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Tölle J, Neugebauer J. The Seamless Connection of Local and Collective Excited States in Subsystem Time-Dependent Density Functional Theory. J Phys Chem Lett 2022; 13:1003-1018. [PMID: 35061387 DOI: 10.1021/acs.jpclett.1c04023] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
The theoretical understanding of photoinduced processes in multichromophoric systems requires, as an essential ingredient, the possibility of accurately describing their electronically excited states. However, the size of these systems often prohibits the usage of conventional electronic-structure methods, so that often multiscale approaches based on phenomenologically motivated models are employed. In contrast, subsystem time-dependent density functional theory (sTDDFT) allows for a subsystem-based ab initio description of multichromophoric systems and therefore allows for, in principle, an exact description of photoinduced processes. This Perspective aims to outline the theoretical foundations and commonly used practical realizations as well as to illustrate benefits of recent developments and open issues in the field of sTDDFT. Prospective, potential future applications and possible methodological developments are discussed.
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Affiliation(s)
- Johannes Tölle
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
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2
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Brunken C, Reiher M. Automated Construction of Quantum–Classical Hybrid Models. J Chem Theory Comput 2021; 17:3797-3813. [DOI: 10.1021/acs.jctc.1c00178] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Affiliation(s)
- Christoph Brunken
- Laboratorium für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Markus Reiher
- Laboratorium für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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3
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Mališ M, Luber S. ΔSCF with Subsystem Density Embedding for Efficient Nonadiabatic Molecular Dynamics in Condensed-Phase Systems. J Chem Theory Comput 2021; 17:1653-1661. [DOI: 10.1021/acs.jctc.0c01200] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Momir Mališ
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Sandra Luber
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
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4
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Niemeyer N, Tölle J, Neugebauer J. Approximate versus Exact Embedding for Chiroptical Properties: Reconsidering Failures in Potential and Response. J Chem Theory Comput 2020; 16:3104-3120. [PMID: 32301613 DOI: 10.1021/acs.jctc.0c00125] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We investigate the suitability of subsystem time-dependent density-functional theory (sTDDFT) for describing chiroptical properties with a focus on optical rotation parameters. Our starting point is a new implementation of the recently proposed projection-based, coupled frozen-density embedding (FDEc) framework. We adapt the generalized, non-Hermitian formulation of TDDFT and derive corresponding expressions for regular and damped response properties from subsystem TDDFT. We verify that our implementation of this "exact" formulation allows to reproduce supermolecular results of electronic circular dichroism (ECD) spectra, of optical rotatory dispersion, and of polarizabilities. We present a systematic test of the main approximations typically introduced in practical frozen-density embedding (FDE) calculations of response properties: (i) the use of approximate nonadditive kinetic-energy (NAKE) functionals, which can be avoided through projection techniques, (ii) the use of monomer (subsystem) basis sets rather than supersystem basis sets, and (iii) the neglect of intersubsystem response coupling within the so-called uncoupled FDE (or FDEu) approximation. While approximation (i) is known to generally lead to large errors for covalently bound subsystems, we present cases in which either the basis set or the coupling step are similarly or even (much) more important. In particular, we explicitly demonstrate by comparison to a fully coupled calculation that missing intersubsystem response couplings are responsible for the failure of FDE reported in a previous study [ J. Chem. Theory Comput. 2015, 11, 5305-5315]. We show that good agreement with reference results can be obtained in this case even with standard NAKE approximations for the FDE potentials and efficient monomer basis sets, making calculations for larger systems well accessible.
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Affiliation(s)
- Niklas Niemeyer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster Corrensstraße 40, 48149 Münster, Germany
| | - Johannes Tölle
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster Corrensstraße 40, 48149 Münster, Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster Corrensstraße 40, 48149 Münster, Germany
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5
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Heuser J, Höfener S. Analytical Nuclear Excited-State Gradients for the Second-Order Approximate Coupled-Cluster Singles and Doubles (CC2) Method Employing Uncoupled Frozen-Density Embedding. J Chem Theory Comput 2018; 14:4616-4628. [PMID: 30086227 DOI: 10.1021/acs.jctc.8b00369] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
We report the derivation and implementation of analytical orbital-relaxed properties and nuclear gradients for excited states using the second-order approximate coupled-cluster singles and doubles (CC2) model combined with uncoupled frozen-density embedding (FDEu). An implementation of the algebraic diagrammatic construction through second-order ADC(2), which arises from simplification of RICC2 FDEu, is also presented. In order to ensure a RICC2 FDEu Lagrange functional that is linear in the Lagrange multipliers, the Hartree-Fock density is employed for the target subsystem in the embedding contributions. The accuracy of the new scheme is assessed using the carbon monoxide molecule, 4-aminophthalimide, and a benzonitrile dimer, revealing that the obtained errors are below the method error of RICC2. Using density functional theory for the environment, the efficiency of the new method is illustrated by computing the perturbed excited-state dipole moment of a chromophore in a biological environment. For this system, comprising 32 molecules consisting of 366 atoms in total, the computation requires only a couple of days on a standard compute node. RICC2 FDEu thus enables large-scale calculations of ab initio wave functions for molecules in complex environments as routine applications.
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Affiliation(s)
- Johannes Heuser
- Institute of Physical Chemistry , Karlsruhe Institute of Technology (KIT) , P.O. Box 6980, D-76049 Karlsruhe , Germany
| | - Sebastian Höfener
- Institute of Physical Chemistry , Karlsruhe Institute of Technology (KIT) , P.O. Box 6980, D-76049 Karlsruhe , Germany
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6
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Böckers M, Neugebauer J. Excitation energies of embedded open-shell systems: Unrestricted frozen-density-embedding time-dependent density-functional theory. J Chem Phys 2018; 149:074102. [DOI: 10.1063/1.5040233] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Affiliation(s)
- Michael Böckers
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
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7
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Heuser J, Höfener S. Communication: Biological applications of coupled-cluster frozen-density embedding. J Chem Phys 2018; 148:141101. [DOI: 10.1063/1.5026651] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Johannes Heuser
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), P.O. Box 6980, D-76049 Karlsruhe, Germany
| | - Sebastian Höfener
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), P.O. Box 6980, D-76049 Karlsruhe, Germany
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8
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van Leeuwen R, Neugebauer J, Visscher L, Bickelhaupt FM. Editorial for PCCP themed issue "Developments in Density Functional Theory". Phys Chem Chem Phys 2018; 18:20864-7. [PMID: 27406292 DOI: 10.1039/c6cp90143c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
This issue provides an overview of the state-of-the-art of DFT, ranging from mathematical and software developments, via topics in chemical bonding theory, to all kinds of molecular and material properties. Through this issue, we also celebrate the enormous contributions that Evert Jan Baerends has made to this field.
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Affiliation(s)
- Robert van Leeuwen
- Department of Physics, University of Jyväskylä, Survontie 9 40014 Jyväskylä, Finland.
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Computation (CMTC), Westfälische Wilhelms-Universität Münster, Corrensstrasse 40, 48149 Münster, Germany.
| | - Lucas Visscher
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling (ACMM), Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands.
| | - F Matthias Bickelhaupt
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling (ACMM), Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands. and Institute of Molecules and Materials (IMM), Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.
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9
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Heuser J, Höfener S. Analytical nuclear excited-state gradients for the Tamm-Dancoff approximation using uncoupled frozen-density embedding. J Comput Chem 2017; 38:2316-2325. [PMID: 28766728 DOI: 10.1002/jcc.24885] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2017] [Revised: 06/24/2017] [Accepted: 06/27/2017] [Indexed: 11/11/2022]
Abstract
We report the derivation and implementation of analytical nuclear gradients for excited states using time-dependent density functional theory using the Tamm-Dancoff approximation combined with uncoupled frozen-density embedding using density fitting. Explicit equations are presented and discussed. The implementation is able to treat singlet as well as triplet states and functionals using the local density approximation, the generalized gradient approximation, combinations with Hartree-Fock exchange (hybrids), and range-separated functionals such as CAM-B3LYP. The new method is benchmarked against supermolecule calculations in two case studies: The solvatochromic shift of the (vertical) fluorescence energy of 4-aminophthalimide on solvation, and the first local excitation of the benzonitrile dimer. Whereas for the 4-aminophthalimide-water complex deviations of about 0.2 eV are obtained to supermolecular calculations, for the benzonitrile dimer the maximum error for adiabatic excitation energies is below 0.01 eV due to a weak coupling of the subsystems. © 2017 Wiley Periodicals, Inc.
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Affiliation(s)
- Johannes Heuser
- Institut für Physikalische Chemie, Fakultät für Chemie und Biowissenschaften, Karlsruher Institut für Technologie (KIT), D-76131, Karlsruhe
| | - Sebastian Höfener
- Institut für Physikalische Chemie, Fakultät für Chemie und Biowissenschaften, Karlsruher Institut für Technologie (KIT), D-76131, Karlsruhe
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10
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Schieschke N, Di Remigio R, Frediani L, Heuser J, Höfener S. Combining frozen-density embedding with the conductor-like screening model using Lagrangian techniques for response properties. J Comput Chem 2017; 38:1693-1703. [DOI: 10.1002/jcc.24813] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2017] [Revised: 03/29/2017] [Accepted: 03/30/2017] [Indexed: 02/06/2023]
Affiliation(s)
- Nils Schieschke
- Institute of Physical Chemistry, Faculty of Chemistry and Biosciences, Karlsruhe Institute of Technology (KIT); P.O. Box 6980 Karlsruhe D-76049 Germany
| | - Roberto Di Remigio
- Department of Chemistry, Centre for Theoretical and Computational Chemistry; UiT, The Arctic University of Norway; Tromsø N-9037 Norway
| | - Luca Frediani
- Department of Chemistry, Centre for Theoretical and Computational Chemistry; UiT, The Arctic University of Norway; Tromsø N-9037 Norway
| | - Johannes Heuser
- Institute of Physical Chemistry, Faculty of Chemistry and Biosciences, Karlsruhe Institute of Technology (KIT); P.O. Box 6980 Karlsruhe D-76049 Germany
| | - Sebastian Höfener
- Institute of Physical Chemistry, Faculty of Chemistry and Biosciences, Karlsruhe Institute of Technology (KIT); P.O. Box 6980 Karlsruhe D-76049 Germany
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11
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Olejniczak M, Bast R, Pereira Gomes AS. On the calculation of second-order magnetic properties using subsystem approaches in a relativistic framework. Phys Chem Chem Phys 2017; 19:8400-8415. [DOI: 10.1039/c6cp08561j] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The implementation of second-order magnetic properties in a frozen density embedding scheme in a four component relativistic framework is outlined and applied to model H2X–H2O systems (X = Se, Te, Po).
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Affiliation(s)
- Małgorzata Olejniczak
- Université de Lille
- CNRS
- UMR 8523 – PhLAM – Physique des Lasers
- Atomes et Molécules
- F-59000 Lille
| | - Radovan Bast
- High Performance Computing Group
- UiT The Arctic University of Norway
- N-9037 Tromsø
- Norway
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12
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Ren S, Caricato M. Multi-state extrapolation of UV/Vis absorption spectra with QM/QM hybrid methods. J Chem Phys 2016; 144:184102. [PMID: 27179466 DOI: 10.1063/1.4948471] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this work, we present a simple approach to simulate absorption spectra from hybrid QM/QM calculations. The goal is to obtain reliable spectra for compounds that are too large to be treated efficiently at a high level of theory. The present approach is based on the extrapolation of the entire absorption spectrum obtained by individual subcalculations. Our program locates the main spectral features in each subcalculation, e.g., band peaks and shoulders, and fits them to Gaussian functions. Each Gaussian is then extrapolated with a formula similar to that of ONIOM (Our own N-layered Integrated molecular Orbital molecular Mechanics). However, information about individual excitations is not necessary so that difficult state-matching across subcalculations is avoided. This multi-state extrapolation thus requires relatively low implementation effort while affording maximum flexibility in the choice of methods to be combined in the hybrid approach. The test calculations show the efficacy and robustness of this methodology in reproducing the spectrum computed for the entire molecule at a high level of theory.
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Affiliation(s)
- Sijin Ren
- Department of Chemistry, University of Kansas, 1251 Wescoe Hall Dr., Lawrence, Kansas 66045, USA
| | - Marco Caricato
- Department of Chemistry, University of Kansas, 1251 Wescoe Hall Dr., Lawrence, Kansas 66045, USA
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13
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Krishtal A, Pavanello M. Revealing electronic open quantum systems with subsystem TDDFT. J Chem Phys 2016; 144:124118. [PMID: 27036438 DOI: 10.1063/1.4944526] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Open quantum systems (OQSs) are perhaps the most realistic systems one can approach through simulations. In recent years, describing OQSs with Density Functional Theory (DFT) has been a prominent avenue of research with most approaches based on a density matrix partitioning in conjunction with an ad-hoc description of system-bath interactions. We propose a different theoretical approach to OQSs based on partitioning of the electron density. Employing the machinery of subsystem DFT (and its time-dependent extension), we provide a novel way of isolating and analyzing the various terms contributing to the coupling between the system and the surrounding bath. To illustrate the theory, we provide numerical simulations on a toy system (a molecular dimer) and on a condensed phase system (solvated excimer). The simulations show that non-Markovian dynamics in the electronic system-bath interactions are important in chemical applications. For instance, we show that the superexchange mechanism of transport in donor-bridge-acceptor systems is a non-Markovian interaction between the donor-acceptor (OQS) with the bridge (bath) which is fully characterized by real-time subsystem time-dependent DFT.
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Affiliation(s)
- Alisa Krishtal
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
| | - Michele Pavanello
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
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14
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Höfener S, Trumm M, Koke C, Heuser J, Ekström U, Skerencak-Frech A, Schimmelpfennig B, Panak PJ. Computing UV/vis spectra using a combined molecular dynamics and quantum chemistry approach: bis-triazin-pyridine (BTP) ligands studied in solution. Phys Chem Chem Phys 2016; 18:7728-36. [PMID: 26907588 DOI: 10.1039/c5cp07540h] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We report a combined computational and experimental study to investigate the UV/vis spectra of 2,6-bis(5,6-dialkyl-1,2,4-triazin-3-yl)pyridine (BTP) ligands in solution. In order to study molecules in solution using theoretical methods, force-field parameters for the ligand-water interaction are adjusted to ab initio quantum chemical calculations. Based on these parameters, molecular dynamics (MD) simulations are carried out from which snapshots are extracted as input to quantum chemical excitation-energy calculations to obtain UV/vis spectra of BTP ligands in solution using time-dependent density functional theory (TDDFT) employing the Tamm-Dancoff approximation (TDA). The range-separated CAM-B3LYP functional is used to avoid large errors for charge-transfer states occurring in the electronic spectra. In order to study environment effects with theoretical methods, the frozen-density embedding scheme is applied. This computational procedure allows to obtain electronic spectra calculated at the (range-separated) DFT level of theory in solution, revealing solvatochromic shifts upon solvation of up to about 0.6 eV. Comparison to experimental data shows a significantly improved agreement compared to vacuum calculations and enables the analysis of relevant excitations for the line shape in solution.
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Affiliation(s)
- Sebastian Höfener
- Institut für Physikalische Chemie, Karlsruher Institut für Technologie, D-76131 Karlsruhe, Germany.
| | - Michael Trumm
- Institut für Nukleare Entsorgung (INE), Karlsruher Institut für Technologie, D-76131 Karlsruhe, Germany.
| | - Carsten Koke
- Institut für Nukleare Entsorgung (INE), Karlsruher Institut für Technologie, D-76131 Karlsruhe, Germany. and Ruprecht Karls Universität Heidelberg, Physikalisch-Chemisches Institut, Im Neuenheimer Feld 253, D-69120 Heidelberg, Germany
| | - Johannes Heuser
- Institut für Physikalische Chemie, Karlsruher Institut für Technologie, D-76131 Karlsruhe, Germany.
| | - Ulf Ekström
- Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Andrej Skerencak-Frech
- Institut für Nukleare Entsorgung (INE), Karlsruher Institut für Technologie, D-76131 Karlsruhe, Germany. and Ruprecht Karls Universität Heidelberg, Physikalisch-Chemisches Institut, Im Neuenheimer Feld 253, D-69120 Heidelberg, Germany
| | - Bernd Schimmelpfennig
- Institut für Nukleare Entsorgung (INE), Karlsruher Institut für Technologie, D-76131 Karlsruhe, Germany.
| | - Petra J Panak
- Institut für Nukleare Entsorgung (INE), Karlsruher Institut für Technologie, D-76131 Karlsruhe, Germany. and Ruprecht Karls Universität Heidelberg, Physikalisch-Chemisches Institut, Im Neuenheimer Feld 253, D-69120 Heidelberg, Germany
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15
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Heuser J, Höfener S. Wave-function frozen-density embedding: Approximate analytical nuclear ground-state gradients. J Comput Chem 2016; 37:1092-101. [DOI: 10.1002/jcc.24301] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2015] [Revised: 12/15/2015] [Accepted: 12/17/2015] [Indexed: 01/31/2023]
Affiliation(s)
- Johannes Heuser
- Institut für Physikalische Chemie, Fakultät für Chemie und Biowissenschaften, Karlsruher Institut für Technologie (KIT); D-76131 Karlsruhe
| | - Sebastian Höfener
- Institut für Physikalische Chemie, Fakultät für Chemie und Biowissenschaften, Karlsruher Institut für Technologie (KIT); D-76131 Karlsruhe
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16
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Dułak M, Kamiński JW, Wesołowski TA. Equilibrium Geometries of Noncovalently Bound Intermolecular Complexes Derived from Subsystem Formulation of Density Functional Theory. J Chem Theory Comput 2015; 3:735-45. [PMID: 26627391 DOI: 10.1021/ct600367t] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The subsystem formulation of density functional theory is used to obtain equilibrium geometries and interaction energies for a representative set of noncovalently bound intermolecular complexes. The results are compared with literature benchmark data. The range of applicability of two considered approximations to the exchange-correlation- and nonadditive kinetic energy components of the total energy is determined. Local density approximation, which does not involve any empirical parameters, leads to excellent intermolecular equilibrium distances for hydrogen-bonded complexes (maximal error 0.13 Å for NH3-NH3). It is a method of choice for a wide class of weak intermolecular complexes including also dipole-bound and the ones formed by rare gas atoms or saturated hydrocarbons. The range of applicability of the chosen generalized gradient approximation, which was shown in our previous works to lead to good interaction energies in such complexes, where π-electrons are involved in the interaction, remains limited to this group because it improves neither binding energies nor equilibrium geometries in the wide class of complexes for which local density approximation is adequate. An efficient energy minimization procedure, in which optimization of the geometry and the electron density of each subsystem is made simultaneously, is proposed and tested.
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Affiliation(s)
- Marcin Dułak
- Département de Chimie Physique, Université de Genève, 30, quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland, and Institute of Physical and Theoretical Chemistry, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - Jakub W Kamiński
- Département de Chimie Physique, Université de Genève, 30, quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland, and Institute of Physical and Theoretical Chemistry, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - Tomasz A Wesołowski
- Département de Chimie Physique, Université de Genève, 30, quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland, and Institute of Physical and Theoretical Chemistry, Wrocław University of Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
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17
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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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18
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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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19
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Tedesco D, Bertucci C. Induced circular dichroism as a tool to investigate the binding of drugs to carrier proteins: Classic approaches and new trends. J Pharm Biomed Anal 2015; 113:34-42. [PMID: 25769668 DOI: 10.1016/j.jpba.2015.02.024] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2015] [Accepted: 02/12/2015] [Indexed: 10/24/2022]
Abstract
Induced circular dichroism (ICD) is a spectroscopic phenomenon that provides versatile and useful methods for characterizing the structural and dynamic properties of the binding of drugs to target proteins. The understanding of biorecognition processes at the molecular level is essential to discover and validate new pharmacological targets, and to design and develop new potent and selective drugs. The present article reviews the main applications of ICD to drug binding studies on serum carrier proteins, going from the classic approaches for the derivation of drug binding parameters and the identification of binding sites, to an overview of the emerging trends for the characterization of binding modes by means of quantum chemical (QC) techniques. The advantages and limits of the ICD methods for the determination of binding parameters are critically reviewed; the capability to investigate the binding interactions of drugs and metabolites to their target proteins is also underlined, as well as the possibility of characterizing the binding sites to obtain a complete picture of the binding mechanism and dynamics. The new applications of ICD methods to identify stereoselective binding modes of drug/protein complexes are then reviewed with relevant examples. The combined application of experimental ICD spectroscopy and QC calculations is shown to identify qualitatively the bound conformations of ligands to target proteins even in the absence of a detailed structure of the binding sites, either obtained from experimental X-ray crystallography and NMR measurements or from computational models of the complex.
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Affiliation(s)
- Daniele Tedesco
- Department of Pharmacy and Biotechnology, University of Bologna, via Belmeloro 6, 40126 Bologna, Italy
| | - Carlo Bertucci
- Department of Pharmacy and Biotechnology, University of Bologna, via Belmeloro 6, 40126 Bologna, Italy.
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Middendorf N, Krause K, Höfener S. Solvatochromic shifts of Br2and I2in water cages of type 512, 51262, 51263, and 51264. J Comput Chem 2015; 36:853-60. [DOI: 10.1002/jcc.23863] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2014] [Revised: 01/16/2015] [Accepted: 01/17/2015] [Indexed: 11/07/2022]
Affiliation(s)
- Nils Middendorf
- Institut für Physikalische Chemie, Fakultät für Chemie und Biowissenschaften, Karlsruher Institut für Technologie (KIT); D-76131 Karlsruhe Germany
| | - Katharina Krause
- Institut für Physikalische Chemie, Fakultät für Chemie und Biowissenschaften, Karlsruher Institut für Technologie (KIT); D-76131 Karlsruhe Germany
| | - Sebastian Höfener
- Institut für Physikalische Chemie, Fakultät für Chemie und Biowissenschaften, Karlsruher Institut für Technologie (KIT); D-76131 Karlsruhe Germany
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21
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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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22
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Jacob CR, Neugebauer J. Subsystem density-functional theory. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2014. [DOI: 10.1002/wcms.1175] [Citation(s) in RCA: 229] [Impact Index Per Article: 22.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Christoph R. Jacob
- Center for Functional Nanostructures and Institute of Physical Chemistry; Karlsruhe Institute of Technology (KIT); Karlsruhe Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut; Westfälische Wilhelms-Universität Münster; Münster Germany
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23
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Höfener S. Coupled-cluster frozen-density embedding using resolution of the identity methods. J Comput Chem 2014; 35:1716-24. [DOI: 10.1002/jcc.23679] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2014] [Revised: 06/17/2014] [Accepted: 06/18/2014] [Indexed: 12/13/2022]
Affiliation(s)
- Sebastian Höfener
- Institut für Physikalische Chemie; Karlsruher Institut für Technologie; Karlsruhe D-76131 Germany
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24
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Humbert-Droz M, Zhou X, Shedge SV, Wesolowski TA. How to choose the frozen density in Frozen-Density Embedding Theory-based numerical simulations of local excitations? Theor Chem Acc 2013. [DOI: 10.1007/s00214-013-1405-1] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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25
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Höfener S, Gomes ASP, Visscher L. Solvatochromic shifts from coupled-cluster theory embedded in density functional theory. J Chem Phys 2013; 139:104106. [DOI: 10.1063/1.4820488] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
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26
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Gomes ASP, Jacob CR, Réal F, Visscher L, Vallet V. Towards systematically improvable models for actinides in condensed phase: the electronic spectrum of uranyl in Cs2UO2Cl4 as a test case. Phys Chem Chem Phys 2013; 15:15153-62. [DOI: 10.1039/c3cp52090k] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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27
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Höfener S, Visscher L. Calculation of electronic excitations using wave-function in wave-function frozen-density embedding. J Chem Phys 2012. [DOI: 10.1063/1.4767981] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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28
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de Silva P, Wesolowski TA. Exact non-additive kinetic potentials in realistic chemical systems. J Chem Phys 2012; 137:094110. [DOI: 10.1063/1.4749573] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Rosta E, Warshel A. On the Origins of the Linear Free Energy Relationships: Exploring the Nature of the Off-Diagonal Coupling Elements in S(N)2 Reactions. J Chem Theory Comput 2012; 8:3574-3585. [PMID: 23329895 PMCID: PMC3544163 DOI: 10.1021/ct2009329] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Understanding the relationship between the adiabatic free energy profiles of chemical reactions and the underlining diabatic states is central to the description of chemical reactivity. The diabatic states form the theoretical basis of Linear Free Energy Relationships (LFERs) and thus play a major role in physical organic chemistry and related fields. However, the theoretical justification for some of the implicit LFER assumptions has not been fully established by quantum mechanical studies. This study follows our earlier works(1,2) and uses the ab initio frozen density functional theory (FDFT) method(3) to evaluate both the diabatic and adiabatic free energy surfaces and to determine the corresponding off-diagonal coupling matrix elements for a series of S(N)2 reactions. It is found that the off-diagonal coupling matrix elements are almost the same regardless of the nucleophile and the leaving group but change upon changing the central group. Furthermore, it is also found that the off diagonal elements are basically the same in gas phase and in solution, even when the solvent is explicitly included in the ab initio calculations. Furthermore, our study establishes that the FDFT diabatic profiles are parabolic to a good approximation thus providing a first principle support to the origin of LFER. These findings further support the basic approximation of the EVB treatment.
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Affiliation(s)
- Edina Rosta
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892-0520
- Department of Chemistry, King’s College London, London, SE1 1UL, UK
| | - Arieh Warshel
- Department of Chemistry, University of Southern California, 3620 S. McClintock Ave., Los Angeles, California, 90089-1062
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30
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Höfener S, Severo Pereira Gomes A, Visscher L. Molecular properties via a subsystem density functional theory formulation: A common framework for electronic embedding. J Chem Phys 2012; 136:044104. [DOI: 10.1063/1.3675845] [Citation(s) in RCA: 80] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Kovyrshin A, Angelis FD, Neugebauer J. Selective TDDFT with automatic removal of ghost transitions: application to a perylene-dye-sensitized solar cell model. Phys Chem Chem Phys 2012; 14:8608-19. [DOI: 10.1039/c2cp40840f] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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32
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33
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Fradelos G, Wesołowski TA. Importance of the Intermolecular Pauli Repulsion in Embedding Calculations for Molecular Properties: The Case of Excitation Energies for a Chromophore in Hydrogen-Bonded Environments. J Phys Chem A 2011; 115:10018-26. [DOI: 10.1021/jp203192g] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Georgios Fradelos
- Département de Chimie Physique, Université de Genève, 30, quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
| | - Tomasz A. Wesołowski
- Département de Chimie Physique, Université de Genève, 30, quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
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34
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The empirical valence bond model: theory and applications. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2011. [DOI: 10.1002/wcms.10] [Citation(s) in RCA: 113] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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35
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Kovyrshin A, Neugebauer J. State-selective optimization of local excited electronic states in extended systems. J Chem Phys 2010; 133:174114. [DOI: 10.1063/1.3488230] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Neugebauer J. Subsystem-Based Theoretical Spectroscopy of Biomolecules and Biomolecular Assemblies. Chemphyschem 2009; 10:3148-73. [DOI: 10.1002/cphc.200900538] [Citation(s) in RCA: 83] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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37
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Neugebauer J. On the calculation of general response properties in subsystem density functional theory. J Chem Phys 2009; 131:084104. [DOI: 10.1063/1.3212883] [Citation(s) in RCA: 48] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
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38
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Lastra JMG, Kaminski JW, Wesolowski TA. Orbital-free effective embedding potential at nuclear cusps. J Chem Phys 2008; 129:074107. [DOI: 10.1063/1.2969814] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
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39
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Nicu VP, Baerends EJ. Effects of Complex Formation on Vibrational Circular Dichroism Spectra. J Phys Chem A 2008; 112:6978-91. [DOI: 10.1021/jp710201q] [Citation(s) in RCA: 70] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Affiliation(s)
- Valentin Paul Nicu
- Theoretical Chemistry, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands, and Laboratorium für Physikalische Chemie, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland
| | - Evert Jan Baerends
- Theoretical Chemistry, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands, and Laboratorium für Physikalische Chemie, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland
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40
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Jacob CR, Visscher L. A subsystem density-functional theory approach for the quantum chemical treatment of proteins. J Chem Phys 2008; 128:155102. [DOI: 10.1063/1.2906128] [Citation(s) in RCA: 81] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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41
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Neugebauer J. Photophysical Properties of Natural Light-Harvesting Complexes Studied by Subsystem Density Functional Theory. J Phys Chem B 2008; 112:2207-17. [DOI: 10.1021/jp709956k] [Citation(s) in RCA: 84] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- Johannes Neugebauer
- Laboratorium für Physikalische Chemie, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland
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42
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Kiewisch K, Eickerling G, Reiher M, Neugebauer J. Topological analysis of electron densities from Kohn-Sham and subsystem density functional theory. J Chem Phys 2008; 128:044114. [DOI: 10.1063/1.2822966] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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43
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Gomes ASP, Jacob CR, Visscher L. Calculation of local excitations in large systems by embedding wave-function theory in density-functional theory. Phys Chem Chem Phys 2008; 10:5353-62. [DOI: 10.1039/b805739g] [Citation(s) in RCA: 130] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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44
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Jacob CR, Neugebauer J, Visscher L. A flexible implementation of frozen-density embedding for use in multilevel simulations. J Comput Chem 2008; 29:1011-8. [DOI: 10.1002/jcc.20861] [Citation(s) in RCA: 126] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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45
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Neugebauer J. Induced Chirality in Achiral Media—How Theory Unravels Mysterious Solvent Effects. Angew Chem Int Ed Engl 2007; 46:7738-40. [PMID: 17886329 DOI: 10.1002/anie.200702858] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Johannes Neugebauer
- Laboratorium für Physikalische Chemie, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland.
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46
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Neugebauer J. Induzierte Chiralität in achiralen Lösungsmitteln – mysteriöse Solvenseffekte, aufgeklärt mit theoretischen Methoden. Angew Chem Int Ed Engl 2007. [DOI: 10.1002/ange.200702858] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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47
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Jacob CR, Beyhan SM, Visscher L. Exact functional derivative of the nonadditive kinetic-energy bifunctional in the long-distance limit. J Chem Phys 2007; 126:234116. [PMID: 17600413 DOI: 10.1063/1.2743013] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
We have investigated the functional derivative of the nonadditive kinetic-energy bifunctional, which appears in the embedding potential that is used in the frozen-density embedding formalism, in the limit that the separation of the subsystems is large. We have derived an exact expression for this kinetic-energy component of the embedding potential and have applied this expression to deduce its exact form in this limit. Comparing to the approximations currently in use, we find that while these approximations are correct at the nonfrozen subsystem, they fail completely at the frozen subsystem. Using test calculations on two model systems, a H2O...Li+ complex and a cluster of aminocoumarin C151 surrounded by 30 water molecules, we show that this failure leads to a wrong description of unoccupied orbitals, which can lead to convergence problems caused by too low-lying unoccupied orbitals and which can further have serious consequences for the calculation of response properties. Based on our results, a simple correction is proposed, and we show that this correction is able to fix the observed problems for the model systems studied.
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Affiliation(s)
- Christoph R Jacob
- Department of Theoretical Chemistry, Faculty of Sciences, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands.
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48
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Neugebauer J. Couplings between electronic transitions in a subsystem formulation of time-dependent density functional theory. J Chem Phys 2007; 126:134116. [PMID: 17430025 DOI: 10.1063/1.2713754] [Citation(s) in RCA: 181] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A subsystem formulation of time-dependent density functional theory (TDDFT) within the frozen-density embedding (FDE) framework and its practical implementation are presented, based on the formal TDDFT generalization of the FDE approach by Casida and Wesolowski [Int. J. Quantum Chem. 96, 577 (2004)]. It is shown how couplings between electronic transitions on different subsystems can be seamlessly incorporated into the formalism to overcome some of the shortcomings of the approximate TDDFT-FDE approach in use so far, which was only applicable for local subsystem excitations. In contrast to that, the approach presented here allows to include couplings between excitations on different subsystems, which become very important in aggregates composed of several similar chromophores, e.g., in biological or biomimetic light-harvesting systems. A connection to Forster- and Dexter-type excitation energy coupling expressions is established. A hybrid approach is presented and tested, in which excitation energy couplings are selectively included between different chromophore fragments, but neglected for inactive parts of the environment. It is furthermore demonstrated that the coupled TDDFT-FDE approach can cure the inability of the uncoupled FDE approach to describe induced circular dichroism in dimeric chromophores, a feature known as a "couplet," which is also related to couplings between (nearly) degenerate electronic transitions.
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Affiliation(s)
- Johannes Neugebauer
- Laboratorium für Physikalische Chemie, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland.
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49
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Jacob CR, Visscher L. Calculation of nuclear magnetic resonance shieldings using frozen-density embedding. J Chem Phys 2006; 125:194104. [PMID: 17129086 DOI: 10.1063/1.2370947] [Citation(s) in RCA: 58] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We have extended the frozen-density embedding (FDE) scheme within density-functional theory [T. A. Wesolowski and A. Warshel, J. Phys. Chem. 97, 8050 (1993)] to include external magnetic fields and applied this extension to the nonrelativistic calculation of nuclear magnetic resonance (NMR) shieldings. This leads to a formulation in which the electron density and the induced current are calculated separately for the individual subsystems. If the current dependence of the exchange-correlation functional and of the nonadditive kinetic-energy functional are neglected, the induced currents in the subsystems are not coupled and each of them can be determined without knowledge of the induced current in the other subsystem. This allows the calculation of the NMR shielding as a sum of contributions of the individual subsystems. As a test application, we have calculated the solvent shifts of the nitrogen shielding of acetonitrile for different solvents using small geometry-optimized clusters consisting of acetonitrile and one solvent molecule. By comparing to the solvent shifts obtained from supermolecular calculations we assess the accuracy of the solvent shifts obtained from FDE calculations. We find a good agreement between supermolecular and FDE calculations for different solvents. In most cases it is possible to neglect the contribution of the induced current in the solvent subsystem to the NMR shielding, but it has to be considered for aromatic solvents. We demonstrate that FDE can describe the effect of induced currents in the environment accurately.
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Affiliation(s)
- Christoph R Jacob
- Faculty of Sciences, Department of Theoritcal Chemistry, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands.
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