Nerantzis Dimitrios, Adjiman Claire S
Department of Chemical Engineering, Imperial College London, London, United Kingdom.
J Glob Optim. 2017;67(3):451-474. doi: 10.1007/s10898-016-0430-8. Epub 2016 May 5.
Transition states (index-1 saddle points) play a crucial role in determining the rates of chemical transformations but their reliable identification remains challenging in many applications. Deterministic global optimization methods have previously been employed for the location of transition states (TSs) by initially finding all stationary points and then identifying the TSs among the set of solutions. We propose several regional tests, applicable to general nonlinear, twice continuously differentiable functions, to accelerate the convergence of such approaches by identifying areas that do not contain any TS or that may contain a unique TS. The tests are based on the application of the interval extension of theorems from linear algebra to an interval Hessian matrix. They can be used within the framework of global optimization methods with the potential of reducing the computational time for TS location. We present the theory behind the tests, discuss their algorithmic complexity and show via a few examples that significant gains in computational time can be achieved by using these tests.
过渡态（索引为1的鞍点）在确定化学转化速率方面起着关键作用，但在许多应用中，可靠地识别它们仍然具有挑战性。确定性全局优化方法以前曾用于通过首先找到所有驻点，然后在解集之中识别过渡态（TSs）来确定过渡态的位置。我们提出了几种适用于一般非线性、二次连续可微函数的区域测试，通过识别不包含任何过渡态或可能只包含唯一过渡态的区域，来加速此类方法的收敛。这些测试基于将线性代数定理的区间扩展应用于区间海森矩阵。它们可用于全局优化方法的框架内，有可能减少确定过渡态位置的计算时间。我们阐述了这些测试背后的理论，讨论了它们的算法复杂度，并通过几个例子表明，使用这些测试可以显著缩短计算时间。
