Cvitaš Marko T, Althorpe Stuart C
Department of Physical Chemistry, Ruđer Bošković Institute , Bijenička Cesta 54, 10000 Zagreb, Croatia.
Department of Chemistry, University of Cambridge , Lensfield Road, Cambridge CB2 1EW, United Kingdom.
J Chem Theory Comput. 2016 Feb 9;12(2):787-803. doi: 10.1021/acs.jctc.5b01073. Epub 2016 Jan 26.
The recently developed ring-polymer instanton (RPI) method [J. Chem. Phys. 2011, 134, 054109] is an efficient technique for calculating approximate tunneling splittings in high-dimensional molecular systems. The key step is locating the instanton tunneling-path at zero temperature. Here, we show that techniques previously designed for locating instantons in finite-temperature rate calculations can be adapted to the RPI method, where they become extremely efficient, reducing the number of potential energy calls by 2 orders of magnitude. We investigate one technique that employs variable time steps to minimize the action integral, and two that employ equally spaced position steps to minimize the abbreviated (i.e., Jacobi) action integral, using respectively the nudged elastic band (NEB) and string methods. We recommend use of the latter because it is parameter-free, but all three methods give comparable efficiency savings. Having located the instanton pathway, we then interpolate the instanton path onto a fine grid of imaginary time points, allowing us to compute the fluctuation prefactor. The crucial modification needed to the original finite-temperature algorithms is to allow the end points of the zero-temperature instanton path to describe overall rotations, which is done using a standard quaternion algorithm. These approaches will allow the RPI method to be combined effectively with expensive potential energy surfaces or on-the-fly electronic structure methods.
最近开发的环形聚合物瞬子（RPI）方法[《化学物理杂志》2011年，第134卷，054109]是一种计算高维分子系统中近似隧穿分裂的有效技术。关键步骤是在零温度下确定瞬子隧穿路径。在这里，我们表明，先前为在有限温度速率计算中定位瞬子而设计的技术可以适用于RPI方法，在该方法中它们变得极其高效，将势能调用次数减少了2个数量级。我们研究了一种采用可变时间步长来最小化作用积分的技术，以及另外两种分别使用推挤弹性带（NEB）和弦方法、采用等间距位置步长来最小化简化（即雅可比）作用积分的技术。我们推荐使用后者，因为它无需参数，但所有三种方法在效率提升方面相当。确定瞬子路径后，我们将瞬子路径插值到虚时间点的精细网格上，从而能够计算涨落预因子。对原始有限温度算法所需的关键修改是允许零温度瞬子路径的端点描述整体旋转，这通过标准四元数算法来实现。这些方法将使RPI方法能够有效地与昂贵的势能面或实时电子结构方法相结合。
