标题： 局部分子场理论的变分公式 显示英文标题

标题： Variational Formulation of Local Molecular Field Theory

摘要： 在本说明中，我们表明Weeks等人提出的局部分子场理论可以重新推导为近似亥姆霍兹自由能的极值问题。使用得到的自由能作为经典流体密度泛函，会得到一种隐式溶剂方法，其形式与Borgis等人提出的分子密度泛函理论相同，但具有'理想'自由能项的显式公式。这个新的理想自由能项可以从仅具有短程相互作用的溶剂的全原子分子动力学计算得出。使该理论有效的关键假设是所有平滑（因此是长程）能量函数遵循高斯统计。这实际上是针对仅具有短程相互作用的“参考”流体的扰动的随机相位近似。这一假设足以证明自洽的LMF过程最小化了一个新的密度泛函，其“理想”自由能是在特定参考哈密顿量下的分子系统，而不是传统密度泛函中的非相互作用气体。将这个新的泛函集成到现有软件中应该简单且稳健。 显示英文摘要

摘要： In this note, we show that the Local Molecular Field theory of Weeks et. al. can be re-derived as an extremum problem for an approximate Helmholtz free energy. Using the resulting free energy as a classical, fluid density functional yields an implicit solvent method identical in form to the Molecular Density Functional theory of Borgis et. al., but with an explicit formula for the 'ideal' free energy term. This new expression for the ideal free energy term can be computed from all-atom molecular dynamics of a solvent with only short-range interactions. The key hypothesis required to make the theory valid is that all smooth (and hence long-range) energy functions obey Gaussian statistics. This is essentially a random phase approximation for perturbations from a short-range only, 'reference,' fluid. This single hypothesis is enough to prove that the self-consistent LMF procedure minimizes a novel density functional whose 'ideal' free energy is the molecular system under a specific, reference Hamiltonian, as opposed to the non-interacting gas of conventional density functionals. Implementation of this new functional into existing software should be straightforward and robust.