Abstract

The singular structure of lower vibrational states of the difluorosilylene molecule (up to four total excitation quanta) is studied by expansion of energies of each state into series of the high-order Rayleigh–Schrödinger perturbation theory and analysis of their implicit properties of multiple-valuedness using Padé–Hermite fourth-order approximants. The quartic surface of potential energy in dimensionless normal coordinates is calculated quantum-mechanically at the MP2/cc-pVTZ level. It is shown that one of values of multiple-valued approximants reproduces the variational solution with a high accuracy, while other values (beginning with the fourth polyad) in many cases coincide with energies of other states of the same polyad. The Fermi and Darling–Dennison resonances are analyzed based on facts of coincidence of singular complex branch points of the approximants for mutually interacting states inside a unit circle or near it on the complex plane. It is found that a pair of states can have several coinciding branch points of the solutions (in particular, inside the unit circle). A conclusion is made that this approach is an effective method for the determination of the polyad structure of vibrational states. Calculation parameters necessary for the reproducibility of key results are selected. The calculations are carried out by means of a Fortran-based software package using an arithmetic calculation package with a long mantissa of real numbers (200 digits).

中文翻译：

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二氟甲硅烷基分子的振动共聚体中奇异和共振现象的基本分析

摘要

通过将每个态的能量扩展成一系列高阶瑞利-薛定er摄动理论，并分析它们的多值隐性，研究了二氟甲硅烷基分子的较低振动态（最多四个总激发量子）的奇异结构。使用Padé–Hermite四阶近似值。在MP2 / cc-pVTZ级别以量子力学方式计算无量纲法向坐标中势能的四次表面。可以看出，多值近似值之一可以高精度地再现变分解，而在许多情况下，其他值（从第四多单元开始）与同一多单元的其他状态的能量一致。费米共振和达林-丹尼森共振是基于单位圆内部或单位平面附近相互相互作用的状态的近似值的奇异复数分支点重合的事实进行分析的。发现一对状态可以具有多个一致的解分支点（特别是在单位圆内部）。结论是，该方法是确定振动状态的多元结构的有效方法。选择关键结果可重复性所需的计算参数。借助于基于Fortran的软件包，使用算术计算程序包进行计算，该程序包具有长的实数尾数（200位数字）。发现一对状态可以具有多个一致的解分支点（特别是在单位圆内部）。结论是，该方法是确定振动状态的多元结构的有效方法。选择关键结果可重复性所需的计算参数。借助于基于Fortran的软件包，使用算术计算程序包进行计算，该程序包具有长的实数尾数（200位数字）。发现一对状态可以具有多个一致的解分支点（特别是在单位圆内部）。结论是，该方法是确定振动状态的多元结构的有效方法。选择关键结果可重复性所需的计算参数。借助于基于Fortran的软件包，使用算术计算软件包来进行计算，该软件包具有长的实数尾数（200位数字）。选择关键结果可重复性所需的计算参数。借助于基于Fortran的软件包，使用算术计算程序包进行计算，该程序包具有长的实数尾数（200位数字）。选择关键结果可重复性所需的计算参数。借助于基于Fortran的软件包，使用算术计算程序包进行计算，该程序包具有长的实数尾数（200位数字）。