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

在目前的研究中，发展了两种新的方法，这对于分子结构和大分子体系（如铁卟啉）的化学反应的理论研究是必不可少的：一种是在原子坐标下计算双电子积分和单电子积分及其导数的高速计算方法。另一种是一种高效、稳定的寻找含环部分子最佳结构的方法。我们发现，任何类型的分子积分都可以由满足递归关系的称为基本积分的积分来约化。然后，任何类型的分子积分都可以用递归形式表示，从而可以进行递归计算，这是众所周知的最有效的计算方法之一。计算结果是可向性的，计算环己烷的电子斥力积分的速度要快28倍。新的优化结构搜索方法避免了常用方法的困难；仅采用内坐标优化的方法在循环部件上出现了灾难性变形，而仅采用笛卡尔坐标优化的方法效率低下。结果表明，该方法稳定有效地得到了环氧乙烷和吡啶的最佳结构，并通过对游离碱卟啉的结构优化验证了该方法的有效性。

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.