Gera Tarun, Sebastian K L
Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India.
J Phys Chem A. 2022 Aug 18;126(32):5449-5457. doi: 10.1021/acs.jpca.2c02359. Epub 2022 Aug 3.
We present an exact method to calculate the electronic states of one electron Hamiltonians with diagonal disorder. We show that in cases where the disorder has a Cauchy distribution, the disorder averaged one particle Green's function can be calculated directly, using a deterministic, complex (non-Hermitian) Hamiltonian. For this we use the supersymmetric method which has already been used in problems of solid state physics. Using the method we find exact solution for the case of molecules with site disorder, confined to a microcavity, for any value of . Our analysis shows that the width of the polaritonic states as a function of depends on the nature of disorder, and hence it can be used to probe the way molecular energy levels are distributed. We also show how one can find exact results for Hückel type Hamiltonians with on-site Cauchy disorder and demonstrate its use.
我们提出了一种精确方法来计算具有对角无序的单电子哈密顿量的电子态。我们表明，在无序具有柯西分布的情况下，无序平均的单粒子格林函数可以直接使用确定性的复（非厄米）哈密顿量来计算。为此，我们使用了已在固态物理问题中使用过的超对称方法。使用该方法，我们找到了对于局限于微腔的具有位点无序的分子情况，在任意值下的精确解。我们的分析表明，极化激元态的宽度作为的函数取决于无序的性质，因此它可用于探测分子能级的分布方式。我们还展示了如何找到具有在位柯西无序的休克尔型哈密顿量的精确结果并演示其用途。
