Origins of the Stability of Imidazole–Imidazole, Benzene–Imidazole

Jan 30, 2012 - High-level ab initio calculations at the CCSD(T)/CBS and DFT-SAPT levels show that classical hydrogen-bonded tilted imidazole–imidazo...
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Origins of the Stability of Imidazole−Imidazole, Benzene−Imidazole, and Benzene−Indole Dimers: CCSD(T)/CBS and SAPT Calculations S. Karthikeyan and Shigeru Nagase* Department of Theoretical and Computational Molecular Science, Institute of Molecular Science, Myodaiji, Okazaki 444-8585, Aichi, Japan ABSTRACT: The respective structures and stabilities of imidazole− imidazole, benzene−imidazole, and benzene−indole dimers have been investigated using different DFT-D functional, MP2, CCSD(T), and SAPT levels of theory with a medium basis set. Comparative analysis of binding energies and structural parameters of the dimers points to a preference for stacking contact or hydrogen bond in an imidazole− imidazole dimer. In contrast, a T-shaped configuration with H−π interaction is maximally advantageous for benzene−imidazole and benzene− indole dimers. High-level ab initio calculations at the CCSD(T)/CBS and DFT-SAPT levels show that classical hydrogen-bonded tilted imidazole−imidazole dimer is a global minimum structure and that it has high electrostatic energy. However, for benzene− imidazole and benzene−indole dimers, the global minimum (N−H···π) structure has high electrostatic energy as well as dispersion energy.

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INTRODUCTION Interactions involving aromatic rings1−5 are widely prevalent in clusters, biomolecules, organic/biomolecular crystals, and nanomaterials. Crystals with aromatic molecules are often selfassembled by noncovalent interactions.6−11 The aromatic rings of phenylalanine, tyrosine, tryptophan, and histidine in proteins bind either other aromatic rings (π−π or π−H interactions) or hydrogen donors (π−H interaction).12−15 The importance of the energy and geometry of π interactions in stabilizing the πinvolving systems has been investigated extensively.16−40 Furthermore, recent advances, which include self-assembly of organic nanotube bundles,8,9 mechanical extraction of inner shells from multiwalled carbon nanotubes,41 and controlled flapping motions of molecular flippers as a precursor of nanomechanical devices or nanovehicles,42 have highlighted the utility of harnessing the aromatic−aromatic interaction in designing functional nanomaterials. Phenylalanine, tyrosine, tryptophan, and histidine are the four neutral amino acids with constituent aromatic moieties. Their respective side chains are commonly modeled with benzene, phenol, indole, and imidazole. Interactions involving tryptophan stabilize the tertiary structure of biological macromolecules through both hydrogen bonding and π interactions, respectively, via the N−H group and the π-cloud of the indole. As a specific example of tryptophan−phenylalanine interactions, [NiFe] hydrogenase43 is an enzyme that is involved directly in the metabolism of molecular hydrogen. This enzyme contains both the T-shaped and parallel-displaced configurations of a tryptophan−phenylalanine noncovalent dimer. Interaction of other aromatic residues, in particular, histidine with an imidazole ring in the side residue, has not been so thoroughly studied. Histidine aggregates are characteristic of metal-binding sites.15 This residue also appears in enzyme catalytic centers © 2012 American Chemical Society

because of its abilities to bind easily and release protons at physiological pH values. The parallel conformation is probably dominant for histidine complexes with aromatic amino acids within proteins.14 In the case of the histidine−phenylalanine dimer, the N−H bond of the histidine is directed at the πelectron density of the phenyl ring.15 This study was undertaken for the accurate evaluation of both the structures and binding energies of imidazole− imidazole, benzene−imidazole, and benzene−indole dimers. Energy differences among different configurations are analyzed using energy component analysis with symmetry adapted perturbation theory (SAPT). These model systems partly explain the stability of protein folding and interprotein interactive structures that are formed between amino acids by stacking and hydrogen bonding.

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COMPUTATIONAL METHOD To identify the lowest-energy structures of imidazole−imidazole, benzene−imidazole, and benzene−indole dimers, we investigated diverse, topologically different conformers using DFT calculations of a few different types. To confirm the minimum energy structures for imidazole−imidazole, benzene− imidazole, and benzene−indole dimers, frequency calculations were carried out using the density functional theory (DFT) and Møller−Plesset second order perturbation (MP2) theory. Then, the low-lying energy structures were optimized with basis set superposition error (BSSE) correction at the MP2 level using the aug-cc-pVDZ (aVDZ) basis sets for the Received: November 15, 2011 Revised: January 29, 2012 Published: January 30, 2012 1694

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Table 1. M06-2X, BLYP-D3, MPWB1K, and CCSD(T)/CBS Binding Energies (ΔE in kcal/mol) for Low-Energy Structures of the Imidazole−Imidazole, Benzene−Imidazole, and Benzene−Indole Dimersa

ImidaD-A ImidaD-B ImidaD-C ImidaD-D BzImidaD-A BzImidaD-B BzImidaD-C BzImidaD-E BzImidaD-F BzImidaD-G BzIndoD-A BzIndoD-B BzIndoD-C BzIndoD-D BzIndoD-E BzIndoD-F

M06-2X/DIDZ

BLYP-D3/TZVPP

MPWB1K/aVDZ

B97-D/TZVP

ΔE

ΔE

ΔE

ΔE

CCSD(T)/ CBS ΔE

−9.59(−0.39) −8.93(−0.50) −8.83(0.73) −8.23(1.40) −1.90(−0.32) −3.36(0.38) −2.57(0.34) −5.63(0.26) −5.53(0.23) −3.39(0.49) −3.52(0.03) −1.09(−1.65) −3.82(−1.98) −0.84(−1.50) −1.11(−1.64) −7.81(4.55)

−10.20(0.22) −9.38(−0.05) −7.82(0.28) −6.00(−0.83) −2.09(−0.13) −2.90(−0.08) −2.18(−0.05) −5.39(0.02) −5.30(0.00) −2.70(−0.20) −4.32(−0.83) −2.62(−0.12) −5.62(−0.18) −2.46(0.12) −2.84(0.09) −4.33(1.07)

−8.74(−1.24) −8.26(−1.17) −6.80(−1.30) −5.39(−1.44) −1.72(−0.50) −2.48(−0.50) −1.93(−0.30) −4.79(−0.58) −4.73(−0.57) −2.56(−0.34) −3.75(0.26) −2.16(−0.58) −4.64(−1.16) −2.01(−0.33) −2.09(−0.66) −3.13(−0.13)

−9.92(−0.06) −9.40(−0.03) −9.92(1.82) −7.07(0.24) −2.41(0.19) −3.16(0.18) −2.60(0.37) −6.10(0.73) −6.11(0.81) −3.32(0.42) −4.80(1.31) −3.23(0.49) −6.40(0.60) −2.78(0.44) −3.23(0.48) −4.96(1.70)

−9.98 −9.43 −8.10 −6.83 −2.22 −2.98 −2.23 −5.37 −5.30 −2.90 −3.49 −2.74 −5.80 −2.34 −2.75 −3.26

For BzImidaD-D structure: M062X/DIDZ, −4.06; BLYP-D3/TZVPP, −4.00; MPWB1K/aVDZ, −3.23; During the B97D and MP2 level optimization, the BzImidaD-D structure converted to the BzImidaD-E structure. The values in parentheses are the difference of the theoretical method dependent binding energies from the CCSD(T)/CBS values. a

is added to Eint. DFT-SAPT calculations were performed with the PBE0 functional60 and aVDZ basis set.

imidazole−imidazole, benzene−imidazole, and benzene−indole dimers. Single-point MP2/aug-cc-pVTZ (aVTZ) calculations were performed to estimate the CBS limit binding energies. The complete basis set (CBS) limit values of the MP2 binding energies were evaluated based on the extrapolation method exploiting the basis set error in the electron correlation energy, which is proportional to N3− for the aVNZ basis set.44,45 Although most extrapolation methods would not be free from inherent overestimation and underestimation problems, the extrapolation method based on the theoretical understanding is found to be quite reliable.45 We also used coupled cluster theory with single, double, and perturbative triple excitation (CCSD(T)/aVDZ) for imidazole−imidazole, benzene− imidazole, and benzene−indole dimers optimized by the BSSEcorrected RIMP2/aVDZ method. Given that the difference in binding energy between MP2/aVNZ and CCSD(T)/aVNZ does not change significantly with increasing basis set size, the CCSD(T)/CBS energies were estimated by assuming that the difference in binding energies between MP2/aVDZ and MP2/ CBS calculations is equivalent to that between CCSD(T)/ aVDZ and CCSD(T)/CBS calculations.45−47 The errors associated with the CCSD(T)/CBS extrapolation scheme fall within 0.1 kcal/mol.45 The B97-D/TZVP,48 BLYP-D3/TZVPP, and (RI-MP2/aVDZ, RIMP2/aVTZ) calculations were performed using the TURBOMOLE 5.10 suite of programs.49 The M06-2X/DIDZ,50 MPWB1K/aVDZ,51 and MP2 calculations were performed using the Gaussian09 suite of programs,52 and the CCSD(T) calculations were done using the MOLPRO suite.53 DFT-SAPT calculations were also done using the MOLPRO suite53 Furthermore, by using SAPT (symmetry adapted perturbation theory)54,55 calculations, the total interaction energy (Eint) is decomposed into electrostatic (Eelec), effective induction (Eind), effective dispersion (Edisp), and effective exchange repulsion (Eexch) energies, as in our earlier work56,57 and others.58,59 Here, Eind and Edisp include the exchange-induction term and exchange-dispersion term, respectively. The coupled Hartree−Fock response term (dHF)

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RESULTS AND DISCUSSION Because many low-energy structures exist for the imidazole− imidazole, benzene−imidazole, and benzene−indole dimers, we searched for candidates for the lowest energy structure using the dispersion corrected density functional (DFT-D) theory. Then, important low-energy structures were further selected for MP2 and CCSD(T) calculations. The predicted binding energies at DFT-D (M06-2X/DIDZ, BLYP-D3/TZVPP, MPWB1K/aVDZ, and B97D/TZVP), (MP2/aVDZ, MP2/ aVTZ, MP2/CBS), and (CCSD(T)/aVDZ, CCSD(T)/CBS) levels are listed in Tables 1 and 2. Important low-lying energy structures of imidazole−imidazole, benzene−imidazole, and benzene−indole dimers are shown in Figures 1−3. Our discussion is based on the CCSD(T)/CBS results, unless otherwise specified, because these results are considered to be the most reliable. Four structures were obtained for the imidazole−imidazole dimer (see Figure 1). The first structure ImidaD-A is a NH···N hydrogen bonded dimer, wherein the N−H bond interacts with the nitrogen atom of another imidazole, which has a tilted shaped structure. The second isomer, ImidaD-B, is a NH···N hydrogen bonded dimer with a planar structure. The ImidaD-C structure has a NH···N hydrogen bond along with π···H interaction between the π electron density of one imidazole ring and hydrogen atom (H−C) of another imidazole. The last structure, ImidaD-D, is a parallel-displaced π-stacked dimer. The ImidaD-B structure has one imaginary frequency; this structure is a transition state of global minimum structure ImidaD-A. Of all these isomers, the tilted shaped structure with NH···N hydrogen bonded structure is more stable than structures of other isomers. The stabilization energy for imidazole−imidazole dimers followed the order of ImidaD-A > ImidaD-B > ImidaDC > ImidaD-D. The N−H bond of the ImidaD-A structure is elongated by 0.02 Å compared to an isolated monomer, and its frequency is red-shifted by 346 cm−1 at the MP2 level of theory. 1695

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Table 2. MP2, SCS-MP2, and CCSD(T) Binding Energies (ΔE in kcal/mol) for Low-Energy Structures of the Imidazole− Imidazole, Benzene−Imidazole, and Benzene−Indole Dimersa MP2

ImidaD-A ImidaD-B ImidaD-C ImidaD-D BzImidaD-A BzImidaD-B BzImidaD-C BzImidaD-E BzImidaD-F BzImidaD-G BzIndoD-A BzIndoD-B BzIndoD-C BzIndoD-D BzIndoD-E BzIndoD-F a

SCS-MP2

CCSD(T)

aVDZ

aVTZ

CBS

aVDZ

aVDZ

ΔE

ΔE

ΔE

ΔE

ΔE

CBS ΔE

−10.01 −9.46 −8.31 −7.63 −2.06 −3.15 −2.61 −5.68 −5.63 −3.33 −4.05 −3.58 −6.33 −3.24 −3.59 −7.22

−10.49 −9.94 −8.91 −8.30 −2.34 −3.51 −3.13 −6.48 −6.43 −3.90 −4.32 −3.94 −6.91 −3.57 −3.96 −7.84

−10.69(0.71) −10.15(0.72) −9.16(1.06) −8.59(1.76) −2.45(0.23) −3.66(0.68) −3.35(1.12) −6.82(1.45) −6.76(1.46) −4.13(1.23) −4.44(0.95) −4.09(1.35) −7.15(1.35) −3.70(1.36) −4.12(1.37) −8.10(4.84)

−8.94(−1.04) −8.41(−1.02) −6.78(−1.32) −5.55(−1.28) −1.36(−0.86) −2.10(−0.88) −1.18(−1.05) −4.01(−1.36) −3.97(−1.33) −1.85(−1.05) −2.88(−0.61) −1.51(−1.23) −4.72(−1.08) −1.24(−1.10) −1.47(−1.28) −2.61(−0.65)

−9.29 −8.74 −7.25 −5.86 −1.82 −2.47 −1.48 −4.23 −4.17 −2.09 −3.10 −1.89 −4.27 −1.55 −1.88 −1.95

−9.98 −9.43 −8.10 −6.83 −2.22 −2.98 −2.23 −5.37 −5.30 −2.90 −3.49 −2.74 −5.80 −2.34 −2.75 −3.26

The values in parentheses are the difference of the theoretical method dependent binding energies from the CCSD(T)/CBS values.

Figure 1. Optimized structure of imidazole−imidazole dimer at the MP2/aVDZ level of theory.

repulsion, and dHF energy and its diagrams are presented, respectively, in Table 3 and Figure 4. According to the DFTSAPT calculations, the electrostatic contribution is dominant for ImidaD-A and ImidaD-B structures, but for the ImidaD-C structure, electrostatic and dispersion are contributed in an approximately 2:1 ratio. For the π-stacked imidazole−imidazole dimer, electrostatic and dispersion energy contributions are dominant. For ImidaD-A and ImidaD-B structures, the electrostatic energy is almost canceled out by the exchange repulsion. Investigation of the DFT-SAPT energies reveals that the firstorder polarization (electrostatic) energy is systematically the largest term. This term is invariably larger than the SAPT interaction energy. For hydrogen-bonded dimers, the dispersion energy is less than the SAPT interaction energy, but the stacked dimer dispersion energy is greater than the SAPT interaction energy. The dHF term is invariably smaller than the electrostatic energy and dispersion energy. The ImidaD-A structure is more stable than those of other isomers, and the electrostatic energy

The C−H bond distance of the ImidaD-A structure is increased, although a decrease is shown for the ImidaD-D structure at the MP2 optimized geometry. The interplane distance of the parallel-displaced imidazole−imidazole dimer (ImidaD-D) structure is 2.90 Å, which is shorter than that of the paralleldisplaced structure of the benzene dimer. In this structure, the nitrogen atoms are located above polarized hydrogen atoms of N−H groups at 2.90 Å. Comparison of the dispersion-corrected DFT with CCSD(T)/CBS results shows that the B97D/TZVP method result is in good agreement with the CCSD(T) result for a planar, T-shaped, and π-stacked structure. For ImidaD-C structures, however, BLYP-D3/TZVPP results show good agreement with CCSD(T) results. The MP2/aVDZ results closely match the CCSD(T)/CBS results, except for a π-stacked dimer. Among the DFT-D and MP2 methods, BLYP-D3 and B97-D methods show good agreement with CCSD(T)/CBS results. The DFT-SAPT/aVDZ interaction energy component data for electrostatic, induction energy, dispersion energy, exchange 1696

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Figure 2. Optimized structure of benzene−imidazole dimer at the MP2/aVDZ level of theory.

Figure 3. Optimized structure of benzene−indole dimer at the MP2/aVDZ level of theory.

is much more crucial in governing the imidazole−imidazole dimer configuration than the dispersion energy. This is true despite the fact that the dispersion energy is the dominant entity. The DFT-SAPT interaction energy is almost equivalent to CCSD(T)/CBS values. Figure 2 presents seven optimized structures of the benzene−imidazole dimer. The first structure, BzImidaD-A, is a C−H···N hydrogen bonded dimer, wherein the C−H bond of the benzene interacts with the nitrogen atom of imidazole, which has a planar structure. For the second structure, BzImidaD-B, two C−H bonds of benzene interact with the nitrogen atom of imidazole along with π···H interaction between aromatic π and hydrogen from imidazole. In BzImidaD-C and BzImidaD-G structures, two C−H groups of imidazole interact with the benzene molecule. In the BzImidaD-E and

BzImidaD-F structures, one N−H and one C−H group of imidazole interact with a benzene molecule that differs in the orientation of the nitrogen atom. Among all these structures, the BzImidaD-E structure is more stable than other structures at all levels of theory. The BzImidaD-C structure is less stable than the BzImidaD-E structure because the C−H bond of imidazole has less polarity than the N−H bond of imidazole. Comparison of M06-2X/DIDZ, BLYP-D3/TZVPP, MPWB1K/aVDZ, B97-D/TZVP, SCS-MP2, and MP2 results with CCSD(T)/CBS values shows that the BLYP-D3/TZVPP method binding energies are in good agreement with the CCSD(T)/CBS values. The CCSD(T)/CBS binding energies for various structures of the benzene−imidazole dimer are in the order of BzImidaD-E > BzImidaD-F > BzImidaD-B > BzImidaD-G > BzImidaD-C > BzImidaD-A. The N−H bond of 1697

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The optimized structures of the benzene−indole dimer are portrayed in Figure 3. The first structure, BzIndoD-A, is characterized by the presence of two π···H interactions between indole π and two C−H hydrogen from benzene molecules. The next structure of BzIndoD-B is π···H interactions between benzene ring and C−H hydrogen from a five-membered ring of the indole. For the BzIndoD-C structure, the N−H bond of the indole interacts with the benzene ring. The next two structures, BzIndoD-D and BzIndoD-E, show C−H···π interactions between the C−H bond of the six-membered ring of the indole and benzene ring. The last structure, BzIndoD-F, is a π-stacked benzene−indole dimer. Table 1 shows the CCSD(T)/CBS stabilization energies together with M06-2X, BLYP-D3, MPWB1K, and B97-D binding energies. The BLYP-D3 method results show good agreement with CCSD(T)/CBS results, except for the π-stacked BzIndoD-F structure. For the π-stacked BzIndoD-F structure, MPWB1K/aVDZ results show good agreement with CCSD(T)/CBS values. For the benzene− indole dimer, the stabilization energies at the CCSD(T)/CBS level for various structures are BzIndoD-C > BzIndoD-A > BzIndoD-F > BzIndoD-E > BzIndoD-B > BzIndoD-D. The BzIndoD-C structure is more stable than other structures at all levels of theory, except for the MP2 and M06-2X/DIDZ levels of theory. For MP2 and M06-2X/DIDZ calculations, the πstacked BzIndoD-F structure is more stable than other structures. Hobza et al.61 reported that the stabilization energy of the BzIndoD-C isomer is −5.72 kcal/mol at the CCSD(T)/CBS limit for the geometry optimized using the counterpoisedcorrected MP2/cVTZ method. Our prediction for the stabilization energy is −5.80 kcal/mol at the CCSD(T)/CBS limit for the geometry optimized using the counterpoisedcorrected MP2/aVDZ method. The distance of the N−H···π

the BzImidaD-E structure is elongated by 0.003 Å compared to an isolated monomer, and its frequency is red-shifted by 41 cm−1 at the MP2 level of theory. According to DFT-SAPT calculations, in all benzene−imidazole structures, the electrostatic and dispersion energies are greater than the SAPT stabilization energy, while the dispersion energy is dominant for all isomers. The DFT-SAPT stabilization energies are comparable to BSSE-corrected CCSD(T) energies obtained using the same basis set. Table 3. DFT-SAPT Interaction Energy Components (kcal/ mol) of the Imidazole−Imidazole, Benzene−Imidazole, and Benzene−Indole Dimers DFT-SAPT (PBE0)/ aVDZ

Eelec

Eind

Edisp

Eexch

dHF

Eint

ImidaD-A ImidaD-B ImidaD-C ImidaD-D BzImidaD-A BzImidaD-B BzImidaD-C BzImidaD-E BzImidaD-F BzImidaD-G BzIndoD-A BzIndoD-B BzIndoD-C BzIndoD-D BzIndoD-E BzIndoD-F

−15.18 −14.13 −10.91 −9.75 −2.51 −3.92 −2.75 −5.39 −5.37 −3.50 −2.63 −3.30 −5.60 −2.95 −3.38 −7.55

−3.26 −3.12 −1.75 −0.92 −0.59 −0.50 −0.28 −1.30 −1.28 −0.40 −0.31 −0.35 −1.22 −0.32 −0.34 −0.53

−4.25 −4.15 −5.97 −8.17 −3.02 −4.25 −5.48 −5.97 −5.98 −5.69 −5.65 −6.58 −7.34 −5.67 −6.78 −13.76

16.19 15.31 12.87 13.93 4.76 6.62 7.48 9.23 9.26 8.04 5.16 8.93 10.87 7.87 9.23 21.08

−2.57 −2.44 −1.47 −1.26 −0.42 −0.55 −0.63 −1.10 −1.09 −0.79 −0.45 −0.77 −1.21 −0.66 −0.78 −1.72

−9.08 −8.53 −7.23 −6.17 −1.77 −2.60 −1.66 −4.53 −4.46 −2.35 −3.88 −2.06 −4.51 −1.72 −2.05 −2.48

Figure 4. SAPT-DFT/aVDZ energy contributions of the imidazole−imidazole, benzene−imidazole, and benzene−indole dimers. 1698

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interaction in the BzIndoD-C isomer is 2.23 Å and 2.27 Å at MP2/cVTZ and MP2/aVDZ, respectively. The stabilization energy and distances are in good agreement with those reported by Hobza et al.61 To understand the nature of stabilization energies, we analyzed the stabilization energy components using the DFT-SAPT method. The results are presented in Table 3. The total stabilization energies at the DFT-SAPT level are underestimated slightly for benzene−indole dimers with respect to the CCSD(T)/CBS results, except for the BzIndoD-F structure. The dispersion energy contributions for these dimers are dominant, although the electrostatic energy contributions are also significant. The difference in binding energies obtained using DFT and MP2/CBS methods with respect to that of the CCSD(T)/CBS method is listed in Tables 1 and 2. By comparing the DFT and MP2 results with the CCSD(T)/CBS results for imidazole− imidazole, benzene−imidazole, and benzene−-indole dimers, we found that for the imidazole−imidazole dimer, the B97-D/ TZPP method performs better than other DFT methods except for the ImidaD-C isomer. The BLYP-D3 method performs the best for the ImidaD-C isomer. For benzene−imidazole and benzene−indole dimers, the BLYP-D3 method performs better than the other methods except for the BzIndoD-F isomer. Overall, among the DFT methods, the results obtained at BLYP-D3/TZVPP are in good agreement with the CCSD(T)/ CBS results. For most of the dimers, the MP2 method tends to overestimate the binding energies when compared to the CCSD(T)/CBS results.

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CONCLUSIONS We have investigated the structural isomers and binding energies of imidazole−imidazole, benzene−imidazole, and benzene− indole dimers. The global minimum structure of the imidazole− imidazole dimer has a classical hydrogen bond, but a T-shaped structure was found for π···H−N interactions for benzene− imidazole and benzene−indole dimers. For the imidazole− imidazole dimer, electrostatic energy is dominant, although the dispersion energy is dominant for the benzene−imidazole and benzene−indole dimers. Prediction of the dimer-optimized geometries reveals tendencies for their preferred interactions, which can serve as the basis for understanding the mechanism of specificity of protein folding and interprotein interactions.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a Grant-in-Aid for Specially Promoted Research (No. 220000009) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

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REFERENCES

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