Schuler Manuel J, Hofer Thomas S, Huck Christian W
Theoretical Chemistry Division, Institute of General, Inorganic and Theoretical Chemistry, Center for Chemistry and Biomedicine, University of Innsbruck, Innrain 80-82, A-6020 Innsbruck, Austria.
Phys Chem Chem Phys. 2017 May 17;19(19):11990-12001. doi: 10.1039/c7cp01662j.
The performance of the grid-based Numerov procedure for the prediction of fundamental as well as the first vibrational overtone has been systematically probed for harmonic and anharmonic model systems. In addition to monitor the prediction with respect to the spacing of the potential grid the influence of higher order approximations to the second derivative (i.e. stencils) in Schrödingers equation is evaluated. The latter enable a significant increase of the grid-spacing to achieve results of similar accuracy obtained with smaller stencil sizes. Application to the hydroxyl vibrational mode of methanol, phenol and the natural product thymol in vacuum and carbon tetrachloride predicted wavenumbers within less than 1% of experiment. Due to the highly localised character of the OH-vibration the ad hoc construction of the associated normal mode yields results of similar accuracy than those obtained using the analytical normal modes, effectively eliminating the requirement of an analytical normal mode evaluation of the entire system. This property was shown to be of particular advantage when considering explicit solute-solvent contacts, which have been demonstrated to be superior compared to an implicit representation of solvent effects. The combination of the observed findings (i.e. enlarged grid-spacing due to the application of higher order stencils, construction of localised normal modes) is envisaged to be of particular benefit when investigating localised modes in large systems, such as OH or NH groups in large (bio)macromolecules or solid-state surfaces.
针对谐波和非谐波模型系统，已系统地探究了基于网格的努默罗夫方法在预测基频以及第一振动泛音方面的性能。除了监测关于势网格间距的预测外，还评估了薛定谔方程中二阶导数高阶近似（即模板）的影响。后者能够显著增加网格间距，以获得与较小模板尺寸下相似精度的结果。将其应用于甲醇、苯酚以及天然产物百里酚在真空和四氯化碳中的羟基振动模式时，预测波数与实验值的偏差小于1%。由于OH振动具有高度局域化的特性，相关简正模式的特殊构建产生的结果精度与使用解析简正模式获得的结果相似，有效地消除了对整个系统进行解析简正模式评估的需求。当考虑明确的溶质 - 溶剂接触时，这一特性显示出特别的优势，已证明其比溶剂效应的隐式表示更优越。当研究大系统中的局域模式时，如大（生物）分子或固态表面中的OH或NH基团，所观察到的结果（即由于应用高阶模板而扩大的网格间距、局域化简正模式的构建）的结合预计将特别有益。
