Uranga-Piña L, Tremblay J C
Facultad de Física, Universidad de la Habana, San Lázaro y L, Vedado, 10400 Havana, Cuba.
Institute for Chemistry and Biochemistry, Freie Universität Berlin, Takustr. 3, D-14195 Berlin, Germany.
J Chem Phys. 2014 Aug 21;141(7):074703. doi: 10.1063/1.4892376.
We investigate the effect of inter-mode coupling on the vibrational relaxation dynamics of molecules in weak dissipative environments. The simulations are performed within the reduced density matrix formalism in the Markovian regime, assuming a Lindblad form for the system-bath interaction. The prototypical two-dimensional model system representing two CO molecules approaching a Cu(100) surface is adapted from an ab initio potential, while the diatom-diatom vibrational coupling strength is systematically varied. In the weak system-bath coupling limit and at low temperatures, only first order non-adiabatic uni-modal coupling terms contribute to surface-mediated vibrational relaxation. Since dissipative dynamics is non-unitary, the choice of representation will affect the evolution of the reduced density matrix. Two alternative representations for computing the relaxation rates and the associated operators are thus compared: the fully coupled spectral basis, and a factorizable ansatz. The former is well-established and serves as a benchmark for the solution of Liouville-von Neumann equation. In the latter, a contracted grid basis of potential-optimized discrete variable representation is tailored to incorporate most of the inter-mode coupling, while the Lindblad operators are represented as tensor products of one-dimensional operators, for consistency. This procedure results in a marked reduction of the grid size and in a much more advantageous scaling of the computational cost with respect to the increase of the dimensionality of the system. The factorizable method is found to provide an accurate description of the dissipative quantum dynamics of the model system, specifically of the time evolution of the state populations and of the probability density distribution of the molecular wave packet. The influence of intra-molecular vibrational energy redistribution appears to be properly taken into account by the new model on the whole range of coupling strengths. It demontrates that most of the mode mixing during relaxation is due to the potential part of the Hamiltonian and not to the coupling among relaxation operators.
我们研究了在弱耗散环境中，模间耦合对分子振动弛豫动力学的影响。模拟是在马尔可夫区域的约化密度矩阵形式体系内进行的，假设系统 - 浴相互作用具有林德布拉德形式。代表两个接近Cu(100)表面的CO分子的典型二维模型系统是根据从头算势能改编的，同时系统地改变双原子 - 双原子振动耦合强度。在弱系统 - 浴耦合极限和低温下，只有一阶非绝热单模耦合项对表面介导的振动弛豫有贡献。由于耗散动力学是非酉的，表象的选择将影响约化密度矩阵的演化。因此，比较了两种用于计算弛豫率和相关算符的替代表象：完全耦合谱基和可分解近似。前者已得到充分确立，并作为求解刘维尔 - 冯·诺伊曼方程的基准。在后者中，定制了一个势能优化离散变量表示的压缩网格基，以纳入大部分模间耦合，而林德布拉德算符表示为一维算符的张量积，以保持一致性。这一过程导致网格大小显著减小，并且相对于系统维度的增加，计算成本的缩放更为有利。发现可分解方法能够准确描述模型系统的耗散量子动力学，特别是态布居的时间演化和分子波包的概率密度分布。新模型在整个耦合强度范围内似乎都能恰当地考虑分子内振动能量重新分布的影响。这表明弛豫过程中的大部分模式混合是由于哈密顿量的势能部分，而不是由于弛豫算符之间的耦合。
