A computer program for simulating many-spin NMR spectra

JOURNAL

OF MAGNETIC

RESONANCE

12,296-306

(1973)

A Computer Program for Simulating Many-Spin NMR Spectra* RAYMOND C. FERGUSON Central Research Department, E. I. du Pont de Nenwurs and Company, Wilmington, Delaware 19898 Received July 16, 1973 A digital computer program has been developed for simulating spectra arising from many coupled nuclear spins. It is particularly designed for the analysis of polymer spectra. The input is any set of transition lists, preferably the output transition frequencies and intensities from one of the conventional spin simulation programs. The transition lists are combined with appropriate statistical weights to simulate the spectra of synthetic polymers. Use of the program is illustrated by tests of various models for quantitatively estimating the tacticity of polypropylene from high resolution ‘H-NMR spectra.

The exact analysis of many-spin NMR spectra requires excessively large computer memory and computational time, so most programs are dimensioned for up to eight spins. Simulation of high resolution polymer spectra is particularly difficult because the number of coupled spins usually exceeds the capacity of any feasible computer program, and many polymers are physically inseparable mixtures of several structural groupings. However, in favorable cases, the X-approximation permits many-spin spectra to be analyzed as sets of subspectra having fewer coupled spins (1-3). We have developed a computer program NMRMRG which is designed particularly for simulating polymer spectra, but is also suitable for simulating any combination of subspectra or spectra of mixtures. Its use is illustrated by tests of various interpretations of the high resolution ‘H-NMR spectra of polypropylenes. EXPERIMENTAL

DETAILS

NMRMRG is a digital computer program written for the Univac 1108 computer and a Calcomp 564 plotter. The program reads as input up to 12 transition lists of not more than 500 transitions each from cards punched in the output format of LAocoon with Magnetic Equivalence (LAME) and LAocoon with Chemical Equivalence and Xfactorization (LACX) (4). This input consists of a transition number, frequency, and intensity, The intensities are normalized, if necessary, by scale factors provided by the operator. For each transition list, a line shape function of the (Lorentzian) form a gCvi>

=

1 + 4(&J - vJ2/b2 is generated, where a, the statistical or fractional weight contribution of the subspectrum, and b, the line width, are supplied by the operator. Each transition is multiplied by this * Contribution

No. 2054, Central Research Department. 296

Copyright 0 1973 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain

SIMULATION

OF MANY-SPIN

297

SPECTRA

function and added into the total intensity at the appropriate address (frequency) locations in memory. Since there can be a large number of transitions, and each transition list can be used repetitively, g(vl) is truncated at ten line widths (about 1% of the maximum intensity) for computing efficiency. This truncation is sometimes too severe, causing steps in the wings of very strong lines. The operator can specify a larger limit. In computing the composite spectrum, each transition list, or part thereof, may be used an arbitrary number of times, with different frequency origins, fractional weights, and line widths. The intensity of the output plot can be scaled to the strongest peak in the plotted spectrum, or to the strongest peak in a given range. Several plots can be generated from a given composite spectrum. Polypropylene samples and spectra. Preparation of the polypropylene samples is reported elsewhere (5). The samples discussed here are the insoluble residue from a hot solvent extraction of a Hercules “Profax” polypropylene, the soluble extract, and a highly syndiotactic polypropylene. The 220-MHz IH-NMR spectra were obtained on 10 % solutions of the polymers in redistilled Eastman practical-grade o-dichlorobenzene at 150°C. The spectra were calibrated vs hexamethyldisiloxane, internal. The chemical shifts vs tetramethylsilane can be approximated by adding 0.04 ppm. A Varian Associates HR-220 NMR spectrometer was employed. COMPUTER

SIMULATIONS

OF POLYPROPYLENE

SPECTRA

Most high resolution NMR studies of polypropylenes have been concerned with estimation of tacticity. Computer simulations of the 220-MHz spectra of polypropylenes were undertaken to test conflicting assignments and interpretations of the spectra, namely the assignments of the tetrad methylene resonances, and estimation of the relative probabilities of r (racemic or syndiotactic) vs m (meso or isotactic) dyad placements (6-10). Heatley et al. (6, 7) made tetrad methylene assignments consistent with loo-MHz and 220-MHz spectra of atactic polymers of cis- and trans-propylene-1,2,3,3,3-d,, and with 220-MHz spectra of isotactic polypropylene. The intensity relations for the isotactic polypropylene indicated about 2 ‘A r-dyads, occurring predominantly as isolated racemic placements breaking long meso sequences. Flory (8) reinterpreted these published spectra, challenged the mrm assignment, and elaborated earlier arguments (9, 10) that isotactic polypropylenes must have considerably more than 2 % r-dyads. He argued that the mrm and rrr resonances should not have the nearly equal chemical shifts assigned by Heatley et al. and that the mrm resonances must be broadened beyond detectability by conformational effects. The conflicting assignments and interpretations have been tested by comparison of computer simulations with the observed spectra. The analyses were based on tetrad methylene, triad methine, and triad methyl sequence pattern assignments and probabilities. The methyl resonance patterns could not all be fitted with a single set of triad chemical shifts; this suggests detectable pentad effects, but there were inadequate data for making pentad assignments.

298

FERGUSON

The number of coupled spins exceeded the capacity of present computer programs, so subspectral approximation analyses were made with LACX, LAME, and NMRMRG. Subspectra for the various n-ad sequences were calculated by suitable approximations of the “cyclic dime? model (1,3-dimethylcyclobutane) :

WC’) I

CH3

I

Since the four-bond proton-proton couplings are known to be small (~0.5 Hz), the following subspectral approximations were adequate: CH, : A, part of A,D case, using LAME; 13CH3 : A, part of A,BX case, using LAME; CH: D part of A3B,C2D case, using LAME; CH, : AB part of [ABC12 case, using LACX. The parameters employed for the subspectra were derived from a combination of sources, mainly values from the literature for deuterated polypropylenes, but were adjusted for best fit to the spectra of this work (Table 1). Except for differences in TABLE NMR n-Ad Pentads mmrm mmmm mrrm

(r)mr(r)

(r)rr(r)

PARAMETERS

FOR

1

VARIOUS n-Ad

SEQUENCES IN POLYPROPYLENE?,

Chemical shift, ppm C&(M)

Ha

HB(HA’)

0.824 0.871 0.788 0.841 0.830

Coupling constant, Hz” Hx

J MX

1.597

6.56 (6.56) (6.56) 6.56

1.589

J AB

J AX

JBX

(8.0)

(8) (5.0)

(6.9)

(6.1)

(8.0)

(5.0)

Tetrads mmm mmr rmr mrm mrr rrr

0.888 0.951 0.974 1.068 1.038 1.075

1.286 I .242 1.194 1.068 1.117 1.075

-13.6 (-13.6) (-13.6) (-13.6) (-13.6) (-13.6)

6.1

(6.9) (8.0) (8.0) (8.0)

(6.1) (6.1) (5.0) (5.0) (5.0)

11Values in parentheses were assumed for the computer runs. The coupling constants Jax = 8.0 and = 5.0 (= Jsx above) for r-centered tetrads are from Heatley et al. (7) and are approximately the values found for deuterated polymers.

JApx

299

SIMULATION OF MANY-SPIN SPECTRA

reference zero, these parameters are in close agreement with those of Heatley et al. and Zambelli et al. (12). The methylene shifts are within experimental error of Flory’s estimates (8), except for mrm. mmm

mrr

FIG. 1. Calculated tetrad CH1 patterns for polypropylene. AB part of [ABCII LACX trials, parameters of Table 1. Line width 1.6 Hz. (a) mmm; (b) mmr; (c) rmr; (d) mrr; (e) mrm; (f) rrr.

FIG.

2. Calculated polypropylene

spectrum, Model A, Bernoullian

P, = 0.01.

The methylene group subspectra for the six tetrad sequences are shown in Fig. 1. Note that mrm and rrr produce triplets which are identical, except for a small chemical shift difference. Similarly, for the mm, mr, and rr triads the methyl patterns are identical doublets. The methine patterns are essentially identical octets, except for chemical shift differences.

300

FERGUSON TABLE NMRMRG Model

P,: n: CH,:

Bernoulli

mmm mmr rmr mrr mrm rrr

1[

mm CH3 13CH3 - - mr CH rr Line width (Hz): Trial No. : Fig. No. :

Pr: Ft: CHI:

2

TRIALSFORISOTACTICPOLYPROPYLENE Nonrandom

0.01

0.05

0.10

0.15

0.9730 0.0196 0.0001 0.0002 0.0098 0.9801 0.0198 0.0001 1 .4h 53

0.8574 0.0903 0.0024 0.0048 0.045 1 0.0001 0.9025 0.0950 0.0025 1.4 15

0.729 0.162 0.009 0.018 0.081 0.001 0.810 0.180 0.010 1.4 16

4(a)

4(b)

4(c)

0.6141 0.2168 0.0191 0.0382 0.1084 0.0034 0.7225 0.2550 0.0225 1.4 17 46-O

mmm

0.01 1 0.97 0.02

0.05 1 0.85 0.10

0.01

0.05

0.98 0.02

0.90 0.10

1.4 22

1.4 23 %a)

0.01

0.05

0.;9

0.;

(3%

mm

1[

13CH3 -mr CH rr Line width (Hz): Trial No. : Fig. No. : ’ 0.8306*

methyl

b mrr,

mrm,

’ mrm

omitted

rrr

doublet assigned to rr. 2.2 Hz; mm CH3 1.2 Hz; mm 13CH3 (assumed broadened) in second trial.

0.01 0.99

0.05 0.95*

0.01” 1.4 18

0.05” 1.4 19 5(c)

2.0 Hz;

0.02 3 0.9667 0.0133

0.05 3 0.9167 0.0333

0.0067

0.0133

0.0333

0.0033 0.9866 0.0067 0.0067 1.4 20

0.0067 0.9733 0.0133 0.0133 1.4 20a

0.0167 0.9334 0.0333 0.0333 1.4 21 5(b)

0.04

0.10

0.91 0.06

0.7; 0.18

0.0020 0.0013 0.0080 0.9843 0.0090 0.0067 1.4 54(55’) 6W(Tb)‘)

all others

.)

0.01 3 0.9833 0.0067

0.0112 10 0.9820 0.0067

mmr rmr mrr mrm rrr

(. . . mmr,mmm..

0.03 0.01 0.92 0.06 0.01 1.4 56(57’) 6(c)(7(c)“)

0.09 0.01 0.81 0.18 0.01 1.4 58(59=) C’(d)“)

1.4 Hz.

These identities simplify application of NMRMRG, since only eight subspectra (five CH, and one each of CH,, 13CH3, and CH) are needed as input for NMRMRG. In principle, 15 subspectra (six for tetrads and nine for triads) are required; the additional ones can be generated by adding a chemical shift to the appropriate subspectrum of the same class, e.g., mrm serves for rrr. NMRMRG trials were made for several limiting models, for which the probabilities were calculated by well known relationships (12). Model A. Bernoulli trials. For this model, we assume random placement of dyads, governed by a single probability P, (the probability of a racemic dyad placement). Trials for P, = 0.01 to 0.15 are summarized in Table 2. Trial 53 (Pr = 0.01) gave the best fit to the spectra of the most highly isotactic polymer (Figs. 2 and 3). Trial 15, P, = 0.15 gave the best approximation for the spectrum of the extract (Figs. 4(d) and 5).

SIMULATION

I

I

I

I

OF MANY-SPIN

I

I

I. 5

I

301

SPECTRA

I

I

1.0

I

I,

PPM

FIG. 3. 220-MHz spectrum of benzene-insoluble residue from extracted Hercules “Pyrofax” polypropylene. 10% w/v solution in o-dichlorobenzene at 145”. Internal reference, hexamethyldisiloxane.

BERNCULLI P, * 0.01

TRIALS

P,=OO5

FIG. 4. Polypropylene spectra, Model A, Bernoulli trials. (a) P, = 0.01, trial No. 53; (b) P, = 0.05, trial No. 15; (c)P, = 0.10, trial No. 16; (d) P, = 0.15, trial No. 17.

302

FERGUSON

I

I

I

400

300

200 HZ

CH~lmmmml

FIG. 5. 220-M& spectrum of benzenssoluble conditions as Fig. 2.

a. n= 1, MODEL

b. n=3.

extract of Hercules’ “Profax”

polypropylene,

same

B

MODELC

c. n=oD.MODEL

C

FIG. 6. Calculated polypropylene spectra, . . .mmmr.mmm.. ., P, = 0.05. (a) n = 1, trial No, 23, model B; (b) it - 3, trial No. 21, model C; (c) n = 00, trial No. 19, model C.

Nonrandom trials. The other proposed models all involve distributions of the type . ..mmmrpmm... instead of or in addition to random placements. Trials 18-23 (Table 2) and other similar trials tested a range of block distributions ranging from the

SIMULATION

OF MANY-SPIN

SPECTRA

303

Heatley et al. (7) isolated r-dyad (n = 1) case to the extreme Flory limit, n = co, with the assignments of Table 1. Model B. r-Dyads isolated. The n = I probabilities are experimentally indistinguishable from the Bernoulli (Model A) trials for P, G 0.02. As P, increases, the relationship mmr = 2 inrm and the absence of the rr triad produce clear differences in both the methylene and methyl regions; e.g., compare Figs. 4(b) and 6(a), for P, = 0.05.

+350

t250

t150

FIG. 7. Calculated polypropylene spectra. Flory rrr and mrm assignments. (a) 0.010, trial No. 21, Bernoulli model; (b) 0.011, trial No. 54, model D; (c) 0.040, trial No. 56, model D.

Model C. Flory rrr assignment. No satisfactory matches to Figs. 3 and 5 were obtained with trials based on the Flory rrr assignment (1.0686*) (n > 3). For n = 3 and P, G 0.02 the deviation from models A and B is perhaps within experimental error if the assignments of the mr and rr methyl doublets are reversed. Even with this unlikely order of methyl assignments, i.e., mr (0.7886*) < rr (0.8246*)
304

FERGUSON

triplet (Fig. 7(a)). Trial 54, P, = 0.011, fails because of an extra high field methyl peak at 160 Hz (Fig. 7(b)). Flory has at various times proposed that the isotactic polypropylenes have P, = 0.20-0.04. Trials 56, P, = 0.04 (Fig. 7(c)), and 58, P, = 0.10, deviate markedly from the observed spectra. Model E. mrm missing. Recognizing the failure of model D, Flory made a crucial additional assumption that the mrm methylene resonance would be broadened beyond detectability by conformational effects. In trials 55, 57, and 59 the mrm pattern was

I J ‘-c - MODEL E

--A t350

+250

t150

+350

t 250

+ 150

FIG. 8. Calculated polypropylene spectra, Flory model, mrm missing. (a) P, = 0.010, trial No. 53, Bernoulli model (conventional mrm assignment); (b) P, = 0.011, trial No. 55, model E; (c)P, = 0.04, trial No. 57, model E; (d) P, = 0.10, trial No. 59, model E.

Comparing Figs. 8(b), (c), (d) with Fig. 8(a) (the Bernoulli trial best fitting Fig. 3) shows that Model E clearly fails for P, 2 0.04. Syndiotacticpolypropylene. A series of Bernoulli trials with P, = 0.95-0.75, were run to refine earlier crude estimates of tacticity of the syndiotactic polymer (5). The spectrum (Fig. 9(b)) was most nearly approximated by P, = 0.85; the strongest methyl doublets were assigned SF,= 0.830 and S& = 0.841. The general appearance of the methylene regions was reproduced moderately well, but with differences indicating that Bernoullian statistics were not strictly applicable and/or that further refinement of the tetrad parameters would be needed. Subsequent to this work, Zambelli et al. have reported resolution of hexad effects in the methylene patterns of deuterated polypropylenes (II). This could well account for difficulties in fitting the spectra of highly syndiotactic polymers. omitted.

SIMULATION

Fro. 9. Calculated 0.75.

OF MANY-SPIN

and observed syndiotactic

SPECTRA

polypropylene

spectra. Bernoulli

305

trials. P, = 0.80,

CONCLUSIONS

A computer program such as NMRMRG is almost essential for testing even qualitative interpretations of complex polymer spectra. Successful application requires reasonably well determined parameters for the various subspectra, although some refinement of the parameters is possible during the fitting procedure. It is particularly important that any interpretation of the spectra should be based on a reasonable statistical model and tested against the appropriate probability sum rules and other applicable relationships (12). These conditions were readily satisfied by data available for polypropylenes. Either Model A or B gave acceptable and almost indistinguishable agreement with the spectra of the most isotactic polypropylenes. For the less stereoregular extracts, and for the syndiotactic polymers, Bernoulli trial statistics (Model A) gave the best fit. Further discussions of the conflicting interpretations of polypropylene spectra appear elsewhere (II). ACKNOWLEDGMENTS Professor C. W. Haigh provided copies of his computer programs LAME and LACX. R. T. Shortess wrote and tested the FORTRAN IV program for NMRMRG. F. W. Barney prepared the computer inputs and ran most of the trials. Their contributions are gratefully acknowledged.

306

FERGUSON

REFERENCES I. R. J. ABRAHAM, “The Analysis of High Resolution NMR Spectra,” p. 182, Elsevier Publishing Co., New York, 1971. 2. P. DIEHL, H. KELLERHALS, AND E. LUSTIG, “NMR Basic Principles and Progress” (P. Diehl, L. Fluck, and R. Kosfeld, Eds.), Vol. 6, Springer Verlag, New York/Berlin, 1972. 3. P. L. CORIO, “Structure of High Resolution NMR Spectra,” Academic Press, New York, 1966. 4. (a) C. W. HAIGH AND R. B. MALLON, J. Mol. Spectrosc. 29,478 (1969); (b) C. W. HA~GH, “Annual Review of NMR Spectroscopy” (E. F. Mooney, Ed.), Vol. 4, Academic Press, London, 1971. 5. R. C. FERGUSON, Macromolecules 4,324 (1971). 6. F. HEATLEY AND A. ZAMBELLI, Macromolecules 2,618 (1969). 7. F. HEATLEY, R. SALOVEY, AND F. A. BOVEY, Macromolecules 2,619 (1969). 8. P. J. FLORY, Macromolecules 3,613 (1970). 9. P. J. FLORY AND Y. FUJIWARA, Macromolecules 2,315 (1969). 10. P. J. FLORY AND J. D. BALDESCHWIELER, J. Amer. Chem. Sot. 88,2873 (1966). II. A. ZAMBELLI, L. ZETTA, C. SACCHI, AND C. WOLFSGRKJBER, Macromolecules 5,440 (1972). 12. H. L. FRISCH, C. L. MALLOWS, AND F. A. BOVEY, J. Chem. Phys. 45,1505 (1966).