Local Energy Decomposition (LED)
局域能量分解(LED)

Decomposition of interaction energies in physically motivated components can be very useful to understand and control interaction patterns of different molecules. The local energy decomposition (LED) approach based on DLPNO-CCSD(T) interaction energies available within ORCA is one of the most sophisticated ones available.
将相互作用能分解为物理上可解释的组成部分，对于理解和调控不同分子间的相互作用模式极为有益。基于 ORCA 中可用的 DLPNO-CCSD(T)相互作用能的局部能量分解（LED）方法，是目前最为精密的分解方法之一。

$$\mathrm{\Delta }{E}_{int.}=\mathrm{\Delta }{E}_{el-prep}^{ref.}+E_{elstat}^{ref.}+E_{exch}^{ref.}+\mathrm{\Delta }{E}_{non-dispersion}^{C-CCSD}+E_{dispersion}^{C-CCSD}+\mathrm{\Delta }{E}_{int}^{C-(T)}$$

Often, the geometry relaxation upon coordination is additionally considered as $\mathrm{\Delta }{E}_{geo-prep}$. This contribution is also known as strain. For more information on the interpretation and physical meaning of the LED contributions refer to the ORCA manual and refs. [Bistoni2020c][Bistoni2021].
通常，配位时的几何弛豫也被视为 $\mathrm{\Delta }{E}_{geo-prep}$ 。这种贡献也被称为应变。关于 LED 贡献的解释及其物理意义，请参阅 ORCA 手册及参考文献[Bistoni2020c][Bistoni2021]。

Example: Alkane coordination in CpRe(CO)₂(n-pentane)
示例：CpRe(CO) ₂ （正戊烷）中的烷烃配位#

As an example, we will decompose the interaction energy of n-pentane in CpRe(CO)₂(n-pentane).
作为一个示例，我们将分解 n-戊烷在 CpRe(CO) ₂ （n-戊烷）中的相互作用能。

Figure: Molecular structure of CpRe(CO)₂(n-pentane).
图：CpRe(CO) ₂ （正戊烷）的分子结构。

The LED analysis can be envoked by the simple input keyword LED. Further, the fragments CpRe(CO)₂ (1) and n-pentane (2) can be defined in the input file:
通过输入关键字 LED 即可调用 LED 分析。此外，输入文件中可以定义片段 CpRe(CO) ₂ (1)和正戊烷(2)：

!DLPNO-CCSD(T) DEF2-SVP DEF2-SVP/C DEF2/J RIJCOSX VERYTIGHTSCF TIGHTPNO LED

*XYZ 0 1
C(1) -4.46463 -0.12110 0.22162
[...]
O(1) -0.99391 0.49487 -2.78478
C(2) 0.15487 -0.43421 0.93360
[...]
H(2) 5.37983 -0.86517 1.10337
*

Important 重要

Note that in practice, basis sets of triple-zeta quality or larger are recommended.
请注意，在实际应用中，建议使用三重ζ质量或更高级别的基组。

This calculation will give you a summary of the LED analysis with all energies in atomic units:
此计算将为您提供 LED 分析的汇总，所有能量均以原子单位表示：

-------------------------------------------------
FINAL SUMMARY DLPNO-CCSD ENERGY DECOMPOSITION (Eh)
------------------------------------------------- 

Intrafragment REF. energy:    
Intra fragment   1 (REF.)              -494.831830000
Intra fragment   2 (REF.)              -196.014013871     

Interaction of fragments  2 and  1:
Electrostatics (REF.)                  -0.191884228
Exchange (REF.)                        -0.064166273
Dispersion (strong pairs)              -0.015681646 
Dispersion (weak pairs)                -0.001188732

Sum of non dispersive correlation terms:
Non dispersion (strong pairs)          -2.466925458  
Non dispersion (weak pairs)            -0.001535283

From this output, we can directly extract three of the contributions:
从这一输出中，我们可以直接提取出三个贡献：

$$E_{elstat}^{ref.}=\text{Electrostatics (REF.)}=-0.191884228$$

$$E_{exch}^{ref.}=\text{Exchange (REF.)}=-0.064166273$$

$$E_{dispersion}^{C-CCSD}=\text{Dispersion (strong pairs)}+\text{Dispersion (weak pairs)}=-0.016870378$$

For the other three terms, we need additional calculations at the same level for the isolated fragments in the complex geometry.
对于其他三个项，我们需要对复杂几何中的孤立片段进行相同级别的额外计算。

For CpRe(CO)₂ (1): 对于 CpRe(CO) ₂ (1):

!DLPNO-CCSD(T) DEF2-SVP DEF2-SVP/C DEF2/J RIJCOSX VERYTIGHTSCF TIGHTPNO LED

*XYZ 0 1
C(1) -4.46463 -0.12110 0.22162
[...]
O(1) -0.99391 0.49487 -2.78478

and for n-pentane (2): 对于正戊烷（2）：

!DLPNO-CCSD(T) DEF2-SVP DEF2-SVP/C DEF2/J RIJCOSX VERYTIGHTSCF TIGHTPNO

*XYZ 0 1
C(2) 0.15487 -0.43421 0.93360
[...]
H(2) 5.37983 -0.86517 1.10337
*

These calculations will give you essential parts needed to calculate the remaining contributions: E(0), E(CORR)(corrected), and Triples Correction (T):
这些计算将为您提供计算剩余贡献所需的关键部分： E(0) 、 E(CORR)(corrected) 和 Triples Correction (T) ：

The respective parts of the output for CpRe(CO)₂ (1) look like:
CpRe(CO) ₂ (1) 的输出各部分如下所示：

E(0)                                       ...   -494.901127802
E(CORR)(strong-pairs)                      ...     -1.652880182
E(CORR)(weak-pairs)                        ...     -0.001184997
E(CORR)(corrected)                         ...     -1.654065179
E(TOT)                                     ...   -496.555192980

Triples Correction (T)                     ...     -0.071314179
Final correlation energy                   ...     -1.725379358
E(CCSD)                                    ...   -496.555192980
E(CCSD(T))                                 ...   -496.626507159

and for n-pentane (2) like:
而对于正戊烷（2）则类似：

E(0)                                       ...   -196.190109425
E(CORR)(strong-pairs)                      ...     -0.806037106
E(CORR)(weak-pairs)                        ...     -0.000302982
E(CORR)(corrected)                         ...     -0.806340087
E(TOT)                                     ...   -196.996449513

Triples Correction (T)                     ...     -0.022482469
Final correlation energy                   ...     -0.828822556
E(CCSD)                                    ...   -196.996449513
E(CCSD(T))                                 ...   -197.018931981

With these data, we can now calculate the missing LED contributions:
根据这些数据，我们现在可以计算缺失的 LED 贡献：

$$\begin{array}{r}\begin{array}{rl}\mathrm{\Delta }{E}_{el-prep}^{ref.}& =[\text{Intra fragment 1 (REF.)}-{\text{E(0)}}_{frag1}]+[\text{Intra fragment 2 (REF.)}-{\text{E(0)}}_{frag2}]\\ & =0.245393356\end{array}\end{array}$$

$$\begin{array}{r}\begin{array}{rl}\mathrm{\Delta }{E}_{non-dispersion}^{C-CCSD}& =(\text{non-dispersion (strong pairs)}+\text{non-dispersion (weak pairs)})\\ & -({\text{E(CORR)(corrected)}}_{frag1}+{\text{E(CORR)(corrected)}}_{frag2})\\ & =-0.008055475\end{array}\end{array}$$

$$\begin{array}{r}\begin{array}{rl}\mathrm{\Delta }{E}_{int}^{C-(T)}& ={\text{Triples Correction (T)}}_{complex}\\ & -({\text{Triples Correction (T)}}_{frag1}+{\text{Triples Correction (T)}}_{frag2})\\ & =-0.002667349\end{array}\end{array}$$

Now, we have all components of the LED analysis of the interaction energy of the fragments:
现在，我们已具备分析片段间相互作用能量的 LED 分析的所有组成部分：

$\mathrm{\Delta }{E}_{int.}$	$\mathrm{\Delta }{E}_{el-prep}^{ref.}$	$E_{elstat}^{ref.}$	$E_{exch}^{ref.}$	$\mathrm{\Delta }{E}_{non-disp.}^{C-CCSD}$	$E_{disp.}^{C-CCSD}$	$\mathrm{\Delta }{E}_{int}^{C-(T)}$	Sum 总和
a.u. 任意单位	0.24539	-0.19188	-0.06417	-0.00806	-0.01687	-0.00267	-0.03825
kcal/mol 千卡/摩尔	153.99	-120.41	-40.26	-5.05	-10.59	-1.67	-24.00

All six contributions sum up to the overall interaction energy that is also obtained from subtracting the total energies of the fragments from that of the complex. The following graphics summarizes the steps that have to be performed and from which calculation data are needed to calculate the individual components.
所有六项贡献总和即为整体相互作用能，该能量亦可通过从复合物总能量中减去各片段总能量获得。以下图示总结了需执行的步骤以及计算各组成部分所需的数据来源。

Figure: Schematic summary of a LED analysis.
图：LED 分析的示意图总结。

Dispersion Interaction Density (DID)
分散相互作用密度 (DID)

Since London dispersion interactions are a crucial component of the interaction energy, understanding and controlling them became an integral part of modern compound design. For example, the concept of dispersion-energy-donors (DED).[Grimme2006][Grimme2011c][Schreiner2015] became particularly useful in this context. One way to visualize the London dispersion component of the LED analysis is the Dispersion Interaction Density (DID) plot.[Mata2016][Bistoni2019]
由于伦敦色散相互作用是相互作用能量的关键组成部分，理解和控制它们成为现代化合物设计的重要部分。例如，色散能量供体（DED）的概念在此背景下变得尤为有用。[Grimme2006][Grimme2011c][Schreiner2015] 一种可视化 LED 分析中伦敦色散分量的方法是使用色散相互作用密度（DID）图。[Mata2016][Bistoni2019]
To obtain the DID, you can simply add %mdci DoDIDplot true end to your LED input and run the calculation as described before.
要获取 DID，只需在 LED 输入中添加 %mdci DoDIDplot true end ，并按照之前所述运行计算即可。

After a successful calculation, the DID will be stored in the basename.densities container as basename.ded21.
计算成功后，DID 将被存储在 basename.densities 容器中，作为 basename.ded21 。

We can now use orca_plot to create a plotable datafile from the DID. To open the interactive interface call
我们现在可以使用 orca_plot 从 DID 创建一个可绘制的数据文件。要打开交互界面，请调用

orca_plot basename.gbw -i

Here, we now choose 1 - Enter type of plot to decide what to plot
在此，我们现选择 1 - Enter type of plot 以确定绘制内容

PlotType       ... MO-PLOT
MO/Operator    ... 0 0
Output file    ... (null)
Format         ... Grid3d/Cube
Resolution     ... 40 40 40
Boundaries     ...   -16.680972    18.410507 (x direction)
                     -12.311453    12.849005 (y direction)
                     -12.262472    11.601143 (z direction)

       1 - Enter type of plot
       2 - Enter no of orbital to plot
       3 - Enter operator of orbital (0=alpha,1=beta)
       4 - Enter number of grid intervals
       5 - Select output file format
       6 - Plot CIS/TD-DFT difference densities
       7 - Plot CIS/TD-DFT transition densities
       8 - Set AO(=1) vs MO(=0) to plot
       9 - List all available densities
      10 - Perform Density Algebraic Operations

      11 - Generate the plot
      12 - exit this program
Enter a number: 

From the given list, we now chose 15 - LED dispersion interaction density (ded21) which is also highlighted as available
从给定列表中，我们现选择 15 - LED dispersion interaction density (ded21) ，该项亦被标记为 available

     1 -   molecular orbitals                          
     2 -   (scf) electron density                              ......  (scfp                     )  => AVAILABLE
     3 -   (scf) spin density                                  ......  (scfr                     )  - NOT AVAILABLE
     4 -   natural orbitals                               
     5 -   corresponding orbitals                         
     6 -   atomic orbitals                                
     7 -   mdci electron density                               ......  (mdcip                    )  - NOT AVAILABLE
     8 -   mdci spin density                                   ......  (mdcir                    )  - NOT AVAILABLE
     9 -   OO-RI-MP2 density                                   ......  (pmp2re                   )  - NOT AVAILABLE
    10 -   OO-RI-MP2 spin density                              ......  (pmp2ur                   )  - NOT AVAILABLE
    11 -   MP2 relaxed density                                 ......  (pmp2re                   )  - NOT AVAILABLE
    12 -   MP2 unrelaxed density                               ......  (pmp2ur                   )  - NOT AVAILABLE
    13 -   MP2 relaxed spin density                            ......  (rmp2re                   )  - NOT AVAILABLE
    14 -   MP2 unrelaxed spin density                          ......  (rmp2ur                   )  - NOT AVAILABLE
    15 -   LED dispersion interaction density                  ......  (ded21                    )  => AVAILABLE
[...]
    42 -   LFT QDPT unrelaxed transition AO density            ......  (Tdens-LFTQDSOC           )  - NOT AVAILABLE
Enter Type: 

Now, the program will ask you if the suggested default basename.ded21density file is the correct one, which we confirm
现在，程序将询问您建议的默认 basename.ded21 密度文件是否正确，我们确认

The default name of the density would be: led.ded21
Is this the one you want (y/n)? y

Via the options 5 - Select output file format we can further choose the format of the output file, in this case Gaussian cube, and via 4 - Enter number of grid intervals and the number of grid points that may be included. 11 - Generate the plot will then create the basename.eldens.cube file. This file now containes the data of the DID that finally may be rendered onto the simple electron density. The respective electron density can be created in the same way by simply choosing 2 - (scf) electron density instead.
通过选项 5 - Select output file format ，我们可以进一步选择输出文件的格式，在此情况下为 Gaussian cube ，并通过 4 - Enter number of grid intervals 和可能包含的网格点数量。随后， 11 - Generate the plot 将生成 basename.eldens.cube 文件。该文件现包含最终可渲染到简单电子密度上的 DID 数据。相应的电子密度可通过简单地选择 2 - (scf) electron density 来以相同方式创建。

These files can now be used to render the DID plot, for example with ChimeraX. On the left, you see the DID (isovalue = 0.12 kJ/mol/bohr³) and on the right the DID mapped to the electron density.
这些文件现在可以用于渲染 DID 图，例如使用 ChimeraX。左侧显示的是 DID（等值线=0.12 kJ/mol/bohr ³ ），右侧则是将 DID 映射到电子密度上的结果。

Figure: Left: direct DID plot (isovalue = 0.12 kJ/mol/bohr³); right: DID mapped to the electron density.
图：左：直接 DID 图（等值线 = 0.12 kJ/mol/bohr ³ ）；右：DID 映射到电子密度。

From the DID plot, we can easily see which parts of the fragments contribute most to the dispersion component of the interaction energy.
从 DID 图中，我们可以轻松看出片段的哪些部分对相互作用能的分散分量贡献最大。

Structures

CpRe(CO)₂(n-pentane)

32

C -4.46463 -0.12110 0.22162 # start fragment 1
C -4.04623 -0.94060 -0.87986
C -3.23056 -2.00842 -0.35445
C -3.13403 -1.81280 1.05377
C -3.91155 -0.67695 1.43080
H -4.06405 -0.30844 2.43482
H -2.55793 -2.42869 1.73308
H -2.78231 -2.81070 -0.92293
H -4.33874 -0.81051 -1.91193
H -5.12295 0.73363 0.15767
Re -2.25459 0.06030 -0.00431
C -2.28573 1.94921 0.30847
O -2.41945 3.09516 0.50242
C -1.42081 0.35728 -1.70388
O -0.99391 0.49487 -2.78478 # end fragment 1
C 0.15487 -0.43421 0.93360 # start fragment 2
C 1.36998 0.37687 0.48298
C 2.65689 -0.45514 0.51279
C 3.88944 0.33865 0.06397
C 5.17382 -0.49523 0.09209
H 6.03818 0.09339 -0.23266
H -0.71033 0.32056 1.08127
H -0.03361 -1.27625 0.26666
H 0.26149 -0.82286 1.95167
H 1.48316 1.25742 1.12785
H 1.19312 0.75113 -0.53133
H 2.53534 -1.33457 -0.13562
H 2.82276 -0.83988 1.52947
H 4.00603 1.21834 0.71103
H 3.71924 0.72157 -0.95085
H 5.09141 -1.36476 -0.57032
H 5.37983 -0.86517 1.10337 # end fragment 2