The Development of a Common and High-Speed Method of Computing Various Kind of Molecular Integrals and Theoretical Study of Iron Porphyrins

在本研究中，发展了两种新的方法，这两种方法对于研究大分子体系的分子结构和化学反应是必不可少的：一种是计算两电子积分和单电子积分及其导数相对于原子坐标的快速计算方法。另一种是一种高效而稳定的寻找含有环状部分的分子的最优结构的方法，任何类型的分子积分都可以从一个满足递推关系的积分可约为基本积分。然后，任何类型的分子积分都可以用递归形式表示，这样就可以进行递归计算，这是众所周知的最有效的计算方法之一。这种寻找最优结构的新方法避免了通常使用的方法中的困难，避免了只优化内部坐标的方法在循环部分发生灾难性变形，以及仅使用笛卡尔坐标的方法的效率低下。该方法稳定有效地优化了环氧乙烷和吡啶的结构，并通过对游离碱卟啉结构的优化，证实了该方法的有效性。

In the present research, two new methods are developed, which are essentially necessary for the theoretical studies of molecular structures and chemical reactions of large molecular systems such as iron porphyrins : one is a high-speed computational method of evaluating two-electron integrals, as well as one-electron intregrals, and their derivatives with respect to atomic coordinates. The other is an efficient and stable method of searching for optimum structures of molecules containing cyclic parts.Any kind of molecular integrals are found to be reducible from an integral termed basic integral which satisfies recurrence relations. Then, any kind of molecular integrals can be expressed in recursive forms, so that one can carry out the recursive computation which is well known as one of the most efficient computational methods. The computations are found to be vectorizable and result in a twenty-eight times faster evaluation of electron repulsion integrals for cyclohexane.The new method of searching for optimum structures aviods the difficulties in the usually used methods ; disastrous deformations occurring at cyclic parts in the method optimizing only the internal coordinates, and inefficiency in the method employing only the Cartesian coordinates. The method is found to result in optimum structures of ethylene oxide and pyridine stably and effeciently, and its usefulness is confirmed by optimizing the structure of a free base porphine.