Recently, the adiabatic connection (AC) formula for the electron correlation energy has been proposed for a broad class of multireference wave functions (Pernal, K. Electron Correlation from the Adiabatic Connection for Multireference Wave Functions. Phys. Rev. Lett. 2018, 120, 013001). We show that the AC formula used together with the extended random phase approximation (ERPA) can be efficiently applied to complete active space (CAS) wave functions to recover the remaining electron correlation. Unlike most of the perturbation theory approaches, the proposed AC-CAS method does not require construction of higher than two-electron reduced density matrices, which offers an immediate computational saving. In addition, we show that typically the AC-CAS systematically reduces the errors of both the absolute value of energy and of the energy differences (energy barrier) upon enlarging active spaces for electrons and orbitals. AC-CAS consistently gains in accuracy from including more active electrons. We also propose and study that the performance of the AC0 approach resulting from the first-order expansion of the AC integrand at the coupling constant equal to 0. AC0 avoids solving the full ERPA eigenequation, replacing it with small-dimension eigenproblems, while retaining good accuracy of the AC-CAS method. Low computational cost, compared to AC-CAS or perturbational approaches, makes AC0 the most efficient ab initio approach to capturing electron correlation for the CAS wave functions.

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来自绝热连接形式主义的相关能量，用于完整的有源空间波函数

最近，电子相关能量绝热连接（AC）式已经提出了一大类多引用的波函数（Pernal，从绝热连接于多参考波函数。物理评论快报。K.电子关联2018，120，013001）。我们表明，与扩展的随机相位近似（ERPA）一起使用的AC公式可以有效地应用于完整的有源空间（CAS）波函数，以恢复剩余的电子相关性。与大多数扰动理论方法不同，所提出的AC-CAS方法不需要构造高于两电子的密度减小矩阵，从而可以立即节省计算成本。另外，我们表明，通常，AC-CAS在扩大电子和轨道的有效空间时，会系统地减少能量绝对值和能量差（能量垒）的误差。AC-CAS通过包含更多的活性电子，不断提高精度。我们还提出并研究，在耦合常数等于0的条件下，由AC积分的一阶展开导致的AC0方法的性能。AC0避免解决完整的ERPA特征方程，而用小尺寸特征问题代替，同时又保留了良好的特征。 AC-CAS方法的准确性。与AC-CAS或微扰方法相比，较低的计算成本使AC0效率最高从头开始为CAS波函数捕获电子相关性的方法。