1
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Abstract
This Communication presents a unified derivation of three different approximations used in density functional theory (DFT): the Perdew-Zunger self-interaction correction (PZSIC), the Hubbard correction DFT+U, and the Rung 3.5 density functionals. All three approximations can be derived by introducing electron self-interaction into the Kohn-Sham (KS) reference system of noninteracting electrons. The derivation uses the Adiabatic Projection formalism: one projects the electron-electron interaction operator onto certain states, introduces the projected operator into the reference system, and defines a density functional for the remainder. Projecting onto individual localized KS orbitals recovers our previous derivation of the PZSIC [B. G. Janesko, J. Phys. Chem. Lett. 13, 5698-5702 (2022)]. Projecting onto localized atom-centered orbitals recovers a variant of DFT+U. Projecting onto localized states at each point in space recovers Rung 3.5 approaches. New results include an "atomic state PZSIC" that does not require localizing the KS orbitals, a demonstration that typical Hubbard U parameters reproduce a scaled-down PZSIC, and a Rung 3.5 variant of DFT+U that does not require choosing atom-dependent states.
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Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry and Biochemistry, Texas Christian University, 2800 S. University Dr., Fort Worth, Texas 76109, USA
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2
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Bryenton KR, Adeleke AA, Dale SG, Johnson ER. Delocalization error: The greatest outstanding challenge in density‐functional theory. WIREs Comput Mol Sci 2022. [DOI: 10.1002/wcms.1631] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Kyle R. Bryenton
- Department of Physics and Atmospheric Science Dalhousie University Halifax Nova Scotia Canada
| | | | - Stephen G. Dale
- Queensland Micro‐ and Nanotechnology Centre Griffith University Nathan Queensland Australia
| | - Erin R. Johnson
- Department of Physics and Atmospheric Science Dalhousie University Halifax Nova Scotia Canada
- Department of Chemistry Dalhousie University Halifax Nova Scotia Canada
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3
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Affiliation(s)
- Benjamin G. Janesko
- Department of Chemistry and Biochemistry, Texas Christian University, Fort Worth, Texas 76129, USA
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4
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Abstract
Density functional theory (DFT) is the most widely-used electronic structure approximation across chemistry, physics, and materials science. Every year, thousands of papers report hybrid DFT simulations of chemical structures, mechanisms, and spectra. Unfortunately, hybrid DFT's accuracy is ultimately limited by tradeoffs between over-delocalization and under-binding. This review summarizes these tradeoffs, and introduces six modern attempts to go beyond them while maintaining hybrid DFT's relatively low computational cost: DFT+U, self-interaction corrections, localized orbital scaling corrections, local hybrid functionals, real-space nondynamical correlation, and our rung-3.5 approach. The review concludes with practical suggestions for DFT users to identify and mitigate these tradeoffs' impact on their simulations.
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Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry & Biochemistry, Texas Christian University, 2800 S. University Dr, Fort Worth, TX 76129, USA.
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5
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Scalmani G, Frisch MJ, Janesko BG. Calculation of magnetic properties with density functional approximations including rung 3.5 ingredients. J Chem Phys 2020; 153:164101. [DOI: 10.1063/5.0026269] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Affiliation(s)
- Giovanni Scalmani
- Gaussian, Inc., 340 Quinnipiac St. Bldg. 40, Wallingford, Connecticut 06492, USA
| | - Michael J. Frisch
- Gaussian, Inc., 340 Quinnipiac St. Bldg. 40, Wallingford, Connecticut 06492, USA
| | - Benjamin G. Janesko
- Department of Chemistry & Biochemistry, Texas Christian University, 2800 S. University Dr., Fort Worth, Texas 76129, USA
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6
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Maier TM, Ikabata Y, Nakai H. Efficient Semi-Numerical Implementation of Relativistic Exact Exchange within the Infinite-Order Two-Component Method Using a Modified Chain-of-Spheres Method. J Chem Theory Comput 2019; 15:4745-4763. [DOI: 10.1021/acs.jctc.9b00228] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Affiliation(s)
- Toni M. Maier
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Yasuhiro Ikabata
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
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7
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Janesko BG, Scalmani G, Frisch MJ. Density functionals for nondynamical correlation constructed from an upper bound to the exact exchange energy density. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1535673] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Benjamin G. Janesko
- Department of Chemistry and Biochemistry, Texas Christian University, Fort Worth, TX, USA
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8
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Abstract
We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.
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Affiliation(s)
- Soumen Ghosh
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Pragya Verma
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Christopher J Cramer
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
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9
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Maier TM, Arbuznikov AV, Kaupp M. Local hybrid functionals: Theory, implementation, and performance of an emerging new tool in quantum chemistry and beyond. WIREs Comput Mol Sci 2018. [DOI: 10.1002/wcms.1378] [Citation(s) in RCA: 65] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Toni M. Maier
- Institut für Chemie Theoretische Chemie/Quantenchemie Technische Universität Berlin Berlin Germany
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering Waseda University Tokyo Japan
| | - Alexei V. Arbuznikov
- Institut für Chemie Theoretische Chemie/Quantenchemie Technische Universität Berlin Berlin Germany
| | - Martin Kaupp
- Institut für Chemie Theoretische Chemie/Quantenchemie Technische Universität Berlin Berlin Germany
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10
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Affiliation(s)
- Benjamin G. Janesko
- Department of Chemistry and Biochemistry, Texas Christian University, Fort Worth, Texas 76110, USA
| | - Emil Proynov
- Department of Chemistry and Biochemistry, Texas Christian University, Fort Worth, Texas 76110, USA
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11
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Giovannini T, Lafiosca P, Cappelli C. A General Route to Include Pauli Repulsion and Quantum Dispersion Effects in QM/MM Approaches. J Chem Theory Comput 2017; 13:4854-4870. [PMID: 28898079 DOI: 10.1021/acs.jctc.7b00776] [Citation(s) in RCA: 52] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
A methodology to account for nonelectrostatic interactions in Quantum Mechanical (QM)/Molecular Mechanics (MM) approaches is developed. Formulations for Pauli repulsion and dispersion energy, explicitly depending on the QM density, are derived. Such expressions are based on the definition of an auxiliary density on the MM portion and the Tkatchenko-Scheffler (TS) approach, respectively. The developed method is general enough to be applied to any QM/MM method and partition, provided an accurate tuning of a small number of parameters is obtained. The coupling of the method with both nonpolarizable and fully polarizable QM/fluctuating charge (FQ) approaches is reported and applied. A suitable parametrization for the aqueous solution, so that its most representative features are well reproduced, is outlined. Then, the obtained parametrization and method are applied to calculate the nonelectrostatic (repulsion and dispersion) interaction energy of nicotine in aqueous solution.
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Affiliation(s)
| | - Piero Lafiosca
- Scuola Normale Superiore , Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Chiara Cappelli
- Scuola Normale Superiore , Piazza dei Cavalieri 7, 56126 Pisa, Italy
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12
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Determan JJ, Poole K, Scalmani G, Frisch MJ, Janesko BG, Wilson AK. Comparative Study of Nonhybrid Density Functional Approximations for the Prediction of 3d Transition Metal Thermochemistry. J Chem Theory Comput 2017; 13:4907-4913. [PMID: 28877436 DOI: 10.1021/acs.jctc.7b00809] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The utility of several nonhybrid density functional approximations (DFAs) is considered for the prediction of gas phase enthalpies of formation for a large set of 3d transition metal-containing molecules. Nonhybrid DFAs can model thermochemical values for 3d transition metal-containing molecules with accuracy comparable to that of hybrid functionals. The GAM-generalized gradient approximation (GGA); the TPSS, M06-L, and MN15-L meta-GGAs; and the Rung 3.5 PBE+ΠLDA(s) DFAs all give root-mean-square deviations below that of the widely used B3LYP hybrid. Modern nonhybrid DFAs continue to show utility for transition metal thermochemistry.
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Affiliation(s)
- John J Determan
- Department of Chemistry, Texas Christian University , Fort Worth, Texas 76129, United States
| | - Katelyn Poole
- Department of Chemistry, Texas Christian University , Fort Worth, Texas 76129, United States.,Department of Chemistry and Center for Advanced Scientific Computing and Modeling (CASCaM), University of North Texas , Denton, Texas 76203-5017, United States
| | - Giovanni Scalmani
- Gaussian, Inc. , 340 Quinnipiac Street, Building 40, Wallingford, Connecticut 06492, United States
| | - Michael J Frisch
- Gaussian, Inc. , 340 Quinnipiac Street, Building 40, Wallingford, Connecticut 06492, United States
| | - Benjamin G Janesko
- Department of Chemistry, Texas Christian University , Fort Worth, Texas 76129, United States
| | - Angela K Wilson
- Department of Chemistry, Michigan State University , East Lansing, Michigan 48824 United States
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13
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Janesko BG, Proynov E, Kong J, Scalmani G, Frisch MJ. Practical Density Functionals beyond the Overdelocalization-Underbinding Zero-Sum Game. J Phys Chem Lett 2017; 8:4314-4318. [PMID: 28837338 DOI: 10.1021/acs.jpclett.7b02023] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
Density functional theory (DFT) uses a density functional approximation (DFA) to add electron correlation to mean-field electronic structure calculations. Standard strategies (generalized gradient approximations GGAs, meta-GGAs, hybrids, etc.) for building DFAs, no matter whether based on exact constraints or empirical parametrization, all face a zero-sum game between overdelocalization (fractional charge error, FC) and underestimation of covalent bonding (fractional spin error, FS). This work presents an alternative strategy. Practical "Rung 3.5" ingredients are used to implement insights from hyper-GGA DFAs that reduce both FS and FC errors. Prototypes of this strategy qualitatively improve FS and FC error over 40 years of standard DFAs while maintaining low cost and practical evaluation of properties. Numerical results ranging from transition metal thermochemistry to absorbance peaks and excited-state geometry optimizations highlight this strategy's promise and indicate areas requiring further development.
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Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry, Texas Christian University , Fort Worth, Texas 76129, United States
| | - Emil Proynov
- Department of Chemistry, Texas Christian University , Fort Worth, Texas 76129, United States
| | - Jing Kong
- Department of Chemistry, Middle Tennessee State University , Murfreesboro, Tennessee 37132, United States
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14
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Mahler A, Janesko BG, Moncho S, Brothers EN. Why are GGAs so accurate for reaction kinetics on surfaces? Systematic comparison of hybrid vs. nonhybrid DFT for representative reactions. J Chem Phys 2017. [DOI: 10.1063/1.4986404] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Abstract
The exact exchange energy and its energy density are useful but computationally expensive ingredients in density functional approximations for Kohn-Sham density functional theory. We present detailed tests of some exact nonempirical upper bounds to exact exchange. These "Rung 3.5" upper bounds contract the Kohn-Sham one-particle density matrix with model density matrices used to construct semilocal model exchange holes and invoke the Cauchy-Schwarz inequality. The contraction automatically eliminates the computationally expensive long-range component of the exact exchange hole. Numerical tests show that the exchange upper bounds underestimate total exchange energies while predicting other properties with accuracy approaching standard hybrid approximations.
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Affiliation(s)
- Emil Proynov
- Department of Chemistry and Biochemistry, Texas Christian University , Fort Worth, Texas 76110, United States
| | - Benjamin G Janesko
- Department of Chemistry and Biochemistry, Texas Christian University , Fort Worth, Texas 76110, United States
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16
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Janesko BG, Proynov E. Accurate alkynyl radical structures from density functional calculations without Hartree-Fock exchange. J Chem Phys 2017; 146:054109. [DOI: 10.1063/1.4974986] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Benjamin G. Janesko
- Department of Chemistry and Biochemistry, Texas Christian University, 2800 S. University Dr., Fort Worth, Texas 76129, USA
| | - Emil Proynov
- Department of Chemistry and Biochemistry, Texas Christian University, 2800 S. University Dr., Fort Worth, Texas 76129, USA
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17
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Abstract
PBE calculations, performed non-self-consistently on densities evaluated with Rung 3.5 density functionals, give improved performance for hydrogen transfer reaction barriers.
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Affiliation(s)
- Benjamin G. Janesko
- Department of Chemistry & Biochemistry
- Texas Christian University
- 2800 S. University Dr
- Fort Worth
- USA
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18
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Janesko BG. Topological analysis of the electron delocalization range. J Comput Chem 2016; 37:1993-2005. [DOI: 10.1002/jcc.24421] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2016] [Revised: 04/01/2016] [Accepted: 05/17/2016] [Indexed: 11/08/2022]
Affiliation(s)
- Benjamin G. Janesko
- Department of Chemistry & BiochemistryTexas Christian University2800 S. University DrFort Worth Texas76129
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Affiliation(s)
| | | | - Giovanni Scalmani
- Gaussian, Inc., 340
Quinnipiac St., Bldg. 40, Wallingford, Connecticut 06492, United States
| | - Michael J. Frisch
- Gaussian, Inc., 340
Quinnipiac St., Bldg. 40, Wallingford, Connecticut 06492, United States
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20
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Affiliation(s)
- Benjamin G. Janesko
- Department
of Chemistry, Texas Christian University, Fort Worth, Texas 76129, United States
| | - Giovanni Scalmani
- Gaussian,
Inc., 340 Quinnipiac Street Building
40, Wallingford, Connecticut 06492, United States
| | - Michael J. Frisch
- Gaussian,
Inc., 340 Quinnipiac Street Building
40, Wallingford, Connecticut 06492, United States
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21
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Abstract
The electron delocalization range EDR(r;uav) (left) captures the spin density (right) of an electron delocalized over uav = 5.77 Å on the surface of an (H2O)20− cluster.
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22
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Affiliation(s)
- Benjamin G. Janesko
- Department of Chemistry, Texas Christian University Fort Worth, Texas 76129, USA
| | - Giovanni Scalmani
- Gaussian, Inc., 340 Quinnipiac St., Bldg. 40 , Wallingford, Connecticut 06492, USA
| | - Michael J. Frisch
- Gaussian, Inc., 340 Quinnipiac St., Bldg. 40 , Wallingford, Connecticut 06492, USA
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