Performance of DFT for C60 Isomerization Energies: A Noticeable Exception to Jacob's Ladder

Amir Karton, Simone L. Waite, Alister J. Page

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The ability to accurately calculate relative energies of fullerenes is important in many areas of computational nanotechnology. Because of the large size of fullerenes, their relative energies cannot normally be calculated by means of high-level ab initio procedures, and therefore, density functional theory (DFT) represents a cost-effective alternative. In an extensive benchmark study, we calculate the electronic energies of eight C60 isomers by means of the high-level G4(MP2) composite procedure. G4(MP2) isomerization energies span a wide range between 307.5 and 1074.0 kJ mol-1. We use these benchmark data to assess the performance of DFT, double-hybrid DFT (DHDFT), and MP2-based ab initio methods. Surprisingly, functionals from the second and third rungs of Jacob's Ladder (i.e., GGA and meta-GGA functionals) significantly and systematically outperform hybrid and hybrid-meta-GGA functionals, which occupy higher rungs of Jacob's Ladder. In addition, DHDFT functionals do not offer a substantial improvement over meta-GGA functionals, with respect to isomerization energies. Overall, the best performing functionals with mean absolute deviations (MADs) below 15.0 kJ mol-1 are (MADs given in parentheses) the GGA N12 (14.7); meta-GGAs M06-L (10.6), M11-L (10.8), MN15-L (11.9), and TPSS-D3BJ (12.8); and the DHDFT functionals B2T-PLYP (9.3), mPW2-PLYP (9.8), B2K-PLYP (12.1), and B2GP-PLYP (12.3 kJ mol-1). In light of these results, we recommend the use of meta-GGA functionals for the calculation of fullerene isomerization energies. Finally, we show that inclusion of very small percentages of exact Hartree-Fock exchange (3-5%) slightly improves the performance of the GGA and meta-GGA functionals. However, their performance rapidly deteriorates with the inclusion of larger percentages of exact Hartree-Fock exchange. ©

Original languageEnglish
Pages (from-to)257-266
Number of pages10
JournalJournal of Physical Chemistry A
Volume123
Issue number1
DOIs
Publication statusPublished - 1 Oct 2019

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Fullerenes
Ladders
Isomerization
Discrete Fourier transforms
ladders
functionals
isomerization
Density functional theory
density functional theory
Nanotechnology
Isomers
fullerenes
energy
Composite materials
inclusions
deviation
Costs
nanotechnology
isomers
costs

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@article{b159ccaa82d544f48b0726c77735c250,
title = "Performance of DFT for C60 Isomerization Energies: A Noticeable Exception to Jacob's Ladder",
abstract = "The ability to accurately calculate relative energies of fullerenes is important in many areas of computational nanotechnology. Because of the large size of fullerenes, their relative energies cannot normally be calculated by means of high-level ab initio procedures, and therefore, density functional theory (DFT) represents a cost-effective alternative. In an extensive benchmark study, we calculate the electronic energies of eight C60 isomers by means of the high-level G4(MP2) composite procedure. G4(MP2) isomerization energies span a wide range between 307.5 and 1074.0 kJ mol-1. We use these benchmark data to assess the performance of DFT, double-hybrid DFT (DHDFT), and MP2-based ab initio methods. Surprisingly, functionals from the second and third rungs of Jacob's Ladder (i.e., GGA and meta-GGA functionals) significantly and systematically outperform hybrid and hybrid-meta-GGA functionals, which occupy higher rungs of Jacob's Ladder. In addition, DHDFT functionals do not offer a substantial improvement over meta-GGA functionals, with respect to isomerization energies. Overall, the best performing functionals with mean absolute deviations (MADs) below 15.0 kJ mol-1 are (MADs given in parentheses) the GGA N12 (14.7); meta-GGAs M06-L (10.6), M11-L (10.8), MN15-L (11.9), and TPSS-D3BJ (12.8); and the DHDFT functionals B2T-PLYP (9.3), mPW2-PLYP (9.8), B2K-PLYP (12.1), and B2GP-PLYP (12.3 kJ mol-1). In light of these results, we recommend the use of meta-GGA functionals for the calculation of fullerene isomerization energies. Finally, we show that inclusion of very small percentages of exact Hartree-Fock exchange (3-5{\%}) slightly improves the performance of the GGA and meta-GGA functionals. However, their performance rapidly deteriorates with the inclusion of larger percentages of exact Hartree-Fock exchange. {\circledC}",
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Performance of DFT for C60 Isomerization Energies : A Noticeable Exception to Jacob's Ladder. / Karton, Amir; Waite, Simone L.; Page, Alister J.

In: Journal of Physical Chemistry A, Vol. 123, No. 1, 01.10.2019, p. 257-266.

Research output: Contribution to journalArticle

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T1 - Performance of DFT for C60 Isomerization Energies

T2 - A Noticeable Exception to Jacob's Ladder

AU - Karton, Amir

AU - Waite, Simone L.

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N2 - The ability to accurately calculate relative energies of fullerenes is important in many areas of computational nanotechnology. Because of the large size of fullerenes, their relative energies cannot normally be calculated by means of high-level ab initio procedures, and therefore, density functional theory (DFT) represents a cost-effective alternative. In an extensive benchmark study, we calculate the electronic energies of eight C60 isomers by means of the high-level G4(MP2) composite procedure. G4(MP2) isomerization energies span a wide range between 307.5 and 1074.0 kJ mol-1. We use these benchmark data to assess the performance of DFT, double-hybrid DFT (DHDFT), and MP2-based ab initio methods. Surprisingly, functionals from the second and third rungs of Jacob's Ladder (i.e., GGA and meta-GGA functionals) significantly and systematically outperform hybrid and hybrid-meta-GGA functionals, which occupy higher rungs of Jacob's Ladder. In addition, DHDFT functionals do not offer a substantial improvement over meta-GGA functionals, with respect to isomerization energies. Overall, the best performing functionals with mean absolute deviations (MADs) below 15.0 kJ mol-1 are (MADs given in parentheses) the GGA N12 (14.7); meta-GGAs M06-L (10.6), M11-L (10.8), MN15-L (11.9), and TPSS-D3BJ (12.8); and the DHDFT functionals B2T-PLYP (9.3), mPW2-PLYP (9.8), B2K-PLYP (12.1), and B2GP-PLYP (12.3 kJ mol-1). In light of these results, we recommend the use of meta-GGA functionals for the calculation of fullerene isomerization energies. Finally, we show that inclusion of very small percentages of exact Hartree-Fock exchange (3-5%) slightly improves the performance of the GGA and meta-GGA functionals. However, their performance rapidly deteriorates with the inclusion of larger percentages of exact Hartree-Fock exchange. ©

AB - The ability to accurately calculate relative energies of fullerenes is important in many areas of computational nanotechnology. Because of the large size of fullerenes, their relative energies cannot normally be calculated by means of high-level ab initio procedures, and therefore, density functional theory (DFT) represents a cost-effective alternative. In an extensive benchmark study, we calculate the electronic energies of eight C60 isomers by means of the high-level G4(MP2) composite procedure. G4(MP2) isomerization energies span a wide range between 307.5 and 1074.0 kJ mol-1. We use these benchmark data to assess the performance of DFT, double-hybrid DFT (DHDFT), and MP2-based ab initio methods. Surprisingly, functionals from the second and third rungs of Jacob's Ladder (i.e., GGA and meta-GGA functionals) significantly and systematically outperform hybrid and hybrid-meta-GGA functionals, which occupy higher rungs of Jacob's Ladder. In addition, DHDFT functionals do not offer a substantial improvement over meta-GGA functionals, with respect to isomerization energies. Overall, the best performing functionals with mean absolute deviations (MADs) below 15.0 kJ mol-1 are (MADs given in parentheses) the GGA N12 (14.7); meta-GGAs M06-L (10.6), M11-L (10.8), MN15-L (11.9), and TPSS-D3BJ (12.8); and the DHDFT functionals B2T-PLYP (9.3), mPW2-PLYP (9.8), B2K-PLYP (12.1), and B2GP-PLYP (12.3 kJ mol-1). In light of these results, we recommend the use of meta-GGA functionals for the calculation of fullerene isomerization energies. Finally, we show that inclusion of very small percentages of exact Hartree-Fock exchange (3-5%) slightly improves the performance of the GGA and meta-GGA functionals. However, their performance rapidly deteriorates with the inclusion of larger percentages of exact Hartree-Fock exchange. ©

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