AI 中文总结
该研究将RPA推广至含Jastrow关联因子三体相互作用的非厄米TC哈密顿量，提出TC-dRPA与TC-RPAx方法，计算原子和小分子的基态关联能及垂直激发能，发现TC处理可大幅提升基态关联能计算精度，为基态势能研究提供高效方法。
AI 中文摘要
我们将随机相位近似（RPA）推广到非厄米跨关联（TC）哈密顿量，该哈密顿量明确包含由Jastrow关联因子产生的三体相互作用。我们同时考虑直接RPA（dRPA）和含交换的RPA（RPAx），将得到的TC-dRPA和TC-RPAx方法应用于计算原子（氦He和氖Ne）及小分子（水H₂O、氨NH₃、甲烷CH₄、甲醛H₂CO）的基态关联能与垂直激发能。对于基态关联能，TC处理大幅提升精度并加速基组收敛，与常规RPA计算相比误差降低近一个数量级；相比之下，其对垂直激发能仅产生微小提升，我们将这一有限效果归因于Jastrow因子的基态优化未充分捕捉激发态的独特电子特征。这些结果确立了TC-RPA是一种精确且计算高效的基态势能方法，同时强调需针对激发态进行态特异性Jastrow优化以实现可靠描述。
英文摘要
We extend the random-phase approximation (RPA) to the non-Hermitian transcorrelated (TC) Hamiltonian, which explicitly includes three-body interactions generated by a Jastrow correlation factor. We consider both the direct RPA (dRPA) and RPA with exchange (RPAx). We apply the resulting TC-dRPA and TC-RPAx methods to calculate ground-state correlation energies and vertical excitation energies for atoms (\ce{He} and \ce{Ne}) and small molecules (\ce{H2O}, \ce{NH3}, \ce{CH4}, and \ce{H2CO}). For ground-state correlation energies, the TC treatment substantially improves accuracy and accelerates basis set convergence, reducing errors by nearly an order of magnitude relative to conventional RPA calculations. By contrast, it yields only marginal improvements in vertical excitation energies. We attribute this limited effect to the ground-state optimization of the Jastrow factor, which does not adequately capture the distinct electronic character of excited states. These results establish TC-RPA as an accurate and computationally efficient approach to ground-state energetics, while highlighting the need for state-specific Jastrow optimization to achieve reliable descriptions of excited states.
Comments14 pages, 2 figures (Supporting Information available)
