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粒子迁移率对于有机电子器件例如场致发射晶体管(OFET)、有机发光二极管、光伏电池非常关键。载流子从一个位置迁移到另一个位置,迁移率主要有转移积分决定。本功能仅适用于分子间的载流子迁移,不适用于分子或团簇内部的电荷转移。
Marcus hopping rate:
k=V2/ћ * (π/λkBT)1/2 * e-λ/4kBT
ADF可以直接计算电子、空穴的V值(电子或空穴的转移耦合),也可以计算λ,上述公式中,其他均为常数,因此这样可以计算得到Marcus hopping rate。之后:
这里以萘之间的电子迁移为例演示计算过程。例子文件下载。下面的数据参考这些文件。
基本的建模操作,见建模:ADF模块分子的基本建模功能演示(视频下载)
建模完成之后,一般需要对结构进行优化(即,能量最小化,找到最稳定的结构).这里我们跳过建模和优化,直接计算下面给定的结构的电子、空穴迁移率:
建模如下图:
并按照如何创建分区将分子分为两个片段,默认分别命名为Region_1、Region_2,如上图所示。
点击SCM LOGO > output,选择Properties > Charge transfer integrals,即看到如下所示的内容:
Charge transfer integrals relevant for hole or electron mobility calculations Electronic coupling V (also known as effective (generalized) transfer integrals J_eff) V = (J-S(e1+e2)/2)/(1-S^2) V for hole transfer: -0.00766 eV V for electron transfer: -0.03780 eV The effective transfer integral, or electronic coupling, is calculated from these components: e1(hole) Site energy HOMO fragment 1: -5.46589 eV e2(hole) Site energy HOMO fragment 2: -5.71529 eV J(hole) Charge transfer integral HOMO fragment 1 - HOMO fragment 2: -0.02237 eV S(hole) Overlap integral HOMO fragment 1 - HOMO fragment 2: 0.00263 e1(electron) Site energy LUMO fragment 1: -2.07825 eV e2(electron) Site energy LUMO fragment 2: -2.33169 eV J(electron) Charge transfer integral LUMO fragment 1 - LUMO fragment 2: -0.05421 eV S(electron) Overlap integral LUMO fragment 1 - LUMO fragment 2: 0.00745
分别得到电子和空穴的V值,以及转移积分。根据前面的Marcus hopping rate公式,还需要另一个数值电子或空穴的λ。以电子的为例:
λ = (Eanion(neutral geometry) - E(neutral)) + (Eneutral(anion geometry) - E(anion))
λ = (-119.25607066 + 119.42662877)+(-119.31572655 + 119.35845577) = 0.21328733 eV
如果不是一种分子,而是两种分子之间转移,参考:两种分子之间的λ值
统一能量单位到J:
得到
带入公式得到温度T=300K时,电子的Marcus hopping rate:
k = V2/ћ * (π/λkBT)1/2 * e-λ/4kBT
=(6.05*10-21)2/1.05457161×10-34*(3.1415927/(3.41*10-20*1.38064881×10-23*300)1/2*exp(-3.41*10-20/(4*1.38064881×10-23*300)) 注意:此处exp指e的指数,不是指10的指数。
=34.708406*10-8*1.4914047*1020*e-2.058211
=6.61*1012 s-1
本例说明的是2个Region之间的计算,实际上如果是多个片段也是一样,例如三个片段:
Site energy (hole) HOMO fragment 1 (eV): -8.97107 Site energy (hole) HOMO fragment 2 (eV): -7.71767 Site energy (hole) HOMO fragment 3 (eV): -5.73653 Charge transfer integral (hole) HOMO fragment 1 - HOMO fragment 2 (eV): -1.84857 Charge transfer integral (hole) HOMO fragment 1 - HOMO fragment 3 (eV): -0.08168 Charge transfer integral (hole) HOMO fragment 2 - HOMO fragment 3 (eV): -1.60740 Site energy (electron) LUMO fragment 1 (eV): -1.97596 Site energy (electron) LUMO fragment 2 (eV): -3.89668 Site energy (electron) LUMO fragment 3 (eV): -1.89409 Charge transfer integral (electron) LUMO fragment 1 - LUMO fragment 2 (eV): -1.05098 Charge transfer integral (electron) LUMO fragment 1 - LUMO fragment 3 (eV): -1.73879 Charge transfer integral (electron) LUMO fragment 2 - LUMO fragment 3 (eV): -0.94651 Overlap integrals relevant for hole or electron mobility calculations --------------------------------------------------------------------- Overlap integral (hole) HOMO fragment 1 - HOMO fragment 2: 0.11500 Overlap integral (hole) HOMO fragment 1 - HOMO fragment 3: 0.00512 Overlap integral (hole) HOMO fragment 2 - HOMO fragment 3: 0.11037 Overlap integral (electron) LUMO fragment 1 - LUMO fragment 2: 0.45551 Overlap integral (electron) LUMO fragment 1 - LUMO fragment 3: 0.16791 Overlap integral (electron) LUMO fragment 2 - LUMO fragment 3: 0.45594
会给出两两之间的数据,如上所示。
块体材料的电子迁移率、Seebeck 系数、热导率、Hall系数以及Hall电导率张量,可以使用VNL-ATK2016计算。