Structures, Stabilization Energies, and Binding Energies of

Article pubs.acs.org/JPCA

Structures, Stabilization Energies, and Binding Energies of Quinoxaline···(H2O)n, Quinoxaline Dimer, and Quinoxaline···Cu Complexes: A Theoretical Study Mwadham M. Kabanda* and Eno E. Ebenso Department of Chemistry, North-West University (Mafikeng Campus), Private Bag x2046, Mmabatho 2735, South Africa S Supporting Information *

ABSTRACT: Quinoxaline is a parent structure for a broad class of N-heteroaromatic compounds, many of which exhibit various biological activities. The interaction of quinoxaline with explicit water molecules or metal ions and the formation of quinoxaline dimer play an important role in many of the biological activities of quinoxaline. This study investigates the structures, stabilization, and binding energies of quinoxaline complexes with water, transition metal ions, and quinoxaline dimer to provide information on the preferred geometries, interaction energies, and type of noncovalent interactions accounting for the stability of the complexes. The investigations are performed in vacuo and in water solution using MP2 and DFT methods. The results of the study on the quinoxaline···(H2O)n show that the preferred adducts in vacuo involve one, two, or three water molecules hydrogen bonded to the N atom and the neighboring H atom of the Csp2−H group. The results in water solution show a preference for water−water clustering. The dimers of quinoxaline are stabilized by either π−π stacking or weak C−H···N intermolecular hydrogen bonds. The relative stability of the quinoxaline···Cu complexes depends on the site on which the Cu ion binds and the binding strength depends on both the nature of the cation and the binding site.

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INTRODUCTION Quinoxaline (1,4-diazanaphthalene, C7H5N2) is a parent structure of several nitrogen containing benzoheterocyclic compounds that have various biologically interesting properties with potential applications in pharmaceutical drug design. These compounds have a wide range of biological activities including antibacterial,1−4 antifungal,5−7 anticancer,8,9 antitubecular,10 antiprotozoal,11−13 etc. Because of their pharmaceutical potentiality, quinoxalines are widely utilized in the production of various insecticides, fungicides, and herbicides.14−17 Beside their pharmacological applications, substituted quinoxalines are also known to form stable complexes that play vital roles in many catalytic reactions and other oxidation−reduction reactions.18−22 However, despite the presence of quinoxaline moiety (QXL) in many biologically active molecules and the continuous dynamic investigations in several experimental studies,1−19 theoretical studies on QXL and its derivatives are very scarce and much of the work has focused on thermochemical studies23−28 and molecular docking analysis.29−31 In view of the need for understanding the binding properties of biologically active molecules, the current work investigates the structures, the relative energies (i.e., stabilization energies), and the binding energies of QXL···(H2O)n complexes, QXL···metal ion complexes, and QXL···QXL dimer. The interactions of QXL with solvent molecules or metal ions in real systems involve very complex processes and the study reported here represents only a simplified model for such interactions. The results obtained from this study are useful for future works on quinoxalines that have minimal © 2013 American Chemical Society

substituent groups on the parent compound and for which, therefore, many of QXL properties could be considered transferable. The importance of studying the interaction of biologically active molecules with explicit water molecules is related to the fact that their biological activities within living organisms are exerted in aqueous medium.32−34 The study of QXL dimer is motivated by the fact that there is scarcity of theoretical studies elucidating the structures and molecular properties for dimers of heterocyclic compounds.35 The study of the QXL···metal ion complexes is meant to investigate the interaction mechanism of QXL with selected transition metal ions in order to understand the mode of interaction leading to stable complexes that play vital roles in various catalytic reactions and other oxidation−reduction reactions involving quinoxalines. In this study, Cu(I) and Cu(II) ions have been selected to model the QXL···metal ion interactions because, from a computational viewpoint, their complexes are easy to model, and also, the difference in the number of their electrons provides a good assessment of the interaction of QXL with transition metal ions that have paired and unpaired electrons, as reported in other works.36,37 Moreover, from a biological viewpoint, copper functions as a key cofactor in a diverse array of biological oxidation−reduction reactions.18 Therefore, a study of the QXL···Cu complexes provides valuable information that could be utilized in understanding a diverse biological Received: September 20, 2012 Revised: January 6, 2013 Published: January 23, 2013 1583

dx.doi.org/10.1021/jp309356b | J. Phys. Chem. A 2013, 117, 1583−1595

The Journal of Physical Chemistry A

Article

solute−solvent interactions), it was considered important to calculate the adducts of QXL···(H2O)n and the QXL···Cu complexes in the presence of bulk solvent. As a preliminary study, isolated QXL was investigated to obtain interesting molecular properties related to its reactivity and to elucidate its reactive centers. This study is considered important because it provides valuable information for subsequent studies presented in this work.

activities involving QXL···metal ion complexes. The objective of this part of the work is to obtain the preferred geometries, the binding energies, and the mode of charge transfer in the QXL···Cu complexes. The schematic representation of QXL and the atom numbering utilized in this study are shown in Figure 1. QXL

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COMPUTATIONAL DETAILS Geometry optimization on the isolated QXL was performed using the Møller−Plesset second order (MP2) and density functional theory (DFT) methods using different standard basis sets (e.g., 6-31G(d), 6-31++G(d,p)). Geometry optimizations for the QXL···(H2O)n complexes were performed by utilizing the ab initio MP2/6-31+G(d) and B3LYP/6-31++G(d,p) and MPWB1K/6-31++G(d,p) density functional methods. The QXL···QXL dimers were calculated using MP2/6-31+G(d,p) and the meta-hybrid MPWB1K/631+G(d,p) DFT method. MP2 and meta-hybrid DFT methods (e.g., DFT/MPWB1K) in conjunction with standard basis sets such as 6-31+G(d), 6-31+G(d,p), and 6-31++G(d,p) are considered adequate for the description of systems involving noncovalent interactions (e.g., hydrogen bonding and stacking interactions).35,44−60 The interaction energy (binding energies) for QXL···(H2O)n and QXL dimers were corrected for the basis set superposition error (BSSE), utilizing the counterpoise method.61 The interaction energies for the QXL···(H2O)n clusters were estimated as

Figure 1. Schematic representation of quinoxaline (QXL) and the atom numbering utilized in the study. The H atoms are numbered with the same number as the C atom to which they are attached.

is characterized by the presence of the benzene ring and the pyrazine moiety fused together resulting in a system with 10π electrons, which determines much of the properties of QXL. Given the presence of a number of aromatic CC bonds and the presence of the N heteroatom with lone pair (lp) electrons, QXL has the ability to form intermolecular hydrogen bonds (H-bonds) of the type lpN···H−O and C−H···O with water molecules. The dimers of QXL are most likely stabilized by both intermolecular C−H···lpN H-bonds and dispersion interactions through π−π stacking interactions. The QXL···Cu complexes are stabilized by both electrostatic and covalent interactions of the type Cu···lpN and Cu···π. Hydrogen bonding, π−π stacking and cation···π interactions play crucial role in many biological activities and in the stabilization of various complexes that have a role not only in pharmacological applications but also other crucial technological applications.38−43 All the three different studies were conducted in vacuo. However, because most biological reactions occur in aqueous medium, where the conformation of a given molecular system may be different from that in vacuo (mainly because of the distortions and conformational changes caused by diverse

ΔE inter = Ecomplex − (EQXL + nE H 2O)isolated − E H2O···H2O (1)

where Ecomplex is the energy of the optimized QXL···(H2O) complex, EQXL is the energy of the isolated QXL, EH2O is the energy of the isolated and optimized water molecule and EH2O···H2O is the energy of interacting water−water molecules, which is estimated through a single-point calculation on the

Figure 2. Optimized conformer, highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), and contour of the electrostatic potential (EP) obtained from total SCF density (isovalue = 0.0004) for the conformer of quinoxaline. 1584



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Table 1. Selected Reactivity Molecular Parameters of Isolated Quinoxaline media and calculation method

EHOMO kcal/mol

EHOMO−1 kcal/mol

EHOMO−2 kcal/mol

ELUMO kcal/mol

IPa kcal/mol

EAb

μc (debye)

in vacuo B3LYP/6-31G(d) B3LYP/6-31++G(d,p) B3LYP/6-311+G(2df,2p) MP2/6-31+G(d) in waterd in acetonitriled in chloroformd

−154.4 −161.1 −162.4 −204.6 −154.8 −155.7 −154.0

−155.2 −162.8 −162.5 −211.3 −158.3 −158.0 −157.1

−163.4 −170.1 −170.9 −259.8 −163.5 −164.5 −162.8

−44.4 −53.0 −53.7 26.7 −46.0 −46.4 −45.1

202.5 205.1 205.8 198.9

3.0 11.6 12.4 3.6

0.610 0.596 0.559 0.245 0.729 0.746 0.765

The experimental IP value is 207.8 kcal/mol.80 bThe experimental EA value is 15.8 kcal/mol.81 cμ denote the dipole moment in Debye. dStudies in different solvents were performed with B3LYP/6-31G(d) method. a

Figure 3. In vacuo MPWB1K/6-31++G(d,p) optimized geometries for the quinoxaline−water adducts. Similar geometry arrangements of quinoxaline···(H2O)n complexes were obtained with B3LYP/6-31++G(d,p) and MP2/6-31+G(d) calculation methods.

description of systems interacting with Cu ions.36,64−71 The QXL···Cu interaction energy was estimated using the equation

water molecules arranged in the same way as in the optimized complex but without QXL.62 The interaction energies for the QXL dimers were estimated as ΔEinter = Edimer − 2(EQXL)isolated The optimization of QXL···Cu complexes were performed using the DFT/B3LYP and the DFT/BHandHLYP methods (with the restricted option for Cu(I) ion and unrestricted option for Cu (II) ion). The DFT/BHandHLYP method is considered to provide results that are in good agreement with CCSD(T) results for ground and low-lying states of Cu(II).63 The 6-31G(d) and the 6-311+G(2df,2p) basis sets were utilized for the optimization of quinoxaline atoms, and the Cu ions were optimized utilizing either the LanL2DZ basis set or the Watchers−Hay basis set (6-311+G(d)) supplemented with a set of (1s2p1d) diffuse functions, two sets of f functions and one set of g functions (i.e., (2f1g) polarization functions) as they have proven to provide satisfactory results for the

E inter = EQXL···Cu n + − ECu n + − EQXL′

(2)

EQXL···Cun+

where is the total energy of the optimized complex, ECun+ is the total energy of the isolated Cun+ cation and EQXL′ is the total energy of the QXL in the complex. Solvent effects on geometries and relative conformational stabilities were taken into consideration using the polarizable continuum model (PCM)72 in the integral equation formalism framework.73 All calculations were performed utilizing the Spartan 10 V1.0174 and the Gaussian03 program.75 The schematic representations of the structures were drawn using ChemOffice package in the UltraChem 2010 version and the optimized structures were drawn using either Spartan 10 V1.01 or gaussView 4.5. 1585



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RESULTS AND DISCUSSION

Table 2. Interaction Energies (kcal/mol) for the Calculated Quinoxaline···(H2O)n Adducts; Results with Different Calculation Methods

Isolated Quinoxaline: Results in Vacuo and in Different Solvents. The optimized QXL conformer and its HOMO and LUMO densities are shown in Figure 2. The frontier molecular orbitals are known to play a significant role in the reactivity of biologically active molecules. The selected molecular properties related to reactivity, such as the dipole moment, the energy of the HOMO (EHOMO), and the energy of the LUMO (ELUMO) are reported in Table 1. EHOMO provides information about the tendency of a molecule to donate electrons to an electron-poor species, while ELUMO provides information about the tendency of a molecule to accept electrons from an electron-rich species. Other molecular properties reported in Table 1 include the ionization energy (IE) and the electron affinity (EA). The HOMO has a high density distribution above and below the benzene ring, indicating that this is the region with high electron density. For the results in vacuo, the energy difference between HOMO and HOMO−1 is marginal (being ≤1 kcal/mol with all the methods), suggesting that HOMO−1, which has a high density distribution in the heterocyclic ring, has also a vital role in the reactivity of QXL. Lower molecular orbitals (e.g., HOMO−1) that are nearly degenerate with the HOMO, are considered to be important and to take part in interactions of various molecular systems.76−79 However, the results also show that, in the presence of a solvent, the energy separation between HOMO and HOMO−1 is greater than 2 kcal/mol (i.e., in solution, the degeneracy of the HOMO and HOMO−1 is removed), and it increases with the increase in solvent polarity. The value of the dipole moment suggests that QXL has very low polarity and would interact better in nonpolar media. The ionization energy value estimated in vacuo is close to the experimental IP value,80 with the percentage error of 2.5 with B3LYP/6-31G(d), 1.3 with B3LYP/6-31++G(d,p), 0.9 with B3LYP/6-311+G(2df,2p), and 4.3 with MP2/6-31+G(d) methods. The electron affinity values estimated in vacuo with the B3LYP/6-31++G(d,p) and B3LYP/6-311+G(2df,2p) are close to the experimental EA value for QXL.81 However, the estimated EA value using B3LYP/6-31G(d,p) and MP2/631+G(d) methods are unrealistic, which emphasizes the significance of inclusion of diffuse functions and the choice of appropriate calculation method for the estimation of EA. Quinoxaline···(H2O)n Complexes: Results of the Study in Vacuo. The optimized geometries for QXL···(H2O)n clusters are shown in Figure 3, the corresponding interaction energies (ΔEinter) and the parameters of the intermolecular Hbonds are reported in Tables 2 and 3, respectively. The complexes are named with the acronym QXL followed by the number of water molecules (aq) in the complexes. Cases in which there is more than one complex with the same number of water molecules are distinguished by using an increasing alphabetic letter after the number of water molecules. For instance, QXL-1aq is a QXL···(H2O) complex with a water molecule H-bonded to QXL; QXL-2aq-a, QXL-2aq-b, and QXL-2aq-c are QXL···(H2O) complexes in which each complex has two water molecules arranged differently from the arrangement of the water molecules in the other two complexes. The results show that, for each geometry obtained, the arrangement of the water molecules in the optimized geometry is similar to the starting input structure. In all the complexes, the main interactions accounting for energy stabilization are the

ΔEinter (kcal/mol) in vacuo

a

in water solution

adduct

MP2/6 -31+G(d)

B3LYP/ 6-31+ +G(d,p)

MPWB1K/ 6-31+ +G(d,p)

B3LYP/ 6-31+ +G(d,p)

MPWB1K/ 6-31+ +G(d,p)

QXL-1aq-a QXL-2aq-a QXL-2aq-b QXL-2aq-c QXL-3aq-a QXL-3aq-b QXL-3aq-c QXL-4aq-a QXL-4aq-b QXL-5aq-a QXL-5aq-b QXL-6aq-a QXL-6aq-b QXL-8aq-a QXL-8aq-b

−5.8 −9.0 −9.5 −11.6 −12.8 −11.3 −14.8 −18.4 −14.5 −22.3 −20.2 −25.4 −20.5 −17.3 −25.7

−5.9 −9.4 −9.7 −11.6 −13.1 −11.9 −14.8 −18.7 −15.3 −22.6 −20.4 −26.0 −24.2 −19.9 −27.1

−6.5 −10.0 −10.5 −12.2 −13.6 −12.4 −15.5 −19.4 −16.0 −23.4 −21.2 −26.8 −25.2 −21.1 −28.1

−2.8 −6.5 −6.7 −5.3 −9.6 −11.0

−2.6 −6.7 −6.3 −5.2 a −11.1

−12.2 −13.8 −15.6

−12.0 −14.0 −15.2

−19.0

−19.2

On optimization, the calculation fails to converge.

lpN···H−O and C−H···O intermolecular H-bonds, with the lpN···H−O being shorter and stronger than the C−H···O Hbond. The lpN···H−O and C−H···O intermolecular H-bonds are strongly determined by the cooperativity effect. The cooperativity effect, which is present when the OH group of the water molecule act as both a proton donor and acceptor in H-bonding interactions,82−90 affects both the H-bond strength (i.e., the interaction energy) and the H-bond parameters. ΔEinter for QXL-2aq-c is nearly double ΔEinter for QXL-1aq, which could be a result of the fact that the number of N···H−O and C−H···O intermolecular H-bonds in QXL-2aq-c is twice that in QXL-1aq. ΔEinter for QXL-2aq-a and QXL-2aq-b is 3.3 kcal/mol (with MP2) higher than ΔEinter of QXL-1aq; this is despite the fact that in both systems the number of N···H−O and C−H···O H-bonds is the same. It is clear, however, from Table 3 that the C−H···O in QXL-1aq is longer and less directional (therefore weaker) than the C−H···O in either QXL-2aq-a or QXL-2aq-b. Therefore, the arrangement of the two water molecules, that are H-bonded to each other and each is in turn H-bonded to QXL, may influence ΔEinter. A comparison of ΔEinter for QXL-2aq-a and QXL-2aq-b suggests that the water molecule has a slight preference to form C− H···O H-bond with H2 than with H9 (i.e., the water molecule prefers to bind to the CH group of the heterocyclic ring than the aromatic ring). This is despite the fact that the C−H9···O in QXL-2aq-a has better directionality (bond angle of 177°) than the C−H2···O in QXL-2aq-b (bond angle of 154°). The preference for the water molecule to H-bond to C2−H2 bond, as compared to H-bonding to C9−H9, may be explained by considering the intrinsic acidity of the CH group. Previous studies have shown that the main factor governing the strength of the CH···O H-bonds is the intrinsic acidity of the CH group.91 One way of estimating the intrinsic acidity of the CH group is to calculate and compare the gas-phase acidity (ΔHacidity, which is defined as the change in enthalpy associated with deprotonation of a molecule HA to form H+ and A−)92 at both C2−H2 and C9−H9 sites. A lower ΔHacidity indicates 1586



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Table 3. Parameters of the N···H−O and C−H···O Intermolecular Hydrogen Bonds in the Quinoxaline···(H2O)n Adducts; DFT/MPWB1K/6-31++G(d,p) Results in Vacuo (a) N···H−O and C−H···O bond lengths H-bond length (Å) adduct

N1···H

Q-1aq-a Q-2aq-a Q-2aq-b Q-2aq-c Q-3aq-a Q-3aq-b Q-3aq-c Q-4aq-a Q-4aq-b Q-5aq-a Q-5aq-b Q-6aq-a Q-6aq-b Q-8aq-a Q-8aq-b

1.983 1.899 1.901 1.998 1.799 1.851 1.909 1.809 1.790 1.816 1.803 1.806 1.801 1.760 1.772

H2···O

H3···O

N4···H

H6···O

H9···O 2.457 2.306

2.250 1.999

2.446

2.454 2.318

2.000 1.994

2.465 2.466

2.301 2.320

2.286 2.318 2.317 2.322 2.303 2.332 2.292 2.420 2.348

C6···O

C9···O

2.326 2.191 2.300 2.189 2.292 2.171 2.298 2.170

2.264

1.905 1.992 1.806 1.901 1.949 1.799

2.298 2.268 2.487 2.460 2.202 (b) N···O and C···O bond distances

2.470 2.332

bond distance (Å) adduct

N1···O


2.922 2.870 2.852 2.934 2.779 2.826 2.880 2.787 2.775 2.793 2.787 2.784 2.785 2.739 2.748

C2···O

C3···O

N4···O

3.330 3.379 3.267 2.934

3.323

3.330 3.392

2.936 2.931

3.340 3.339

3.363 3.392 3.391 3.394 3.378 3.406 3.368 3.489 3.407

3.268 3.249 3.255 3.261 3.256 3.244 3.255 3.238

3.261

3.255 3.271 3.333 3.360 3.164 (c) N···H−O and C−H···O bond angles

2.860 2.928 2.784 2.855 2.903 2.773

3.343 3.406 3.363 3.385

bond angle (deg) adduct

N1···H−O


163.90 177.29 165.38 162.91 174.33 177.10 178.17 173.51 178.97 173.83 178.91 173.86 178.76 170.80 169.70

C2−H2···O

C3−H3···O

N4···H−O

C6−H6···O

C9−H9···O 137.07 172.09

155.65 162.66

137.49

137.38 172.70

163.08 163.08

137.40 137.22

174.14 172.41 172.75 171.44 173.11 172.27 174.14 169.39 166.19

144.52 164.94 146.20 170.48 147.366 170.52 146.51 168.71 139.96

152.22 146.51 153.23 134.36 146.84

166.97 163.14 173.86 166.61 169.08 170.74

137.18 172.27 166.81 168.23

give values of 394.6 and 397.0 kcal/mol, respectively, suggesting that the C2−H2 site is more acidic than the C9− H9 site.

greater tendency by the group to donate the H atom. The estimated ΔH acidity for the C2−H2 and C9−H9 sites (calculated in this work using B3LYP/6-31++G(d,p) method) 1587



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mol) is slightly lower than that for pyridine-aq (6.2 kcal/mol) calculated with the same method and basis set.93 As the number of water molecules H-bonded to QXL (and to each other) increase, the length of the lpN1···H−O H-bond shortens; it is shortest in QXL-4aq-b and QXL-8aq-b, where the water molecule H-bonded to N1 is also H-bonded to two other water molecules that are in turn H-bonded to QXL through C−H···O H-bonds. The shortening of the lpN1···H− O H-bond is also a consequence of the cooperativity effect.90 The trends in ΔEinter values are similar across methods. For each complex, ΔEinter estimated using DFT/MPWB1K is slightly higher (0.6−1.2 kcal/mol) than that estimated with DFT/B3LYP. A plot of ΔEinter, where MPWB1K values are plotted against the B3LYP ones (Figure 4) give a correlation

The role of the bridging water molecules in determining the strength of ΔEinter was studied by comparing ΔEinter for a pair of adducts in which one has a bridging water molecule and the other does not have a bridging water molecule. For instance, in QXL-3aq-a and QXL-3aq-b, the results show that the third water prefer to H-bond directly to QXL than to bridge the other two water molecules, probably because in the geometry with bridging water molecules there is less QXL···(H2O) intermolecular H-bonds. A comparison of ΔEinter for QXL-2aqb and QXL-3aq-b, in which two water molecules are H-bonded to QXL, and a comparison of ΔEinter for QXL-3aq-a and QXL4aq-b, in which three water molecules are H-bonded to QXL, suggests that the bridging water molecule in QXL-3aq-b and QXL-4aq-b substantially increase ΔEinter of the complexes. Therefore, geometries that have consecutive arrangement of water molecules (i.e., systems in which the water molecules are H-bonded to each other without a discontinuity in the arrangement of the water molecules) and in which the same number of water molecules are H-bonded to QXL, the preferred arrangement is one in which there are bridging water molecules between water molecules H-bonded to QXL. Investigation of pairs of geometries in which equal number of water molecules interacts with QXL (but the water molecules are not necessarily H-bonded to each other while arranged in the vicinity of QXL) was also made as part of assessing the effect of the different arrangements of water molecules in the vicinity of QXL. The pair of geometries considered include QXL-3aq-a and QXL-3aq-c; QXL-4aq-a and QXL-4aq-b; QXL5aq-a and QXL-5aq-b; and QXL-6aq-a and QXL-6aq-b. For each pair of adducts considered, the results show that the geometry with the highest number of water molecules Hbonded to QXL has the highest ΔEinter and therefore is the most preferred. Increasing the number of water molecules H-bonded to QXL, as in the case of QXL-4aq-a, QXL-5aq-a, and QXL-6aq-a, results in high ΔEinter because, as the number of QXL···(H2O) H-bonds increases, so does the cooperativity effects. The two geometries with eight water molecules (QXL-8aq-a and QXL8aq-b) provide a better understanding for the stabilization role of water molecules that are directly interacting with QXL; in QXL-8aq-a complex, only four water molecules are H-bonded to QXL, while in QXL-8aq-b, six water molecules are directly H-bonded to QXL. Consequently, QXL-8aq-b is better energetically stabilized than QXL-8aq-a because it has more cooperative H-bonding effects. However, a comparison of ΔEinter for QXL-8aq-b and QXL-6aq-a suggests minimal preference for QXL-8aq-b, indicating that, after six water molecules H-bond to QXL, the addition of water molecules has minimal contribution to the stabilization of the complexes. The H-bond geometry parameters of the complexes suggest that the lpN···H−O H-bond in QXL-1aq is 0.026 Å longer than the lpN···H−O H-bond in pyridine−1aq cluster (calculated with the same method and basis set93) and it is 0.050 Å longer than the experimental lpN···H−O H-bond length in pyrazine1aq cluster.94 The lpN···H−O H-bond in QXL-1aq is longer than that of pyridine-1aq and pyrazine-1aq because the water molecule in QXL-1aq complex is engaged in two intermolecular H-bonds simultaneously (i.e., lpN···H−O and C−H···O Hbonds), which is not observed in pyridine-1aq and pyrazine-1aq complexes. The weaker binding property of QXL-1aq with respect to pyridine-1aq is also reflected in values of ΔEinter for the complexes which show that ΔEinter for QXL-1aq (5.8 kcal/

Figure 4. Comparison between ΔEinter values obtained using DFT/ MPWB1K and DFT/B3LYP methods (with 6-31++G(d,p) basis set) for a number of quinoxaline···(H2O)n complexes.

coefficient of 0.9998. Trends in the geometry parameters (i.e., bond length, bond distance, and bond angle) are also similar across methods. The lpN1···H−O H-bond is often 0.020− 0.036 Ǻ longer with DFT/MPWB1K than with DFT/B3LYP. Quinoxaline···(H2O)n Complexes: Results of the Study in the Presence of Water Solvent. The investigation of the complexes in the presence of a solvent is crucial for understanding the influence of the solvent on the geometry and energies of the complexes. For better comparison with the results in vacuo, geometry optimizations in water utilized the in vacuo DFT/B3LYP or DFT/MPWB1K optimized geometries as inputs to evaluate whether the solvent may cause significant geometry changes. In order to keep track of geometric changes, as a result of change in media, the name of the complex optimized in water is the same as the name it has when optimized in vacuo, even if there are substantial geometric changes. The optimized geometries are shown in Figure 5 and the interaction energies are reported in Table 2. QXL-1aq, QXL-2aq-a, QXL-2aq-c, and QXL-3aq-b maintain similar geometry arrangement of water molecules as in vacuo. However, QXL-2aq-b, QXL-4aq-a, QXL-4aq-b, QXL-5aq-a, and QXL-6aq-a show clustering together of some water molecules. In these geometries, the water molecule that was previously H-bonded to the H atom of the heterocyclic ring is clustering to the water molecule H-bonded to N atom of the heterocyclic ring. A comparison of QXL-2aq-a and QXL-2aq-b suggests that the only way by which a water molecule would 1588



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Figure 5. Optimized geometries of the quinoxaline···(H2O)n adducts calculated in water solution with MPWB1K/6-31++G(d,p). Similar geometry arrangements for quinoxaline···(H2O)n complexes were obtained with the B3LYP/6-31++G(d,p) calculation method.

Figure 6. Optimized geometries for the dimers of quinoxaline calculated in vacuo at MP2/6-31+G(d,p). Similar geometry arrangements of quinoxaline dimers were obtained with MPWB1K/6-31++G(d,p) method.

ΔEinter for the complexes calculated in water is lower than in vacuo with all the methods. The weakening of the ΔEinter in solution could be attributed to two factors; the absence of some C−H···O H-bonds and the lengthening of the lpN1···H−O Hbond in most complexes. All complexes (with the exception of QXL-3aq-b) are therefore stabilized by fewer H-bonds than similar complexes obtained in vacuo. The QXL-3aq-b complex offers a possibility for comparing similar geometries between results in vacuo and in solution because ,in this complex, there is no loss of C−H···O H-bond in solution, so that similar geometric factors accounts for the stabilization of the complexes obtained in different media. An examination of the intermolecular H-bond parameters in vacuo and in water solution indicates that, in solution, both lpN1···H−O and C− H···O are longer (1.849 and 2.294 Ǻ , respectively, Supplementary Table 2) than in vacuo (1.825 and 2.173 Ǻ ,

remain H-bonded to H2 is if there is another water molecule bridging the water molecules forming H-bonds with QXL. A similar result is obtained for QXL-4aq-b, where the arrangement of the water molecules at H2 remains similar to that observed in vacuo and the water molecule that in vacuo is Hbonded to H9 is now clustering with the water molecule Hbonded to N1. It is therefore reasonable to infer that, in the presence of a polar solvent, the weaker Csp2−H···O H-bonds are broken in favor of water−water clustering and that the water−water clustering may be minimized by introducing a bridging water molecule between two water molecules Hbonded to QXL. Clustering of water molecules in the presence of aqueous medium is a phenomenon also observed in other molecule−(H2O)n complexes in which the central molecule has stronger H-bond acceptor centers than the Csp2−H group in QXL.95 1589



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Table 4. Relative Stabilization Energies (ΔE, kcal/mol),a Binding Energies (Einter, kcal/mol), and Hydrogen Bond Parameters for the C−H···N H-Bonds relative energy (ΔE, kcal/mol)

interaction energy (ΔEinter, kcal/mol

dimer

MP2/6-31+G(d,p)

MP2/6-311+G(d)

MPWB1K/6-31+G(d,p)

MP2/6-31+G(d,p)

MP2/6-311+G(d)

MPWB1K/6-31+G(d,p)

QXL-QXL-1 QXL-QXL-2 QXL-QXL-3 QXL-QXL-4 QXL-QXL-5 QXL-QXL-6 QXL-QXL-7

0.0 0.4 0.6 3.9 3.9 4.3 4.9

0.0 0.2 0.4 4.7 5.1 5.4 5.8

0.0 0.6 0.5 1.0 0.9 1.7 2.0

−7.7 −7.3 −7.1 −3.8 −3.8 −3.4 −2.8

−8.8 −8.5 −8.4 −4.1 −3.7 −3.4 −3.0

−4.2 −3.6 −3.7 −3.2 −3.3 −2.5 −2.2

Relative stabilization energy is estimated as total electronic energy of given dimer − total electronic energy of the lowest-energy dimer and expressed in kcal/mol. The total electronic energy (Hartree) of QXL-QXL-1 is −833.4831756 with MP2/6-31+G(d,p), −833.6423271 with MP2/6311+G(d), and −835.5672055 with MPWB1K/6-31+G(d,p).

a

Figure 7. Optimized geometries of the quinoxaline···Cu complexes obtained with different calculation methods and in different media. For panels b and c, similar geometries were obtained when the Cu ions were described using the Watchers−Hay basis set. 1590



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Table 5. Calculated Relative Stabilization Energies (ΔE, kcal/mol),a Change in Enthalpies (ΔHth), Change in Free Energies (ΔG, kcal/mol), and Binding Energies (ΔEinter) for the Studied Quinoxaline···Cu Complexes DFT/B3LYP structure, calculation method, and medium Results in Vacuo 6-31G(d)b N···Cu(I) π···Cu(I) N···Cu(II) π···Cu(II) 6-311+G(2df, 2p)c N···Cu(I) π···Cu(I) N···Cu(II) π···Cu(II) 6-311+G(2df, 2p)d N···Cu(I) π···Cu(I) N···Cu(II) π···Cu(II) Results in Water 6-31G(d)b N···Cu(I) π···Cu(I) N···Cu(II) π···Cu(II)

DFT/BHLYP

ΔE

ΔHth

ΔG

ΔEinter

ΔE

ΔHth

ΔG

ΔEinter

0.0 16.0 0.0 13.4

0.0 14.6 0.0 11.5

0.0 15.4 0.0 11.1

260.4 245.3 449.8 435.9

0.0 14.0 0.0 23.1

0.0 13.1 0.0 22.2

0.0 13.9 0.0 21.7

269.2 258.2 427.7 415.1

0.0 16.5 0.0 12.7

0.0 15.7 0.0 10.8

0.0 14.4 0.0 9.9

271.3 254.0 613.9 440.4

0.0 14.3 0.0 21.5

0.0 13.5 0.0 20.5

0.0 14.2 0.0 20.1

274.0 262.0 429.8 417.8

0.0 16.9 0.0 13.1

0.0 16.6 0.0 12.2

0.0 15.5 0.0 11.6

271.3 253.6 614.2 440.3

0.0 14.6 0.0 28.7

0.0 14.4 0.0 28.0

0.0 11.7 0.0 26.8

273.2 261.0 427.0 407.8

0.0 9.4 0.0 4.7

187.5 177.1 264.6 260.7

0.0 7.7 0.0 15.0

0.0 7.4 0.0 14.7

197.7 173.7 242.3 238.5

0.0 9.9 0.0 5.1

Relative stabilization energy is estimated as total electronic energy of a given QXL···Cu complex − total electronic energy of the lowest-energy QXL···Cu and expressed in kcal/mol. The QXL···Cu (I) complexes are estimated separately from the QXL···Cu (II) complexes. bThe C, N, and H atoms are calculated with the 6-31G(d) basis set, and the Cu ion is calculated with the LanL2DZ basis set. cThe C, N, and H atoms are calculated with the 6-311+G(2df,2p) basis set, and the Cu ion is calculated with the LanL2DZ basis set. dAll atoms are calculated with the 6-311+G(2df,2p) basis set. For Cu, the basis set 6-311+G(2df,2p) corresponds to the 14s9p5d(9s5p3d) Wachters−Hay basis supplemented with a set of (1s2p1d) diffuse functions and with two sets of f functions and one set of g functions.

a

reported by other researchers,96,97 with those of QXL dimers provides a good analysis of the influence of the N atom on the structures and ΔEinter for aromatic systems. A study on the dimers of naphthalene concluded that the cross-displaced and the slipped-parallel displaced are the preferred geometries,96−98 what is also in agreement with the results for QXL dimer obtained in the current work. A comparison of ΔEinter for the dimers of naphthalene98 and the dimers of QXL (both obtained using the MP2 method) suggests that the presence of the N heteroatoms in QXL favors greater ΔEinter. In an attempt to confirm our observation, we studied the preferred dimer for naphthalene (i.e., the slipped-parallel displaced geometry) using the DFT/MPWB1/6-31+G(d,p) method. The result shows that its ΔEinter is −3.0 kcal/mol, indicating that it is 1.2 kcal/ mol lower than the preferred geometry for QXL dimer (calculated with the same method). Furthermore, a comparison of ΔEinter for benzene and pyridine dimers also reached a similar conclusion that pyridine dimers are better stabilized than benzene dimers.35,99 The QXL-QXL-7 dimer, in which the two monomers have a near T/perpendicular stacking arrangement, has the highest ΔE and the weakest ΔEinter. The studies on naphthalene dimers also reported that the weakest ΔEinter corresponds to the dimer with a T-shaped arrangement of the monomer.96,98 Although the trend in ΔEinter for the dimers is the same across methods, the results indicate that ΔEinter obtained with MP2/6-31+G(d,p) are overestimated with respect to ΔEinter obtained with MPWB1K/6-31+G(d,p). In comparison to MP2/6-31+G(d,p) results, the DFT/MPWB1 interaction

respectively). The weakening of the H-bonds provides an explanation for the fact that ΔEinter in solution is 0.9 kcal/mol lower than in vacuo. For all other complexes, where ΔEinter in solution is lower than that in vacuo by more than 3 kcal/mol, the largest contributing factor to the lowering of ΔEinter is the loss of the C−H···O H-bond. Quinoxaline Dimers. The optimized geometries of QXL dimers are shown in Figure 6. The dimers are named using the notation QXL-QXL and differentiated using an increasing arabic number. The increasing numbering system is related to the increasing order of relative energy of the dimers. The dimers are stabilized by either stacking π−π interactions (e.g., QXL-QXL-1, QXL-QXL-2, and QXL-QXL-3) or weak Csp2− H···N intermolecular H-bonds (e.g., QXL-QXL-4, QXL-QXL5, and QXL-QXL-6). Among the dimers stabilized by π−π interactions QXL-QXL-1 and QXL-QXL-2 have a crossdisplaced arrangement of the planes of the monomers, while QXL-QXL-3 has a slipped antiparallel displacement of the planes of the monomers (i.e., the two monomers are arranged in such a way that the heterocyclic ring on one monomer is oriented on the same side as the benzene ring on the other monomer). The relative energies (ΔE) and the binding energy (ΔEinter) for the dimers, calculated with different methods, are reported in Table 4. The lowest-energy geometries correspond to π−π stacking interactions with a cross-displaced or a slipped antiparallel displacement of the monomer units. These dimers also have the best ΔEinter among the investigated dimers. A comparison of the structures and ΔEinter of naphthalene dimers, 1591



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the total spin density of the QXL···Cu(II) complexes (Figure 8) suggests that the unpaired electron is exclusively located on

energies have larger error for stacking dimers (45% for QXLQXL-1, 51% for QXL-QXL-2, and 48% for QXL-QXL-3) than dimers stabilized by intermolecular H-bonds (17% for QXLQXL-4, 14% for QXL-QXL-5, and 25% for QXL-QXL-6). Quinoxaline···Cu Complexes: Results of the Study in Vacuo. Input structures were prepared by taking into consideration the fact that the electron-poor Cu ion would prefer to interact with electron-rich sites in QXL, which are the π electrons of the aromatic ring and the lone pair of electrons on the N atoms (Figure 2). Therefore, inputs for the QXL···Cu complexes were prepared by arranging the Cu ion in the vicinity of the benzene ring, close enough to result in cation···π interaction, and in the vicinity of the lone pair of N atom, close enough to result in lpN···Cu interactions. The optimized geometries are shown in Figure 7 for both Cu(I) and Cu(II) complexes; the relative energies (ΔE) and the binding energies (ΔEinter), calculated with different methods, are reported in Table 5. The bond lengths in QXL and the lpN···Cu distances for the complexes are reported in Tables S6 and S7 (Supporting Information); the charges on the Cu ion, spin density on Cu(II), and the donor−acceptor stabilization energies (obtained from Natural Bond Order (NBO) analysis) are reported in Table S8 (Supporting Information). ΔE values indicate that complexes stabilized by cation···π interactions are negligibly populated with respect to complexes stabilized by lpN···Cu interactions. ΔEinter for each complex stabilized by lpN···Cu interaction is also higher than ΔEinter for each complex stabilized by cation···π interaction, which suggests that the most preferred interactions in QXL···Cu complexes are the lpN···Cu interactions. A comparison of ΔEinter for the Cu(I) and Cu(II) complexes suggests that Cu(II) complexes are better stabilized than Cu(I) complexes by a factor of 1.6 with all the methods. Interestingly enough, however, the donor−acceptor stabilization energy (Table S4, Supporting Information) for the vacant or partially filled s or d orbital in the Cu ion is strongest for the Cu(I) complexes than for the Cu(II) complexes. This difference could be attributed to the fact that, on interaction with quinoxaline, the Cu(II) ion is reduced to Cu(I) so that the information obtained from NBO analysis, for the quinoxaline···Cu(II) complexes, corresponds to the interaction between quinoxaline radical cation (QXL+) and Cu+ rather than QXL and Cu2+ ion.66,67,100−102 In the lpN···Cu complexes, the N1−C2 and the C10−N1 bond lengths are longer than in the isolated QXL, indicating that the formation of the N···Cu bond weakens the N1−C2 and the C10−N1 bonds as a result of electron withdrawal on the N atom to stabilize the Cu ion. The N1···Cu bond length is shorter in Cu(I) complexes than in Cu(II) complexes, which is in agreement with the NBO analysis that Cu(I) cation is better stabilized than Cu(II) cation by the lone pair of electrons on the N atom. The charges on the isolated Cu(I) and Cu(II) ions is +1 and +2, respectively. The natural charge (obtained from the natural population analysis, NPA) on the Cu(I) in the QXL···Cu complexes has a value of 0.823e for the N···Cu complex and a value of 0.891e for the π···Cu complex. The NPA charge on Cu(II) in the QXL···Cu complexes has a value of 0.912e for the lpN···Cu complex and a value of 0.891e for the Cu···π complex, representing a significant decrease in the charge on the Cu(II) ion with respect to the isolated QXL. This means that, on the formation of QXL···Cu(II) complexes, the Cu(II) ion is reduced to Cu(I) ion and QXL is oxidized. The spin density on Cu(II) in the complexes is vanishingly small, and the study of

Figure 8. Electron spin density from spin SCF density (isovalue = 0.0004) for the optimized quinoxaline···Cu(II) complexes.

QXL so that the [QXL···Cu]2+ complexes can be considered as the interaction between Cu(I) and QXL•+ radical ion, as also observed in other molecular complexes.65,66,100−102 Separate studies on the complexes were performed in which the Cu ions were described by either the LANL2DZ basis set or the 6-311+G(2df,2p) basis set. A comparison of ΔEinter (kcal/ mol) for the complexes obtained when the copper ions are described using the LANL2DZ basis set (274.0 for Cu(I) and 429.8 for Cu(II), obtained with DFT/BHLYP) and when the copper ions are described using the 6-311+G(2df,2p) basis set (273.2 for Cu(I) and 427.0 for Cu(II), obtained with DFT/ BHLYP) suggests that the differences in ΔEinter are within marginal errors, indicating that both basis sets provide adequate description for Cu ions interacting with a base. The QXL···Cu(I) interaction energies obtained with DFT/ B3LYP and DFT/BHLYP methods are not very different, with the % error remaining below 5% with all the methods. However, the QXL···Cu(II) interaction energies obtained with DFT/B3LYP method are overestimated with respect to interaction energies obtained with DFT/BHLYP, with the % error in some cases being as large as 42%. The high ΔEinter for QXL···Cu(II) complexes obtained with DFT/B3LYP are consistent with the observed trend, by other researchers, that BHLYP functional provides better estimation of ΔEinter for Cu(II) complexes than B3LYP functional.36,63 Quinoxaline···Cu Complexes: Results of the Study in Water Solution. The optimized geometries in water solution are also shown in Figure 7. Geometries of the optimized lpN···Cu complexes and that of π···Cu(I) complex are similar for the results in vacuo and water solution. However, the geometry of π···Cu(II) complex suggests that, in vacuo, the Cu(II) ion prefers to bind to the C7C8 π bond, while in water solution, it prefers to bind to C8C9 π bond. The energy-gap between lpN···Cu and π···Cu complexes is smaller in the presence of water solvent than in vacuo, and ΔEinter are overestimated in vacuo with respect to the results in water solution. The overestimation in ΔEinter (considering DFT/ BHLYP results) is highest for the Cu(II) complexes (∼−185 kcal/mol for N···Cu and −175 kcal/mol for π···Cu) than for the Cu(I) complexes (∼−72 kcal/mol for N···Cu and −84 kcal/mol for π···Cu). All these results point to the influence of the solute−solvent polarization extent on the geometry (in the case of π···Cu(II) complexes) and on the energetics of the complexes. Solute polarization effects also affect the Cu charges in the complexes, with the results that the NPA charge on Cu ions is higher in water solution than in vacuo (an increase of 0.05988e for N···Cu(I), 0.0352e for π···Cu(I), 0.05306e for N···Cu(II), and 0.09425e for π···Cu(II). 1592



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CONCLUSIONS Quantum chemical studies were performed to determine the structures, relative stabilization energies, and binding energies of quinoxaline···(H2O)n complexes, quinoxaline dimer, and quinoxaline···Cu complexes. The studies were performed with different calculation methods, different basis sets, and in different media because of the individual requirements for the different systems considered and the desirability for obtaining meaningful results while keeping computations within an affordable range. The study of the quinoxaline···(H2O)n adducts has shown that, in vacuo, the preferred arrangements of water molecules on quinoxaline correspond to the formation of strong intermolecular N···H−O H-bond and weak Csp2− H···O H-bond. The study of the quinoxaline···(H2O)n adducts in water solution (to take into consideration the bulk solvent effects) has highlighted the preference for water−water clustering as a result of disruption of some C−H···O intermolecular H-bonds, with the only exception being cases in which the water molecules directly H-bonded to quinoxaline are bridged by a third water molecule. The outcome of the study in solution may also be interpreted to mean that the interaction between the explicit water molecules and the bulk solvent are stronger than the interaction between explicit water molecule and the CH groups of the quinoxaline moiety, leading to the disruption of the C−H···O intermolecular H-bonds. The dimers of quinoxaline are stabilized by either intermolecular Csp2−H···N hydrogen bonds or π−π stacking interactions. The binding energies suggest that dimers with π−π stacking interactions are preferred to dimers stabilized by hydrogen bonds. The study of the quinoxaline···Cu complexes has shown that complexes in which the Cu ion is interacting with the lone pair of the N heteroatom are preferred to complexes in which the Cu ion is interacting with the π system of the aromatic ring. The binding energies suggest that the preferred Cu binding sites are determined by both the nature of Cu cation and the nature of the binding site. The difference in the affinity of Cu(I) and Cu(II) ions to the quinoxaline moiety is related to the ability of Cu(II) to oxidize quinoxaline, which is not observed in the interaction of quinoxaline with Cu(I). The NBO analysis of the complexes has shown that covalent a charge transfer mechanism may account for the interaction of Cu(I) or Cu(II) with quinoxaline. The study in the presence of water solvent highlights the overestimation of the binding energies in vacuo and an overestimation of the charges on Cu ions in water solution. Overall, the results provide valuable information for understanding the binding properties of benzoheterocyclic compounds. The outcomes of the study may be compared with similar results of other aromatic systems (e.g., benzene, naphthalene, pyridine, etc.) or could be utilized as starting information for studies of other N-heterocyclic compounds whose binding properties have yet to be investigated.

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MP2/6-31+G(d,); Table S3 reports the parameters of the Hbonds in the quinoxaline···(H2O) adducts obtained in vacuo with B3LYP/6-31++G(d,p); Table S4 reports the parameters of the H-bonds in the quinoxaline···(H2O)n adducts for the B3LYP/6-31++G(d,p) results in water solution; Table S5 reports the parameters of the H-bonds in the quinoxaline···(H2O)n adducts for the DFT/MPWB1K/6-31++G(d,p) results in water solution; Tables S6 and S7 reports bond length (Å) and bond distances (Å) between atoms in the quinoxaline···Cu complexes for DFT/B3LYP results in vacuo and in the presence of water solvent; Table S8 reports charges on the Cu ion, spin density on Cu(II), and the donor−acceptor stabilization energy for the results in water solution. Figure S1 compares relative energy values (ΔE) and interaction energy values (ΔEinter) obtained using DFT/MPWB1K/6-31+G(d,p) and MP2/6-31+G(d,p) methods for a number of quinoxaline dimers. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +27-18-389-2239. Fax: +27-18-389-2051. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.M.K. wishes to express his gratitude to the North-West University (South Africa) for granting him a Postdoctoral fellow scholarship. We wish to thank Professor Liliana Mammino of the University of Venda (South Africa) for her technical assistance with some computations. We wish to dedicate this work to Professor Liliana Mammino for her hard work to advance the development of Computational and Theoretical Chemistry in Africa. Finally, we wish to express our gratitude to the reviewers for their fruitful suggestions.

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ASSOCIATED CONTENT

S Supporting Information *

Eight tables are included as supplementary material; table S1 reports the geometrical parameters of quinoxaline (calculated with different methods) and compares them with similar geometrical information from crystal structural data for quinoxaline; Table S2 reports the parameters of the H-bonds in the quinoxaline···(H2O) adducts obtained in vacuo with 1593



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