Vibrational frequencies#
振动频率

After performing a Geometry optimization, you might want to compute the vibrational frequency of your system and plot normal mode animations. Here is how to do it, using the acetic acid as an example:
在完成几何优化后，您可能希望计算系统的振动频率并绘制正常模式动画。以下是使用乙酸作为示例的操作方法：

../_images/aceticacid.png

Figure: Molecular structure of acetic acid.
图：乙酸的分子结构。#

Frequencies# 频率 #

In order to first compute the frequencies, e.g. using DFT and the B3LYP functional use:
为了首先计算频率，例如使用 DFT 和 B3LYP 泛函，请执行以下操作：

!B3LYP D4 DEF2-SVP FREQ
* XYZ 0 1
C         -0.81589       -0.51571       -0.02512
C          0.30690        0.49327       -0.06114
H         -0.42809       -1.56713       -0.28060
H         -1.26914       -0.51520        1.06962
H         -1.64631       -0.14518       -0.75104
O          0.16587        1.68279       -0.21470
O          1.51380       -0.07303        0.21899
H          2.16801        0.64625        0.13143
*

or one can also do that immediately after an optimization run using:
或者也可以在优化运行后立即执行此操作：

!B3LYP D4 DEF2-SVP OPT FREQ
* XYZFILE 0 1 aceticacid.xyz

and a geometry optimization will be performed. In case of success, it will be followed by the frequency calculation. When the computation of the Hessian matrix starts, a header will be printed:
并将进行几何优化。若成功，随后将进行频率计算。当 Hessian 矩阵的计算开始时，将打印一个标题：

-------------------------------------------------------------------------------
                               ORCA SCF HESSIAN
-------------------------------------------------------------------------------

Hessian of the Kohn-Sham DFT energy:
Kohn-Sham wavefunction type                      ... RKS
Hartree-Fock exchange scaling                    ...    0.200
Number of operators                              ...    1
Number of atoms                                  ...    8
Basis set dimensions                             ...   76
Integral neglect threshold                       ... 2.5e-11
Integral primitive cutoff                        ... 2.5e-12

followed by the calculation of all of the necessary terms. After it is completed, one will directly see the vibrational frequencies in cm−1:
随后计算所有必要项。完成后，将直接在 cm−1 中看到振动频率：

-----------------------
VIBRATIONAL FREQUENCIES
-----------------------

Scaling factor for frequencies =  1.000000000  (already applied!)

0:         0.00 cm**-1
1:         0.00 cm**-1
2:         0.00 cm**-1
3:         0.00 cm**-1
4:         0.00 cm**-1
5:         0.00 cm**-1
6:        82.29 cm**-1
7:       424.53 cm**-1
8:       544.40 cm**-1
9:       593.63 cm**-1
[...]

The first few frequencies are always zero, for they correspond to the rotational and translational modes. They should be five for linear molecules and six for non-linear molecules, the rest are corresponding to actual vibrational modes.
前几个频率总是为零，因为它们对应于转动和移动模式。对于线性分子，这些模式应有五个；对于非线性分子，则应有六个，其余的频率则对应于实际的振动模式。

Scaling frequencies# 缩放频率

In case you want to multiply all your frequency values by some number after the thermodynamic functions are computed, you can use:
如果你想在计算完热力学函数后将所有频率值乘以某个数，可以使用：

%FREQ SCALFREQ 1.035 END

and all frequencies would be multiplied by 1.035.
所有频率都将乘以 1.035。

Visualizing normal modes#
可视化正常模式

The vibrational modes can be animated using a suitable GUI. With Avogadro or Avogadro 2, simply open the basename.out file, and you should see a panel on the right, such as:
振动模式可以通过适当的图形用户界面进行动画展示。使用 Avogadro 或 Avogadro 2 时，只需打开 basename.out 文件，右侧应会出现如下面板：

../_images/aceticacid-avogadro2.png

Figure: ORCA output visualized with Avogadro 2.
图：使用 Avogadro 2 可视化的 ORCA 输出。#

In ChimeraX (with SEQCROW plugin installed), you can do so as well and navigate to Tools → Quantum Chemistry → Visualize Normal Modes
在 ChimeraX（已安装 SEQCROW 插件）中，您也可以这样做，并导航至 Tools → Quantum Chemistry → Visualize Normal Modes

../_images/aceticacid-chimerax.png

Figure: ORCA output visualized with ChimeraX.
图：使用 ChimeraX 可视化的 ORCA 输出。#

There you can select a frequency and use the given animation option to see how exactly is the mode that corresponds to that frequency. If one clicks at the mode at about ∼1800cm−1, which is expected to be a C=O stretching mode from classical organic chemistry, one sees:
在那里，您可以选择一个频率，并使用提供的动画选项来观察与该频率相对应的模式究竟是如何的。如果点击大约 ∼1800cm−1 的模式，预计这是经典有机化学中的 C=O 伸缩模式，您将看到：

../_images/aceticacid-1800.gif

Animation: Normal mode at 1869.95 cm-1.
动画：1869.95 cm -1 处的正常模式。#

which corresponds to the classical prediction. The same applies for the other modes, e.g, the one at ∼3150cm−1, normally assigned as C-H stretchings:
这与经典预测相符。其他模式也是如此，例如，位于 ∼3150cm−1 的模式，通常被指定为 C-H 伸缩振动：

../_images/aceticacid-3100.gif

Animation: Normal mode at 3126.68 cm-1.
动画：3126.68 cm -1 处的正常模式。#

Removing negative frequencies#
去除负频率

After your calculation, if there is one or more negative frequencies, that means your structure is not a minimum on the given potential energy surface. These negative frequencies are also called imaginary modes and are specifically highlighted in the output file. Any movement along the direction of that mode reduces the energy of the molecule:
经过计算，若存在一个或多个负频率，则表明您的结构并非给定势能面上的最小值。这些负频率亦称为虚模，在输出文件中会特别标出。沿该模式方向的任何移动都会降低分子的能量：

-----------------------
VIBRATIONAL FREQUENCIES
-----------------------

Scaling factor for frequencies =  1.000000000  (already applied!)

     0:       0.00 cm**-1
     1:       0.00 cm**-1
     2:       0.00 cm**-1
     3:       0.00 cm**-1
     4:       0.00 cm**-1
     5:       0.00 cm**-1
     6:     -83.22 cm**-1 ***imaginary mode***
     7:     435.79 cm**-1
     8:     544.50 cm**-1
     9:     592.38 cm**-1

Important 重要

If possible, it is generally recommended to check your structures for imaginary modes even after an optimization run. In rare cases geometry optimizations can also converge to a non-minimum structure, e.g. a saddle-point on the potential energy surface. If your geometry is a minimum, there should be no negative frequencies. If it is a transition state, there must be only one!
如果可能，通常建议在优化运行后检查您的结构是否存在虚模。在极少数情况下，几何优化也可能收敛到一个非最小结构，例如势能面上的鞍点。如果您的几何结构是最小值，则不应存在负频率。如果是过渡态，则必须且仅有一个负频率！

In this case, the imaginary mode refers to a rotation of the methyl group.
在这种情况下，虚模态指的是甲基团的旋转。

../_images/aceticacid-imag.gif

Animation: Imaginary mode at -83.22 cm-1.
动画：虚模式在 -83.22 cm -1 。#

To remove such imaginary modes and converge to a minimum structure one can either try to tighten the convergence thresholds of the optimization by the TightOPT or VeryTightOPT keywords. Sometimes tightening the numerical integration grid to DEFGRID3 can also help to remove imaginary modes. If such measures fail, displacing the respective mode manually and restart the optimization can help:
为了消除这些虚频并收敛至最小结构，可以通过 TightOPT 或 VeryTightOPT 关键词收紧优化收敛阈值。有时，将数值积分网格细化至 DEFGRID3 也能有助于消除虚频。若这些措施无效，手动偏移相应模式并重新启动优化可能会有所帮助：

!B3LYP D4 DEF2-SVP TIGHTOPT DEFGRID3 FREQ
* XYZFILE 0 1 aceticacid.xyz

Numerical Frequencies# 数值频率

The computation of the Hessian matrix is not available for all methods in ORCA, but one can always do a numerical Hessian calculation, using the NUMFREQ keywords, such as:
ORCA 中并非所有方法都能计算 Hessian 矩阵，但始终可以使用 NUMFREQ 关键字进行数值 Hessian 计算，例如：

!RI-B2PLYP DEF2-SVP DEF2-SVP/C NUMFREQ

and the Hessian will be computed by the central differences approach, after 6N displacements, where N is the number of atoms in your system. This can be fully parallelised and sometimes is actually a better option than the analytical FREQ calculation, depending on your memory.
并且 Hessian 矩阵将通过中心差分法计算，在 6N 次位移后，其中 N 是系统中的原子数。这可以完全并行化，并且在某些情况下，根据您的内存情况，这实际上可能比解析 FREQ 计算更优。

Restarting NUMFREQ calculations#
重新启动 NUMFREQ 计算#

These calculations can take a long time if one has a large system or a heavier method. In case anything happens and the calculation ends, it can be restarted using:
如果系统庞大或方法复杂，这些计算可能耗时较长。若计算过程中发生任何情况导致中断，可使用以下方式重新启动：

!RI-B2PLYP DEF2-SVP DEF2-SVP/C NUMFREQ
%FREQ RESTART TRUE END

If the basename.hess file is present on the same folder as the input, the computation will be restarted from where stopped.
如果 basename.hess 文件存在于与输入文件相同的文件夹中，计算将从停止处重新开始。

Important 重要

There are many extra options for %FREQ, please check the ORCA manual for more info.
%FREQ 有许多额外选项，请查阅 ORCA 手册获取更多信息。