interactions. In this Perspective, we will discuss the efficient ΔSCF electronic structure method and its applications with respect to the NAMD of solvated compounds, with a particular focus on explicit quantum mechanical solvation. As more research is required for this method to reach its full potential, some challenges and possible directions for future research are presented as well.
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Affiliation(s)
- Eva Vandaele
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Momir Mališ
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Sandra Luber
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
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Vandaele E, Mališ M, Luber S. The photodissociation of solvated cyclopropanone and its hydrate explored via non-adiabatic molecular dynamics using ΔSCF. Phys Chem Chem Phys 2022; 24:5669-5679. [PMID: 35179527 PMCID: PMC8890323 DOI: 10.1039/d1cp05187c] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The decay of cyclopropanone is a typical example of a photodecomposition process. Ethylene and carbon monoxide are formed following the excitation to the first singlet excited state through a symmetrical or asymmetrical pathway. The results obtained with non-adiabatic molecular dynamics (NAMD) using the delta self-consistent field (ΔSCF) method correspond well to previous experimental and multireference theoretical studies carried out in the gas phase. Moreover, this efficient methodology allows NAMD simulations of cyclopropanone in aqueous solution to be performed, which reveal analogue deactivation mechanisms, but a shorter lifetime and reduced photodissociation as compared to the gas-phase. The excited state dynamics of cyclopropanone hydrate, an enzyme inhibitor, in an aqueous environment are reported as well. Cyclopropanone hydrate strongly interacts with the surrounding solvent via the formation of hydrogen bonds. Excitation to the first singlet excited state shows an asymmetric pathway with cyclopropanone hydrate and propionic acid as the main photoproducts. The lifetime and photodissociation of cyclopropanone are reduced in aqueous solution, while the excitation of solvated cyclopropanone hydrate yields a range of photoproducts.![]()
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Affiliation(s)
- Eva Vandaele
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland.
| | - Momir Mališ
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland.
| | - Sandra Luber
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland.
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Zhao R, Grofe A, Wang Z, Bao P, Chen X, Liu W, Gao J. Dynamic-then-Static Approach for Core Excitations of Open-Shell Molecules. J Phys Chem Lett 2021; 12:7409-7417. [PMID: 34328742 DOI: 10.1021/acs.jpclett.1c02039] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Delta self-consistent-field methods are widely used in studies of electronically excited states. However, the nonaufbau determinants are generally spin-contaminated. Here, we describe a general approach for spin-coupling interactions of open-shell molecules, making use of multistate density functional theory (MSDFT). In particular, the effective exchange integrals that determine spin coupling are obtained by enforcing the multiplet degeneracy of the S+1 state in the MS = S manifold. Consequently, they are consistent with the energy of the high-spin state that is adequately treated by Kohn-Sham density functional theory (DFT) and, thereby, free of double counting of correlation. The method was applied to core excitations of open-shell molecules and compared with those by spin-adapted time-dependent DFT. An excellent agreement with experiment was found employing the BLYP functional and aug-cc-pCVQZ basis set. Overall, MSDFT provides an effective combination of the strengths of DFT and wave function theory to achieve efficiency and accuracy.
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Affiliation(s)
- Ruoqi Zhao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, Guangdong, China
- Institute of Theoretical Chemistry, Jilin University Changchun 130023, Jilin, China
| | - Adam Grofe
- Institute of Theoretical Chemistry, Jilin University Changchun 130023, Jilin, China
| | - Zikuan Wang
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, Shandong, China
| | - Peng Bao
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
| | - Xin Chen
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, Guangdong, China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, Shandong, China
| | - Jiali Gao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518055, Guangdong, China
- Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis 55455, Minnesota, United States
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