研究・研究者
研究会・セミナー
| 演 題 | 「Constructing molecular potential energy surfaces with help from invariant theory and computer algebra」 |
|---|---|
| 日 時 | 2008年04月23日(水) 14:30 |
| 講演者 | Bastiaan J. Braams (Emory University, Atlanta, GA) |
| 場 所 | 南実験棟111号室 |
| 概 要 | Analytical fitted potential energy surfaces are a valuable tool for study of reaction dynamics and molecular spectroscopy. In full generality the surface depends on 3N-6 independent coordinates, where N is the number of nuclei, and the construction of such surfaces is a problem of high-dimensional approximation already for small systems, say of 5-9 atoms. For the effective construction of such surfaces we have found it essential to enforce strictly the property of invariance of the surface under permutation of like nuclei; we build this property into the basis of fitting functions expressed in internuclear distances. The construction of these permutationally invariant basis functions (and covariant basis functions for properties such as the dipole moment) is a nontrivial task that cannot well be carried out by hand except for the simplest systems. We rely on computational invariant theory and on the MAGMA computer algebra system to construct suitable bases for each possible molecular permutation symmetry group, and have pursued that approach for systems up to 9 and 10 atoms. Illustrative challenging recent applications in the Bowman group at Emory University include photodissociation of acetaldehyde and spectroscopy of malonaldehyde and the water trimer. In the talk I will describe the mathematical background and highlights of new applications. This work is supported by ONR and USDOE. |
| お問合せ先 | 柳井 毅（理論・計算分子科学研究領域） |
