Quadratic Corrections to Harmonic Vibrational Frequencies Outperform Linear Models

Area of Science:

• Computational quantum chemistry
• Spectroscopy
• Theoretical chemistry

Background:

• Simulating accurate infrared spectra is a key challenge in computational quantum chemistry.
• Linearly scaling harmonic frequencies is a common empirical method to approximate anharmonic effects and correct for theoretical method/basis set deficiencies.
• This empirical approach is nonvariational and unbounded, necessitating robust error quantification.

Purpose of the Study:

• To isolate and assess the intrinsic accuracy of frequency scaling methods by removing confounding factors like methodological incompleteness.
• To evaluate the performance of different scaling models (single-coefficient linear, two-parameter polynomial, single-parameter quadratic) in predicting infrared spectra.

Main Methods:

• Analysis of single-coefficient linear scaling methods for harmonic frequencies.
• Development and evaluation of a two-parameter polynomial scaling model.
• Parameterization and assessment of a single-parameter quadratic scaling model.

Main Results:

• Single-coefficient linear scaling methods exhibit systematic overcorrection of low frequencies and undercorrection of high frequencies.
• A two-parameter polynomial model provides significantly improved spectral predictions without regional bias.
• A single-parameter quadratic model offers a balance, minimizing overcorrection with only a slight reduction in predictive power.

Conclusions:

• The intrinsic accuracy of simple linear scaling for infrared spectra is limited.
• More sophisticated scaling models, such as the two-parameter polynomial approach, offer superior accuracy and reduced bias in spectral simulations.
• A quadratic scaling model presents a viable alternative for balancing accuracy and predictive power.