Estimation, computation, and experimental correction of molecular zero-point vibrational energies

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Physical Chemistry

Background:

• Accurate thermochemical data are essential for validating electronic structure theories.
• Zero-point vibrational energy (ZPVE) is a critical component of thermochemical calculations.
• Existing methods for calculating ZPVE(true) have limitations in accuracy and practicality.

Purpose of the Study:

• To evaluate and compare different methods for obtaining accurate true anharmonic zero-point vibrational energies (ZPVE(true)).
• To identify the most reliable and practical method for ZPVE(true) calculation for both diatomics and polyatomics.
• To assess the performance of various density functionals in predicting molecular geometries.

Main Methods:

• Empirical scaling of harmonic ZPVEs from density functional theory (DFT).
• Direct DFT calculation of ZPVE using anharmonic second-order perturbation theory (PT2).
• Weighted averaging of harmonic ZPVEs and experimental fundamental ZPVEs.
• Experimental correction of PT2-calculated ZPVEs using experimental fundamental ZPVEs.

Main Results:

• DFT methods (B3LYP, PBE, TPSS) with scaling or direct PT2 calculation yield errors around 0.1 kcal/mol for polyatomics.
• Weighted averaging (Method 3) achieves ~0.02 kcal/mol error but requires highly accurate harmonic ZPVE input.
• The proposed experimental correction (Method 4) provides errors of ~0.05 kcal/mol, independent of functional and basis set, using readily available experimental data.

Conclusions:

• Method 4, an additive correction using experimental fundamental ZPVEs, is the most accurate and practical approach for determining ZPVE(true).
• The performance of DFT functionals in predicting equilibrium geometries was also evaluated.
• Accurate ZPVE(true) is vital for advancing the accuracy of computational thermochemistry.