Mulliken Center for Theoretical Chemistry, Institute of Physical and Theoretical Chemistry, University of Bonn, Beringstr. 4, 53115 Bonn, Germany.
J Chem Theory Comput. 2021 Mar 9;17(3):1701-1714. doi: 10.1021/acs.jctc.0c01306. Epub 2021 Feb 8.
The calculation of harmonic vibrational frequencies (HVF) to interpret infrared (IR) spectra and to convert molecular energies to free energies is one of the essential steps in computational chemistry. A prerequisite for accurate thermostatistics so far was to optimize the molecular input structures in order to avoid imaginary frequencies, which inevitably leads to changes in the geometry if different theoretical levels are applied for geometry optimization and frequency calculations. In this work, we propose a new method termed single-point Hessian (SPH) for the computation of HVF and thermodynamic contributions to the free energy within the modified rigid-rotor-harmonic-oscillator approximation for general nonequilibrium molecular geometries. The key ingredient is the application of a biasing potential given as Gaussian functions expressed with the root-mean-square-deviation (RMSD) in Cartesian space in order to retain the initial geometry. The theory derived herein is generally applicable to quantum mechanical (QM), semiempirical QM, and force-field (FF) methods. Besides a detailed description of the underlying theory including the important back-correction of the biased HVF, the SPH approach is tested for reaction paths, molecular dynamics snapshots of crambin, and supramolecular association free energies in comparison to high-level density functional theory (DFT) values. Furthermore, the effect on IR spectra is investigated for organic dimers and transition-metal complexes revealing improved spectra at low theoretical levels. On average, DFT reference free energies are better reproduced by the newly developed SPH scheme than by conventional calculations on freely optimized geometries or without any relaxation.
计算谐振动频率（HVF）以解释红外（IR）光谱并将分子能量转换为自由能是计算化学中的基本步骤之一。迄今为止，精确统计力学的一个前提条件是优化分子输入结构，以避免虚频，而如果为几何优化和频率计算应用不同的理论水平，则不可避免地会导致几何形状发生变化。在这项工作中，我们提出了一种新方法，称为单点 Hessian（SPH），用于计算 HVF 和热力学对自由能的贡献，该方法在一般非平衡分子几何形状下应用修正的刚性转子谐振荡器近似。关键要素是应用偏置势，该偏置势表示为具有均方根偏差（RMSD）的笛卡尔空间中的高斯函数，以保留初始几何形状。本文推导的理论通常适用于量子力学（QM）、半经验 QM 和力场（FF）方法。除了详细描述基本理论，包括偏置 HVF 的重要反向校正之外，还针对反应路径、克拉明分子动力学快照和超分子缔合自由能进行了 SPH 方法测试，与高精度密度泛函理论（DFT）值进行了比较。此外，还研究了它对 IR 光谱的影响，结果表明在低理论水平下可以改善有机二聚体和过渡金属配合物的光谱。平均而言，新开发的 SPH 方案比传统的自由优化几何或不进行任何松弛的计算更能重现 DFT 参考自由能。
