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Prediction of the handedness of the domains of monolayers of d -N-palmitoyl aspartic acid: Integrated molecular orbital and molecular mechanics based calculation
Colloids and Surfaces A: Physicochem. Eng. Aspects 282–283 (2006) 222–226
Prediction of the handedness of the domains of monolayers of d-N-palmitoyl aspartic acid: Integrated molecular orbital and molecular mechanics based calculation K. Thirumoorthy a , N. Nandi a,∗ , D. Vollhardt b,∗ a
Chemistry Department, Birla Institute of Technology and Science, Pilani, Rajasthan 333031, India b Max Planck Institute of Colloids and Interfaces, D-14424, Potsdam/Golm, Germany
Received 23 September 2005; received in revised form 19 October 2005; accepted 21 October 2005 Available online 7 December 2005 Dedicated to Professor Ivan B. Ivanov (LCPE, University of Sofia) on the occasion of his 70th birthday.
Abstract The condensed phase monolayer domain forms interesting curvature due to chirality of the molecule. The handedness of d-N-palmitoyl aspartic acid is studied using the three-layered ONIOM (MO:MO:MM) model. Optimized structures of a pair of molecules are used to calculate the azimuthal projection of the molecular pairs. The pair of molecules shows a distinct minimum at the mutual azimuthal orientation corresponding to the lefthandedness at the optimized separation. The other handedness is completely unfavorable. This is in nice agreement with the experimental data that d-enantiomer gives rise to left-handedness of the domains. Mutual large tilt between the molecules is also unfavored which is in agreement with the concept that molecules should not have large mutual tilt at the condensed phase. The energy surface gradually becomes flattened with increasing intermolecular separation. This is in agreement with the common wisdom that chirality induced effects decreases with increasing intermolecular separation. Present hybrid method based study reveals that the molecular chirality of the amphiphile can dictate the domain morphology in the condensed phase and is in agreement with experimental data and previous theoretical results based on effective pair potential theory and mechanics calculations. © 2005 Elsevier B.V. All rights reserved. Keywords: Chirality of amphiphiles; Condensed-phase monolayers; Palmitoyl aspartic acid
1. Introduction Chirality plays a major role in the structure and function of important biomolecules like proteins, nucleic acid and bilayer. The chirality of the basic subunit like amino acid, sugar and lipid are specific for the naturally occurring biomolecules. Limited knowledge is available why nature is so specific about the chirality because the energy difference between two enantiomers is negligibly small. However, recent theoretical and experimental studies in biomimetic systems shows that there is a direct correlation between the chirality of the molecule and chirality of the higher level aggregate formed by the corresponding molecule
∗
Corresponding authors. Fax: +49 331 567 9202. E-mail addresses: [email protected] (N. Nandi), [email protected] (D. Vollhardt). 0927-7757/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2005.10.086
[1–5]. Monolayers are important two-dimensional biomimetic systems, which provided insight into how molecular interactions leads to the aggregation and structure of higher-level structure. Now it is known that electrostatic interaction, line tension around the aggregate structure and the molecular chirality plays a decisive role in determining the aggregate shape [6,7]. Recent studies showed that how the study of molecular interactions can lead to the understanding the domain shapes and lead to correlation of the microscopic and mesoscopic structural features, which are often of varied nature [8,9]. The handedness of the domains composed of N-palmitoyl aspartic acid has been studied in detail by experiment as well as by theory. The theoretical calculations were performed at various degrees of consideration of molecular details, ranging from effective sphere, coarse grained to atomistic model based on molecular mechanics calculation [10–13]. All studies indicated that molecular chirality of d-enantiomer of N-palmitoyl aspartic
K. Thirumoorthy et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 282–283 (2006) 222–226
acid drives the formation of domain of left-handedness while the opposite enantiomer results in developing right-handedness. It is also shown that the results are not dependent on the choice of parameter or molecular model considered. However, consideration of molecular chiral structure in detail (such as coarse grained or atomistic model) helps to reveal the chirality related effects better than less coarse-grained models (such as equivalent sphere model). Additionally, electronic structure methods gives better estimate of the interactions due to limited use of parameters compared to molecular mechanics method. One reason for use of molecular mechanics is the size of the system, which is rather large. However, it is possible to use combined quantum mechanical and molecular mechanical calculations and is proved to be useful for large systems. The combined quantum mechanical/molecular mechanical approach has recently received attention as applied to larger systems [14,15]. Optimization of macromolecule system is relatively faster in the multilevel hybrid method that includes quantum and molecular mechanics such as multilayered ONIOM model (abbreviation of the title “our n-layered integrated molecular orbital and molecular mechanics” as used by the developers) [16–19]. The major approximations in theoretical treatments of large systems are two-fold: use of smaller models and use of lower level of calculation. Small models exclude the electronic and steric effects from the remaining part of large molecule and lower level calculation excludes correlation effects. Thus, in a three-layered ONIOM model, the energy of a large system calculated using theory at high level with its real structure (High level, Real system) is approximated energy as E(High level, Real system) = E(High level, Small model) +E(High level, Intermediate model ← Small model) +E(High level, Real system ← Intermediate model) (1) Here, E (High level, Intermediate model ← Small model) and E (High level, Real ← Intermediate model) accounts for the differences in energy due to small model and intermediate model with that of the real model. In ONIOM scheme, these two quantities are approximated as: E(High level, Intermediate model ← Small model) ≈ E(Medium level, Intermediate model ← Small model)
223
← Small model) + E(Low level, Real system ← Intermediate model)
(2)
Eq. (2) can be explicitly written as, E(High level, Real system) = E(High level, Small model) +E(Medium level, Intermediate model) +E(Low level, Real system) −E(Medium level, Small model) −E(Low level, Intermediate model)
(3)
The most important step is to correctly partition the system. The molecular segments involved in the major important interactions of interest should be treated at high level while the molecular segments with minor interactions are to be treated at low level. In the present work, the handedness is expected to be driven by the chirality of the molecule. Also, the electrostatic interactions involved in the hydrogen bonding groups and groups with partial charges in head group region is expected to be important in determining the mutual molecular azimuthal orientation. Hence, the groups directly participating in the interaction to be treated at higher level and groups attached to these segments can be treated at intermediate level. The alkyl chain is far located from the chiral center and does not bear significant partial charge to be involved in long-range electrostatic interaction. Hence, such a segment can be treated at lower level. Since the focus of the present work on the molecular chirality which is responsible for driving the aggregate morphology, the spatial arrangements of the atoms far away from chiral center (for example, atoms in the long alkyl chains) has less importance in driving the morphology than the atoms in close proximity of the chiral center (for example, the sugar ring) and a multilayered model is suitable where the molecular segments away from chiral center (for example, alkyl chains) can be treated using lower level methods because the conformational states of these segments are well known. We used ONIOM model to study the handedness of d-N-palmitoyl aspartic acid in the present theoretical calculation. The present work shows that the favorable molecular interaction depends on mutual azimuthal orientation, tilt and mutual separation of the molecular pair and one can successfully predict the handedness using ONIOM model which is in nice agreement with experimental result and theoretical calculation. The theoretical calculation is presented in the next section followed by discussions.
E(High level, Real system ← Intermediate model) ≈ E(Low level, Real system ← Intermediate model) Assuming that the approximations give correct energy differences, Eq. (1) can be rewritten as E(High level, Real system) = E(High level, Small model) +E(Medium level, Intermediate model
2. Theoretical calculation The aspartic acid and palmitic acid are optimized separately at the level of ab-initio Hartree Fock theory with 6-31G** basis set (HF/6-31G**). We compared the optimized structure of aspartic acid of with the corresponding crystal structure. To the best of our knowledge, no crystallographic structure is available for d- or l-palmitoyl aspartic acid and the crystal structure of laspartic acid is only available [20]. However, the handedness of
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Fig. 1. (a) The representative molecular structure of d-N-palmitoyl aspartic acid. (b) The molecular arrangement of d-N-palmitoyl aspartic acid at the air–water interface.
d-amino acid is calculated in the previous studies [10–13]. We optimized both l- and d-aspartic acid and compared with the crystal structure and among themselves. The individual energy minimized structures are used to generate the d-enantiomer of N-palmitoyl aspartic acid. The structure of N-palmitoyl aspartic acid is shown in Fig. 1. The palmitoyl aspartic acid generated by combining the palmitic acid and aspartic acid is further subjected for energy minimization with the hybrid method. The three-layered ONIOM (MO:MO:MM) method is used for the optimization. The ab-initio level theory (HF/3-21G**) is applied to the atoms of the head group region involved in hydrogen bonding (O1 , O2 , O3 , O4 , O5 , N10 , H13 , H17 , H18 ) in the head group region. The semi-empirical level theory (PM3) [21] is used to atoms of the head group region, which are not involving in the hydrogen bonding (C6 , C7 , C8 , C9 , C11 , C12 , H14 , H15 , H16 , H19 , H20 ). The low level molecular mechanical theory (UFF) is applied for the alkyl chain part [22]. A pair of d-N-palmitoyl aspartic acid at their individual optimized state structure is used to calculate the energy as a function of mutual azimuthal angle, tilt and intermolecular separation. Keeping one molecule as reference, the second molecule of the pair is oriented at different azimuthal and tilt orientation. First, the optimum distance between the molecules in the double pair is calculated. Keeping the molecule at the optimum separation, the mutual tilt and mutual azimuthal angles of the pair are varied and corresponding energies are calculated.
Projections of the azimuthal direction of any reference molecule and its neighboring second molecule (arranged progressively away from eye) will determine the handedness of the amphiphiles in the domain. The magnitude of the mutual azimuthal angle is not sufficient for describing the handedness because the same magnitude of the mutual azimuthal angle (␦␣) can exist for the right handed oriented pair of molecules as well as the left handed oriented pair of molecules. Hence, we used a convention that the right handed oriented pair of molecules are represented by positive range of 0◦ to +360◦ orientations and the left handed oriented pair of molecules represented by negative range of 0◦ to −360◦ orientations. Note that the generality of the calculation is independent of the convention used. All calculations are performed using the Gaussian suite of programs [23]. The results are presented in the next section. 3. Results and discussion The structures of l- and d-aspartic acid generated by the ab-initio method and the crystal structure of l-aspartic acid is compared in Table 1. The comparison indicates that the crystal structure compares well with the HF/6-31G** level structure and l- and d-isomers are mirror images of each other. In all cases azimuthal angles of both molecules in the pair are calculated and handedness is concluded from the change in azimuth variation of the second molecule with reference to the first or reference molecule. Large tilt variations between neighboring
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Table 1 Comparison of structural parameters of l- and d-aspartic acid generated at HF/6-31G** and crystal structure of l-aspartic acid Structural parameters Bond length C5 · · · O1 C5 · · · O2 C8 O3 C8 O4 C6 C5 C7 C6 C8 C7 C6 N9 O4 H10 C7 H11 C7 H12 N9 H13 N9 H14 N9 H15 C6 H16 Bond angle O1 C5 O2 O1 C5 C6 O2 C5 C6 C5 C6 N9 N9 C6 C7 C6 C7 H11 C6 C7 H12 H11 C7 C8 H12 C7 C8 C7 C8 O3 C7 C8 O4 O3 C8 O4 C6 N9 H14 C6 N9 H15 H14 N9 H13 H13 N9 H15 C5 C6 C7 C6 C7 C8
HF/6-31G** level d-aspartic acid ˚ 1.239 A ˚ 1.209 A ˚ 1.195 A ˚ 1.317 A ˚ 1.571 A ˚ 1.514 A ˚ 1.505 A ˚ 1.499 A ˚ 0.949 A ˚ 1.088 A ˚ 1.081 A ˚ 1.005 A ˚ 1.039 A ˚ 1.004 A ˚ 1.083 A 133.4◦ 111.7◦ 114.9◦ 104.7◦ 113.2◦ 111.5◦ 108.2◦ 107.9◦ 110.6◦ 124.3◦ 113.0◦ 122.7◦ 99.8◦ 113.3◦ 107.6◦ 107.9◦ 114.2◦ 112.8◦
molecules (large mutual tilt) are not allowed in the condensed phase domain of Langmuir monolayers and only a small range of mutual tilt variation is relevant to investigate the intermolecular energy profile. All configurations of molecular pairs are generated for mutual tilt variation in the range of 0–15◦ . The plots ´˚ separation (optimum separation between a pair) generated at 5 A are shown in Fig. 2. A deep minimum is observed at low mutual tilt within the negative range of mutual orientation. According to the convention described in Section 2, two molecules of palmitoyl aspartic acid exhibit left-handedness between neighboring molecules. This is in nice agreement with the experiment and theoretical calculation. Fig. 2 also shows that the mutual interaction is completely unfavorable at the orientations, which leads to right-handedness. This explains why the domain shape is specific about the chirality of the molecule. The energy surface becomes unfavorable gradually with increased mutual tilt between neighboring molecules. It corroborates the fact that large mutual tilt is not favored in the condensed phase. It is well known that the chirality induced effects gradually decay with larger intermolecular separation which can be realized at LE phase or increasing the temperature. In the later
HF/6-31G** level l-aspartic acid ˚ 1.239 A ˚ 1.209 A ˚ 1.197 A ˚ 1.315 A ˚ 1.573 A ˚ 1.525 A ˚ 1.506 A ˚ 1.500 A ˚ 0.949 A ˚ 1.088 A ˚ 1.079 A ˚ 1.004 A ˚ 1.040 A ˚ 1.006 A ˚ 1.080 A 133.4◦ 112.1◦ 114.4◦ 105.0◦ 112.2◦ 110.2◦ 107.7◦ 106.8◦ 110.8◦ 124.1◦ 113.4◦ 122.5◦ 99.9◦ 113.3◦ 107.5◦ 108.2◦ 109.2◦ 114.5◦
Crystal structure of l-aspartic acid ˚ 1.252 A ˚ 1.242 A ˚ 1.202 A ˚ 1.306 A ˚ 1.543 A ˚ 1.518 A ˚ 1.512 A ˚ 1.495 A ˚ 1.036 A ˚ 0.981 A ˚ 0.902 A ˚ 0.879 A ˚ 1.013 A ˚ 1.088 A ˚ 1.027 A 126.4◦ 116.6◦ 117.0◦ 109.3◦ 111.1◦ 103.2◦ 114.3◦ 111.0◦ 106.3◦ 122.1◦ 113.0◦ 124.1◦ 102.6◦ 110.0◦ 118.2◦ 101.1◦ 108.0◦ 115.3◦
Fig. 2. Plot of intermolecular pair potential of same type of d-N-palmitoyl aspar˚ intermolecular separation between the pair molecules based on tic acid at 5 A three layer (MO:MO:MM) ONIOM calculation. See text for detail. Right handed oriented pair of molecules are represented by positive range of 0◦ to +360◦ orientations and left handed oriented pair of molecules represented by negative range of 0◦ to −360◦ orientations. See theoretical calculation for detail.
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Fig. 3. Plot of intermolecular pair potential of same type of d-N-palmitoyl aspar˚ intermolecular separation between the pair molecules based on tic acid at 10 A three layer (MO:MO:MM) ONIOM calculation. See text for detail. Right handed oriented pair of molecules are represented by positive range of 0◦ to +360◦ orientations and left handed oriented pair of molecules represented by negative range of 0◦ to −360◦ orientations. See theoretical calculation for detail.
case, the molecule has more orientational degrees of freedom and essentially the dissymmetry is averaged out by such rota˚ tion. We plotted the energy of a pair at larger separation (10 A) than the optimum intermolecular separation as shown in Fig. 3. The intermolecular energy surface shows no clear minima and only shows lower energy for left-handedness. Hence, no clearly preferred handedness is observed at larger separation, which is in nice agreement with common wisdom that chirality induced effects decrease with distance. It may be noted that the vertical scale of both Figs. 2 and 3 represents the relative energy of the molecular pair at a given mutual azimuthal orientation and mutual tilt for a fixed distance between two chiral centers with respect to the lowest energy of the same pair (later corresponds to a particular mutual azimuthal orientation and mutual tilt). The chiral centers of the molecular pairs are at a separation corresponding to the optimum energy in Fig. 2. Hence, the orientation dependent interaction due to molecular chiral structure is observed in the features of Fig. 2. The orientation dependent interaction due to molecular chiral structure is expected to vanish at larger separation between the chiral centers. This is shown in Fig. 3. As the interaction energy between the pairs is small, the energy of the pair does not change significantly with variation in mutual azimuthal orientation and mutual tilt. Hence, the relative energy in the vertical scale is close to zero. This is expected from the earlier studies and common wisdom [3]. Summarily, we generated palmitic acid and aspartic acid using HF/6-31G** level of theory. The alkyl chain is in all-trans state and the aspartic acid is in good agreement with the crystal data. The combined d-N-palmitoyl aspartic acid is further optimized using three-layered ONIOM (MO:MO:MM) model
where the first neighbor atoms participating in the hydrogen bonding pattern are subjected to ab-initio level theory (HF/321G**), the atoms which directly do not participate in the hydrogen bonding are subjected to semi-empirical (PM3) level of theory and the alkyl tails are subjected to molecular mechanics calculation. Optimized structures of a pair of molecules are used to calculate the azimuthal projection of the molecular pairs. The pair of molecules shows a distinct minimum at the mutual azimuthal orientation corresponding to the left-handedness at the optimized separation. The other handedness is completely unfavorable. This is in nice agreement with the experimental data that d-enantiomer gives rise to left-handedness of the domains. Mutual large tilt between the molecules is also unfavored which is in agreement with the concept that molecules should not have large mutual tilt at the condensed phase. The energy surface gradually becomes flattened with increasing intermolecular separation. This is in agreement with the common wisdom that chirality induced effects decreases with increasing intermolecular separation. Present hybrid method based study reveals that the molecular chirality of the amphiphile can dictate the domain morphology in the condensed phase and is in agreement with experimental data and previous theoretical results based on effective pair potential theory and mechanics calculations. Acknowledgement This work is partially supported by CSIR, India. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
N. Nandi, D. Vollhardt, Chem. Rev. 103 (2003) 4035. N. Nandi, D. Vollhardt, Thin Solid Films 433 (2003) 12. N. Nandi, D. Vollhardt, G. Brezesinski, J. Phys. Chem. 103 (2003) 4033. N. Nandi, J. Phys. Chem. B 108 (2004) 789. K. Thirumoorthy, N. Nandi, Chem. Phys. Lett. 414 (2005) 336. H.M. McConnell, Annu. Rev. Phys. Chem. 42 (1991) 171. H. M¨ohwald, Annu. Rev. Phys. Chem. 41 (1990) 441. N. Nandi, D. Vollhardt, J. Phys. Chem. B 108 (2004) 18793. K. Thirumoorthy, N. Nandi, D. Vollhardt, J. Phys. Chem. B 109 (2005) 10820. N. Nandi, D. Vollhardt, Colloids Surf. A 183–185 (2001) 67. N. Nandi, D. Vollhardt, Colloids Surf. A 198–200 (2002) 207. N. Nandi, D. Vollhardt, J. Phys. Chem. B 107 (2003) 3464. N. Nandi, D. Vollhardt, R. Rudert, Colloids Surf. A 250 (2004) 279. J. Gao, Acc. Chem. Res. 29 (1996) 298. D.G. Truhlar, J. Gao, C. Alhambra, M. Garcia-Vilosa, J. Corchado, M.L. Sanchez, J. Villa, Acc. Chem. Res. 35 (2002) 341. F. Maseras, K. Morokuma, J. Comp. Chem. 16 (1995) 1170. S. Humbel, S. Sieber, K. Morokuma, J. Chem. Phys. 16 (1996) 1959. M. Svensson, S. Humbel, R.D.J. Froese, T. Matsubara, S. Sieber, K. Morokuma, J. Phys. Chem. 100 (1996) 19357. T. Vreven, K. Morokuma, J. Comp. Chem. 21 (2000) 1419. J.L. Derissen, H.J. Endeman, A.F. Peerdeman, Acta Cryst. B24 (1968) 1349. J.J.P. Stewart, J. Comp. Chem. 10 (1989) 209. A.K. Rappe, C.J. Casewit, K.S. Colwell, W.A. Goddard, W.M. Skiff, J. Am. Chem. Soc. 114 (1992) 10025. M.J. Frisch, et al., Gaussian 03, Revision C.02, Gaussian, Inc., Wallingford CT, 2004.
Prediction of the handedness of the domains of monolayers of d-N-palmitoyl aspartic acid: Integrated molecular orbital and molecular mechanics based calculation K. Thirumoorthy a , N. Nandi a,∗ , D. Vollhardt b,∗ a
Chemistry Department, Birla Institute of Technology and Science, Pilani, Rajasthan 333031, India b Max Planck Institute of Colloids and Interfaces, D-14424, Potsdam/Golm, Germany
Received 23 September 2005; received in revised form 19 October 2005; accepted 21 October 2005 Available online 7 December 2005 Dedicated to Professor Ivan B. Ivanov (LCPE, University of Sofia) on the occasion of his 70th birthday.
Abstract The condensed phase monolayer domain forms interesting curvature due to chirality of the molecule. The handedness of d-N-palmitoyl aspartic acid is studied using the three-layered ONIOM (MO:MO:MM) model. Optimized structures of a pair of molecules are used to calculate the azimuthal projection of the molecular pairs. The pair of molecules shows a distinct minimum at the mutual azimuthal orientation corresponding to the lefthandedness at the optimized separation. The other handedness is completely unfavorable. This is in nice agreement with the experimental data that d-enantiomer gives rise to left-handedness of the domains. Mutual large tilt between the molecules is also unfavored which is in agreement with the concept that molecules should not have large mutual tilt at the condensed phase. The energy surface gradually becomes flattened with increasing intermolecular separation. This is in agreement with the common wisdom that chirality induced effects decreases with increasing intermolecular separation. Present hybrid method based study reveals that the molecular chirality of the amphiphile can dictate the domain morphology in the condensed phase and is in agreement with experimental data and previous theoretical results based on effective pair potential theory and mechanics calculations. © 2005 Elsevier B.V. All rights reserved. Keywords: Chirality of amphiphiles; Condensed-phase monolayers; Palmitoyl aspartic acid
1. Introduction Chirality plays a major role in the structure and function of important biomolecules like proteins, nucleic acid and bilayer. The chirality of the basic subunit like amino acid, sugar and lipid are specific for the naturally occurring biomolecules. Limited knowledge is available why nature is so specific about the chirality because the energy difference between two enantiomers is negligibly small. However, recent theoretical and experimental studies in biomimetic systems shows that there is a direct correlation between the chirality of the molecule and chirality of the higher level aggregate formed by the corresponding molecule
∗
Corresponding authors. Fax: +49 331 567 9202. E-mail addresses: [email protected] (N. Nandi), [email protected] (D. Vollhardt). 0927-7757/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2005.10.086
[1–5]. Monolayers are important two-dimensional biomimetic systems, which provided insight into how molecular interactions leads to the aggregation and structure of higher-level structure. Now it is known that electrostatic interaction, line tension around the aggregate structure and the molecular chirality plays a decisive role in determining the aggregate shape [6,7]. Recent studies showed that how the study of molecular interactions can lead to the understanding the domain shapes and lead to correlation of the microscopic and mesoscopic structural features, which are often of varied nature [8,9]. The handedness of the domains composed of N-palmitoyl aspartic acid has been studied in detail by experiment as well as by theory. The theoretical calculations were performed at various degrees of consideration of molecular details, ranging from effective sphere, coarse grained to atomistic model based on molecular mechanics calculation [10–13]. All studies indicated that molecular chirality of d-enantiomer of N-palmitoyl aspartic
K. Thirumoorthy et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 282–283 (2006) 222–226
acid drives the formation of domain of left-handedness while the opposite enantiomer results in developing right-handedness. It is also shown that the results are not dependent on the choice of parameter or molecular model considered. However, consideration of molecular chiral structure in detail (such as coarse grained or atomistic model) helps to reveal the chirality related effects better than less coarse-grained models (such as equivalent sphere model). Additionally, electronic structure methods gives better estimate of the interactions due to limited use of parameters compared to molecular mechanics method. One reason for use of molecular mechanics is the size of the system, which is rather large. However, it is possible to use combined quantum mechanical and molecular mechanical calculations and is proved to be useful for large systems. The combined quantum mechanical/molecular mechanical approach has recently received attention as applied to larger systems [14,15]. Optimization of macromolecule system is relatively faster in the multilevel hybrid method that includes quantum and molecular mechanics such as multilayered ONIOM model (abbreviation of the title “our n-layered integrated molecular orbital and molecular mechanics” as used by the developers) [16–19]. The major approximations in theoretical treatments of large systems are two-fold: use of smaller models and use of lower level of calculation. Small models exclude the electronic and steric effects from the remaining part of large molecule and lower level calculation excludes correlation effects. Thus, in a three-layered ONIOM model, the energy of a large system calculated using theory at high level with its real structure (High level, Real system) is approximated energy as E(High level, Real system) = E(High level, Small model) +E(High level, Intermediate model ← Small model) +E(High level, Real system ← Intermediate model) (1) Here, E (High level, Intermediate model ← Small model) and E (High level, Real ← Intermediate model) accounts for the differences in energy due to small model and intermediate model with that of the real model. In ONIOM scheme, these two quantities are approximated as: E(High level, Intermediate model ← Small model) ≈ E(Medium level, Intermediate model ← Small model)
223
← Small model) + E(Low level, Real system ← Intermediate model)
(2)
Eq. (2) can be explicitly written as, E(High level, Real system) = E(High level, Small model) +E(Medium level, Intermediate model) +E(Low level, Real system) −E(Medium level, Small model) −E(Low level, Intermediate model)
(3)
The most important step is to correctly partition the system. The molecular segments involved in the major important interactions of interest should be treated at high level while the molecular segments with minor interactions are to be treated at low level. In the present work, the handedness is expected to be driven by the chirality of the molecule. Also, the electrostatic interactions involved in the hydrogen bonding groups and groups with partial charges in head group region is expected to be important in determining the mutual molecular azimuthal orientation. Hence, the groups directly participating in the interaction to be treated at higher level and groups attached to these segments can be treated at intermediate level. The alkyl chain is far located from the chiral center and does not bear significant partial charge to be involved in long-range electrostatic interaction. Hence, such a segment can be treated at lower level. Since the focus of the present work on the molecular chirality which is responsible for driving the aggregate morphology, the spatial arrangements of the atoms far away from chiral center (for example, atoms in the long alkyl chains) has less importance in driving the morphology than the atoms in close proximity of the chiral center (for example, the sugar ring) and a multilayered model is suitable where the molecular segments away from chiral center (for example, alkyl chains) can be treated using lower level methods because the conformational states of these segments are well known. We used ONIOM model to study the handedness of d-N-palmitoyl aspartic acid in the present theoretical calculation. The present work shows that the favorable molecular interaction depends on mutual azimuthal orientation, tilt and mutual separation of the molecular pair and one can successfully predict the handedness using ONIOM model which is in nice agreement with experimental result and theoretical calculation. The theoretical calculation is presented in the next section followed by discussions.
E(High level, Real system ← Intermediate model) ≈ E(Low level, Real system ← Intermediate model) Assuming that the approximations give correct energy differences, Eq. (1) can be rewritten as E(High level, Real system) = E(High level, Small model) +E(Medium level, Intermediate model
2. Theoretical calculation The aspartic acid and palmitic acid are optimized separately at the level of ab-initio Hartree Fock theory with 6-31G** basis set (HF/6-31G**). We compared the optimized structure of aspartic acid of with the corresponding crystal structure. To the best of our knowledge, no crystallographic structure is available for d- or l-palmitoyl aspartic acid and the crystal structure of laspartic acid is only available [20]. However, the handedness of
224
K. Thirumoorthy et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 282–283 (2006) 222–226
Fig. 1. (a) The representative molecular structure of d-N-palmitoyl aspartic acid. (b) The molecular arrangement of d-N-palmitoyl aspartic acid at the air–water interface.
d-amino acid is calculated in the previous studies [10–13]. We optimized both l- and d-aspartic acid and compared with the crystal structure and among themselves. The individual energy minimized structures are used to generate the d-enantiomer of N-palmitoyl aspartic acid. The structure of N-palmitoyl aspartic acid is shown in Fig. 1. The palmitoyl aspartic acid generated by combining the palmitic acid and aspartic acid is further subjected for energy minimization with the hybrid method. The three-layered ONIOM (MO:MO:MM) method is used for the optimization. The ab-initio level theory (HF/3-21G**) is applied to the atoms of the head group region involved in hydrogen bonding (O1 , O2 , O3 , O4 , O5 , N10 , H13 , H17 , H18 ) in the head group region. The semi-empirical level theory (PM3) [21] is used to atoms of the head group region, which are not involving in the hydrogen bonding (C6 , C7 , C8 , C9 , C11 , C12 , H14 , H15 , H16 , H19 , H20 ). The low level molecular mechanical theory (UFF) is applied for the alkyl chain part [22]. A pair of d-N-palmitoyl aspartic acid at their individual optimized state structure is used to calculate the energy as a function of mutual azimuthal angle, tilt and intermolecular separation. Keeping one molecule as reference, the second molecule of the pair is oriented at different azimuthal and tilt orientation. First, the optimum distance between the molecules in the double pair is calculated. Keeping the molecule at the optimum separation, the mutual tilt and mutual azimuthal angles of the pair are varied and corresponding energies are calculated.
Projections of the azimuthal direction of any reference molecule and its neighboring second molecule (arranged progressively away from eye) will determine the handedness of the amphiphiles in the domain. The magnitude of the mutual azimuthal angle is not sufficient for describing the handedness because the same magnitude of the mutual azimuthal angle (␦␣) can exist for the right handed oriented pair of molecules as well as the left handed oriented pair of molecules. Hence, we used a convention that the right handed oriented pair of molecules are represented by positive range of 0◦ to +360◦ orientations and the left handed oriented pair of molecules represented by negative range of 0◦ to −360◦ orientations. Note that the generality of the calculation is independent of the convention used. All calculations are performed using the Gaussian suite of programs [23]. The results are presented in the next section. 3. Results and discussion The structures of l- and d-aspartic acid generated by the ab-initio method and the crystal structure of l-aspartic acid is compared in Table 1. The comparison indicates that the crystal structure compares well with the HF/6-31G** level structure and l- and d-isomers are mirror images of each other. In all cases azimuthal angles of both molecules in the pair are calculated and handedness is concluded from the change in azimuth variation of the second molecule with reference to the first or reference molecule. Large tilt variations between neighboring
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Table 1 Comparison of structural parameters of l- and d-aspartic acid generated at HF/6-31G** and crystal structure of l-aspartic acid Structural parameters Bond length C5 · · · O1 C5 · · · O2 C8 O3 C8 O4 C6 C5 C7 C6 C8 C7 C6 N9 O4 H10 C7 H11 C7 H12 N9 H13 N9 H14 N9 H15 C6 H16 Bond angle O1 C5 O2 O1 C5 C6 O2 C5 C6 C5 C6 N9 N9 C6 C7 C6 C7 H11 C6 C7 H12 H11 C7 C8 H12 C7 C8 C7 C8 O3 C7 C8 O4 O3 C8 O4 C6 N9 H14 C6 N9 H15 H14 N9 H13 H13 N9 H15 C5 C6 C7 C6 C7 C8
HF/6-31G** level d-aspartic acid ˚ 1.239 A ˚ 1.209 A ˚ 1.195 A ˚ 1.317 A ˚ 1.571 A ˚ 1.514 A ˚ 1.505 A ˚ 1.499 A ˚ 0.949 A ˚ 1.088 A ˚ 1.081 A ˚ 1.005 A ˚ 1.039 A ˚ 1.004 A ˚ 1.083 A 133.4◦ 111.7◦ 114.9◦ 104.7◦ 113.2◦ 111.5◦ 108.2◦ 107.9◦ 110.6◦ 124.3◦ 113.0◦ 122.7◦ 99.8◦ 113.3◦ 107.6◦ 107.9◦ 114.2◦ 112.8◦
molecules (large mutual tilt) are not allowed in the condensed phase domain of Langmuir monolayers and only a small range of mutual tilt variation is relevant to investigate the intermolecular energy profile. All configurations of molecular pairs are generated for mutual tilt variation in the range of 0–15◦ . The plots ´˚ separation (optimum separation between a pair) generated at 5 A are shown in Fig. 2. A deep minimum is observed at low mutual tilt within the negative range of mutual orientation. According to the convention described in Section 2, two molecules of palmitoyl aspartic acid exhibit left-handedness between neighboring molecules. This is in nice agreement with the experiment and theoretical calculation. Fig. 2 also shows that the mutual interaction is completely unfavorable at the orientations, which leads to right-handedness. This explains why the domain shape is specific about the chirality of the molecule. The energy surface becomes unfavorable gradually with increased mutual tilt between neighboring molecules. It corroborates the fact that large mutual tilt is not favored in the condensed phase. It is well known that the chirality induced effects gradually decay with larger intermolecular separation which can be realized at LE phase or increasing the temperature. In the later
HF/6-31G** level l-aspartic acid ˚ 1.239 A ˚ 1.209 A ˚ 1.197 A ˚ 1.315 A ˚ 1.573 A ˚ 1.525 A ˚ 1.506 A ˚ 1.500 A ˚ 0.949 A ˚ 1.088 A ˚ 1.079 A ˚ 1.004 A ˚ 1.040 A ˚ 1.006 A ˚ 1.080 A 133.4◦ 112.1◦ 114.4◦ 105.0◦ 112.2◦ 110.2◦ 107.7◦ 106.8◦ 110.8◦ 124.1◦ 113.4◦ 122.5◦ 99.9◦ 113.3◦ 107.5◦ 108.2◦ 109.2◦ 114.5◦
Crystal structure of l-aspartic acid ˚ 1.252 A ˚ 1.242 A ˚ 1.202 A ˚ 1.306 A ˚ 1.543 A ˚ 1.518 A ˚ 1.512 A ˚ 1.495 A ˚ 1.036 A ˚ 0.981 A ˚ 0.902 A ˚ 0.879 A ˚ 1.013 A ˚ 1.088 A ˚ 1.027 A 126.4◦ 116.6◦ 117.0◦ 109.3◦ 111.1◦ 103.2◦ 114.3◦ 111.0◦ 106.3◦ 122.1◦ 113.0◦ 124.1◦ 102.6◦ 110.0◦ 118.2◦ 101.1◦ 108.0◦ 115.3◦
Fig. 2. Plot of intermolecular pair potential of same type of d-N-palmitoyl aspar˚ intermolecular separation between the pair molecules based on tic acid at 5 A three layer (MO:MO:MM) ONIOM calculation. See text for detail. Right handed oriented pair of molecules are represented by positive range of 0◦ to +360◦ orientations and left handed oriented pair of molecules represented by negative range of 0◦ to −360◦ orientations. See theoretical calculation for detail.
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Fig. 3. Plot of intermolecular pair potential of same type of d-N-palmitoyl aspar˚ intermolecular separation between the pair molecules based on tic acid at 10 A three layer (MO:MO:MM) ONIOM calculation. See text for detail. Right handed oriented pair of molecules are represented by positive range of 0◦ to +360◦ orientations and left handed oriented pair of molecules represented by negative range of 0◦ to −360◦ orientations. See theoretical calculation for detail.
case, the molecule has more orientational degrees of freedom and essentially the dissymmetry is averaged out by such rota˚ tion. We plotted the energy of a pair at larger separation (10 A) than the optimum intermolecular separation as shown in Fig. 3. The intermolecular energy surface shows no clear minima and only shows lower energy for left-handedness. Hence, no clearly preferred handedness is observed at larger separation, which is in nice agreement with common wisdom that chirality induced effects decrease with distance. It may be noted that the vertical scale of both Figs. 2 and 3 represents the relative energy of the molecular pair at a given mutual azimuthal orientation and mutual tilt for a fixed distance between two chiral centers with respect to the lowest energy of the same pair (later corresponds to a particular mutual azimuthal orientation and mutual tilt). The chiral centers of the molecular pairs are at a separation corresponding to the optimum energy in Fig. 2. Hence, the orientation dependent interaction due to molecular chiral structure is observed in the features of Fig. 2. The orientation dependent interaction due to molecular chiral structure is expected to vanish at larger separation between the chiral centers. This is shown in Fig. 3. As the interaction energy between the pairs is small, the energy of the pair does not change significantly with variation in mutual azimuthal orientation and mutual tilt. Hence, the relative energy in the vertical scale is close to zero. This is expected from the earlier studies and common wisdom [3]. Summarily, we generated palmitic acid and aspartic acid using HF/6-31G** level of theory. The alkyl chain is in all-trans state and the aspartic acid is in good agreement with the crystal data. The combined d-N-palmitoyl aspartic acid is further optimized using three-layered ONIOM (MO:MO:MM) model
where the first neighbor atoms participating in the hydrogen bonding pattern are subjected to ab-initio level theory (HF/321G**), the atoms which directly do not participate in the hydrogen bonding are subjected to semi-empirical (PM3) level of theory and the alkyl tails are subjected to molecular mechanics calculation. Optimized structures of a pair of molecules are used to calculate the azimuthal projection of the molecular pairs. The pair of molecules shows a distinct minimum at the mutual azimuthal orientation corresponding to the left-handedness at the optimized separation. The other handedness is completely unfavorable. This is in nice agreement with the experimental data that d-enantiomer gives rise to left-handedness of the domains. Mutual large tilt between the molecules is also unfavored which is in agreement with the concept that molecules should not have large mutual tilt at the condensed phase. The energy surface gradually becomes flattened with increasing intermolecular separation. This is in agreement with the common wisdom that chirality induced effects decreases with increasing intermolecular separation. Present hybrid method based study reveals that the molecular chirality of the amphiphile can dictate the domain morphology in the condensed phase and is in agreement with experimental data and previous theoretical results based on effective pair potential theory and mechanics calculations. Acknowledgement This work is partially supported by CSIR, India. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
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