School of Chemistry, The University of Sydney, Sydney, NSW 2006, Australia.
J Chem Phys. 2011 Dec 28;135(24):244110. doi: 10.1063/1.3671386.
We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with tendencies towards double welled potentials. In these bipartite systems, the von Neumann entropy of the reduced density matrix is used to quantify the electron-vibration entanglement for the lowest two vibronic wavefunctions obtained from a model Hamiltonian based on coupled harmonic diabatic potential-energy surfaces. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local maxima). However, in this region two distinct types of density and entanglement profiles are found: one type arises purely from the degeneracy of energy levels in the two potential wells and is destroyed by slight asymmetry, while the other arises through strong interactions between the diabatic levels of each well and is relatively insensitive to asymmetry. These two distinct types are termed fragile degeneracy-induced entanglement and persistent entanglement, respectively. Six classic molecular systems describable by two diabatic states are considered: ammonia, benzene, BNB, pyridine excited triplet states, the Creutz-Taube ion, and the radical cation of the "special pair" of chlorophylls involved in photosynthesis. These chemically diverse systems are all treated using the same general formalism and the nature of the entanglement that they embody is elucidated.
我们考虑了具有双势阱倾向的分子中电子和振动自由度的量子纠缠。在这些双体系统中，使用约化密度矩阵的冯·诺依曼熵来量化从基于耦合谐波非绝热势能面的模型哈密顿量得出的最低两个振子波函数的电子-振动纠缠。只有在基态振子态的密度分布呈双峰（即包含两个独立的局部最大值）的区域中才会发现显著的纠缠。然而，在该区域中发现了两种不同类型的密度和纠缠分布：一种类型纯粹是由两个势阱中能级的简并引起的，并且由微小的不对称性破坏，而另一种类型则是通过每个势阱的非绝热能级之间的强烈相互作用产生的，并且对不对称性相对不敏感。这两种不同的类型分别称为脆弱的简并诱导纠缠和持久的纠缠。考虑了六个可以用两个非绝热态描述的经典分子系统：氨、苯、BNB、吡啶激发三重态、Creutz-Taube 离子和光合作用中涉及的叶绿素“特殊对”的自由基阳离子。这些化学多样性的系统都使用相同的一般形式进行处理，并阐明了它们所体现的纠缠的性质。
