基于双正交轨道技术的价键计算方法

The proposal of this project is to study the applications of biorthogonal orbitals in valence bond (VB) theory. In recent years, the application of the nonorthogonal orbital based N-body reduced density matrices in VB theory has been extensively explored, as a result of which the efficient implementation of many classical VB methods become feasible. By using the tensor analysis formulism and the nonorthogonal orbital based second quantization, the methodology development of VB theory becomes more and more convenient. In the tensor analysis, the nonorthogonal orbitals and its contravariant basis expand the same single-particle space. These two sets of orbitals form the so-called biorthogonal sets. Inasmuch as the two sets of orbitals are orthonormal to each other mutually, the introduction of biorthogonal orbitals will improve the efficient of the classical VB calculation. Henceforth, this project will extend the research field of VB theory to more complicated chemical systems.

本项目将开展基于双正交轨道技术的价键计算方法研究。近年来，随着非正交约化密度矩阵在价键理论方法研究 的深入，经典价键方法的高效程序实现已具备可行的理论基础。结合张量分析工具和非正交轨道的二次量子化，价键理论方法的发展也越来越方便。在张量分析中，非正交轨道和它的逆变基矢展开同样的线性空间。两者间关系有如正交轨道那样有简单的双正交性质。为此双正交轨道的引入可提高价键计算的效率，同时项目拟开展的方法研究成果将保留价键理论化学图像清晰易于定性解释化学现象，从而有望将价键理论的应用研究领域拓展到复杂体系的量子化学计算。

本项目自2017年实施以来，根据研究计划开展了基于双正交轨道技术的价键计算方法、算法研究，提出了基于Seniority数的多组态波函数的倒易变换算法；提出了基于Seniority数（Ω）截断的价键自洽场(snVBSCF)方法的更高效计算方法；提出了直接构造电荷定域透热态的价键块对角化（VBBDA）方法；提出了一般向量物理可观察量下从绝热态到透热态的（Adiabatic-To-Diabatic, ATD）变换公式；实现了上述方法算法的程序化进而颁布了更新版本的XMVB程序，并应用项目发展的方法和算法开展了电子转移、典型双自由基单三重态垂直激发能等的计算研究。本项目发表了10篇相关学术论文。