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Density-functional approaches to noncovalent interactions: A comparison of dispersion corrections (DFT-D), exchange-hole dipole moment (XDM) theory, and specialized functionals
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10.1063/1.3545971
/content/aip/journal/jcp/134/8/10.1063/1.3545971
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/8/10.1063/1.3545971

Figures

Image of FIG. 1.
FIG. 1.

Measures of error for a model dissociation curve. A Lennard-Jones potential (shown scaled) and its duplicate, displaced vertically by 1% of its well depth, are compared according to absolute, relative, and balanced definitions of deviation. Their summary statistics MAD, MA%D, and MA%BD, respectively, are computed over the chemically relevant portion of the curve [0.8 − 2.4 · R eq ] for potentials of depth one and ten. The graph demonstrates the difficulties in employing MA%D for nonequilibrium geometries and a possible solution in the form of balanced error, which follows the profile of the absolute error while being readily comparable over ranges of interaction energy.

Image of FIG. 2.
FIG. 2.

Double-ζ functional performance. For each DFT technique considered, individual member errors and MAD summary statistics are plotted for five test sets at the non-CP-corrected aug-cc-pVDZ level of theory. Consult Sec. II D in the text for a concise guide to the plotting mode used here.

Image of FIG. 3.
FIG. 3.

Triple-ζ functional performance. For each DFT technique considered, individual member errors and MAD summary statistics are plotted for five test sets at the non-CP-corrected aug-cc-pVTZ level of theory. Consult Sec. II D in the text for a concise guide to the plotting mode used here.

Image of FIG. 4.
FIG. 4.

Basis set and BSSE influence on S22 interaction energies. For representative DFT techniques, individual member errors and MAD summary statistics are illustrated using six hierarchical basis sets. Consult Sec. II D in the text for a concise guide to the plotting mode used here. The graph clearly demonstrates that while CP-corrected results are largely insensitive to basis set size and composition, non-CP-corrected calculations require diffuse functions for accurate treatment of hydrogen-bonded systems, and overall success for NCI is attained typically [e.g., (a) B3LYP-D3] only at triple-ζ levels of theory, though some functionals [e.g., (b) B970-D2] achieve satisfactory results with double-ζ at the cost of less-predictable patterns of error.

Image of FIG. 5.
FIG. 5.

Efficiency results for functionals. The total wall time relative to a B3LYP-D calculation is depicted for a number of functionals run in (a) Q-Chem and (b) NWChem, with the indicated qualities of numerical integration grid and two basis sets, aug-cc-pVDZ (upper portion) and aug-cc-pVTZ (lower portion). These results derive from a single system, S22-7, such that the basis sets differ in size by approximately a factor of 2. The right-hand axis conveys the absolute wall time. Whereas functionals in the double-ζ regime exhibit only a threefold span in relative cost, the triple-ζ results show twentyfold changes between GGAs and double-hybrids.

Tables

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Table I.

Classification and performance of density functionals. In this and subsequent tables, functionals are ordered (within DFT, dispersion-including DFT, and XDM sections) by improving results for the overall S22 test set with the aug-cc-pVTZ basis. Methods exhibit, according to the symbols, satisfactory (✓) or excellent (*) performance for purely hydrogen-bonded (HB), purely dispersion-bound (DD), and overall (TT) systems with double-ζ and triple-ζ basis sets. The MAD (kcal/mol) averaged over all test sets is also charted.

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Table II.

Test set statistics. Interaction energy means and, in parenthesis, ranges (kcal/mol) are presented for each test set and subcategory.

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Table III.

Mean absolute deviation of the interaction energy (kcal/mol) for the S22 test set with noncounterpoise-corrected DFT methods.

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Table IV.

Mean absolute deviation of the interaction energy (kcal/mol ) for the NBC10 and HBC6 test sets with noncounterpoise-corrected DFT methods.

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Table V.

Mean absolute deviation of the interaction energy (kcal/mol) for the HSG test set with noncounterpoise-corrected DFT methods.

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Table VI.

Mean absolute deviation of the interaction energy (kcal/mol) for the JSCH test set with noncounterpoise-corrected DFT methods.

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Table VII.

Comparison of noncounterpoise- and CP-corrected results for six hierarchical double-ζ and triple-ζ basis sets (additional doubly augmented sets available for B3LYP-D3). The mean absolute deviation of the interaction energy (kcal/mol) is presented for the S22 test set and subsets.

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/content/aip/journal/jcp/134/8/10.1063/1.3545971
2011-02-25
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Density-functional approaches to noncovalent interactions: A comparison of dispersion corrections (DFT-D), exchange-hole dipole moment (XDM) theory, and specialized functionals
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/8/10.1063/1.3545971
10.1063/1.3545971
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