Department of Chemistry and Chemical Biology, Harvard University Cambridge, MA, USA.
Department of Chemistry, The University of Notre Dame South Bend, IN, USA.
Front Chem. 2013 Oct 25;1:26. doi: 10.3389/fchem.2013.00026. eCollection 2013.
Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.
费曼和希布斯首次变分确定了一个有效势，其相关的经典正则系综近似于精确的量子配分函数。我们研究了在局部势和匹配精确量子平衡密度和配分函数的有效经典势之间存在映射的可能性。这种映射的有用性在于它能够方便地改进用于经典采样的玻恩-奥本海默势。我们证明了这样的映射是唯一的，并且必须存在。为了探索将此结果用于改进经典分子力学的可行性，我们从随机生成的一维势/有效势对的库中生成映射，然后在独立的测试问题上评估其性能。我们还将该映射应用于模拟液氢，发现所得的径向对分布函数与路径积分蒙特卡罗模拟吻合良好。该技术的惊人可访问性和可转移性表明，这是一种定量调整玻恩-奥本海默势的方法，其动机与密度泛函理论的强大思想和近似相似。
