Spin-orbit coupling# 自旋-轨道耦合

Spin-orbit coupling (SOC) is the relativistic effect that mixes states with different multiplicities, e.g. singlets and triplets. In Dirac's equation framework - which is closest to the real physics since it accounts for relativity in quantum mechanics - there is no differentiation between spin and regular angular momentum, so there is no such a thing as pure spin states in practice.
自旋-轨道耦合（SOC）是一种相对论效应，它混合了具有不同多重性的态，例如单重态和三重态。在狄拉克方程框架下——这是最接近真实物理的，因为它在量子力学中考虑了相对论效应——自旋和常规角动量之间没有区别，因此在实践中不存在纯粹的自旋态。

Usually, this is an effect that mostly affects systems containing heavy atoms, so it does not need to be included in each and every calculation. Nonetheless, there are many experimental phenomena that stem from that, such as phosphorescence, the intersystem crossing between excited states, TADF, and even some reactivity through unconventional spin states.
通常，这种现象主要影响包含重原子的系统，因此并非每次计算都需要考虑。尽管如此，许多实验现象都源于此，例如磷光、激发态间的系间窜越、热激活延迟荧光（TADF），甚至通过非常规自旋态引发的某些反应性。

As an example, let's try to predict the phosphorescence lifetime and color of the Ir(ppy)₃ complex in solution. That is a yellow-green emitter, part of an important family of compounds used in the fabrication of OLEDs:
作为一个例子，让我们尝试预测溶液中 Ir(ppy) ₃ 配合物的磷光寿命和颜色。这是一种黄绿色发射体，属于用于 OLED 制造的重要化合物家族的一部分：

SOC with TD-DFT# 含时密度泛函理论的 SOC #

In ORCA, there are many ways to include SOC in your calculations at various levels of theory, and maybe the simplest one is using TD-DFT [Iszak2019c]. From now on, we will assume that everything related to that section is known and we will only discuss the new aspects related to SOC.
在 ORCA 中，有多种方法可以在不同理论水平上将自旋轨道耦合（SOC）纳入计算，或许最简单的方法是使用 TD-DFT[Iszak2019c]。从现在开始，我们假设与该部分相关的所有内容都已知，我们将仅讨论与 SOC 相关的新方面。

However, before jumping into the more complicated Iridium(III) complex, let us start with something simpler: formaldehyde. This is a molecule that presents a quite strong SOC besides being an organic molecule.
然而，在深入探讨更复杂的铱(III)配合物之前，让我们先从更简单的形式开始：甲醛。这种分子不仅是有机分子，还表现出相当强的自旋-轨道耦合效应。

That is because the $π - π^{*}$ and $n - π^{*}$ excited states can be orthogonal to others, and a change in spin can be compensated by a change in angular momentum caused be the "rotation" of the electrons during the transition (more on that later) [Turro2010]. In order to compute the excited states and its SOC just run, e.g. with B3LYP:
这是因为 $π - π^{*}$ 和 $n - π^{*}$ 激发态可以与其他态正交，并且自旋的变化可以通过跃迁过程中电子“旋转”引起的角动量变化来补偿（稍后详述）[Turro2010]。为了计算激发态及其自旋-轨道耦合，只需运行例如 B3LYP：

 !B3LYP DEF2-SVP
 %TDDFT  NROOTS  5
         DOSOC   TRUE
 END
 * xyz 0 1
   O      0.000000    0.000000    0.601105
   C     -0.000000    0.000000   -0.598757
   H      0.000000   -0.944973   -1.202781
   H      0.000000    0.944973   -1.202781
*

As you can see, the only extra input needed is the DOC TRUE under %TDDFT. The output will present some other information now, starting with the computation not only of the singlet excited states, but also of the triplets:
如您所见，唯一需要的额外输入是%TDDFT 下的 DOC TRUE。输出现在将呈现一些其他信息，首先计算的不仅是单重激发态，还有三重态：

********************************
* Entering triplet calculation *
********************************

[...]

     ****Iteration    0****
<<< Triplet sigma vectors requested >>>

Memory handling for direct AO based CIS:
Memory per vector needed      ...     1 MB
Memory needed                 ...     0 MB
Memory available              ...   512 MB
Number of vectors per batch   ...   512
Number of batches             ...     1
[...]

The printing of the excited state is also done in an analogous way, with the contribution of the excitations to each state printed:
激发态的打印同样以类似方式进行，各态的激发贡献均被打印出来：

------------------------------------
TD-DFT/TDA EXCITED STATES (TRIPLETS)
------------------------------------

the weight of the individual excitations are printed if larger than 1.0e-02

STATE  1:  E=   0.123186 au      3.352 eV    27036.2 cm**-1 <S**2> =   2.000000
     7a ->   8a  :     0.996653 (c=  0.99832517)

STATE  2:  E=   0.219375 au      5.969 eV    48147.2 cm**-1 <S**2> =   2.000000
     6a ->   8a  :     0.993680 (c= -0.99683484)

After having both singlets and triplets, comes the SOC-specific part:
在同时拥有单重态和三重态之后，接下来是自旋轨道耦合（SOC）特有的部分：

------------------------------
TD-DFT/TDA SPIN-ORBIT COUPLING
------------------------------

[...]
------------------------------------------------------------------------------
                         ORCA SPIN-ORBIT COUPLING CALCULATION
------------------------------------------------------------------------------

GBW file                                    ... form.gbw
Input density                               ... form.cisp0
Output integrals                            ... form.cis
Operator type                               ... Mean-field/Effective potential
   One-Electron Terms                       ... 1
   Coulomb Contribution                     ... 2
   Exchange Contribution                    ... 3
   Correlation Contribution                 ... 0
   Maximum number of centers                ... 4
[...]

Here, the integrals necessary to compute the coupling are calculated first. There are many algorithms in ORCA for how to do that, and the complete details can be found in the ORCA manual, however the defaults can be trusted for the vast majority of cases.
在此，首先计算了用于耦合计算的积分。ORCA 中存在多种算法来实现这一点，完整细节可在 ORCA 手册中查阅，然而对于绝大多数情况，默认设置是可信赖的。

Note 注释

The calculation of these integrals can take some time. For larger systems, one can use the RI-SOMF(1X) on the main input, that will invoke the use of RI for the Coulomb part. This will accelerate the calculation significantly with only a small error associated [Neese2005].
这些积分的计算可能需要一些时间。对于较大的系统，可以在主输入中使用 RI-SOMF(1X)，这将调用 RI 用于库仑部分。这样可以在仅引入微小误差的情况下显著加速计算[Neese2005]。

Analysing the SOC-TD-DFT Output#
分析 SOC-TD-DFT 输出结果

If everything succeeds, first the matrix elements $⟨ T_{n} | {\hat{H}}_{s} | S_{n} ⟩$ will be printed on a Cartesian basis:
如果一切顺利，首先将以笛卡尔基底打印矩阵元素 $⟨ T_{n} | {\hat{H}}_{s} | S_{n} ⟩$ ：

--------------------------------------------------------------------------------
                CALCULATED SOCME BETWEEN TRIPLETS AND SINGLETS
--------------------------------------------------------------------------------
     Root                          <T|HSO|S>  (Re, Im) cm-1
   T      S             Z                     X                     Y
--------------------------------------------------------------------------------
   1      0    (   0.00 ,   59.19 )    (   0.00 ,    0.00 )    (  -0.00 ,    0.00 )
   1      1    (   0.00 ,   -0.00 )    (   0.00 ,   -0.00 )    (  -0.00 ,    0.00 )
   1      2    (   0.00 ,    0.00 )    (   0.00 ,   -0.00 )    (  -0.00 ,    7.52 )
   1      3    (   0.00 ,   -0.00 )    (   0.00 ,  -49.15 )    (  -0.00 ,    0.00 )

and one can immediately see that the coupling between the first excited triplet ( $T_{1}$ ) and the ground singlet ( $S_{0}$ ) is quite strong through the $z$ component of the SOC operator.
可以立即看出，第一激发三重态（ $T_{1}$ ）与基态单重态（ $S_{0}$ ）之间的耦合通过 SOC 算符的 $z$ 分量相当强。

This is expected from the analysis of the components of these states. The $T_{1}$ is mostly composed of a HOMO-LUMO transition, which makes it a $n - π^{*}$ excited state. A transition from that to the ground state involves a change of angular momentum, which then facilitates the change of spin state by increasing the SOC [Turro2010]:
这可以从这些态的组分分析中预见。 $T_{1}$ 主要由 HOMO-LUMO 跃迁构成，使其成为 $n - π^{*}$ 激发态。从该态到基态的跃迁涉及角动量的变化，进而通过增强自旋-轨道耦合（SOC）促进自旋态的转变[Turro2010]：

The next part is the stabilization energy of the ground state cause by the SOC and a list of energies of the new mixed SOC-states:
下一部分是基态由于自旋-轨道耦合（SOC）引起的稳定化能，以及新的混合 SOC 态的能量列表：

SOC stabilization of the ground state:  -0.2024 cm-1
Eigenvalues of the SOC matrix:

State:        cm-1         eV
  0:          0.00         0.0000
  1:      27036.26         3.3521
  2:      27036.27         3.3521
  3:      27036.45         3.3521
  4:      32861.46         4.0743

Followed by their composition, which are now mixtures of singlets and triplets:
随后是其组成，现为单重态与三重态的混合体：

            E(cm-1)  Weight      Real         Imag     : Root  Spin  Ms
STATE  0:      0.00
                     0.99999     -0.00683     -0.99997 : 0     0     0
STATE  1:  27036.26
                     0.50000      0.00000     -0.70710 : 1     1    -1
                     0.50000      0.00000     -0.70710 : 1     1     1
STATE  2:  27036.27
                     0.50000     -0.00000      0.70710 : 1     1    -1
                     0.50000      0.00000     -0.70710 : 1     1     1
STATE  3:  27036.45
                     0.99999      0.99994      0.01093 : 1     1     0
STATE  4:  32861.46
                     0.99999     -0.99938      0.03514 : 1     0     0

Here ORCA computed, for instance, that the ground SOC state is 99.99% equal to the DFT ground state, which is expected since there is a quite large energy difference between $S_{0}$ and the higher energy ones.
例如，ORCA 计算得出，基态 SOC 状态与 DFT 基态的相似度高达 99.99%，这在意料之中，因为 $S_{0}$ 与更高能量状态之间存在相当大的能量差异。

The second SOC state now, is a mixture of two spin sublevels of the first triplet (Root 1), those with angular momentum -1 and +1 in spherical harmonics. The third state is a similar mixture, the fourth state is again basically the $S_{1}$ , and so on.
第二种 SOC 态现在，是第一三重态（根 1）中两个自旋子能级的混合态，它们在球谐函数中具有角动量-1 和+1。第三种态是类似的混合态，第四种态基本上又是 $S_{1}$ ，依此类推。

In the end, the "spectrum" is also printed:
最终，“频谱”也被打印出来：

---------------------------------------------------------------------------------
SPIN ORBIT CORRECTED ABSORPTION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
---------------------------------------------------------------------------------
  States    Energy  Wavelength   fosc         T2         TX        TY        TZ
            (cm-1)    (nm)                  (au**2)     (au)      (au)      (au)
---------------------------------------------------------------------------------
   0   1   27036.3    369.9   0.000000002   0.00000   0.00000   0.00016   0.00000
   0   2   27036.3    369.9   0.000000001   0.00000   0.00010   0.00000   0.00000
   0   3   27036.5    369.9   0.000000132   0.00000   0.00000   0.00000   0.00127
   0   4   32861.5    304.3   0.000000000   0.00000   0.00000   0.00000   0.00000
   0   5   48147.4    207.7   0.000000000   0.00000   0.00000   0.00001   0.00000
   0   6   48147.4    207.7   0.000000000   0.00000   0.00000   0.00000   0.00000

Note that now even the triplets are included in the spectrum, as in fact, all SOC states have components of both singlets and triplets and will have some intensity. In this case, the SOC is just not strong enough to make the triplet to ground state transition really bright.
注意，现在三重态也被包含在光谱中，事实上，所有自旋轨道耦合（SOC）态都具有单重态和三重态的成分，因此会有一定的强度。在这种情况下，SOC 的强度还不足以使三重态到基态的跃迁变得非常明亮。

SOC on a Iridium(III) complex#
铱(III)配合物上的 SOC

Now let's come back to the aforementioned example of a phosphorescent Iridium(III) complex. That is a case when the SOC is so strong that there are no clear singlets or triplets anymore, and the excited change change drastically due to coupling.
现在让我们回到前面提到的磷光铱(III)配合物的例子。这是一个自旋-轨道耦合极强的情况，以至于不再有明确的单重态或三重态，激发态由于耦合而发生剧烈变化。

The first step is to optimize this heavy metal complex. We will look after the fac- $I r (p p y)_{3}$ , for we have plenty of experimental data to compare with for that isomer. The optimization can be done running:
第一步是对该重金属配合物进行优化。我们将重点关注面式异构体 $I r (p p y)_{3}$ ，因为我们拥有丰富的实验数据可供比较。优化过程可通过运行以下命令完成：

!B3LYP DEF2-TZVP OPT CPCM(CH2CL2) D4
* XYZFILE 0 1 fac-Irppy_guess.xyz

Here we use the B3LYP functional with the DEF2-TZVP basis, which in practice uses a pseudo-potential for heavy atoms such as Ir. This helps to accelerate the calculation and also somewhat accounts for the relativistic effects on the geometry, since the pseudo-potential are fitted to relativistic calculations.
在此，我们采用 B3LYP 泛函结合 DEF2-TZVP 基组进行计算，实际操作中对铱等重原子使用赝势。这不仅加速了计算过程，还在一定程度上考虑了相对论效应对几何结构的影响，因为赝势是根据相对论计算结果拟合的。

We also use larger grids, which is important and such heavy atoms are present, together with CPCM for a solvation correction and the D4 for the dispersion interaction. The result is:
我们还采用了更大的网格，这一点至关重要，因为存在大量重原子，同时结合 CPCM 进行溶剂化校正，并使用 D4 处理色散相互作用。结果如下：

which shows good agreement with the average experimental bond length values found at the CCDB [Yersin2005]. After optimizing, the SOC-TD-DFT can be called again with:
这与 CCDB 中发现的平均实验键长值非常吻合[Yersin2005]。优化后，可以再次调用 SOC-TD-DFT：

!B3LYP ZORA ZORA-DEF2-TZVP SARC/J CPCM(CH2CL2) RI-SOMF(1X)
%TDDFT  NROOTS  25
        DOSOC   TRUE
        TDA     FALSE
END
%BASIS  NEWGTO  IR      "SARC-ZORA-TZVP" END
END
* XYZFILE 0 1 fac-Irppy_optimized.xyz

Now we do a full calculation with Relativistic corrections, using ZORA and its required basis. Note that we also need to specify the SARC-ZORA-TZVP basis for the Ir, as there is no simple ZORA-DEF2-TZVP for that. Here we added the RI-SOMF(1X) to accelerate the SOC integrals and choose the TDA FALSE to compute a full TD-DFT calculation, for later comparison.
现在我们进行包含相对论修正的完整计算，采用 ZORA 及其所需基组。注意，对于 Ir 元素，我们还需指定 SARC-ZORA-TZVP 基组，因为不存在简单的 ZORA-DEF2-TZVP 基组。此处我们添加了 RI-SOMF(1X)以加速 SOC 积分计算，并选择 TDA FALSE 以执行完整的 TD-DFT 计算，以便后续对比。

In contrast to the formaldehyde, that had no heavy atom, the SOC matrix elements are much larger now:
与不含重原子的甲醛相比，SOC 矩阵元现在要大得多：

--------------------------------------------------------------------------------
                CALCULATED SOCME BETWEEN TRIPLETS AND SINGLETS
--------------------------------------------------------------------------------
     Root                          <T|HSO|S>  (Re, Im) cm-1
   T      S             Z                     X                     Y
--------------------------------------------------------------------------------
   1      0    (   0.00 , -178.70 )    (   0.00 ,  -14.24 )    (  -0.00 ,  -17.11 )
   1      1    (   0.00 ,    2.90 )    (   0.00 ,  -12.51 )    (  -0.00 ,  -17.41 )
   1      2    (   0.00 ,    3.48 )    (   0.00 , -107.34 )    (  -0.00 ,   26.81 )
   1      3    (   0.00 ,    0.93 )    (   0.00 ,   24.18 )    (  -0.00 ,  116.53 )
   1      4    (   0.00 ,   17.00 )    (   0.00 ,  351.96 )    (  -0.00 , -883.26 )
   1      5    (   0.00 ,  -16.51 )    (   0.00 , -869.91 )    (  -0.00 , -351.62 )
   1      6    (   0.00 ,  -91.84 )    (   0.00 ,   -5.33 )    (  -0.00 ,   19.66 )
   1      7    (   0.00 ,   -2.39 )    (   0.00 , -141.03 )    (  -0.00 ,  -70.48 )

and the states are much more mixed:
而各州的情况则更为复杂多样：

            E(cm-1)  Weight      Real         Imag     : Root  Spin  Ms
STATE  0:      0.00
                     0.99610      0.94204      0.32965 : 0     0     0
STATE  1:  20774.54
                     0.64085      0.35966      0.71519 : 1     1     0
                     0.01154     -0.04825     -0.09595 : 4     1     0
                     0.01206      0.04933      0.09810 : 9     1     0
                     0.03186      0.16645      0.06448 : 2     1    -1
                     0.03295     -0.05381      0.17335 : 3     1    -1
                     0.03337     -0.10929     -0.14639 : 5     1    -1
                     0.03657     -0.15165      0.11650 : 6     1    -1
                     0.01374      0.11174      0.03540 : 7     1    -1
                     0.01194     -0.03024      0.10500 : 8     1    -1
                     0.03186      0.04749     -0.17207 : 2     1     1
                     0.03295     -0.17125     -0.06018 : 3     1     1
                     0.03337      0.05234      0.17502 : 5     1     1
                     0.03657     -0.18395      0.05227 : 6     1     1
                     0.01374      0.03821     -0.11081 : 7     1     1
                     0.01194     -0.10233     -0.03833 : 8     1     1

The ground SOC state is still essentially the DFT ground state, as the energy differences are still high. However, the first SOC state is already a hybrid of many. It is not a simple triplet, but a mixture of $T_{1}$ to $T_{9}$ , with various amounts and spin components. That shows the impact of the SOC on these cases!
地面 SOC 态本质上仍然是 DFT 的地面态，因为能量差异仍然很大。然而，第一个 SOC 态已经是多种态的混合体。它不是一个简单的三重态，而是 $T_{1}$ 到 $T_{9}$ 的混合，具有不同的比例和自旋分量。这显示了 SOC 在这些情况下的影响！

The closest state to a singlet now is the SOC state 10:
最接近单态的现在是 SOC 态 10：

STATE 10:  21813.90
                     0.34904      0.07012      0.58662 : 1     0     0
                     0.02377      0.01830      0.15309 : 6     0     0
                     0.06868     -0.26022      0.03111 : 4     1     0
                     0.02809     -0.16640      0.01989 : 9     1     0
                     0.01415      0.05254      0.10672 : 2     1    -1
                     0.01493     -0.10540      0.06177 : 3     1    -1
                     0.08208      0.11662      0.26169 : 5     1    -1
                     0.08432      0.26221     -0.12478 : 6     1    -1
                     0.03076     -0.11179     -0.13513 : 7     1    -1
                     0.02740      0.12544     -0.10801 : 8     1    -1
                     0.01415     -0.02591      0.11610 : 2     1     1
                     0.01493      0.11699      0.03518 : 3     1     1
                     0.08208     -0.05165      0.28180 : 5     1     1
                     0.08432     -0.28423     -0.05945 : 6     1     1
                     0.03076      0.07679     -0.15768 : 7     1     1
                     0.02740     -0.14737     -0.07540 : 8     1     1

which has 34% of $S_{1}$ and 2% of $S_{6}$ , but there is nothing like a pure state anymore.
其中含有 34%的 $S_{1}$ 和 2%的 $S_{6}$ ，但已不存在纯粹的状态。

ZFS and phosphorescence lifetime#
ZFS 与磷光寿命

This strong mixing is now reflected in the spectrum as well:
这种强烈的混合现象如今也在频谱中得到了体现：

---------------------------------------------------------------------------------
SPIN ORBIT CORRECTED ABSORPTION SPECTRUM VIA TRANSITION ELECTRIC DIPOLE MOMENTS
---------------------------------------------------------------------------------
  States    Energy  Wavelength   fosc         T2         TX        TY        TZ
            (cm-1)    (nm)                  (au**2)     (au)      (au)      (au)
---------------------------------------------------------------------------------
   0   1   20774.5    481.4   0.000013163   0.00021   0.00153   0.00311   0.01402
   0   2   20836.2    479.9   0.003033212   0.04792   0.16473   0.14418   0.00118
   0   3   20844.5    479.7   0.003563760   0.05629   0.15169   0.18239   0.00281
   0   4   20990.7    476.4   0.000283714   0.00445   0.03702   0.05532   0.00437
   0   5   20993.2    476.3   0.000109527   0.00172   0.01850   0.02990   0.02194
   0   6   21011.1    475.9   0.000366203   0.00574   0.06107   0.04481   0.00074

and the previous "triplets" - now SOC states - have actually very bright transitions with the ground state.
而先前的“三重态”——现为自旋轨道耦合态——实际上与基态之间具有非常明亮的跃迁。

The approximate zero-field splitting (ZFS), obtained as the energy difference between SOC state 3 and SOC state 1 is of about $70 c m^{- 1}$ , in quite good agreement with the experimental value of $85 - 170 c m^{- 1}$ [Wang2014].
所得近似零场分裂（ZFS），即 SOC 态 3 与 SOC 态 1 之间的能量差，约为 $70 c m^{- 1}$ ，与实验值 $85 - 170 c m^{- 1}$ 相当吻合[Wang2014]。

From the oscillator strengths it is also possible to predict the phosphorescence lifetime for these complexes, and the calculated value using Eq. 4 from the same reference, is about $1.17 μ s$ , also close to the $1.6 - 1.8 μ s$ from measurements.
从振子强度出发，同样可以预测这些配合物的磷光寿命，利用同一文献中的公式 4 计算得到的值约为 $1.17 μ s$ ，与测量结果的 $1.6 - 1.8 μ s$ 也十分接近。

Using a very simplistic approach, if one takes the energy difference from the $S_{1}$ to the ground state and assumes a ZPE difference of $2000 c m^{- 1}$ , the expected emission color would be blue. Even using the $T_{1}$ energy alone, it would be green, but not yellow enough. Now using the SOC state 1, the color at about $532 n m$ matches the yellow-green emission color of this complex quite well:
采用一种非常简化的方法，如果取从 $S_{1}$ 态到基态的能量差，并假设零点能差为 $2000 c m^{- 1}$ ，预期的发射颜色将是蓝色。即使仅使用 $T_{1}$ 能量，它也会是绿色，但不够黄。现在使用 SOC 态 1，大约在 $532 n m$ 处的颜色与该配合物的黄绿色发射颜色非常吻合：

SOC with other methods#
与其他方法的系统级芯片

The inclusion of SOC can be done through ORCA in many other theory levels such as CASSCF, ROCIS, STEOM and MRCI. The input is somewhat different, depending on the method, but the output in general is the same. For more detailed information on these other methods, please check the ORCA manual.
SOC 的引入可以通过 ORCA 在多种理论层面实现，如 CASSCF、ROCIS、STEOM 和 MRCI。输入方式因方法而异，但输出结果大体相同。如需了解这些其他方法的详细信息，请查阅 ORCA 手册。

Structures# 结构

fac-Ir(ppy)₃ - C3 symmetry
fac-Ir(ppy) ₃ - C3 对称性

C        3.393895879     -0.289566719      2.776304932
C        4.076284431     -1.374299959      2.244246939
C        3.562788518     -2.026286944      1.144617313
C        2.365194919     -1.600441421      0.563698783
C        1.656920791     -0.490717084      1.087023288
C        2.209908242      0.138316955      2.204838066
C        1.779556093     -2.262575837     -0.593808565
C        2.310998596     -3.397126504     -1.214621244
C        1.678633212     -3.946679457     -2.310344980
C        0.513725976     -3.353425417     -2.779039051
C        0.041132843     -2.238327622     -2.115943483
N        0.643735830     -1.703611386     -1.062120264
C       -3.228320892     -2.843015891      2.244246939
C       -1.947720074     -2.794416690      2.776304932
C       -0.985168124     -1.982995155      2.204838066
C       -1.253433856     -1.189576955      1.087023288
C       -2.568620388     -1.248098174      0.563698783
C       -3.536210228     -2.072321893      1.144617313
C       -2.849226199     -0.409852865     -0.593808565
N       -1.797238653      0.294314111     -1.062120264
C       -1.959015004      1.083541724     -2.115943483
C       -3.161014589      1.231812963     -2.779039051
C       -4.257241276      0.519600723     -2.310344980
C       -4.097497151     -0.302820240     -1.214621244
C       -0.403486935      1.680294039      1.087023288
C       -1.224740118      1.844678200      2.204838066
C       -1.446175805      3.083983409      2.776304932
C       -0.847963539      4.217315849      2.244246939
C       -0.026578290      4.098608837      1.144617313
C        0.203425469      2.848539595      0.563698783
C        1.069670107      2.672428702     -0.593808565
C        1.786498555      3.699946745     -1.214621244
C        2.578608064      3.427078734     -2.310344980
C        2.647288613      2.121612454     -2.779039051
C        1.917882161      1.154785898     -2.115943483
N        1.153502823      1.409297275     -1.062120264
Ir       0.000000000      0.000000000      0.043448572
H        3.792342787      0.222162593      3.641507453
H        5.002872009     -1.707739869      2.689139743
H        4.102575829     -2.869480849      0.738507580
H        1.696641422      0.983426029      2.641159087
H        3.213678708     -3.847263406     -0.836341679
H        2.081671478     -4.823466100     -2.794933558
H       -0.013921102     -3.747584685     -3.633027960
H       -0.865398626     -1.751267403     -2.451342694
H       -3.980382114     -3.478744318      2.689139743
H       -1.703772945     -3.395346490      3.641507453
H        0.003351213     -1.961047587      2.641159087
H       -4.536331226     -2.118194464      0.738507580
H       -1.083942747      1.625090897     -2.451342694
H       -3.238542989      1.885848371     -3.633027960
H       -5.218079916      0.608952668     -2.794933558
H       -4.938667199     -0.859495698     -0.836341679
H       -1.699992635      0.977621558      2.641159087
H       -2.088569843      3.173183897      3.641507453
H       -1.022489895      5.186484186      2.689139743
H        0.433755396      4.987675313      0.738507580
H        1.724988490      4.706759104     -0.836341679
H        3.136408438      4.214513433     -2.794933558
H        3.252464091      1.861736314     -3.633027960
H        1.949341373      0.126176507     -2.451342694

Spin-orbit coupling# 自旋-轨道耦合

SOC with TD-DFT# 含时密度泛函理论的 SOC #

Analysing the SOC-TD-DFT Output#分析 SOC-TD-DFT 输出结果

SOC on a Iridium(III) complex#铱(III)配合物上的 SOC

ZFS and phosphorescence lifetime#ZFS 与磷光寿命

SOC with other methods#与其他方法的系统级芯片

Structures# 结构

Analysing the SOC-TD-DFT Output#
分析 SOC-TD-DFT 输出结果

SOC on a Iridium(III) complex#
铱(III)配合物上的 SOC

ZFS and phosphorescence lifetime#
ZFS 与磷光寿命

SOC with other methods#
与其他方法的系统级芯片