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Hu G, Liu P, Jensen L. Calculating Molecular Polarizabilities Using Exact Frozen Density Embedding with External Orthogonality. J Chem Theory Comput 2024. [PMID: 39105755 DOI: 10.1021/acs.jctc.4c00692] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/07/2024]
Abstract
Frozen density embedding (FDE) with freeze-thaw cycles is a formally exact embedding scheme. In practice, this method is limited to systems with small density overlaps when approximate nonadditive kinetic energy functionals are used. It has been shown that the use of approximate nonadditive kinetic energy functionals can be avoided when external orthogonality (EO) is enforced, and FDE can then generate exact results even for strongly overlapping subsystems. In this work, we present an implementation of exact FDEc-EO (coupled FDE TDDFT with EO) for the calculation of polarizabilities in the Amsterdam density functional program package. EO is enforced using the level-shift projection operator method, which ensures that orbitals between fragments are orthogonal. For pure functionals, we show that only the symmetric EO contributions to the induced density matrix are needed. This leads to a simplified implementation for the calculation of polarizability that can exactly reproduce the supermolecular TDDFT results. We further discuss the limitation of exact FDEc-EO in interpreting subsystem polarizabilities due to the nonunique partitioning of the total density. We show that this limitation is due to the fact that subsystem polarizability partitioning is dependent on how the subsystems are initially polarized. As supermolecular virtual orbitals are exactly reproduced, this dependence is attributed to the description of the occupied orbitals. In contrast, for excitations of subsystems that are localized within one subsystem, we show that the excitation energies are stable with respect to the order of polarization. This observation shows that impacts from the nonunique nature of exact FDE on subsystem properties can be minimized by better fragmentation of the supermolecular systems if the property is localized. For global properties like polarizability, this is not the case, and nonuniqueness remains independent of the fragmentation used.
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Affiliation(s)
- Gaohe Hu
- Department of Chemistry, The Pennsylvania State University, 104 Benkovic Building, University Park, Pennsylvania 16802, United States
| | - Pengchong Liu
- Department of Chemistry, The Pennsylvania State University, 104 Benkovic Building, University Park, Pennsylvania 16802, United States
| | - Lasse Jensen
- Department of Chemistry, The Pennsylvania State University, 104 Benkovic Building, University Park, Pennsylvania 16802, United States
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2
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Kolodzeiski E, Stein CJ. Automated, Consistent, and Even-Handed Selection of Active Orbital Spaces for Quantum Embedding. J Chem Theory Comput 2023; 19:6643-6655. [PMID: 37775093 PMCID: PMC10569175 DOI: 10.1021/acs.jctc.3c00653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Indexed: 10/01/2023]
Abstract
A widely used strategy to reduce the computational cost of quantum-chemical calculations is to partition the system into an active subsystem, which is the focus of the computational efforts, and an environment that is treated at a lower computational level. The system partitioning is mostly based on localized molecular orbitals. When reaction paths or energy differences are to be calculated, it is crucial to keep the orbital space consistent for all structures. Inconsistencies in orbital space can lead to unpredictable errors on the potential energy surface. While successful strategies to ensure this consistency have been established for organic and even metal-organic systems, these methods often fail for metal clusters or nanoparticles with a high density of near-degenerate and delocalized molecular orbitals. However, such systems are highly relevant for catalysis. Accurate yet feasible quantum-mechanical ab initio calculations are therefore highly desired. In this work, we present an approach based on the subsystem projected atomic orbital decomposition algorithm that allows us to ensure automated and consistent partitioning even for systems with delocalized and near-degenerate molecular orbitals and demonstrate the validity of this method for the binding energies of small molecules on transition-metal clusters.
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Affiliation(s)
- Elena Kolodzeiski
- Technical University of Munich, TUM
School of Natural Sciences, Department of Chemistry, Lichtenbergstr. 4, Garching D-85748, Germany
| | - Christopher J. Stein
- Technical University of Munich, TUM
School of Natural Sciences, Department of Chemistry, Lichtenbergstr. 4, Garching D-85748, Germany
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3
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Belleflamme F, Hehn AS, Iannuzzi M, Hutter J. A variational formulation of the Harris functional as a correction to approximate Kohn-Sham density functional theory. J Chem Phys 2023; 158:054111. [PMID: 36754794 DOI: 10.1063/5.0122671] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023] Open
Abstract
Accurate descriptions of intermolecular interactions are of great importance in simulations of molecular liquids. We present an electronic structure method that combines the accuracy of the Harris functional approach with the computational efficiency of approximately linear-scaling density functional theory (DFT). The non-variational nature of the Harris functional has been addressed by constructing a Lagrangian energy functional, which restores the variational condition by imposing stationarity with respect to the reference density. The associated linear response equations may be treated with linear-scaling efficiency in an atomic orbital based scheme. Key ingredients to describe the structural and dynamical properties of molecular systems are the forces acting on the atoms and the stress tensor. These first-order derivatives of the Harris Lagrangian have been derived and implemented in consistence with the energy correction. The proposed method allows for simulations with accuracies close to the Kohn-Sham DFT reference. Embedded in the CP2K program package, the method is designed to enable ab initio molecular dynamics simulations of molecular solutions for system sizes of several thousand atoms. Available subsystem DFT methods may be used to provide the reference density required for the energy correction at near linear-scaling efficiency. As an example of production applications, we applied the method to molecular dynamics simulations of the binary mixtures cyclohexane-methanol and toluene-methanol, performed within the isobaric-isothermal ensemble, to investigate the hydrogen bonding network in these non-ideal mixtures.
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Affiliation(s)
- Fabian Belleflamme
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Anna-Sophia Hehn
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Marcella Iannuzzi
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Jürg Hutter
- Department of Chemistry, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
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Initial Maximum Overlap Method Embedded with Extremely Localized Molecular Orbitals for Core-Ionized States of Large Systems. MOLECULES (BASEL, SWITZERLAND) 2022; 28:molecules28010136. [PMID: 36615331 PMCID: PMC9822432 DOI: 10.3390/molecules28010136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Revised: 12/21/2022] [Accepted: 12/22/2022] [Indexed: 12/28/2022]
Abstract
Despite great advances in X-ray absorption spectroscopy for the investigation of small molecule electronic structure, the application to biosystems of experimental techniques developed within this research field remains a challenge. To partially circumvent the problem, users resort to theoretical methods to interpret or predict the X-ray absorption spectra of large molecules. To accomplish this task, only low-cost computational strategies can be exploited. For this reason, some of them are single Slater determinant wavefunction approaches coupled with multiscale embedding techniques designed to treat large systems of biological interest. Therefore, in this work, we propose to apply the recently developed IMOM/ELMO embedding method to the determination of core-ionized states. The IMOM/ELMO technique resulted from the combination of the single Slater determinant Δself-consistent-field-initial maximum overlap approach (ΔSCF-IMOM) with the QM/ELMO (quantum mechanics/extremely localized molecular orbital) embedding strategy, a method where only the chemically relevant region of the examined system is treated at fully quantum chemical level, while the rest is described through transferred and frozen extremely localized molecular orbitals (ELMOs). The IMOM/ELMO technique was initially validated by computing core-ionization energies for small molecules, and it was afterwards exploited to study larger biosystems. The obtained results are in line with those reported in previous studies that applied alternative ΔSCF approaches. This makes us envisage a possible future application of the proposed method to the interpretation of X-ray absorption spectra of large molecules.
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Sharma M, Sierka M. Efficient Implementation of Density Functional Theory Based Embedding for Molecular and Periodic Systems Using Gaussian Basis Functions. J Chem Theory Comput 2022; 18:6892-6904. [PMID: 36223886 DOI: 10.1021/acs.jctc.2c00380] [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 practical and effective implementation of density functional theory based embedding is reported, which allows us to treat both periodic and aperiodic systems on an equal footing. Its essence is the expansion of orbitals and electron density of the periodic system using Gaussian basis functions, rather than plane-waves, which provides a unique all-electron direct-space representation, thus avoiding the need for pseudopotentials. This makes the construction of embedding potential for a molecular active subsystem due to a periodic environment quite convenient, as transformation between representations is far from trivial. The three flavors of embedding, molecule-in-molecule, molecule-in-periodic, and periodic-in-periodic embedding, are implemented using embedding potentials based on non-additive kinetic energy density functionals (approximate) and level-shift projection operator (exact). The embedding scheme is coupled with a variety of correlated wave function theory (WFT) methods, thereby providing an efficient way to study the ground and excited state properties of low-dimensional systems using high-level methods for the region of interest. Finally, an implementation of real time-time-dependent density functional embedding theory (RT-TDDFET) is presented that uses a projection operator-based embedding potential and provides accurate results compared to full RT-TDDFT for systems with uncoupled excitations. The embedding potential is calculated efficiently using a combination of density fitting and continuous fast multipole method for the Coulomb term. The applicability of (i) WFT-in-DFT embedding, in predicting the adsorption and excitation energies, and (ii) RT-TDDFET, in predicting the absorption spectra, is explored for various test systems.
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Affiliation(s)
- Manas Sharma
- Otto Schott Institute of Materials Research, Friedrich Schiller University Jena, Löbdergraben 32, 07743Jena, Germany
| | - Marek Sierka
- Otto Schott Institute of Materials Research, Friedrich Schiller University Jena, Löbdergraben 32, 07743Jena, Germany
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Macetti G, Genoni A. Initial Maximum Overlap Method for Large Systems by the Quantum Mechanics/Extremely Localized Molecular Orbital Embedding Technique. J Chem Theory Comput 2021; 17:4169-4182. [PMID: 34196174 DOI: 10.1021/acs.jctc.1c00388] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Quantum chemistry offers a large variety of methods to treat excited states. Many of them are based on a multireference wave function ansatz and are therefore characterized by an intrinsic complexity and high computational costs. To overcome these drawbacks and also some limitations of simpler single-reference approaches (e.g., configuration interaction singles and time-dependent density functional theory), the single-determinant Δself-consistent field-initial maximum overlap method (ΔSCF-IMOM) has been proposed. This strategy substitutes the aufbau principle with a criterion that occupies molecular orbitals at successive SCF iterations on the basis of their maximum overlap with a proper set of guess orbitals for the target excited state. In this way, it prevents the SCF process to collapse to the ground state wave function and provides excited state single Slater determinant solutions to the SCF equations. Here, we propose to extend the applicability of the IMOM to the treatment of localized excited states of large systems. To accomplish this task, we coupled it with the QM/ELMO (quantum mechanics/extremely localized molecular orbitals) strategy, a quantum mechanical embedding method in which the most chemically relevant part of the system is treated with traditional quantum chemical approaches, while the rest is described by extremely localized molecular orbitals transferred from recently constructed libraries or proper model molecules. After presenting the theoretical foundations of the new IMOM/ELMO technique, in this paper, we will show and discuss the results of preliminary test calculations carried out on both model systems (i.e., decanoic acid, decene, decapentaene, and solvated acrolein) and a system of biological interest (flavin mononucleotide in the flavodoxin protein). We observed that, for localized excited states, the new IMOM/ELMO method provides reliable results, and it reproduces the outcomes of fully IMOM calculations within the chemical accuracy threshold (i.e., 0.043 eV) by including only a limited number of atoms in the QM region. Furthermore, the first application of our embedding technique to a larger biological system gave completely plausible results in line with those obtained through more traditional quantum mechanical methods, thus opening the possibility of using the new approach in future investigations of photobiology problems.
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Affiliation(s)
- Giovanni Macetti
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Alessandro Genoni
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
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Shao X, Mi W, Pavanello M. GGA-Level Subsystem DFT Achieves Sub-kcal/mol Accuracy Intermolecular Interactions by Mimicking Nonlocal Functionals. J Chem Theory Comput 2021; 17:3455-3461. [PMID: 33983729 DOI: 10.1021/acs.jctc.1c00283] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
The key feature of nonlocal kinetic energy functionals is their ability to reduce to the Thomas-Fermi functional in the regions of high density and to the von Weizsäcker functional in the region of low-density/high reduced density gradient. This behavior is crucial when these functionals are employed in subsystem DFT simulations to approximate the nonadditive kinetic energy. We propose a GGA nonadditive kinetic energy functional which mimics the good behavior of nonlocal functionals, retaining the computational complexity of typical semilocal functionals. Crucially, this functional depends on the inter-subsystem density overlap. The new functional reproduces Kohn-Sham DFT and benchmark CCSD(T) interaction energies of weakly interacting dimers in the S22-5 and S66 test sets with a mean absolute deviation well below 1 kcal/mol.
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Affiliation(s)
- Xuecheng Shao
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
| | - Wenhui Mi
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
| | - Michele Pavanello
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States.,Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
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8
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Ma H, Sheng N, Govoni M, Galli G. Quantum Embedding Theory for Strongly Correlated States in Materials. J Chem Theory Comput 2021; 17:2116-2125. [DOI: 10.1021/acs.jctc.0c01258] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- He Ma
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Nan Sheng
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Marco Govoni
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Giulia Galli
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
- Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
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9
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Fink K, Höfener S. Combining wavefunction frozen-density embedding with one-dimensional periodicity. J Chem Phys 2021; 154:104114. [PMID: 33722017 DOI: 10.1063/5.0041501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present the combination of wavefunction frozen-density embedding (FDE) with a periodic repetition in one dimension (1D) for molecular systems in the KOALA program. In this periodic orbital-uncoupled FDE ansatz, no wavefunction overlap is taken into account, and only the electron density of the active subsystem is computed explicitly. This density is relaxed in the presence of the environment potential, which is obtained by translating the updated active subsystem density, yielding a fully self-consistent solution at convergence. Treating only one subsystem explicitly, the method allows for the calculation of local properties in condensed molecular systems, while no orbital band structure is obtained preventing the application, e.g., to systems with metallic bonding. In order to illustrate possible applications of the new implementation, selected case studies are presented, ranging from ground-state dipole moments using configuration interaction methods via excitation energies using time-dependent density-functional theory to ionization potentials obtained from equation-of-motion correlation methods. Different levels of approximations are assessed, revealing that an active subsystem consisting of two or three molecules leads to results that are converged with respect to the environment contributions.
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Affiliation(s)
- Karin Fink
- Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), P.O. Box 3630, 76021 Karlsruhe, Germany
| | - Sebastian Höfener
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), P.O. Box 6980, 76049 Karlsruhe, Germany
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10
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Macetti G, Wieduwilt EK, Genoni A. QM/ELMO: A Multi-Purpose Fully Quantum Mechanical Embedding Scheme Based on Extremely Localized Molecular Orbitals. J Phys Chem A 2021; 125:2709-2726. [DOI: 10.1021/acs.jpca.0c11450] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Affiliation(s)
- Giovanni Macetti
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Erna K. Wieduwilt
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Alessandro Genoni
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
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11
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Quantum mechanics/extremely localized molecular orbital embedding technique: Theoretical foundations and further validation. ADVANCES IN QUANTUM CHEMISTRY 2021. [DOI: 10.1016/bs.aiq.2021.05.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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12
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Macetti G, Genoni A. Quantum Mechanics/Extremely Localized Molecular Orbital Embedding Strategy for Excited States: Coupling to Time-Dependent Density Functional Theory and Equation-of-Motion Coupled Cluster. J Chem Theory Comput 2020; 16:7490-7506. [PMID: 33241930 DOI: 10.1021/acs.jctc.0c00956] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The QM/ELMO (quantum mechanics/extremely localized molecular orbital) method is a recently developed embedding technique in which the most important region of the system under examination is treated at fully quantum mechanical level, while the rest is described by means of transferred and frozen extremely localized molecular orbitals. In this paper, we propose the first application of the QM/ELMO approach to the investigation of excited states, and, in particular, we present the coupling of the QM/ELMO philosophy with Time-Dependent Density Functional Theory (TDDFT) and Equation-of-Motion Coupled Cluster with single and double substitutions (EOM-CCSD). The proposed TDDFT/ELMO and EOM-CCSD/ELMO strategies underwent a series of preliminary tests that were already considered for the validation of other embedding methods for excited states. The obtained results showed that the novel techniques allow the accurate description of localized excitations in large systems by only including a relatively small number of atoms in the region treated at fully quantum chemical level. Furthermore, for TDDFT/ELMO, it was also observed that (i) the method enables to avoid the presence of artificial low-lying charge-transfer states that may affect traditional TDDFT calculations, even using functionals that do not take into account long-range corrections, and (ii) the novel approach can be also successfully exploited to investigate local electronic transitions in quite large systems (e.g., reduced model of the Green Fluorescent Protein), and the accuracy of the results can be improved by including a sufficient number of chemically crucial fragments/residues in the quantum mechanical region. Finally, concerning EOM-CCSD/ELMO, it was also seen that, despite the quite crude approximation of an embedding potential given by frozen extremely localized molecular orbitals, the new strategy is able to satisfactorily account for the effects of the environment. This work paves the way to further extensions of the QM/ELMO philosophy for the study of local excitations in extended systems, suggesting the coupling of the QM/ELMO approach with other quantum chemical strategies for excited states, from the simplest ΔSCF techniques to the most advanced and computationally expensive multireferences methods.
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Affiliation(s)
- Giovanni Macetti
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Alessandro Genoni
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
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13
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Chen X, Gao J. Fragment Exchange Potential for Realizing Pauli Deformation of Interfragment Interactions. J Phys Chem Lett 2020; 11:4008-4016. [PMID: 32308000 DOI: 10.1021/acs.jpclett.0c00933] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
In fragment-based methods, the lack of explicit short-range exchange interactions between monomers can result in unphysical deformation in charge density. In this study, we describe a fragment exchange potential (XFP) to explicitly account for interfragmental Pauli deformation. In our implementation, a Kohn-Sham exchange potential is adopted along with the Yukawa potential. The method has been validated by comparison of the computed exchange energies using the XFP potential with results obtained from antisymmetrized fragmental orbitals on the S66×8 data set containing 528 bimolecular interactions of equilibrium and arbitrary geometries. It was also found that it is only necessary to deploy numerical grids on atoms within their van der Waals contacts, significantly reducing the small, albeit extra, computational cost. We anticipate that the XFP presented here may be applied to molecular dynamics simulations of macromolecules using a fragment-based quantum mechanical potential with improved SCF convergence and computational accuracy.
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Affiliation(s)
- Xin Chen
- Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, College of Chemistry, Jilin University, Changchun 130023, P. R. China
| | - Jiali Gao
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen, Guangdong, China
- Department of Chemistry and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455, United States
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14
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Macetti G, Wieduwilt EK, Assfeld X, Genoni A. Localized Molecular Orbital-Based Embedding Scheme for Correlated Methods. J Chem Theory Comput 2020; 16:3578-3596. [PMID: 32369363 DOI: 10.1021/acs.jctc.0c00084] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Embedding strategies currently provide the best compromise between accuracy and computational cost in modeling chemical properties and processes of large and complex systems. In this framework, different methods have been proposed all over the years, from the very popular QM/MM approaches to the more recent and very promising density matrix and density functional embedding techniques. Here, we present a further development of the quantum mechanics/extremely localized molecular orbital technique (QM/ELMO) method, a recently proposed multiscale embedding strategy in which the chemically active region of the investigated system is treated at a fully quantum mechanical level, while the rest is described by frozen extremely localized molecular orbitals previously transferred from proper libraries or tailor-made model molecules. In particular, in this work we discuss and assess in detail the extension of the QM/ELMO approach to density functional theory and post-Hartree-Fock techniques by evaluating its performances when it is used to describe chemical reactions, bond dissociations, and intermolecular interactions. The preliminary test calculations have shown that, in the investigated cases, the new embedding strategy enables the results of the corresponding fully quantum mechanical computations to be reproduced within chemical accuracy in almost all the cases but with a significantly reduced computational cost, especially when correlated post-Hartree-Fock strategies are used to describe the quantum mechanical subsystem. In light of the obtained results, we already envisage the future application of the new correlated QM/ELMO techniques to the investigation of more challenging problems, such as the modeling of enzyme catalysis, the study of excited states of biomolecules, and the refinement of macromolecular X-ray crystal structures.
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Affiliation(s)
- Giovanni Macetti
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Erna K Wieduwilt
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Xavier Assfeld
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, Boulevard des Aiguilletes, BP 70239, F-54506 Vandoeuvre-lès-Nancy, France
| | - Alessandro Genoni
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
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15
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Mazurek AH, Szeleszczuk Ł, Pisklak DM. Periodic DFT Calculations-Review of Applications in the Pharmaceutical Sciences. Pharmaceutics 2020; 12:E415. [PMID: 32369915 PMCID: PMC7284980 DOI: 10.3390/pharmaceutics12050415] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Revised: 04/28/2020] [Accepted: 04/29/2020] [Indexed: 12/31/2022] Open
Abstract
In the introduction to this review the complex chemistry of solid-state pharmaceutical compounds is summarized. It is also explained why the density functional theory (DFT) periodic calculations became recently so popular in studying the solid APIs (active pharmaceutical ingredients). Further, the most popular programs enabling DFT periodic calculations are presented and compared. Subsequently, on the large number of examples, the applications of such calculations in pharmaceutical sciences are discussed. The mentioned topics include, among others, validation of the experimentally obtained crystal structures and crystal structure prediction, insight into crystallization and solvation processes, development of new polymorph synthesis ways, and formulation techniques as well as application of the periodic DFT calculations in the drug analysis.
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Affiliation(s)
| | - Łukasz Szeleszczuk
- Chair and Department of Physical Pharmacy and Bioanalysis, Department of Physical Chemistry, Faculty of Pharmacy, Medical University of Warsaw, Banacha 1 str., 02-093 Warsaw, Poland; (A.H.M.); (D.M.P.)
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16
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Smith B, Akimov AV. Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:073001. [PMID: 31661681 DOI: 10.1088/1361-648x/ab5246] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.
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Affiliation(s)
- Brendan Smith
- Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, New York 14260-3000, United States of America
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17
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Bensberg M, Neugebauer J. Density functional theory based embedding approaches for transition-metal complexes. Phys Chem Chem Phys 2020; 22:26093-26103. [PMID: 33201953 DOI: 10.1039/d0cp05188h] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
Transition metal species are commonly discussed by considering the metal atom embedded in a ligand environment. This apparently makes them interesting targets for modern embedding strategies based on Kohn-Sham density functional theory (DFT), which aim at modelling accurate predictions for large systems by combining different quantum chemical methods. In this perspective, we will focus on subsystem density functional theory and projection-based embedding. We review the developments in the field for transition metal species, demonstrate benefits, drawbacks and analyse error sources of the different strategies using the example of chromium hexacarbonyle, before giving a perspective where the field is currently heading.
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Affiliation(s)
- Moritz Bensberg
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster Corrensstraße 36, 48149 Münster, Germany.
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18
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Ma H, Sheng N, Govoni M, Galli G. First-principles studies of strongly correlated states in defect spin qubits in diamond. Phys Chem Chem Phys 2020; 22:25522-25527. [PMID: 33084673 DOI: 10.1039/d0cp04585c] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Using a recently developed quantum embedding theory, we present first-principles calculations of strongly correlated states of spin defects in diamond. Using this theory, effective Hamiltonians are constructed, which can be solved by classical and quantum computers; the latter promise a much more favorable scaling as a function of system size than the former. In particular, we report a study on the neutral group-IV vacancy complexes in diamond, and we discuss their strongly correlated spin-singlet and spin-triplet excited states. Our results provide valuable predictions for experiments aimed at optical manipulation of these defects for quantum information technology applications.
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Affiliation(s)
- He Ma
- Department of Chemistry, University of Chicago, Chicago, IL 60637, USA
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19
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Mi W, Ramos P, Maranhao J, Pavanello M. Ab Initio Structure and Dynamics of CO 2 at Supercritical Conditions. J Phys Chem Lett 2019; 10:7554-7559. [PMID: 31738567 DOI: 10.1021/acs.jpclett.9b03054] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Green technologies rely on green solvents and fluids. Among them, supercritical CO2 already finds many important applications. The molecular-level understanding of the dynamics and structure of this supercritical fluid is a prerequisite for rational design of future green technologies. Unfortunately, the commonly employed Kohn-Sham density functional theory (DFT) is too computationally demanding to produce meaningfully converged dynamics within a reasonable time and with a reasonable computational effort. Thanks to subsystem DFT, we analyze finite-size effects by considering simulation cells of varying sizes (up to 256 independent molecules in the cell) and finite-time effects by running 100 ps trajectories. We find that the simulations are in reasonable and semiquantitative agreement with the available neutron diffraction experiments and that, as opposed to the gas phase, the CO2 molecules in the fluid are bent with an average OCO angle of 175.8°. Our simulations also confirm that the dimer T-shape is the most prevalent configuration. Our results further strengthen the experiment-simulation agreement for this fluid when comparing radial distribution functions and diffusion coefficient, confirming subsystem DFT as a viable tool for modeling structure and dynamics of condensed-phase systems.
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Affiliation(s)
- Wenhui Mi
- Department of Chemistry , Rutgers University , Newark , New Jersey 07102 , United States
| | - Pablo Ramos
- Department of Chemistry , Rutgers University , Newark , New Jersey 07102 , United States
| | - Jack Maranhao
- Department of Chemistry , Rutgers University , Newark , New Jersey 07102 , United States
| | - Michele Pavanello
- Department of Chemistry , Rutgers University , Newark , New Jersey 07102 , United States
- Department of Physics , Rutgers University , Newark , New Jersey 07102 , United States
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Schulz A, Jacob CR. Description of intermolecular charge transfer with subsystem density-functional theory. J Chem Phys 2019; 151:131103. [PMID: 31594348 DOI: 10.1063/1.5125218] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Efficient quantum-chemical methods that are able to describe intermolecular charge transfer are crucial for modeling organic semiconductors. However, the correct description of intermolecular charge transfer with density-functional theory (DFT) is hampered by the fractional charge error of approximate exchange-correlation (xc) functionals. Here, we investigate the charge transfer induced by an external electric field in a tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) complex as a test case. For this seemingly simple model system, a supermolecular DFT treatment fails with most conventional xc functionals. Here, we present an extension of subsystem DFT to subsystems with a fractional number of electrons. We show that within such a framework, it becomes possible to overcome the fractional charge error by enforcing the correct dependence of each subsystem's total energy on the subsystem's fractional charge. Such a subsystem DFT approach allows for a correct description of the intermolecular charge transfer in the TTF-TCNQ model complex. The approach presented here can be generalized to larger molecular aggregates and will thus allow for modeling organic semiconductor materials accurately and efficiently.
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Affiliation(s)
- Anika Schulz
- Technische Universität Braunschweig, Institute of Physical and Theoretical Chemistry, Gaußstr. 17, 38106 Braunschweig, Germany
| | - Christoph R Jacob
- Technische Universität Braunschweig, Institute of Physical and Theoretical Chemistry, Gaußstr. 17, 38106 Braunschweig, Germany
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Chulhai DV, Goodpaster JD. Projection-Based Correlated Wave Function in Density Functional Theory Embedding for Periodic Systems. J Chem Theory Comput 2018; 14:1928-1942. [DOI: 10.1021/acs.jctc.7b01154] [Citation(s) in RCA: 55] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Affiliation(s)
- Dhabih V. Chulhai
- Department of Chemistry, University of Minnesota, 207 Pleasant St. SE, Minneapolis, Minnesota 55455, United States
| | - Jason D. Goodpaster
- Department of Chemistry, University of Minnesota, 207 Pleasant St. SE, Minneapolis, Minnesota 55455, United States
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Ricardi N, Zech A, Gimbal-Zofka Y, Wesolowski TA. Explicit vs. implicit electronic polarisation of environment of an embedded chromophore in frozen-density embedding theory. Phys Chem Chem Phys 2018; 20:26053-26062. [DOI: 10.1039/c8cp05634j] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A comparison of strategies to account for environment polarisation in Frozen Density Embedding Theory (FDET).
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Affiliation(s)
- Niccolò Ricardi
- Department of Physical Chemistry
- University of Geneva
- CH-1211 Genève
- Switzerland
| | - Alexander Zech
- Department of Physical Chemistry
- University of Geneva
- CH-1211 Genève
- Switzerland
| | - Yann Gimbal-Zofka
- Department of Physical Chemistry
- University of Geneva
- CH-1211 Genève
- Switzerland
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23
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Schlüns D, Franchini M, Götz AW, Neugebauer J, Jacob CR, Visscher L. Analytical gradients for subsystem density functional theory within the slater-function-based amsterdam density functional program. J Comput Chem 2016; 38:238-249. [DOI: 10.1002/jcc.24670] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2016] [Revised: 10/14/2016] [Accepted: 10/19/2016] [Indexed: 11/09/2022]
Affiliation(s)
- Danny Schlüns
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster; Corrensstraße 40 Münster 48149 Germany
| | - Mirko Franchini
- Amsterdam Center for Multiscale Modeling; Vrije Universiteit Amsterdam; De Boelelaan 1083 HV Amsterdam 1081 The Netherlands
- Scientific Computing & Modelling NV; Vrije Universiteit; Theoretical Chemistry, De Boelelaan 1083 HV Amsterdam 1081 The Netherlands
| | - Andreas W. Götz
- San Diego Supercomputer Center; University of California San Diego; 9500 Gilman Drive La Jolla, California 92093-0505 USA
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster; Corrensstraße 40 Münster 48149 Germany
| | - Christoph R. Jacob
- Institute of Physical and Theoretical Chemistry; TU Braunschweig, Hans-Sommer-Straße 10 Braunschweig 38106 Germany
| | - Lucas Visscher
- Amsterdam Center for Multiscale Modeling; Vrije Universiteit Amsterdam; De Boelelaan 1083 HV Amsterdam 1081 The Netherlands
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Genova A, Ceresoli D, Pavanello M. Avoiding fractional electrons in subsystem DFT based ab-initio molecular dynamics yields accurate models for liquid water and solvated OH radical. J Chem Phys 2016; 144:234105. [DOI: 10.1063/1.4953363] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alessandro Genova
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
| | - Davide Ceresoli
- CNR-ISTM: Institute of Molecular Sciences and Technologies, Milano, Italy
| | - Michele Pavanello
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
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Sakai Y, Lee AJ, Chelikowsky JR. First-Principles Atomic Force Microscopy Image Simulations with Density Embedding Theory. NANO LETTERS 2016; 16:3242-3246. [PMID: 27050710 DOI: 10.1021/acs.nanolett.6b00741] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We present an efficient first-principles method for simulating noncontact atomic force microscopy (nc-AFM) images using a "frozen density" embedding theory. Frozen density embedding theory enables one to efficiently compute the tip-sample interaction by considering a sample as a frozen external field. This method reduces the extensive computational load of first-principles AFM simulations by avoiding consideration of the entire tip-sample system and focusing on the tip alone. We demonstrate that our simulation with frozen density embedding theory accurately reproduces full density functional theory simulations of freestanding hydrocarbon molecules while the computational time is significantly reduced. Our method also captures the electronic effect of a Cu(111) substrate on the AFM image of pentacene and reproduces the experimental AFM image of Cu2N on a Cu(100) surface. This approach is applicable for theoretical imaging applications on large molecules, two-dimensional materials, and materials surfaces.
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Affiliation(s)
- Yuki Sakai
- Center for Computational Materials, Institute for Computational Engineering and Sciences, ‡Department of Chemical Engineering, §Department of Physics, The University of Texas at Austin , Austin, Texas 78712, United States
| | - Alex J Lee
- Center for Computational Materials, Institute for Computational Engineering and Sciences, ‡Department of Chemical Engineering, §Department of Physics, The University of Texas at Austin , Austin, Texas 78712, United States
| | - James R Chelikowsky
- Center for Computational Materials, Institute for Computational Engineering and Sciences, ‡Department of Chemical Engineering, §Department of Physics, The University of Texas at Austin , Austin, Texas 78712, United States
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Genova A, Pavanello M. Exploiting the locality of periodic subsystem density-functional theory: efficient sampling of the Brillouin zone. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:495501. [PMID: 26596499 DOI: 10.1088/0953-8984/27/49/495501] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In order to approximately satisfy the Bloch theorem, simulations of complex materials involving periodic systems are made n(k) times more complex by the need to sample the first Brillouin zone at n(k) points. By combining ideas from Kohn-Sham density-functional theory (DFT) and orbital-free DFT, for which no sampling is needed due to the absence of waves, subsystem DFT offers an interesting middle ground capable of sizable theoretical speedups against Kohn-Sham DFT. By splitting the supersystem into interacting subsystems, and mapping their quantum problem onto separate auxiliary Kohn-Sham systems, subsystem DFT allows an optimal topical sampling of the Brillouin zone. We elucidate this concept with two proof of principle simulations: a water bilayer on Pt[1 1 1]; and a complex system relevant to catalysis-a thiophene molecule physisorbed on a molybdenum sulfide monolayer deposited on top of an α-alumina support. For the latter system, a speedup of 300% is achieved against the subsystem DTF reference by using an optimized Brillouin zone sampling (600% against KS-DFT).
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27
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Yu K, Libisch F, Carter EA. Implementation of density functional embedding theory within the projector-augmented-wave method and applications to semiconductor defect states. J Chem Phys 2015; 143:102806. [DOI: 10.1063/1.4922260] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kuang Yu
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
| | - Florian Libisch
- Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10/136, 1040 Vienna, Austria
| | - Emily A. Carter
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
- Program in Applied and Computational Mathematics and Andlinger Center for Energy and the Environment, Princeton University, Princeton, New Jersey 08544-5263, USA
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Wesolowski TA, Shedge S, Zhou X. Frozen-Density Embedding Strategy for Multilevel Simulations of Electronic Structure. Chem Rev 2015; 115:5891-928. [DOI: 10.1021/cr500502v] [Citation(s) in RCA: 219] [Impact Index Per Article: 24.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Tomasz A. Wesolowski
- Department of Physical Chemistry, University of Geneva, CH-1211 Geneva 4, Switzerland
| | - Sapana Shedge
- Department of Physical Chemistry, University of Geneva, CH-1211 Geneva 4, Switzerland
| | - Xiuwen Zhou
- Department of Physical Chemistry, University of Geneva, CH-1211 Geneva 4, Switzerland
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29
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Krishtal A, Ceresoli D, Pavanello M. Subsystem real-time time dependent density functional theory. J Chem Phys 2015; 142:154116. [DOI: 10.1063/1.4918276] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Ramos P, Papadakis M, Pavanello M. Performance of Frozen Density Embedding for Modeling Hole Transfer Reactions. J Phys Chem B 2015; 119:7541-57. [DOI: 10.1021/jp511275e] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Affiliation(s)
- Pablo Ramos
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
| | - Markos Papadakis
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
| | - Michele Pavanello
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
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31
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Luber S. Local electric dipole moments for periodic systems via density functional theory embedding. J Chem Phys 2014; 141:234110. [DOI: 10.1063/1.4903828] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
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