Theoretical studies on superexcited states and photoionization processes of molecules by analytical continuation of Hamiltonian.

利用哈密顿量的解析延拓对分子超激发态和光电离过程进行理论研究。

• 批准号: 13640516
• 负责人: YABUSHITA Satoshi
• 金额: $ 2.37万
• 依托单位: Keio University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640516/
• 关键词: resonance state; Photoionization; Complex coordinate method; derivative basis; STO; GTO; Generic algorithm; Newton-Raphson method; 超励起状態; 自動イオン化; 軌道指数最適化; スピン軌道相互作用; 振動数依存分極率

The purpose of this study is to construct basis sets that are suitable for the complex coordinate method(CCM) and to develop the optimization scheme for the scaling angle θ with the energy gradient method, so that the CCM can be applied to general molecular problems.We first constructed a so-called derivative basis set, with a minimum θ-dependence. In this basis, all the functions have a common orbital exponent. However, since the derivative basis still contains a small θ-dependence, we further applied the variational principle to have the completely optimal scaling angle θ, or equivalently, complex orbital exponents. By applying this method, the flexibility of the basis set is enhanced greatly, thus the resonance energy can be calculated with a smaller number of basis functions than the case of the derivative basis set. We applied both the Genetic Algorithm and the Newton-Raphson method for the optimization.The photoionization cross section can be extracted from the imaginary part of the frequency-dependent polarizability, which is in turn derived as a stationary expression of a functional. We applied this variational principle to the calculation of photoionization cross sections of H atom. Contrary to previous L^2 methods, we could obtain very accurate results with only a few complex basis functions, both STOs and GTOs, suggesting the general applicability.

为了构造适用于复坐标方法（CCM）的基组，并利用能量梯度法对标度角θ进行优化，使CCM能够应用于一般的分子问题，我们首先构造了一个具有最小θ依赖性的导数基组。在此基础上，所有的功能有一个共同的轨道指数。然而，由于导数基仍然包含小的θ依赖性，我们进一步应用变分原理来获得完全最优的标度角θ，或者等价地，复轨道指数。该方法大大增强了基组的灵活性，从而可以用比导数基组更少的基函数计算共振能量。我们采用遗传算法和Newton-Raphson方法进行优化，从频变极化率的虚部中提取光电离截面，并将虚部作为泛函的稳态表达式导出。我们将这一变分原理应用于H原子光电离截面的计算。与以前的L^2方法不同，我们只需要几个复杂的基函数就可以得到非常精确的结果，包括STO和GTO，这表明了该方法的普遍适用性。

项目成果

Theoretical Analysis on the Fundamental and Overtone OH Stretching Spectra of Several Simple Acids and Alcohols

几种简单酸和醇的基波和泛音OH拉伸谱的理论分析

• 发表时间: 2003
• 期刊: J.Phys.Chem.A 107
• 作者: K.Takahashi

K.Miyajima: "Quasi-band electronic structure of V_n(Benzene)_<n+1> clusters"J. Phys. Chem. A. 106. 10777-10781 (2002)

K.Miyajima：“V_n(苯)_<n 1>簇的准带电子结构”J。

Theoretical Study on the Photochromic Reactions of Dithienylethenes; On the role of Conical Intersections

二噻吩乙烯光致变色反应的理论研究；

• 发表时间: 2004
• 期刊: J. Am. Chem. Soc. 126
• 作者: Y.Asano

Theoretical Analysis on the Fundamental and Overtone OH Stretching Spectra of Several Simple Acides and Alcohols

几种简单酸和醇的基波和泛音OH拉伸谱的理论分析

• 发表时间: 2003
• 期刊: J. Phys. Chem.A 107
• 作者: K.Takahashi

Y.Asano: "Theoretical study on novel quantum yields of dithienylethenes cyclization reactions in crystals"THEOCHEM(J.Molec.Struct.). 625. 227-234 (2003)

Y.Asano：“晶体中二噻吩乙烯环化反应的新型量子产率的理论研究”THEOCHEM（J.Molec.Struct.）。