AI 中文总结
该研究提出QBE-SCF方法，利用动力学弛豫解决平均场奇异性，无需多参考波函数即可恢复关联绝热表面，为电子结构计算提供新途径。
AI 中文摘要
我们提出了一种用于分子电子结构的量子玻尔兹曼方程自洽场（QBE-SCF）形式，其中单电子约化密度矩阵在固定的高斯轨道基组中传播，并通过Bhatnagar-Gross-Krook碰撞算子弛豫至由瞬时Fock矩阵定义的费米-狄拉克平衡态。在稳态下，收敛的密度矩阵和Fock矩阵满足[F,P]=0，即Hartree-Fock条件。零温平衡目标退化为整数Aufbau投影算子，而阻尼碰撞算子确保稳态密度矩阵不一定是幂等的。这种动力学特性使其具备解决平均场奇异性的双重能力：对于空间简并情况（如H₃对称解离），零温动力学遍历性会将活性空间分数化，从而恢复GVB极限；对于BeH₂中的锥形交叉以及H₄结构畸变（D₂h→D₄h→D₂h），有限温度熵正则化可从实值单参考密度中恢复关联绝热表面。通过在基组层级间保持稳定的数值收敛性，且无需多参考波函数即可解决静态关联问题，这些结果确立了动力学弛豫是单参考电子结构与量子统计力学的一种综合方法。
英文摘要
We present a Quantum Boltzmann Equation self-consistent-field (QBE-SCF) formulation for molecular electronic structure in which the one-electron reduced density matrix is propagated in an atomic orbital basis and relaxed by a Bhatnagar-Gross-Krook collision operator toward a Fermi-Dirac equilibrium defined by the instantaneous Fock matrix. At stationarity, the converged density and Fock matrices satisfy $[\mathbf{F},\mathbf{P}]=0$, the Hartree-Fock condition. While the zero-temperature equilibrium target reduces to the integer Aufbau projector, the damped collision operator ensures the steady-state density matrix is not necessarily idempotent. This kinetic relaxation affords a dual pathway to resolve mean-field singularities. For spatial degeneracies, such as H$_3$ symmetric dissociation, zero-temperature kinetic ergodicity fractionalizes the active space to recover the Generalized Valence Bond (GVB) limit. For the conical intersection in BeH$_2$ and the H$_4$ structural distortion ($D_{2h} \rightarrow D_{4h} \rightarrow D_{2h}$), finite-temperature entropic regularization recovers correlated adiabatic surfaces from a real-valued single-reference density. By maintaining stable numerical convergence across basis-set hierarchies and resolving static correlation without multi-reference wavefunctions, these results establish kinetic relaxation as a synthesis of single-reference electronic structure and quantum statistical mechanics.
Comments14 pages, 7 figures. Includes Supplementary Information. Submitted to The Journal of Chemical Physics. Data underlying this study are available at https://doi.org/10.5281/zenodo.21940451
