目录

分子间的转移积分、电子迁移率、空穴迁移率的计算

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。

理论公式

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。根据Marcus hopping rate再进行后续处理,一般有两种:

这里以萘之间的电子迁移为例演示计算V、λ值,以及Marcus hopping rate的过程。

建模

建模的操作,参考:AMS软件建模教程

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。

设置计算参数

保存任务,并运行。提交任务的方式,参考:正式版的安装、维护与升级

查看结果

Marcus hopping rate公式中的V值

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)
 For electron mobility calculations the fragment LUMO are considered.
 For hole mobility calculations the fragment HOMO are considered.
 Warning: (near) degeneracies found in fragment HOMO/LUMO orbitals.
 Couplings are printed also for (near) degenerate fragment orbitals within 0.100     eV of fragment HOMO or LUMO.
 This threshold for treating fragment MOs as degenerate can be set by the TIDegeneracyThreshold key.
 
 e1(hole) Site energy HOMO-1 fragment 1:                                    -6.39747 eV
 e2(hole) Site energy HOMO-1 fragment 2:                                    -6.39742 eV
 J(hole) Charge transfer integral HOMO-1 fragment 1 - HOMO-1 fragment       -0.18135 eV
 S(hole) Overlap integral HOMO-1 fragment 1 - HOMO-1 fragment 2:             0.00901
 V for hole transfer:                                                       -0.12373 eV
 
 e1(hole) Site energy HOMO-1 fragment 1:                                    -6.39747 eV
 e2(hole) Site energy HOMO fragment 2:                                      -6.40353 eV
 J(hole) Charge transfer integral HOMO-1 fragment 1 - HOMO fragment 2:      -0.07501 eV
 S(hole) Overlap integral HOMO-1 fragment 1 - HOMO fragment 2:               0.00564
 V for hole transfer:                                                       -0.03893 eV
 
 e1(hole) Site energy HOMO fragment 1:                                      -6.40361 eV
 e2(hole) Site energy HOMO-1 fragment 2:                                    -6.39742 eV
 J(hole) Charge transfer integral HOMO fragment 1 - HOMO-1 fragment 2:      -0.07500 eV
 S(hole) Overlap integral HOMO fragment 1 - HOMO-1 fragment 2:               0.00564
 V for hole transfer:                                                       -0.03893 eV
 
 e1(hole) Site energy HOMO fragment 1:                                      -6.40361 eV
 e2(hole) Site energy HOMO fragment 2:                                      -6.40353 eV
 J(hole) Charge transfer integral HOMO fragment 1 - HOMO fragment 2:         1.10836 eV
 S(hole) Overlap integral HOMO fragment 1 - HOMO fragment 2:                -0.08709
 V for hole transfer:                                                        0.55490 eV
 
 e1(electron) Site energy LUMO+1 fragment 1:                                    -1.35037 eV
 e2(electron) Site energy LUMO+1 fragment 2:                                    -1.35036 eV
 J(electron) Charge transfer integral LUMO+1 fragment 1 - LUMO+1 fragment       -0.27885 eV
 S(electron) Overlap integral LUMO+1 fragment 1 - LUMO+1 fragment 2:             0.03415
 V for electron transfer:                                                       -0.23301 eV
 
 e1(electron) Site energy LUMO+1 fragment 1:                                    -1.35037 eV
 e2(electron) Site energy LUMO fragment 2:                                      -1.31648 eV
 J(electron) Charge transfer integral LUMO+1 fragment 1 - LUMO fragment 2:      -0.05813 eV
 S(electron) Overlap integral LUMO+1 fragment 1 - LUMO fragment 2:               0.00680
 V for electron transfer:                                                       -0.04908 eV
 
 e1(electron) Site energy LUMO fragment 1:                                      -1.31658 eV
 e2(electron) Site energy LUMO+1 fragment 2:                                    -1.35036 eV
 J(electron) Charge transfer integral LUMO fragment 1 - LUMO+1 fragment 2:      -0.05814 eV
 S(electron) Overlap integral LUMO fragment 1 - LUMO+1 fragment 2:               0.00680
 V for electron transfer:                                                       -0.04908 eV
 
 e1(electron) Site energy LUMO fragment 1:                                      -1.31658 eV
 e2(electron) Site energy LUMO fragment 2:                                      -1.31648 eV
 J(electron) Charge transfer integral LUMO fragment 1 - LUMO fragment 2:         0.17239 eV
 S(electron) Overlap integral LUMO fragment 1 - LUMO fragment 2:                -0.02920
 V for electron transfer:                                                        0.13407 eV
 
 e1 Site energy HOMO-1 fragment 1:                                                          -6.39747 eV
 e2 Site energy LUMO+1 fragment 2:                                                          -1.35036 eV
 S(Charge_Recombination) Overlap integral HOMO-1 fragment 1 - LUMO+1 fragment 2:            -0.00592
 J(Charge_Recombination) Charge transfer integral HOMO-1 fragment 1 - LUMO+1 fragment        0.05209 eV
 V for charge_recombination 1-2:                                                             0.02917 eV
 
 e1 Site energy HOMO-1 fragment 1:                                                          -6.39747 eV
 e2 Site energy LUMO fragment 2:                                                            -1.31648 eV
 S(Charge_Recombination) Overlap integral HOMO-1 fragment 1 - LUMO fragment 2:               0.04109
 J(Charge_Recombination) Charge transfer integral HOMO-1 fragment 1 - LUMO fragment 2:      -0.39978 eV
 V for charge_recombination 1-2:                                                            -0.24171 eV
 
 e1 Site energy HOMO fragment 1:                                                            -6.40361 eV
 e2 Site energy LUMO+1 fragment 2:                                                          -1.35036 eV
 S(Charge_Recombination) Overlap integral HOMO fragment 1 - LUMO+1 fragment 2:              -0.08832
 J(Charge_Recombination) Charge transfer integral HOMO fragment 1 - LUMO+1 fragment 2:       0.91775 eV
 V for charge_recombination 1-2:                                                             0.57986 eV
 
 e1 Site energy HOMO fragment 1:                                                            -6.40361 eV
 e2 Site energy LUMO fragment 2:                                                            -1.31648 eV
 S(Charge_Recombination) Overlap integral HOMO fragment 1 - LUMO fragment 2:                -0.02649
 J(Charge_Recombination) Charge transfer integral HOMO fragment 1 - LUMO fragment 2:         0.27771 eV
 V for charge_recombination 1-2:                                                             0.17557 eV
 
 e1 Site energy LUMO+1 fragment 1:                                                          -1.35037 eV
 e2 Site energy HOMO-1 fragment 2:                                                          -6.39742 eV
 J(Charge_Recombination) Charge transfer integral LUMO+1 fragment 1 - HOMO-1 fragment       -0.05207 eV
 S(Charge_Recombination) Overlap integral LUMO+1 fragment 1 - HOMO-1 fragment 2:             0.00592
 V for charge_recombination 2-1:                                                            -0.02915 eV
 
 e1 Site energy LUMO+1 fragment 1:                                                          -1.35037 eV
 e2 Site energy HOMO fragment 2:                                                            -6.40353 eV
 J(Charge_Recombination) Charge transfer integral LUMO+1 fragment 1 - HOMO fragment 2:      -0.91758 eV
 S(Charge_Recombination) Overlap integral LUMO+1 fragment 1 - HOMO fragment 2:               0.08830
 V for charge_recombination 2-1:                                                            -0.57976 eV
 
 e1 Site energy LUMO fragment 1:                                                            -1.31658 eV
 e2 Site energy HOMO-1 fragment 2:                                                          -6.39742 eV
 J(Charge_Recombination) Charge transfer integral LUMO fragment 1 - HOMO-1 fragment 2:       0.39992 eV
 S(Charge_Recombination) Overlap integral LUMO fragment 1 - HOMO-1 fragment 2:              -0.04110
 V for charge_recombination 2-1:                                                             0.24181 eV
 
 e1 Site energy LUMO fragment 1:                                                            -1.31658 eV
 e2 Site energy HOMO fragment 2:                                                            -6.40353 eV
 J(Charge_Recombination) Charge transfer integral LUMO fragment 1 - HOMO fragment 2:        -0.27776 eV
 S(Charge_Recombination) Overlap integral LUMO fragment 1 - HOMO fragment 2:                 0.02650
 V for charge_recombination 2-1:                                                            -0.17560 eV
 
 Electronic coupling V (summed over printed couplings)
 Square root of (sum of squares of printed V's):
 -----------------------------------------------------
 
 V for hole transfer:                    0.57118 eV
 V for electron transfer:                0.27764 eV
 V for charge_recombination 1-2:         0.65295 eV
 V for charge_recombination 2-1:         0.65290 eV
Engine ADF
    Basis
        Type TZP
    End
    Fragments
        Region_1 Region_1.rkf 
        Region_2 Region_2.rkf 
    End
    
    XC
        GGA PBE
        DISPERSION GRIMME4
    End
    Relativity
        Level None
    End
    Symmetry NOSYM
    TransferIntegrals Yes
    TIDegeneracyThreshold 0.2
EndEngine

这里我们得到了电子和空穴的V值0.57118 eV、0.27764 eV。这个值是考虑到单分子存在两个简并HOMO、LUMO的结果。

Marcus hopping rate公式中的λ值

根据前面的Marcus hopping rate公式,还需要另一个数值,也就是电子或空穴的重组能λ。重组能的计算公式:

其中,

Marcus hopping rate公式中的常数

Marcus hopping rate公式中用到的数据,统一能量单位到J,则各个常数的数值为:

知道V、λ值,以及上述常数,带入Marcus hopping rate公式,即可得到迁移率(单位为s-1,也就是每秒跳跃多少次)。

两个以上分子

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,会给出两两之间的数据。

 Site energy (hole) HOMO fragment 1 (eV):      -6.90814
 Site energy (hole) HOMO fragment 2 (eV):      -6.31622
 Site energy (hole) HOMO fragment 3 (eV):      -6.75325
 Charge transfer integral (hole) HOMO fragment 1 - HOMO fragment 2 (eV):   0.10886E+01
 Charge transfer integral (hole) HOMO fragment 1 - HOMO fragment 3 (eV):   0.16242E+01
 Charge transfer integral (hole) HOMO fragment 2 - HOMO fragment 3 (eV):   0.18609E+00
 
 Site energy (electron) LUMO fragment 1 (eV):      -1.80417
 Site energy (electron) LUMO fragment 2 (eV):      -1.22862
 Site energy (electron) LUMO fragment 3 (eV):      -1.63222
 Charge transfer integral (electron) LUMO fragment 1 - LUMO fragment 2 (eV):       0.16682
 Charge transfer integral (electron) LUMO fragment 1 - LUMO fragment 3 (eV):       0.22993
 Charge transfer integral (electron) LUMO fragment 2 - LUMO fragment 3 (eV):       0.17881
 
Charge transfer integral (Charge_Recombination) HOMO fragment 1 - LUMO fragment 2 (eV):       0.27072
Charge transfer integral (Charge_Recombination) HOMO fragment 1 - LUMO fragment 3 (eV):      -0.25022
Charge transfer integral (Charge_Recombination) HOMO fragment 2 - LUMO fragment 3 (eV):      -0.04055
 
 Charge transfer integral (Charge_Recombination) LUMO fragment 1 - HOMO fragment 2 (eV):      -0.27291
 Charge transfer integral (Charge_Recombination) LUMO fragment 1 - HOMO fragment 3 (eV):       0.25191
 Charge transfer integral (Charge_Recombination) LUMO fragment 2 - HOMO fragment 3 (eV):       0.05039
 ---------------------------------------------------------------------

 Overlap integrals relevant for hole or electron mobility calculations
 ---------------------------------------------------------------------

 Overlap integral (hole) HOMO fragment 1 - HOMO fragment 2:  -0.87092E-01
 Overlap integral (hole) HOMO fragment 1 - HOMO fragment 3:  -0.10910E+00
 Overlap integral (hole) HOMO fragment 2 - HOMO fragment 3:  -0.12533E-01
 
 Overlap integral (electron) LUMO fragment 1 - LUMO fragment 2:      -0.02920
 Overlap integral (electron) LUMO fragment 1 - LUMO fragment 3:      -0.02923
 Overlap integral (electron) LUMO fragment 2 - LUMO fragment 3:      -0.01751
 
 Overlap integral HOMO (Charge_Recombination) fragment 1 - LUMO fragment 2:      -0.02650
 Overlap integral HOMO (Charge_Recombination) fragment 1 - LUMO fragment 3:       0.01887
 Overlap integral HOMO (Charge_Recombination) fragment 2 - LUMO fragment 3:       0.00325
 
 Overlap integral LUMO (Charge_Recombination) fragment 1 - HOMO fragment 2:       0.02650
 Overlap integral LUMO (Charge_Recombination) fragment 1 - HOMO fragment 3:      -0.01888
 Overlap integral LUMO (Charge_Recombination) fragment 2 - HOMO fragment 3:      -0.00323

需要用户根据公式V = (J-S(e1+e2)/2)/(1-S2)手动计算一下V值。

内层电子、空穴引起的电荷转移

如果电子、空穴的转移不是发生在HOMO、LUMO之间,而是发生在内层轨道,可以通过修改碎片的电子占据情况实现。

固体

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QuantumATK计算。