MAGNETIC RESONANCE IN CHEMISTRY, VOL. 33, 701-704 (1995)

Ab Initio 13C Nuclear Shielding Calculations for Some Solid Amino Acids using the GIAO Procedure

Yong He, Donghdi Wu, Lianfang Sben* and Baiwen Li Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics, Chinese Academy of Sciences, Wuhan 430071, China

Graham A. Webb Department of Chemistry, University of Surrey, Guildford, Surrey GU2 SXH, UK

The results of ab initio GIAO-CHF ''C nuclear shielding calculations for some solid amino acids, performed with the 6-311G** and a locally dense basis set are reported. Comparison of the present calculation with the observed shieldings shows an RMS error of 6.6 ppm. Shieldings of the carbon nuclei which are multiply bonded are strongly influenced by electron correlation effects. Experimental molecular geometries used in these calculations were taken from crystal structures of amino acids.

KEY WORDS ab initio GIAO-CHF; 13C nuclear shielding; amino acids

INTRODUCTION

A comparison of experimental and theoretical NMR spectra can be very useful in making correct assign- ments and understanding the basic chemical shift- molecular structure relationship.'*2 Amino acids have proved to be unusually attractive compounds for use by research groups exploring extensions of NMR spectros- copy into non-routine structural techniques. Recently, crystal powder samples of some amino acids were studied, and using the dipolar dephasing technique a proposal was made for separating the SSB spectra of the non-protonated carbons3 from those of the proto- nated carbons. Hence this technique assists the 13C assignments of these molecules. The solid-state struc- tures may reflect both intra- and inter-molecular inter- actions, which differ from those found in solutions, but which will influence the 13C NMR spectra.

It is well known that NMR chemical shifts are very sensitive to the secondary and tertiary structures of pro- t e i n ~ . ~ - ~ Conformation,' bond length, bond angle,8 torsion angle,' substituent effects and other structural parameter dependences of NMR chemical shift tensor component values have been extensively studied. Differ- ences in chemical shift tensor components are also related to rotational motion." Hence structure opti- mization is a crucial process for NMR chemical shield- ing calculations.'OJ1

There are some recent reviews and monograph on ab initio calculations of NMR shielding.' 2-14 Am ong the ab initio methods commonly used for chemical shielding tensor calculations, IGLO (individual gauge for local- ized orbitals)' '-" and GIAO (gauge invariant atomic

* Author to whom correspondence should be addressed.

orbitals) are most popularly applied. For polar com- pounds, modification of the GIAO program with charge-field perturbation leads to more accurate results. ' *

Calculations of nuclear shielding tensors have been reported at various theoretical levels. l s 2 Semi-empirical methods provide a correct qualitative understanding but are not usually quantitatively accurate. Almost all ab initio results are reported at the SCF level, and are thus based on the coupled Hartree-Fock perturbation theory (CHF)." An efficient means of using the GIAO" method for nuclear shielding calculations of the CHF level has now been reported.'l It has also been shown that the results of 13C shielding calcu- lations using a locally dense basis set can reproduce the observed solution NMR data with the desired accu- racy.22

In this paper we discuss the results of some ab initio 13C shielding calculations for 14 solid amino acids using the GIAO method and the 6-311G** and a locally dense basis set.22 The molecular geometries of solid amino acids were taken from the experimental data obtained using x-ray and neutron diffraction method^.^^-^^

CALCULATION

In general, accurate ab initio nuclear shielding calcu- lations reveal the requirement of including the effects of electron correlation.' However, such effects are most pronounced when nuclei with lone pair electrons and multiple bonds are concerned, e.g. N, 0 or P. Our present investigation involved a study of 13C nuclei in amino acids. As shown in Table 1, the carbon atoms are

CCC 0749-1 58 1/95/090701-O4 0 1995 by John Wiley & Sons, Ltd.

Received 9 September 1994 Accepted (revised) 14 April 1995

702 Y. HE ET AL.

singly bonded and the calculations of their chemical shifts are unlikely to be strongly influenced by electron correlation effect^.^' However, the ,C-0 carbon nuclei are multiply bonded to oxygen, which has lone pair electrons, and thus nuclear shielding at carbon atoms may be more susceptible to electron correlation effectsi4

We used the GIAO approach without including elec- tron correlation effect.21 The basis sets are the 6- 3 1 lG**, which includes polarization functions (p orbital for the hydrogen atom and d orbital for other atoms,38 and a locally dense basis set with a large number of atomic basis functions which are placed on the reson- ating atom (R) of interest and a smaller set of atomic functions used on other heavy atoms (X) in the mol- ecule.22 Because of limitations of disk capacity, we chose the 6-311G** basis set for Gly, Ala, Ser and Asp, the locally dense basis set R: 6-31 lG**/X : 6-311G/ H:311G for Val, Thr, Glu, His, Asn, Gln, Cys and Pro and the locally dense basis set R : 6-31 lG**/X: 6-31G/ H : 31G for Lys and Arg.

We also found that the results of the nuclear shielding calculations are sensitive to the molecular geometry. For example, the shielding values obtained are different depending on the choice of DL-serine or L-serine because of small differences in their geometric param- eters in the solid state. In addition, the calculated

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shielding results, using the molecular geometries of solid amino acids taken from neutral diffraction, are in better agreement with the experimental shieldings than those obtained from x-ray crystal structures of amino acids. Shielding calculations performed using experi- mental geometries provide the best agreement with the experimental results3 for single-crystal glycine ( ~ i ~ ) , ~ ~ alanine (Ala),24 valine (Val),” serine (Ser),26 threonine (Thr),” asparatic acid (Asp),28 glutamic acid ( G ~ u ) , ~ ~ histidine (His),30 lysine (LYs),~’ arginine (Arg),” aspara- gine glutamine (Gln),34 cysteine (CYS)~’ and 4- hydroxy-L-proline (Pro).36

These calculations were performed on an Indigo/ Entry work-station at the Wuhan Institute of Physics.

RESULTS AND DISCUSSION

Calculated and experimental isotropic chemical shifts of some solid amino acids are given in Table 1. The chemical shifts, 6, with respect to a given standard are given by

= OStd - Ox (1) In general, the nuclear shielding o is an unsymmetric second-rank tensor, i.e. aij # oji . The nuclear shielding

Table 1. Calculated and observed I3C chemical shifts of some amino acidsP

Carbon Amino acid ritea

a-Gly CO c,

L-Ala CO c, c,

L-Val CO c, c, CY c,

DL-Ser

L-Ser

L-Thr

DL-ASP

L-Glu

Semi-empirical

4.‘ 147.8 60.3

145.7 61.2 55.7

141.6 59.5 58.9 52.2 51.4

143.4 61.7 47.7

131.3 60.6 50.5

125.6 63.3 53.7 55.6

136.4 57.7 56.0

125.2

125.6 56.8 57.1 59.4

127.1

Calculated chemical shift (ppm)

Ab initio

6acd

173.6 43.1

176.1 51.4 18.0

178.7 58.6 31.9 19.0 11.1

175.5 51.8 45.3

172.0 50.6 53.6

190.6 60.6 64.0 23.7

175.3 50.3 21.7

184.8

179.6 56.2 30.8 28.8

181.7

4 I d

283.3 67.0

280.0 71.7 35.2

282.3 76.1 45.7 33.8 20.4

284.4 74.9 69.2

277.9 71.8 75.4

298.1 77.0 81.5 49.6

280.6 80.1 41.9

296.1

287.4 67.4 44.0 40.1

297.3

6zzd

128.7 45.8

140.7 58.8 20.5

149.3 60.2 28.4 23.0 16.7

133.3 52.2 52.0

130.4 53.0 57.2

167.6 54.7 68.1 16.5

136.1 54.7 27.7

161.9

144.2 61.6 33.3 33.4

150.1

Ld 108.7 16.5

107.6 23.6 -1.8

104.3 39.5 21.6 0.2

-3.8

108.8 28.3 14.8

107.6 26.9 28.2

106.1 50.1 42.3 4.9

109.1 16.0 -4.5 96.4

107.2 39.6 15.2 12.9 97.6

6;

176.2 43.5

176.8 50.9 19.8

175.9 61.5 30.7 21.5 19.2

175.1 55.6 62.9

175.1 55.6 62.9

172.1 61.2 67.0 20.5

176.0 53.8 37.7

174.7

178.0 54.6 25.6 27.9

179.9

Experimental chemical rhih (ppm)

4 1 a

246 61

239 63 31

244 72 42 34 30

238 69 87

238 69 87

247 72 89 31

247 68 55

250‘

237 71 36 41

254

4 z e

179 46

1 84 56 19

176 62 29 25 25

175 59 66

175 59 66

167 63 72 26

176 56 38

170

195 56 36 31

180

4 3 “

106 24

1 06 30 7

1 08 51 21 6 3

113 39 35

113 39 35

100 48 40 4

105 38 20

104

103 38 4

11 1 06

4B I N I T I O CALCULATIONS OF I3C NMR SHIELDING IN AMINO ACIDS 703

Table 1.-Continued

Calculated chemical shift (ppm)

Carbon Amino acid siteb

L- Lys

L-Arg

L-Asn

L-Gln

L- cys

L- Pro

RMS error

Semi-empirical

6scc

122.9 58.2 56.4

11 5.9 11 2.1 125.6

131.5 60.4 54.8 53.1 54.1 50.8

133.1 55.0 53.2 51.5 47.5

109.2

125.3 61.6 58.1

122.2

1 15.0 61.3 54.5 56.8

126.3

124.4 61.6 58.9

122.5 58.3 54.4 52.2 52.4

30.6

Ld 177.8 54.9 34.0

148.5 117.4 149.8

174.6 53.5 30.7 23.0 28.2 43.1

180.1 51 .O 26.1 16.0 38.5

163.0

175.0 51.7 32.4

180.6

157.9 57.5 27.2 26.1

178.2

174.5 58.3 31.3

173.2 57.5 33.7 67.7 51.6

6.6

6 , I d

280.1 73.6 45.6

239.6 209.6 237.6

282.1 71.9 44.4 35.1 49.2 69.9

271.1 64.7 41.1 33.4 64.8

230.6

283.9 74.4 46.7

286.6

261.6 79.5 40.2 44.1

278.9

281.4 82.6 40.7

273.5 100.3 57.3 84.3 83.8

Ab initio Experimental chemical shiff (ppm)

622d

145.5 52.5 38.1

140.3 95.3

157.1

131.8 57.0 33.9 24.5 27.4 42.9

168.4 58.3 28.1 16.7 45.6

193.7

132.1 55.3 39.8

173.2

109.5 59.5 30.1 30.1

175.5

145.2 51 .O 32.4

141.9 58.0 34.4 68.4 39.9

107.7 38.5 18.3 65.5 47.3 54.7

109.9 31.5 13.9 9.5 8.1

16.7

100.7 30.0 9.1

-2.0 5.2

64.5

109.0 25.3 10.8 81.9

102.5 33.5 11.4 4.2

80.2

96.9 41.5 20.7

104.2 14.2 9.4

50.3 31.2

4‘ 172.8 54.3 26.8

136.1 119.2 128.1

176.2 55.0 35.6 25.8 29.0 41.7

176.0 56.2 28.7 25.7 43.1

157.3

175.7 51 .O 34.6

173.6

177.3 53.8 26.1 29.1

173.6

175.1 53.7 35.4

177.4 61.3 30.2 25.9 48.5

4,* 235 70 38

190 179 203

243 73 58 47 48 67

239 76 48 44 72

222

244 71 49

243

247 70 36 46

244

241 66 47

245 79 49 44 83

622.

168 57 26

164 126 128

180 55 35 31 33 50

179 60 32 33 45

182

1 84 51 42

174

197 59 36 34

172

175 58 38

180 64 31 23 41

633.

116 37 16 54 52 54

107 36 14 -1

6 10

110 33 6 0

13 68

100 31 13

1 04

88 33 7 8

105

109 37 22

107 42 11 11 23

a Chemical shifts have all been converted to the TMS scale. bSchematic representation of amino acids NH,RCOOH, where Co is the ‘C-0 carbon and R contains the chain carbons C,, Ca, C,, C, and C.. /

c INDO/S-SOS calculated results in this work. *Ab initio GIAO-CHF calculated results in this work.

‘There is an error in Ref. 3. gMolecular structure of 4-hydroxy-~-proline is used in calculation, whereas the 13C chemical shifts of L-proline were observed in Ref. 3. They are different for the case of Cy in both molecules and therefore the chemical shift of C, in L-Pro is not included in the RMS error estimation.

Experimental data taken from Ref. 3.

is produced by the influence on the total electronic energy, E, of a molecule due to the nuclear magnetic moment p and the applied static magnetic field B. Thus the shielding tensor components can be defined by

The independent principal components of 0 in the prin- cipal axis system can be converted into chemical shifts according to Eqn (1). Hence there are three principal components, 6,,, hZ2 and 833, with conventionally

> bz2 > Sj33, the average of these three components is the isotropic chemical shift a,, , where

(3)

The values of al l , and a,,, calculated from the ab initio GIAO-CHF method using the 6-311G** and a locally dense set, are essentially in agreement with those obtained from the experimental spectra for some solid amino acids, as shown in Table 1.

In this work, the standard as,,, of the 13C chemical shifts is the shielding of TMS. Since the 13C chemical

704 Y. HE ET AL.

shift of CH, is -2.3 ppm39 and the experimental absol- ute 13C shielding of CH, is 197.35 ppm?' the absolute 13C shielding of TMS is 195.05 ppm according to Eqn

In Table 1, the chemical shifts 6, represent the observed results from solid ~amples ,~ 6,, represent the chemical shifts from semi-empirical calculations obtained using the INDO/S-SOS method' and 6,, rep- resent the chemical shifts from the ab initio calculations obtained using the GIAO-CHF procedure. Comparison of the various results in Table 1 shows that there is a large difference between the 13C chemical shifts calcu- lated by the semi-empirical method and those from the experimental data, but a smaller difference between the chemical shifts given by the ab initio GIAO-CHF calcu- lations and those of the experimental data. Compared with the experimental results, the chemical shifts calcu- lated by the semi-empirical INDO/S-SOS method show a root-mean-square (RMS) error of 30.6 ppm for the 13C nuclei given in Table 1. There is an RMS error of 6.6 ppm for the corresponding comparison of the chemical shifts calculated by the ab initio GIAO-CHF method using the 6-311G** and a locally dense basis set.

Hence the ab initio shielding results show a much better agreement with the experimental 13C shieldings than do those from the semi-empirical procedure. As shown in Table 1, in some cases the INDO/S-SOS

(1).

results do not predict the observed relative order of the 13C shielding in a given molecule, e.g. L-valine. Hence semi-empirical 13C shielding calculations cannot be recommended for amino acids.

Turning to the ab initio 13C shielding results, a com- parison of the calculated and observed shieldings for the >C= groups shows an RMS error of 8.3 ppm, whereas for the carbons which are singly bonded the RMS error is only 5.5 ppm. The RMS error of 72 principal com- ponents of 24 carbons for the ,C= groups is 31.3 ppm, whereas the RMS error of 117 principal com- ponents of 39 carbons which are singly bonded is only 7.8 ppm. This demonstrates the importance of including electron correlation effects in the calculation of the 13C shieldings of the ,C= groups. It seems that the influ- ence of the electron correlation on the principal com- ponents of the nuclear shielding tensor is more obvious than that on the average of the three components, naV. In general, the GIAO ab initio 13C shielding data reported here are sufficiently accurate for use in assign- ing the ' 3C NMR spectra of solid amino acids.

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Acknowledgements

Th is project was supported by NSFC (National Natural Science Foundation of China). We thank Professor J. Hinton for a copy of the GIAO shielding program.

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