J. Chem. If. Comput. Sci. 1992,32, 299-303
299
lH and 13C N M R Spectra Simulation M. TuHarJ L. TuSarJ S. Bohanec, and J. Zupan' Boris KidriE Institute of Chemistry, Ljubljana, Slovenia Received February 14, 1992 Similarities and differences between the systems for IH and 13CNMR simulation of spectra are described. Both methods use semiempirical chemical shift calculation. Input for the simulation is the chemical structure edited by a two-dimensional structure editor. Both systems consist of tables of basic chemical shifts (for hydrogen or carbon atoms, respectively), tables containing different corrections and the coupling constants of protons, a LAOCOON program for higher-order spectra calculation, and programs for the graphical output of spectra. INTRODUCTION
SIMULATION OF NMR SPECTRA
The importance of simulation of different types of spectra can be clearly seen in any structure elucidation process. Due to the fact that structure identification cannot be accomplished in a straightforward manner:
In general, the simulation of any type of NMR spectrum, of lH,W, or any other nucleus having a spin different from zero, is based on the evaluation of chemical shifts for all corresponding nuclei in the molecule (Le., shifting of the resonance RF line with the respect to the standard line due to the magnetic field caused by the neighboring atoms). The chemical shifts can be observed only for the atomic nuclei having a spin different from zero. Due to the fact that the hydrogen atom (spin l/2) is much more common in nature than the carbon isotope 13C(spin I/2; 12C has spin equal to zero) the IH NMR spectrum shows features different from those found in the I3CNMR spectrum. The most significant influence in the 'H NMR spectrum is the coupling of magnetic effects between different neighboring hydrogens. Due to a very low probability of 13Ccarbon isotope atoms being neighbors in an molecule, the effect of spin-spin coupling is marginal in I3C NMR spectroscopy. Decoupled Spectrum. Each chemical shift dnuclcus i in the decoupled spectrum (i.e., a spectrum without coupling) can be calculated according to the same formula for any NMR spectroscopy:
-
different spectra structure of the compound simply by deducing the entire structure from the spectroscopic data, the process in the other direction:
-
candidate structures simulated spectra must also be possible. The principles of the spectral simulation process are theoretically more readily explained (vibrational analysis, resonance theory, etc.) than spectra-based structure identification. However, with the exception of relatively small molecules, the theoretical equations (Hamiltonians) with which the spectral features can be calculated from the structural data become excessively large and complex for "realworld" compounds. Spectra simulation procedures therefore are mainly carried out using correlation tables and different semiempirical methods, similar to those used in the structure elucidation process. Consequently, the entire structure determination process must be performed iteratively, going from initial guesses of structural fragments and structural parts toward larger and larger structural groups until few final candidate structures are obtained. But even at this last step, having few molecules as possible candidates for the actual solution, the best way to select the correct one is to simulate all spectra of all candidates and search for the best agreement with the experiment. Besides the structure elucidation process, where the spectral simulation plays a very important role as feedback information, the simulation of spectra is used for other purposes as well: theoretical consideration testing of hypotheses checking of large databases for possible errors aiding the isomer generation process etc. The above considerationof the structure elucidation process clearly shows that the more different spectroscopies are involved, the more structural information can be extracted from measurements. Therefore, the need for multispectroscopy simulation as a feedback corrective process is doubtless necessary. In this paper, the simulation of IH and 13CNMR spectra is discussed and the role of simulation in the structure elucidation process is shown in a short example. f
SRC, d.o.0. Ljubljana, Slovenia.
Ai is the basic chemical shift of the nucleus i for a given neighborhood (for example, a carbon in a benzene ring, proton in a CH3- group, etc.). Zji are changes of the basic chemical shift Aicaused by the specific substituentj in a given topological environment in the basic group with respect to the nucleus i. The last sum represents empirical corrections that should be applied in certain cases in order to obtain better agreement with the experimental data. These corrections are applied in the case when more substituents from the same substituting position have to be taken into account, in the case of conformations, and/or in the case of configurational corrections. One of theveryimportant tasksof each NMR simulator is to detect automatically the cases where corrections corrk have to be applied. For the simulation of the 13CNMR spectrum, the values Ai, Zji, and corrk are stored in tables addressable according to the specific structural features. The program S I M U L A I - ~ contains the chemical shifts for 39 basic environments (Table I) and 2479 values of increments Zji. Theoretically, for 150 substituentsj acting in all 39 basic environments i from 2 to 7 different substituent positions (a,al,8, 81, y, y1, and 6) 24 600 different corrections Zji would be needed. Although
0095-2338/92/1632-0299$03.00/0 0 1992 American Chemical Society
300 J. Chem. Inf. Comput. Sci., Vol. 32, No. 4, 1992
TDARET AL.
Table I. All 39 Basic 13C NMR Chemical Shifts A, (in ppm relative to TMS) functional group i alkane alkene alkyne carboxylic acid, ester amide C=Cl=C C 4 = C aldehyde, ketone CF CF3 CCl
AI (ppm) -2.3 123.3 71.9 166.0 165.0 213.5 74.5 193.0 75.2 116.4 24.9 54.0 77.2 10.2 21.4 12.1 -20.7
cc12 cc13
CBr CBr2 CBr3 CI structures with three-membered rings cyclopropane oxirane structures with four-membered rings cyclobutane
-2.8 39.8
functional group
cc1 cc12 cc13
CBr CBr2 CBr3 CI cyclopropane oxirane cyclobutane cyclopentane pyrrole Cr2,5 pyrrole C,-3,4 pyrrole N furan C,-2,5 furan Cr3,4 cyclohexane benzene pyridine Cr2,6 pyridine C,-3,5 pyridine C r 4 indole C-2 indole C-3 indole C-3a indole C-4 indole C-5 indole C-6 indole C-7 indole C-7a total
possible no.
-4(ppm) 26.3 118.0 107.7 143.0 109.9 27.6 128.5 149.8 123.6 135.7 124.1 102.1 127.6 120.5 121.7 119.6 11 1.0 135.5
23.1
Table II. Percentage of Available Z,,for All Basic Shifts alkane alkene alkyne carboxylic acid, ester amide C = C 4 C 4 = C aldehyde, ketone CF CF3
functional group i structures with five-membered rings cyclopentane pyrrole Cr2,5 pyrrole Cr3,4 pyrrole N furan Cr2,5 furan Ci-3,4 structures with six-memberedrings cyclohexane benzene pyridine Cr2,6 pyridine Cr3,5 pyridine Cl-4 indole C-2 indole C-3 indole C-3a indole C-4 indole C-5 indole C-6 indole C-7 indole C-7a
actual available
% -
600 300 300 600 600 300 150 450 600 600 600 600 600 600 600 600 600 300 300 450 450 600 600 300 600 600 600 600 750 750 450 1050 1050 1050 1050 1050
467 116 62 153 78 44 20 110 2 10 20 14 21 23 8 3 3 39 23 24 33 25 17 6 72 44 201 360 92 106 60 28 27 34 27 27
77.8 38.7 20.7 25.5 13.0 14.7 13.3 22.4 0.3 1.7 3.3 2.3 3.5 3.8 1.3 0.5 0.5 13.0 7.7 5.3 7.3 4.2 2.8 2.0 12.0 7.3 33.5 60.0 12.3 14.1 13.3 2.7 2.6 3.2 2.6 2.6
1050
26
2.5
1050 1050
27 27
2.6 2.6
24 600
2479
10.1
the number 2479 for different contributions (representing only 10% of all possible corrections Zji) seems to be small, the missing contributions are largely from the less-common substituents. As can be seen from Table 11, the percentage of available corrections Zji for the most frequent substituents like alkanes, alkenes, carboxylic acids and esters, ketones, benzenes, cyclohexanes, etc. are far above this average value.
Less than half of the data (1049 Zji values) used by the the literature,”I5 while the rest of them (1430) were obtained in our laboratory.2J In contrast to the 13CNMR simulation, in the case of *H NMR spectra the decoupled approach (eq 1) is seldom used as a final result; its value is mainly as the starting or initial step for more complicated procedures. Due to the fact that the protons form a smaller number of basic structural environments than the carbon atoms do, the list of basic shifts (Table 111) is shorter than the list in Table I (22 vs 39), and the list of substructures is smaller in the case of ‘HNMR compared to 13CNMR (85 vs 150, Table IV). The same is true for the list of different topological positions of the substituents with respect to the basic group (4 vs 7). Simulation of First-Order Spectra. When the coupling constants JABbetween two nuclei A and B with the nonzero spins have to be taken into the account, the basic chemical shifts IJA and IJB of the particular two nuclei are always split into more peaks. In the first-order approximation each coupling constant JAB produces four peaks instead of two peaks IJA and UB: SIMULA program were taken from
Each of the four peaks (eq 2) has the following relative intensity:
J. Chem. If. Comput. Sci., Vol. 32, No.4, 1992 301
NMR SPECTRAL SIMULATION Table III. All 22 Basic 1H NMR Chemical Shifts A, (in ppm relative to TMS) functional group i
Ai (ppm)
methyl (-CH3) 0.23 ethyl (-CHz-CH,) 0.86 n-propyl (-CHZ-CHZ-CH~) 1.33 n-propyl (-CHz-CH2-CH3) 0.91 isopropyl (-CH(CH3)2) 1.33 isopropyl (-CH(CH&) 0.91 0.89 t-butyl (-C(CHj)3) other alkane (CH2R1R2) 1.25 other alkane (CHR1R2R3) 1.SO 5.25 alkene 1.80 alkyne
Ai
functional group i
(ppm)
benzene pyrrole (HI-substituent) pyrrole (HI-substituent) pyrrole (H3-substituent) thiophene (Hz-substituent) thiophene (H3-substituent) pyridine (HI-substituent) pyridine (H3-substituent) pyridine (b-substituent) furan (HI-substituent) furan (H3-substituent)
7.26 9.50 6.62 6.05 7.20 6.96 8.59 7.38 7.75 7.38 6.30
The first-order approximation is valid as long as the coupling constant JAB is considerably smaller than the absolute difference UA - UB. In one structure this condition for some nuclei may be met and may not be met for some others. As was mentioned above, the coupling constants are of various sizes compared to the chemical shifts. Not only this, the coupling constants depend on many structural features such as C-C distance, dihedral angle, electronegativity of
substituents, influence of II-bond,16 etc. Therefore, only the few most common and standard coupling constants are included in the database of our 'H NMR spectra simulation program VODIK.~'J* Table V shows the coupling constants JABbetween some most common protons A and B used in our progam VODIK for the simulation of 'HNMR spectra. Due to the fact that the magnetic field strength heavily influences the splitting of the chemical shifts in the NMR spectrum one of the input data that must be provided by the chemist is the frequency of the field at which the NMR measurements are made (e.g., 60 MHz, 250 MHz, etc.). At the initial step of simulation of 'H NMR spectrum, the program VODIK enables the user to enter different coupling constants from those proposed by the program. If such "userdetermined" coupling constants turn out to be better than the system's they can be easily exchanged and permanently stored in the program's data base. Spectra of Higher Order. In cases where the coupling constants between the nuclei are comparable to the shifts and involve more nuclei with nonzero spin, the first-order ap-
Table IV. List of Substituents for I3C and 'H NMR Handled by Programs SIMUW and VODIK,Respectively 1 2 3 4 5 6 I 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49 50 a
-csp3 -CH3 -CH2-CH3 -CH~-CHZ-CH~ -CH~-CH~-CH~-CHS -CH2-O-CH2-CH3 -CRz-CI -CRZ-Br CR2-I -CHz-OH -CH2-NH2 -CH-CN -CH(CH3)2 -C(C&h -CF3 -OH
-0-0-R -0-CH3 -0-CHz-CH3 -O-(CHZ)~-CH~ -0-CO-R -0-CO-CH3 -0-N=O -0-Ph -S-H -S-R -S-CH3 -S-CHz-CH, -S-CH,-Ph -S-(CHs)s -S-CO-R -S-CN -NH2 -NR2 -N+R3 -NtH3 -NHR -N+(CHd3 -NH-CHs -N(CHyCH,)2 -NH-CO-CHl -NH-NH2 -N(Ph)z -F -CI -Br -I -Si(CH& -Si(Cl)3
*
* * * *
* * * * * *
* * * * * * * *
* * * * *
*
* * * * * * *
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 71 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
.P(Phji -CR=R2 -CHI-O-CH:, -CHO -CO-R -CO-CHp -CO-NH2 -CO-NR2 -co-CI -COOH -COO-COO-R -COO-CH, -COO-CH2-CH, -CR=OHsp -CR=OHanti -0-0-R -N=C=O -N=O -N=N-Ph -N=N=cyclohexyl -NO2 -SO-R
*
* * * * * * * * *
* *
-s02-c1 -S02-CH=CH2 -SOz-OH -C=C-R -C=C-H -C=N -N+=N - N + e -cyclopropy 1 -oxiryl -pyridyl(2/6) -Ph -cyclohexyl -N(CHah -NR-CO-R -CR=N-Ph -Si(R)3 -CR=N-R -0-CO-0-R -NC -PYidYl(3/5) -pyridyl(4) -CR=C=C(R)2 -CR=C=N-R -CR=C=O -CR=N=N-R
* * * *
* * * * * *
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150
-CO-0-CO-R -CS-R -SO+R -aziridyl -N=N-R -N-C=N-R -P(R)z -CO-S-R -CS-OR -NR-CS-OR -S-CS-S-R -0-CS-OR -S-CS-NRz -NR-CO-NRz -N=C=S -NR-CS-NRz -0-CO-NRz -NR-CS-R -CO-NR-CO-R -C(R)2F -C(R)F2 -CH=CH2 -CR=N-OH -C(R)C12
-cc12
-Ph with substituent -C(R)Br2 -CBr3 40-Ph -C(R)I2 -CIS -S-CS-R -pyrrolyl(2/5) -pyrrolyl(3/4) -indolyl( 1) -indolyl(2) -indolyl(3) -indolyl(4) -indolyl(5 ) -indolyl(6) -indolyl(7) -cyclopentyl -cyclobutyl -NR-CO-0-R -furyl(2/5) -fury1(3/4) -pyrrolyl(1) -thienyl(2/5) -thienyl(3/4) -cycloheptyl
*
*
* * * * * *
*
* *
All listed substituents are for the I3C NMR spectra simulation. Substituents marked with an asterisk are for the 'H NMR spectra simulation.
302 J. Chem. Inf. Comput. Sci.. Vol. 32, No. 4, 1992
TUARET AL.
Tattle V. All 27 Coupling Constants Jtj (in Hz)Used in Program VODlK
functional group
Jij
alkane (CH-CH) alkene (gem substituent) alkene (cis substituent) alkene (trans substituent) benzene (ortho substituent) benzene (meta substituent) benzene (para substituent) pyrrole (Hz-H3) pyrrole (Hz-H,) pyrrole (H2-h) pyrrole (Hz-HI) pyrrole (H3-H4) pyrrole (Hs-HI) thiophene (H2-H3)
(Hz)
7.10 2.00 8.50 15.0 8.40 2.00 0.15 2.60 1.30 2.10 2.60 3.50 2.30 4.80
functional group thiophene (Hz-H4) thiophene (Hz-H5) thiophene (H3-H4) pyridine (Hz-Hs) pyridine (Hz-H4) pyridine (Hz-Hs) pyridine (Hz-Hb) pyridine (H3-H4) pyridine (H3-Hs) furan (HZ-H~) furan (HyH4) furan (H2-H5) furan (H3-H4)
Jij
(Hz)
1
1.00 2.80 3.50 5.00 1.30 1.00 0.30 8.00 1.60 1.80 0.90 1S O 3.40
SELECTION
-
all possible sets set 3
set 2
set1
0-C
c-c
0-C
11
I1
I1 P
0-c
C-C
\C
\C
C
IC
a
'
6!5
C
bc
epl
C
I1
i
c-c-0
c-0-c
\
\C
I
C
1
C
Figure 2. Selection of possible sets from the complete set, and the resulting possible structures are generated by the structure generator b
GENSTR.24
Tattle VI. Simulated 'H and I3C NMR Spectra for Six Possible Structures I
I Resanancc
Structure freouency
'H NhfR spectrum
uC NhfR spectrum
(in PPm)
(in PPm)
0 -CHZ
3.55,3.55,5.22,5.22
74.2,74.2, 106.5, 149.1
T-7
2.05,3.55,3.83,3.90
39.4,60.9,78.4, 164.8
1.80,4.35,6.23
13.4, 74.1, 110.3, 135.6
1.00,2.00,6.24
7.5,27.7, 105.7, 130.9
1.80,3.50,3.82,3.90
23.7,51.1,76.5, 163.3
60 Rtlz
I I CH2 - C = CH2
C
CHZ-C
= CHZ
0-CH
I I/ CHZ- C-CH3
/%C-CH2-CH3
d
0
~
CHz
I1
CH3-C-O-CH3
Figure 1. Comparison between the experimental (a) and simulated (d) IH NMR spectra of thiophene. The simulation is made in a
C*s-O-CH=CHz
1.30,3.70,4.04,4.18,6.47 14.8, 62.7,83.5, 151.8
Experimental
2.2 T, 3.6 S, 3.8-4.1
three-step process: decoupled (b), first-order (c), and higher-order (d) simulation.
proximation of the spectrum does not adequately simulate the experimental spectrum. For such, more realistic cases, the diagonalization of the wave function matrix with the Hamiltonian in the formlg n
n-1
n
(4)
must be solved. The value Jij has the same meanings as in the above eqs 2 and 3. The value vi is the resonance frequency
20.8,51.5,76.7, 163.5
of nucleus i in the absence of other nuclei and is linearly dependent from U ~ . ~ OIi is the angular momentum operator and Iziis the zcomponent of angular momentum for t h e nucleus i.
The input values for this diagonalization program are actually the first-order spectrum and the chemical shifts of 'active' nuclei with mutual coupling constants. For two
J. Chem. If. Comput. Sci., Vol. 32, No. 4, 1992 303
NMR SPECTRAL SIMULATION different spin orientations (fl/z) of n nuclei in the magnetic field there are 2"different wave functions, and the energy of such a system is described by a 2" X 2" dimensional matrix. The solutions of this system can be achieved using iterative programs like L A W O O N . ~ ~ Considering the symmetry of the active (nonzero spin) nuclei in each particular structure, the large 2" X 2" dimensional matrix can be factorized into smaller parts. However, in spite of the factorization and rapidly increasing computational power of modern personal computer hardware and software, the simulation of complex spin systems is still limited to a small number of (d10) nuclei with nonzero spins. For such high-order calculations of lH NMR spectra in VODIK, the well-known program L A W N - ~ A , ~is used. SIMULATION BY THE PROGRAM VODIK The structure of the compound for which the 'H NMR spectrum should be simulated is entered via the structure editor, which was already described else~here.~, Next, the program VODIK finds and enumerates the active nuclei and calculates the first-order spectrum (eqs 2 and 3) as the initial approximation and passes the calculated result to the next step. In the second step, the results of the first approximation simulation are handled by the L A W N - 4 ~ program, and the result is displayed in Figure 1. Before the first-order spectrum is calculated, the user has to give the radio frequency (RF in MHz) for which the simulation has to be performed. At this step the user can change the coupling constants as well. Where the output is concerned, the user can select the width of the peaks (resolution of the "instrument") and choose the way the spectra are displayed (with or without the integral, specific region of the spectrum, etc.). EXAMPLE OF USE OF THE SYSTEM As an example of how the simulations can be used, a real case where both simulations (13C and lH NMR) were employed to solve the unknown structure will be presented in this paragraph. First, a 13C NMR spectrum consisting of four peaks (at 20.8, 51.5, 76.7, and 163.5 ppm relative to TMS) was recorded. Using the 'FRAGMENT' option in the system CARBON, the two most common fragments at each peak were selected: =(C-)-O-CH,
=CHz
)C=
-0-CHz+CH=
-O-CH,
-CH2-
-CH,
From this set of eight fragments and the constraint that the resulting structure should have only four carbon atoms, the system GENSTRz4 has selected five possible sets: -0-CH=,
)C=, -CH,-,
)C=, -O-CH,, =(C-)-O-CH,, -0-CHz-, -0-CH=,
-CH,, -CH,,
and -CH, and =CHz and =CH,
)C=, -CH,-,
and = C H ,
=CH,, -CH,-,
and -CH,
out of which six different structures (Figure 2) weregenerated. For all six possible structures, both the lH NMR and the 13CNMR spectra were simulated, and the results are shown
in Table VI. From the results obtained it is clearly seen that structure 5 has produced the best pair of spectra compared to the experimental ones. CONCLUSION The simulationof different types of spectra has a very broad application in many fields of chemistry. On the market there are more and more powerful and user-friendly computer programs performing this tasks. Such software can be used in analytical, spectroscopic, chemometrics,and qualimetrics, and in other laboratories. The best performance is achieved if the simulation procedure is linked with other all-purpose chemistry-oriented packages as an additional stone in the mosaic of the particular computerized tool. The described simulation programs VODIK and SIMULA are written in Turbo Pascal language and can handle VGA/EGA and Hercules graphics. Both can be used together with the general package CARBONz3and GENSTR.z4 REFERENCES AND NOTES (1) Lah. L.: Tuiar. M.: Zuoan. J. Simulation of I3C NMR SDectra. Tetrahedron Comput. Mithobol. 1989, 2, 5-15. TuSar, L. Automatical assignation and simulation of I3CNMR spectra: (in Slovenian). M.Sc. Thesis, Universityof Ljubljana, Ljubljana, 1990. Tuhr, L.; Zupan, J. Evaluation of new parameters for the simulation of I T NMR spectra (in Slovenian) Vest.Slov. Kem. Drus. 1991,38(4), 557-572. Pretsch, E.; Furst, A.; Robien, W. Parameter set for the prediction of the "C NMR chemical shifts of I$- and sphybridized carbon atoms in organic compounds. Anal. Chim. Acta 1991, 248,415428. Pretsch, E.;Clerc, J. T.;Seibl, J.;Simon, W. T~bc1lenzurStrukturau~larung organischer Verbindungen mit spectroskopischen Methoden; Springer-Verlag: Berlin, 1976. Brown, D. W. A Short Set of C-13 NMR Correlation Tables. J. Chem. Educe 1985,62, 209-212. Kalinowski,H. 0.; Berger, S.;Braun, S.Carbon-13 NMRSpecrroscopy; John Wiley & Sons: Chichester, 1988. Shamma, M.; Hindenlang, D. M. Carbon-13 NMR Shut Assignments of Amines and Alkaloids; Plenum Press: New York, 1979. Levy, G. C.; Nelson, G. L. Carbon-13 Nuclear Magnetic Resonancefor Organic Chemists; John Wiley & Sons: New York, 1972. Grant,D. M.;Paul,E.G.Carbon-13 MagneticResonance. 11. Chemical Shift Data for the Alkanes. J. Am. Chem. Soc. 1964,86,2984-2990. MoraIe-Ria, M. S.; Espineira, J.; Joseph-Nathan, P. I3C NMR spectroscopy of indole derivates. Magn. Reson. Chem. 1987,25, 377395. Stibor, I.; Trika, P.; srogl, J.; Janda, M. INDO Calculations and 'Hand W-NMR Spectra of Furan Methyl Derivatcs. Coll. Czech. Chem. Commun. 1978.43, 2170-2173. Stothers, J. B. Carbon-I3 NMR Spectroscopy; Academic Press: New York and London, 1972. Johnson, L. F.; Jankowski, W. C. Carbon-13 NMRSpectra, A Collection of Assigned, Coded, and Indexed Spectra; John Wiley & Sons: New York, 1972. In order to extract many new contributions, Z,, a collection of about SO00 I T NMR spectra has been kindly made available to us by Prof. M. E. Munk from the Chemistry Department of the Arizona State University, Tempe, AZ. Williams, D. H.; Fleming, I. Spektroskopische Metoden in der organischen Chemic; Gcorg Thieme Verlag: Stuttgart, 1971. Tuhr, M. Simulation of IH NMRspectra (in Slovenian). M.Sc. Thesis, University of Ljubljana, Ljubljana, 1990. Zupan, J.; Tuhr, L.; TuSar, M. Comparison of Two Spectra Simulation Methods: IH and I3C NMR Spectra: Second Course on Computer Chemistry(Informaticaper1a Chimica); Rivadel Garda,Oct 14,1991. Ferguson, R. C.; Marquardt, D. W. Computer AnalysisofNMRSpectra: Magnetic Equivalence Factoring. J . Chem. Phys. 1964,41,2087-2095. Carrington, A.; McLachlan, A. D. Introduction to Magnetic Resonance; Chapman and Hall: London, 1979. Castellano, S.;Bother-By, A. A. Analysis of N M R Spectra by Least Squares. J. Chem. Phys. 1964,41, 3863-3869. Musso,J. A. NMR LAOCN-4A; Computer Program, QPM, Indiana University Chemistry Department, 1973; No. 232. Bohanec, S.;Tuhr, M.; Tuhr, L.; LjubiE, T.; Zupan, J. A System for Creating Collections of Chemical Compounds Based on Structures; Scientific Computing and Automation (Europe) 1990, Data Handling in Science and Technology No. 6; Karjalainen, E.J., Ed.; Elsevier: Amsterdam, 1990, Chapter 35, pp 393-405. Bohanec, S.;Zupan, J. Structure Generation of Constitutional Isomers from Structural Fragments. J. Chem. In/. Compur.Sci. 1991,31,531540.
