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Selective complexation of alkali metal ions and nanotubular cyclopeptides: a DFT study

  • Alireza Najafi Chermahini
  • Mehdi Rezapour
  • Abbas Teimouri
Original Article

Abstract

A density functional theory based on interaction of alkali metal cations (Li+, Na+, K+, Rb+ and Cs+) with cyclic peptides constructed from 3 or 4 alanine molecule (CyAla3 and CyAla4), has been investigated using mixed basis set (C, H, O, Li+, Na+ and K+ using 6-31+G(d), and the heavier cations: Rb+ and Cs+ using LANL2DZ). The minimum energy structures, binding energies, and various thermodynamic parameters of free ligands and their metal cations complexes have been determined with B3LYP and CAM-B3LYP functionals. The order of interaction energies were found to be Li> K> Na> Rb> Cs+ and Li> Na> K≫ Rb> Cs+, calculated at CAM-B3LYP level for the M/CyAla3 and M/CyAla4 complexes, respectively. Their selectivity trend shows that the highest cation selectivity for Li+ over other alkali metal ions has been achieved on the basis of thermodynamic analysis. The main types of driving force host–guest interactions are investigated, the electron-donating O offers lone pair electrons to the contacting LP* of alkali metal cations.

Keywords

Nanotubular cyclic peptides Cation selectivity Host–guest interaction CAM-B3LYP 

Introduction

The cyclic compounds are ordinary in nature and their arrangement and properties have been more concerned by chemists. In recent years, a new interesting class of organic compounds has been reported in which amino acid unites make a macrocycle named cyclic peptide [1, 2, 3, 4, 5, 6, 7, 8, 9]. These species exhibit various biological activities, such as antibacterial [10, 11], antiviral [12], antifungal [13], immunosuppressant [14] and antinociceptive properties [15]. Their amphiphilic characteristics make them to be potential superior candidates of surfactants [16]. Besides, cyclic peptides can self-assemble into peptide nanotubes, as models of biological transmembrane channels [17, 18]. Such surface and biological properties have attracted interest in the structures of cyclic peptides and their behaviors at the hydrophilic/hydrophobic interfaces. The structure and properties of cyclic peptides have been studied and results reported in literature [1, 2, 4, 5, 6, 7, 8, 9, 19, 20, 21, 22]. Theoretical calculations have become a powerful tool for solving the mechanism of selective capture and transportation of alkali metal ions by host molecules such as crown ethers [23, 24, 25, 26, 27]. However, no theoretical investigation has been reported on the selective extraction of metal ions by cyclic peptides. The present work was performed to investigate how the metal’s properties can be used to predict the selective transport and separation of metal ions. Our aim in this paper is to employ density functional theory (DFT) approaches, using pseudo-potentials with polarization functions in the basis set, to investigate the influence of the metal ion’s nature on the metal binding selectivity by CyAla3 and CyAla4 cyclic peptides. The second goal of the study is theoretically prediction of the selective extraction power of cyclic peptides for different metal ions. The results from our study will provide contributions towards the prediction of the applicability of an extractant for different metal ions, the material design of metal ion recognition and other related fields.

Computational methods

The DFT calculations were applied to optimize the structures of cyclic peptides considered in this work. The initial geometries of cyclic peptides were taken from the structures reported by Poteau and Trinquier [7]. Vibrational frequency calculations were also performed to verify that the optimized structures are in the local minimum on the potential energy surface. The optimized structures of cyclic peptides were used for studying the interaction of alkali metal ions based on the DFT/CAM-B3LYP theory. Briefly, CAM-B3LYP combines the features of hybrid functionals such as B3LYP [28, 29, 30, 31, 32] with the long-range corrected functionals of Hirao and colleagues [29]. The exchange functional is considered as a mixture of exact, i.e., Hartree–Fock (HF) and DFT exchange, but, unlike B3LYP, the ratio of exact to DFT exchange varies in different regions of the molecule. The key improvement in this method is that the short-range DFT exchange interaction is incorporated in the short-range DFT exchange functional, but the correct long-range interaction is described via HF exchange. The 6-31+G(d) basis set was used for carbon, nitrogen, hydrogen and oxygen. Metal basis sets used in structure calculations of the complexes were obtained from two sources. The 6-31+G(d) all-electron basis set was chosen for Li+, Na+ and K+. The effective core potential of LANL2DZ was selected for Rb+ and Cs+ metal ions. All calculations were performed with the GAUSSIAN 09 program package [33] without any restriction. In addition, the natural bond orbital (NBO) analysis [34, 35] was carried out on all of the optimized geometries to characterize the second-order interaction energies.

Results and discussion

Geometric structures of crown ethers and their complexes

In the present study two cyclic peptides constructed from 3 or 4 (S) alanine molecules named CyAla3 and CyAla4 and in the cis conformation have been considered. The optimized structures for the cyclic peptides considered in the present investigation in their ground states are shown in Fig. 1.
Fig. 1

The optimized structures of CyAla3 and CyAla4 calculated by the CAM-B3LYP/6–31+G(d) method

The fully relaxed equilibrated geometry of free cyclic peptide molecules are given in Fig. 1. The minimum energy structure was confirmed by the absence of any imaginary frequency in the Hessian matrix. As it can be seen in the optimized structures oxygen atoms are pointed upward from the cyclic peptide rings. The calculated bond lengths of C=O, C–N and N–H bonds in the amide group of CyAla3 found to be 1.232, 1.375 and 1.015 Å, respectively.

The fully relaxed minimum energy structures of the metal ion–cyclic peptide complexes calculated at B3LYP/6-31+G(d) and CAM-B3LYP/6-31+G(d) levels of the theory are given in Fig. 2. As can be seen from Figs. 2 and 3, for the smaller cations like Li+ and Na+, metal cations can fit in cyclic peptide cavity and form stable complex with three nitrogen atoms in Li+/CyAla3 and Na + /CyAla3 complexes. However for larger metal ions (e.g. K+, Rb+ and Cs+) those cations can not lie in the cavity of cyclic peptide and form stable complex with three O atoms of the cyclic peptide backbone where these atoms pointed upward to the metal ion as seen in the case of the free CyAla3 molecule. Similar results observed when calculation repeated with CAM-B3LYP method. The comparison of results of calculated structural parameters of metal complexes in Figs. 2 and 3, indicates that the C=O bond length decreased from 1.232 for the free molecule to 1.203 and 1.209 Å for the Li+/CyAla3 and Na+/CyAla3 complexes, respectively. However for the K+, Rb+ and Cs+ cations that interact with oxygen lone pairs the calculated C=O bond lengths dose not changed generally. In the other hand the C–N amide bond with complex formation lengthened in overall and with going from Li+ to Cs+ increased in the range of 0.007–0.078 Å. The analysis of metal–ligand distances may be useful. For the Li+ and Na+ cations that are symmetrically bonded to three nitrogen atoms the calculated bond lengths were found to be 2.043 and 2.534 Å, respectively. While the K+, Rb+ and Cs+ cations that interact with oxygen lone pairs have 2.810, 3.021 and 3.260 Å, bond lengths, respectively. Comparing the free cyclic peptide CyAla3 molecule with cationic metal complexes indicates that the C–C bond lengths were almost invariable in for the K+, Rb+ and Cs+ cations. As expected, the K+, Rb+ and Cs+ ions were placed away from the three C=O moieties of alanine residues, which is reflected in the larger O···M distances of >2.5 Å approximately (see Figs. 2, 3). Since the ionic radii of K+, Rb+ and Cs+ ions are larger than Li+ and Na+ the corresponding electronic cloud would spread out more for former ions than the latter. Because of this field, larger ions move away from the C=O groups of peptidic backbone more effectively than Li+ ion. For more evaluation of geometrical changes through complexation, the dihedral angle between carbonyl groups and N–H bonds was investigated. In addition with aggregation the dihedral angle increased in the range of 0.8–12.9°.
Fig. 2

Optimized structure of M/CyAla3 complexes with alkali metal ions calculated at the B3LYP level with Li+, Na+, K+, Rb+, and Cs+ metallic ions

Fig. 3

Optimized structure of M/CyAla3 complexes with alkali metal ions calculated at the CAM-B3LYP level with Li+, Na+, K+, Rb+, and Cs+ metallic ions

The geometric structures of the “host” ligand constructed from four alanine molecule (CyAla4) and its “host–guest” complexes with Li+, Na+, K+, Rb+ and Cs+ ions calculated at B3LYP/6-31+G(d) and CAM-B3LYP/6-31+G(d) levels presented in Figs. 4 and 5, respectively. It is seen from Fig. 4 that based on B3LYP calculations for the Li+/CyAla4 complex during metal ion complexation, each accessible backbone carbonyl oxygen atom of CyAla4 acts as an independent metal ion binding site. The average Li+–O bond length was found to be 2.266 Å. Interestingly based on calculations at CAM-B3LYP level two carbonyl oxygen atoms were found to bind with Li+ ion with an average bond length of 1.859 Å. Whereas, results of calculation using B3LYP and CAM-B3LYP methods predict that during the formation of Na+ and K+ complexes, only two alanine carbonyl oxygen atoms were found to interact with the metal ions. The calculated distances between two carbonyl oxygens nearby Na+ and K+ ion in the upward cavity are 2.292 and 2.715 Å for the Na+/CyAla4 and K+/CyAla4 complexes at B3LYP level, respectively. These values were found to be 1.859, 2.292 and 2.676 Å for the Li+/CyAla4, Na+/CyAla4 and K+/CyAla4 complexes calculated at CAM-B3LYP level of theory, respectively. Consideration of Figs. 4 and 5 indicates that both B3LYP and CAM-B3LYP calculations predict that three oxygen atoms of CyAla4 interact with Rb+ and Cs+ ion metals. The average bond length for the Rb–O and Cs–O bond lengths found to be 2.964 and 3.183 Å calculated at B3LYP/631+G(d) level of theory, respectively. Comparing the M/CyAla4 complexes with correspond the free cyclic peptide molecules indicates the C–C bond lengths in the cationic metal complexes were almost invariable. In addition for the Na+/CyAla4, K+/CyAla4, Rb+/CyAla4 and Cs+/CyAla4 that oxygen of carbonyl groups interact with metal ions the C–O bonds were lengthened in the range of 0.012–0.015 Å. Whereas for the Li +/CyAla4 that metal ion coordinated to nitrogen atoms a decrease of carbonyl bond length was observed at B3LYP/6-31+G(d) level of theory.
Fig. 4

Optimized structure of M/CyAla4 complexes with alkali metal ions calculated at the B3LYP level with Li+, Na+, K+, Rb+, and Cs+ metallic ions

Fig. 5

Optimized structure of M/CyAla4 complexes with alkali metal ions calculated at the CAM-B3LYP level with Li+, Na+, K+, Rb+, and Cs+ metallic ions

Binding energies

Generally, the energy decreases systematically with formation of a host–guest aggregation. The decreased energy named the binding energy, which is related to the stability of the corresponding host–guest complex and the extraction power of an extractant for a given metal ion. A stable complex always gives a negative value of ΔE. Hence, the stability of complexes will increase with the negative value of ΔE, and the extraction power of an extractant for metal ions will be stronger. The BE of M/CyAla3 or M/CyAla4 complexes for the complexation reaction:
$$ {\text{M}}^{ + } + CyAla3 \to {\text{M}}/CyAla3, $$
(1)
is defined by the following general equation:
$$ {\text{BE}} = E_{{{\text{M}}^{ + } /{\text{CyAla}}}} -\left( {E_{{{\text{M}}^{ + } }} + \, E_{\text{CyAla}} } \right), $$
(2)
where \( E_{{{\text{M}}^{ + } /{\text{CyAla}}}} , \) \( E_{{{\text{M}}^{ + } }} \) and E CyAla refer to the energy of the M+–CyAla complex, M+ ion and the cyclic peptide system, respectively. The binding energies, calculated using B3LYP and CAM-B3LYP methods at the 6-31+G(d) at level, for the interaction of M/CyAla3 complexes are listed in Table 1. The results clearly show the effect of the metal ion’s nature on the selective binding capacity. The order of binding energies calculated at B3LYP level was found to be Li> K> Na> Rb> Cs+. Obviously, the binding energy results did not correlate completely with the radii of the metal ions because the ionic effective radii of Na+ is shorter than that of K+ metal ion. Because of the shorter Li+–N distance than the Na+···N distance, and shorter radii the Li+ ion binds the cyclic peptide more effective than the Na+ ion as one goes from Li+/CyAla3 to Na+/CyAla3 complexes. In addition it is clear that M+–O bonds are stronger than M+–N ones so interaction of K+ with oxygens is stronger than interaction of Na with nitrogen atoms.
Table 1

The binding energies ΔE (kcal/mol), corrected binding energies, binding enthalpies, Gibbs free energies ΔG (kcal/mol) and formation constants in gas phase for the complexes calculated at B3LYP and CAM-B3LYP levels of theory

 

B3LYP

CAM-B3LYP

ΔE

ΔE ZPE

ΔH

ΔG

Log K

ΔE

ΔE ZPE

ΔH

ΔG

Log K

M/CyAla3

 Li+

−47.11

−45.59

−46.34

−37.69

27.64

−50.34

−48.71

−50.13

−38.65

28.34

 Na+

−20.09

−19.26

−19.35

−11.49

8.42

−21.00

−20.23

−20.92

−10.52

7.71

 K+

−22.99

−21.91

−21.92

−13.61

9.98

−25.47

−24.52

−25.12

−14.20

10.41

 Rb+

−19.135

−18.13

−18.03

−9.98

7.32

−21.33

−20.405

−20.91

−10.18

7.47

 Cs+

−15.75

−14.80

−14.64

−6.90

5.06

−17.68

−16.85

−17.26

−6.94

5.09

M/CyAla4

 Li+

−31.19

−29.61

−30.52

−21.04

15.43

−59.23

−57.39

−58.39

−48.73

35.73

 Na+

−34.16

−33.05

−33.54

−24.25

17.78

−35.13

−34.24

−34.66

−25.83

18.94

 K+

−22.42

−21.77

−21.96

−14.02

10.28

−24.76

−24.07

−24.31

−16.082

11.79

 Rb+

−18.72

−17.99

−18.17

−9.79

7.18

−20.79

−20.11

−20.29

−12.01

8.81

 Cs+

−15.24

−14.48

−14.0

−6.38

4.66

−17.74

−16.37

−16.50

−8.37

6.14

ΔE and ΔG in kcal/mol

The smaller the ion, the shorter the M+···O bond length and the stronger the interaction which, in turn, increases the electrostatic binding energy. Addition of zero-point energy (ZPE) does not affect the order of relative stabilities. It is worthy that the calculated relative stabilities using CAM-B3LYP level slightly differs from those obtained using B3LYP method. Here the order of stability finds to be Li> K≫ Rb+ > Na> Cs+ and giving the values 50.34, 25.47, 21.33, 21.00 and 17.68 kcal/mol, respectively. One can compare the consistency of B3LYP and CAM-B3LYP methods with looking to Fig. 6, which demonstrate a good correlation between two levels of theory.
Fig. 6

Correlation between B3LYP and CAM-B3LYP binding energies for M/CyAla3 complexes

The results of calculated binding energies for complex formation of alkali metal ions and CyAla4 cavities presented in Table 1. From Table 1, it is seen that the binding energy of cation–peptide complexes calculated at B3LYP and CAM-B3LYP levels found in the order of Na> Li> K≫ Rb> Cs+ and Li> Na> K≫Rb> Cs+, respectively. As you can see two methods give different stability order for the Na+ and Li+ cations. This is due to different optimized structures predicted by B3LYP and CAM-B3LYP methods where former calculations showed Li ion interacted with four amide nitrogens but the later methods predicts that Li ion linked to two carbonyl oxygens. The binding enthalpy (ΔH) and binding free energy (ΔG) for the metal cyclic peptide complexation reaction are calculated at B3LYP and CAM-B3LYP levels for the M/CyAla3 and M/CyAla4 complexes and the results gathered in the Table 1. It is clear that formation of metal ion complexes is exothermic as revealed from values of ΔH given in Table 1. The binding enthalpy is increased in the order of Li> K> Na> Rb> Cs+ calculated at B3LYP and CAM-B3LYP methods for the M/CyAla3 aggregates. One can compare the calculated binding energies obtained in this study with previously reported data. For example Praveena and Kolandaivel have reported the binding energies of alkali metal ions with cyclohexan carboxylic acid–glycine type nanotubular cyclopeptides in the range of −51.8 to −79.9 kcal/mol at B3LYP/6-311+G(d) level of theory [36, 37]. In addition Ali and co-workers have been reported binding energies of complexes of various conformers of some cyclic crown ethers and alkali metals. The most effective complexes have binding energies in the range of 17.5–35.95 kcal/mol for the Li+ and Na+ metal ions [38].

NBO analysis

For more detailed investigation of the origin of the favorable interaction energy and for explain the different metal binding selectivities the NBO analysis was carried out. In NBO analysis, the stabilization energies values can be related to the strength of the coordination interaction. A complex will generally be more stable if it has a large corresponding stabilization energy E (2). The stabilization energy E (2) associates with i → j delocalization could be estimated by following equation:
$$ E_{2} = \Updelta E_{ij} = q_{i} \frac{{F^{2} (i,\,j)}}{{\varepsilon_{j} - \varepsilon_{i} }}, $$
where q i is the donor orbital occupancy, ε i , ε j are diagonal elements (orbital energies) and F(i, j) are off-diagonal elements, respectively, associated with NBO Fock matrix. The perturbation stabilization energies E 2 obtained by NBO analysis are summarized in Table 2. The stabilization energy is relative to the intensity of the charge–transfer interaction between a Lewis type NBOs (donor) and non-Lewis NBOs (acceptor). The stronger the donor → acceptor interaction, the bigger is the value of relevant stabilization energy, and more charge will be transferred from the donor (cyclic peptide) to the acceptor (metal ion). Because of the symmetry of optimized structures and similarity of stabilization energies only one value from three or four identical ones presented in Table 2. As a whole, the results of NBO analysis indicate that for the M+/CyAla3 complexes the most important interaction for the Li+ and Na+ ions are the LP1 N1 → LP*1 Li and LP1 N1 → LP*1 Na with 14.50 and 4.96 kcal/mol, respectively. In addition the most important interaction for Li+ and Na+ ions in the M+/CyAla4 complexes were found to be 10.87 and 3.51 kcal/mol for the LP1 O3 → LP*1 Li and LP1 O3 → LP*1 Na interactions, respectively. These results suggest that in the course of the coordination of the host–guest molecules, the main driving forces are the electrostatic interactions between the lone pair electrons of electron-donating in oxygen and nitrogen in cyclopeptides and LP* orbitals of the alkali cations Li+, Na+, K+, Rb+, Cs+.
Table 2

Selected stabilization interaction E (2) for M/CyAla3 and M/CyAla4 complexes at CAM-B3LYP level

LP1 N1 → LP*1 Li

14.51

LP1 N1 → LP*2 Li

8.45

LP1 N1 → LP*3 Li

3.65

LP1 N1 → LP*1 Na

4.96

LP1 N1 → LP*1 Na

1.91

LP1 N1 → LP*1 K

2.40

LP1 N1 → LP*1 K

1.58

LP1 N1 → LP*1 Cs

0.92

LP1 N1 → LP*1 K

0.37

LP1 O3 → LP*1 Li

10.87

LP1 O3 → LP*2 Li

7.90

LP1 O3 → LP*3 Li

2.32

LP2 O3 → LP*1 Li

3.26

LP2 O3 → LP*2 Li

3.17

LP1 O3 → LP*1 Na

3.51

LP1 O3 → LP*2 Na

1.16

LP1 O17 → LP*1 Na

3.51

LP1 O3 → LP*1 K

1.06

BD2 C16–O17 → LP*1 Rb

4.48

LP1 O17 → LP*1 Rb

2.36

LP2 O3 → LP*1 Rb

1.68

BD1 C16–C18 → LP*1 Cs

0.40

LP1 O8 → LP*1 Cs

0.26

LP1 O17 → LP*1 Cs

0.24

LP1 O22 → LP*1 Cs

0.26

LP1 O3 → LP*1 Li

10.87

LP 1-center valence lone pair (LP1 and LP2 are the tow lone pairs of each oxygen and nitrogen atoms, respectively. One of the NBO is in the plane, the other is the corresponding NBO perpendicular to the plane), LP* 1-center valance antibond lone pair, BD 2-center bond

In order to analyze the electrostatic interactions of the alkali metal cations with cyclic peptide host molecules, we have tabulated the CAM-B3LYP calculated partial charges of the selected atoms of complexes in consideration in Tables 3 and 4 for the M/CyAla3 and M/CyAla4 complexes, respectively. It is recognized that the complexation of metal ions and peptides can proceed through electrostatic effects taking place between metal ions with main-chain carbonyl groups or side chains groups. However, molecular modeling and experimental results suggested that preference for the interaction of backbone carbonyl groups of cyclic peptides with metal ions inside the cavity [36, 37, 38, 39]. Although the charge–transfer is not significant, it occurs to some extent between the metal ion and the lone pairs of nitrogen and oxygen atoms of the cyclic peptide molecule. For charge distributions there is no perfect method to accurately calculate electron populations at atoms. Although different methods led to different populations, one might expect that the changes in population between the uncomplexed and complexed states would be similar for different methods. For the present molecules, the charge–transfer was defined as the charge difference between a free metal ion and its complexed form.
Table 3

Calculated NBO charges on the metals and selected atoms of cyclic peptide in M/CyAla3

 

CyAla3

Li

Na

K

Rb

Cs

N1

−0.684

−0.822

−0.843

−0.675

−0.777

−0.761

N7

−0.684

−0.822

−0.844

−0.675

−0.769

−0.761

N12

−0.684

−0.822

−0.843

−0.675

−0.767

−0.761

O5

−0.637

−0.515

−0.313

−0.670

−0.779

−0.757

O13

−0.637

−0.515

−0.314

−0.670

−0.778

−0.757

O18

−0.637

−0.515

−0.314

−0.669

−0.779

−0.757

M

1.000

0.819

0.946

0.952

0.999

0.996

Table 4

Calculated NBO charges on the metals and selected atoms of cyclic peptide in M/CyAla4

 

CyAla4

Li

Na

K

Rb

Cs

N2

−0.665

−0.467

−0.425

−0.655

−0.374

−0.743

N6

−0.668

−0.463

−0.435

−0.665

−0.381

−0.741

N13

−0.665

−0.467

−0.424

−0.655

−0.371

−0.743

N19

−0.668

−0.463

−0.435

−0.665

−0.364

−0.765

O3

−0.645

−0.307

−0.424

−0.729

−0.345

−0.725

O8

−0.645

−0.419

−0.423

−0.617

−0.304

−0.805

O17

−0.645

−0.307

−0.424

−0.617

−0.404

−0.770

O22

−0.645

−0.419

−0.423

−0.729

−0.353

−0.754

M

1.000

0.588

0.929

0.974

0.974

0.998

As it can be seen from Table 3 and in consistence with binding energies, the most charge–transfer was observed for the Li+ with 0.181 esu. In addition the negative charge on the nitrogen atoms increased from −0.684 esu for the free cyclic peptide to −0.822, −0.843, −0.675, −0.777, −0.761 esu for the Li+, Na+, K+, Rb+, Cs+, metal ions respectively. Moreover the negative charge on the oxygen atoms changed from −0.637 esu for the free molecule to −0.515, −0.314, −0.670, −0.778, −0.757 esu for the cyclic peptide hosted to Li+, Na+, K+, Rb+, Cs+, metal ions respectively.

The results of calculated NBO charges of M/CyAla4 complexes collected in Table 4. As you can see here the most charge–transfer observed for the Li+ with 0.412 esu. For the Li/CyAla4, Na/CyAla4 and K/CyAla4 complexes the contrary nitrogen atoms take equal values. For example for the Li/CyAla4 aggregate the N2 and N13 atoms take 0.665 esu, but N6 and N19 atoms take −0.668 esu.

Conclusion

The structure and interaction energies of nanotubular cyclic peptides complexes M/CyAla3 and M/CyAla4 where M = Li+, Na+, K+, Rb+ and Cs+ have been determined with B3LYP and CAM-B3LYP methods. The key findings revealed in our calculations are as follows:
  1. (1)

    Analyzing the geometry of M/CyAla3 and M/CyAla4 complexes indicates after complexation the C=O bond length decreased from 1.232 for the free molecule to 1.203 and 1.209 Å for the Li+/CyAla3 and Na+/CyAla3 complexes, respectively. However for the K+, Rb+ and Cs+ cations that interact with oxygen lone pairs the calculated C=O bond lengths dose not changed generally.

     
  2. (2)

    One crucial inference drawn from the present work demonstrates the gas phase binding energies and Gibbs free energies indicated that CyAla3 and CyAla4 cyclic peptides are suitable resolving agent for the separation of Li+ and Na+ from other alkali metal ions. In addition the binding energy of Li+ is greater than Na+ metal ion due to the smaller size of the Li+ ion.

     
  3. (3)

    Calculations of the vibration frequencies showed that these cyclic peptides and their complexes with alkali metal ions are all located at the stable, minimum points of the potential energy surfaces. Therefore, they are all stable “host–guest” complexes. Calculated thermodynamic properties, including the Gibbs energy of formation, indicate that these complexes are stable and easy-to-form with high reactivity.

     
  4. (4)

    We found a good correlation between B3LYP and CAM-B3LYP results except for the Li+/CyAla4 complex where B3LYP results predicts the amide nitrogen groups act as electron donor but CAM-B3LYP results indicate that carbonyl oxygens are donor atoms.

     
  5. (5)

    The main types of driving force host–guest interactions are investigated, the electron-donating O offers lone pair electrons to the contacting LP* of alkali metal cations.

     

Notes

Acknowledgments

We would like to acknowledge the Isfahan University of Technology for the financial support of this work.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Alireza Najafi Chermahini
    • 1
  • Mehdi Rezapour
    • 1
  • Abbas Teimouri
    • 2
  1. 1.Department of ChemistryIsfahan University of TechnologyIsfahanIslamic Republic of Iran
  2. 2.Chemistry DepartmentPayame Noor UniversityTehranIslamic Republic of Iran

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