Department of Chemistry, Southern Methodist University, 3215 Daniel Avenue, Dallas, TX 75275-0314, USA.
J Mol Model. 2013 Jul;19(7):2865-77. doi: 10.1007/s00894-012-1697-4. Epub 2012 Dec 21.
Local vibrational modes can be directly derived from normal vibrational modes using the method of Konkoli and Cremer (Int J Quant Chem 67:29, 1998). This implies the calculation of the harmonic force constant matrix F (q) (expressed in internal coordinates q) from the corresponding Cartesian force constant matrix f (x) with the help of the transformation matrix U = WB (†)(BWB (†))(-1) (B: Wilson's B-matrix). It is proven that the local vibrational modes are independent of the choice of the matrix W. However, the choice W = M (-1) (M: mass matrix) has numerical advantages with regard to the choice W = I (I: identity matrix), where the latter is frequently used in spectroscopy. The local vibrational modes can be related to the normal vibrational modes in the form of an adiabatic connection scheme (ACS) after rewriting the Wilson equation with the help of the compliance matrix. The ACSs of benzene and naphthalene based on experimental vibrational frequencies are discussed as nontrivial examples. It is demonstrated that the local-mode stretching force constants provide a quantitative measure for the C-H and C-C bond strength.
局部振动模式可以使用 Konkoli 和 Cremer 的方法（Int J Quant Chem 67:29, 1998）直接从正则振动模式推导出来。这意味着从相应的笛卡尔力常数矩阵 f (x) 使用变换矩阵 U = WB (†)(BWB (†))(-1) (B: Wilson 的 B 矩阵)来计算谐波力常数矩阵 F (q) (用内部坐标 q 表示)。证明了局部振动模式与矩阵 W 的选择无关。然而，与选择 W = I（I：单位矩阵）相比，选择 W = M (-1)（M：质量矩阵）在数值上具有优势，后者在光谱学中经常使用。借助柔度矩阵重写 Wilson 方程后，可以将局部振动模式以绝热连接方案（ACS）的形式与正则振动模式相关联。讨论了基于实验振动频率的苯和萘的 ACS 作为非平凡的例子。结果表明，局部模式伸缩力常数为 C-H 和 C-C 键强度提供了定量的衡量标准。
