Bond Analysis# 债券分析 #

Analysis of chemical bonding is crucial to understand the reactivity and properties of any compound. ORCA provides various tools to investigate and visualize chemical bonds based on quantum chemical methods.
化学键合分析对于理解任何化合物的反应性和性质至关重要。ORCA 提供了多种工具，基于量子化学方法来研究和可视化化学键。

Localized Orbitals# 局域轨道 #

While canonical molecular orbitals yield valuable information, they can be difficult to interpret due to their delocalized nature. This is particularly the case for large molecules. A more convenient alternative is localizing the molecular orbitals to identify bonding overlaps in line with chemically established bonding concepts. The most prominent localization techniques are Foster-Boys (FB) and Pipek-Mezey (PM) localizations.
虽然正则分子轨道提供了宝贵的信息，但由于其离域性，解释起来可能颇具挑战，尤其是在大型分子中。一种更为便捷的替代方案是将分子轨道局域化，以便根据化学上已确立的成键概念识别成键重叠。最突出的局域化技术是 Foster-Boys（FB）和 Pipek-Mezey（PM）局域化方法。

Example 1: Cr-Cr Bonding in Dichromium Tetraacetate Dihydrate#
示例 1：二铬四乙酸二水合物中的铬-铬键合

In this tutorial we will use a Pipek-Mezey localization to study the bonding situation in dichromium tetraacetate dihydrate, a well-known textbook example of a metal-metal quadruple bond. The PM localization on the previously optimized geometry of the complex is envoked by:
在本教程中，我们将采用 Pipek-Mezey 局域化方法研究二铬四乙酸二水合物的成键情况，这是一个著名的金属-金属四重键教科书案例。通过以下命令，在先前优化过的该配合物几何结构上进行 PM 局域化：

!r2SCAN-3c

%LOC
 LOCMET PM
END

*XYZFILE 0 1 structure.xyz

In the output file the details of the localization will be printed after
在输出文件中，本地化详情将在之后打印

------------------------------------------------------------------------------
                           ORCA ORBITAL LOCALIZATION
------------------------------------------------------------------------------

and the summary of the localized molecular orbitals (LMOs) is given. Further, the localized orbitals are stored in the basename.loc file.
并给出了局域化分子轨道（LMOs）的总结。此外，局域化轨道存储在 basename.loc 文件中。

--------------------------------------------------------------------------------
                    LOCALIZED MOLECULAR ORBITAL COMPOSITIONS
--------------------------------------------------------------------------------

The Mulliken populations for each LMO on each atom are computed
The LMO`s will be ordered according to atom index and type
  (A) Strongly localized MO`s have populations of >=0.950 on one atom
  (B) Two center bond orbitals have populations of >=0.850 on two atoms
  (C) Other MO`s are considered to be `delocalized`

FOUND  -  20 strongly local MO`s
       -  48 two center bond MO`s
       -   0 significantly delocalized MO`s

Rather strongly localized orbitals:
MO  47:  32O  -   0.964883
[...]
MO  28:   0Cr -   1.014036
Bond-like localized orbitals:
MO  95:  35H  -   0.340608  and  30O  -   0.658898
[...]
MO  66:  12O  -   0.869229  and   9Cr -   0.109159
MO  65:  11O  -   0.876956  and   9Cr -   0.092742
MO  64:  11O  -   0.587896  and   5C  -   0.415626
MO  63:  11O  -   0.793870  and   5C  -   0.182382
MO  62:  10O  -   0.869257  and   9Cr -   0.109543
MO  61:   9Cr -   0.488121  and   0Cr -   0.526559
MO  60:   9Cr -   0.472239  and   0Cr -   0.471944
MO  59:   9Cr -   0.541468  and   0Cr -   0.525393
MO  58:   9Cr -   0.541872  and   0Cr -   0.524219
MO  57:   8C  -   0.463590  and   7C  -   0.609424
[...]
MO  48:   1O  -   0.869095  and   0Cr -   0.109446
Localized MO's were stored in: orca.loc

From this output, we can see that ORCA identified 4 "bond-like" LMOs between the two chromium atoms with almost 50/50 electron populations. This indicates four relevant bonding contributions in line with the expected σ-, 2×π-, and δ-bonds. To visualize these bonds after successful calculation, we can utilize orca_plot. To do so, we rename the basename.loc file to loc.gbw and call orca_plot in its interactive mode (-i).
从这一输出结果中，我们可以看到 ORCA 识别出两个铬原子间存在 4 个“类键”的 LMOs，其电子分布接近 50/50。这表明存在四个与预期σ-、2×π-和δ-键相符的相关键合贡献。为了在计算成功后可视化这些键，我们可以利用 orca_plot 。为此，我们将 basename.loc 文件重命名为 loc.gbw ，并在其交互模式下调用 orca_plot （ -i ）。

orca_plot loc.gbw -i

We can now plot the LMOs like normal MOs by choosing the respective orbital number via option 2 - Enter no of orbital to plot (for high-quality plots, we adjusted the number of grid intervals to 100 via 4 - Enter number of grid intervals). The obtained .cube files can now be visualized with ChimeraX or any other program of choice.
我们现在可以通过选择相应的轨道编号（通过选项 2 - Enter no of orbital to plot ）像绘制普通分子轨道一样绘制 LMOs（为了获得高质量的图像，我们通过 4 - Enter number of grid intervals 将网格间隔数调整为 100）。生成的 .cube 文件现在可以使用 ChimeraX 或任何其他选择的程序进行可视化。

../_images/cracetate-locbonds.png

Figure: Localized Molecular Orbitals of the Cr-Cr quadruple bond.
图：Cr-Cr 四重键的局域分子轨道。#

We see, that the visualized LMOs perfectly match our expectations.
我们看到，可视化的 LMOs 完全符合我们的预期。

Structures# 结构

Dichromium Tetraacetate Dihydrate
二铬四乙酸二水合物
36

  Cr          3.63292803675582      4.78285607739625     -0.63639358256050
  O           2.34785749491859      4.48652278178970     -2.12009832625825
  O           5.13493229672345      5.30466992720158      0.58344087799744
  O           4.73076207322555      3.26794262826257     -1.29923843647248
  O           2.73716250606921      6.52977972635174     -0.24223293301648
  C           1.34714372264977      3.77755038643592     -1.79342034446331
  C           0.28882874973655      3.46634459556225     -2.81104036856054
  C           4.49276620679543      2.16989237310360     -0.70883979137882
  C           5.25046716873396      0.93386548365656     -1.09583669544289
  Cr          2.72281835907000      3.84276439529425      0.61069113865845
  O           4.00842988963071      4.13941356801647      2.09374138676694
  O           1.22096071474473      3.32092019482001     -0.61027879254538
  O           1.62460073626451      5.35790230455260      1.27270500588077
  O           3.61876789645852      2.09613885710674      0.21605424661246
  C           5.00922985477937      4.84802707447584      1.76669231158828
  C           6.06814229046835      5.15890455396898      2.78377912360696
  C           1.86247448824412      6.45579094664928      0.68192448021066
  C           1.10332879431268      7.69141916931006      1.06747861321807
  H           0.53643199444775      3.91479455350269     -3.77316600096031
  H           0.19363516930407      2.38162440858367     -2.91892115129840
  H          -0.67646851589299      3.84412291439512     -2.46031116829040
  H           5.82036413122407      0.57284519899174     -0.23393409530863
  H           4.54651848337104      0.14401323934197     -1.37402597678676
  H           7.03354834642659      4.78268981767564      2.43171518212094
  H           6.16212212277575      6.24359469909520      2.89312979871985
  H           5.82180818584082      4.70895962627934      3.74553075821521
  H           5.92625733753088      1.14156035056277     -1.92544044162556
  H           0.42730948584067      7.48388311065848      1.89692409507629
  H           1.80630411261855      8.48232991810399      1.34513931752921
  H           0.53353311936446      8.05099140285292      0.20489050593958
  O           1.41030940144609      2.25034914090934      2.03754830017122
  H           0.69456507333094      2.16354974421073      1.39521339423714
  O           4.95323562321733      6.38396944730196     -2.06427896840346
  H           4.37901353165716      7.13631180534098     -1.87274555994989
  H           5.66469043982413      6.46222396268224     -1.41594550916286
  H           1.98371067809123      1.49606161555666      1.85174960593545