显关联全等变换哈密顿量的无限阶图解求和法
Infinite-order diagrammatic summation approach to explicitly correlated congruent transformed Hamiltonian
摘要：
提出了显关联同余变换哈密顿量（CTH）的恒等式分解方法。与多电子哈密顿量的全等变换相关的主要挑战之一是产生三、四、五和六个粒子算符。全等变换的成功应用需要多粒子算子的有效实现。本文提出了用单位同余变换哈密顿方法处理多粒子算符的方法。利用恒等式分解将显关联算子投影到N粒子有限基上，避免了多粒子算子的显式计算。单粒子态通过Hartee-Fock计算得到，然后用于构建多粒子态。通过发展部分无限阶（PIOS）图解求和技术，解决了恒等式分解有限性的局限性。在PIOS方法中，投影全等变换哈密顿量的矩阵元用图解法表示，并将一个图解子集求和到无穷阶。将RI-CTH和RI-CTH-PIOS方法应用于等电子系列的10电子体系（Ne，HF，H_2O，NH_3，CH_4），并与CISD和CCSD（T）计算结果进行了比较。结果表明，在相同的基组下，RI-CTH-PIOS的能量比CISD和CCSD（T）的能量低。
英文摘要：
A resolution of identity approach to explicitly correlated congruent transformed Hamiltonian (CTH) is presented. One of the principle challenges associated with the congruent transformation of the many-electron Hamiltonian is the generation of three, four, five, and six particle operators. Successful application of the congruent transformation requires efficient implementation of the many-particle operators. In this work, we present the resolution of identity congruent transformed Hamiltonian (RI-CTH) method to handle many-particle operators. The resolution of identity was used to project the explicitly correlated operator in a N-particle finite basis to avoid explicit computation of the many-particle operators. Single-particle states were obtained by performing Hartee-Fock calculations, which were then used for construction of many-particle states. The limitation of the finite nature of the resolution of identity was addressed by developing partial infinite order (PIOS) diagrammatic summation technique. In the PIOS method, the matrix elements of the projected congruent transformed Hamiltonian was expressed in terms of diagrammatic notation and a subset of diagrams were summed up to infinite order. The RI-CTH and RI-CTH-PIOS methods were applied to isoelectronic series of 10-electron systems (Ne,HF,H2O,NH3,CH4) and results were compared with CISD and CCSD(T) calculations. One of the key results from this work is that for identical basis set, the RI-CTH-PIOS energies are lower than CISD and CCSD(T) values.
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