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Condensed matter effects on the structure of crystalline glucose
29 August 1997
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 275 (1997) 409-413
Condensed matter effects on the structure of crystalline glucose C. Molteni, M. Parrinello Max Planck lnstitut fiir Festkgrperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany Received 12 May 1997; in final form 12 June 1997
Abstract By means of ab initio simulations based on the Car-Parrinello method, we have calculated the crystalline structures of a-D-glucose, a-D-glucose monohydrate and [3-D-glucose. The good agreement with the available experimental data gives us confidence in the applicability of the method to carbohydrates and opens the path towards the investigation of more complex problems, where a quantum mechanical description is essential. Condensed matter effects are discussed by comparing the structures of the glucose molecule in the crystalline and gas phases. © 1997 Published by Elsevier Science B.V.
The importance of carbohydrates in biochemistry is universally known: they play an essential role in processes such as energy storage, structural support, molecular recognition and water control in cold and drought-resistant organisms. Nevertheless, even apparently simple problems, like the behaviour of glucose in water solution, are still far from being properly understood [1]. This is mainly due to the lack of theoretical techniques able to describe in an accurate and reliable way both the sugar solute and the water solvent. However, recent calculations [2] have demonstrated that an excellent description of liquid water can be obtained from density functional theory simulations based on the Car-Parrinello method [3]. In this Letter we investigate the reliability and accuracy of such a method when applied to glucose crystalline structures, as a prelude to a more complex study of glucose-water solutions. Since the crystalline structures are known from experiment [4-8], they are a crucial test for our technique. We have also performed structural calculations for selected glucose molecules in the gas phase, with the aim of investigating the influence of the different
environments which the glucose molecule experiences in crystals and vacuum. A distinct situation occurs in solution, where glucose is surrounded by water molecules able to create a dynamic hydrogen bond network. The glucose molecule, with the conventional numbering of the heavy atoms, is shown in Fig. 1. Its main structure is a puckered six-membered ring, in the chair configuration 4C 1, composed of five carbon atoms (C 1, C 2, C 3, C 4 and C 5) and one oxygen ( 0 5) and held together by single bonds. A methyl alcohol group CH2OH is attached to one of the carbons next to the ring oxygen, while every other carbon of the ring carries both a hydroxyl group and a hydrogen atom. The hydroxyl group (-O~H), attached to the carbon next to the ring oxygen which does not carry the methyl alcohol group (C l), can be either in an axial or equatorial position with respect to the ring, giving rise to two possible anomers, called a and 13 respectively. Experimental crystalline structures are available for aD-glucose (neutron diffraction data) [4,5], a-D-glucose monohydrate [6,7] and 13-D-glucose [8] (X-ray
0009-2614/97/$17.00 © 1997 Published by ELsevier Science B.V. All rights reserved. PH S 0 0 0 9 - 2 6 1 4 ( 9 7 ) 0 0 7 0 1 -X
410
C. Molteni, M. Parrinello / Chemical Physics Letters 275 (1997) 409-413
06
Fig. 1. The glucose molecule with conventional numbering of the atoms.
techniques). It is known from experiment [9] that the ratio of the axial e~ anomer to the equatorial 13 anomer in aqueous solution is 3 6 / 6 4 ; what determines this ratio is still unclear. Both the methyl alcohol and the hydroxyl groups can assume different orientations, giving rise to a great number of conformers. In particular, there are three possible orientations for the methyl alcohol group associated with the C 5 - C 6 internal rotation. They are characterized by the dihedral angle 05 C5-C6-O6, which can be gauche clockwise ( = 60 °, G+), anti ( = 180 °, T), or gauche counterclockwise ( = 60 °, G - ) . In the crystalline structures, the G + rotamer was found for e~-D-glucose, while the G rotamer was found for both c~-D-glucose monohydrate and 13-D-glucose. According to N M R results [10], in aqueous solution the G - and G + rotamers are almost equally populated, while the population of the T rotamer is negligible. Starting from the experimental crystallographic data, we have performed Car-Parrinello molecular dynamics simulations [3] in order to determine, through a quenching procedure, the theoretical minimum energy structures for the three experimentally known glucose crystals. In the following, we will call e~-D-glucose CRy, a-D-glucose monohydrate CR~h and 13-D-glucose CRy. The simulations have been performed within density functional theory, in the generalized gradient approximation: the BLYP (Becke, Lee, Yang and Parr) gradient corrected density functional has been used [11,12]. The interaction between valence electrons and ionic cores is described by Troullier-Martins norm-conserving pseudopotentials [13], with an energy cutoff of 70 Ry. The BLYP functional has proved to be suitable for
describing liquid water [2] and has therefore been chosen in the perspective of future glucose-water solution studies. The time step for the molecular dynamics was 3 au and the electronic mass was set to 200 au. The maximum forces on the atoms at the end of the simulations were about 10 3 au. Both CR~ and CR~ crystallize in the P2~2~2~ space group, with an orthorhombic cell containing four molecules. The exoperimental lattice constants are: a=10.36-!-_0.02 A, b = 1 4 . 8 4 + 0 . 0 2 A and c = 4.97 + 0.002 ,~ for CR~ [4]; and a = 9.205 + 0.004 A, b = 1 2 . 6 4 0 _ 0 . 0 0 5 A and c = 6 . 6 5 4 _ 0.003 ~, for CRI3 [8]. CR~h crystallizes in the space group P21: the cell is monoclinic with lattice constants a = 8.803 + 0.001 ~,, b = 5.085 __+0.001 A, c = 9.708 _ 0.002 A and /3 = 97.67 + 0.01 ° [6]; two glucose molecules and two water molecules are present in the unit cell. The cell parameters were not optimized during the simulations, but kept fixed at the experimental values and periodic boundary conditions were applied. No constraints on either bond lengths or bond angles were imposed. Force field calculations for the crystalline structure of glucose have been performed [14-16] previously, but to the best of our knowledge no ab initio simulation. We have compared the calculated and experimental crystalline structures in order to assess the reliability of our method. The root mean square deviations from the experimental structure are: 0.15 ,~ for CRy, 0.10 ~, for CR~ and 0.21 ,~ for CR~h. These values reduce respectively to 0.14, 0.06 and 0.14 ,~ if only the heavy atoms are considered. The C - O and C - C bond lengths are generally overestimated with respect to the experimental ones by up to about 2%. Keeping in mind that the experiments were performed at finite temperature, while the calculated structures are at zero temperature, and that the comparison is done without taking into account thermal parameters, the agreement is satisfactory. Moreover, our theoretical results provide a refinement of the experimental hydrogen positions, useful for identifying the hydrogen bond network. This is particularly important in the case of the structures determined by X-ray techniques [6,8], where the uncertainty in the hydrogen positions is quite high. In Fig. 2 the calculated structures for CR~ (top), C R ~ (centre) and CR~ (bottom) are shown.
C. Molteni, M. Parrinello / Chemical Physics Letters 275 (1997) 409-413
411
Table 1 Hydrogen bond scheme for c~-D-glucose. Experimental values for the O - O distance are shown in parentheses Bond
O - H (,~)
H - -- O (,~)
O - O (,~)
01210
(deg) O I- H . • • 0 5
1.00
1.70
2.69(2.85) ~
169
02 -H • • • 06
1.01
1.66
2.67(2.78) a
170
O 3 - H "" ' 0 2
1.01
1.67
2.68(2.71) a
172
O4-H • ' • 04
1.00
1.87
2.85(2.77) a
168
Or-H
1.01
1.68
2.68(2.71) a
172
' • • 03
Ref. [4].
In Table 1, Tables 2 and 3 the hydrogen bonding schemes for CRy, CR,h and CRI3 are presented. The calculated hydrogen bonding scheme is in agreement with experiment. In particular, in CR~ the long O 4 - H . - . O 2 is reproduced, in contrast with the force field calculation of Ref. [15]. Five different kinds of hydrogen bonds connect the glucose molecules in both CR~ and CRI3. In CR~h, three different kinds of hydrogen bonds connect the glucose molecules, while four connect the glucose and the water molecules. Regarding the free molecule, we have chosen to analyze a few structures, obtained by relaxing the structures of the molecules as found in the different crystals in a cubic box (lattice parameter 12.7 ,~). In the following we will refer to these molecules as M~, M~ and M~h. Besides the three free molecules obtained from the crystalline structures, we have studied an additional conformer of the a anomer, obtained by rotating in axial position the equatorial C i - O l bond of M~. This molecule (M~) maintains Table 2 Hydrogen bond scheme for a-D-glucose monohydrate. The oxygens of the water molecules are indicated as O w and O w. Experimental values for the O - O distance are shown in parentheses Bond
O - H (.~)
H . . • O (,~)
O - O (,~)
01210
(deg) O ~ - H •. • 0 2
1.01
1.65
2.64(2.73) a
166
O4-H . • • 04
0.99
1.84
2.83(2.80) "
173
Or-H
0.99
1.99
2 . 8 9 ( 2 . 8 3 ) '~
149
1.01
1.75
2.73(2.73) a
164
1.01
1.70
2 . 7 0 ( 2 . 7 3 ) ~'
169
02 -H.
•.. 05 ••Ow
O 3 - H • • - O~ O,~-H • . • 03
1.00
1.68
2.68(2.75) "
169
O~-H
1.00
1.80
2.80(2.79) a
175
- - • 06
Fig. 2. The calculated structures of a-D-glucose (top), a - D - g l u cose monohydrate (centre) and 13-D-glucose (bottom).
a Ref. [61.
412
C. Molteni, M. Parrinello
/ Chemical Physics Letters 275 (1997) 409-413
Table 3 Hydrogen bond scheme for 13-D-glucose. Experimental values for the O - O distance are shown in parentheses Bond
O i - H • • . 06 O 2 - H " • "O 3 0 3 - H • • - 05 04-H'''O 2 O6-H . • . 0 2
O - H (.~) 1.01 1.01 1.00 0.99 1.00
H... 1.61 1.67 1.75 2.06 1.66
O(A)
O-O(A) 2.61(2.67) 2.66(2.69) 2.76(2.77) 3.04(3.26) 2.65(2.71)
3OO 240
OI2IO (deg) a a a a a
~
120
~
60
174 167 175 168 167
~
360
i
~ soo
~
__.~ 240
~ 16o
Ref. [8].
the same orientation of the methyl alcohol and hydroxyl groups (except -O~H) of M~ and can therefore provide information about the specific influence of the C1-O 1 bond orientation. This is far from being a complete study of glucose conformers, but is intended mainly as an exploration of the influence of the local environment on the structural features of glucose. Glucose conformers in the gas phase have been investigated extensively both with quantum chemistry [16-22] and force-field [23-26] methods. When the glucose molecules pass from the crystal environment to the vacuum, they undergo a process of rearrangement of the orientation of the hydroxyl groups and of deformation of bond lengths and bond angles. In particular, in MI3 the hydroxyl groups rearrange themselves according to an ordered pattern of concerted counterclockwise orientation, generating internal strained hydrogen bonds. For the other molecules, except M~ because of the way it has been constructed, the ordered pattern is somehow disrupted. All the free molecules maintain the methyl alcohol group orientation of the corresponding crystals. In Fig. 3 a comparison between the hydroxyl and hydroxymethyl dihedral angles for the crystals and the corresponding molecules is shown. The four calculated molecular structures have similar total energies: the lowest energy was found for M~3, followed by Mah (A[Mah-MI3] = 1.5 kcal/mol), M~ (A[M~ - M~h] = 0.4 kcal/mol) and M~ (A[M~ - M~] = 2.6 kcal/mol). These results do not support the picture of the so-called 'anomeric effect', according to which the c~ anomer in the gas phase is energetically more stable than the 13 one [27,28]. Our set of investigated conformers is actually too small to give definitive conclusions. How-
~
180
"0
120
•
6O
t'~
360
I
I
I
i
i
¢1
1;2
1;3
I
I
7:4
1;5
I
F
1;6
1;7
300 240 180 120 6O i
, --
Fig. 3. Hydroxyl ( z l - r 5) and hydroxymethyl group (r6-~- 7) dihedral angles for the crystals (squares and solid line) and the corresponding molecules (circles and dashed line). Top panel: CR~ and M~; central panel: CR~h and Mc~h; bottom panel: CR~ and MI3. r l : C 2 - C t - O i - H o , ; r2:C3-C2-O2-Ho,; T3:C4-C ~ O 3 - H o ~ ; 74:C5-C4-O4-H0.~; " r s : C 5 - C 6 - O r - H 0 6 ; 76:O5-C 5 C 6 - O 6 ; T 7 : C 4 - C 5 - C 6 - O 6,
0.10
0,05
o
oo
000
°
-0.05
g
-O.lO
;
± \ \\ 0 / / ) l r ~ \
"e
\,-
~
~
,
~
~
Fig. 4. The variation in length of the C - O bonds containing either the anomeric (O I) or the ring (05) oxygen with respect to the average of the other C - O bonds, for the crystals and the free molecules. Filled circles and dashed line: AC t - O t (open circles: experiment); filled diamonds and dotted line: A C I - O 5 (open diamonds: experiment); filled square and dashed-dotted line: A C s - O 5 (open squares: experiment). The error bar is the maximum deviation from the average value of the C - O bonds that contain neither O I nor 05. The numbers on the horizontal axis indicate the different structures: l: CR,~; 2: M~; 3: C R , ~ ; 4: M,~h; 5: CRI3; 6: MI3; 7: M~.
c. Molteni, M. Parrinello / Chemical Physics Letters 275 (1997) 409-413
ever, recent quantum chemistry calculations found that the alleged preference for the ot anomer in the gas phase is much reduced when a larger 6-31G* basis set is used [19-21]. Finally, we have analyzed the behaviour of the C - O bonds containing either the anomeric oxygen (01 ) or the ring oxygen (05). In crystals of glucose and other pyranose sugars, the bond length of the C 1-O~ bond has been found to be remarkably shorter than all the other C - O bond lengths in the sugar [29]. The differences between the C 1 - O l, C i - O 5 and C s - O 5 bond lengths and the average of the other C - O bond lengths are shown in Fig. 4 for the crystals and the corresponding molecules. The maxim u m deviation from the average value (error bar in Fig. 4) provides an indication of the spread in the C - O bond lengths which do not contain O~ and O s. In each case, the shortening of the C ~-O~ is more pronounced in the crystal than in the corresponding free molecule and in the 13 anomer than in the ot one. The shortening and strengthening of the C ~-O~ bond is therefore an effect of the crystal field. Among the molecules M~ shows the most remarkable shortening. The C - O bonds in the ring are both lengthened in the crystals, while in the free molecules one is lengthened ( C 5 - O 5 in the a anomer C ~ - O 5 in the 13 one) and the other shortened. However, the trend is not clearly defined, since several of these variations fall within the error bar. A similar trend for the crystals is shown by the experiments (open symbols in Fig. 4). With the present calculations we have demonstrated that a good description of glucose can be obtained by means of Car-Parrinello molecular dynamics simulations. Not only do we obtain satisfactory agreement with experiment, but we are also able to give a reliable description of the positions of the hydrogens where experiment lacks precision. The changes in the molecular structures from the crystalline to the gas phase confirm the importance of an accurate modelling of the molecular environment and of the inadequacy of transferring conclusions from one case to another.
413
References
[1] J. Maddox, Nature 364 (1993) 669. [2] M. Sprik, J. Hutter, M. Parrinello,J. Chem. Phys. 105 (1996) 1142.
[3] [4] [5] [6]
R. Car, M. Parrinello,Phys. Rev. Lett. 55 (1985) 2471. G.M. Brown, H.A. Levy, Science 147 (1965) 1038. G.M. Brown, H.A. Levy, Acta Crystallogr. B 35 (1979) 656. E. Hough, S. Neidle, D. Rogers, P.G.H. Troughton, Acta Crystallogr. B 29 (1973) 365. [7] R.C.G. Killean, W.G. Ferrier, D.W. Young, Acta Crystallogr. 15 (1962) 911. [8] S.C.C. Chu, G.A. Jeffrey, Acta Crystallogr. B 24 (1968) 830. [9] S.J. Angyal, Angew. Chem. Int. Ed. Engl. 8 (1969) 157. [10] Y. Nishida, H. Ohrui, H. Meguro, Tetrahedron Lett. 25 (1984) 1575. [11] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [12] C. Lee, W. Yang, R.C. Parr, Phys. Rev. B 37 (1988) 785. [13] N. Trouiller, J.L. Martins, Phys. Rev. B 43 (1991) 1993. [14] M.L.C.E. Kouwijzer,B.P. Van Eijck, S.J. Kroes, J. Kroon,J. Comput. Chem. 14 (1993) 1281. [15] M.L.C.E. Kouwijzer,B.P. Van Eijck, H. Kooijman,J. Kroon, Acta Crystallogr. B 51 (1995) 209. [16] S.E. Barrows, F.J. Dulles, C.J. Cramer, A.D. French, D.G. Truhlar, Carbohydr. Res. 276 (1996) 219. [17] G.I. Csonka, K. Elias, I.G. Csimadia, Chem. Phys. Lett. 257 (1996) 49. [18] J.W. Brown, B.D. Wladkowski, J. Am. Chem. Soc. 118 (1995) 1190. [19] P.L. Polavarapu, C.S. Edwig, J. Comput. Chem. 13 (1992) 1255. [20] C.J. Cramer, D.G. Truhlar, J. Am. Chem. Soc. 115 (1993) 5745. [21] K.A. Jebber, K. Zhang, C.J. Cassady, A. Chung-Phillips,J. Am. Chem. Soc. 118 (1996) 10515. [22] C.J. Cramer, D.G. Truhlar, A.D. French, Carbohydr. Res. 298 (1997) 1. [23] J.W. Brady, J. Am. Chem. Soc. 108 (1986) 8153. [24] J.W. Brady, Carbohydr. Res. 165 (1987) 306. [25] M.K. Dowd, A.D. French, P.J. Reilly, Carbohydr. Res. 264 (1994) 1. [26] S.N. Ha, A. Giammona, M. Field, J.W. Brady, Carbohydr. Res. 180 (1988) 207. [27] J.T. Edward, Chem. Ind. (1955) 1102-1104. [28] R.U. Lemieux,Explorationswith Sugars: How Sweet It Was, American Chemical Society, Washington,DC, 1990. [29] H.M. Berman, S.S.C. Chu, G.A. Jeffrey, Science 157 (1967) 1576.
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 275 (1997) 409-413
Condensed matter effects on the structure of crystalline glucose C. Molteni, M. Parrinello Max Planck lnstitut fiir Festkgrperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany Received 12 May 1997; in final form 12 June 1997
Abstract By means of ab initio simulations based on the Car-Parrinello method, we have calculated the crystalline structures of a-D-glucose, a-D-glucose monohydrate and [3-D-glucose. The good agreement with the available experimental data gives us confidence in the applicability of the method to carbohydrates and opens the path towards the investigation of more complex problems, where a quantum mechanical description is essential. Condensed matter effects are discussed by comparing the structures of the glucose molecule in the crystalline and gas phases. © 1997 Published by Elsevier Science B.V.
The importance of carbohydrates in biochemistry is universally known: they play an essential role in processes such as energy storage, structural support, molecular recognition and water control in cold and drought-resistant organisms. Nevertheless, even apparently simple problems, like the behaviour of glucose in water solution, are still far from being properly understood [1]. This is mainly due to the lack of theoretical techniques able to describe in an accurate and reliable way both the sugar solute and the water solvent. However, recent calculations [2] have demonstrated that an excellent description of liquid water can be obtained from density functional theory simulations based on the Car-Parrinello method [3]. In this Letter we investigate the reliability and accuracy of such a method when applied to glucose crystalline structures, as a prelude to a more complex study of glucose-water solutions. Since the crystalline structures are known from experiment [4-8], they are a crucial test for our technique. We have also performed structural calculations for selected glucose molecules in the gas phase, with the aim of investigating the influence of the different
environments which the glucose molecule experiences in crystals and vacuum. A distinct situation occurs in solution, where glucose is surrounded by water molecules able to create a dynamic hydrogen bond network. The glucose molecule, with the conventional numbering of the heavy atoms, is shown in Fig. 1. Its main structure is a puckered six-membered ring, in the chair configuration 4C 1, composed of five carbon atoms (C 1, C 2, C 3, C 4 and C 5) and one oxygen ( 0 5) and held together by single bonds. A methyl alcohol group CH2OH is attached to one of the carbons next to the ring oxygen, while every other carbon of the ring carries both a hydroxyl group and a hydrogen atom. The hydroxyl group (-O~H), attached to the carbon next to the ring oxygen which does not carry the methyl alcohol group (C l), can be either in an axial or equatorial position with respect to the ring, giving rise to two possible anomers, called a and 13 respectively. Experimental crystalline structures are available for aD-glucose (neutron diffraction data) [4,5], a-D-glucose monohydrate [6,7] and 13-D-glucose [8] (X-ray
0009-2614/97/$17.00 © 1997 Published by ELsevier Science B.V. All rights reserved. PH S 0 0 0 9 - 2 6 1 4 ( 9 7 ) 0 0 7 0 1 -X
410
C. Molteni, M. Parrinello / Chemical Physics Letters 275 (1997) 409-413
06
Fig. 1. The glucose molecule with conventional numbering of the atoms.
techniques). It is known from experiment [9] that the ratio of the axial e~ anomer to the equatorial 13 anomer in aqueous solution is 3 6 / 6 4 ; what determines this ratio is still unclear. Both the methyl alcohol and the hydroxyl groups can assume different orientations, giving rise to a great number of conformers. In particular, there are three possible orientations for the methyl alcohol group associated with the C 5 - C 6 internal rotation. They are characterized by the dihedral angle 05 C5-C6-O6, which can be gauche clockwise ( = 60 °, G+), anti ( = 180 °, T), or gauche counterclockwise ( = 60 °, G - ) . In the crystalline structures, the G + rotamer was found for e~-D-glucose, while the G rotamer was found for both c~-D-glucose monohydrate and 13-D-glucose. According to N M R results [10], in aqueous solution the G - and G + rotamers are almost equally populated, while the population of the T rotamer is negligible. Starting from the experimental crystallographic data, we have performed Car-Parrinello molecular dynamics simulations [3] in order to determine, through a quenching procedure, the theoretical minimum energy structures for the three experimentally known glucose crystals. In the following, we will call e~-D-glucose CRy, a-D-glucose monohydrate CR~h and 13-D-glucose CRy. The simulations have been performed within density functional theory, in the generalized gradient approximation: the BLYP (Becke, Lee, Yang and Parr) gradient corrected density functional has been used [11,12]. The interaction between valence electrons and ionic cores is described by Troullier-Martins norm-conserving pseudopotentials [13], with an energy cutoff of 70 Ry. The BLYP functional has proved to be suitable for
describing liquid water [2] and has therefore been chosen in the perspective of future glucose-water solution studies. The time step for the molecular dynamics was 3 au and the electronic mass was set to 200 au. The maximum forces on the atoms at the end of the simulations were about 10 3 au. Both CR~ and CR~ crystallize in the P2~2~2~ space group, with an orthorhombic cell containing four molecules. The exoperimental lattice constants are: a=10.36-!-_0.02 A, b = 1 4 . 8 4 + 0 . 0 2 A and c = 4.97 + 0.002 ,~ for CR~ [4]; and a = 9.205 + 0.004 A, b = 1 2 . 6 4 0 _ 0 . 0 0 5 A and c = 6 . 6 5 4 _ 0.003 ~, for CRI3 [8]. CR~h crystallizes in the space group P21: the cell is monoclinic with lattice constants a = 8.803 + 0.001 ~,, b = 5.085 __+0.001 A, c = 9.708 _ 0.002 A and /3 = 97.67 + 0.01 ° [6]; two glucose molecules and two water molecules are present in the unit cell. The cell parameters were not optimized during the simulations, but kept fixed at the experimental values and periodic boundary conditions were applied. No constraints on either bond lengths or bond angles were imposed. Force field calculations for the crystalline structure of glucose have been performed [14-16] previously, but to the best of our knowledge no ab initio simulation. We have compared the calculated and experimental crystalline structures in order to assess the reliability of our method. The root mean square deviations from the experimental structure are: 0.15 ,~ for CRy, 0.10 ~, for CR~ and 0.21 ,~ for CR~h. These values reduce respectively to 0.14, 0.06 and 0.14 ,~ if only the heavy atoms are considered. The C - O and C - C bond lengths are generally overestimated with respect to the experimental ones by up to about 2%. Keeping in mind that the experiments were performed at finite temperature, while the calculated structures are at zero temperature, and that the comparison is done without taking into account thermal parameters, the agreement is satisfactory. Moreover, our theoretical results provide a refinement of the experimental hydrogen positions, useful for identifying the hydrogen bond network. This is particularly important in the case of the structures determined by X-ray techniques [6,8], where the uncertainty in the hydrogen positions is quite high. In Fig. 2 the calculated structures for CR~ (top), C R ~ (centre) and CR~ (bottom) are shown.
C. Molteni, M. Parrinello / Chemical Physics Letters 275 (1997) 409-413
411
Table 1 Hydrogen bond scheme for c~-D-glucose. Experimental values for the O - O distance are shown in parentheses Bond
O - H (,~)
H - -- O (,~)
O - O (,~)
01210
(deg) O I- H . • • 0 5
1.00
1.70
2.69(2.85) ~
169
02 -H • • • 06
1.01
1.66
2.67(2.78) a
170
O 3 - H "" ' 0 2
1.01
1.67
2.68(2.71) a
172
O4-H • ' • 04
1.00
1.87
2.85(2.77) a
168
Or-H
1.01
1.68
2.68(2.71) a
172
' • • 03
Ref. [4].
In Table 1, Tables 2 and 3 the hydrogen bonding schemes for CRy, CR,h and CRI3 are presented. The calculated hydrogen bonding scheme is in agreement with experiment. In particular, in CR~ the long O 4 - H . - . O 2 is reproduced, in contrast with the force field calculation of Ref. [15]. Five different kinds of hydrogen bonds connect the glucose molecules in both CR~ and CRI3. In CR~h, three different kinds of hydrogen bonds connect the glucose molecules, while four connect the glucose and the water molecules. Regarding the free molecule, we have chosen to analyze a few structures, obtained by relaxing the structures of the molecules as found in the different crystals in a cubic box (lattice parameter 12.7 ,~). In the following we will refer to these molecules as M~, M~ and M~h. Besides the three free molecules obtained from the crystalline structures, we have studied an additional conformer of the a anomer, obtained by rotating in axial position the equatorial C i - O l bond of M~. This molecule (M~) maintains Table 2 Hydrogen bond scheme for a-D-glucose monohydrate. The oxygens of the water molecules are indicated as O w and O w. Experimental values for the O - O distance are shown in parentheses Bond
O - H (.~)
H . . • O (,~)
O - O (,~)
01210
(deg) O ~ - H •. • 0 2
1.01
1.65
2.64(2.73) a
166
O4-H . • • 04
0.99
1.84
2.83(2.80) "
173
Or-H
0.99
1.99
2 . 8 9 ( 2 . 8 3 ) '~
149
1.01
1.75
2.73(2.73) a
164
1.01
1.70
2 . 7 0 ( 2 . 7 3 ) ~'
169
02 -H.
•.. 05 ••Ow
O 3 - H • • - O~ O,~-H • . • 03
1.00
1.68
2.68(2.75) "
169
O~-H
1.00
1.80
2.80(2.79) a
175
- - • 06
Fig. 2. The calculated structures of a-D-glucose (top), a - D - g l u cose monohydrate (centre) and 13-D-glucose (bottom).
a Ref. [61.
412
C. Molteni, M. Parrinello
/ Chemical Physics Letters 275 (1997) 409-413
Table 3 Hydrogen bond scheme for 13-D-glucose. Experimental values for the O - O distance are shown in parentheses Bond
O i - H • • . 06 O 2 - H " • "O 3 0 3 - H • • - 05 04-H'''O 2 O6-H . • . 0 2
O - H (.~) 1.01 1.01 1.00 0.99 1.00
H... 1.61 1.67 1.75 2.06 1.66
O(A)
O-O(A) 2.61(2.67) 2.66(2.69) 2.76(2.77) 3.04(3.26) 2.65(2.71)
3OO 240
OI2IO (deg) a a a a a
~
120
~
60
174 167 175 168 167
~
360
i
~ soo
~
__.~ 240
~ 16o
Ref. [8].
the same orientation of the methyl alcohol and hydroxyl groups (except -O~H) of M~ and can therefore provide information about the specific influence of the C1-O 1 bond orientation. This is far from being a complete study of glucose conformers, but is intended mainly as an exploration of the influence of the local environment on the structural features of glucose. Glucose conformers in the gas phase have been investigated extensively both with quantum chemistry [16-22] and force-field [23-26] methods. When the glucose molecules pass from the crystal environment to the vacuum, they undergo a process of rearrangement of the orientation of the hydroxyl groups and of deformation of bond lengths and bond angles. In particular, in MI3 the hydroxyl groups rearrange themselves according to an ordered pattern of concerted counterclockwise orientation, generating internal strained hydrogen bonds. For the other molecules, except M~ because of the way it has been constructed, the ordered pattern is somehow disrupted. All the free molecules maintain the methyl alcohol group orientation of the corresponding crystals. In Fig. 3 a comparison between the hydroxyl and hydroxymethyl dihedral angles for the crystals and the corresponding molecules is shown. The four calculated molecular structures have similar total energies: the lowest energy was found for M~3, followed by Mah (A[Mah-MI3] = 1.5 kcal/mol), M~ (A[M~ - M~h] = 0.4 kcal/mol) and M~ (A[M~ - M~] = 2.6 kcal/mol). These results do not support the picture of the so-called 'anomeric effect', according to which the c~ anomer in the gas phase is energetically more stable than the 13 one [27,28]. Our set of investigated conformers is actually too small to give definitive conclusions. How-
~
180
"0
120
•
6O
t'~
360
I
I
I
i
i
¢1
1;2
1;3
I
I
7:4
1;5
I
F
1;6
1;7
300 240 180 120 6O i
, --
Fig. 3. Hydroxyl ( z l - r 5) and hydroxymethyl group (r6-~- 7) dihedral angles for the crystals (squares and solid line) and the corresponding molecules (circles and dashed line). Top panel: CR~ and M~; central panel: CR~h and Mc~h; bottom panel: CR~ and MI3. r l : C 2 - C t - O i - H o , ; r2:C3-C2-O2-Ho,; T3:C4-C ~ O 3 - H o ~ ; 74:C5-C4-O4-H0.~; " r s : C 5 - C 6 - O r - H 0 6 ; 76:O5-C 5 C 6 - O 6 ; T 7 : C 4 - C 5 - C 6 - O 6,
0.10
0,05
o
oo
000
°
-0.05
g
-O.lO
;
± \ \\ 0 / / ) l r ~ \
"e
\,-
~
~
,
~
~
Fig. 4. The variation in length of the C - O bonds containing either the anomeric (O I) or the ring (05) oxygen with respect to the average of the other C - O bonds, for the crystals and the free molecules. Filled circles and dashed line: AC t - O t (open circles: experiment); filled diamonds and dotted line: A C I - O 5 (open diamonds: experiment); filled square and dashed-dotted line: A C s - O 5 (open squares: experiment). The error bar is the maximum deviation from the average value of the C - O bonds that contain neither O I nor 05. The numbers on the horizontal axis indicate the different structures: l: CR,~; 2: M~; 3: C R , ~ ; 4: M,~h; 5: CRI3; 6: MI3; 7: M~.
c. Molteni, M. Parrinello / Chemical Physics Letters 275 (1997) 409-413
ever, recent quantum chemistry calculations found that the alleged preference for the ot anomer in the gas phase is much reduced when a larger 6-31G* basis set is used [19-21]. Finally, we have analyzed the behaviour of the C - O bonds containing either the anomeric oxygen (01 ) or the ring oxygen (05). In crystals of glucose and other pyranose sugars, the bond length of the C 1-O~ bond has been found to be remarkably shorter than all the other C - O bond lengths in the sugar [29]. The differences between the C 1 - O l, C i - O 5 and C s - O 5 bond lengths and the average of the other C - O bond lengths are shown in Fig. 4 for the crystals and the corresponding molecules. The maxim u m deviation from the average value (error bar in Fig. 4) provides an indication of the spread in the C - O bond lengths which do not contain O~ and O s. In each case, the shortening of the C ~-O~ is more pronounced in the crystal than in the corresponding free molecule and in the 13 anomer than in the ot one. The shortening and strengthening of the C ~-O~ bond is therefore an effect of the crystal field. Among the molecules M~ shows the most remarkable shortening. The C - O bonds in the ring are both lengthened in the crystals, while in the free molecules one is lengthened ( C 5 - O 5 in the a anomer C ~ - O 5 in the 13 one) and the other shortened. However, the trend is not clearly defined, since several of these variations fall within the error bar. A similar trend for the crystals is shown by the experiments (open symbols in Fig. 4). With the present calculations we have demonstrated that a good description of glucose can be obtained by means of Car-Parrinello molecular dynamics simulations. Not only do we obtain satisfactory agreement with experiment, but we are also able to give a reliable description of the positions of the hydrogens where experiment lacks precision. The changes in the molecular structures from the crystalline to the gas phase confirm the importance of an accurate modelling of the molecular environment and of the inadequacy of transferring conclusions from one case to another.
413
References
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