Computational scheme to determine local vibrations of large systems using elongation method

Abstract

Vibration analysis is important to understand the structures and characteristics of biomolecules and materials. It remains a challenge to obtain the vibrational frequencies of large systems using conventional ab initio calculations. Hence, we developed a new calculation scheme for local vibrations using the elongation method (ELG–VIB) at the Hartree–Fock level. Unlike the conventional method, the ELG–VIB method divides the entire system into a frozen region and an active region, and only the Hessian matrix elements of the active region are calculated. Test calculations were performed on model systems to demonstrate the accuracy and efficiency of the ELG–VIB method. The frequencies and Hessian matrix elements determined using the ELG–VIB method were compared with the results of conventional computation. All ELG–VIB frequencies of the (H₂)₁₅ system were in good agreement with the conventional results. Most of the ELG–VIB frequencies of polyethylene (CH₃–(CH₂)₃₈–CH₃) and polyglycine (C₂H₄NO–(C₂H₃NO)₁₆–C₂H₄NO₂) systems were also in good agreement with the conventional results; only a few modes including the vibration of the unit neighboring the frozen region were specific to the ELG–VIB results. The difference in the Hessian matrix elements of the model systems illustrates that the largest discrepancy was in the first unit of the active region (B region), which was directly connected to the frozen region (A region); the end unit (M region) showed the smallest difference. The frequencies of the interactive B region and M region of a larger polyglycine system, C₂H₄NO–(C₂H₃NO)₂₈–C₂H₄NO₂, were also calculated. The results indicate that the ELG–VIB method provides frequencies similar to those calculated using the conventional method for large systems.