NMR coupling constant calculation
NMR analysis is one of the indispensable measurement methods for analyzing the molecular structures of organic compounds.
Especially for vicinal coupling constant 3J, which depends on the dihedral angle around the center bond (between atoms at the positions 2 and 3), it can be used for the prediction of the three-dimensional structure of the organic compounds by setting the appropriate formulas and parameters. Recently, it has become possible to predict the three-dimensional structures of proteins and other biopolymers by combining the torsion angle based on 3J coupling constant and the predicted distances between proximate protons based on NMR-NOE information. On the other hand, the number of conformational isomers to be considered is increased with increasing the size of molecule, so the measured coupling constants are observed as the average value of the mixture of conformational isomers. As a result, relying solely on measurements enhance the possibility of predicting an "unnatural" mean three-dimensional structure which does not actually exist.
CONFLEX has two types of 3J calculations.
- 3JHH around Csp3-Csp3 bond using Karplus-Imai equation
- 3J for arbitrary combination of four atoms using Karplus equation with user-defined parameters
Furthermore, it is also possible to calculate the 3J values for each conformer generated by the conformational search, and calculate their thermodynamic average. By comparing the calculated values with the measured ones, the state of the molecule observed in NMR analysis can be inferred. In addition, a variety of conformational analyses such as measuring the steric effect on the physical properties and the reactivity and more accurate three-dimensional structure analysis can be supported.
This chapter gives an overview of the calculation of NMR coupling constants and the procedure for using the function in CONFLEX.
[Vicinal proton-proton coupling constant (3JHH) calculation using Karplus-Imai equation]
Karplus-Imai equation (below equation) [1], which is one of the improved Karplus equation and was developed to calculate the vicinal proton-proton coupling constant 3JHH around the Csp3-Csp3 bond, has implemented in CONFLEX 7 and later with parameter set [1].
Where the constants and symbols have the following meanings:
| Symbol | Explanation |
|---|---|
| 3JHH | Vicinal coupling constant |
| θ | Dihedral angle between coupling protons |
| Δχi | Difference between group electronegativity of substituent and hydrogen (=2.08) calculated according to Mullay's methods. |
| φi | Dihedral angle between coupling proton and substituent |
| Δχβj | Difference between Mullay's group electronegativity of β-substituents and averaged electronegativity of alkane (=2.40) |
| ψj | Dihedral angle between coupling proton and β-substituent |
| ω1, ω2 | H-C-C bond angle |
| rC-C | C-C bond length |
| r | Distance between coupling proton and nearest atom except directly connected carbon atoms and α-substituents |
| A-I, K | Constants |
| W, M | Constants varied for the type of substitution |
| L | Constant varied for the type of nearest atom carbon or oxygen |
Please see ref. [1] for details of the Karplus-Imai equation. Generally, the NMR analytical function using Karplus-Imai equation is based on the 3JHHM method included in 3JHH2 program [2] published by the Japanese Chemical Program Exchange Organization (JCPE; currently Japan Computer Chemistry Society).
NMR-3JHH calculation of initial and optimized structures
This section explains how to calculate 3JHH value by using 3,3-Dimethyl-1-mercapto-2-butanol as a example.
Structure data (DMB.mol)
3,3-DIMETHYL-1-MERCAPTO-2-BUTANOL
22 21 0 0 0 1 V2000
-0.42228 1.47032 -0.03918 C 0 0 0 0 0
0.00590 -0.00052 -0.00318 C 0 0 0 0 0
-0.52383 -0.87942 -1.16021 C 0 0 0 0 0
0.05386 -2.30850 -1.02981 C 0 0 0 0 0
0.14718 2.32958 1.47446 S 0 0 0 0 0
1.43693 -0.05700 0.03175 O 0 0 0 0 0
-2.06329 -0.99499 -1.09495 C 0 0 0 0 0
-0.12896 -0.31902 -2.54213 C 0 0 0 0 0
-1.52983 1.55723 -0.10193 H 0 0 0 0 0
0.01067 1.97322 -0.93329 H 0 0 0 0 0
-0.34401 -0.45530 0.95369 H 0 0 0 0 0
-0.36277 -2.99093 -1.80548 H 0 0 0 0 0
-0.18224 -2.75288 -0.03596 H 0 0 0 0 0
1.16022 -2.32442 -1.15440 H 0 0 0 0 0
-0.32229 3.55489 1.17617 H 0 0 0 0 0
1.68463 -0.92111 0.31239 H 0 0 0 0 0
-2.45015 -1.70017 -1.86565 H 0 0 0 0 0
-2.56803 -0.02106 -1.28092 H 0 0 0 0 0
-2.40160 -1.36949 -0.10193 H 0 0 0 0 0
-0.45439 -1.00120 -3.36038 H 0 0 0 0 0
0.97328 -0.19276 -2.63627 H 0 0 0 0 0
-0.60365 0.66747 -2.74267 H 0 0 0 0 0
1 2 1 0 0 0
1 5 1 0 0 0
1 9 1 0 0 0
1 10 1 0 0 0
2 3 1 0 0 0
2 6 1 0 0 0
2 11 1 0 0 0
3 4 1 0 0 0
3 7 1 0 0 0
3 8 1 0 0 0
4 12 1 0 0 0
4 13 1 0 0 0
4 14 1 0 0 0
5 15 1 0 0 0
6 16 1 0 0 0
7 17 1 0 0 0
7 18 1 0 0 0
7 19 1 0 0 0
8 20 1 0 0 0
8 21 1 0 0 0
8 22 1 0 0 0
M END
[Execution by Interface]
Open the DMB.mol file by CONFLEX Interface.
Select [CONFLEX] in Calculation menu, and click in the calculation setting dialog displayed.
A detail setting dialog will be displayed.
Next, check the check-box of [NMR 3J_HH calculation by Karplus-Imai equation] in the [NMR] dialog on the detail setting dialog. CONFLEX automatically determines all possible coupled proton pairs.
The calculation of 3JHH value is applied to the optimized structure. If you want to apply the calculation to the initial structure, select [No Optimization] in the pull-down menu of [Optimization Method:] in the [Geometry Optimization] dialog.
When the calculation settings are complete, click . The calculation will start.
[Execution by command line]
The calculation settings are defined by describing keywords in the DMB.ini file.
DMB.ini file
NMR
[NMR] keyword means to calculate 3JHH value by using Karplus-Imai equation. CONFLEX automatically determines all possible coupled proton pairs.
The calculation of 3JHH value is applied to the optimized structure. If you want to apply the calculation to the initial structure, add [OPT=NONE] to the DMB.ini file.
DMB.ini file
NMR OPT=NONE
Store the two files of DMB.mol and DMB.ini in an one folder, and execute below command. The calculation will start.
C:\CONFLEX\bin\flex9a_win_x64.exe -par C:\CONFLEX\par DMBenter
The above command is for Windows OS. For the other OS, please refer to [How to execute CONFLEX].
Calculation results
CONFLEX provides a file with the suffix of [.nmr] that contains results of NMR 3J calculation.
The 3JHH calculation results of 3,3-Dimethyl-1-mercapto-2-butanol initial structure are shown below (DMB.nmr).
In this case, two proton pairs around C1-C2 that has H9 and H10 bonded to C1 and H11 bonded to C2 (3JH9H11 and 3JH10H11) are calculated.
In the first half of the output, Karplus-Imai equation and the parameters used in this equation are outputted.
In the next “3JHHM TABLES:”, the serial numbers of the coupled proton pair (columns “HI” and “HJ”) to be calculated are outputted.
!====================================================================================! ! ! ! NMR-3JHHM: VICINAL H-H COUPLING CONSTANTS CALCULATION ! ! ! !------------------------------------------------------------------------------------! ! ! ! DATE: 2021/02/08 TIME: 12:47:34.37 ! ! DMB: 3,3-DIMETHYL-1-MERCAPTO-2-BUTANOL ! ! EMPIRICAL FORMULA: C6H14OS MW = 134.077 ! ! FORCE FIELD: MMFF94S(2010-12-04HG) ! ! ! !------------------------------------------------------------------------------------! ! ! ! 3JHHM (KARPLUS-IMAI) EQUATION FORMULA: ! ! 3JHH = P1*COS(A) + P2*COS(2*A) + P3*COS(3*A) + P4*COS(2*A)*COS(2*A) + ! ! C1*[ P5*ELENEG*COS(A)*COS(B) + P6*ELENEG*COS(2*B) + P7*ELENEG ] + ! ! P8*(ANGLE - 110.0) + P9*(LENGTH - 1.5) + P10*E(BETA)*|COS(2*C)| + ! ! P11/R(C)**4 + P12/R(O)**4 + CONSTANT ! ! ! ! ! ! PARAMETERS: ! ! P1 P2 P3 P4 P5 P6 ! ! -1.2246 5.0935 -0.1055 0.5711 0.8319 0.0433 ! ! P7 P8 P9 P10 P11 P12 ! ! 0.0345 -0.2058 -8.9222 0.1438 -8.9395 6.9202 ! ! ! ! MONO 1,1-DI 1,2-DI TRI TETRA ! ! WEIGHT 1.0000 2.5500 1.1600 2.2900 1.4000 ! ! CONSTANT 7.5075 7.0306 6.4793 6.5432 5.5319 ! ! ! !------------------------------------------------------------------------------------! ! ! ! 3JHHM TABLES: ! ! ! ! NUMBER OF CENTRAL BONDS HAVING VICINAL COUPLING PROTONS: 1 ! ! LIST OF COUPLING PROTON PAIRS AND CENTRAL BONDS: ! ! COUPLED NO HI I J HJ ! ! ---------- ------------------- ------------------- ! ! 1 9 1 2 11 ! ! 2 10 1 2 11 ! ! -------------------------------------------------- ! ! ! !====================================================================================! ! TOTAL NUMBER OF CONFORMERS FOUND: 1 ! ! TEMPERATURE: 298.15 KELVIN ! !=====================================================================================
In the second half of the output, the 3JHH value (column “3JHH”) and the internal coordinates around the proton pair for each conformer which are required to calculate are outputted at the section “GEOMETRICAL PARAMETERS OF EACH CONFORMER:”. If there are multiple proton pairs around the same C-C bond, the average value of them is also outputted (3JHH (AV.) =) at section “AVERAGED VICINAL H-H COUPLING CONSTANTS:”.
!=====================================================================================================================! ! ! GEOMETRICAL PARAMETERS OF EACH CONFORMER: ! ! NO. CONF ID ENERGY DISTRIB I-J BOND LENGTH H-H PAIR 3JHH PHI ANGLE !---------------------------------------------------------------------------------------------------------------------! ! 1 -------- 36.8731 100.0000 1 - 2 1.5323 9 - 11 2.010 -66.928 110.758 108.891 ! 1 -------- 36.8731 100.0000 1 - 2 1.5323 10 - 11 10.063 173.879 110.105 108.891 !=====================================================================================================================! !====================================================================================! ! ! ! AVERAGED VICINAL H-H COUPLING CONSTANTS: ! ! ! ! 3JHH ( 1 ) = 2.010 (Hz) ! ! 3JHH ( 2 ) = 10.063 (Hz) ! ! 3JHH ( AV. ) = 6.036 (Hz) ! ! ! !====================================================================================!
Note that there may be some insufficient results obtained by this NMR 3JHH calculation using MMFF94s optimized structure because the parameters of Karplus-Imai equation are determined based on MM2 force field.
Therefore, it is highly likely that the results of 3JHH calculation obtained by optimized structures using EMM2 force field are better. When the NMR 3JHH calculation is carried out using EMM2 optimization, you perform CONFLEX like below.
[Execution by Interface]
Select [EMM2] in the pull-down menu of [Force Field:] in the [Force Field] dialog on the detail setting dialog.
[Execution by command line]
You should make the DMB.ini file containing [EMM2] keyword.
DMB.ini file
NMR EMM2
The nmr file obtained by EMM2 calculation is shown below.
!=====================================================================================================================! ! ! GEOMETRICAL PARAMETERS OF EACH CONFORMER: ! ! NO. CONF ID ENERGY DISTRIB I-J BOND LENGTH H-H PAIR 3JHH PHI ANGLE !---------------------------------------------------------------------------------------------------------------------! ! 1 ----- 12.1470 100.0000 1 - 2 1.5420 9 - 11 1.785 -69.875 110.048 ! 1 ----- 12.1470 100.0000 1 - 2 1.5420 10 - 11 9.573 170.843 109.734 !=====================================================================================================================! !====================================================================================! ! ! ! AVERAGED VICINAL H-H COUPLING CONSTANTS: ! ! ! ! 3JHH ( 1 ) = 1.785 (Hz) ! ! 3JHH ( 2 ) = 9.573 (Hz) ! ! 3JHH ( AV. ) = 5.679 (Hz) ! ! ! !====================================================================================!
NMR-3JHH calculation of multiple conformational isomers
The NMR-3JHH calculation can be used in combination with conformation search. Here, we uses β-D-Glucose as a example.
Steric structure of β-D-Glucose
Structure data of β-D-Glucose (b-D-glucose.mol)
b-D-glucose
24 24 0 0 0 1 V2000
1.3695 0.2061 0.1154 O 0 0 0 0 0
1.2178 -1.0943 0.6579 C 0 0 0 0 0
-1.0088 0.3669 -0.2565 C 0 0 0 0 0
0.3824 0.4861 -0.8691 C 0 0 0 0 0
-2.0178 0.5729 -1.2448 O 0 0 0 0 0
-2.4798 -1.0576 0.9937 O 0 0 0 0 0
-0.2327 -2.5652 1.8842 O 0 0 0 0 0
0.6403 1.8795 -1.4228 C 0 0 0 0 0
2.2841 -1.1000 1.6064 O 0 0 0 0 0
-0.1084 -1.2465 1.3563 C 0 0 0 0 0
-1.2097 -1.0083 0.3471 C 0 0 0 0 0
-0.2182 2.1250 -2.5390 O 0 0 0 0 0
1.4145 -1.8634 -0.1200 H 0 0 0 0 0
-1.1510 1.1467 0.5281 H 0 0 0 0 0
0.5017 -0.2533 -1.6973 H 0 0 0 0 0
-2.8280 0.2840 -0.8591 H 0 0 0 0 0
-2.5257 -1.8924 1.4288 H 0 0 0 0 0
0.4375 -2.6616 2.5390 H 0 0 0 0 0
1.6888 1.9818 -1.7842 H 0 0 0 0 0
0.4468 2.6616 -0.6552 H 0 0 0 0 0
2.8280 -0.3665 1.3741 H 0 0 0 0 0
-0.1927 -0.5339 2.2095 H 0 0 0 0 0
-1.1998 -1.7977 -0.4398 H 0 0 0 0 0
-1.0984 1.9144 -2.2779 H 0 0 0 0 0
1 2 1 0 0 0
1 4 1 0 0 0
2 9 1 0 0 0
2 10 1 0 0 0
2 13 1 0 0 0
3 4 1 0 0 0
3 5 1 0 0 0
3 11 1 0 0 0
3 14 1 0 0 0
4 8 1 0 0 0
4 15 1 0 0 0
5 16 1 0 0 0
6 11 1 0 0 0
6 17 1 0 0 0
7 10 1 0 0 0
7 18 1 0 0 0
8 12 1 0 0 0
8 19 1 0 0 0
8 20 1 0 0 0
9 21 1 0 0 0
10 11 1 0 0 0
10 22 1 0 0 0
11 23 1 0 0 0
12 24 1 0 0 0
M END
[Execution of Interface]
Open the b-D-glucose.mol file by CONFLEX Interface.
Select [CONFLEX] in Calculation menu, and click in the calculation setting dialog displayed.
A detail setting dialog will be displayed.
Next, in [General Settings] dialog on the detail setting dialog, select [Conformation Search] in the pull-down menu of [Calculation Type:].
Next, check the check-box of [NMR 3J_HH calculation by Karplus-Imai equation] in the NMR dialog.
When the calculation settings are complete, click . The calculation will start.
CONFLEX performs a conformation search first and calculates NMR 3JHH value of each conformer found. Furthermore, it provides coupling constants weighted based on an existence probability.
[Execution by command]
The calculation settings are defined by describing keywords in the b-D-glucose.ini file.
b-D-glucose.ini file
NMR CONFLEX
[MMR] means to calculate 3JHH value by using Karplus-Imai equation.
[CONFLEX] means to perform a conformation search.
Store the two files of b-D-glucose.mol and b-D-glucose.ini in an one folder, and execute below command. The calculation will start.
C:\CONFLEX\bin\flex9a_win_x64.exe -par C:\CONFLEX\par b-D-glucoseenter
The above command is for Windows OS. For the other OS, please refer to [How to execute CONFLEX].
CONFLEX performs a conformation search first and calculates NMR 3JHH value of each conformer found. Furthermore, it provides coupling constants weighted based on an existence probability.
Calculation results
When the 3JHH calculation is applied to multiple conformers, the 3JHH values and internal coordinate information of multiple proton pairs in each conformation are outputted and the thermodynamic average based on Boltzmann distribution is also outputted.
A part of contents in the b-D-glucose.nmr file
... !=====================================================================================================================! ! ! GEOMETRICAL PARAMETERS OF EACH CONFORMER: ! ! NO. CONF ID ENERGY DISTRIB I-J BOND LENGTH H-H PAIR 3JHH PHI ANGLE !---------------------------------------------------------------------------------------------------------------------! ! 1 00000001 79.8320 49.0347 2 - 10 1.5376 13 - 22 8.078 171.796 111.222 110.519 ! 3 - 4 1.5395 14 - 15 9.471 -176.573 109.804 109.384 ! 3 - 11 1.5300 14 - 23 9.059 170.407 109.839 110.494 ! 4 - 8 1.5350 15 - 19 4.390 -67.989 108.838 110.176 ! 4 - 8 1.5350 15 - 20 9.133 174.032 109.247 110.993 ! 10 - 11 1.5257 22 - 23 8.829 -169.298 110.301 110.781 !---------------------------------------------------------------------------------------------------------------------! ! 2 00000002 79.8625 46.5768 2 - 10 1.5353 13 - 22 8.164 173.410 111.296 110.739 ! 3 - 4 1.5385 14 - 15 9.351 -171.357 110.368 109.897 ! 3 - 11 1.5309 14 - 23 8.720 167.539 109.812 110.347 ! 4 - 8 1.5342 15 - 19 0.616 67.424 109.939 112.095 ! 4 - 8 1.5342 15 - 20 3.173 -53.305 108.931 110.080 ! 10 - 11 1.5238 22 - 23 8.935 -169.970 110.281 110.564 !---------------------------------------------------------------------------------------------------------------------! ! 3 00000009 81.7252 2.0081 2 - 10 1.5352 13 - 22 8.211 173.300 111.147 110.580 ! 3 - 4 1.5390 14 - 15 9.396 -172.203 110.326 109.893 ! 3 - 11 1.5318 14 - 23 8.705 167.362 109.759 110.273 ! 4 - 8 1.5341 15 - 19 0.634 67.748 109.885 112.066 ! 4 - 8 1.5341 15 - 20 3.185 -52.960 108.922 110.141 ! 10 - 11 1.5247 22 - 23 8.835 -169.118 110.310 110.552 !---------------------------------------------------------------------------------------------------------------------! ! 4 00000003 81.9524 1.3687 2 - 10 1.5354 13 - 22 8.094 172.342 111.443 110.626 ! 3 - 4 1.5362 14 - 15 9.320 -174.765 110.457 110.531 ! 3 - 11 1.5312 14 - 23 8.887 169.039 109.858 110.365 ! 4 - 8 1.5368 15 - 19 8.184 -169.220 109.281 110.569 ! 4 - 8 1.5368 15 - 20 2.477 69.460 109.957 111.922 ! 10 - 11 1.5245 22 - 23 8.865 -169.387 110.255 110.616 !---------------------------------------------------------------------------------------------------------------------! ...
!====================================================================================! ! ! ! AVERAGED VICINAL H-H COUPLING CONSTANTS: ! ! ! ! 3JHH ( 1 ) = 8.122 (Hz) ! ! ! ! 3JHH ( 2 ) = 9.411 (Hz) ! ! ! ! 3JHH ( 3 ) = 8.890 (Hz) ! ! ! ! 3JHH ( 4 ) = 2.572 (Hz) ! ! 3JHH ( 5 ) = 6.082 (Hz) ! ! 3JHH ( AV. ) = 4.327 (Hz) ! ! ! ! 3JHH ( 6 ) = 8.880 (Hz) ! ! ! !====================================================================================!
It is also possible to perform the 3JHH calculation on the conformers obtained by the conformation search that has already been performed.
[Execution by Interface]
Store the fxf file obtained by the conformation search that has already been performed and the input file used in the search in one folder. For example, store the b-D-glucose.mol and b-D-glucose.fxf files in the one folder. Next, open the b-D-glucose.mol file by CONFLEX Interface.
Select [CONFLEX] in Calculation menu, and click in the calculation setting dialog displayed.
A detail setting dialog will be displayed.
Next, in [General Settings] dialog on the detail setting dialog, select [Conformation Search] in the pull-down menu of [Calculation Type:].
Next, check the check-box of [NMR 3J_HH calculation by Karplus-Imai equation] in the NMR dialog.
When the calculation settings are complete, click .
Add [NOSEARCH] keyword to the dialog displayed.
By including both the keywords “CONFLEX” and “NOSEARCH”, the structure data of conformers is obtained from the fxf file. New or additional conformation search is not performed.
When the calculation settings are complete, click . The calculation will start.
CONFLEX calculates NMR 3JHH values of each conformer obtained from the fxf file. Furthermore, it provides coupling constants weighted based on an existence probability.
[Execute by command line]
Store the fxf file obtained by the conformation search that has already been performed and the input file used in the search in one folder. For example, store the b-D-glucose.mol and b-D-glucose.fxf files in the one folder. The contents in the b-D-glucose.ini file are shown below.
b-D-glucose.ini file
NMR CONFLEX NOSEARCH
By including both the keywords “CONFLEX” and “NOSEARCH”, the structure data of conformers is obtained from the fxf file. New or additional conformation search is not performed.
Execute below command. The calculation will start.
C:\CONFLEX\bin\flex9a_win_x64.exe -par C:\CONFLEX\par b-D-glucoseenter
The above command is for Windows OS. For the other OS, please refer to [How to execute CONFLEX].
CONFLEX calculates NMR 3JHH values of each conformer obtained from the fxf file. Furthermore, it provides coupling constants weighted based on an existence probability.
[3J coupling constant calculation using Karplus equation and customized parameters]
In the previous section, the coupling constants 3JHH were calculated by Karplus-Imai equation based on the dihedral angle and the bond angle with automatically extraction of H-Csp3-Csp3-H from the structural information.
On the other hand, there are a wide variety of combinations of 3J used for NMR structural analysis. Therefore, it would be useful when other 3J values could be calculated using the Karplus equation and linked with the conformation search.
In CONFLEX8.C and later, it has become possible to calculate the 3JWZ value for any combination of four bonded atoms W-X-Y-Z by setting the parameters based on eq. (1).
where the A, Bm, and Cn are parameter, the θ is dihedral angle of W-X-Y-Z, the δcos and δsin are phase angle of cosine and sine terms, respectively. These parameters can be specified by the atom type number of the MMFF94s (keyword “NMR_3J_ATYPE =”) or by the serial number of the input data (keyword “NMR_3J_NUMBER =”). These two can be set at the same time, and the specification with the serial number has priority when the parameter set for W-X-Y-Z are specified by both keywords.
Conformation search and 3J calculation of β-D-Glucose
We use β-D-Glucose as a example.
Steric structure of β-D-Glucose
Here, we calculate 3JCH of Csp3-Osp3-Csp3-H (Representation by atom types in MMFF94s: 1-6-1-5) by using the eq. 2.
Here, the first term of eq. 2, 1.0, corresponds to the first term of eq. 1, A. The cosine functions correspond to the second term of eq. 1 (m=2,B1=2.0,B2=3.0,δcos=30.0). The sine functions correspond to the third term of eq. 1 (n=2,C1=4.0,C2=5.0,δsin=0.0).
Although the 2-1-4-15 in the serial number belongs to Csp3-Osp3-Csp3-H combination, we calculate the 3JCH of 2-1-4-15 by using the eq. 3.
The eq. 3 corresponds to the eq. 1 with A=1.0, m=3, B1=2.0, B2=3.0, B3=4.0, and δcos=30.0.
Furthermore, we calculate 3JO1C11 of O1-C2-C10-C11 (Representation by serial number:1-2-10-11) by using the eq. 4.
The eq. 4 corresponds to the eq. 1 with A=11.0, m=3, B1=12.0, B2=13.0, B3=14.0, and δcos=0.0.
[Execution by Interface]
Open the b-D-glucose.mol file by CONFLEX Interface.
Select [CONFLEX] in Calculation menu, and click in the calculation setting dialog displayed.
A detail setting dialog will be displayed.
First, in [General Settings] dialog on the detail setting dialog, select [Conformation Search] in the pull-down menu of [Calculation Type:].
Next, we make settings for the eqs. 2 ~ 4.
Check the check-box of [NMR 3J_WZ calculation by Karplus equation] in the NMR dialog. A dialog for setting the equation will be displayed.
We make the eq. 2. Select [Atom type] in the pull-down menu of [Set parameters:]. Set the i, j, k, and l to 1, 6, 1, and 5, respectively, and set the A to 1.0.
Select 2 in the pull-down menu of [m:]. Set the Delta_cos to 30.0. Set the B1 and B2 to 2.0 and 3.0, respectively.
Next, select 2 in the pull-down menu of [n:]. Set the Delta_sin to 0.0. Set the C1 and C2 to 4.0 and 5.0, respectively.
When the settings are complete, click .
You can see the parameters for the eq. 2 in the NMR dialog.
Next, in order to make settings for the eq. 3, click [+]. The dialog for setting the equation will be displayed again.
We make the eq. 3. Select [Atom serial number] in the pull-down menu of [Set parameters:]. Set the i, j, k, and l to 2, 1, 4, and 15, respectively, and set the A to 1.0.
Select 3 in the pull-down menu of [m:]. Set the Delta_cos to 30.0. Set the B1, B2, and B3 to 2.0, 3.0, and 4.0, respectively.
When the settings are complete, click .
You can see the parameters for the eq. 3 in the NMR dialog.
Next, in order to make settings for the eq. 4, click [+]. The dialog for setting the equation will be displayed.
We make the eq. 4. Select [Atom serial number] in the pull-down menu of [Set parameters:]. Set the i, j, k, and l to 1, 2, 10, and 11, respectively, and set the A to 11.0.
Select 3 in the pull-down menu of [m:]. Set the Delta_cos to 0.0. Set the B1, B2, and B3 to 12.0, 13.0, and 14.0, respectively.
When the settings are complete, click .
You can see the parameters for the eq. 4 in the NMR dialog.
When the all settings are complete, click .
CONFLEX performs a conformation search first and calculates NMR 3J value of each conformer found by using the defined equations. Furthermore, it provides coupling constants weighted based on an existence probability.
[Execution by command line]
The calculation settings are defined by describing keywords in the b-D-glucose.ini file.
b-D-glucose.ini file
CONFLEX NMR NMR_3J_ATYPE=(1,6,1,5)(1.0)(COS,30.0,2,2.0,3.0)(SIN,0.0,2,4.0,5.0) NMR_3J_NUMBER=(2,1,4,15)(1.0)(COS,30.0,3,2.0,3.0,4.0) NMR_3J_NUMBER=(1,2,10,11)(11.0)(COS,0.0,3,12.0,13.0,14.0)
Regarding the [NMR_3J_ATYPE=] and [NMR_3J_NUMBER=] keywords, the black letters set [W-X-Y-Z], the red ones set the A of eq. 1, the blue ones set the second term of eq. 1, and the green ones set the third term of eq. 1.
The parentheses in blue represents (COS,δcos,m,B1,B2,...,Bm), and the parentheses in green represents (SIN,δsin,n,C1,C2,...,Cn). These keywords at lines 3, 4, and 5 set the eqs. 2, 3, and 4, respectively.
Store the two files of b-D-glucose.mol and b-D-glucose.ini in an one folder, and execute below command. The calculation will start.
C:\CONFLEX\bin\flex9a_win_x64.exe -par C:\CONFLEX\par b-D-glucoseenter
The above command is for Windows OS. For the other OS, please refer to [How to execute CONFLEX].
CONFLEX performs a conformation search first and calculates NMR 3J value of each conformer found by using the defined equations. Furthermore, it provides coupling constants weighted based on an existence probability.
Calculation results
The contents in the b-D-glucose.nmr obtained by the calculation are shown below. At the beginning of the file, there are information of the molecule calculated and Karplus equation.
!====================================================================================!
! !
! NMR 3J COUPLING CONSTANTS CALCULATION !
! !
!------------------------------------------------------------------------------------!
! !
! DATE: 2019/10/02 TIME: 10:49:25.87 !
! BGLU: b-glucose.mol !
! EMPIRICAL FORMULA: MW = 180.063 !
! FORCE FIELD: MMFF94S(2010-12-04HG) !
! !
!------------------------------------------------------------------------------------!
! !
! CALCULATION USING KARPLUS EQUATION FORMULA AS BELOW: !
! !
! 3JWZ = A0 + SUM_I {B_I*COS(I*(D + P_COS))} !
! + SUM_J {C_J*SIN(J*(D + P_SIN))} !
! !
! D : DIHEDRAL ANGLE OF W-X-Y-Z !
! P_COS : PHASE ANGLE FOR COS !
! P_SIN : PHASE ANGLE FOR SIN !
! !
...
Next, the file shows the parameters of the eq. 2 and the atom members to which the eq. 2 are assigned.
! ! ! *** SETTING PARAMETERS BY ATOM TYPES *** ! ! ! ! NO. 1: ATOM TYPES OF DIHEDRAL= 1 - 6 - 1 - 5 ! ! ! ! *** PARAMETER SET *** ! ! ! ! A0 : 1.00000 ! ! ! ! COS PART, P_COS(DEGREE)= 30.00 ! ! I B_I ! ! 1 2.000 ! ! 2 3.000 ! ! ! ! SIN PART, P_SIN(DEGREE)= 0.00 ! ! J C_J ! ! 1 4.000 ! ! 2 5.000 ! ! ! ! ASSIGNED DIHEDRAL: INPUT NO. 4 - 1 - 2 - 13 ! ! ASSIGNED DIHEDRAL: INPUT NO. 2 - 1 - 4 - 15 ! ! ! ...
Next, the file shows the parameters of the eqs. 3 and 4 and the atom members to which the eqs. 3 and 4 are assigned, respectively.
Here, the C2-O1-C4-H15 has already defined by the eq. 2 (see above). Therefore, the program outputs "THEN OVERWRITE THE PARAMETERS AS BELOW." and newly applies the eq. 3 to the C2-O1-C4-H15.
! ! ! *** SETTING PARAMETERS BY INPUT NO. *** ! ! ! ! INPUT NO.: 2 - 1 - 4 - 15 ! ! ! ! CHECK CONNECTIVITY ... EXISTED. ! ! ! ! *** BUT ALREADY SETTING BY ABOVE ATOM TYPES (NO. 1)!!! *** ! ! *** THEN OVERWRITE THE PARAMETERS AS BELOW. *** ! ! ! ! *** PARAMETER SET *** ! ! ! ! A0 : 1.00000 ! ! ! ! COS PART, P_COS(DEGREE)= 30.00 ! ! I B_I ! ! 1 2.000 ! ! 2 3.000 ! ! 3 4.000 ! ! ! ! INPUT NO.: 1 - 2 - 10 - 11 ! ! ! ! CHECK CONNECTIVITY ... EXISTED. ! ! ! ! *** PARAMETER SET *** ! ! ! ! A0 : 11.00000 ! ! ! ! COS PART, P_COS(DEGREE)= 0.00 ! ! I B_I ! ! 1 12.000 ! ! 2 13.000 ! ! 3 14.000 ! ! ! ...
Next, the 3J value, dihedral angle, and values of each term in Karplus equation in each conformer are shown.
!------------------------------------------------------------------------------------! ! TOTAL NUMBER OF CONFORMERS FOUND: 15 ! ! TEMPERATURE: 298.15 KELVIN ! !=====================================================================================================================! ! ! GEOMETRICAL PARAMETERS OF EACH CONFORMER: ! ! NO. CONF ID ENERGY DISTRIB X-Y BOND LENGTH W-Z PAIR 3JWZ PHI A0 COS SIN !---------------------------------------------------------------------------------------------------------------------! ! 1 00000001 79.8320 49.0347 1 - 2 1.4198 4 - 13 5.532 62.88 1.000 -3.085 7.618 ! 1 - 4 1.4357 2 - 15 4.533 -59.05 1.000 3.533 0.000 ! 2 - 10 1.5376 1 - 11 -1.380 56.72 11.000 -12.380 0.000 !---------------------------------------------------------------------------------------------------------------------! ! 2 00000002 79.8625 46.5768 1 - 2 1.4181 4 - 13 5.528 62.92 1.000 -3.086 7.615 ! 1 - 4 1.4425 2 - 15 3.334 -62.81 1.000 2.334 0.000 ! 2 - 10 1.5353 1 - 11 -2.574 58.48 11.000 -13.574 0.000 !---------------------------------------------------------------------------------------------------------------------! ! 3 00000009 81.7252 2.0081 1 - 2 1.4184 4 - 13 5.593 62.23 1.000 -3.069 7.662 ! 1 - 4 1.4435 2 - 15 3.655 -61.81 1.000 2.655 0.000 ! 2 - 10 1.5352 1 - 11 -2.237 57.96 11.000 -13.237 0.000 !---------------------------------------------------------------------------------------------------------------------! ...
The thermodynamic average based on the Boltzmann distribution is outputted at the end of file.
!====================================================================================! ! ! ! AVERAGED VICINAL W-Z COUPLING CONSTANTS: ! ! ! ! 3J_WZ ( 1 ) = 5.531 (Hz) ! ! ! ! 3J_WZ ( 2 ) = 3.938 (Hz) ! ! ! ! 3J_WZ ( 3 ) = -1.968 (Hz) ! ! ! !====================================================================================!
References
- “An Extension of multiparametric Karplus equation”, Keisuke Imai, Eiji Ōsawa, Tetrahedron Lett., Vol. 30, No. 32, 4251-4254 (1989).
- “3JHH2”, Keisuke Imai, Eiji Ōsawa, JCPE, P012.