电子波函数的多项式逼近
Polynomial Approximations of Electronic Wave Functions
摘要：
这项工作完成了构建纯代数版本的非线性量子化学理论的方法。它表明，在这些方法的心脏有谎言某些代数在他们的定义接近著名的Clifford代数，但在他们的性质完全不同。这些代数最重要的量子化学性质是：对于固定数量的电子，Fock空间的相应扇区成为交换代数，其理想由Hartree-Fock参考态的激发阶确定。该代数的商也可以被赋予交换代数结构，商Schr{<$}dinger方程正是耦合簇型方程.在上述代数乘法的可能的计算机实现进行了说明。用具体例子说明了组态相互作用波函数不同多项式近似的性质。讨论了无限分离子系统代数在联合系统代数中的嵌入问题
英文摘要：
This work completes the construction of purely algebraic version of the theory of non-linear quantum chemistry methods. It is shown that at the heart of these methods there lie certain algebras close in their definition to the well-known Clifford algebra but quite different in their properties. The most important for quantum chemistry property of these algebras is the following : for a fixed number of electrons the corresponding sector of the Fock space becomes a commutative algebra and its ideals are determined by the order of excitations from the Hartree-Fock reference state. Quotients of this algebra can also be endowed with commutative algebra structures and quotient Schr{ö}dinger equations are exactly the couple cluster type equations. Possible computer implementation of multiplication in the aforementioned algebras is described. Quality of different polynomial approximations of configuration interaction wave functions is illustrated with concrete examples. Embedding of algebras of infinitely separated subsystems in algebra of the united system is discussed
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