J Mol Model (2014) 20:2408 DOI 10.1007/s00894-014-2408-0
ORIGINAL PAPER
Molecular modeling in dioxane methanol interaction Dipti Sharma & Sagarika Sahoo & Bijay K. Mishra
Received: 1 May 2014 / Accepted: 29 July 2014 # Springer-Verlag Berlin Heidelberg 2014
Abstract Molecular interaction between dioxane and methanol involves certain polar and nonpolar bonding to form a one to one complex. Interatomic distances between hydrogen and oxygen within 3 Å have been considered as hydrogen bonding. Optimizations of the structures of dioxane-methanol complexes were carried out considering any spatial orientation of a methanol molecule around a chair/boat/twisted-boat conformation of dioxane. From 45 different orientations of dioxane and water, 23 different structures with different local minima were obtained and the structural characteristics like interatomic distances, bond angles, dihedral angles, dipole moment of each complex were discussed. The most stable structure, i.e., with minimum heat of formation is found to have a chair form dioxane, one O-H…O, and two C-H…O hydrogen bonds. In general, the O-H…O hydrogen bonds have an average distance of 1.8 Å while C-H…O bonds have 2.6 Å. The binding energy of the dioxane-methanol complex is found to be a linear function of number of O-H…O and C-H…O bonds, and hydrogen bond length. Keywords Binding energy . Binary system . DFT . Dioxane . Methanol . Unconventional hydrogen bond
Introduction Protein folding and protein-substrate binding phenomena involve intramolecular and intermolecular interactions through Electronic supplementary material The online version of this article (doi:10.1007/s00894-014-2408-0) contains supplementary material, which is available to authorized users. D. Sharma : S. Sahoo : B. K. Mishra (*) Centre of Studies in Surface Science and Technology School of Chemistry, Sambalpur University, Jyoti Vihar 768019, India e-mail: [email protected]
molecular recognition. Out of several conformations and orientations of the involved groups/molecules in these phenomena, a specific stabilized structure is derived with the lowest energy. During the conversion to this structure with global minima from a large number of possible conformers, some possible conformations with local minima are encountered, which can be taken care of analogous to Levinthal paradox [1]. Solvation phenomenon is akin to this type of binding, where solvent interacts with the solute through the interactions like (a) hydrogen bonding, (b) polar interactions, (c) Van der Waal interactions, (d) hydrophobic/apolar interactions, etc. The orientation of the molecules in the bound structure affects its physical and chemical characteristics as well as that of the constituent molecules. To investigate the complex phenomena small molecules can be considered as the model systems. By using ab initio molecular dynamics calculation Sieffert et al. have demonstrated the structure of methanol in a cluster, wherein one methanol is linked to two other methanol molecules through hydrogen bonding in –O-H groups as hydrogen bond donor and acceptor units [2]. They proposed a linear polymeric structure of methanol in the liquid state. When water molecules enter into a methanol cluster, oligomeric system of methanol–water is formed with a higher binding energy than the neat methanol and water clusters [3]. The change in binding energy was attributed to the cooperative polarization and cooperative charge transfer in the methanol and mixed clusters. Here also the –OH groups of methanol and water play the role of hydrogen bond acceptor and donor in the formation of the cluster. The H-bond distances vary with variation in the type of hydrogen bonding. In water–methanol cluster, the hydrogen bond is longer when water acts as hydrogen bond acceptor than that when methanol acts as hydrogen bond acceptor. In acetonitrile-methanol binary mixtures, acetonitrile acts as a pure hydrogen bond acceptor and methanol as both donor and acceptor. The molecular interaction leads to the formation of dimer and/or trimer with linear
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or bifurcated hydrogen bonding, the bond angle being 170.6° and 143.4° respectively [4]. The interatomic distance of hydroxyl H of methanol and nitrogen of acetonitrile were reported to be 2.073 and 2.158 Å respectively. As a typical organic solvent, dioxane (Dx) has hydrogen bond accepting ability and nonpolar characteristics [5]. It can be solubilized in water (W) as well as in methanol (M) and the binary mixtures can have a wide range of polarity. Hence, in binary solvent mixtures, it plays a crucial role in preferential solvation. Further due to flexibility in the molecular structure it can have a large number of conformations for intermolecular interactions with other solvents. Due to its specific conformation, it was found to be a suitable scaffold for the development of M3 muscarinic receptor antagonist [6]. In solvent mixtures Dx exhibits nonideal behavior and a lot of work has been done on their thermodynamic properties [7–10]. Marcus extensively investigated the role of Dx in preferential solvations of solutes in binary mixtures and reported the formation of solvation shell with equimolar quantity of Dx and methanol [11]. While solubilizing some cyanine dyes in binary mixtures of Dx and methanol, Panigrahi et al. have proposed a cliphydrogen bonding, wherein, the Dx assumes boat conformation and trap the hydroxyl unit through hydrogen bonding with the two –O- of Dx and the hydrogen atom of methanolic hydroxyl group [12]. Thereby, the solvation shell provides a relatively nonpolar environment, when compared to neat Dx and methanol. In a Dx cluster, the introduction of a methanol changes the intermolecular interactions among the Dx and forms a relatively stable complex. The approaches of the two solvents, methanol and Dx, for the interaction may steer the structural characteristics of the solvation shell. In the present study attempts have been made to find out the effect of the directional approach of methanol towards a Dx in the Dx-methanol (Dx-M) complex through optimization of the structure by using quantum mechanical calculations.
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Construction of solvation cage To find out the structure of Dx-M for single point energy calculations, a solvation cage was constructed by placing Dx in the centre of a sphere having radius 7.5 Å using the software VEGAZZ [20] and methanol molecules were added into the cage up to the saturation point. Beyond this dimension the methanol groups are found to form bilayer around the Dx molecule. Considering the molecular volume of Dx and methanol, a cluster of methanols around a single Dx was formed, wherein the maximum distance of O(Dx) and H(M) was kept to be 5 Å (Fig. 1). To obtain a Dx-M complex, the position and orientation of each methanol with respect to Dx was fixed (henceforth, corresponding structure will be termed as single point energy structure: SPES) and the corresponding single point energy was calculated.
Results and discussion In this study, a one to one interaction of Dx and methanol has been considered avoiding all other intermolecular interactions in dimeric or oligomeric clusters of Dx and water. A Dx molecule has two oxygen atoms as hydrogen bond acceptor, and a methanol molecule has one hydrogen bond acceptor oxygen and a hydrogen bond donor hydroxyl groups. However, the eight –C-H groups of Dx and three –C-H groups of methanol can also be involved in the molecular interaction as hydrogen bond donor. To conceive a hydrogen bond, the maximum O-H-O distance is assumed to be 2 Å for O-H..O and 3 Å for O..H-C. Akin to cyclohexane, Dx has different conformations, which include chair, boat, and twisted boat conformations each having discrete energy. The optimization of the Dx-M complexes has been attempted with these three conformers and the results have been analyzed vide infra.
Dx–methanol system in chair form
Methods of calculations All the quantum mechanical calculations were performed using GAUSSIAN 09 electronic structure package [13]. The single point energies of each conformer of Dx-M complexes were calculated by using ab initio method, and the geometries were optimized using Hartree-Fock (HF) level of theory, which were further optimized using density functional theory (DFT) with B3LYP hybrid functional [14, 15] and 6-31G* basis set [16–19]. The insertion of HF in between single point energy and DFT is mostly to reduce the computational cost at the same time to have a comparison of the results obtained by two different methods.
Within the stipulated solvation shell with a radius of 7.5 Å, around a Dx molecule in its chair form, 16 methanol molecules could be accommodated considering the molecular volume, hydrogen bonding, and apolar interactions (Fig. 1). The methanol hydroxyl groups are found to have hydrogen bonding interaction with each other and with the –O- of Dx having a minimum distance of 1.789 Å in SPES. Assuming the position of methanol is fixed, for each SPES the heat of formation was calculated and listed in Table 1, which also enlists the dipole moments and HOMO-LUMO energy gaps of different SPESs. The 16 different SPESs have initial energy differences in the range of 25.5 kJ mol-1. A minor difference in the dipole moment (0.48 D) among the 16 SPESs (dipole moment of Dx in chair form=0 and that
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Fig. 1 Ball-stick presentation of Dx–Methanol solvation cage in chair form
of methanol=1.69 D) indicates the occurrence of a weak interaction between methanol and Dx in the SPESs. Each SPES was optimized by using HF theory with 6-31G* basis set and the energy among the optimized conformers are found to be in the range of 15.8 kJ mol-1. Upon subsequent optimization by B3LYP with the same basis set, the structures were converged to six local minima with different Dx-M conformations (Fig. 2) having convergence distributions of nine, two, one, two, one, and
one. Though the optimized energies of two of the conformers are almost the same, there is significant change in the dipole moment, indicating a difference in the orientation of the two molecules in the Dx-M complex. Thus, the distribution is found to be on the basis of the orientation of the methanol with respect to Dx. The energy difference from highest to lowest energy (highest local minima to global minima) is found to be 19.9 kJ mol-1. Binding energy (BE) of the Dx and methanol in the solvation shell was obtained from the difference of the heat of formation of the complex (Dx-M) and the summation of the heat of formation of the constituent molecules (Dx and M). The BEs are found to be in the range of 18–38 kJ mol-1 (Table S1), conformer 2a having the highest. Mizuno et al. have determined the BE value for tetrahydrofuran-water complex to be 25.1 kJ mol-1 [21]. The binding energy is found to be more with more number of O-H…O interactions when compared to C-H…O bonds. A significant statistical correlation (Eq. 1) between the BE and number of O-H,,,O and C-H…O hydrogen bonds and the corresponding bond distance was obtained (R2 =0.991). BE ¼ BE 0 þ aPOHO þ bDOHO þ cPCHO þ dDCHO
ð1Þ
Where POHO and PCHO refer to the number of OH…O and CH…O hydrogen bonds; DOHO and DCHO are the respective hydrogen bond distance; a, b, c, and d are the regression coefficient of the corresponding parameters; and BE0 is the
Table 1 SPES energies, optimized energies, dipole moment (μ) of 16 Dxchair–M complexes by HF and DFT method, the HOMO and LUMO energy difference and the binding energy (BE) calculated by DFT method for the sixteen different conformers Sl. No.
μ in debye (D)
ΔE kJ mol-1
ΔE (LUMO-HOMO) kJ mol-1
BE in kJ mol-1
SPES
HF/ 6–31g*
DFT/ 6–31 *
SPES
HF/ 6–31 *
DFT/ 6–31 *
1 2 3 4 5 6 7
7.4 6.7 9.4 2.8 3.7 4.9 0.3
0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0
1.92 2.01 2.01 1.83 1.85 1.91 2.07
1.74 1.74 1.74 1.74 1.74 1.74 1.74
1.60 1.60 1.60 1.60 1.60 1.60 1.60
846.88 847.04 847.01 847.12 847.04 847.12 847.12
38.54 38.54 38.54 38.54 38.54 38.54 38.54
8 9 10 11 12 13 14 15 16
5.8 25.5 3.1 3.1 0.0 2.7 6.4 2.1 5.7
0.0 0.0 1.7 1.7 2.9 13.1 13.1 15.8 15.7
0.0 0.0 4.1 4.1 5.4 17.6 17.6 18.9 19.97
1.81 1.59 1.92 1.90 1.93 1.94 1.86 2.00 1.90
1.74 1.74 2.17 2.17 1.98 2.01 2.01 1.81 2.05
1.60 1.60 2.09 2.09 1.85 1.84 1.84 1.63 1.99
847.12 847.12 841.05 841.08 843.44 776.86 777.04 755.57 770.14
38.54 38.54 34.45 34.45 33.14 20.98 20.98 19.68 18.57
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Fig. 2 Schematic presentation of energy profile of Dx-M system in chair form
binding energy for a hypothetical system with no hydrogen bonds but Dx and M are close to each other. The regression coefficients for the propensity of O-H…O is found to be (a=194.5) around 60 times more than that for CH…O (c=3.3) hydrogen bonds, indicating a major contribution of the former toward the binding energy than the later. Further, increasing the hydrogen bond distance in the Dx-M complex the BE decreases, which is more significant in OH…O (b=−90.8) than in C-H…O (d=−16.7). Thus the results corroborate the importance of O-H…O hydrogen bonding in the stability of the Dx-M complex. Figure 2 presents the energy profile of the convergence of SPESs to the local and global minima for the optimized structures. Among the optimized conformers, the most stable conformer is due to the symmetrical Dx-M complex 2a, where the methanol –O-H group forms a hydrogen bond with the –
O- of Dx, and the –O- of methanol forms two hydrogen bonds with the axial hydrogens of Dx. By using quantum mechanical calculations, Zierke et al. reported that C-H···O hydrogen bond is the most prominent factor in stabilization of some oligosaccharides, contributing 40 % of the total stabilization energy [22]. The -O-H…O hydrogen bond (1.902 Å) is found to be shorter than the –C-Haxial…O hydrogen bond (2.672 Å). In dimethyl ether dimers the –C-H..O- hydrogen bond distance was reported to be in the range of 2.52–2.59 Å [23]. Further, these interactions in Dx-M led to the formation of three six membered cyclic structures, which supplement to the stability of the Dx-M complex. The C-H..O bond angle being 126.4 matches well with the reported value of 124 for C-H… O bond angle in a phthalate monohydrate complex [24]. This deviation from linearity of C-H..O bonds support the proposition that directionality is important in C-H…O bonding [25].
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The conformer 2b has 4.1 kJ mol-1 higher energy than 2a. The Dx-M interactions involve two hydrogen bonds one with –ODx- and H-OM and the other with –OM- and equatorial H of Dx adjacent to concern –ODx- constituting a five membered ring. The methanol orients itself in one side of the symmetrical axis of Dx with the O-C bond almost perpendicular (Dihedral angle of ODx-ODx-OM-CM =84°) to the ODx-ODx axis. As ususal the O-H..O hydrogen bond is shorter than that of the C-H…O. The dipole moment, which is also considered as a contribution of molecular interaction, is found to be more in 2b than that of 2a. The dipole moment of Dx and methanol being zero and 1.69 D, the dipole moment of 1.60 D for 2a indicates the decrease of polarity of methanol due to its symmetrical orientation with respect to Dx; while in the case of 2b the increase in dipole moment (2.09 D) is due to the sidedness of the methanol. With almost similar interactions the dipole moment decreases more in 2c than that in 2b. In 2c, which is of 1.3 kJ mol-1 higher energy than 2b, methanol is symmetrically oriented with respect to ODx-ODx axis of Dx (dihedral angle of ODx-ODx-OM-CM =180°) with one –O-H…. ODx hydrogen bond and two C-Haxial..O hydrogen bonds. The hydrogen bonds led to formation of two five membered rings and one six membered ring in the 2c. The other three local minima (2d, e, and f) are found to be substantially high in energy when compared to 2a-c. In these conformers H of hydroxyl group of methanol is not involved in the hydrogen bonding. In all the three cases, a hydrogen of methyl group links with –ODx- having the inter atomic distance 2.493–2.590 Å. The other bondings are due to –OM- with the C-H hydrogen of Dx: in 2d with one axial and one equatorial C-H, in 2e with one axial C-H, and in 2f two axial C-H groups. The hydrogen bonds are almost of equal length within the range of 2.525–2.694 Å. In Dx-M complex the structural variation of Dx were found to be significant. The bond lengths and bond angle of Dx remain intact for all the conformers in the binary mixtures. The high values of HOMO-LUMO gap (ΔELUMO-HOMO), an important stability index [26], also support the stability of the Dx-M complexes, the decreasing trend being 2a-2f.
Dx–methanol system in boat form In the boat conformation Dx can accommodate 15 methanols around it indicating a slight increase in the molecular volume than that of the chair form (Fig. S3). The boat conformation of Dx has 35.1 kJ mol-1 higher energy than the chair conformation. Considering the interaction between each methanol with Dx, the deviation in the single point energies are found to be within the range of 38.2 kJ mol-1 (Table 2). The dipole moments are found to be of wide differences ranging from 0.27 D to 3.6 D. This diversity, when compared to that in chair
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form, may be attributed to the structural artifact of boat form, which has a dipole moment 1.75 D . On optimization, the 15 SPESs, obtained due to the different orientations of the methanol around Dx, converge to six different local minima referring to nine specific conformations of Dx-M complexes (Fig. 3). For different conformations of the Dx-M complexes, the energy may be the same but there is a significant change in the dipole moment values due to change in the structure. The most stable conformer, 3a, among these optimized structures was derived from one single point minima only. This structure, 3a, is characterized by one –OH…ODx, one –OM-…H-C, and one –ODx…H-CM type of hydrogen bonding with bond distances of 1.941, 2.637, and 2.806 Å respectively. The Dx-M interaction generates two six membered ring systems, which probably contribute to the stability of the Dx-M complex. However, this conformer has 28.8 kJ mol-1 higher in energy than that of 2a. This is also similar to the difference in energy of chair and twisted boat form of 1,4-dioxane (30.1 kJ mol-1) [27]. The dipole moment of the conformer is found to be 3.25 D, though that of the boat conformation and methanol are found to be 1.75 and 1.69 D. On optimization, the Dx-M structures suffer change in the structure of Dx, which can be visualized from the –O-C-C-O dihedral angle of Dx. Considering the dihedral angle of O-CC-O of boat form and twisted boat form as 0 and 60° respectively, the extent of twisting of the boat form in 3a is found to be 55 %. The trapping of the methanolic –O-H by the ethereal O atom of Dx can give an insight to the preferential solvation and type of interaction involved in the solvatochromism of different substrates in binary mixture of different extent of polarity. In a recent work Panigrahi et al. have proposed a similar orientation of Dx and methanol in Dx-M binary solvents involved in the preferential solvation of a styryl pyridinium dye (Fig. 4) [12]. The next higher energetic Dx-M, 3b, is due to optimization of one SPES from those of 15 conformers, and has an energy difference of 0.98 kJ mol-1 from 3a with a dipole moment value of 3.57 D. The structure of the Dx-M complex, 3b, is found to be almost the same with that of 3a with slight variation in the orientation of methanol (dihedral angles HO-C-C of methanol being 3a: 56. 1 and 3b: 52.6°). With almost similar energy with 3b, another optimized structure 3c, derived from one SPES has a significantly different dipole moment (1.63D). The Dx-M complex (3c) is due to one ODx…H-O (1.886 Å), and two OM…H-CD (2.724 and 2.770 Å) bonds generating two six-membered cycles. The Dx-M complex is found to have a complete twisted-boat conformation. The HOMO-LUMO gap of 3c is the highest among all the structures derived from boat form. On optimization, two SPESs with wide difference in dipole moment and energy converged to one structure of Dx-M complex (3d). The Dx assumes a twisted boat conformation and there is only one OM…H-CDx bond with a distance of
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Table 2 SPES energies, optimized energies, dipole moment (μ) of 15 Dxboat –methanol complexes by HF and DFT method, the HOMO and LUMO energy difference and the binding energy calculated by DFT method for the fifteen different conformers Sl. No.
μ in debye (D)
ΔE kJ mol-1
ΔE (LUMO-HOMO) kJ mol-1
BE in kj mol-1
SPES
HF/ 6–31g*
DFT/ 6–31g*
SPES
hf/6–31g*
dft/6–31g*
1
38.2
0.1
0.0
1.87
3.30
3.25
793.51
38.86
2 3 4 5 6 7 8 9 10 11 12 13 14 15
1.0 2.4 9.5 1.1 0.0 5.3 11.1 7.6 10.6 7.6 4.6 9.2 3.9 2.9
1.3 0.3 0.0 0.0 0.9 0.9 1.2 2.2 1.1 1.8 1.8 13.9 0.9 19.0
1.0 1.1 1.7 1.7 2.1 2.1 2.1 2.1 3.4 3.6 3.6 18.3 21.6 27.5
2.75 3.60 3.54 0.27 3.36 2.50 1.76 3.28 2.41 2.10 2.66 3.29 1.94 3.21
3.77 2.03 2.03 2.03 3.20 3.22 3.22 3.22 2.47 1.35 1.35 3.35 3.23 1.86
3.57 1.63 1.92 1.92 2.90 2.90 2.90 2.90 2.33 0.90 0.88 2.96 1.60 1.76
788.67 859.48 843.89 843.91 823.88 823.99 823.78 824.46 813.12 827.03 827.11 779.46 763.73 834.44
37.72 37.89 37.17 37.17 36.77 36.77 36.77 36.76 35.24 35.24 35.48 20.53 17.28 11.40
2.600 Å. Another higher energetic Dx-M complex 3e, with a more significant difference in the dipole moment than that of 3d, is a convergent of four SPESs. In this structure the methanol –Ois found to be linked to two adjacent H of Dx unit having interatomic distances of 2.816and 2.738 Å. The –O-H—ODx hydrogen bond distance is 1.909 Å. The hydrogen bonds form two fused five membered rings which may contribute to the higher energy of the structure. Another optimized structure 3f has almost similar energy and dipole moment with that of 3e but with a sidedness in the orientation of Dx and M. In this structure, including one O-H…ODx hydrogen bonding, there is only one OM..H-CDx- with a bond distance of 2.612 Å. Structure 3g is a convergent of two SPESs with a higher energy of 3.6 kJ mol-1 than that of 3a. Its dipole moment (0.88–0.89 D) is found to be the minimum in the series. The Dx-M complex has one O-H… ODx (1.896 Å) and one OM…H-CDx (2.657 Å) bond. The polarity of the complex is neutralized due to the specific orientation of the methanol group on a partial twisted-boat form, the extent of twist being 73 %. Highly energetic three optimized structures 3h-j were derived from three different SPEs. In these structures the hydrogen of methanolic O-H group is not involved in the bonding interaction. The –OM- is close to three hydrogens of Dx within a distance of 3 Å in 3h and 3i, while in 3j there is no bonding interaction with the methanolic O-H and Dx. In the later structure, a hydrogen bond of ODx–H-CM is observed with a distance of 2.868 Å. The Dx units are also found to be partially twisted. In the Dx–M complex, there is almost no change in the interatomic bond distances in Dx nucleus, while there is a significant change in the dihedral angels due to change in the
conformation of the ring. In the lowest energy structure the change in dihedral angle was found to be 34.227° compared to the single Dx molecule in boat form. Among all the local minima, conformer 3a is the most stable one having energy 1.0, 1.1, 1.7, 2.1, 3.4, 3.6, 18.3, 21.5, and 27.5 kJ mol-1 less than the conformers (3b), (3c), (3d), (3e), (3f), (3 g), (3 h), (3i), and (3j) respectively.
Dx–methanol system in twisted-boat form In twisted boat form Dx is 29.2 kJ mol-1 higher in energy than the chair form and 6.0 kJ mol-1 less energetic than the boat form. Around the twisted boat conformer of Dx, 15 methanol molecules could be accommodated within a radius of 7.5 Å. The single point energy of each Dx-M complex was calculated and was found to be within the range of 22.3 kJ mol-1 with dipole moment variation of 0.50 D (Table 3). On optimization of the concerned SPESs the methanol and Dx molecules suffer orientational changes leading to the formation of some stable Dx-M complexes with different conformations. Out of these conformations, the most stable conformation, 5a having a dipole moment 1.62 D, is a convergent of two SPESs having energy difference of 11.4 kJ mol-1. The orientation of methanol and Dx in the Dx-M complex leads to generate three hydrogen bonds, one O-H…O bond with distance 1.887 Å and two O…H-C bonds having distance 2.774 Å and 2.737 Å in structure 5a. The methyl group was found to remain away from the methylene groups of Dx. The next higher energetic conformer 5b has 0.6 kJ mol-1 higher energy than 5a, and was derived from the
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Fig. 3 Schematic presentation of energy profile of Dx-M system in boat form
convergence of five SPESs with an energy difference of 2.88 kJ mol-1 and the dipole moment range 1.87–2.03 D. 5b has a dipole
O
O
O
O
H O
H3 C
O
CH3
O
H3C
O
O O
O H O
CH3 H3 C
H
H O
O
H
O H
O O
CH3
O
Fig. 4 Schematic representation of orientation of the solvent molecules around the probe in the binary mixture of methanol and Dx
moment 1.92 D, and two O…H bonds having distances of 1.891 and 2.599 Å. The conformers 5c and 5d have the same energy minima but with different dipole moments, e.g., 2.07 and 2.34 D respectively. The two structures involve a sidewise interaction of methanol with Dx through two bonds, which consists of one OH…O bond having distance 1.908 Å and one C-H…O bond with distance 2.611 Å. Conformer 5e refers to the local minima having 14.4 kJ mol-1 higher than that of 5c and dipole moment 1.78 D. In this conformer methanol interacts with Dx through one O…. H-C bond of distance 2.479 Å and one C-HM…O bond of distance 2.711 Å. Conformer 5f has a dipole moment value of 1.62 D and has 1.6 kJ mol-1 more energy than 5e. There exist three C-H…O bonds of distance 2.582, 2.853, and 2.571 Å respectively in conformer 5g and has 2.9 kJ mol-1 more energy than 5f with a dipole moment of 2.41 D. This conformation has a symmetrical arrangement of methanol and Dx, where methanol
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Table 3 SPES energies, optimized energies, dipole moment (μ) of 15 Dxtwist-boat–methanol complexes by HF and DFT method, the HOMO and LUMO energy difference and the binding energy calculated by DFT method for the fifteen different conformers Sl. No.
μ in debye (D)
ΔE kJ mol-1
ΔE (LUMO-HOMO) kJ mol-1
BE in kJ mol-1
SPES
hf/ 6–31g*
dft/ 6–31g*
SPES
hf/6–31g*
dft/6–31g*
1
22.3
0.0
0.0
1.97
2.03
1.62
860.43
31.73
2 3 4 5 6 7 8 9 10 11 12 13 14 15
10.9 5.9 4.6 4.7 5.4 7.5 0.0 1.6 3.0 2.5 1.5 6.8 12.0 8.7
0.0 0.0 0.0 0.0 0.0 0.0 1.15 1.15 1.15 1.15 1.1 12.5 15.4 14.6
0.0 0.6 0.6 0.6 0.6 0.6 2.1 2.1 2.1 2.1 2.2 16.5 18.1 21.0
1.73 2.03 1.94 1.93 1.96 1.87 1.87 2.05 1.99 1.82 2.13 1.64 1.96 1.94
2.03 2.03 2.03 2.03 2.03 2.03 2.12 2.12 2.12 2.12 2.51 2.00 1.82 2.44
1.62 1.92 1.92 1.92 1.92 1.92 2.07 2.07 2.07 2.07 2.34 1.78 1.62 2.41
860.40 843.99 843.99 843.99 843.99 843.99 827.90 827.90 827.98 827.82 813.22 791.22 769.06 762.05
31.73 31.18 31.18 31.18 31.18 31.18 29.65 29.65 29.65 29.65 29.48 15.24 13.60 10.69
forms two nearly symmetrical bonds with distances 2.704 and 2.688 Å. Upon interaction with methanol, no significant change has been observed in the structure of Dx. Among the seven conformers the conformer (a) is the most stable conformation having energy 0.6, 2.1, 2.2, 16.5, 18.1, and 21.0 kJ mol-1 less than conformers (b), (c), (d), (e), (f), and (g) respectively. Though, through VEGAZZ program some specific SPESs were generated for Dx-M system, there are an infinite number of possible SPESs within the intermolecular distance of 7.5 Å. For each conformations of Dx, some more arbitrary structures were generated by changing the position and orientation of methanol and the Dx-M structures were optimized by using HF and subsequently DFT with basis set 6–31g*. However, all the structures converged to the local minima presented in Figs. 2, 3, and 5.
Conclusions Structurally, Dx and methanol have different groups of hydrogen bond donating and accepting abilities, and hence, they can form a large number of one to one structural
complexes. Considering three specific conformations (chair, boat, and twisted boat) of Dx, methanol can have an infinite number of orientations around Dx with an intermolecular distance of 7.5 Å to form a Dx-methanol complex. On optimization for energy minima of heat of formation, 46 conformations of Dx-methanol complex have been selected by using VEGAZZ. From these conformations 23 local minima having –O…H-C and –O-H—O hydrogen bonds were obtained. The global minima corresponds to a structure where the hydroxyl group of methanol is completely involved in the hydrogen bonding with –Oand –C-H of Dx with a binding energy of 38.64 kJ mol1 . The contribution of nonconventional hydrogen bonding, i.e., –C-H…O in the formation of Dx-methanol is found to be significant. The local minima which are derived from the convergence of stationary structures of Dx-methanol complex, may have similarity with the misfolding of protein, where the inter conversion needs a high energetic transition state and the structure with global minima may be considered as the native structure of the protein. Further, the existence of structure with local minima may be conceived in conducive environment or in the preferential solvation of solutes by Dx and methanol.
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Fig. 5 Schematic presentation of energy profile of Dx-M system in twist-boat form
Supporting information Additional details for the solvation models, conformation of the complexes, statistical correlation are presented as supplementary materials.
Acknowledgments B.K.M. thanks University Grants Commission and Council of Scientific and Industrial Research,New Delhi, for financial assistance through BSR-Faculty Fellowship and a Research Project respectively. S.S. thanks the Department of Science and Technology, New Delhi, for Innovation of Science Pursuit for Inspire Research (INSPIRE) research fellowship.
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ORIGINAL PAPER
Molecular modeling in dioxane methanol interaction Dipti Sharma & Sagarika Sahoo & Bijay K. Mishra
Received: 1 May 2014 / Accepted: 29 July 2014 # Springer-Verlag Berlin Heidelberg 2014
Abstract Molecular interaction between dioxane and methanol involves certain polar and nonpolar bonding to form a one to one complex. Interatomic distances between hydrogen and oxygen within 3 Å have been considered as hydrogen bonding. Optimizations of the structures of dioxane-methanol complexes were carried out considering any spatial orientation of a methanol molecule around a chair/boat/twisted-boat conformation of dioxane. From 45 different orientations of dioxane and water, 23 different structures with different local minima were obtained and the structural characteristics like interatomic distances, bond angles, dihedral angles, dipole moment of each complex were discussed. The most stable structure, i.e., with minimum heat of formation is found to have a chair form dioxane, one O-H…O, and two C-H…O hydrogen bonds. In general, the O-H…O hydrogen bonds have an average distance of 1.8 Å while C-H…O bonds have 2.6 Å. The binding energy of the dioxane-methanol complex is found to be a linear function of number of O-H…O and C-H…O bonds, and hydrogen bond length. Keywords Binding energy . Binary system . DFT . Dioxane . Methanol . Unconventional hydrogen bond
Introduction Protein folding and protein-substrate binding phenomena involve intramolecular and intermolecular interactions through Electronic supplementary material The online version of this article (doi:10.1007/s00894-014-2408-0) contains supplementary material, which is available to authorized users. D. Sharma : S. Sahoo : B. K. Mishra (*) Centre of Studies in Surface Science and Technology School of Chemistry, Sambalpur University, Jyoti Vihar 768019, India e-mail: [email protected]
molecular recognition. Out of several conformations and orientations of the involved groups/molecules in these phenomena, a specific stabilized structure is derived with the lowest energy. During the conversion to this structure with global minima from a large number of possible conformers, some possible conformations with local minima are encountered, which can be taken care of analogous to Levinthal paradox [1]. Solvation phenomenon is akin to this type of binding, where solvent interacts with the solute through the interactions like (a) hydrogen bonding, (b) polar interactions, (c) Van der Waal interactions, (d) hydrophobic/apolar interactions, etc. The orientation of the molecules in the bound structure affects its physical and chemical characteristics as well as that of the constituent molecules. To investigate the complex phenomena small molecules can be considered as the model systems. By using ab initio molecular dynamics calculation Sieffert et al. have demonstrated the structure of methanol in a cluster, wherein one methanol is linked to two other methanol molecules through hydrogen bonding in –O-H groups as hydrogen bond donor and acceptor units [2]. They proposed a linear polymeric structure of methanol in the liquid state. When water molecules enter into a methanol cluster, oligomeric system of methanol–water is formed with a higher binding energy than the neat methanol and water clusters [3]. The change in binding energy was attributed to the cooperative polarization and cooperative charge transfer in the methanol and mixed clusters. Here also the –OH groups of methanol and water play the role of hydrogen bond acceptor and donor in the formation of the cluster. The H-bond distances vary with variation in the type of hydrogen bonding. In water–methanol cluster, the hydrogen bond is longer when water acts as hydrogen bond acceptor than that when methanol acts as hydrogen bond acceptor. In acetonitrile-methanol binary mixtures, acetonitrile acts as a pure hydrogen bond acceptor and methanol as both donor and acceptor. The molecular interaction leads to the formation of dimer and/or trimer with linear
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or bifurcated hydrogen bonding, the bond angle being 170.6° and 143.4° respectively [4]. The interatomic distance of hydroxyl H of methanol and nitrogen of acetonitrile were reported to be 2.073 and 2.158 Å respectively. As a typical organic solvent, dioxane (Dx) has hydrogen bond accepting ability and nonpolar characteristics [5]. It can be solubilized in water (W) as well as in methanol (M) and the binary mixtures can have a wide range of polarity. Hence, in binary solvent mixtures, it plays a crucial role in preferential solvation. Further due to flexibility in the molecular structure it can have a large number of conformations for intermolecular interactions with other solvents. Due to its specific conformation, it was found to be a suitable scaffold for the development of M3 muscarinic receptor antagonist [6]. In solvent mixtures Dx exhibits nonideal behavior and a lot of work has been done on their thermodynamic properties [7–10]. Marcus extensively investigated the role of Dx in preferential solvations of solutes in binary mixtures and reported the formation of solvation shell with equimolar quantity of Dx and methanol [11]. While solubilizing some cyanine dyes in binary mixtures of Dx and methanol, Panigrahi et al. have proposed a cliphydrogen bonding, wherein, the Dx assumes boat conformation and trap the hydroxyl unit through hydrogen bonding with the two –O- of Dx and the hydrogen atom of methanolic hydroxyl group [12]. Thereby, the solvation shell provides a relatively nonpolar environment, when compared to neat Dx and methanol. In a Dx cluster, the introduction of a methanol changes the intermolecular interactions among the Dx and forms a relatively stable complex. The approaches of the two solvents, methanol and Dx, for the interaction may steer the structural characteristics of the solvation shell. In the present study attempts have been made to find out the effect of the directional approach of methanol towards a Dx in the Dx-methanol (Dx-M) complex through optimization of the structure by using quantum mechanical calculations.
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Construction of solvation cage To find out the structure of Dx-M for single point energy calculations, a solvation cage was constructed by placing Dx in the centre of a sphere having radius 7.5 Å using the software VEGAZZ [20] and methanol molecules were added into the cage up to the saturation point. Beyond this dimension the methanol groups are found to form bilayer around the Dx molecule. Considering the molecular volume of Dx and methanol, a cluster of methanols around a single Dx was formed, wherein the maximum distance of O(Dx) and H(M) was kept to be 5 Å (Fig. 1). To obtain a Dx-M complex, the position and orientation of each methanol with respect to Dx was fixed (henceforth, corresponding structure will be termed as single point energy structure: SPES) and the corresponding single point energy was calculated.
Results and discussion In this study, a one to one interaction of Dx and methanol has been considered avoiding all other intermolecular interactions in dimeric or oligomeric clusters of Dx and water. A Dx molecule has two oxygen atoms as hydrogen bond acceptor, and a methanol molecule has one hydrogen bond acceptor oxygen and a hydrogen bond donor hydroxyl groups. However, the eight –C-H groups of Dx and three –C-H groups of methanol can also be involved in the molecular interaction as hydrogen bond donor. To conceive a hydrogen bond, the maximum O-H-O distance is assumed to be 2 Å for O-H..O and 3 Å for O..H-C. Akin to cyclohexane, Dx has different conformations, which include chair, boat, and twisted boat conformations each having discrete energy. The optimization of the Dx-M complexes has been attempted with these three conformers and the results have been analyzed vide infra.
Dx–methanol system in chair form
Methods of calculations All the quantum mechanical calculations were performed using GAUSSIAN 09 electronic structure package [13]. The single point energies of each conformer of Dx-M complexes were calculated by using ab initio method, and the geometries were optimized using Hartree-Fock (HF) level of theory, which were further optimized using density functional theory (DFT) with B3LYP hybrid functional [14, 15] and 6-31G* basis set [16–19]. The insertion of HF in between single point energy and DFT is mostly to reduce the computational cost at the same time to have a comparison of the results obtained by two different methods.
Within the stipulated solvation shell with a radius of 7.5 Å, around a Dx molecule in its chair form, 16 methanol molecules could be accommodated considering the molecular volume, hydrogen bonding, and apolar interactions (Fig. 1). The methanol hydroxyl groups are found to have hydrogen bonding interaction with each other and with the –O- of Dx having a minimum distance of 1.789 Å in SPES. Assuming the position of methanol is fixed, for each SPES the heat of formation was calculated and listed in Table 1, which also enlists the dipole moments and HOMO-LUMO energy gaps of different SPESs. The 16 different SPESs have initial energy differences in the range of 25.5 kJ mol-1. A minor difference in the dipole moment (0.48 D) among the 16 SPESs (dipole moment of Dx in chair form=0 and that
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Fig. 1 Ball-stick presentation of Dx–Methanol solvation cage in chair form
of methanol=1.69 D) indicates the occurrence of a weak interaction between methanol and Dx in the SPESs. Each SPES was optimized by using HF theory with 6-31G* basis set and the energy among the optimized conformers are found to be in the range of 15.8 kJ mol-1. Upon subsequent optimization by B3LYP with the same basis set, the structures were converged to six local minima with different Dx-M conformations (Fig. 2) having convergence distributions of nine, two, one, two, one, and
one. Though the optimized energies of two of the conformers are almost the same, there is significant change in the dipole moment, indicating a difference in the orientation of the two molecules in the Dx-M complex. Thus, the distribution is found to be on the basis of the orientation of the methanol with respect to Dx. The energy difference from highest to lowest energy (highest local minima to global minima) is found to be 19.9 kJ mol-1. Binding energy (BE) of the Dx and methanol in the solvation shell was obtained from the difference of the heat of formation of the complex (Dx-M) and the summation of the heat of formation of the constituent molecules (Dx and M). The BEs are found to be in the range of 18–38 kJ mol-1 (Table S1), conformer 2a having the highest. Mizuno et al. have determined the BE value for tetrahydrofuran-water complex to be 25.1 kJ mol-1 [21]. The binding energy is found to be more with more number of O-H…O interactions when compared to C-H…O bonds. A significant statistical correlation (Eq. 1) between the BE and number of O-H,,,O and C-H…O hydrogen bonds and the corresponding bond distance was obtained (R2 =0.991). BE ¼ BE 0 þ aPOHO þ bDOHO þ cPCHO þ dDCHO
ð1Þ
Where POHO and PCHO refer to the number of OH…O and CH…O hydrogen bonds; DOHO and DCHO are the respective hydrogen bond distance; a, b, c, and d are the regression coefficient of the corresponding parameters; and BE0 is the
Table 1 SPES energies, optimized energies, dipole moment (μ) of 16 Dxchair–M complexes by HF and DFT method, the HOMO and LUMO energy difference and the binding energy (BE) calculated by DFT method for the sixteen different conformers Sl. No.
μ in debye (D)
ΔE kJ mol-1
ΔE (LUMO-HOMO) kJ mol-1
BE in kJ mol-1
SPES
HF/ 6–31g*
DFT/ 6–31 *
SPES
HF/ 6–31 *
DFT/ 6–31 *
1 2 3 4 5 6 7
7.4 6.7 9.4 2.8 3.7 4.9 0.3
0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0
1.92 2.01 2.01 1.83 1.85 1.91 2.07
1.74 1.74 1.74 1.74 1.74 1.74 1.74
1.60 1.60 1.60 1.60 1.60 1.60 1.60
846.88 847.04 847.01 847.12 847.04 847.12 847.12
38.54 38.54 38.54 38.54 38.54 38.54 38.54
8 9 10 11 12 13 14 15 16
5.8 25.5 3.1 3.1 0.0 2.7 6.4 2.1 5.7
0.0 0.0 1.7 1.7 2.9 13.1 13.1 15.8 15.7
0.0 0.0 4.1 4.1 5.4 17.6 17.6 18.9 19.97
1.81 1.59 1.92 1.90 1.93 1.94 1.86 2.00 1.90
1.74 1.74 2.17 2.17 1.98 2.01 2.01 1.81 2.05
1.60 1.60 2.09 2.09 1.85 1.84 1.84 1.63 1.99
847.12 847.12 841.05 841.08 843.44 776.86 777.04 755.57 770.14
38.54 38.54 34.45 34.45 33.14 20.98 20.98 19.68 18.57
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Fig. 2 Schematic presentation of energy profile of Dx-M system in chair form
binding energy for a hypothetical system with no hydrogen bonds but Dx and M are close to each other. The regression coefficients for the propensity of O-H…O is found to be (a=194.5) around 60 times more than that for CH…O (c=3.3) hydrogen bonds, indicating a major contribution of the former toward the binding energy than the later. Further, increasing the hydrogen bond distance in the Dx-M complex the BE decreases, which is more significant in OH…O (b=−90.8) than in C-H…O (d=−16.7). Thus the results corroborate the importance of O-H…O hydrogen bonding in the stability of the Dx-M complex. Figure 2 presents the energy profile of the convergence of SPESs to the local and global minima for the optimized structures. Among the optimized conformers, the most stable conformer is due to the symmetrical Dx-M complex 2a, where the methanol –O-H group forms a hydrogen bond with the –
O- of Dx, and the –O- of methanol forms two hydrogen bonds with the axial hydrogens of Dx. By using quantum mechanical calculations, Zierke et al. reported that C-H···O hydrogen bond is the most prominent factor in stabilization of some oligosaccharides, contributing 40 % of the total stabilization energy [22]. The -O-H…O hydrogen bond (1.902 Å) is found to be shorter than the –C-Haxial…O hydrogen bond (2.672 Å). In dimethyl ether dimers the –C-H..O- hydrogen bond distance was reported to be in the range of 2.52–2.59 Å [23]. Further, these interactions in Dx-M led to the formation of three six membered cyclic structures, which supplement to the stability of the Dx-M complex. The C-H..O bond angle being 126.4 matches well with the reported value of 124 for C-H… O bond angle in a phthalate monohydrate complex [24]. This deviation from linearity of C-H..O bonds support the proposition that directionality is important in C-H…O bonding [25].
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The conformer 2b has 4.1 kJ mol-1 higher energy than 2a. The Dx-M interactions involve two hydrogen bonds one with –ODx- and H-OM and the other with –OM- and equatorial H of Dx adjacent to concern –ODx- constituting a five membered ring. The methanol orients itself in one side of the symmetrical axis of Dx with the O-C bond almost perpendicular (Dihedral angle of ODx-ODx-OM-CM =84°) to the ODx-ODx axis. As ususal the O-H..O hydrogen bond is shorter than that of the C-H…O. The dipole moment, which is also considered as a contribution of molecular interaction, is found to be more in 2b than that of 2a. The dipole moment of Dx and methanol being zero and 1.69 D, the dipole moment of 1.60 D for 2a indicates the decrease of polarity of methanol due to its symmetrical orientation with respect to Dx; while in the case of 2b the increase in dipole moment (2.09 D) is due to the sidedness of the methanol. With almost similar interactions the dipole moment decreases more in 2c than that in 2b. In 2c, which is of 1.3 kJ mol-1 higher energy than 2b, methanol is symmetrically oriented with respect to ODx-ODx axis of Dx (dihedral angle of ODx-ODx-OM-CM =180°) with one –O-H…. ODx hydrogen bond and two C-Haxial..O hydrogen bonds. The hydrogen bonds led to formation of two five membered rings and one six membered ring in the 2c. The other three local minima (2d, e, and f) are found to be substantially high in energy when compared to 2a-c. In these conformers H of hydroxyl group of methanol is not involved in the hydrogen bonding. In all the three cases, a hydrogen of methyl group links with –ODx- having the inter atomic distance 2.493–2.590 Å. The other bondings are due to –OM- with the C-H hydrogen of Dx: in 2d with one axial and one equatorial C-H, in 2e with one axial C-H, and in 2f two axial C-H groups. The hydrogen bonds are almost of equal length within the range of 2.525–2.694 Å. In Dx-M complex the structural variation of Dx were found to be significant. The bond lengths and bond angle of Dx remain intact for all the conformers in the binary mixtures. The high values of HOMO-LUMO gap (ΔELUMO-HOMO), an important stability index [26], also support the stability of the Dx-M complexes, the decreasing trend being 2a-2f.
Dx–methanol system in boat form In the boat conformation Dx can accommodate 15 methanols around it indicating a slight increase in the molecular volume than that of the chair form (Fig. S3). The boat conformation of Dx has 35.1 kJ mol-1 higher energy than the chair conformation. Considering the interaction between each methanol with Dx, the deviation in the single point energies are found to be within the range of 38.2 kJ mol-1 (Table 2). The dipole moments are found to be of wide differences ranging from 0.27 D to 3.6 D. This diversity, when compared to that in chair
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form, may be attributed to the structural artifact of boat form, which has a dipole moment 1.75 D . On optimization, the 15 SPESs, obtained due to the different orientations of the methanol around Dx, converge to six different local minima referring to nine specific conformations of Dx-M complexes (Fig. 3). For different conformations of the Dx-M complexes, the energy may be the same but there is a significant change in the dipole moment values due to change in the structure. The most stable conformer, 3a, among these optimized structures was derived from one single point minima only. This structure, 3a, is characterized by one –OH…ODx, one –OM-…H-C, and one –ODx…H-CM type of hydrogen bonding with bond distances of 1.941, 2.637, and 2.806 Å respectively. The Dx-M interaction generates two six membered ring systems, which probably contribute to the stability of the Dx-M complex. However, this conformer has 28.8 kJ mol-1 higher in energy than that of 2a. This is also similar to the difference in energy of chair and twisted boat form of 1,4-dioxane (30.1 kJ mol-1) [27]. The dipole moment of the conformer is found to be 3.25 D, though that of the boat conformation and methanol are found to be 1.75 and 1.69 D. On optimization, the Dx-M structures suffer change in the structure of Dx, which can be visualized from the –O-C-C-O dihedral angle of Dx. Considering the dihedral angle of O-CC-O of boat form and twisted boat form as 0 and 60° respectively, the extent of twisting of the boat form in 3a is found to be 55 %. The trapping of the methanolic –O-H by the ethereal O atom of Dx can give an insight to the preferential solvation and type of interaction involved in the solvatochromism of different substrates in binary mixture of different extent of polarity. In a recent work Panigrahi et al. have proposed a similar orientation of Dx and methanol in Dx-M binary solvents involved in the preferential solvation of a styryl pyridinium dye (Fig. 4) [12]. The next higher energetic Dx-M, 3b, is due to optimization of one SPES from those of 15 conformers, and has an energy difference of 0.98 kJ mol-1 from 3a with a dipole moment value of 3.57 D. The structure of the Dx-M complex, 3b, is found to be almost the same with that of 3a with slight variation in the orientation of methanol (dihedral angles HO-C-C of methanol being 3a: 56. 1 and 3b: 52.6°). With almost similar energy with 3b, another optimized structure 3c, derived from one SPES has a significantly different dipole moment (1.63D). The Dx-M complex (3c) is due to one ODx…H-O (1.886 Å), and two OM…H-CD (2.724 and 2.770 Å) bonds generating two six-membered cycles. The Dx-M complex is found to have a complete twisted-boat conformation. The HOMO-LUMO gap of 3c is the highest among all the structures derived from boat form. On optimization, two SPESs with wide difference in dipole moment and energy converged to one structure of Dx-M complex (3d). The Dx assumes a twisted boat conformation and there is only one OM…H-CDx bond with a distance of
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Table 2 SPES energies, optimized energies, dipole moment (μ) of 15 Dxboat –methanol complexes by HF and DFT method, the HOMO and LUMO energy difference and the binding energy calculated by DFT method for the fifteen different conformers Sl. No.
μ in debye (D)
ΔE kJ mol-1
ΔE (LUMO-HOMO) kJ mol-1
BE in kj mol-1
SPES
HF/ 6–31g*
DFT/ 6–31g*
SPES
hf/6–31g*
dft/6–31g*
1
38.2
0.1
0.0
1.87
3.30
3.25
793.51
38.86
2 3 4 5 6 7 8 9 10 11 12 13 14 15
1.0 2.4 9.5 1.1 0.0 5.3 11.1 7.6 10.6 7.6 4.6 9.2 3.9 2.9
1.3 0.3 0.0 0.0 0.9 0.9 1.2 2.2 1.1 1.8 1.8 13.9 0.9 19.0
1.0 1.1 1.7 1.7 2.1 2.1 2.1 2.1 3.4 3.6 3.6 18.3 21.6 27.5
2.75 3.60 3.54 0.27 3.36 2.50 1.76 3.28 2.41 2.10 2.66 3.29 1.94 3.21
3.77 2.03 2.03 2.03 3.20 3.22 3.22 3.22 2.47 1.35 1.35 3.35 3.23 1.86
3.57 1.63 1.92 1.92 2.90 2.90 2.90 2.90 2.33 0.90 0.88 2.96 1.60 1.76
788.67 859.48 843.89 843.91 823.88 823.99 823.78 824.46 813.12 827.03 827.11 779.46 763.73 834.44
37.72 37.89 37.17 37.17 36.77 36.77 36.77 36.76 35.24 35.24 35.48 20.53 17.28 11.40
2.600 Å. Another higher energetic Dx-M complex 3e, with a more significant difference in the dipole moment than that of 3d, is a convergent of four SPESs. In this structure the methanol –Ois found to be linked to two adjacent H of Dx unit having interatomic distances of 2.816and 2.738 Å. The –O-H—ODx hydrogen bond distance is 1.909 Å. The hydrogen bonds form two fused five membered rings which may contribute to the higher energy of the structure. Another optimized structure 3f has almost similar energy and dipole moment with that of 3e but with a sidedness in the orientation of Dx and M. In this structure, including one O-H…ODx hydrogen bonding, there is only one OM..H-CDx- with a bond distance of 2.612 Å. Structure 3g is a convergent of two SPESs with a higher energy of 3.6 kJ mol-1 than that of 3a. Its dipole moment (0.88–0.89 D) is found to be the minimum in the series. The Dx-M complex has one O-H… ODx (1.896 Å) and one OM…H-CDx (2.657 Å) bond. The polarity of the complex is neutralized due to the specific orientation of the methanol group on a partial twisted-boat form, the extent of twist being 73 %. Highly energetic three optimized structures 3h-j were derived from three different SPEs. In these structures the hydrogen of methanolic O-H group is not involved in the bonding interaction. The –OM- is close to three hydrogens of Dx within a distance of 3 Å in 3h and 3i, while in 3j there is no bonding interaction with the methanolic O-H and Dx. In the later structure, a hydrogen bond of ODx–H-CM is observed with a distance of 2.868 Å. The Dx units are also found to be partially twisted. In the Dx–M complex, there is almost no change in the interatomic bond distances in Dx nucleus, while there is a significant change in the dihedral angels due to change in the
conformation of the ring. In the lowest energy structure the change in dihedral angle was found to be 34.227° compared to the single Dx molecule in boat form. Among all the local minima, conformer 3a is the most stable one having energy 1.0, 1.1, 1.7, 2.1, 3.4, 3.6, 18.3, 21.5, and 27.5 kJ mol-1 less than the conformers (3b), (3c), (3d), (3e), (3f), (3 g), (3 h), (3i), and (3j) respectively.
Dx–methanol system in twisted-boat form In twisted boat form Dx is 29.2 kJ mol-1 higher in energy than the chair form and 6.0 kJ mol-1 less energetic than the boat form. Around the twisted boat conformer of Dx, 15 methanol molecules could be accommodated within a radius of 7.5 Å. The single point energy of each Dx-M complex was calculated and was found to be within the range of 22.3 kJ mol-1 with dipole moment variation of 0.50 D (Table 3). On optimization of the concerned SPESs the methanol and Dx molecules suffer orientational changes leading to the formation of some stable Dx-M complexes with different conformations. Out of these conformations, the most stable conformation, 5a having a dipole moment 1.62 D, is a convergent of two SPESs having energy difference of 11.4 kJ mol-1. The orientation of methanol and Dx in the Dx-M complex leads to generate three hydrogen bonds, one O-H…O bond with distance 1.887 Å and two O…H-C bonds having distance 2.774 Å and 2.737 Å in structure 5a. The methyl group was found to remain away from the methylene groups of Dx. The next higher energetic conformer 5b has 0.6 kJ mol-1 higher energy than 5a, and was derived from the
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Fig. 3 Schematic presentation of energy profile of Dx-M system in boat form
convergence of five SPESs with an energy difference of 2.88 kJ mol-1 and the dipole moment range 1.87–2.03 D. 5b has a dipole
O
O
O
O
H O
H3 C
O
CH3
O
H3C
O
O O
O H O
CH3 H3 C
H
H O
O
H
O H
O O
CH3
O
Fig. 4 Schematic representation of orientation of the solvent molecules around the probe in the binary mixture of methanol and Dx
moment 1.92 D, and two O…H bonds having distances of 1.891 and 2.599 Å. The conformers 5c and 5d have the same energy minima but with different dipole moments, e.g., 2.07 and 2.34 D respectively. The two structures involve a sidewise interaction of methanol with Dx through two bonds, which consists of one OH…O bond having distance 1.908 Å and one C-H…O bond with distance 2.611 Å. Conformer 5e refers to the local minima having 14.4 kJ mol-1 higher than that of 5c and dipole moment 1.78 D. In this conformer methanol interacts with Dx through one O…. H-C bond of distance 2.479 Å and one C-HM…O bond of distance 2.711 Å. Conformer 5f has a dipole moment value of 1.62 D and has 1.6 kJ mol-1 more energy than 5e. There exist three C-H…O bonds of distance 2.582, 2.853, and 2.571 Å respectively in conformer 5g and has 2.9 kJ mol-1 more energy than 5f with a dipole moment of 2.41 D. This conformation has a symmetrical arrangement of methanol and Dx, where methanol
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Table 3 SPES energies, optimized energies, dipole moment (μ) of 15 Dxtwist-boat–methanol complexes by HF and DFT method, the HOMO and LUMO energy difference and the binding energy calculated by DFT method for the fifteen different conformers Sl. No.
μ in debye (D)
ΔE kJ mol-1
ΔE (LUMO-HOMO) kJ mol-1
BE in kJ mol-1
SPES
hf/ 6–31g*
dft/ 6–31g*
SPES
hf/6–31g*
dft/6–31g*
1
22.3
0.0
0.0
1.97
2.03
1.62
860.43
31.73
2 3 4 5 6 7 8 9 10 11 12 13 14 15
10.9 5.9 4.6 4.7 5.4 7.5 0.0 1.6 3.0 2.5 1.5 6.8 12.0 8.7
0.0 0.0 0.0 0.0 0.0 0.0 1.15 1.15 1.15 1.15 1.1 12.5 15.4 14.6
0.0 0.6 0.6 0.6 0.6 0.6 2.1 2.1 2.1 2.1 2.2 16.5 18.1 21.0
1.73 2.03 1.94 1.93 1.96 1.87 1.87 2.05 1.99 1.82 2.13 1.64 1.96 1.94
2.03 2.03 2.03 2.03 2.03 2.03 2.12 2.12 2.12 2.12 2.51 2.00 1.82 2.44
1.62 1.92 1.92 1.92 1.92 1.92 2.07 2.07 2.07 2.07 2.34 1.78 1.62 2.41
860.40 843.99 843.99 843.99 843.99 843.99 827.90 827.90 827.98 827.82 813.22 791.22 769.06 762.05
31.73 31.18 31.18 31.18 31.18 31.18 29.65 29.65 29.65 29.65 29.48 15.24 13.60 10.69
forms two nearly symmetrical bonds with distances 2.704 and 2.688 Å. Upon interaction with methanol, no significant change has been observed in the structure of Dx. Among the seven conformers the conformer (a) is the most stable conformation having energy 0.6, 2.1, 2.2, 16.5, 18.1, and 21.0 kJ mol-1 less than conformers (b), (c), (d), (e), (f), and (g) respectively. Though, through VEGAZZ program some specific SPESs were generated for Dx-M system, there are an infinite number of possible SPESs within the intermolecular distance of 7.5 Å. For each conformations of Dx, some more arbitrary structures were generated by changing the position and orientation of methanol and the Dx-M structures were optimized by using HF and subsequently DFT with basis set 6–31g*. However, all the structures converged to the local minima presented in Figs. 2, 3, and 5.
Conclusions Structurally, Dx and methanol have different groups of hydrogen bond donating and accepting abilities, and hence, they can form a large number of one to one structural
complexes. Considering three specific conformations (chair, boat, and twisted boat) of Dx, methanol can have an infinite number of orientations around Dx with an intermolecular distance of 7.5 Å to form a Dx-methanol complex. On optimization for energy minima of heat of formation, 46 conformations of Dx-methanol complex have been selected by using VEGAZZ. From these conformations 23 local minima having –O…H-C and –O-H—O hydrogen bonds were obtained. The global minima corresponds to a structure where the hydroxyl group of methanol is completely involved in the hydrogen bonding with –Oand –C-H of Dx with a binding energy of 38.64 kJ mol1 . The contribution of nonconventional hydrogen bonding, i.e., –C-H…O in the formation of Dx-methanol is found to be significant. The local minima which are derived from the convergence of stationary structures of Dx-methanol complex, may have similarity with the misfolding of protein, where the inter conversion needs a high energetic transition state and the structure with global minima may be considered as the native structure of the protein. Further, the existence of structure with local minima may be conceived in conducive environment or in the preferential solvation of solutes by Dx and methanol.
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Fig. 5 Schematic presentation of energy profile of Dx-M system in twist-boat form
Supporting information Additional details for the solvation models, conformation of the complexes, statistical correlation are presented as supplementary materials.
Acknowledgments B.K.M. thanks University Grants Commission and Council of Scientific and Industrial Research,New Delhi, for financial assistance through BSR-Faculty Fellowship and a Research Project respectively. S.S. thanks the Department of Science and Technology, New Delhi, for Innovation of Science Pursuit for Inspire Research (INSPIRE) research fellowship.
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