The interaction of electronic spin and molecular vibrations mediated by spin–orbit coupling governs spin relaxation in molecular qubits. We derive an extended molecular spin Hamiltonian that includes both adiabatic and non-adiabatic spin-dependent interactions, and we implement the computation of its matrix elements using state-of-the-art density functional theory. The new molecular spin Hamiltonian contains a novel spin–vibrational orbit interaction with a non-adiabatic origin, together with the traditional molecular Zeeman and zero-field splitting interactions with an adiabatic origin. The spin–vibrational orbit interaction represents a non-Abelian Berry curvature on the ground-state electronic manifold and corresponds to an effective magnetic field in the electronic spin dynamics. We further develop a spin relaxation rate model that estimates the spin relaxation time via the two-phonon Raman process. An application of the extended molecular spin Hamiltonian together with the spin relaxation rate model to Cu(II) porphyrin, a prototypical S = 1/2 molecular qubit, demonstrates that the spin relaxation time at elevated temperatures is dominated by the non-adiabatic spin–vibrational orbit interaction. The computed spin relaxation rate and its magnetic field orientation dependence are in excellent agreement with experimental measurements.

中文翻译：

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分子量子位中新型非绝热自旋弛豫机制

自旋轨道耦合介导的电子自旋和分子振动的相互作用控制着分子量子位中的自旋弛豫。我们推导出一个扩展的分子自旋哈密顿量，其中包括绝热和非绝热自旋相关相互作用，并使用最先进的密度泛函理论实现其矩阵元素的计算。新的分子自旋哈密顿量包含一种新颖的非绝热起源的自旋振动轨道相互作用，以及传统的分子塞曼和绝热起源的零场分裂相互作用。自旋振动轨道相互作用代表基态电子流形上的非阿贝尔贝里曲率，对应于电子自旋动力学中的有效磁场。我们进一步开发了一个自旋弛豫率模型，通过双声子拉曼过程估计自旋弛豫时间。将扩展分子自旋哈密顿量与自旋弛豫率模型一起应用于 Cu(II) 卟啉（一种典型的 S = 1/2 分子量子位）表明，高温下的自旋弛豫时间主要由非绝热自旋–振动轨道相互作用。计算出的自旋弛豫率及其磁场方向依赖性与实验测量结果非常一致。