Properties and isomerization mechanism of the singlet state imidazole–imidazolium system

Journal of Molecular Structure: THEOCHEM 758 (2006) 1–8 www.elsevier.com/locate/theochem

Properties and isomerization mechanism of the singlet state imidazole–imidazolium system Shihai Yana, Yuxiang Bua,b,* a

Institute of Theoretical Chemistry, Shandong University, 27 Shanda Nan Road, Jinan 250100, People’s Republic of China b Department of Chemistry, Qufu Normal University, Qufu 273165, People’s Republic of China Received 29 March 2005; revised 31 May 2005; accepted 31 May 2005

Abstract The singlet state complexes of imidazole and imidazolium are optimized using the B3LYP method in conjunction with the 6-311CG* basis set. Totally, four stable complexes are found on the global potential energy surface, and they are classified as: N–H/N mode, C–H/N mode, and C–N mode. The harmonic vibrational frequency and the Mulliken population analyses are carried out. The stability of the isomers are compared, and the most stable complexes are those with N–H/N type H-bonds. Another important finding is that the HOMO electrons of the N–H/N type coupling mode complexes are more difficult to be excited or to be removed for their low HOMO energies as compared with the other isomers, while these complexes are easier to be reduced by the electron attachment for their high LUMO energies. The low barriers for the self-isomerization pathways of C(N)–H/N mode complexes demonstrate that their N–H/N or C–H/N type H-bonds belong to the low barrier hydrogen bond, implying their flexibility for isomerization. The C–N mode complex should be a metastable isomer that has finite lifetime, and upon interconversion, it should transform to C–H/N mode complex and release a lot of energies. q 2005 Elsevier B.V. All rights reserved. Keywords: Coupling mode; Harmonic vibrational frequency; HOMO and LUMO; Stabilization energy; Isomerization mechanism; Transition state

1. Introduction The imidazole (Im) and its derivatives are becoming increasingly important in chemical processes because they can form a class of nucleophilic and general base catalysts [1,2]. The possibility of hydrogen bond formation is widely used in pharmaceuticals. The Im ring is a model molecule for more complicated systems, and is of particular interest in biology, where it is involved in nucleic acid bases and amino acids. Im is of importance in biological systems, especially, in enzyme action and protein structure determination [3–5]. As the functional group of histidine residue, Im is commonly associated with protein subunits that act to transport protons from one place to the other [6–10]. The unique ring structure of Im permits the proton to be picked

* Corresponding author. Address: Institute of Theoretical Chemistry, Shandong University, 27 Shanda Nan Road, Jinan 250100, People’s Republic of China. Tel.: C86 531 8365740; fax: C86 531 8564464. E-mail address: [email protected] (Y. Bu).

0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.05.038

up by one N atom to form a cation and another hydrogen to be released from the other N atom. This action has been proposed to explain the proton conductivity properties [11] of Im in the solid-state and also in the actual biological surrounding where a long H-bond chain is present. Therefore, it is of interest to investigate Im and its ramifications. Experimental [11–17] and theoretical [18–28] investigations have been carried out for the studying of the properties of imidazole and its ramifications in recent years. In the experiment fields, the vibrations and intra- and intermolecular force constants of crystalline Im [13–15] have been explored. High-pressure infrared spectroscopy is used in probing the C–H/O interaction in aqueous protonated Im [16]. The protonic conduction [17] of Im in solid-state is investigated with NMR study. In theoretical aspect, the cation binding effect [18] on hydrogen bonding of Im, the low-lying electronic states [20] of Im and the proton transfer shuttling [10] with stationary and mobile Im have also been investigated. In our previous [23–25] papers, the coupling character between Im and Im radical cation, the effects of donors and accepters on the energetics and mechanisms of proton, hydrogen, and hydride release from

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Im, and alteration of Im dimer on oxidation or water ligation have been investigated in detail. The calculations [26] about the diffusion mechanism of an excess electron in Im molecule chains have been performed using ab initio molecular dynamics. The harmonic vibrational frequency of Im and its different forms have also been investigated theoretically [27,28]. The significance of the imidazole–imidazolium (Im– ImHC) system has been demonstrated by the investigations about proton transfer and protonic conductivity of the Im chains, furthermore, the Im–ImHC system can be taken as a model system for investigation on the biomolecular, such as histidine, guanine and adenine, where the Im ring is included in. The importance of Im–ImHC has intrigued the theoretical investigation about structures, energies, and vibrational spectra of the system, which has been carried out by Tatara et al. [21], but only one complex with the N–H/ N coupling mode has been investigated. In order to make-up this insufficiency, the focus of this paper is paid on additional coupling modes of the Im–ImHC system, the properties, and the isomerization mechanisms of the isomers.

2. Calculation details The hybrid density functional theory (DFT) methods have been successfully used in the electronic structure determinations, especially they are uniquely successful and computationally inexpensive in describing large free radicals and intermolecular complexes [29–33]. Furthermore, the reliability of the B3LYP/6-311CG* basis set level on the Im system has also been verified in previous papers [23,25]. Therefore, the Im–ImHC geometry structures are optimized using B3LYP method in conjunction with a 6-311CG* basis set. The harmonic vibrational frequency is determined to confirm that the optimized stable structures correspond to genuine local minima on the global potential energy surface (PES). The HOMO and LUMO of the isomers are investigated for the prediction of the geometry alterations on electron detachment and electron attachment. It should be noted that although the corrections of the basis set superposition error (BSSE) on the binding enthalpy at 0 K (DH0) could improve the energy quantities, they could not change the relative regularity of the DH0 because the contributions from the BSSE correction is significantly smaller as compared with the corresponding uncorrected values. This point has been illuminated in previous investigations [23–25]. Therefore, the DH0 of these isomers are determined according to the following relationship DH0 ðImKImHCÞ ZH0 ðImKImHCÞKH0 ðImÞKH0 ðImHCÞCDZPVE

(1)

DZPVEZZPVEðImKImHCÞKZPVEðImÞ KZPVEðImHCÞ

(2)

To find the correlations among the isomers, the transition state structure searches are performed, only one imaginary frequency is found in the harmonic vibrational frequency for each transition state. The corresponding state–state isomerization pathways are established using the intrinsic reaction coordination (IRC) method [34,35]. The relative Gibbs free energy of these complexes are also calculated. Density functional theory calculations are performed using the GAUSSIAN 98 program package [36] throughout this paper.

3. Results and discussion Three kinds of coupling modes, totally four isomers of the Im–ImHC system are optimized. These intriguing coupling modes can be classified as N–H/N mode, C– H/N mode, and C–N mode. They are denoted with I–IV in short, respectively. These optimized geometries are all collected in Fig. 1, and the corresponding atomic serial numbering is depicted. The harmonic vibrational frequencies of the complexes are exhibited in Fig. 2. The primary vibrational modes of the H-bonds are assigned in the figure. The Mulliken charge populations (Q) of the isomers are collected in Table 1. The HOMO and LUMO contour plots are presented at 0.02 e/au3 isocontour values in Fig. 3, which shows the major distribution of the HOMO and LUMO, the corresponding energies are also depicted in this figure. The calculated binding enthalpies (DH0) of the complexes are given in Table 2. The transition states and the state–state correlations are described in Figs. 4 and 5, respectively. The transition states are denoted with TS1–TS7 in short, respectively. 3.1. Geometry structures It easily can be seen that the optimized geometry structures of four stable isomers depicted in Fig. 1 can be classified as the following three coupling modes: N–H/N type H-bond coupling mode, which includes I and II two isomers; C–H/N coupling mode (III), and C–N coupling mode (IV). The electronic states of all these four isomers are 1A. I and II are two different isomers with N–H/N type H-bond in their structures, and they form a pair of enantiomers. For each isomer, two fragments are in contact with H9 atom and perpendicular to each other. The length of ˚ , while the length of the the N5–H9 bond is about 1.086 A ˚ . The distance between the N5 N10–H9 H-bond is 1.626 A ˚ , which is shorter and N10 atoms in this complex is 2.712 A as compared with the experimentally measured distance

S. Yan, Y. Bu / Journal of Molecular Structure: THEOCHEM 758 (2006) 1–8

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Fig. 1. The optimized geometry structures of ImHImC with the atom symbol and the serial numbering.

between the nitrogen atoms involved in the H-bond in the ˚ [37]. Clearly, this observation reveals that Im chains, 2.86 A the shortening of the N–H/N type H-bond should be the result of the attachment of HC on the bare N atom. The bond ˚ , almost equal to that of length of N1–H19 is about 1.011 A ˚ N14–H18, 1.010 A. This bond is shorter as compared to the ˚ , obtained at same N–H length in the isolated ImHC, 1.012 A

3628.8(N5-H9) IV

2885.9(C-H...N)

3629.8(N10-H19+N14-H18) III 3645.4(N14-H18) 3636.1(N1-H19)

2325.9(N-H...N)

3645.4(N14-H18)

2327.9(N-H...N)

3635.6(N1-H19)

0

1000

I

2000

3000

II

4000

Wavemumbers/cm-1 Fig. 2. Harmonic vibrational frequency of four complexes obtained at B3LYP/6-311CG* basis set level.

level; which indicates that the combination of ImHC with Im stabilizes the proton (H19). The proton transfer between the nitrogen atoms involved in the H-bond could not change the geometry structures of the isomers for the two indistinctive Im rings. The III isomer is characterized by its C–H/N type H-bond. The distance between the C3 and N10 atoms in this Table 1 The Mulliken charge populations (Q) of four isomers of Im–ImHC determined at B3LYP/6-311CG* Level

N1 C2 C3 C4 N5 H6 H7 H8 H9 N10 C11 C12 C13 N14 H15 H16 H17 H18 H19

I

II

III

IV

K0.260 K0.232 K0.087 K0.123 K0.393 0.289 0.290 0.285 0.687 K0.331 K0.117 K0.146 K0.300 K0.247 0.245 0.249 0.265 0.451 0.475

K0.260 K0.233 K0.087 K0.121 K0.394 0.289 0.290 0.285 0.687 K0.330 K0.119 K0.146 K0.299 K0.247 0.245 0.249 0.265 0.451 0.475

K0.270 K0.138 K0.266 K0.134 K0.272 0.290 0.512 0.290 0.476 K0.335 K0.026 K0.119 K0.396 K0.255 0.232 0.235 0.258 0.442 0.475

K0.238 K0.139 K0.866 K0.157 K0.199 0.265 0.307 0.266 0.378 0.281 0.014 K0.025 K0.383 K0.244 0.284 0.308 0.291 0.487 0.369

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Fig. 3. The HOMO and LUMO orbitals and the corresponding energies (in kcal/mol) of the isomers of ImHImC obtained at B3LYP/6-311CG* level. All orbitals are contoured at 0.02 e/au3.

˚ , longer as compared to the N–H/N complex is w3.045 A type H-bond of I/II, which demonstrates the weaker of C– H/N H-bond than N–H/N H-bond, the length of the N10– ˚ . While as compared with the C–H/N H7 H-bond is 1.942 A type H-bond of ðImÞC 2 discussed in Ref. [23], this H-bond is ˚ . No stable configuration with the C– shortened by w0.23 A H/N type coupling mode for the neutral Im dimer is found, therefore, the attachment of the proton (H19) on the bare N (N1) atom stabilizes the dimer for the decreasing of the electron density located on its C–H group. Two fragments of this isomer are perpendicular to each other. The characteristic of the IV isomer is its unique C–N covalent bond connection between two fragments. The length of this bond (C3–N10) obtained at B3LYP/6-311CG* ˚ . The dihedral angle of the frameworks of level is 1.553 A two Im rings is 114.38. The effect brought by the association of two moieties to the fragment in which C3 is included is significant, as can be seen from Fig. 1 for the deviation of H7, H9, and H19 atoms from the plane of the Im ring. This phenomenon should be attributed to the connection of C3 and N10 for a part of the aromaticity is lost for the breakage of

the big P65 bond and a rehybridization to the N1, C3, and N5 atoms to sp3 one, as a consequence of the nucleophilic attack. The alteration brought to Im ring by the connection of two fragments is unremarkable as compared with the free Im. 3.2. Harmonic vibrational spectra It has been pointed out [21] that the formation of the complex strongly influences the harmonic vibrational spectra as compared to the ones for the free Im and ImHC parts, the most affected modes by the hydrogen bond formation are the N–H stretching modes of the ImHC molecule. The vibrational frequencies of the isomers are obtained for the inspection of the stability of the optimized geometry Table 2 Binding enthalpies (DH0) of the isomers obtained at B3LYP/6-311CG* level

DH0

I

II

III

IV

K26.7

K26.7

K17.6

6.9

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5

Fig. 4. The geometry structures of transition states optimized at B3LYP/6-311CG* level.

vibrational frequency of the ðImÞC 2 complexes (nN–H: K1 3621.2–3627.0 cm ) discussed in Ref. [23] that the influence of the H19 attachment on the bare N1 atom to the harmonic vibrational frequency of N14–H18 bond is weak. 3.3. HOMO and LUMO Removal of one electron from the HOMO oxidizes the complex, whereas injection of one electron in the LUMO reduces the complex. According to Koopman’s theorem, (35.4) TS7

(36.0) IV

35.0

30.0

H0 (kcal/mol)

structures discussed above, and they are collected in Fig. 2. The assignment of the primary H-bonds vibrational modes is performed and depicted in this figure. For the harmonic vibrational frequency of the enantiomers, I and II, the follow point can be drawn that the N–H/N type H-bond vibrational mode is red-shifted distinctly as compared with the corresponding vibrations of the Im dimer radical cation, K1 (see Refs. [23,25]), say ðImÞC 2 , 2721.8–2723.2 cm nothing of the corresponding vibrations of the neutral Im dimer, (Im)2, 3365.1–3366.6 cmK1 (Ref. [25]). It has been pointed out in Ref. [21] that these large shifts may be attributed to the strong hydrogen bond between Im and ImHC. The harmonic vibrational frequency of N–H bond of I/II are similar to those of ðImÞC 2 and (Im)2. The harmonic vibrational frequency for the typical C– H/N type H-bond of the III isomer is 2885.9 cmK1, and it is red-shifted as compared to the corresponding one of ðImÞC 2 (see Ref. [23]) by more than 200.0 cmK1, which indicates that the interaction strength of this H-bond is weakened. The strengthening of the interaction of two fragments of this isomer demonstrates that the significance of the C–H/N H-bond in the interaction is decreased. The harmonic vibrational frequency of the hybrid symmetrical stretching of the N1–H19 and N5–H9 bonds is 3629.8 cmK1, and it is also assigned in the figure. The harmonic vibrational frequency of the N14–H18 stretching mode is 3647.5 cmK1, a little bigger than the hybrid stretching of N1–H19 and N5–H9. The harmonic vibrational frequency of the stretching of N14–H18 bond of the IV isomer is 3628.8 cmK1, assigned in the figure. The harmonic vibrational frequencies of the other two N–H bonds are influenced significantly for the connection of two fragments, while it can be seen from the figure that the intensity of them is weak. It can be drawn with the comparison of the corresponding harmonic

25.0

20.0

(9.9) TS5

15.0

10.0

(8.7) III

(0.0) TS1 (0.4) I

(10.8) TS6 III

(2.8) TS2 I

(0.0) TS4

(2.9) TS3 II

(0.4) II

5.0

Fig. 5. The state–state correlations and the isomerization mechanism among four isomers obtained at B3LYP/6-311CG* basis set level. The data in the bracket denote the relative Gibbs free energy.

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the calculations of the ionization potential (IP) and the electron affinity (EA) are related directly to the energies of the HOMO (3HOMO) and the LUMO (3LUMO) [38]. The HOMO–LUMO energy separation has been used as a conventional measure of kinetic stability [39–44]. Therefore, the calculated energies of the HOMO and LUMO, the Mulliken charge populations, 3HOMO, and 3LUMO are represented in Tables 1 and 2, respectively. From the parameters represented in Table 1, it can be seen that the Mulliken positive charges of I and II mainly locate on H9, H18, and H19 atoms, and the charges on these atoms are 0.687, 0.451, and 0.475, respectively. The conclusion can be drawn that the Mulliken positive charges are mainly located on respective ImHC residue. For the III isomer, the positive charges are mainly distributed on H7, H9, H18, and H19 atoms (Table 1), the magnitude of the positive charges distributed on them are 0.512, 0.476, 0.442, and 0.475, respectively. Thus, the conclusion can be drawn that the Mulliken positive charges are mainly located on ImHC residue of III. Table 1 demonstrates that almost all of the positive charges of IV are located on Im residue, which N10 atom is in connection directly with the C3 atom of the ImHC. Fig. 3 demonstrates that for the complexes with H-bond coupling mode (I/II and III), the HOMO corresponds to the Im residue, while the LUMO corresponds to the ImHC one. For IV, the HOMO is located in the ImHC residue while the LUMO is located in the Im, as a consequence of the charge transfer along the reaction. The HOMO of I/II indicates that the N10–C11 and C13–N14 bonds are in the anti-bonding regions; on oxidation, these two bonds situated in the antibonding regions should be strengthened. The LUMO demonstrates that the C2–C4, all of the C–H, and N–H bonds of the ImHC residue are situated predominantly in bonding regions. On reduction, these bonds situated in the bonding regions are expected to be strengthened. The HOMO of III illustrates that the N10–C11 and C13–N14 bonds are situated in predominantly anti-bonding regions. The LUMO of this isomer is situated wholly in the ImHC residue, and it can be seen that all of the C–N bonds of this fragment are situated in the anti-bonding regions while the other bonds of ImHC are situated in the bonding regions. Fig. 3 indicates that the HOMO electrons are distributed mainly on the ImHC residue of IV. The bonding nature of the HOMO for the bonds of the ImHC fragment (except N1–C2 and C4–N5) leads to a lengthening of all bonds on oxidation. Furthermore, distinct anti-bonding nature of N10–C3 bond of IV is expected to lead to a shortening of this bond on oxidation. It also demonstrates that the LUMO of IV is situated predominantly in the Im residue. The antibonding nature of the LUMO for N10–C3 would lead to a lengthening of this bond on reduction. The energies of the HOMO and LUMO of these isomers obtained at B3LYP/6-311CG* level are represented in Fig. 3. The following point is demonstrated that the energy gap of the HOMO and LUMO of I/II is larger as compared

with that of III and IV. It can be drawn that the HOMO electrons of I/II are more difficult to be excited or to be removed than those of III and IV for its lower HOMO energy, while the higher LUMO energy indicates that they are easier to be reduced by the electron attachment than III and IV. 3.4. Isomerization mechanism Before analyzing the isomerization mechanism among these four isomers, it is necessary to first discuss the structures and the properties of the transition states. For TS1, it can be seen from Fig. 4 that H9 situates just in the middle of two fragments, and the distance of N5 and H9 is ˚ , equals to that of N10 and H9. The distance between 1.289 A ˚ , which is the N atoms involved in the H-bond is 2.577 A shorter as compared to the corresponding distance of I/II by ˚ . The position of two fragments of this transition w0.135 A state is more similar to that of I, these two fragments are almost perpendicular to each other. The dihedral angle of two fragments of TS2 is zero, namely, two fragments are ˚ , shorter than coplanar. The length of N5–H9 bond is 1.083 A ˚ . The the distance of N10 and H9 atoms, which is 1.649 A contact distance of two N atoms participated in the N–H/N ˚ , which is longer as compared with type H-bond is 2.732 A ˚ . Similar to the corresponding distance of I/II by w0.02 A TS2, two fragments of TS3 are also situated in one plane, and the distances of N5–H9, N10–H9, and N5–N10 are also equal to those of TS2. The difference mainly lies in the orientation of two fragments. TS4 and TS1 form a pair of enantiomers. Two fragments of TS5 are perpendicular to each other. N10 atom is situated in the plane of the other fragment and interacts with H7 and H9 atoms. Thus, an incompact five-member-ring is created by C3, N5, H7, H9, and N10 atoms. The distance of N10 and H7 atoms is ˚ , the shortest one of N10 with the atoms of the other 2.065 A fragment. The :C3H7N10 angle is about 145.28. It can be seen from Fig. 4 that the characteristics of TS6 are the C–H/N type H-bond and coplanar of two fragments. The ˚, bond lengths of C3–H7 and N10–H7 are 1.103 and 1.968 A respectively, and the angle of :C3–H7–N10 is 180.08. The coupling mode of this transition state is very similar to that of III. Judging from the geometry of TS7, it can be easily seen that the configuration of TS7 is similar to that of IV. ˚, The contact distance of two fragments (C3–N10) is 1.694 A ˚ . The dihedral angle of longer than that of IV by w0.141 A two fragments framework is 118.48, bigger as compared to that of IV by 4.18. The above analyses have assigned how the transition state and the isomers correlate to each other from the geometrical viewpoint. The state–state correlations and the isomerization mechanism among the isomers are established using the IRC method and represented in Fig. 5. The binding enthalpies at 0 K (DH0) of the isomers obtained at B3LYP/6-311CG* level are represented in Table 2. It can also be seen that the DH0 of I/II agree with the results

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calculated in Ref. [21] (K27.7 (no ZPVE) and K27.6 (with ZPVE) kcal/mol). The DH0 of III indicates that it is higher than I/II in energy by 9.1 kcal/mol. The positive DH0 value of IV demonstrates that the energy of this isomer is even higher than the sum of the corresponding monomers, Im and ImHC, while no imaginary frequency is found in its harmonic vibrational frequency indicates that it is a stable structure. Therefore, it is easy to know that there must be a transition state whose energy is higher than that of IV in its dissociation process. This kind of configuration with high energy is ubiquitous in biological system and has intriguing a lot of investigations [45]. The activation barrier for proton transfer along the N– H/N type H-bond between Im and ImHC has been determined before [21], and the barrier height is 0.57 kcal/ mol at B3LYP/6-31CCG** level. The calculated energy barrier (ETS1KEI) at B3LYP/6-311CG* level is 1.6 kcal/ mol (it is only 0.43 kcal/mol at B3LYP/6-31CCG**// B3LYP/6-311CG* level), therefore, the N–H/N type H-bond of I should belong to low barrier hydrogen bond (LBHB), and the proton transfer occurs spontaneously for this isomer at room temperature, which is in accordance with the former investigation [21]. The alteration of the Gibbs free energy (GTS1KGI) represented in Fig. 5 also illustrates that this reaction is spontaneous. TS2 and TS3, two transition states are found for the isomerization reaction between I and II, the calculated barriers of these two isomerization processes are 1.3 and 1.4 kcal/mol, respectively. This is in well agreement with the results calculated in Ref. [21]. The forward and backward activation energies for the isomerization process from I to III by experiencing the TS5 are 9.1 and 0.4 kcal/mol, respectively, which indicates that the backward isomerization is easier than the forward one. The Gibbs free energy of TS5 is higher as compared to those of I and III, which indicates that both the forward and backward reactions of I/TS5/III are thermodynamically determined. The energy barrier of the fragment rotation isomerization process of III is 1.1 kcal/mol, indicating the LBHB characteristic of this C–H/N type H-bond. The calculated Gibbs free energy demonstrates that this self-isomerization is not a spontaneous process. For III, optimizations have indicated that the other pathway may undergo, viz. isomerization into IV by experiencing the TS7 transition state. The forward and backward activation energies are 24.0 and 0.9 kal/mol, respectively. Obviously, the isomerization process from III to IV by experiencing TS7 is an endothermic reaction while the inverse process is surely an exothermic one. The Gibbs free energy of TS7 is lower as compared to that of IV, which indicates that the reverse reaction of III/TS7/IV is kinetic control. Thus, it can be concluded that the IV should be a metastable isomer that has finite lifetime, and upon interconversion, it should transform to III and release a lot of energies simultaneously.

7

4. Conclusions Four stable geometry structures of the Im–ImHC complex are optimized using the DFT/B3LYP method in conjunction with the 6-311CG* basis set. Two fragments are connected with the N–H/N type H-bond and perpendicular to each other for I and II, a pair of enantiomers. The dihedral of the C–H/N type coupling mode complex (III) is near to 90.08. The energy of the C–N coupling mode complex, IV, is very high for the rehybridization to the N1, C3, and N5 atoms to sp3 one, as a consequence of the nucleophilic attack. No imaginary frequency is found in the harmonic vibrational frequency indicate that they are stable and represent the local minima on the potential energy surface. The distinct red-shifts are found for the harmonic vibrational frequency of the N– H/N and C–H/N type H-bonds as compared with the corresponding ones of (Im)2 and ðImÞC 2. The Mulliken charge populations of the isomers are determined, and the HOMO and LUMO also have been investigated. The conclusions are drawn from the characteristics of the HOMO and LUMO on oxidation by the electron detachment from the HOMO and on reduction by the electron attachment on the LUMO. For the N–H/N type coupling mode complexes, their HOMO electrons are more difficult to be excited or to be removed as compared to other isomers for their low HOMO energy, while they are easier to be reduced than other isomers for the high LUMO energy. The state–state correlations and the isomerization mechanisms are determined at the same level. The transition states of the proton transfer and the fragment rotation are found for the N–H/N type coupling mode complexes. The low energy barriers for the self-isomerization pathways of I, II, and III indicate that the LBHB characteristic of the corresponding N–H/N and C–H/N type H-bond. Both the forward and backward reactions of I/TS5/III are thermodynamically determined for the higher Gibbs free energy of TS5, and this process is an endothermic reaction. The III/TS7/IV isomerization process also is an endothermic one, while the reverse reaction is kinetic control. The IV should be a metastable isomer that has finite lifetime, and upon interconversion, it should transform to III and release a lot of energies.

Acknowledgements This work is supported by the National Natural Science Foundation of China (20273040), NCET and the Natural Science Foundation of Shandong Province (Z2003B01). Supports from SRFDP and SCF for ROCS, SEM are also acknowledged. A part of the calculations were performed at the Supercomputer Center, CNIC, CAS and the Highperformance Computational Center in Shandong University.

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References [1] M.L. Bender, R.J. Bergeron, M. Komiyama, The Bioorganic Chemistry of Enzymatic Catalysis, Wiley–Interscience, New York, 1984. p. 312. [2] P. Stewart, The Proton: Applications to Organic Chemistry, vol. 46, Academic Press, Orlando, FL, 1985. p. 313. [3] W.W. Bachovchin, Biochemistry 25 (1986) 7751. [4] T. Noguchi, Y. Inoue, X.S. Tang, Biochemistry 38 (1999) 399. [5] M. Sorlie, J. Christiansen, B.J. Lemon, J.W. Peters, D.R. Dean, B.J. Hales, Biochemistry 40 (2001) 1540. [6] B.D. Cain, R.D. Simoni, J. Biol. Chem. 264 (1989) 3292. [7] R.N. Lightowlers, S.M. Howitt, L. Hatch, F. Gibson, G. Cox, Biochim. Biophys. Acta 933 (1988) 241. [8] S.M. Howitt, F. Gibson, G.B. Cox, Biochim. Biophys. Acta 936 (1988) 74. [9] S.B. Vik, B.J. Antonio, J. Biol. Chem. 269 (1994) 30364. [10] S. Scheiner, M.Y. Yi, J. Phys. Chem. 100 (1996) 9235. [11] A. Kawada, A.R. McGhie, M.M. Labes, J. Chem. Phys. 52 (1970) 3121. [12] C. Perchard, A. Novak, J. Chem. Phys. 48 (1968) 3079. [13] L. Colombo, P. Bleckmann, B. Schrader, R. Schneider, Th. Plesser, J. Chem. Phys. 61 (1974) 3270. [14] D. Christen, J. Griffiths, Z. Naturforsch. 37a (1982) 1378. [15] P.W. Loeffen, R.F. Pettifer, F. Fillaux, G.J. Kearley, J. Chem. Phys. 103 (1995) 8444. [16] Ch.Ch. Su, H.Ch. Chang, J.Ch. Jiang, P.Y. Wei, L.Ch. Liu, Sh.H. Lin, J. Chem. Phys. 119 (2003) 10753. [17] B.S. Hickman, M. Mascal, J.J. Titman, I.G. Wood, J. Am. Chem. Soc. 121 (1999) 11486. [18] H. Basch, M. Krauss, W.J. Stevens, J. Am. Chem. Soc. 107 (1985) 7267. [19] P.J. O’Malley, J. Am. Chem. Soc. 120 (1998) 11732. [20] F.B.C. Machado, E.R. Davidson, J. Chem. Phys. 97 (1992) 1881. [21] W. Tatara, M.J. Wo´jcik, J. Lindgren, M. Probst, J. Phys. Chem. A 107 (2003) 7827. [22] H. Chojnacki, J. Lipinski, Adv. Mol. Relax. Interact. Process. 18 (1980) 149. [23] S.H. Yan, Y.X. Bu, Z.H. Cao, P. Li, J. Phys. Chem. A 108 (2004) 7038. [24] Y.X. Bu, R.I. Cukier, J. Phys. Chem. B 108 (2004) 10089. [25] S.H. Yan, Y.X. Bu, J. Phys. Chem. B 108 (2004) 13874.

[26] W. Mu¨nch, K.D. Kreuer, W. Silvestri, J. Maier, G. Seifert, Solid State Ionics 145 (2001) 437. [27] M. Majoube, M. Henry, L. Chinsky, P.Y. Turpin, Chem. Phys. 169 (1993) 231. [28] J. Sadlej, A. Jaworski, K. Miaskiewiez, J. Mol. Struct. 274 (1992) 247. [29] P.J. O’Malley, S.J. Collins, Chem. Phys. Lett. 259 (1996) 296; P.J. O’Malley, Chem. Phys. Lett. 262 (1996) 797. [30] P.J. O’Malley, J. Phys. Chem. A 101 (1997) 6334; P.J. O’Malley, J. Phys. Chem. A 101 (1997) 9813; P.J. O’Malley, J. Phys. Chem. A 102 (1998) 248. [31] C. Adamo, V. Barone, in: D.P. Chong (Ed.), Recent Development in Density Functional Methods, World Scientific Publishing, Singapore, 1997 [Part II]. [32] F. Himo, A. Graslund, L.E. Eriksson, Biophys. J. 72 (1997) 1556. [33] Y. Qin, R.A. Wheeler, J. Chem. Phys. 102 (1995) 1689. [34] C. Gonzalez, H.B. Schlegel, J. Chem. Phys. 90 (1989) 2154. [35] C. Gonzalez, H.B. Schlegel, J. Phys. Chem. 94 (1990) 5523. [36] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J. R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, R.E. Stratmann, Jr., J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. HeadGordon, E.S. Replogle, J.A. Pople, Gaussian Inc., Pittsburgh, PA, 1998. [37] B.M. Craven, R.K. McMullan, J.D. Bell, H.C. Freeman, Acta Crystallogr. Sect. B B33 (1977) 2585. [38] T.A. Koopmans, Physica 1 (1933) 104. [39] R.C. Haddon, T. Fukunaga, Tetrahedron Lett. 21 (1980) 1191. [40] T.G. Schmalz, W.A. Seitz, D.J. Klein, G.E. Hite, J. Am. Chem. Soc. 110 (1988) 1113. [41] D.S. Bethune, G. Meijer, W.C. Tang, H.J. Rosen, Chem. Phys. Lett. 174 (1990) 219. [42] P. Fowler, Nature 350 (1991) 20. [43] X. Liu, T.G. Schmalz, D.J. Klein, Chem. Phys. Lett. 188 (1992) 550. [44] A. Jun-ichi, Theor. Chem. Acc. 102 (1999) 134. [45] (a) H.Q. Ai, Y.X. Bu, K.L. Han, J. Chem. Phys. 117 (2002) 7593; (b) H.Q. Ai, H.Q. Ai, Y.X. Bu, Z.D. Chen, J. Chem. Phys. 118 (2003) 1761.