Electronic Circular Dichroism (ECD)#
电子圆二色性 (ECD)

Electronic circular dichroism (ECD) is a method closely related to UV/Vis spectroscopy that makes use of circular polarized light instead of "regular" unpolarized light, and that is extremely helpful to identify chiral compounds.
电子圆二色性（ECD）是一种与紫外/可见光谱学密切相关的方法，它使用圆偏振光而非常规的非偏振光，对于识别手性化合物极为有效。

As an example, suppose you need to determine the absolute configuration of a compound such as the opioid codeine. It can be obtained as a (+) or (-) isomer, and suppose there is no other structural proof of it, what could one do?
举个例子，假设你需要确定如阿片类药物可待因的绝对构型。它可以作为（+）或（-）异构体获得，并且假设没有其他结构证据，那么可以采取什么方法呢？

The (-) isomer is the one that has important medical applications, and one might need be sure about which compound corresponds to which 3D structure. That problem can be tackled with the aid of theory using ORCA, if the ECD spectrum of a pure compound is measured and compared to predicted one.
(-)异构体具有重要的医学应用价值，因此可能需要明确确定哪个化合物对应哪种三维结构。借助 ORCA 理论工具，若能测得纯化合物的 ECD 光谱并与预测光谱进行比对，这一问题便可迎刃而解。

Predicting ECD spectra# 预测 ECD 光谱 #

Let's try to predict the ECD spectra in water for both enantiomers using TD-DFT, starting from the (-)-codeine, which was already studied in the recent literature [Horváth2016].
让我们尝试使用 TD-DFT 从(-)-可待因开始，预测两种对映体在水中的 ECD 光谱，该对映体已在最近的文献[Horváth2016]中进行了研究。

Important 重要

The main steps to obtain the ECD spectra from TD-DFT are the same as those for UV/Vis. Please read the related UVVis spectroscopy (UV/Vis) section before going any further. From now on that will be assumed as known.
获取 TD-DFT 的 ECD 光谱的主要步骤与 UV/Vis 相同。请在继续之前阅读相关 UVVis 光谱学（UV/Vis）部分。从现在起，这将被视为已知。

The first step is to draw and optimize the correct geometry for this molecule:
第一步是绘制并优化该分子的正确几何结构：

!B3LYP DEF2-TZVP D4 OPT FREQ CPCM(WATER)
* XYZFILE 1 1 minuscodeine_guess.xyz

Here we are using a charge +1, we want to reproduce the spectra of this alkaloid in water, and its pKa is about 8. It is necessary to add a proton to the nitrogen group of the structures above to account for protonation at pH 7.
这里我们使用+1 电荷，旨在重现该生物碱在水中的光谱，其 pKa 约为 8。为了解释在 pH 7 时氮原子团的质子化现象，有必要向上述结构中的氮原子团添加一个质子。

The ECD spectra is computed automatically when a TD-DFT is requested, so the input follows the same principles:
当请求 TD-DFT 计算时，ECD 光谱会自动计算，因此输入遵循相同的原则：

!B3LYP DEF2-TZVP CPCM(WATER)
%TDDFT
      NROOTS  25
END
* XYZFILE 1 1 codeine_optimized.xyz

As a solvation model to account for the effect of water on the electronic structure, we will use the CPCM model for the ground state, and the LR-CPCM for the excited state (which is automatically selected together with !CPCM).
作为一种考虑水对电子结构影响的溶剂化模型，我们将对基态使用 CPCM 模型，对激发态使用 LR-CPCM 模型（后者与!CPCM 自动选择）。

Note 注释

Polar solvents can have a large impact on excited states of a charged molecule, don't forget to consider these in such cases!
极性溶剂对带电分子激发态有显著影响，此类情况下切勿忽略这些因素！

Since the ECD is particularly sensitive to the predicted intensities of the transitions, we will also do the calculation using the full TD-DFT instead of the default TDA approximation. In general, the TDA is more stable and gives reliable results, but the prediction of ECD is often better when using the full TD-DFT. The input then is:
由于 ECD 对跃迁的预测强度特别敏感，我们将使用完整的 TD-DFT 进行计算，而不是默认的 TDA 近似。通常，TDA 更为稳定且能给出可靠的结果，但使用完整的 TD-DFT 进行 ECD 预测时，效果往往更佳。因此，输入如下：

!B3LYP DEF2-TZVP CPCM(WATER)
%TDDFT
      NROOTS  25
      TDA     FALSE
END
* XYZFILE 1 1 codeine_optimized.xyz

where now TDA FALSE has been added to suppress it.
其中现已添加 TDA FALSE 以抑制其功能。

The output is exactly how it was shown for UV-Vis before, and in the end the ECD "spectrum" is printed:
输出与之前 UV-Vis 展示的完全一致，最终打印出 ECD“光谱”：

-------------------------------------------------------------------
                             CD SPECTRUM
-------------------------------------------------------------------
State  Energy     Wavelength     R         MX        MY        MZ
       (cm-1)       (nm)     (1e40*cgs)   (au)      (au)      (au)
-------------------------------------------------------------------
   1   38539.1    259.5     -7.97318  -0.08936  -0.09057   0.28910
   2   39977.7    250.1     32.07887   0.18900  -0.02049  -0.22614
   3   43324.1    230.8     12.30861  -0.09352  -0.02155   0.30521
   4   44246.4    226.0    -85.09304   0.38524   0.23404  -0.59099
   5   46657.1    214.3     50.33474   0.08844  -0.07182   0.09990

As you can see, the excited states are followed by their energies, the R value for the excitation (which is proportional to the ECD intensity) and the components of the magnetic dipole. A more detailed description of these states can be obtained from an Analysis of the Excited States.
如您所见，激发态后紧随其能量值、激发态的 R 值（与 ECD 强度成正比）以及磁偶极矩的分量。通过激发态分析，可以获得这些态的更详细描述。

Shifting the predicted spectra#
转换预测光谱

After completion, the spectrum can be plotted in an analogous way to what is described in Plotting the calculated spectrum, except that "CD" has to be selected on the left drop-down menu. And the result is:
完成后，光谱可以以类似于“绘制计算光谱”中所述的方式进行绘制，只是需要在左侧下拉菜单中选择“CD”。结果如下：

As you can see, the main features are reproduced, except that the calculated spectra are shifted to the right. That is a common situation with these predictions and is due to the expected error in the calculated excited state energies. These errors are usually rather systematic, and can be eliminated by doing a counter-shift on the prediction:
如您所见，主要特征得以再现，只是计算的光谱向右偏移。这种情况在预测中很常见，是由于计算激发态能量时预期的误差所致。这些误差通常较为系统性，可以通过在预测中进行反向偏移来消除：

And now both peaks at about 250 nm and 220 nm are coherent with the experimental result.
现在，约 250 nm 和 220 nm 处的两个峰值与实验结果一致。

Important 重要

The shift is not given in nanometers, but in energy units, because the wavelength is not directly proportional to the energy. However common in the literature, there is not much sense to apply a shift in wavelength scale, since the energy correction would be different for each peak!
这种偏移并非以纳米为单位，而是以能量单位表示，因为波长与能量并非直接成正比。尽管在文献中常见，但在波长尺度上应用偏移并无太大意义，因为每个峰的能量校正都会有所不同！

Comparing functionals# 比较泛函

A closer look at the predicted spectra will reveal that they are missing the negative lower energy band, that gives rise to the (-) on the name of that stereoisomer. This is an error caused by the B3LYP functional, that can not be known a priori.
仔细观察预测的光谱会发现，它们缺少了产生该立体异构体名称中“(-)”符号的负低能带。这是由 B3LYP 泛函引起的错误，无法事先知晓。

What we can do is to use a higher level unparametrized methods such as the DLPNO-STEOM, or a different functional, which is what we will do here. Following the reference by [Horváth2016], range-separated functionals should work better on this case. We can then try the modern wB97x functional using:
我们所能做的是采用更高层次的无参数方法，如 DLPNO-STEOM，或选择不同的泛函，这正是我们在此将采取的做法。根据[Horváth2016]的参考文献，范围分离泛函在此情况下应表现更佳。随后，我们可以尝试使用现代的 wB97x 泛函，具体操作如下：

!wB97X DEF2-TZVP CPCM(WATER)
%TDDFT
      NROOTS  25
END
* XYZFILE 1 1 codeine_optimized.xyz

both using TDA and full TD-DFT. The results, already including the necessary shifts are in much better agreement:
两者均采用 TDA 和全 TD-DFT 方法。结果，已经包含了必要的位移，与实际情况更加吻合：

As one can see, the lower energy band now is predicted accordingly. We even plotted the calculated spectrum for the other stereoisomer, (+)-codeine, which has a simulated spectrum that is indeed almost a mirror image of the one from (-)-codeine, in accordance to the experimental results.
由此可见，低能带如今得以相应预测。我们甚至绘制了另一种立体异构体（+）-可待因的计算光谱，其模拟光谱确实与（-）-可待因的光谱几乎呈镜像关系，这与实验结果相符。

Note 注释

There is no need to reoptimize the geometry when looking for stereoisomers. These can be easily generated by choosing one axis, e.g the z, and multiplying all components of the coordinates along that by -1. That is equivalent to a reflection over the xy plane, which generates the "mirror image" of our target molecule.
寻找立体异构体时无需重新优化几何结构。只需选择一个轴，例如 z 轴，并将该轴上所有坐标的分量乘以-1 即可轻松生成。这相当于对 xy 平面进行反射，从而生成目标分子的“镜像”。

Important 重要

ECD spectra are very sensitive to minor geometrical changes! Usually we can only get results close to the experiment by computing the lower energy conformers and making a Boltzmann sum. In this case, the molecule is rather rigid and the problem was minimized, however that is not the usual case.
ECD 光谱对微小的几何变化非常敏感！通常，我们只能通过计算较低能量的构象并进行玻尔兹曼加和来获得接近实验的结果。在这种情况下，分子较为刚性，问题得以最小化，但这并非普遍情况。

Starting structure# 起始结构 #

The (+)-codeine is obtained by reflection!
(+)-可待因通过反射获得！

Electronic Circular Dichroism (ECD)#电子圆二色性 (ECD)

Predicting ECD spectra# 预测 ECD 光谱 #

Shifting the predicted spectra#转换预测光谱

Comparing functionals# 比较泛函

Starting structure# 起始结构 #

Electronic Circular Dichroism (ECD)#
电子圆二色性 (ECD)

Shifting the predicted spectra#
转换预测光谱