Solving the Problem of Electron-Vibrational-Rotational Energy Levels of a Polyatomic Molecule of Arbitrary Structure in Generalized Coordinates

Gribov L. A.

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Solving the Problem of Electron-Vibrational-Rotational Energy Levels of a Polyatomic Molecule of Arbitrary Structure in Generalized Coordinates

机译：求解广义坐标中任意结构多元素的电子振动旋转能量水平的问题

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In classical mechanics, the problems of the motion of objects with many degrees of freedom are formulated and solved using generalized coordinates rather than Cartesian coordinates. It is shown that a similar approach is also applicable to quantum mechanics. In both cases, the problem statement requires introduction of the potential function in appropriate coordinates and construction of the matrix of kinematic coefficients as a part of the classical expression of kinetic energy in the momentum representation. The possibility of the same problem statement is consistently discussed for the energy levels of polyatomic molecules. Some examples of its solution using generalized coordinates are provided.

机译：在古典力学中，使用广义坐标而不是笛卡尔坐标制定和解决了具有多种自由度的物体运动的问题。结果表明，类似的方法也适用于量子力学。在这两种情况下，问题陈述需要在适当的坐标和施工中引入运动系数的基质的潜在功能，作为动能在动量表示中动能的经典表达的一部分。对于多原子分子的能量水平，始终讨论相同问题陈述的可能性。提供了使用广义坐标的其解决方案的一些例子。

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来源
《Journal of structural chemistry》 |2019年第3期|共9页
作者
Gribov L. A.;
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作者单位

Russian Acad Sci Vernadsky Inst Geochem &

Analyt Chem Moscow Russia;

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原文格式 PDF
正文语种 eng
中图分类结构化学;
关键词
quantum theory of molecules; generalized coordinates; energy levels;

机译：量子分子理论;概括的坐标;能量水平;

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专利

1. Solving the Problem of Electron-Vibrational-Rotational Energy Levels of a Polyatomic Molecule of Arbitrary Structure in Generalized Coordinates [J] . Gribov L. A. Journal of structural chemistry . 2019,第3期

机译：求解广义坐标中任意结构多元素的电子振动旋转能量水平的问题
2. Computing rovibrational levels of polyatomic molecules with polyspherical coordinates and a contracted basis built with a K-independent vibrational primitive basis [J] . Xiao-Gang Wang, Tucker Carrington Jr Molecular physics . 2013,第14a15期

机译：计算具有多球坐标的多原子分子的振动水平，以及利用与K无关的振动原始基础建立的收缩基础
3. Using a nondirect product discrete variable representation for angular coordinates to compute vibrational levels of polyatomic molecules [J] . Wang XG, Carrington T The Journal of Chemical Physics . 2008,第19期

机译：使用角坐标的非直接乘积离散变量表示来计算多原子分子的振动能级
4. Direct Solver in Cartesian and Generalized Coordinate Systems for Solving Rarefied Flows of Gases of Arbitrary Statistics [C] . Bagus Putra Muljadi, Jaw-Yen Yang AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition . 2013

机译：直角坐标系和广义坐标系中的直接求解器，用于求解任意统计气体的稀疏流
5. FEMVib, an ab initio multi-dimensional solver for probing vibrational dynamics in polyatomic molecules and free radicals [D] . Xu, Dong 2008

机译：FEMVib，从头开始的多维求解器，用于探测多原子分子和自由基中的振动动力学
6. Some studies on generalized coordinate sets for polyatomic molecules [O] . Wenjin Li, Ao Ma -1

机译：多原子分子广义坐标集的一些研究
7. Tentatively Standardized Symmetry Coordinates for Vibrations of Polyatomic Molecules. XII. Some Planar Five-Membered Ring Structures. [O] . B. N. Cyvin, S. J. Cyvin, R. Stølevik 1968

机译：暂定标准化对称性对称性的多元素振动坐标。 XII。一些平面五元环形结构。
8. New Ro-Vibrational Kinetic Energy Operators using Polyspherical Coordinates for Polyatomic Molecules [R] . Schwenke, D. W. 2002

机译：利用多球坐标的多原子分子新型Ro-振动动能算子

Solving the Problem of Electron-Vibrational-Rotational Energy Levels of a Polyatomic Molecule of Arbitrary Structure in Generalized Coordinates

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