### Abstract

For accurate thermochemical tests of electronic structure theory, accurate true anharmonic zero-point vibrational energies ZPVE ^{true} are needed. We discuss several possibilities to extract this information for molecules from density functional or wave function calculations and/or available experimental data: (1) Empirical universal scaling of density-functional-calculated harmonic ZPVE ^{harm}s, where we find that polyatomics require smaller scaling factors than diatomics. (2) Direct density-functional calculation by anharmonic second-order perturbation theory PT2. (3) Weighted averages of harmonic ZPVE ^{harm} and fundamental ZPVE ^{fund} (from fundamental vibrational transition frequencies), with weights (3/4, 1/4) for diatomics and (5/8,3/8) for polyatomics. (4) Experimental correction of the PT2 harmonic contribution, i.e., the estimate ZPVE _{PT2} ^{true} + (ZPVE _{expt} ^{fund} -ZPVE _{PT2} ^{fund}) for ZPVE ^{true}. The (5/8,3/8) average of method 3 and the additive correction of method 4 have been proposed here. For our database of experimental ZPVE ^{true}, consisting of 27 diatomics and 8 polyatomics, we find that methods 1 and 2, applied to the popular B3LYP and the nonempirical PBE and TPSS functional and their one-parameter hybrids, yield polyatomic errors on the order of 0.1 kcal/mol. Larger errors are expected for molecules larger than those in our database. Method 3 yields errors on the order of 0.02 kcal/mol, but requires very accurate (e.g., experimental, coupled cluster, or best-performing density functional) input harmonic ZPVE ^{harm}. Method 4 is the best-founded one that meets the requirements of high accuracy and practicality, requiring as experimental input only the highly accurate and widely available ZPVE _{expt} ^{fund} and producing errors on the order of 0.05 kcal/mol that are relatively independent of functional and basis set. As a part of our study, we also test the ability of the density functionals to predict accurate equilibrium bond lengths and angles for a data set of 21 mostly polyatomic molecules (since all calculated ZPVEs are evaluated at the correspondingly calculated molecular geometries).

Original language | English |
---|---|

Pages (from-to) | 6779-6789 |

Number of pages | 11 |

Journal | Journal of Physical Chemistry A |

Volume | 109 |

Issue number | 30 |

DOIs | |

Publication status | Published - aug. 4 2005 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*Journal of Physical Chemistry A*,

*109*(30), 6779-6789. https://doi.org/10.1021/jp0519464

**Estimation, Computation, and Experimental Correction of Molecular Zero-Point Vibrational Energies.** / Csonka, G.; Ruzsinszky, Adrienn; Perdew, John P.

Research output: Article

*Journal of Physical Chemistry A*, vol. 109, no. 30, pp. 6779-6789. https://doi.org/10.1021/jp0519464

}

TY - JOUR

T1 - Estimation, Computation, and Experimental Correction of Molecular Zero-Point Vibrational Energies

AU - Csonka, G.

AU - Ruzsinszky, Adrienn

AU - Perdew, John P.

PY - 2005/8/4

Y1 - 2005/8/4

N2 - For accurate thermochemical tests of electronic structure theory, accurate true anharmonic zero-point vibrational energies ZPVE true are needed. We discuss several possibilities to extract this information for molecules from density functional or wave function calculations and/or available experimental data: (1) Empirical universal scaling of density-functional-calculated harmonic ZPVE harms, where we find that polyatomics require smaller scaling factors than diatomics. (2) Direct density-functional calculation by anharmonic second-order perturbation theory PT2. (3) Weighted averages of harmonic ZPVE harm and fundamental ZPVE fund (from fundamental vibrational transition frequencies), with weights (3/4, 1/4) for diatomics and (5/8,3/8) for polyatomics. (4) Experimental correction of the PT2 harmonic contribution, i.e., the estimate ZPVE PT2 true + (ZPVE expt fund -ZPVE PT2 fund) for ZPVE true. The (5/8,3/8) average of method 3 and the additive correction of method 4 have been proposed here. For our database of experimental ZPVE true, consisting of 27 diatomics and 8 polyatomics, we find that methods 1 and 2, applied to the popular B3LYP and the nonempirical PBE and TPSS functional and their one-parameter hybrids, yield polyatomic errors on the order of 0.1 kcal/mol. Larger errors are expected for molecules larger than those in our database. Method 3 yields errors on the order of 0.02 kcal/mol, but requires very accurate (e.g., experimental, coupled cluster, or best-performing density functional) input harmonic ZPVE harm. Method 4 is the best-founded one that meets the requirements of high accuracy and practicality, requiring as experimental input only the highly accurate and widely available ZPVE expt fund and producing errors on the order of 0.05 kcal/mol that are relatively independent of functional and basis set. As a part of our study, we also test the ability of the density functionals to predict accurate equilibrium bond lengths and angles for a data set of 21 mostly polyatomic molecules (since all calculated ZPVEs are evaluated at the correspondingly calculated molecular geometries).

AB - For accurate thermochemical tests of electronic structure theory, accurate true anharmonic zero-point vibrational energies ZPVE true are needed. We discuss several possibilities to extract this information for molecules from density functional or wave function calculations and/or available experimental data: (1) Empirical universal scaling of density-functional-calculated harmonic ZPVE harms, where we find that polyatomics require smaller scaling factors than diatomics. (2) Direct density-functional calculation by anharmonic second-order perturbation theory PT2. (3) Weighted averages of harmonic ZPVE harm and fundamental ZPVE fund (from fundamental vibrational transition frequencies), with weights (3/4, 1/4) for diatomics and (5/8,3/8) for polyatomics. (4) Experimental correction of the PT2 harmonic contribution, i.e., the estimate ZPVE PT2 true + (ZPVE expt fund -ZPVE PT2 fund) for ZPVE true. The (5/8,3/8) average of method 3 and the additive correction of method 4 have been proposed here. For our database of experimental ZPVE true, consisting of 27 diatomics and 8 polyatomics, we find that methods 1 and 2, applied to the popular B3LYP and the nonempirical PBE and TPSS functional and their one-parameter hybrids, yield polyatomic errors on the order of 0.1 kcal/mol. Larger errors are expected for molecules larger than those in our database. Method 3 yields errors on the order of 0.02 kcal/mol, but requires very accurate (e.g., experimental, coupled cluster, or best-performing density functional) input harmonic ZPVE harm. Method 4 is the best-founded one that meets the requirements of high accuracy and practicality, requiring as experimental input only the highly accurate and widely available ZPVE expt fund and producing errors on the order of 0.05 kcal/mol that are relatively independent of functional and basis set. As a part of our study, we also test the ability of the density functionals to predict accurate equilibrium bond lengths and angles for a data set of 21 mostly polyatomic molecules (since all calculated ZPVEs are evaluated at the correspondingly calculated molecular geometries).

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U2 - 10.1021/jp0519464

DO - 10.1021/jp0519464

M3 - Article

C2 - 16834032

AN - SCOPUS:23844496449

VL - 109

SP - 6779

EP - 6789

JO - Journal of Physical Chemistry A

JF - Journal of Physical Chemistry A

SN - 1089-5639

IS - 30

ER -