Eraković Mihael, Vaillant Christophe L, Cvitaš Marko T
Department of Physical Chemistry, Rudđđer Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia.
Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.
J Chem Phys. 2020 Feb 28;152(8):084111. doi: 10.1063/1.5145278.
We derive a multidimensional instanton theory for calculating ground-state tunneling splittings in Cartesian coordinates for general paths. It is an extension of the method by Mil'nikov and Nakamura [J. Chem. Phys. 115, 6881 (2001)] to include asymmetric paths that are necessary for calculating tunneling splitting patterns in multi-well systems, such as water clusters. The approach avoids multiple expensive matrix diagonalizations to converge the fluctuation prefactor in the ring-polymer instanton (RPI) method, and instead replaces them by an integration of a Riccati differential equation. When combined with the string method for locating instantons, we avoid the need to converge the calculation with respect to the imaginary time period of the semiclassical orbit, thereby reducing the number of convergence parameters of the optimized object to just one: the number of equally spaced system replicas used to represent the instanton path. The entirety of the numerical effort is thus concentrated in optimizing the shape of the path and evaluating hessians along the path, which is a dramatic improvement over RPI. In addition to the standard instanton approximations, we neglect the coupling of vibrational modes to external rotations. The method is tested on the model potential of malonaldehyde and on the water dimer and trimer, giving close agreement with RPI at a much-reduced cost.
我们推导了一种多维瞬子理论，用于计算笛卡尔坐标系中一般路径的基态隧穿分裂。它是米尔尼科夫和中村[《化学物理杂志》115, 6881 (2001)]方法的扩展，以包括计算多阱系统（如水簇）中的隧穿分裂模式所需的不对称路径。该方法避免了在环聚合物瞬子（RPI）方法中为使涨落前置因子收敛而进行多次昂贵的矩阵对角化，而是用一个里卡蒂微分方程的积分来代替它们。当与用于定位瞬子的弦方法相结合时，我们避免了关于半经典轨道虚时间周期的计算收敛的需要，从而将优化对象的收敛参数数量减少到仅一个：用于表示瞬子路径的等间距系统副本的数量。因此，整个数值工作都集中在优化路径形状和评估沿路径的海森矩阵上，这比RPI有了显著改进。除了标准的瞬子近似外，我们忽略了振动模式与外部旋转的耦合。该方法在丙二醛的模型势以及水二聚体和三聚体上进行了测试，以低得多的成本与RPI取得了密切一致。
