用于非线性波函数方程鲁棒延拓的二阶导数修正FANPT
Second-Derivative-Corrected FANPT for Robust Continuation of Nonlinear Wavefunction Equations
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中文总结 AI 辅助
本研究提出二阶导数修正的FANPT方法，在保留原响应矩阵结构的同时纳入主导非线性响应，经测试可减小参数偏差、抑制参数空间大幅偏移，提升了FANPT作为非线性波函数方程延拓策略的可靠性。
中文摘要 AI 辅助
我们提出了柔性N体微扰理论（FANPT）的二阶导数修正扩展方法，用于求解非线性柔性N体组态相互作用（FANCI）波函数方程。原始的准线性FANPT近似忽略了行列式重叠相对于波函数参数的二阶及更高阶导数；本工作保留了重叠海森矩阵，仅忽略三阶及更高阶参数导数，从而在保留原始FANPT公式所用响应矩阵结构的同时，纳入了波函数近似的主导非线性响应。新增项仅通过响应方程的常数向量引入，并在FanPy/FANCI框架中针对耦合簇波函数实现。我们在氢化锂分子、铍插入H₂的体系上测试了该新近似，采用STO-6G基组下的 seniority 限制耦合簇波函数。二阶导数修正的主要优势在于，它能为绝热连接下一个点的投影FANCI方程求解提供更优的初始猜测；通过比较FANPT传播的参数与相同λ值下独立优化的FANCI参数可验证该改进。对于非线性耦合簇近似，尤其是使用较大λ步长时，修正后的近似减小了相同λ下的参数偏差，抑制了参数空间的大幅偏移。这些结果表明，主导非线性重叠修正提升了FANPT作为非线性波函数方程延拓策略的可靠性。
英文摘要
We present a second-derivative-corrected extension of the Flexible Ansatz for N-body Perturbation Theory (FANPT) for solving nonlinear Flexible Ansatz for N-body Configuration Interaction (FANCI) wavefunction equations. The original quasilinear FANPT approximation neglects second- and higher-order derivatives of the determinant overlap with respect to wavefunction parameters. In this work, we retain the overlap Hessian and neglect only third- and higher-order parameter derivatives, thereby including the leading nonlinear response of the wavefunction ansatz while preserving the same response-matrix structure used in the original FANPT formulation. The resulting additional terms enter only through the constant vector of the response equations and are implemented for coupled-cluster wavefunctions in the FanPy/FANCI framework. The new approximation is tested on the Lithium Hydride molecule and the insertion of Beryllium into H$_2$ using seniority-restricted coupled-cluster wavefunctions in the STO-6G basis. The main advantage of the second-derivative correction is that it provides a better initial guess for solving the projected FANCI equations at the next point along the adiabatic connection. This improvement is diagnosed by comparing the FANPT-propagated parameters with the independently optimized FANCI parameters at the same value of $λ$. For nonlinear coupled-cluster ansatzes, especially when larger $λ$-steps are used, the corrected approximation reduces the same-$λ$ parameter deviations and suppresses large parameter-space excursions. These results show that the leading nonlinear overlap correction improves the reliability of FANPT as a continuation strategy for nonlinear wavefunction equations.
