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An efficient approach for the calculation of Franck-Condon integrals of large molecules

机译：一种计算大分子弗朗克-康登积分的有效方法

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摘要

A general and efficient approach for the calculation of Franck-Condon integrals (FCIs) of large molecules is presented.In a first step,by exploiting the diagonally dominant and sparse structure of the Duschinsky matrix,a model system is constructed for which the Duschinsky matrix takes a block-diagonal form.For each of these blocks separately,the FCIs are calculated discarding all below a certain threshold.From those integrals retained the FCIs of the model system are obtained by simple multiplication.These serve as an estimate for the FCIs of the exact system which are calculated for those integrals which lie above a certain threshold.By systematically decreasing the threshold,the simulation can be reliably converged to the exact result with an arbitrary accuracy.Using this scheme,a considerable reduction of the number of FCIs which have to be calculated is achieved which leads to an improved scaling behavior of the computational effort with system size.The approach has been tested thoroughly for a set of molecules including difficult cases.For the larger systems a speedup of up to three orders of magnitude compared to an exact calculation is observed while the errors can be kept negligible.With this approach accurate calculations of FCIs are feasible also for large molecules encountered in "real-life" chemistry,especially biochemistry and material science.
机译：提出了一种大分子弗朗克-康登积分（FCI）计算的通用有效方法。第一步，通过利用Duschinsky矩阵的对角占优和稀疏结构，构建了一个Duschinsky矩阵的模型系统。采取块对角线形式。对于每个块分别计算FCI，并将所有低于某个阈值的值丢弃，从保留的那些积分中，通过简单乘法获得模型系统的FCI，这些值用作对FCI的估计。通过精确地计算高于某个阈值的积分的精确系统。通过系统地降低阈值，可以以任意精度将仿真可靠地收敛到精确结果。使用该方案，可以大大减少FCI的数量。必须进行计算，这导致了系统规模下计算工作量的改进缩放行为。该方法已经过测试对于较大的系统，与精确的计算相比，速度提高了三个数量级，而误差却可以忽略不计。通过这种方法，对于大型的FCI的精确计算也是可行的。在“现实生活”化学中遇到的分子，尤其是生物化学和材料科学。

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