Nuclear Magnetic Resonance (NMR)#
核磁共振 (NMR)
General Use# 通用用途
NMR spectroscopy is a powerful tool to analyze the structural features of any molecule. In ORCA, NMR spectroscopic properties like shielding
tensors and shifts, J coupling constants, and NMR spin-rotation constants can be calculated. These properties can be calculated by a wide range of
different methods and we generally recommend to check recent benchmark studies like those by Kaupp and co-workers to [Kaupp2021a][Kaupp2021b] find a suitable method.
核磁共振（NMR）光谱是一种强大的工具，用于分析任何分子的结构特征。在 ORCA 中，可以计算诸如屏蔽张量、化学位移、J 耦合常数和 NMR 自旋-旋转常数等 NMR 光谱特性。这些特性可以通过多种不同方法计算，我们通常建议参考 Kaupp 及其同事的最新基准研究，如[Kaupp2021a][Kaupp2021b]，以找到合适的方法。
NMR Shielding Tensors# 核磁屏蔽张量
A basic NMR shielding tensor calculation can be requested by the NMR input keyword.
可以通过 NMR 输入关键字请求进行基本的 NMR 屏蔽张量计算。
!TPSSh DEF2-TZVPP NMR
*XYZFILE 0 1 structure.xyz
This input will compute the shielding tensors for all nuclei present in the given molecule.
此输入将计算给定分子中所有核的屏蔽张量。
J Coupling Constants# J 耦合常数
J coupling constants can be requested via the SSALL keyword in the %EPRNMR block:
J 耦合常数可以通过 %EPRNMR 块中的 SSALL 关键字请求：
!TPSSh DEF2-TZVPP NMR
* XYZFILE 0 1 structure.xyz
%EPRNMR
NUCLEI = ALL H {SHIFT, SSALL}
END
Important 重要
The %EPRNMR block must be placed after the coordinates specification!
%EPRNMR 块必须放置在坐标指定之后！
Hint 提示
The SHIFT keyword in the example above will limit the computed shieldings to the H-atoms.
上述示例中的 SHIFT 关键词将限制计算的屏蔽值仅限于 H 原子。
Spin-Rotation Constants#
自旋-转动常数
Spin-rotation constants can be requested by the SROT keyword.
自旋-转动常数可通过 SROT 关键词请求。
!TPSSh DEF2-TZVPP MASS2016
*XYZ 0 1
C -1.98519000000000 1.12204043805165 0.00000000000000
O -1.98519000000000 -0.00136043805165 0.00000000000000 M=16.999131
*
%EPRNMR
NUCLEI = ALL O {SROT, IST=17}
END
Note 注释
We have to define the masses of the individually requested nuclei via the coordinates input! The MASS2016 keyword will only use the atomic masses for the most abundant isotope that were
redetermined in 2016. The IST keyword defines the magnetogyric ratio that will be used via the chosen isotope, in this case 17O.
我们必须通过输入的坐标来定义各个请求核的质量！ MASS2016 关键词将仅使用 2016 年重新确定的丰度最高的同位素的原子质量。 IST 关键词定义了将通过所选同位素使用的磁旋比，在此情况下为 17 氧。
Warning 警告
The ORCA implementation follows that described in [Helgaker1996]. Therefore, the sign convention of the rotation constant components may differ when compared to different sources.
ORCA 的实现遵循[Helgaker1996]中所述。因此，与不同来源相比，转动常数分量的符号约定可能有所不同。
Example 1: 13C-NMR Chemical Shifts of Propionic Acid#
示例 1： 13 丙酸的碳-13 核磁共振化学位移 #
In this example, we will compute the isotropic shieldings of the 13C nuclei of propionic acid in CHCl3 solution.
Experimental data for this molecule can be found in the SDBS database.
在此示例中，我们将计算丙酸在 CHCl 溶液中 13 C 核的各向同性屏蔽值。该分子的实验数据可在 SDBS 数据库中找到。
Figure: Molecular structure of propionic acid and the experimental 13C NMR chemical shifts.
图：丙酸的分子结构及实验所得的 13 C NMR 化学位移。#
These will be used to compute the chemical shifts of the respective nuclei with reference to TMS according to:
这些将用于根据以下公式计算各核相对于 TMS 的化学位移：
Important 重要
For very large shielding tensors, e.g. of very heavy nuclei such as Pb, the denominator (
对于非常大的屏蔽张量，例如铅等极重核的情况，分母（
As we use TMS as reference, we will first compute the isotropic shieldings for the TMS molecule with the TPSSh hybrid functional and Jensen's pcSseg-2 basis set. This method typically yields
reasonably good NMR properties for most nuclei.
由于我们以 TMS 为参考，首先将使用 TPSSh 杂化泛函和 Jensen 的 pcSseg-2 基组计算 TMS 分子的各向同性屏蔽值。该方法通常能为大多数核素提供相当不错的 NMR 性质。
!TPSSh PCSSEG-2 AUTOAUX NMR CPCM(CHCl3)
*XYZFILE 0 1 tms.xyz
Hint 提示
Instead of calculating a reference molecule you can use an internal standard. In this case, you just apply a constant shift to the calculated peaks, so that one of them is equal to a known value. For example, one could use the value of an assigned methyl or an aromatic H or C and benefit from possible error cancellations. This also makes more sense if the reference is too different from the target molecule or complicated to simulate, like phosphoric acid in water for 31P-NMR.
After the successful SCF calculation, ORCA will initiate the property calculation summarizing the requested properties:
------------------------------------------------------------------------------
ORCA PROPERTY CALCULATIONS
------------------------------------------------------------------------------
GBWName ... nmr.gbw
Number of atoms ... 17
Number of basis functions ... 355
Max core memory ... 1024 MB
[...]
NMR properties:
Chemical shifts ... YES ( 17 nuclei)
Spin-rotation constants ... NO ( 0 nuclei)
Spin-spin couplings ... NO ( 0 nuclei, 0 pairs)
Choice of magnetic origin ... GIAO
Position of magnetic origin ... 0.000000 0.000000 0.000000
Note 注释
The default algorithm uses Gauge-Independent Atomic Orbitals (GIAOs, [Ditchfield1973] and [Pulay1990]). This is quite important in NMR calculations and we do not recommended turning this off unless you really know what you are doing.
The calculated NMR shieldings are now printed after:
-------------------
CHEMICAL SHIELDINGS (ppm)
-------------------
with more detailed information on the computed components for each individual nucleus.
--------------
Nucleus 1C :
--------------
Diamagnetic contribution to the shielding tensor (ppm) :
242.422 0.000 0.049
0.000 242.416 0.000
0.003 -0.000 257.207
Paramagnetic contribution to the shielding tensor (ppm):
-58.053 -0.000 -0.045
-0.000 -58.104 -0.000
-0.019 -0.000 -64.963
Total shielding tensor (ppm):
184.369 -0.000 0.003
0.000 184.312 0.000
-0.016 -0.000 192.244
Diagonalized sT*s matrix:
sDSO 242.416 242.422 257.207 iso= 247.348
sPSO -58.104 -58.053 -64.963 iso= -60.373
--------------- --------------- ---------------
Total 184.312 184.369 192.244 iso= 186.975
Orientation:
X -0.0017605 0.9999981 -0.0008447
Y -0.9999985 -0.0017605 -0.0000017
Z -0.0000031 0.0008447 0.9999996
The desired isotropic shieldings are further summarized:
--------------------------------
CHEMICAL SHIELDING SUMMARY (ppm)
--------------------------------
Nucleus Element Isotropic Anisotropy
------- ------- ------------ ------------
0 Si 341.516 0.029
1 C 186.975 7.904
2 C 186.946 7.938
3 C 186.976 7.906
4 C 186.976 7.906
[...]
Note 注释
Chemically equivalent nuclei might have slight different shieldings, due to geometric asymmetries. In that case, the best thing to do is to simply average them.
After we got our reference shieldings for TMS, we can now calculate the respective 13C shieldings for propionic acid:
!TPSSh PCSSEG-2 AUTOAUX NMR CPCM(CHCl3)
*XYZFILE 0 1 propionic_acid.xyz
%EPRNMR
NUCLEI = ALL C {SHIFT}
END
--------------------------------
CHEMICAL SHIELDING SUMMARY (ppm)
--------------------------------
Nucleus Element Isotropic Anisotropy
------- ------- ------------ ------------
0 C 176.897 12.661
1 C 157.417 35.788
5 C -2.675 -148.292
We can now calculate the respective chemical shifts and see that they are in reasonable agreement with the experimental data.
我们现在可以计算各自的化学位移，并发现它们与实验数据合理一致。
Method 方法 |
|||
|---|---|---|---|
TPSSh |
11.8 |
30.5 |
185.9 |
Exp. 实验。 |
8.9 |
27.6 |
181.5 |
Note 注释
Have in mind that the refence should always use the same level of theory as the target molecule, including any solvation effects or approximations such as the RI.
请记住，参考体系应始终采用与目标分子相同的理论水平，包括任何溶剂化效应或近似方法，如 RI（Resolution of Identity）。
Important 重要
Always have in mind that NMR shifts are quite sensitive to the conformer you choose. For flexible molecules, a conformer search with GOAT and
subsequent Boltzmann weighting of the NMR properties for the conformer ensemble should be considered!
始终牢记，NMR 位移对所选构象非常敏感。对于柔性分子，应考虑使用 GOAT 进行构象搜索，并对构象集合的 NMR 性质进行玻尔兹曼加权！
Example 2: J(H-H) Coupling Constants of Toluene and Plot with ChimeraX#
示例 2：甲苯的 J(H-H)偶合常数与 ChimeraX 绘图
In this example, we calculate the J(H-H) couplings of toluene in chloroform for which experimental data are again extracted from the SDBS database.
Here we highlight some of the J couplings between hydrogen atoms of the aromatic ring, as labeled in the database:
在此示例中，我们计算了甲苯在氯仿中的 J(H-H)耦合常数，实验数据再次从 SDBS 数据库中提取。这里我们重点展示芳环上氢原子间的一些 J 耦合，这些氢原子在数据库中已标注：
Figure: Selected experimental J(H-H) coupling constants of toluene.
图：甲苯中选定的实验 J(H-H)耦合常数。#
We use a similar input as used in the previous example and add the SSALL keyword.
我们使用与前例相似的输入，并添加了 SSALL 关键字。
!TPSSh PCSSEG-2 AUTOAUX NMR CPCM(CHCl3)
*XYZFILE 0 1 toluene.xyz
%EPRNMR
NUCLEI = ALL H {SHIFT, SSALL}
END
The output will now show the details on the computed coupling constants:
输出将显示计算的耦合常数详细信息：
-----------------------------------------------------------------------
NMR SPIN-SPIN COUPLING CONSTANTS
================================
Number of nuclear pairs to calculate something: 22
----
Number of nuclear pairs to calculate DSO terms: 22
Number of nuclear pairs to calculate PSO terms: 22
Number of nuclear pairs to calculate FC terms: 22
Number of nuclear pairs to calculate SD terms: 22
Number of nuclear pairs to calculate SD/FC terms: 22
-----------------------------------------------------------------------
Performing DSO num. integration ... done ( 0.1 sec)
Processing PSO nuclear pairs ... done ( 0.0 sec)
Processing SD/FC nuclear pairs ... done ( 0.0 sec)
-----------------------------------------------------------
NUCLEUS A = H 0 NUCLEUS B = H 3
( 1H gnA = 5.586 1H gnB = 5.586) r(AB) = 2.4644
-----------------------------------------------------------
Diamagnetic contribution to J (Hz):
3.9326 3.7596 -0.0014
-3.8935 -3.7106 0.0009
0.0006 0.0003 -1.2840
Paramagnetic contribution to J (Hz):
-2.8211 -3.8016 0.0012
3.9469 2.6118 -0.0008
-0.0007 -0.0002 0.6851
Fermi-contact contribution to J (Hz):
7.3084 0.0000 0.0000
0.0000 7.3084 0.0000
0.0000 0.0000 7.3084
Spin-dipolar contribution to J (Hz):
0.1745 0.2651 -0.0001
-0.2678 0.1216 -0.0000
0.0000 -0.0001 -0.0887
Spin-dipolar/Fermi contact cross term contribution to J (Hz):
-0.3444 -0.0087 0.0000
-0.0087 0.1193 0.0001
0.0000 0.0001 0.2247
Total spin-spin coupling tensor J (Hz):
8.2501 0.2145 -0.0002
-0.2231 6.4505 0.0001
-0.0001 0.0001 6.8455
Diagonalized JT*J matrix:
J[0,3](DSO) -3.708 -1.284 3.930 iso= -0.354
J[0,3](PSO) 2.609 0.685 -2.818 iso= 0.159
J[0,3](FC) 7.308 7.308 7.308 iso= 7.308
J[0,3](SD) 0.122 -0.089 0.174 iso= 0.069
J[0,3](SD/FC) 0.119 0.225 -0.345 iso= -0.000
--------------- --------------- --------------- ---------------
J[0,3](Total) 6.451 6.846 8.250 iso= 7.182
[...]
With a final summary in the end:
最终总结如下：
-----------------------------------------------------------------------------
SUMMARY OF ISOTROPIC COUPLING CONSTANTS J (Hz)
-----------------------------------------------------------------------------
0 H 3 H 7 H 9 H 11 H 12 H
0 H 0.000 7.182 0.720 1.917 7.058 0.060
3 H 7.182 0.000 2.463 0.662 1.648 -0.375
7 H 0.720 2.463 0.000 7.398 1.618 0.069
9 H 1.917 0.662 7.398 0.000 6.897 0.000
11 H 7.058 1.648 1.618 6.897 0.000 0.000
12 H 0.060 -0.375 0.069 0.000 0.000 0.000
13 H 0.000 -1.331 -1.327 0.437 0.000 -14.460
14 H 0.000 -1.323 -1.321 0.434 0.000 -14.441
13 H 14 H
0 H 0.000 0.000
3 H -1.331 -1.323
7 H -1.327 -1.321
9 H 0.437 0.434
11 H 0.000 0.000
12 H -14.460 -14.441
13 H 0.000 -19.069
14 H -19.069 0.000
Important 重要
The values are printed in Hz, so in order to convert them to ppm one has to take into account the equipment's frequency. In our case, the database says it was measured in 300 MHz NMR, so that the coupling in ppm would be:
数值以赫兹为单位打印，因此要将其转换为 ppm，必须考虑设备的频率。在我们的例子中，数据库显示测量是在 300 MHz 核磁共振仪上进行的，因此耦合常数以 ppm 表示为：
Again, we can compare our computed data to the experiment:
同样，我们可以将计算数据与实验结果进行比较：
Coupling 耦合 |
Calculated (Hz) 计算值（赫兹） |
Experiment (Hz) 实验（赫兹） |
|---|---|---|
A (H3) - A' (H7) |
2.46 |
1.97 |
A (H7) - B (H9) |
7.40 |
7.68 |
A (H7) - C (H11) |
1.62 |
1.27 |
After we computed the NMR shieldings and J coupling constants, we can visualize the coupled NMR spectrum with ChimeraX (with the SEQCROW plugin).
To do so, we simply open the ORCA output file with ChimeraX, navigate to Tools→Quantum Chemistry→NMR Spectrum.
ChimeraX offers many settings, including the choice of a reference shift, the pulse frequency, and manual choice of equivalent nuclei. The spectrum can further be exported as picture or as .csv data for further processing.
Figure: Calculated NMR spectrum of toluene visualized with ChimeraX.
图：使用 ChimeraX 可视化的甲苯计算 NMR 谱。#
Example 3: NMR Chemical Shifts with Double-Hybrid DFT#
示例 3：双杂化 DFT 的 NMR 化学位移
In ORCA, the NMR shielding constants can also be computed using the double-hybrid functionals, that profit from adding MP2 correlation to DFT [Neese2018].
在 ORCA 中，NMR 屏蔽常数亦可采用双杂化泛函计算，该方法通过结合 MP2 相关性与 DFT 而获益[Neese2018]。
!revDSD-PBEP86-D4/2021 PCSSEG-3 AUTOAUX NMR NOFROZENCORE
*XYZFILE 0 1 opt.xyz
Important 重要
Per default MP2 and double-hybrid DFT uses the frozen core approximation. As NMR properties are strongly influenced by the core electrons, we need to deactivate it
with the NOFROZENCORE keyword.
默认情况下，MP2 和双杂化 DFT 使用冻结内核近似。由于 NMR 性质受内层电子强烈影响，我们需要使用 NOFROZENCORE 关键字将其停用。
Note 注释
Note, that double-hybrid functionals typically require larger basis sets like pcSseg-3 for converged results.
注意，双杂化泛函通常需要更大的基组，如 pcSseg-3，以获得收敛结果。
ORCA will compute the NMR properties at the SCF DFT level first:
ORCA 将首先在 SCF DFT 水平上计算 NMR 性质：
-------------------
CHEMICAL SHIELDINGS (ppm)
-------------------
Method : SCF
Type of density : Electron Density
[...]
and the properties based on the unrelaxed and the relaxed MP2 density afterwards:
并基于未弛豫和弛豫后的 MP2 密度计算其性质：
-------------------
CHEMICAL SHIELDINGS (ppm)
-------------------
Method : MP2
Type of density : Electron Density
Type of derivative : Magnetic Field (with GIAOs) (Direction=X)
Multiplicity : 1
Level : Unrelaxed density
-------------------
CHEMICAL SHIELDINGS (ppm)
-------------------
Method : MP2
Type of density : Electron Density
Type of derivative : Magnetic Field (with GIAOs) (Direction=X)
Multiplicity : 1
Level : Relaxed density
The results based on the relaxed density are the desired properties.
基于松弛密度的结果是所需的特性。
Warning 警告
Double-hybrids typically give better results than lower-level DFT approaches, however, for some systems, e.g., those with small HOMO-LUMO gaps or 3d transition metal complexes, MP2-based approaches are prone to large errors and may be avoided in favor of a robust meta-GGA like B97M-V and r2SCAN or hybrid functionals like r2SCAN0, TPSSh, and ωB97X-V.
Tip
Even though no J coupling constants are available from MP2 or double-hybrid DFT, coupled spectra can be obtained from mixing theories for shieldings and couplings. For example, we can combine chemical shifts calculated at the double-hybrid DFT level with J coupling constants from a hybrid DFT calculation.
Example 4: Spin-Rotation Constants of 12C17O#
In this example, we will compute the NMR spin-rotation constant of 12C17O. In the respective input, we defined the atomic mass of O to match 17O and adjusted the magnetogyric ratio for the chosen isotope.
! TPSSh PCSSEG-3 AUTOAUX MASS2016
*XYZ 0 1
C -1.98519000000000 1.12204043805165 0.00000000000000
O -1.98519000000000 -0.00136043805165 0.00000000000000 M=16.999131
*
%EPRNMR
NUCLEI = ALL O {SROT, IST=17}
END
After successful calculation, the results are printed to the output.
---------------------------
NMR SPIN-ROTATION CONSTANTS
---------------------------
Analytic diamagnetic shielding integrals (local origin) (SHARK) ... done ( 0.0 sec)
------------------------------------------------
Nucleus 1O (Isotope = 17 GN = -0.75751600):
------------------------------------------------
Nuclear contribution to the spin-rotation tensor (kHz) :
-3.535 0.000 0.000
0.000 0.000 0.000
0.000 0.000 -3.535
Electronic contribution to the spin-rotation tensor (kHz) :
35.729 0.000 0.000
-0.000 0.000 0.000
0.000 0.000 35.705
Total spin-rotation tensor (kHz):
32.194 0.000 0.000
-0.000 0.000 0.000
0.000 0.000 32.170
Diagonalized MT*M matrix:
M(Nuc) -0.000 -3.535 -3.535 iso= -2.356
M(El) -0.000 35.705 35.729 iso= 23.811
--------------- --------------- ---------------
M(Tot) -0.000 32.170 32.194 iso= 21.455
-----------------------------------
NMR SPIN-ROTATION CONSTANTS SUMMARY
-----------------------------------
Nucleus Isotope Atomic Mass g-factor Spin-Rot. Const. (kHz)
------- ------- ----------- ---------- ----------------------
1 17-O 16.9991310 -0.7575160 21.455
here M(Tot) gives the aa, bb, and cc (or XX, YY, and ZZ) components and the isotropic NMR spin-rotation constant. The latter is further summarized in the end with some additional information like the atomic mass.
-----------------------------------
NMR SPIN-ROTATION CONSTANTS SUMMARY
-----------------------------------
Nucleus Isotope Atomic Mass g-factor Spin-Rot. Const. (kHz)
------- ------- ----------- ---------- ----------------------
1 17-O 16.9991310 -0.7575160 22.379
If we now compare the spin-rotation constant components with the experiment, we see that the absolute value is in excellent agreement with the experimental data. Note that the sign convention used in the original implementation followed in ORCA[Helgaker1996] may differ from that used in other works.
Component |
Calculated (kHz) |
Experiment (kHz) |
|---|---|---|
aa |
0.00 |
0.000 |
bb = cc |
32.17 |
-31.609 |
Structures# 结构
1-propionic acid
11
C -2.02727527554235 -0.06655130656306 0.00037392908842
C -0.75679471221434 0.75631573207355 -0.00012855244818
H -2.07991021538891 -0.70955234104354 -0.87882169434027
H -2.89912000279840 0.58830528850859 -0.00322251101424
H -2.08298208770946 -0.70385824832254 0.88351978507734
C 0.49305145889248 -0.07125461785103 0.00054681142313
H -0.70522440144489 1.41749189951821 0.86998810223388
H -0.70520776302305 1.41676824159293 -0.87073904389322
O 1.59469763588682 0.69133816497292 -0.00209843924434
H 2.36249659648209 0.10385573531668 -0.00149870485071
O 0.54282876686002 -1.27602854820272 0.00280031796818
TMS
17
Si -0.00016217760413 -0.00000200966369 -0.00001724916921
C -0.00000381060783 -0.00000292410772 1.87604035066756
C 1.76890263153042 -0.00000220438520 -0.62476798792801
C -0.88452969047227 -1.53170003319882 -0.62565336419779
C -0.88451803763557 1.53170284867113 -0.62564941393828
H -1.02024320585180 -0.00004763673129 2.26807747150872
H 0.51041349194385 0.88367742102248 2.26744728207030
H 0.51049406579855 -0.88363545598283 2.26744932583441
H 1.79889713542055 -0.00002636281349 -1.71733986918209
H 2.30802219317048 0.88363945655706 -0.27386690302155
H 2.30803592092593 -0.88361814255887 -0.27382577782536
H -0.90062854341904 -1.55578670297871 -1.71826319426016
H -1.91903757060460 -1.55776918964915 -0.27388248209104
H -0.38800706817058 -2.44075463393491 -0.27679593332374
H -0.90062145682280 1.55579443985819 -1.71826001944301
H -1.91902290654613 1.55778308725346 -0.27387187984590
H -0.38798097105504 2.44074804264236 -0.27679035585484
Toluene
15
H -1.35604030632667 -2.14062097490572 0.00064845084188
C -0.81881186265084 -1.19920744744936 0.00036920002554
C 0.57048137420035 -1.19832779892086 0.00026808880500
H 1.10835381829194 -2.14039396264630 0.00046230443757
C 1.28750860478784 -0.00560299513861 -0.00011156472044
C 2.78618878796062 -0.00087766989700 0.00001333464042
C 0.57330375607799 1.19242335570751 -0.00043685135727
H 1.11365279206821 2.13339476273244 -0.00080313848306
C -0.81287809106069 1.19760459513790 -0.00033526034055
H -1.34757760412811 2.14049019369371 -0.00061393156388
C -1.51637266595660 -0.00071299542650 0.00007861209975
H -2.59983293655610 0.00175614049417 0.00013091762840
H 3.18457831555614 -1.01559669047846 -0.00219503682240
H 3.17734526715488 0.51581479390032 0.87984977178833
H 3.17754075058104 0.51985669319674 -0.87732489697927
CO
2
C -1.98519000000000 1.12204043805165 0.00000000000000
O -1.98519000000000 -0.00136043805165 0.00000000000000