ANATOLIA: NMR software for spectral analysis of total lineshape (original) (raw)

ANATOLIA: NMR software for spectral analysis of total lineshape

D.A. Cheshkov 1,2{ }^{1,2} (D) I K.F. Sheberstov 1{ }^{1} (D) I D.O. Sinitsyn 3{ }^{3} (D) I V.A. Chertkov 4{ }^{4} (D)

[1]In this paper we present a new fast and free open-source software package ANATOLIA for the total lineshape analysis of NMR spectra. It performs fitting of experimental 1D NMR spectra based on quantum mechanical formalism. The program serves for the determination of JJ-coupling constants and elucidation of complicated multiplet structures including strongly coupled systems. The program utilizes the Lorentzian broadening approach for local minima suppression. It is developed in the C++ language for standard personal computers. ANATOLIA is adapted to work with the Bruker NMR spectral format and could be conveniently integrated into the TopSpin software package. This tutorial contains a program description, 2 demonstration examples, and general recommendations for NMR spectra analysis.

KEYWORDS

1D NMR simulation, broadening approach, multiplet structure elucidation, total lineshape analysis

1 | INTRODUCTION

Liquid state NMR spectroscopy is a powerful method for structure elucidation of small molecules in organic chemistry, pharmacology, and biochemistry. [1−3]{ }^{[1-3]} The spin-spin JJ-coupling constants provide essential information on molecular structure, stereochemistry, and conformation, but determination of their values can be rather complicated. [4−6]{ }^{[4-6]} Knowledge of JJ-couplings has recently found important applications for creating of long-lived states in multiple spin systems [7]{ }^{[7]} and for the description of SABRE hyperpolarisation dependency on the magnetic field. [8]{ }^{[8]} Development of new experimental approaches to measure JJ-couplings is an actively growing area. [9−12]{ }^{[9-12]} Nevertheless, measuring JJ-coupling values directly from 1D NMR spectra is the oldest and altogether the most straightforward and precise way to do it. [13−15]{ }^{[13-15]} Values of JJ-couplings could be determined directly from signals splitting only for
weakly coupled spin systems; moreover, in cases of multiple spins, it could require automated procedures. [16]{ }^{[16]} In general, multiplet structure elucidation requires performing automated spectral analysis, taking into account quantum mechanical description of a spin system in magnetic field. [3,14]{ }^{[3,14]}

Total lineshape analysis consists in the optimization of spin system parameters (chemical shifts and JJ-couplings) and finding their values providing the best agreement between experimental and theoretical spectra. This problem implies prior knowledge about the molecule structure and its spin system type. The main difficulty is the presence of a large number of local minima, in which the optimization often ends up. A local minimum corresponds to a coincidence of some lines in the experimental and calculated spectra. We recently found that the number of local minima could reach thousands even for relatively small spin systems. [6]{ }^{[6]}

1. 1{ }^{1} State Scientific Research Institute of Chemistry and Technology of Organoelement Compounds, 38 Shosse Entuziastov, 105118 Moscow, Russia
   2{ }^{2} A.N. Frumkin Institute of Physical chemistry and Electrochemistry RAS, 31 Leninsky prospect, 199071 Moscow, Russia
   3{ }^{3} Research Center of Neurology, 80 Volokolamskoye Shosse, 125367 Moscow, Russia
   4{ }^{4} Department of Chemistry, Moscow State University, 1 b. 3 Leninskiye Gory, 119991 Moscow, Russia
   Correspondence
   Dmitry Cheshkov, State Scientific Research Institute of Chemistry and Technology of Organoelement Compounds, 38 Shosse Entuziastov, 105118, Moscow, Russia.
   Email: dcheshkov@gmail.com ↩︎

Using a Monte Carlo method to find a global minimum is an effective approach to overcome this problem, however, it requires significant computational resources and can be efficiently realized using a computer cluster. [6,17]{ }^{[6,17]} In this tutorial we discuss another concept, well suitable for a personal computer, which is the broadening approach. [4,5,18]{ }^{[4,5,18]} An idea behind this method is to apply additional broadening to experimental and theoretical spectra before parameters optimization, which leads to merging of the neighboring spectral lines and, therefore, eliminates most of the local minima. Additional broadening is consequently decreased in the course of the spectrum analysis.

In this tutorial we present a new, easy-to-use, fast open-source software called ANATOLIA (for ANAlysis of TOtal LIneshApe) available under GNU GPLv3 license. It uses Lorentzian broadening of experimental spectrum for local minima suppression. The existing programs for spectral analysis are either not publically available (DAVINS, [4]{ }^{[4]} NMRCON, [19]{ }^{[19]} PERCHit [20]{ }^{[20]} ) or commercial (ChemAdder [21]{ }^{[21]} ). The program DAISY [22]{ }^{[22]} is integrated into the TopSpin software package, however, the result of its optimization often ends up in a local minimum. It failed to find solutions for the test spectra used in this paper, when starting from the same parameters as for ANATOLIA. There are some packages without usage of any method for a local minima suppression (NUTS, [23]gNMR,[24]{ }^{[23]} \mathrm{gNMR},{ }^{[24]} MestRenova, [25]{ }^{[25]} Spinach [26]{ }^{[26]} ). The procedures used for calculations in ANATOLIA are essentially optimized with respect to computational resources, allowing one to analyze spectra of systems with up to 12 spins-1/2. Usually total lineshape analysis of a spectrum requires thousands of simulations. A single calculation of an error function by ANATOLIA for an 8 -spin system requires approximately 10 ms , for example, the complete analysis of the 1H{ }^{1} \mathrm{H} spectrum of styrene takes several minutes (using personal computer with Intel Core i7 3.5 GHz CPU). For comparison, one simulation of the same 1H{ }^{1} \mathrm{H} styrene spectrum in Spinach takes about 30 s using the same personal computer. Note, however, that Spinach, in contrast to ANATOLIA, performs spin dynamic calculations, which is not necessary for conventional 1D NMR spectra simulation [13,14]{ }^{[13,14]} but allows simulating complicated multipulse NMR experiments. ANATOLIA is fully compatible with the Bruker NMR spectral format and could be executed directly from the TopSpin software package.

This paper is organized as a manual with two examples. All the data including experimental spectra, input data, program source code and binary files are available in the Supporting Information, at GitHub Repository dcheshkov/ANATOLIA, and at http://anatolia.nmrclub. ru. The program updates will be also available there.

2 STRUCTURE OF THE ANATOLIA INPUT DATA

The program uses two input files, the file “Input_Data. txt” contains all the information needed for the spectrum simulation and optimization process, except for the values of chemical shifts and JJ-couplings. These parameters are modified by the program during the spectral analysis and are stored in a separate file with default name “parameters.txt”. Such an organization of the data allows continuing the spectral analysis conveniently until the satisfactory solution is found.

2.1 | Description of the “Input_Data.txt” file

The input file controls the action of the program and contains information about the spin system, the experimental spectrum, a set of additional broadenings and a list of parameters to optimize.

It consists of several sections separated by empty lines. Each section starts with its name on a separate line, after which the parameters of the section are given. Each parameter is located in its own line starting from “ParameterName” (fused) and followed, after any number of space and/or tabulation characters, by its value. The newline character should follow the parameter value immediately. The specific section and parameter names are used only to facilitate reading by the user and do not matter for the program. The proper location of the parameters is necessary for successful input parsing. In what follows we demonstrate the process of spectral analysis using 1H{ }^{1} \mathrm{H} NMR spectrum of orthodichlorbenzene (ODCB) as an example (Figure 1). A template of the input file is given below:

Analysis of ODCB 1H NMR spectrum
SimMode 0
Spin System
NSpins 4
Chemical shift indices
1 1 2 2
J-coupling indices
    3 4 5
    5 4
                            6
Spectral parameters
PathToDataSet D:\data\user\nmr\ODCB\1000

FIGURE 1 Chemical structure and spin system numbering of orthodichlorbenzene

The input file starts with a title line. In our case, this is “Analysis of ODCB 1H NMR spectrum”. An empty line should follow the title. The next line contains the control parameter for the simulation mode “SimMode”. It should be " 1 " or 0 ". The program loads the parameters required for spectrum simulation, calculates the theoretical spectrum, saves it, and is terminated in case when “SimMode” is set to " 1 ".

The next section of the input file is devoted to the description of the spin system. First of all, the number of spins “NSpins” should be given. The line after
subsection “Chemical shift indices” serves for assignment of the chemical shifts, allowing to specify the chemical equivalence. The user should provide NSpins indices (four in our case) corresponding to chemical shifts. Subsection " JJ-coupling indices" further specifies the spin system type, allowing one also to set the magnetic equivalence. The shift and coupling indices in principle can be spread over several lines with space and/or tabulation delimiters.

In case of ODCB, there are two groups of chemically equivalent nuclei. The second chemical shift index in the input file equals " 1 ", setting the same chemical shift for the first and second nuclei. Chemical shifts indices should begin with " 1 " and increase monotonically, the same chemical shift index is allowed to be successively repeated.

We recommend to organize the input for JJ-coupling indices as an upper triangle (see Scheme 1), where the row refers to the first nucleus and the column to the second, so the index at the first row and the last column corresponds to J14J_{14}. Because the coupling constants J14J_{14} equals to J23J_{23} due to molecular symmetry (see Figure 1), the index number " 5 " is repeated twice.

Chemical shift indices

JJ-coupling indices

SCHEME 1 Triangle of chemical shifts and JJ-couplings indices for ODCB

The user should provide NSpins(NSpins−1)/2N S p i n s(N S p i n s-1) / 2 indices (number of cells in the triangle) for JJ-coupling constants (six in our case). The index of the first coupling constant J12J_{12} should be one more than the last chemical shift index. The indices of the JJ-coupling constants should also consecutively increase although it is allowed in any position to repeat indices with a smaller value, but not smaller than the index of J12J_{12}.

The next section “Spectral parameters” contains information about the spectrum. Our program is designed to work with spectra in the Bruker NMR format (TopSpin dataset). If the spectrum is stored in a different format, it should be converted into the Bruker NMR format before the analysis. The program reads all the necessary acquisition and processing data from a dataset directory “PathToDataSet”, which should be ended by an “expno” value. Acquisition data are read from an “acqus” file and the processing data are fetched from a “procs” file, located in the “procno” folder with experimental spectrum. The program generates theoretical and broadened experimental spectra. Therefore, the user should create in TopSpin two additional spectral processings with identical processing parameters before executing the program. It is possible not to save these spectra, by setting just “-” instead of a number.

The section “Optimization parameters” specifies the files with chemical shifts and JJ-coupling values. ANATOLIA takes input values from the “InputParameters” file and saves the optimized values in the “OutputParameters” file, however, we usually use the same file “parameters.txt”, thus overwriting the parameter values.
“SpectraTxtOutput” option allows saving the theoretical and broadened spectra into ASCII text format, the file is not written if the parameter equals to “-”.

The line “LBs” contains a list of additional broadenings, which is a sequence of gradually decreasing numbers, located in the same line. At least one number is necessary.

The option “MagnitudeFromExpSpec” allows to replace the spectrum magnitude by one determined from the experimental spectrum right after reading parameters from the file. In this case, magnitude is determined as maximal intensity on spectral intervals used for optimization. It is active in simulation and optimization modes. “MagnitudeFromExpSpec” can be " 1 " or " 0 ".

The last section “List of optimized parameters” is used for specification of the parameters to be optimized. The first index can be any number from " 1 " up to the total number of parameters, the following indices should increase with possible skipping.

2.2 | Description of the “InputParameters” file

Before the start of the analysis, the user should give a set of initial parameters to the program. Below is an example of the “parameters.txt” file for ODCB:

The file contains three columns: the parameter index, which should coincide with the number of the line in the file, the parameter’s short name (fused in one word), and its value separated by space and/or tabulation characters. The parameter index corresponds to that given in the “Spin System” and “List of optimized parameters” sections of the “input.txt” file. After the chemical shifts and JJ-couplings, there are two additional parameters, which correspond to linewidth (LW)(L W) and magnitude used for the calculation of the theoretical spectrum. The initial LWL W value can be determined from a single line of the experimental spectrum as full width at half height. The initial value of spectrum magnitude can be set in the range of 106−10810^{6}-10^{8}.

2.3 | Spectral intervals for optimization

The last input information necessary for running an analysis is the spectral intervals that are taken into account for the optimization process. For its setting user should specify the integration regions using TopSpin integration toolbox (see Figure 2). ANATOLIA reads the “integrals.txt” file in the experimental spectrum processing directory.

FIGURE 2 Setting the optimization intervals as integration regions of the experimental 1H{ }^{1} \mathrm{H} NMR spectrum of orthodichlorbenzene ( 300MHz,303 K300 \mathrm{MHz}, 303 \mathrm{~K}, standard sample 15%15 \% in acetone- d6)\left.d_{6}\right)

3 | ANALYSIS OF 1H{ }^{1} \mathrm{H} NMR SPECTRA

3.1 | Analysis of ODCB 1H{ }^{1} \mathrm{H} spectrum

There are two possibilities for ANATOLIA execution. The first is to copy an executable file in a directory with input data and run it there. The second is to put the ANATOLIA executable file in the “TopSpinHome/prog/anatolia/” directory (it should be created by user) and run it by AU program “anatolia” from the TopSpin command line. In this case, the files “Input_Data.txt” and “parameters.txt” should be located in the “expno” directory of the analyzed spectrum and “PathToDataSet” in the “Input_Data.txt” file should be “./” or " \ \mathrm{~} ".

All the input data necessary for the analysis are now ready. First, we recommend to simulate an initial theoretical spectrum. To do this, just set the “SimMode” to " 1 " in the “Input_Data.txt” file and run ANATOLIA. It will save entire theoretical spectrum and also an experimental one with the first broadening and zero intensities outside spectral intervals. Check the overall appearance of this theoretical spectrum, its similarity with the experimental one and also the spectral intervals. If there is a chemical shift outside of all defined spectral intervals, or some interval without any chemical shift, there will be a warning such as

Warning! Chemical shift no. 1 (0.251876) does not fall into any of defined spectral intervals.
Warning! Spectral interval no. 1 does not contain any chemical shift.

However, these warnings do not influence the workflow of the program.

It is now ready to run an analysis of the ODCB1H\mathrm{ODCB}^{1} \mathrm{H} spectrum with the large enough broadening of 3.0 Hz and optimize linewidth, spectral magnitude and chemical shifts (variable parameter numbers 1,2,7,81,2,7,8 ). Then unfreeze large JJ-couplings with numbers 4 and 6 . After that, set all the parameters for optimization and run the sequence of gradually decreasing broadenings 3.0,2.03.0,2.0, 1.0,0.8,0.6,0.4,0.2,0.1,0.0 Hz1.0,0.8,0.6,0.4,0.2,0.1,0.0 \mathrm{~Hz}. ANATOLIA prints out a number of iteration, a value of an error function and the length of the parameter increments vector during spectrum analysis. Figure 3 illustrates the evolution of the
theoretical spectrum of ODCB during the decrease of the broadening LBL B.

Using the same file “parameters.txt” for input and output allows speeding up the process. ANATOLIA stores the theoretical and experimental spectra with the last broadening used, so they can be easily compared using TopSpin multiple display. Note that in case of optimization, ANATOLIA saves the theoretical spectrum with linewidth equal to LW+LBL W+L B. It saves the optimized parameter values and adds some information:

Analysis of ODCB 1H NMR spectrum
Line Broadening: 0.000000
Theoretical spectrum linewidth: 0.130841
RSS Value: 7.091817e+16
R-Factor: 12.04%12.04 \%

Chemical shifts (ppm):
7.524 7.524 7.314 7.314

J-coupling constants (Hz):
0.3345
8.0797
1.5259
1.5259
8.0797
7.4852

ANATOLIA prints out the standard deviations according to Heinzer. [18]{ }^{[18]} It should be noted that this approach does not account for linewidth variations, which can introduce additional errors into the parameter estimates. The following lines present a title of the task, the last broadening, and the theoretical spectrum linewidth used in the optimization process.
“RSS Value” is the residual sum of squares:

RSS=Σi(Iexp i−Itheor i)2R S S=\Sigma_{i}\left(I_{\text {exp }}^{i}-I_{\text {theor }}^{i}\right)^{2}

FIGURE 3 Evolution of the theoretical spectrum (right) during the course of spectrum analysis compared with the experimental spectrum (left) with the corresponding broadening

It is also often convenient to present a normalized value of the R-factor:

Rfactor =100×RSS/∑iIexp i2R_{\text {factor }}=100 \times \sqrt{R S S / \sum_{i} I_{\text {exp }}^{i}{ }^{2}}

The lower the R-factor, the better the agreement between experimental and theoretical spectra. Usually, values below 15%15 \% are satisfactory. At the same time, visual control is also important, especially how the frequencies of the theoretical spectrum coincide with experimental ones (see Figure 3). Finally, the program prints out the parameters as an upper triangle for user convenience. The optimized parameter values are stored in the “OutputParameters” file. All this additional information will be ignored during the parsing of the “InputParameters” file in the next execution of the program. The format of this file allows using it as an input for further calculations, so user can simply edit the file and rerun the program.

FIGURE 4 Chemical structure and spin system numbering of styrene

3.2 | Analysis of the spectrum of styrene

We consider here a more complicated example: the analysis of the 1H{ }^{1} \mathrm{H} styrene spectrum, which we have previously reported. [27]{ }^{[27]} The styrene molecule is an 8 -spin system shown in Figure 4. 1H{ }^{1} \mathrm{H} spectrum of styrene includes some severe second-order effects (Figure 5).

First, chemical shifts, all vicinal JJ-couplings, and LWL W were optimized with an LBL B of 4.0 Hz . After that, all 26 parameters were unfrozen and the following sequence of broadening was applied: 4.0,3.0,2.0,1.0,0.8,0.6,0.44.0,3.0,2.0,1.0,0.8,0.6,0.4, 0.2,0.1,0.05,0.0 Hz0.2,0.1,0.05,0.0 \mathrm{~Hz}.

The calculation time of multidimensional optimization strongly depends on the number of optimized parameters. In this case, the average number of iterations was about 2000 per broadening value, and the average time of a single iteration was 0.05 s for a total calculation time of about 10 min . This is a good result in terms of program efficiency. The resulting R-Factor was 12.7%12.7 \%.

In this system, nine long-range coupling constants with small absolute values are undefined with respect to their relative signs. In general, the broadening approach is not capable to suppress local minima caused by different signs of small J-couplings. Thus, it is a common practice to perform additional optimizations with sign alternation of all the J-couplings whose signs are not known. [6]{ }^{[6]} In the case of styrene, we performed 512 calculations varying the signs of 9 long-range JJ-couplings. The results are summarized in Table 1. It can be observed that after alternation of relative signs, a solution was found with R-Factor of 5.9%5.9 \%. A comparison of the theoretical spectra with initial and resulting parameters and the experimental spectrum is shown in Figure 5.

FIGURE 5 Comparison of (a) theoretical spectrum with initial parameters, (b) experimental spectrum, and © resulted theoretical spectrum after refinement of JJ-couplings. The region with aromatic protons is shown ( 300MHz,303 K,0.5M300 \mathrm{MHz}, 303 \mathrm{~K}, 0.5 \mathrm{M} in benzene- d6d_{6} )

TABLE 1 Parameters for the analysis of styrene 1H{ }^{1} \mathrm{H} NMR spectrum

3.3 General recommendations

It is useful to perform reference deconvolution [28]{ }^{[28]} of the experimental spectrum before starting the total lineshape analysis, [6]{ }^{[6]} thus compensating for distortions of the experimental lineshape. Recently we showed how reference deconvolution can improve the quality and resolution in 2D phase sensitive spectra, which opens possibility to perform total lineshape analysis of 2D spectra. [29]{ }^{[29]}

The broadening approach allows setting the initial parameters in relatively broad ranges, however, user should try to make them as close to the actual ones as possible. Some parameters can be measured directly from the experimental spectrum quite accurately, although sometimes it is impossible, for example, for styrene. In such cases user should set some rough estimates based on chemical

TABLE 2 Average values and ranges of 1H−1HJ{ }^{1} \mathrm{H}-{ }^{1} \mathrm{H} J-couplings according to Pretsch [30]{ }^{[30]}

structure, that is, define groups of JJ-couplings belonging to geminal ( sp3\mathrm{sp}^{3} and sp2\mathrm{sp}^{2} ), vicinal, or long-range interaction and set appropriate values for them (see Table 2). It is also possible to use prediction software (MestreNova, [24]{ }^{[24]} ACDLabs, [31]{ }^{[31]} ChemOffice [32]{ }^{[32]} ) or literature data [1,30]{ }^{[1,30]} as starting point.

The first broadening should correspond to twice the maximal uncertainty in JJ-coupling values. For example, in case of styrene, large vicinal JJ-couplings between olefinic protons can be determined from the experimental spectrum quite accurately, but vicinal JJ-couplings in the benzene ring cannot and may vary within 7.5±2.0 Hz7.5 \pm 2.0 \mathrm{~Hz}; all other JJ-couplings have smaller uncertainties. Thus, there is no need to set the first broadening larger than 4.0 Hz . In general, multiplicity becomes resolved when the linewidth (LW+LB)(L W+L B) is comparable to the JJ-coupling, making the error function sensitive to the variation of it. Too large broadenings will only waste computational time, but nevertheless, the proper solution will be found.

If there is no satisfactory correspondence between theoretical and experimental spectra after parameters optimization with a large broadening, further optimizations with smaller broadenings are unlikely to lead to an acceptable result. Therefore, it may be worthwhile to make a deliberate stop and achieve the desired spectrum correspondence, early on, and only continue to decrease the broadening if the first match is satisfactory. At first, the broadenings could decrease rather fast (e.g., in steps of 1.0 Hz ), and the last broadenings can be set as multiples of the spectrum linewidth (×4,×2,×1(\times 4, \times 2, \times 1, 0 ). A universal sequence of broadenings for the analysis of the spectrum with linewidth of approximately 0.1 Hz is 6.0,5.0,4.0,3.0,2.0,1.5,1.0,0.8,0.6,0.4,0.2,0.1,0.0 Hz6.0,5.0,4.0,3.0,2.0,1.5,1.0,0.8,0.6,0.4,0.2,0.1,0.0 \mathrm{~Hz}

4 A ANATOLIA PROGRAMMING NOTES

ANATOLIA is written in the C++ programming language. It uses the free GNU scientific library [33]{ }^{[33]} for

matrix diagonalization and the Powell’s BOBYQA optimizer. [34]{ }^{[34]} Spectrum simulations are performed according to Pople et al. and Gunter [13,14]{ }^{[13,14]} by Hamiltonian diagonalization and calculation of a perturbation operator mathrmI+\mathrm{I}^{+}mathrmI+to find transition frequencies and their intensities. The stick spectrum is further convoluted with Lorentzian lineshape to obtain the simulated spectrum.

The spin basis functions in ANATOLIA are set as a binary representation of integer numbers, allowing to use processor bitwise operations for calculation of the Hamiltonian and the perturbation operator matrix elements, which significantly speeds up calculation time of a theoretical spectrum. Hamiltonian matrix is factorized with respect to z-projection total spin number. For the broadening of experimental spectrum, our program uses discrete convolution with a Lorentzian curve of linewidth LBL B (such as the VALISA algorithm [17]{ }^{[17]} ). Calculation of the spectrum and the error function only on the selected regions during optimization significantly increases the program’s performance. We found that it is reasonable to optimize the theoretical spectrum linewidth and its magnitude before the optimization of the other parameters. Thus, each broadening step consists of the preliminary and main optimization stages. The program is compiled and statically linked resulting in a single executable file, available for Linux, MacOS X, and Windows operating systems. ANATOLIA is available for download at http:// anatolia.nmrclub.ru and https://github.com/dcheshkov/ ANATOLIA.

ACKNOWLEDGEMENTS

The authors thank Alexey Kiryutin and Sergey Tsukanov for helpful discussions that helped make ANATOLIA more user-friendly and for thorough program testing.

ORCID

D.A. Cheshkov (1) http://orcid.org/0000-0002-9024-4353
K.F. Sheberstov (2) http://orcid.org/0000-0002-3520-6258
D.O. Sinitsyn (3) http://orcid.org/0000-0001-9951-9803
V.A. Chertkov (4) http://orcid.org/0000-0001-8699-5894

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How to cite this article: Cheshkov DA, Sheberstov KF, Sinitsyn DO, Chertkov VA. ANATOLIA: NMR software for spectral analysis of total lineshape. Magn Reson Chem. 2018;56:449-457. https://doi.org/10.1002/mrc. 4689