Pseudorotation in heterocyclic five-membered rings: tetrahydrofuran and pyrrolidine

THEO CHEM Journal of Molecular Structure (Theochem) 369 (1996) 157-165

Pseudorotation in heterocyclic five-membered rings: tetrahydrofuran and pyrrolidine Seong Jun Han, Young Kee Kang* Department of Chemistry, Chungbuk National University, Cheongju, Chungbuk 361-763, South Korea

Received 25 March 1996; accepted 9 April 1996

Abstract Using the 6-31G ** basis set the HF-SCF and Moller-Plesset second-order (MP2) perturbation calculations have been carried out for tetrahydrofuran (THF) and pyrrolidine (PY) with the symmetries given by pseudorotation. On the whole, the MP2 calculations give better results on the puckered structures and energetics of both molecules, which are consistent with diffraction and spectroscopic results. From the MP2/6-31G** calculations, the twist conformation 4T3 is found to be the most stable one for THF, and the twist ‘Tr(ux) and the envelope ‘E(U) forms appear to be energetically identical and most feasible for PY. We investigate the correlation between the puckering amplitudes and the sum of deviations of endocyclic bond angles from the standard value. The better correlation may support that the revised pseudorotation model proposed here is more appropriate to describe the puckering of non-equilateral five-membered rings than earlier models. Keywords:

Ab initio calculation; Pseudorotation; Pyrrolidine; Ring puckering; Tetrahydrofuran

1. Introduction Tetrahydrofttran (THF) and pyrrolidine (PY) are the representatives of heterocyclic five-membered ring compounds, i.e. sugar and proline, which are known to play an important role as a fundamental structural unit of nucleic acids and proteins, respectively. Due to their importance, the conformational

properties of both molecules have been extensively studied by experimental and theoretical methods [l]. The conformations of saturated cyclic compounds are usually flexible along the pseudorotation path and take various conformations by the ring puckering. The conformational analysis of five-membered rings has been generally done by using the concept of * Corresponding author.

pseudorotation which describes the ring puckering by two parameters, i.e. the phase angle (I$) and puckering amplitude (q). For an equilateral cyclic ring, its pseudorotational motion can be well described by the phase angle with a fixed puckering amplitude. However, if a hetero atom is incorporated into the ring, its pseudorotational potential surface will be considerably dependent on both pseudorotational parameters. The relationship between the change in conformational properties of the ring and the electronic nature of hetero atoms has been investigated in some cases [2-51. It seems worthwhile to reinvestigate the structures of THF and PY by ab initio calculations with a large basis set in order to compare their conformational characteristics with each other. In the previous work [6], we proposed a pseudorotation function expressed in terms of the puckering

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SJ. Han, Y.K. KanglJournal of Molecular Structure (Theochem) 369 (1996) 157-165

angle Cyjand the phase angle C#J, and applied it to the conformational analysis of cyclopentane. The ring puckering of cyclopentane was found to proceed freely along the pseudorotation path with a fixed puckering amplitude. Differing from cyclopentane with five equivalent ring carbons, the pseudorotation of heterocyclic compounds encounters the shifts in atomic phase from the regular pentagon because of different endocyclic bond lengths. In the present work, we propose a revised pseudorotation function by incorporating a correction term in order to describe the ring puckering of THF and PY, and compare the results with those obtained by an earlier pseudorotation model [7,8] based on the z-displacement.

2. Pseudorotation model In order to describe the puckering of fivemembered rings, the pseudorotation model has been applied after the first proposal by Kilpatrick et al. [7]. They proposed that the conformational change of cyclopentane occurs along the pseudorotation path and defined the displacement Zj of the jth atom perpendicular to the mean plane of the ring by the formula: Zj=(2/5)"*q,COS[~+4nO’-1)/5]

j- 1, ....5

(1)

where qr means the puckering amplitude and #I the phase angle. Cremer and Pople improved this pseudorotation model by deriving mathematically the mean plane and extending to a general monocyclic puckered rings [2,8]. According to Eq. (l), for an equilateral fivemembered ring each atomic phase can be well expressed by 4r(j - 1)/5. On the other hand, for a non-equilateral ring there will be shifts of atomic phase from the values of a regular pentagon due to different endocyclic bond lengths and a movement of the origin defined by the geometrical center. Therefore, the pseudorotation function requires a correction term ascribed to these shifts in atomic phase. Diez and his co-workers [9-121 modified the pseudorotation function of Altona and Sundararingam (AS) [13] to describe the interrelated changes in endocyclic torsion angles by introducing the correction term Ej, i.e. the atomic phase shift. #j=Uj8*COS[P+Ej+

4?i+-1)/5]

j=l,...,S

(2)

where Uj is a parameter correlating qz of Eq. (1) with $, of the AS formalism [13], Cp, a maximum endocyclic torsion angle, and P the phase angle. Though Eq. (2) is valid for infinitesimal 9, values, it was shown that an empirical correction of the atomic phase led to better results than those obtained by Eq. (1) 1111. In the previous work [6], we developed a pseudorotation model by combining the expression of Eq. (1) and the puckering angle aj of Adams et al. [14] as follows: ~j'q~COS[~+4S~-1)/5]

j=l,...,5

(3)

where qti is the maximum puckering angle, i.e. the puckering amplitude. This model was proposed to analyze the puckering of the five-membered ring and to construct the ring geometry with specified pseudorotation parameters (4, qa). As seen in the earlier models, the atomic phase problem still remains in Eq. (3). Therefore, a correction to the pseudorotation needs to describe more accurately the puckering of a non-equilateral five-membered ring. The pseudorotation function proposed here is ~j=q,COSC~+Ej+4K~-1)/5]

j31(...(5

(4)

where Ejis the atomic phase shift for the jth ring atom. The expression of Eq. (4) can solve the shortcomings embedded in the previous model of Eq. (3) and be well applicable to both equilateral and non-equilateral five-membered rings. The additional parameter Ejcan be simply calculated from the geometrical center and x - y coordinates projected on the mean plane.

3. Calculations The pseudorotation potentials associated with the ring puckering of THF and PY were calculated by using the ab initio molecular orbital theory. With the 6-31** basis set [15], the Hartree-Fock (HF) and Moller-Plesset second-order (MP2) perturbation optimizations have been done for the structures of both molecules with the symmetries given by pseudorotation. The GAUSSIAN 92 package [16] was used for ab initio calculations, which was implemented on the Cray YMP C90 supercomputer of the System Engineering Research Institute (SERI) of Korea. Five-membered rings have two characteristic

1.59

S.J. Han, Y.K. KanglJournal of Molecular Structure (Theochem) 369 (1996) 157-165

(a)

from the conformational analysis by the pseudorotation function. We chose empirically the nearly planar conformation as a starting point to find the global energy minimum because the optimized geometry strongly depends on starting conformations. The program RING of Cremer [18] was used to calculate the puckering parameters for each optimized structure. For puckering amplitudes qZ and qa, Eq. (I), Eq. (3) and Eq. (4) were used as the pseudorotation functions.

(b)

Fig. 1. Atomic numbering and conformational notations (X = 0, N): (a) the envelope conformation ‘E; (b) the twist conformation “r,.

conformations, which are the envelope (E) and twist (T) forms (Fig. 1). These two conformations appear alternatively along the pseudorotation path, and the notation of each conformation follows the abbreviated nomenclature suggested in Ref. [13]. However, the superscript and subscript of each notation are switched from the left side to the right side and vice versa, respectively, for the more pictorial description of each conformation. THF can have three kinds of the envelope and twist forms, while PY can have six envelopes and five twists due to the different orientations of an imino hydrogen, i.e. equatorial and axial. Using the dummy atoms as suggested by Clark [17], we imposed the symmetrical constraint on each conformation of both molecules to keep its conformational properties given by pseudorotation. All independent variables, except for the dummy variables imposed by the geometry constraints, are allowed to vary during the geometry optimization. In addition, the full geometry optimizations from a planar conformation were performed on both molecules so as to be compared with the results obtained

Table 1 Puckering

6 (deg)

0 18 36 54 72 90 opt.c planar

parameters Conf.

‘E *TL 2J3 92

‘E 4T’ 4T’ C2”

4. Results and discussion 4.1. Conformational analysis The pseudorotational motions of THF and PY are different from that of cyclopentane, of which the conformational energy depends only upon the puckering amplitude but not upon the phase angle. The incorporation of a hetero atom into the ring results in the changes of puckering amplitudes along the pseudorotation path. Tables 1 and 3 list the puckering amplitudes qa and the conformational energies calculated along the pseudorotation phase angle for THF and PY, respectively, together with the maximum z-displacement qz obtained from the RING program [18]. In addition, the structural parameters of representative conformations of THF and PY calculated at the MP2/6-31G** level are shown in Tables 2 and 4, respectively.

and relative energies of THF obtained from HF/6-31G** 4. (deg)

and MP2/6-31G**

91 (A)

calculations AE (kcal mol-‘)

HF

MP2

HF

MP2

HF

MP2

10.9 10.9 10.7 10.5 10.5 10.5 10.5

12.2 12.2 12.0 11.6 11.5 11.4 11.4

0.354 0.356 0.358 0.361 0.364 0.366 0.366

0.398 0.400 0.400 0.397 0.395 0.395 0.395

0.0

0.0

0.000

0.000

0.428 0.402 0.327 0.180 0.057 0.000” 0.000” 3.410

0.394 0.334 0.223 0.111 0.033 O.OOOb O.OO@ 4.771

a,bZero of energies are -230.9887197 and -231.7345141 hartrees, respectively. ’ The fully optimized conformation from a nearly planar conformation without any constraints.

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SJ. Han, Y.K. KanglJournal

Table 2 Structural parameters

of THF calculated

Parameter

at MP2/6-31G**

1.435 1.524 1.092

91 (AS

level

‘E

J’

Bond length (A) c-o c-c C-Hd Bond angle (deg) c-o-c o-c-c c-c-c Torsion angle (deg) c5-Ol-cz-c3 C2-Ol-C5-C4 Ol-C2-C3-C4 Ol-c5-c4-c3 C2-C3-C4-C5

of Molecular Structure (Theochem) 369 (1996) 157-165

Planar

1.426 1.535 1.093

109.3 106.1 101.1

104.0 105.3 103.2

-12.9 -12.9 33.0 33.0 -39.2 0.395

-42.6 42.6 25.4 -25.4 0.0 0.398

EDa

1.427 1.537 1.091

X-ray b

1.428 1.536 1.115

111.8 108.6 105.6 0.0 0.0 0.0 0.0 0.0 0.000

ND”

1.429 1.511 1.050

1.438 1.516 1.097”

110.5 106.5 101.8

108.2 107.4 102.0

109.9 106.4 102.6

-11.6 -11.6 29.6 29.6 -35.0 0.38

-11.5 -11.5 29.7 29.7 -34.9 0.348

-11.3 -11.3 28.8 28.8 -34.5 0.343

’ Electron diffraction data, taken from Ref. [22]. b X-ray diffraction data at -17O”C, taken from Ref. [23]. ‘Neutron powder diffraction data at 5 K, taken from Ref. [24]. d Averaged value. ’ Bond length for C-D. f Puckering amplitude defined in Eq. (1).

4.1.1. Tetrahydrofuran

If the conformational change of the ring compound occurs on the one-dimensional potential surface along the pseudorotation path, the pseudorotation barrier Table 3 Puckering

(b(de&

parameters

and relative energies of PY obtained from HF/6-31G**

Conf.”

‘E(Q.4

J’W

zW4

‘T~(4 ‘E 4T’ 4E 5T4(es) WY) ,fkd &@q) &(eq), C,

J’(au)’

10.3 10.4 10.4 10.5 10.6 11.0 11.3 11.6 11.9 12.3 12.5 12.5 0.0

and MP2/6-31G**

calculations AE (kcal mol-‘)

qr (A)

qu (deg) HF

0 18 36 54 72 90 108 126 144 162 180 opt.d

can be directly defined by the energy difference between maximum and minimum. The barriers of THF obtained from the HF/6-31** and MP2/631G** calculations are 0.43 and 0.39 kcal mol-‘,

MP2 10.9 11.0 11.2 11.2 11.4 11.7 12.1 12.5 13.0 13.5 13.7 11.0 0.0

HF

MP2

HF

MP2

0.347 0.350 0.356 0.363 0.371 0.382 0.391 0.396 0.402 0.409 0.413 0.413 0.000

0.370 0.373 0.381 0.387 0.394 0.405 0.418 0.427 0.438 0.448 0.452 0.374 0.000

0.523 0.544 0.636 0.776 0.827 0.739 0.552 0.398 0.254 0.093 o.OOoc o.OOoc 4.809

0.009 O.OOOb 0.068 0.335 0.617 0.798 0.781 0.658 0.473 0.244 0.118 o.OOob 5.986

a The notations ux and eq correspond to the axial and equatorial imino hydrogen of PY, respectively. eq for the conformations ‘E, 4T3 and 4E. ‘*‘Zero of energies are -211.9017224 and -211.1610591 hartrees, respectively. d See footnote c of Table 1. e The first and second notations correspond to those of the HF and MP2 calculations, respectively.

It is ambigous to distinguish

either ax or

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S.J. Han, Y.K. KangJJournal of Molecular Structure (Theochem) 369 (1996) 157-165

Table 4 Structural

parameters

Parameter

of PY calculated rT’(t=)

at MP2/631G**

level

’E@x)

‘lT’

Planar

EDa

Bond length (A) Nl-C2 Nl-C5 C2-C3 c4-c5 c3-c4 C-Hb N-H Bond angle (de&

1.471 1.468 1.552 1.537 1.544 1.091 1.018

1.468 1.468 1.544 1.544 1.546 1.090 1.018

1.478 1.480 1.528 1.531 1.526 1.092 1.012

C2-Nl-C5 Nl-C2-C3 Nl-C5-C4 C2-C3-C4 c3-c4-c5 Torsion angle (deg)

103.0 107.7 106.1 104.2 103.5

102.7 107.0 107.0 104.0 104.0

108.1 106.0 105.1 101.3 102.5

C5-Nl-C2-C3 C2-Nl-C5-C4 Nl-C2-C3-C4 Nl-C5-C4-C3 C2-C3-C4-C5 91 (A)c

33.1 -40.4 -13.3 31.9 -10.8 0.373

-38.1 38.1 23.4 -23.4 0.0 0.370

-13.4 -12.7 33.8 33.7 -40.8 0.405

1.472 1.472 1.543 1.543 1.540 1.091 1.011 110.7 108.1 108.1 106.6 106.6 0.0 0.0 0.0 0.0 0.0 0.000

1.469 1.469 1.543 1.543 1.543 1.090 1.020 105.2 104.6 104.6 104.9 104.9

0.38

a Electron diffraction data, taken from Ref. [4]. Torsion angles are not shown explicitly in Ref. [4]. Instead, they reported the angle o to be 39.0” between the C2-Nl-C3 and C2-C3-C4-C5 planes. b Averaged value. ’ Puckering amplitude defined in Eq. (1).

respectively (Table 1). Both calculations give very similar values of about 0.4 kcal mol-‘, which are reasonably consistent with experimental values. From a far-infrared measurement this barrier is estimated to be less than 0.5 kcal mol-’ in the gas phase [19] and from a microwave experiment it is found to be 0.2 kcal mol-’ at dry-ice temperature [20]. For each stationary conformation constrained by the phase angle 4 of the pseudorotation, the electron correlation slightly lowers its conformational energy along the pseudorotation path. However, for the planar conformation this effect is more notable due to the repulsions between the lone electron pairs of oxygen and the adjacent hydrogens bonded to ring carbons. As a result, the barrier to planar conformation at the MP2/631G** level is calculated to be 4.8 kcal mol-‘, which is 1.4 kcal mol-’ higher than that at the HF/6-31G** level. The HF/6-31G** and MP2/631G** calculations seem to some extent to underestimate and overestimate the barrier to planar conformation as compared with observed values, respectively,

since the microwave [20] and far-infrared [21] experiments predicted the barrier to be 3.5 and 3.9 + 0.2 kcal mol-‘, respectively. The HF and MP2 calculations with the 6-31G** basis set predict the twist form (4T3) as the most stable conformation, which has a C2 symmetry. The full geometry optimization without any constraints gives the same results as those of the conformational analysis by using the pseudorotation model. As found by Cadioli et al. [5], the geometrical parameters calculated at the MP2 level are closer to the experimental values than those at the HF level. The structural parameters of the 4T3, ‘E, and planar conformations of THF optimized at the MP2/631G** level are shown in Table 2. The values for the most preferred conformation .+T3 are consistent with those obtained from electron [22], X-ray [23], and neutron powder [24] diffractions. In addition, the puckering amplitudes of the lowest energy conformations are calculated to be 0.36 t 0.01 and 0.40 t 0.01 A at the HF and MP2 levels, respectively,

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of Moiecuiar Structure (Theochem) 369 (1996) 157-165

which0 are in good agreement with the value 0.38 2 0.02 A of an electron diffraction experiment [22]. 4.1.2. Pyrrolidine As shown in Table 3, the 6-31G** calculations for PY with and without electron correlations yield different results from each other. The HF/6-31G** results show that the ,E(eq) conformer is the most stable one and that the conformational energy difference between the ‘E(ux) and rE(eq) conformers is 0.5 kcal mol-‘. On the other hand, the electron correlation lowers the energies of the axial ‘E(U), 2T’(~), and zE(ax) conformers rather than the rE(eq) conformer. The ‘E(m) and 2T1(ax) conformers are energetically identical within 0.01 kcal mol-’ and the energy difference between the ‘E(ux) and rE(eq) conformers is only 0.1 kcal mol-‘. In a microwave study [25] Caminati et al, showed that the calculated structural parameters of PY are consistent with experimental values only for the Blax and T3-ax conformers, which correspond to the ‘E(a) and zT1(~) conformers, respectively. In addition, they suggested that the Bl-ux is the most likely conformation of the observed species and that the rE(eq) conformer may be not probable because its rotational spectrum is very weak. The present results of MP2 calculations are consistent with this microwave experiment. From IR and Raman spectroscopic studies [26], Krueger and Jan estimated the AH value for the lone pair axial-equatorial equilibrium of PY to be 0.2 kcal mol-’ in dilute Ccl4 solution, which is similar to our calculated value of 0.1 kcal mol-’ at the MP2/6-31G ** level. Though using a higher basis set 6-31G**, the HF energy for each conformation of PY is more deviated from the experimental value than the MP2 energy. It means that the electron correlations are of consequence to solve conformational problems which arise from the orientation of lone pair orbital of a nitrogen atom. From the MP2/6-31G** calculations, the pseudorotational barrier is estimated to be 0.8 kcal mol-’ and the barrier to the planar conformation is found to be about 6 kcal mol-‘. The present calculated barrier for pseudorotation is reasonably consistent with experimental values 0.3-1.3 kcal mol-’ derived from thermodynamic studies of PY [27,28]. The first two lowest energy conformations ‘E(U) and IT’ are puckered with the amplitude qa of 11.0” (i.e. qz = 0.37 A), which

agrees well with the value qr = 0.38 A obtained from an electron diffraction study [4]. The structural parameters of the ZT1(~), ‘E(a), qT3, and planar conformations of PY optimized at the MP2/6-31G** level are listed in Table 4. The values for the most preferred conformation ‘E(a) are in good agreement with those obtained from an electron diffraction [4]. 4.2. Comparison of puckering amplitudes In the previous work [6], we reported that the pseudorotational motion in cyclopentane proceeds freely within a narrow range of puckering amplitudes. As mentioned above, if a hetero atom having one or two lone electron pair(s) is incorporated into the fivemembered ring, it no longer makes the puckering amplitude invariant on the pseudorotation path. This seems to be caused by the repulsions between lone electron pair(s) of the hetero atom and the adjacent hydrogens bonded to ring carbons and the changes in geometrical parameters due to the hetero atom. We list two types of the puckering amplitude based on different geometrical parameters in Tables 1 and 3. It is expected that the amplitudes qa and qz estimated for a series of conformations along the pseudorotation path have a linear correlation as found in cyclopentane [6]. In Table 1, however, these two amplitudes for THF show the different aspects from each other. In particular, the HF/6-31G** calculations give the reverse ordering of two puckering amplitudes on going from 0” to 90” of the phase angle. To analyze this problem, we investigated the correlation between the puckering amplitudes and the sum of deviations of endocyclic bond angles from the standard value. Dunitz [29] proposed that any infinitesimal deviation from planarity is associated with a decrease in the average bond angle from the standard angle (i.e. 108” for an equilateral five-membered ring), and derived the linear relationship as follows:

where 6j is the decease in the endocyclic bond angle at the jth atom resulting from the ring puckering and k is a proportional constant. Similar relationships were derived by Dfez et al. [9,12] and also empirically demonstrated by us in the previous work 161. Therefore, the sum of 6j’s can be used as an alternative parameter to express the degree of puckering. It is

ofMolecularStructure

S.J. Han, Y.K. KanglJournal

163

(Theochem) 369 (1996) 157-165

(4 20

I9

,’

I8

I9

:)

\)

A’ :I

18

/’

ca W

/

I7

6 W %

I7

/ /

0

16

I5

:I

16

I

I

I

0.156

0.158

0.160

-1

15 :

1

1

I

130

I40

150

4,’

9,’

Fig. 2. The correlation diagram of (a) q: and (b) q2with 16, for THF. Units of qzare in i and those of and filled triangles correspond to qa’s expressed in Eq. (3) and Eq. (4), respectively.

worthwhile to correlate two types of the puckering amplitude with the sum of 6,‘s. We use the puckering parameters obtained from the MP2/6-3 lG* * calculations for the correlation, because they give better results than the HF/6-31G** calculations. In Fig. 2

qaand d, in degrees. In (b), open circles

and Fig. 3, the sums of 6,‘s are plotted against the squares of puckering amplitudes qz and qa for THF and PY, respectively. The puckering parameter qr shows the values 0.6724 and 0.9594 for correlation coefficients, whereas qa has the values 0.9999 and

(4

@> 24

22-

I

20 -

i

I 18 ,

I6 -

I A’

/

,

I

,’

d ,..;

,

‘44

0.12

0.14

0.16

‘44 0.18

0.20

9.2 Fig. 3. The correlation

0.22

9,’ diagram of (a)

q: and (b) q’, with 16, for PY. See the legends of Fig. 2

/

/:1

164

&I. Han, Y.K. KanglJournal of Molecular Structure (Theochetn) 369 (1996) 157-165

0.9987 (the corresponding slopes are 0.1461 and

0.1190, represented by open circles in Fig. 2(b) and Fig. 3(b)) for THF and PY, respectively. As a result, a good correlation of qa supports that the revised pseudorotation function of Eq. (4) expressed by the puckering angle aj is more appropriate to describe the puckering of non-equilateral five-membered rings. Furthermore, the puckering parameter qa of Eq. (4) shows a better correlation than qm of Eq. (3), for which the coefficients are 0.9931 and 0.9865 for THF and PY (represented by filled triangles in Fig. 2(a) and Fig. 3(a)), respectively. Thus, the incorporation of a correction term into the pseudorotation function of Eq. (3) is of consequence in analyzing nonequilateral five-membered rings and gives improved results.

Acknowledgements We thank the System Engineering Research Institute (SERI), Korea for using the Cray YMP C90 supercomputer. This work is partially supported by MOST (No. N81540).

References [l] [Z] [3] [4] [5] [6]

5. Conclusions The revised pseudorotation function is proposed so

as to incorporate the effects of hetero atoms on the ring structures. The MP2/6-31G** calculations give better results on the puckered structures and energetics for both THF and PY molecules than the HF/6-31G** calculations. This indicates the important role of electron correlations in describing the repulsions between the lone electron pair(s) of the hetero atom and the adjacent hydrogens bonded to ring carbons. From the MP2 calculations, the twist conformation 4T3 is found to be the most stable one for THF, and the twist ‘Tz(ax) and the envelope ‘E(a) forms appear to be energetically identical and most feasible for PY. The barriers to pseudorotation are estimated to be 0.4 and 0.8 kcal mol-’ and the barrier to planar conformation to be about 5 and 6 kcal mol-’ for THF an PY, respectively. These results on structures and energetics are consistent with diffraction and spectroscopic experiments. Furthermore, the better correlation between the puckering amplitude qa and the sum of deviations of endocyclic bond angles from the standard value may support that the revised pseudorotation model proposed here is more appropriate to describe the puckering of nonequilateral five-membered rings than earlier models. The application of the present pseudorotation function to the conformational analysis of proline and prolinecontaining peptides is now being carried out.

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