使用準確波函數之高精準量子化學方法

Abstract

此計畫提出一個集合高精度計算量子化學技術的發展。這個方法是基於最近被 Nakatsuji 教授所提出之精確波函數的觀念 [J. Chem. Phys. 113, 2949 (2000)]。此方法設計 理念為在化學精度下的量子化學計算，也就是計算誤差小於10−3 千卡/莫耳。這種精度 主要來自正確的分子波函數解析結構，其使用飽合的基底函數當作可擴展的解析函數的 集合，且使用新穎及有效的技術來決定函數係數。本計畫目標為解決現代量子化學最擾 人的問題：計算過程中缺乏可信賴的誤差估計方法。分子波函數正確解析結構考慮所有 的單獨行為且伴隨適當數量的自動生成解析擴展函數，使之可用於在任意精度內計算能 量以及所有用於計算分子性質的能量微分。計算誤差小於10−3 千卡/莫耳應足夠滿足大 多數對於精確波函數、能量，以及分子性質的實際需求。我們希望此計畫能建立一個新 的方向，對於未來數十年的計算量子化學的發展有貢獻，並且同時提供一個實際、精確、 有力的計算工具。

A development of a collection of very accurate computational quantum chemical techniques is proposed. The new approach is based on the concept of the exact wave function introduced recently by Nakatsuji [J. Chem. Phys. 113, 2949 (2000)]. The developed methods are designed to perform quantum chemical calculations with sub-chemical accuracy, i.e., with the computational error smaller than 10−3 kcal/mol. This superb accuracy will be possible owing to a conjunction of the correct analytical structure of the molecular wave functions, use of saturated basis sets given as a self-expandable collection of analytical functions, and novel, efficient techniques of determination the variational coefficients based on the idea of local energy. This project is aimed at solving the most disturbing problem of modern quantum chemistry: lack of reliable estimates of error in the computational process. The correct analytical structure of the molecular wave function that accounts for all its singular behavior together with appropriate number of automatically-generated analytical expansion functions will enable to compute the energies—and consequently all its derivatives needed for calculating molecular properties—with arbitrary accuracy. The error bars of order ±10−3 kcal/mol, suggested here, should be sufficient to satisfy the most stringent practical requirements anticipated for accurate wave functions, energies, and molecular properties. We hope that the proposed research will constitute a new direction of development of quantum chemistry for the next few decades and will simultaneously provide a practical, accurate, and conclusive computational tool available even for novice practitioners in the field.