Calculating accurate energy barriers#
计算精确的能量势垒

Besides studying the mechanistic details of chemical reactions, ORCA can also be used to calculate accurate energy barriers, and thus predict reaction rates to a certain accuracy.
除了研究化学反应的机制细节外，ORCA 还可用于计算精确的能量势垒，从而在一定精度内预测反应速率。

It must be clear here that it is rather difficult to compare the absolute values of the experimental energy barriers with the calculates ones. First, because these "experimental" values are never measured directly, but obtained from measured data only after a series of assumptions.
这里必须明确，将实验能量势垒的绝对值与计算值进行比较是相当困难的。首先，因为这些“实验”值从未直接测量，而是仅在做出一系列假设后从测量数据中获得。

Second because, unless your are modeling the solvent explicitly, there will always be a relatively large error associated to solvation. And that is to say the least if one also does not account for conformational entropy, transmission coefficients and so on.
其次，因为除非你明确地对溶剂进行建模，否则总是会与溶剂化过程相关联一个相对较大的误差。更不用说，如果再不考虑构象熵、透射系数等因素，那误差就更大了。

Study case: the Diels-Alder reaction#
研究案例：Diels-Alder 反应

Still, it does make sense to compare relative reaction energy barriers and rates, and we will show here how one could do that for a classic Diels-Alder (DA) reaction between cyclopentadiene and some dieneophiles:
尽管如此，比较相对反应能垒和速率仍然是有意义的，我们将在此展示如何对经典的二烯加成（DA）反应进行此类比较，该反应涉及环戊二烯与某些亲二烯体的反应：

That is an important reaction, that conserves all of the atoms from the reactants, and particularly useful to synthesize chiral compounds. Its reaction rate varies drastically with the nature of the reactants, from $10^{- 8}$ to $10^{2} s^{- 1}$ [Guo2012], and its known that electron-withdrawing groups on the dieneophile accelerate the formation of the cyclic products:
这是一种重要的反应，保留了反应物中的所有原子，尤其适用于合成手性化合物。其反应速率随反应物性质的差异而剧烈变化，从 $10^{- 8}$ 到 $10^{2} s^{- 1}$ 不等[Guo2012]，已知二烯亲电体上的吸电子基团会加速环状产物的形成：

Let's try to investigate the relative barrier heights for the reaction between cyclopentadiene and the cyanide compounds above using the NEB-TS method to find the transition states, and investigate the effect of adding proper Correlation energy to it.
让我们尝试使用 NEB-TS 方法研究环戊二烯与上述氰化物化合物反应的相对势垒高度，以寻找过渡态，并探讨添加适当相关能对其的影响。

First, the transition state#
首先，过渡态#

The transition state (TS) for DA reactions is nothing unusual, except for the fact that three double bonds are being broken and two single bonds are being formed at the same time, which is sometimes hard to track using the usual TS-search algorithms that rely on a single coordinate search.
DA 反应的过渡态（TS）并无特别之处，只是同时有三条双键断裂和两条单键形成，这在使用依赖单一坐标搜索的常规 TS 搜索算法时有时难以追踪。

By using ORCA's NEB-TS method, the TS search is made much simpler, and all that is needed are the structures of the reactant and products. To optimize these using, e.g, B3LYP and a good DEF2-TZVP basis, one can use:
通过使用 ORCA 的 NEB-TS 方法，过渡态搜索变得简单得多，只需反应物和产物的结构即可。例如，使用 B3LYP 方法和良好的 DEF2-TZVP 基组来优化这些结构，可以采用以下步骤：

!B3LYP D4 DEF2-SVP OPT FREQ CPCM(TOLUENE)
* XYZFILE 0 1 4CN_reactant.xyz

Here we are using the D4 correction [Grimme2017] to account for dispersion interaction, which is key in this case, and the CPCM solvation model [Truhlar2009] to include solvation effects to some extent.
在此，我们采用 D4 校正[Grimme2017]来处理色散相互作用，这在当前情况下至关重要，并使用 CPCM 溶剂化模型[Truhlar2009]来在一定程度上纳入溶剂化效应。

After checking that both reactant and product are real minima, without any negative frequencies, one can already start the NEB-TS calculation using the optimized structures:
在确认反应物和产物均为无虚频的实极小点后，即可利用优化后的结构开始 NEB-TS 计算：

!B3LYP D4 DEF2-SVP NEB-TS FREQ CPCM(TOLUENE)
%NEB
      NEB_END_XYZFILE "4CN_product_optimized.xyz"
END
* XYZFILE 0 1 4CN_reactant_optimized.xyz

The new keywords here are the NEB-TS and FREQ on the main input, and the name of the file containing the product geometry under %NEB. If everything goes well, a TS having a single negative frequency of about $- 368 c m^{- 1}$ will be automatically found:
这里的新关键词是主输入中的 NEB-TS 和 FREQ，以及%NEB 下包含产品几何形状的文件名。如果一切顺利，将自动找到一个具有约 $- 368 c m^{- 1}$ 的单个负频率的过渡态：

Calculating the energy barrier#
计算能量势垒

With the TS and reactant in hands, one can immediately compute the $Δ G^{‡} = G_{T S}^{o} - G_{r e a c t a n t}^{o}$ from the Gibbs free energy difference between them. Here is a table summarizing the results for the three cyanides shown above:
有了 TS 和反应物，便可立即根据它们之间的吉布斯自由能差计算出 $Δ G^{‡} = G_{T S}^{o} - G_{r e a c t a n t}^{o}$ 。以下是上述三种氰化物结果的汇总表：

Summary of the energy barriers ( $Δ G^{‡}$ ) calculated to far, in kcal/mol.
计算得出的能量势垒（ $Δ G^{‡}$ ）总结，单位为千卡/摩尔。#
Compound 复合物	B3LYP	Exp. 实验。
2 CN	9.90	17.7
3 CN	10.69	16.2
4C	10.21	13.6

Well, that is actually not very helpful, since there is not even a clear trend! There is no clear trend resulting from the B3LYP calculation, however, the geometries look fine and the transition states are indeed saddle-points on the potential energy surface. Can we get something better than this?
嗯，这实际上并没有太大帮助，因为甚至没有明确的变化趋势！B3LYP 计算并未显示出清晰的趋势，然而，几何结构看起来合理，过渡态确实是势能面上的鞍点。我们能否得到比这更好的结果呢？

Using DLPNO-CCSD(T) to correct the electronic energy#
使用 DLPNO-CCSD(T)校正电子能量

In general DFT is known to reproduce geometries and frequencies with reasonable quality for its low cost, but the energies are definitely a weak point. And they are even worse if the system studied is outside the training set of the functionals, which normally do not included transition states or atypical bonding situations.
通常，DFT 以其低成本能够合理地重现几何结构和频率，但其能量计算无疑是一个薄弱环节。若所研究的体系超出了泛函的训练集范围，情况尤为糟糕，这些泛函通常不包含过渡态或非典型成键情况。

There is where higher level ab initio methods should be used to compute the electronic energy of these systems. Correlated methods such as CCSD(T) are unparametrized, based on real physical principles and should truly reproduce the experimental results.
这就是应采用高级别从头计算方法来计算这些系统电子能量的地方。诸如 CCSD(T)之类的相关方法无参数化，基于真实的物理原理，并应能真正再现实验结果。

Using those methods together with the The DLPNO scheme developed by the ORCA team allows for fast a accurate calculations of these barriers task. To compute an accurate electronic energy in this case, we could take the DFT geometry and run:
结合 ORCA 团队开发的 DLPNO 方案使用这些方法，能够快速且准确地计算这些势垒任务。为在此情况下计算精确的电子能量，我们可以采用 DFT 几何结构并运行：

!DLPNO-CCSD(T) DEF2-TZVPP DEF2-TZVPP/C
* XYZFILE 0 1 4CN_reactant_optimized.xyz

for both the reactant and the TS.
对于反应物和过渡态均如此。

Converting $E_{e l}$ to $G^{o}$ #
将 $E_{e l}$ 转换为 $G^{o}$ #

In order to transform the DLPNO-CCSD(T) electronic energy ( $E_{e l}$ ) into a true $G^{o}$ , we have to include the vibrational corrections already discussed in the Thermodynamics section. As DFT predicts frequencies relatively well, we can use the correction obtained previously here.
为了将 DLPNO-CCSD(T)电子能量（ $E_{e l}$ ）转换为真正的 $G^{o}$ ，我们必须包含在热力学部分已讨论过的振动修正。由于 DFT 在预测频率方面表现相对良好，我们可以在此使用之前获得的修正。

To account for solvation, we can also take the $Δ G_{s o l v}$ presented in the Implicit Solvation Models section, as computed with DFT and add them up to obtained a better final $Δ G^{‡}$ :
为了考虑溶剂化效应，我们可以采用隐式溶剂模型部分中通过 DFT 计算得到的 $Δ G_{s o l v}$ ，并将它们相加，以获得更优的最终 $Δ G^{‡}$ ：

Δ G_{s o l v}^{‡} = E_{e l} (D L N P O - C C) + Δ G_{c o r r e c t i o n} (D F T) + Δ G_{s o l v}^{o} (D F T)

Using these results, our updated table is now:
基于这些结果，我们更新后的表格如下：

Summary of the energy barriers ( $Δ G^{‡}$ ) calculated, in kcal/mol.
计算所得的能量势垒（ $Δ G^{‡}$ ）总结，单位为 kcal/mol。#
Compound 复合物	B3LYP	CCSD(T)	Exp. 实验。
2 CN	9.90	14.71	17.7
3 CN	10.69	12.73	16.2
4 CN	10.31	9.48	13.6

And the patter is clearly there. We can even plot a graphic to show that there is indeed a linear correlation between the calculated and the experimental energy barriers:
这种规律性显而易见。我们甚至可以绘制图表来展示计算得到的能垒与实验测得的能垒之间确实存在线性相关性：

That means now we could, in principle, use this model to predict the experimental reaction barriers for unknown compounds with quite good accuracy, by calculating them and adjusting them to the fit!
这意味着，原则上我们现在可以利用这一模型，通过计算并调整拟合，相当准确地预测未知化合物的实验反应能垒！

Important 重要

Again: it is very unlikely that the predicted and measured energy barriers will be equal, unless by coincidence. We not necessarily calculating the same quantity that was measured, but there should be relations like the one demonstrated above.
再次强调：除非巧合，否则预测的能量势垒与实测值几乎不可能相等。我们未必在计算与实测相同的量，但应存在如上所示的关系。

Calculating accurate energy barriers#计算精确的能量势垒

Study case: the Diels-Alder reaction#研究案例：Diels-Alder 反应

First, the transition state#首先，过渡态#

Calculating the energy barrier#计算能量势垒

Using DLPNO-CCSD(T) to correct the electronic energy#使用 DLPNO-CCSD(T)校正电子能量

Converting Eel to Go#将 Eel 转换为 Go #

Structures# 结构