DOI: 10.1063/1.4916070. Benchmarking DFT and semiempirical methods on structures and lattice energies for ten ice polymorphs

Benchmarking DFT and semiempirical methods on structures and lattice energies for ten ice polymorphs

10.1063/1.4916070

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Water in different phases under various external conditions is very important in bio-chemical systems and for material science at surfaces. Density functional theory methods and approximations thereof have to be tested system specifically to benchmark their accuracy regarding computed structures and interaction energies. In this study, we present and test a set of ten ice polymorphs in comparison to experimental data with mass densities ranging from 0.9 to 1.5 g/cm3 and including explicit corrections for zero-point vibrational and thermal effects. London dispersion inclusive density functionals at the generalized gradient approximation (GGA), meta-GGA, and hybrid level as well as alternative low-cost molecular orbital methods are considered. The widely used functional of Perdew, Burke and Ernzerhof (PBE) systematically overbinds and overall provides inconsistent results. All other tested methods yield reasonable to very good accuracy. BLYP-D3atm gives excellent results with mean absolute errors for the lattice energy below 1 kcal/mol (7% relative deviation). The corresponding optimized structures are very accurate with mean absolute relative deviations (MARDs) from the reference unit cell volume below 1%. The impact of Axilrod-Teller-Muto (atm) type three-body dispersion and of non-local Fock exchange is small but on average their inclusion improves the results. While the density functional tight-binding model DFTB3-D3 performs well for low density phases, it does not yield good high density structures. As low-cost alternative for structure related problems, we recommend the recently introduced minimal basis Hartree-Fock method HF-3c with a MARD of about 3%.

Bibliography

Brandenburg, J. G., Maas, T., & Grimme, S. (2015). Benchmarking DFT and semiempirical methods on structures and lattice energies for ten ice polymorphs. The Journal of Chemical Physics, 142(12).

Authors 3

Jan Gerit Brandenburg (first)
Tilo Maas (additional)
Stefan Grimme (additional)

References 88 Referenced 100

{'volume-title': 'Density-Functional Theory of Atoms and Molecules', 'year': '1989', 'key': '2023073104004383300_c1a'} / Density-Functional Theory of Atoms and Molecules (1989)
{'volume-title': 'A Chemist’s Guide to Density Functional Theory', 'year': '2001', 'key': '2023073104004383300_c1b'} / A Chemist’s Guide to Density Functional Theory (2001)
{'volume-title': 'Density Functional Theory, An Approach to the Quantum Many-Body Problem', 'year': '1990', 'key': '2023073104004383300_c1c'} / Density Functional Theory, An Approach to the Quantum Many-Body Problem (1990)
10.1098/rsta.2012.0476 / Philos. Trans. R. Soc. A (2014)
10.1016/j.comptc.2010.09.002 / Comput. Theor. Chem. (2011)
10.1016/0009-2614(94)01027-7 / Chem. Phys. Lett. (1994)
10.1016/0009-2614(94)01402-H / Chem. Phys. Lett. (1995)
10.1002/jcc.540161102 / J. Comput. Chem. (1995)
10.1063/1.1522715 / J. Chem. Phys. (2002)
10.1063/1.3382344 / J. Chem. Phys. (2010)
10.1103/PhysRevLett.102.073005 / Phys. Rev. Lett. (2009)
10.1103/PhysRevLett.108.236402 / Phys. Rev. Lett. (2012)
10.1063/1.2065267 / J. Chem. Phys. (2005)
10.1063/1.3521275 / J. Chem. Phys. (2010)
10.1021/cr1000173 / Chem. Rev. (2010)
10.1002/wcms.30 / WIREs Comput. Mol. Sci. (2011)
10.1021/jz5021313 / J. Phys. Chem. Lett. (2014)
10.1103/RevModPhys.84.885 / Rev. Mod. Phys. (2012)
{'volume-title': 'Aqueous Systems at Elevated Temperatures and Pressure', 'year': '2004', 'key': '2023073104004383300_c9'} / Aqueous Systems at Elevated Temperatures and Pressure (2004)
10.1021/ct4002202 / J. Chem. Theory Comput. (2013)
10.1021/jz401931f / J. Phys. Chem. Lett. (2013)
10.1038/nmat3354 / Nat. Mater. (2012)
10.1021/jp3098268 / J. Phys. Chem. B (2012)
10.1063/1.4893377 / J. Chem. Phys. (2014)
10.1002/wcms.84 / WIREs Comput. Mol. Sci. (2012)
10.1021/ct100466k / J. Chem. Theory Comput. (2011)
10.1039/c3cp52293h / Phys. Chem. Chem. Phys. (2013)
10.1063/1.4738961 / J. Chem. Phys. (2012)
10.1063/1.4812819 / J. Chem. Phys. (2013)
10.1063/1.4824481 / J. Chem. Phys. (2013)
10.1039/c2cp41495c / Phys. Chem. Chem. Phys. (2012)
10.1063/1.4865748 / J. Chem. Phys. (2014)
10.1063/1.4820906 / J. Chem. Phys. (2013)
10.1016/j.molliq.2004.10.020 / J. Mol. Liq. (2005)
{'volume-title': 'Ice Physics', 'year': '1974', 'key': '2023073104004383300_c19a'} / Ice Physics (1974)
10.1039/b418934e / Phys. Chem. Chem. Phys. (2005)
10.1107/S0021889805014226 / J. Appl. Cryst. (2005)
10.1063/1.1495837 / J. Chem. Phys. (2002)
10.1063/1.448153 / J. Chem. Phys. (1984)
10.1126/science.150.3693.205 / Science (1965)
10.1063/1.2140277 / J. Chem. Phys (2006)
10.1063/1.448027 / J. Chem. Phys. (1984)
10.1063/1.464942 / J. Chem. Phys. (1993)
10.1063/1.1679238 / J. Chem. Phys. (1973)
10.1126/science.1123896 / Science (2006)
10.1103/PhysRevLett.103.105701 / Phys. Rev. Lett. (2009)
10.1016/0927-0256(96)00008-0 / J. Comput. Mat. Sci. (1996)
10.1103/PhysRevB.54.11169 / Phys. Rev. B by Kresse (1996)
10.1103/PhysRevB.50.17953 / Phys. Rev. B (1994)
10.1103/PhysRevB.59.1758 / Phys. Rev. B (1999)
10.1021/om4004225 / Chem. - Eur. J. (2013)
10.1103/PhysRevLett.77.3865 / Phys. Rev. Lett. (1996)
10.1103/PhysRevLett.78.1396 / Phys. Rev. Lett. by Perdew (1997)
10.1103/PhysRevB.59.7413 / Phys. Rev. B (1999)
10.1103/PhysRevLett.80.890 / Phys. Rev. Lett. (1998)
10.1103/PhysRevA.38.3098 / Phys. Rev. A (1988)
10.1103/PhysRevB.37.785 / Phys. Rev. B (1988)
10.1103/PhysRevLett.91.146401 / Phys. Rev. Lett. (2003)
10.1063/1.2370993 / J. Chem. Phys. (2006)
10.1063/1.478522 / J. Chem. Phys. (1999)
10.1063/1.464913 / J. Chem. Phys. (1993)
10.1021/j100096a001 / J. Phys. Chem. (1994)
10.1063/1.2404663 / J. Chem. Phys. (2006)
10.1002/jcc.21759 / J. Comput. Chem. (2011)
10.1063/1.1723844 / J. Chem. Phys. (1943)
{'key': '2023073104004383300_c40b', 'first-page': '629', 'volume': '17', 'year': '1944', 'journal-title': 'Proc. Phys. Math. Soc. Jpn.'} / Proc. Phys. Math. Soc. Jpn. (1944)
10.1002/qua.24658 / Int. J. Quantum Chem. (2014)
10.1063/1.3700154 / J. Chem. Phys. (2012)
10.1021/jp406658y / J. Phys. Chem. A (2013)
10.1002/jcc.23317 / J. Comput. Chem. (2013)
10.1007/128_2013_488 / Top. Curr. Chem. (2014)
10.1103/PhysRevB.58.7260 / Phys. Rev. B (1998)
10.1021/jz500755u / J. Phys. Chem. Lett. (2014)
10.1021/jp070186p / J. Phys. Chem. A (2007)
10.1021/jp071338j / J. Phys. Chem. A (2007)
10.1021/ct300849w / J. Chem. Theory Comput. (2013)
See supplementary material at http://dx.doi.org/10.1063/1.4916070 for explicit k-point grid utilized in all calculations, unit cell parameters and lattice energies of all tested method combinations, explicit error distributions, and optimized geometries at the PBE-D3/1000 eV level.
10.1007/s00214-013-1399-8 / Theor. Chem. Acc. (2013)
10.1103/PhysRevLett.107.185701 / Phys. Rev. Lett. (2011)
10.1103/PhysRevLett.108.105502 / Phys. Rev. Lett. (2012)
10.1002/cphc.201100826 / ChemPhysChem (2011)
10.1103/PhysRevLett.80.891 / Phys. Rev. Lett. (1998)
10.1021/jp501237c / J. Phys. Chem. C (2014)
10.1021/jz401931f / J. Phys. Chem. Lett. (2013)
10.1063/1.4892400 / J. Chem. Phys. (2014)
10.1021/jo302156p / J. Org. Chem. (2012)
10.1021/ct800549f / J. Chem. Theory Comput. (2009)
10.1002/jcc.23539 / J. Comput. Chem. (2014)

Dates

Type	When
Created	10 years, 5 months ago (March 27, 2015, 9:42 a.m.)
Deposited	2 years ago (July 31, 2023, midnight)
Indexed	1 week ago (Aug. 21, 2025, 2:09 p.m.)
Issued	10 years, 5 months ago (March 26, 2015)
Published	10 years, 5 months ago (March 26, 2015)
Published Online	10 years, 5 months ago (March 26, 2015)
Published Print	10 years, 5 months ago (March 28, 2015)

Funders 0

None

BibTeX

@article{Brandenburg_2015, title={Benchmarking DFT and semiempirical methods on structures and lattice energies for ten ice polymorphs}, volume={142}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.4916070}, DOI={10.1063/1.4916070}, number={12}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Brandenburg, Jan Gerit and Maas, Tilo and Grimme, Stefan}, year={2015}, month=mar }

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      "DOI": "10.1016/0009-2614(94)01402-H",
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      "volume-title": "Ice Physics",
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