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Lao KU, Yang Y, DiStasio RA. Electron confinement meet electron delocalization: non-additivity and finite-size effects in the polarizabilities and dispersion coefficients of the fullerenes. Phys Chem Chem Phys 2021; 23:5773-5779. [PMID: 33666598 DOI: 10.1039/d0cp05638c] [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
In this work, we used finite-field derivative techniques and density functional theory (DFT) to compute the static isotropic polarizability series (αl with l = 1, 2, 3) for the C60-C84 fullerenes and quantitatively assess the intrinsic non-additivity in these fundamental response properties. By comparing against classical models of the fullerenes as conducting spherical shells (or solid spheres) of uniform electron density, a detailed critical analysis of the derived effective scaling laws (α1 ∼ N1.2, α2 ∼ N2.0, α3 ∼ N2.7) demonstrates that the electronic structure of finite-sized fullerenes-a unique dichotomy of electron confinement and delocalization effects due to their quasi-spherical cage-like structures and encapsulated void spaces-simultaneously limits and enhances their quantum mechanical response to electric field perturbations. Corresponding frequency-dependent polarizabilities were obtained by inputting the αl series into the hollow sphere model (within the modified single frequency approximation), and used to compute the molecular dispersion coefficients (Cn with n = 6, 8, 9, 10) needed to describe the non-trivial van der Waals (vdW) interactions in fullerene-based systems. Using first-order perturbation theory in conjunction with >140 000 DFT calculations, we also computed the non-negligible zero-point vibrational contributions to α1 in C60 and C70, thereby enabling a more accurate and direct comparison between theory and experiment for these quintessential nanostructures.
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Affiliation(s)
- Ka Un Lao
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853, USA.
| | - Yan Yang
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853, USA.
| | - Robert A DiStasio
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853, USA.
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Tao J, Perdew JP, Tang H, Shahi C. Origin of the size-dependence of the equilibrium van der Waals binding between nanostructures. J Chem Phys 2018; 148:074110. [PMID: 29471641 DOI: 10.1063/1.5018572] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Nanostructures can be bound together at equilibrium by the van der Waals (vdW) effect, a small but ubiquitous many-body attraction that presents challenges to density functional theory. How does the binding energy depend upon the size or number of atoms in one of a pair of identical nanostructures? To answer this question, we treat each nanostructure as a whole object, not as a collection of atoms. Our calculations start from an accurate static dipole polarizability for each considered nanostructure, and an accurate equilibrium center-to-center distance for the pair (the latter from experiment or from the vdW-DF-cx functional). We consider the competition in each term -C2k/d2k (k = 3, 4, 5) of the long-range vdW series for the interaction energy, between the size dependence of the vdW coefficient C2k and that of the 2kth power of the center-to-center distance d. The damping of these vdW terms can be negligible, but in any case, it does not affect the size dependence for a given term in the absence of non-vdW binding. To our surprise, the vdW energy can be size-independent for quasi-spherical nanoclusters bound to one another by vdW interaction, even with strong nonadditivity of the vdW coefficient, as demonstrated for fullerenes. We also show that, for low-dimensional systems, the vdW interaction yields the strongest size-dependence, in stark contrast to that of fullerenes. We illustrate this with parallel planar polycyclic aromatic hydrocarbons. The size dependences of other morphologies or bonding types lie between, as shown by sodium clusters.
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Affiliation(s)
- Jianmin Tao
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122-1801, USA
| | - John P Perdew
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122-1801, USA
| | - Hong Tang
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122-1801, USA
| | - Chandra Shahi
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122-1801, USA
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Fransson T, Rehn DR, Dreuw A, Norman P. Static polarizabilities and C6 dispersion coefficients using the algebraic-diagrammatic construction scheme for the complex polarization propagator. J Chem Phys 2017. [DOI: 10.1063/1.4977039] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Thomas Fransson
- Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Dirk R. Rehn
- Department of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, SE-10691 Stockholm, Sweden
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Patrick Norman
- Department of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, SE-10691 Stockholm, Sweden
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Grimme S, Hansen A, Brandenburg JG, Bannwarth C. Dispersion-Corrected Mean-Field Electronic Structure Methods. Chem Rev 2016; 116:5105-54. [DOI: 10.1021/acs.chemrev.5b00533] [Citation(s) in RCA: 799] [Impact Index Per Article: 99.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Stefan Grimme
- Mulliken Center for Theoretical
Chemistry, Universität Bonn, 53113 Bonn, Germany
| | - Andreas Hansen
- Mulliken Center for Theoretical
Chemistry, Universität Bonn, 53113 Bonn, Germany
| | | | - Christoph Bannwarth
- Mulliken Center for Theoretical
Chemistry, Universität Bonn, 53113 Bonn, Germany
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Ambrosetti A, Ferri N, DiStasio RA, Tkatchenko A. Wavelike charge density fluctuations and van der Waals interactions at the nanoscale. Science 2016; 351:1171-6. [PMID: 26965622 DOI: 10.1126/science.aae0509] [Citation(s) in RCA: 124] [Impact Index Per Article: 15.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
Recent experiments on noncovalent interactions at the nanoscale have challenged the basic assumptions of commonly used particle- or fragment-based models for describing van der Waals (vdW) or dispersion forces. We demonstrate that a qualitatively correct description of the vdW interactions between polarizable nanostructures over a wide range of finite distances can only be attained by accounting for the wavelike nature of charge density fluctuations. By considering a diverse set of materials and biological systems with markedly different dimensionalities, topologies, and polarizabilities, we find a visible enhancement in the nonlocality of the charge density response in the range of 10 to 20 nanometers. These collective wavelike fluctuations are responsible for the emergence of nontrivial modifications of the power laws that govern noncovalent interactions at the nanoscale.
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Affiliation(s)
- Alberto Ambrosetti
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195 Berlin, Germany. Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, 35131 Padova, Italy
| | - Nicola Ferri
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195 Berlin, Germany
| | - Robert A DiStasio
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853, USA.
| | - Alexandre Tkatchenko
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195 Berlin, Germany. Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg.
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Tao J, Rappe AM. Communication: Accurate higher-order van der Waals coefficients between molecules from a model dynamic multipole polarizability. J Chem Phys 2016; 144:031102. [DOI: 10.1063/1.4940397] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jianmin Tao
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Andrew M. Rappe
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
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Schröder H, Creon A, Schwabe T. Reformulation of the D3(Becke–Johnson) Dispersion Correction without Resorting to Higher than C6 Dispersion Coefficients. J Chem Theory Comput 2015; 11:3163-70. [DOI: 10.1021/acs.jctc.5b00400] [Citation(s) in RCA: 57] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Heiner Schröder
- Center for Bioinformatics
and Institute of Physical Chemistry, University of Hamburg, Bundesstraße
43, 20146 Hamburg, Germany
| | - Anne Creon
- Center for Bioinformatics
and Institute of Physical Chemistry, University of Hamburg, Bundesstraße
43, 20146 Hamburg, Germany
| | - Tobias Schwabe
- Center for Bioinformatics
and Institute of Physical Chemistry, University of Hamburg, Bundesstraße
43, 20146 Hamburg, Germany
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Tao J, Yang J, Rappe AM. Dynamical screening of van der Waals interactions in nanostructured solids: Sublimation of fullerenes. J Chem Phys 2015; 142:164302. [DOI: 10.1063/1.4918761] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Jianmin Tao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Jing Yang
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Andrew M. Rappe
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
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Hollett JW. Non-pairwise additivity of the leading-order dispersion energy. J Chem Phys 2015; 142:084105. [PMID: 25725710 DOI: 10.1063/1.4908134] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The leading-order (i.e., dipole-dipole) dispersion energy is calculated for one-dimensional (1D) and two-dimensional (2D) infinite lattices, and an infinite 1D array of infinitely long lines, of doubly occupied locally harmonic wells. The dispersion energy is decomposed into pairwise and non-pairwise additive components. By varying the force constant and separation of the wells, the non-pairwise additive contribution to the dispersion energy is shown to depend on the overlap of density between neighboring wells. As well separation is increased, the non-pairwise additivity of the dispersion energy decays. The different rates of decay for 1D and 2D lattices of wells is explained in terms of a Jacobian effect that influences the number of nearest neighbors. For an array of infinitely long lines of wells spaced 5 bohrs apart, and an inter-well spacing of 3 bohrs within a line, the non-pairwise additive component of the leading-order dispersion energy is -0.11 kJ mol(-1) well(-1), which is 7% of the total. The polarizability of the wells and the density overlap between them are small in comparison to that of the atomic densities that arise from the molecular density partitioning used in post-density-functional theory (DFT) damped dispersion corrections, or DFT-D methods. Therefore, the nonadditivity of the leading-order dispersion observed here is a conservative estimate of that in molecular clusters.
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Affiliation(s)
- Joshua W Hollett
- Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba R3B 2G3, Canada and Department of Chemistry, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
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Tao J, Fang Y, Hao P, Scuseria GE, Ruzsinszky A, Perdew JP. Van der Waals coefficients beyond the classical shell model. J Chem Phys 2015; 142:024312. [DOI: 10.1063/1.4905259] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Jianmin Tao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Yuan Fang
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - Pan Hao
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - G. E. Scuseria
- Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA and Department of Chemistry, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
| | - Adrienn Ruzsinszky
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - John P. Perdew
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
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