Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 72–81

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Quantum chemical exploration of the intramolecular hydrogen bond interaction in 2-thiazol-2-yl-phenol and 2-benzothiazol-2-yl-phenol in the context of excited-state intramolecular proton transfer: A focus on the covalency in hydrogen bond Bijan Kumar Paul 1,2, Aniruddha Ganguly 1, Nikhil Guchhait ⇑ Department of Chemistry, University of Calcutta, 92 A.P.C. Road, Calcutta 700009, India

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

 Hydrogen bonding interaction in 2-

thiazol-2-yl-phenol and 2benzothiazol-2-yl-phenol.  Exploration of IMHB by Atoms-InMolecule and NBO analysis.  Covalancy in intramolecular hydrogen bond.  Interplay between aromaticity and RAHB.  Potential energy surface calculation for ESIPT reaction.

a r t i c l e

i n f o

Article history: Received 7 January 2014 Received in revised form 25 March 2014 Accepted 29 March 2014 Available online 16 April 2014 Keywords: Intramolecular hydrogen bond Hyperconjugative charge transfer Aromaticity ESIPT Atoms-In-Molecules Natural Bond Orbital

a b s t r a c t The present work demonstrates a computational exploration of the intramolecular H-bond (IMHB) interaction in two model heterocyclic compounds – 2-thiazol-2-yl-phenol (2T2YP) and 2-benzothiazol2-yl-phenol (2B2YP) by meticulous application of various quantum chemical tools. Major emphasis is rendered on the analysis of IMHB interaction by calculation of electron density q(r) and Laplacian r2q(r) at the bond critical point using the Atoms-In-Molecule methodology. Topological features based on q(r) suggest that at equilibrium geometry the IMHB interaction develops certain characteristics typical of a covalent interaction. The interplay between aromaticity and Resonance-Assisted H-Bond (RAHB) has also been discussed using both geometrical and magnetic criteria. The occurrence of IMHB interaction in 2T2YP and 2B2YP has also been criticized under the provision of the Natural Bond Orbital (NBO) analysis. The ESIPT phenomenon in the molecular systems is also critically addressed on the lexicon of potential energy surface (PES) analysis. Ó 2014 Elsevier B.V. All rights reserved.

Introduction ⇑ Corresponding author. Tel.: +91 33 2350 8386; fax: +91 33 2351 9755. E-mail address: [email protected] (N. Guchhait). Equal contribution. Present address: Department of Chemistry and Biochemistry, University of Colorado, Boulder, CO 80309, United States. 1 2

http://dx.doi.org/10.1016/j.saa.2014.03.124 1386-1425/Ó 2014 Elsevier B.V. All rights reserved.

The hydrogen bonding (H-bond) interaction has formed the nucleus of intensive research for years. This is, however, readily understandable given the pivotal roles played by this important weak interaction to a plethora of structural and mechanistic consequences in chemistry, biology and condensed matter phenomena.

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The H-bonding interaction is ubiquitous in nature and an inevitable conduit of the natural system to sustain and maintain life-cycle on this planet. The directional nature of H-bond deserves a special mention because of its key roles in phenomena like crystal engineering, stabilization of the secondary structure of biomolecules like proteins, nucleic acids (DNA, RNA) and so forth [1–4]. Therefore, a thorough understanding of the interaction promises to yield critical acumen into many effects taking place not only in the crystal state, but also in solutions and living organisms. One particular type of H-bonding interaction is the one found in association with excited-state intramolecular proton transfer (ESIPT) phenomenon, i.e. the intramolecular hydrogen bond (IMHB), which is a particular case of the interaction occurring within the same molecular framework. Ever since the pioneering report by Weller [5], the ESIPT phenomenon has continued to garner attention on fundamental as well as applicative research arenas, particularly given the achievement of some serendipitous applications of a variety of ESIPT probes on grounds e.g., development of photostabilizers, ESIPT lasers, UV absorbers, molecular logic gates and so forth [6–8]. Further, the prolific use of various ESIPT probes as molecular reporters for many biological, biomimicking and supramolecular assemblies has been recognized since years [9–12]. Thus obviously, the attention focused on the phenomenon (ESIPT) is both cognitive and applied. The four-level photophysical scheme associated with the ESIPT reaction yielding the characteristic large Stokes shifted emission feature not only rationalizes the aforementioned applications of ESIPT probes but also provide reasonable grounds for understanding of improved operations of these probes as molecular reporters through facile minimization of common experimental artifacts e.g., selfabsorption, inner filter effect and so on [9–13]. The basic photophysical process accompanying ESIPT phenomenon has been illustrated in a generalized manner in Scheme 1. The ESIPT photophysics has been extensively investigated since years using chromophoric design based on benzothiazole and benzimidazole molecular framework [6,14–17]. Apart from serving as typical molecular architecture for study of various aspects of the phenomenon from both experimental and computational standpoints [14–17], organic chromophores based on these molecular units have shown potential for multi-faceted applications as well [6,18–21]. Organic compounds based on this particular chromophoric design have recently claimed their proficiency as molecular probes in detecting protein tyrosine phosphatase (PTP) activity [18] which, in recent time, is demanding critical attention in biomedical research in the context of cellular regulation and signal transduction pathways in several human diseases, e.g., cancer,

diabetes, and Alzheimer’s [22–24]. Also many structurally analogous derivatives of these compounds are capturing attention in development of drugs for detrimental diseases with anti-cancer [18], anti-leishmanial [25] activities and so forth. Further, these classes of compounds have found prospective applications in development of two-photon absorbing organic materials with tailored luminescence properties [19,20] and as efficient sensors for trace and biologically and/or environmentally important metal ions/anions [21]. The IMHB interaction is well-documented to have its crucial impact on the feasibility and rate of ESIPT process [26–28]. The present investigation is focused on a meticulous exploration of the effect in two archetypical ESIPT molecular systems viz., 2-thiazol-2-yl-phenol (2T2YP) and 2-benzothiazol-2-yl-phenol (2B2YP) (vide Scheme 2) from theoretical viewpoint. Particular emphasis has been rendered on the application of different quantum chemical tools for detection and evaluation of the strength of IMHB in the studied molecules. The topological properties of IMHB interaction are assayed from the Atoms-In-Molecules (AIM) [29] methodology, while a critical evaluation of the role of hyperconjugative charge transfer interaction is deduced from Natural Bond Orbital (NBO) population analysis [30]. The presence of covalency in IMHB interaction accounting for Resonance-Assisted Hydrogen Bond (RAHB) interaction [31] is also tested from geometrical criteria as well as quantum chemical analysis. Further, the interplay between aromaticity and RAHB has been explored in this context. In brief, in this contribution we wish to present an in-depth understanding into the nature of IMHB interactions present in the studied ESIPT molecular systems by applying quantum chemical techniques. Subsequently, a computational study of the photoinduced proton transfer process [1–3,30] in the studied molecular systems has also been undertaken.

Computational details Geometry optimization All structural calculations have been performed with the Gaussian 03W suite of programs [32] using Density Functional Theoretical (DFT) method. Theoretical calculations were performed with θ

θ

θ

θ H

Scheme 1. Simplified paradigm showing the principal photophysics of a typical ESIPT process. Usually X = O, N or S in the schematic molecular framework.

Scheme 2. Schematic structures of the molecular systems under investigation along with the numbering of atoms as used throughout the study. The IMHB and the IMHB ring site are also highlighted. The open form (O-form) as produced through rotation across the dihedral angle h (lacking the IMHB interaction) is also shown here.

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the hybrid B3LYP functional, i.e., a combination of the Becke’s three-parameter (B3) exchange functional [33] and Lee–Yang–Parr (LYP) nonlocal correlation functional [34]. In this calculation particular emphasis is delivered on the 6-311++G(d,p) basis set because this basis set is of triple-f quality [27,35] for valence electrons with diffuse functions which are useful for anions and structures with lone pair electrons [27,35]. We have exploited the 6-311++G(d,p) basis set by considering the necessity of diffuse functions for full characterization of the hydrogen bond interaction. The geometrical constraints were not imposed in equilibrium geometry optimizations. Frequency calculations were carried out for the optimized structures in order to assess the nature of stationary points and to obtain zero point energy (ZPE) corrections. The characteristic of local minimum was verified by establishing that matrices of energy second derivatives (Hessian) have no imaginary frequency [27,32]. NBO and AIM calculations The Natural Bond Orbital (NBO) analysis has been employed to evaluate the direction and magnitude of donor–acceptor interactions. The necessary computations for NBO analysis [30,36] has been performed on Gaussian 03W software package [32] The contour plot is generated on NBO View (Version 1.1) suite of programs [30,36] using the standard keywords implemented therein. Similarly, the AIM [29] calculation has also been performed on Gaussian 03W software at B3LYP/6-31G(d,p) level using the standard keywords implemented therein. Calculation of aromaticity indices The Harmonic Oscillator Model of Aromaticity (HOMA) [37] index has been employed as a geometrical criterion of local aromaticity. According to the definition proposed by Kruszewski and Krygowski [37,38] the applied formula is as follows:

HOMA ¼ 1 

n   1X ai Ropt;i  Rj 2 n j¼1

ð1Þ

where n corresponds to the number of bonds within the analyzed ring. In case of the present study n is equal to 6, The term a being a constant fitted to give a value of HOMA = 1 for ideally aromatic systems with all bond lengths equal to optimal value, Ropt and HOMA = 0 for nonaromatic species (for CC bonds: a = 257.7 and Ropt = 1.388 Å). As defined by Schleyer et al. the Nucleus Independent Chemical Shift (NICS) index has been used for the measure of magnetic indicator of local aromaticity [39]. This is one of the most widely employed indicators of aromaticity. NICS(0) is defined as the negative value of the absolute shielding computed at a ring center determined by the nonweighted average of the heavy atoms’ coordinates in the ring. Rings with large negative NICS(0) values are considered aromatic. The more negative the NICS(0) value, the more aromatic the ring is. However, it has been shown by Lazzeretti and Aihara [40,41] that NICS(0) values may contain important spurious contributions from the in-plane tensor components that are not related to aromaticity. So, to complement the NICS analysis, NICS(1) values have also been calculated as the negative values of absolute shielding measured 1 Å above the center of the ring. It has been postulated that NICS(1) better reflects aromaticity patterns because at 1 Å the effects of the p-electron ring current are dominant and local r-bonding contributions are diminished. Elucidation of potential energy curve (PEC) The ground-state potential energy surface (PES) for the proton transfer process in 2T2YP and 2B2YP has been evaluated from a

relaxed scan performed at B3LYP/6-311++G(d,p) level of theory while the excited-state PES has been obtained from TD-DFT optimization method. The necessary calculations for the construction of the GSIPT and ESIPT PESs have been performed on Gaussian 09 suite of programs [42]. Results and discussion Intramolecular H-bond (IMHB) in 2T2YP and 2B2YP Implication for the presence of IMHB interaction in 2T2YP and 2B2YP from optimized geometry parameters The initial insights into the presence of IMHB interaction in the studied molecular systems, viz., 2T2YP and 2B2YP are assessed from comparison of the optimized geometrical parameters of the closed conformers (i.e., C-forms) with those in the respective open counterparts (cf. Scheme 2). Since the open forms of the molecules are devoid of IMHB interaction a comparison of their geometry parameters with those of the corresponding closed forms will reflect the modulations in optimized geometry parameters as imparted by the presence of IMHB. As seen in Table 1, the shortening of the proton donating bond length (H1AOd distance) in the open form compared to the closed form is in line with the occurrence of IMHB interaction in all the molecular systems under investigation [27,28]. Apart from this, the data compiled in Table 1 also reveals some detectable modulations in geometry parameters surrounding the entire IMHB site in the studied molecules, e.g., shortening of C4@Na and C2@C3 bonds along with lengthening of C3AC4 and OdAC2 distances. The changes in the optimized geometry parameters in these directions upon moving from the closed to the open form can be corroborated to the presence of resonance assistance in the IMHB interaction present in these molecular systems [27,28]. This point will be further explored in the forthcoming discussions. In this context, endeavors are made toward evaluation of verisimilar estimates for the energy of the IMHB interactions in the molecular systems under study. This attempt is, however, fraught with ambiguities in the literature given the lack of any unequivocally accepted approach as against the intermolecular hydrogen bonding case. Such tailback has eventually led to the proposition of various approaches in the literature to estimate the energy of an intramolecular hydrogen bond; the methods adopted in the present work are outlined below: Closed vs. open forms. In this approach the energy of the IMHB is approximated to the energy difference between the intramolecularly hydrogen bonded closed form and the open form in which

Table 1 Differences in selective optimized geometry parameters (B3LYP/6-311++G(d,p)) at the IMHB site between the closed form and the open form of 2T2YP and 2B2YP. D = Rclosed  Ropen in Å. The numericals in parenthesis indicate the corresponding optimize geometry parameters of the closed form. Geometry parameters

2T2YP

2B2YP

D(C4@Na)

0.01394 (1.31514) 0.02471 (0.98766) 0.01612 (1.34422) 0.01046 (1.42034) 0.01505 (1.45723) 0.28673 (2.63795)

0.01558 (1.30663) 0.02509 (0.98814) 0.01661 (1.34274) 0.01074 (1.42128) 0.01622 (1.45543) 0.26053 (2.63459)

D(H1AOd) D(OdAC2) D(C2@C3) D(C3AC4) D(OdANa)

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the hydrogen donor AOH group is rotated 180° apart from the hydrogen bonded configuration to generate the non-hydrogen bonded open form [43]:

Scheme 1), EZ and ZE conformers are obtained by rotating respectively the donor and acceptor groups across their respective carbon–carbon linkages and the EE conformer designates the fictitious conformer in which both the donor and the acceptor groups have been rotated about their bonds. Following the scheme used in the literature [45] the hydrogen bond energy is assayed as: ð3Þ

EHB ¼

 1 f EEZ þ EfEE  EZZ 2

ð4Þ

In this equation, EfEZ ðEfEE Þ designates the energy of the fictitious EZ (EE) conformer in which the bond lengths are the same as in the ZZ conformer whose energy is given by EZZ in its equilibrium config1 ð3Þ uration. The results from this method are: EHB ¼ 9:76 kcal mol for 1 2T2YP and 10.22 kcal mol for 2B2YP. ð1Þ

Hydrogen bond energy; EHB ¼ DE ¼ EClosed  EOpen

ð2Þ

This approach, however, comprises the intrinsic assumption of ignoring the influence of the aforementioned rotation on overall geometry parameters of the concerned molecule other than simply cleavage of the hydrogen bond from the contiguous IMHB circuit. 1 ð1Þ The results from this method are: EHB ¼ 11:75 kcal mol for 2T2YP and 11.90 kcal mol1 for 2B2YP (Fig. 1 displays the potential energy curves for rotation of the OH functional moiety 180° apart from that in the H-bonded closed form to the non-hydrogen bonded O-form). Empirical energygeometry correlations. Establishing the correlation between energetic properties and geometry parameters within IMHB frameworks has remained a concern on the vanguard of research on the topic. The one that has been widely accepted till date appears to be the proposition by Musin and Mariam [44] which suggests an exponential correlation as follows:

EHB ¼ ð5:554  105 Þ expð4:12  ROO Þ ð2Þ

ð3Þ

in which RO  N represents the distance between the Od and Na atoms in the equilibrium geometry in Å (cf. Scheme 1). The negative sign before EHB has been introduced to maintain the consistency in the use of notation throughout the work, cf. in Ref. [44], the hydrogen bond energy is denoted as a negative number while in the present work it is denoted as a positive number. The results from this 1 ð2Þ method are: EHB ¼ 10:58 kcal mol for 2T2YP and 10.73 kcal mol1 for 2B2YP. Conformational analysis. This method accounts for the IMHB energy in a given molecular system from a complex conformational analysis of the four possible conformers, viz., ZZ, EZ, ZE and EE, emanating from rotation of the donor and acceptor functional moieties [45]. The ZZ conformer represents the lowest energy intramolecularly hydrogen bonded closed conformer (vide

Local potential energy density. In this method, the IMHB energy is connected to the local potential energy density at the hydrogen   bond critical point (VCP) and the atomic volume element a30 through the following equation [46]: ð4Þ

EHB ¼ 

a30 V CP 2

ð5Þ ð4Þ

1

The results from this method are: EHB ¼ 13:62 kcal mol and 13.76 kcal mol1 for 2B2YP.

for 2T2YP

Analyzing the presence and strength of IMHB in 2T2YP and 2B2YP from simulated infrared (IR) spectra IR spectroscopy has been conventionally applied as a powerful tool for characterizing the presence and assessing the strength of H-bond in a given molecular system. Herein, we have exploited the strategy to rationalize the presence of IMHB in the studied molecular systems using computationally simulated IR spectra (cf. Fig. S1 in Supporting Information). Conventionally, the formation of IMHB is described as to involve a hyperconjugative charge transfer from the lone pair of the acceptor atom (here Na) to the r(OdAH1) orbital (to be elaborated in forthcoming section), which is necessarily to accompany some decrement in the OdAH1 bond order as reflected in weakening of the OdAH1 bond energy in the closed form compared to that in the open form which is devoid of the IMHB and thereby accounts for the observed blue-shift in the OdAH1 IR stretching frequency on moving from the intramolecularly H-bonded closed from to the open form (512 cm1 for 2T2YP and 521 cm1 for 2B2YP) [27,28]. This result advocates for the presence of IMHB interaction in the studied molecules. Topological parameters: Atoms-In-Molecules (AIM) analysis Atoms-In-Molecule (AIM) method of Bader [29], which is mainly based on an analysis of electron density at specific points (q(r)), provides an effective measure of detection as well as

Fig. 1. Plot of variation of energy for (a) 2T2YP (– d –) and (b) 2B2YP (solid sphere) as a function of rotation of the torsional angle, h, for transformation of the intramolecularly hydrogen bonded C-form to the non-hydrogen bonded O-form as obtained from calculation at B3LYP/6-311++G(d,p).

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characterization of H-bonding [27–29]. Based on this theory, Koch and Popelier has proposed a few criteria relying on the electron density parameter q(r), to detect the presence of hydrogen bond [27,28,47,48]. According to them, the existence of a hydrogen bond will be characterized by (i) the presence of a bond critical point (BCP) between the hydrogen atom and the acceptor atom; (ii) the value of q(r) at this BCP (qc) is within the range [0.002, 0.04] a.u.; (iii) the Laplacian of q(r) at this BCP (r2qc) is positive and within the range [0.02, 0.15] a.u. and (iv) the hydrogen atom and the acceptor atom must mutually penetrate, i.e., the bonded radius of the hydrogen atom and the acceptor atom must each be smaller than the corresponding nonbonded radii [47,48]. However, recent time has witnessed fruitful extension of the AIM methodology including other parameters like electronic energy densities [27,28]. As far as many AIM studies deal only with equilibrium geometries, our effort extends to a more elaborate exploitation of the hydrogen bonding interaction scenario by exploring the evolution of the molecular geometries over a range of intramolecular hydrogen bond (HB) distances [27,28]. In the present work, the wave functions of H-bonded molecular geometries obtained from 6-31G(d,p) level of calculation has been employed to characterize topological properties of the electronic charge density. Electron density of the bond critical point (BCP). According to Bader’s theory, identification of the critical point (CP) and the existence of a bond path in the equilibrium geometry are necessary and sufficient conditions to assign the presence of a bond between two atoms [29]. However, Cioslowski et al. have claimed that it should be interpreted as attractive or repulsive interactions leading to either bonding or nonbonding situation [49], which was further validated by Bickelhaupt and coworkers [50]. Therefore, care has been taken during interpretation of the AIM topological parameters in the present program. Fig. 2 displays the variation of qc (q(r) at BCP) and its Laplacian r2qc (r2q(r) at BCP) as a function of the IMHB distance for the both the studied systems. The relevant parameters corresponding to the optimized geometries are summarized in Table 2 which shows that qc, i.e., q(r) at the BCP for the ground-state optimized geometry is hovering around 0.040 a.u. (the maximum Popelier threshold value) for both the studied molecules [47,48]. Therefore, the presence of intramolecular hydrogen bond in the molecules is quite well justified by the theory (Fig. 2). The sharp variation of the AIM topological parameters (qc and r2qc; Fig. 2) as a function of the IMHB distance dictates steep change in magnitude of the parameters with the variation of IMHB distance. Such notable sensitivity of these parameters with the variation of IMHB distance, advocates for the presence of strong hydrogen bonding interaction in the studied molecular systems and is the result of decrease in

extent of orbital overlap with elongation of IMHB distance [27– 29,51,52]. It is interesting to note in the present context that qc corresponding to the optimize geometry for the studied systems is slightly greater than the maximum Popelier threshold value of 0.04 [27,51,52]. On the basis of Bader’s theory, this can be treated as an indication for the presence of partial covalency in the concerned IMHB interactions [29,51,52]. This observation thus points towards the presence of resonance assistance in the IMHB interactions and is further assessed and explored in forthcoming discussions. Also the existence of Ring Critical Points (RCPs; vide Table 2) within the quasi-rings formed by the IMHB frameworks in the optimized geometry of the studied molecules (cf. Scheme 2) substantiate the presence of IMHB interaction in the molecular systems according to the Bader’s theory of AIM [27–29,51,52]. Following similar track of argument as discussed above, the sharp decrement of qc(RCP) with perturbation of the IMHB distance from that of the equilibrium geometry, Fig. 3, further substantiates the presence of a strong H-bonding interaction within the studied molecular systems. Electronic energy density. The local energy densities computed at the BCP yield valuable information to fathom deeper into the nature of an interaction. The local expression for the virial theorem is given as [27–29,51,52]:

VðrÞ þ 2GðrÞ ¼

1 2 r qðrÞ 4

ð6Þ

where V(r) and G(r) are the electronic potential and kinetic energy densities, respectively. Since G(r) > 0 and V(r) < 0, the sign of the Laplacian at the BCP determines which energy density dominates at r [27–29,51,52]. Now, the total energy density H(r) = V(r) + G(r) at the BCP: Hc = Vc + Gc, characterizes the type of bond. A negative Hc reflects the dominance of V which according to Eq. (2) may be viewed as a consequence of accumulating charge at the BCP [27– 29,51,52]. Therefore, in bonds with any degree of covalency the following condition will hold: |Vc| > Gc and Hc < 0. However, bonds in which this condition is satisfied but |Vc| < 2Gc will be characterized by r2qc > 0 leading to a closed-shell interaction, while Hc < 0 implying a shared interaction. This type of interaction is described to be partially covalent and partially electrostatic [27–29,51,52]. Fig. 4 displays the energetic properties of BCP as a function of IMHB distance in the studied molecules and it is apparent that both Vc and Gc are well correlated to the presence of hydrogen bonding interaction. The results in Table 2 show a positive value for the Laplacian of electron density in all cases characteristic of a closed shell interaction. However, a slightly negative value of

Fig. 2. Plot of variation of qc (q(r) at BCP) (– d –, green) and r2qc (r2q(r) at BCP) (– s –, purple) as a function of the IMHB distance (Na  H1) for the C-form of (a) 2T2YP and (b) 2B2YP. The solid lines only provide a visual guide to the pattern of variation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Table 2 Summary of the AIM topological parameters for 2T2YP and 2B2YP at the IMHB bond critical points (BCPs) corresponding to the ground-state optimize structures of the studied molecular systems [hydrogen bond distances (R), electron densities (qc), Laplacian (r2qc) of electron densities, kinetic energy densities (Gc), potential energy densities (Vc), total energy densities (Hc) at the respective BCPs and electron densities at the Ring Critical Points (qc(RCP)) within the IMHB quasi-rings].

a

Molecular system

R (Å)

qc (a.u.)

r2qc (a.u.)

Gca (a.u.)

Vca (a.u.)

Hca (a.u.)

qc(RCP) (a.u.)

2T2YP 2B2YP

1.75701 1.75423

0.04595 0.04628

0.1146 0.1148

0.03603 0.03627

0.04342 0.04384

0.00739 0.00757

0.01640 0.01657

1 1 a.u. of energy density = Eha3 m3. 0 = 1.77178  1034 kJ mol

Fig. 3. Plot of variation of qc (q(r) at RCP) as a function of the IMHB distance (Na  H1) for the C-form of 2T2YP and 2B2YP. The solid lines only provide a visual guide to the pattern of variation.

Hc at the BCP implies the presence of partial covalency. This finding is reinforcing to the aforementioned observation with q(r) at BCP (qc). Population analysis from NBO perspective The Natural Bond Orbital (NBO) method, proposed by Weinhold et al. has been recognized as a potential tool for the rationalization of H-bonds, which correlates well with the changes in bond length in accordance with basic chemical concepts. It is also used to gain information on the changes of charge densities at the proton donor and acceptor as well as in the bonding and antibonding orbitals. Now, the interaction between the filled (e.g., the lone-pair) and antibonding orbitals represents the deviation of the molecule from the Lewis structure and can be used as a measure of delocalization due to the presence of hydrogen bonding interaction [30]. Hydrogen bonds, within the NBO framework, are conventionally interpreted to be formed as a result of charge transfer from the proton acceptor to the proton donor, and hence the amount of charge transfer plays a significant role in determining the elongation or contraction of the H  Y bond (XAH  Y). For each donor and acceptor, the stabilization energy DE2 associated with i–j delocalization is calculated from the following equation [30]:

Fig. 5. Variation of E2 (LP (Na) ? r(OdH1)) hyperconjugative interaction energy as a function of the Na  H1 IMHB distance for the C-form of 2T2YP and 2B2YP. The solid lines only provide a visual guide to the pattern of variation.

DE2 ¼ DEijð2Þ ¼

D 2  F jUj   Ui j b ðei  ej Þ

ð7Þ

where b F is the Fock operator and ei and ej correspond to the energy eigenvalues of the donor NBO, Ui, and the acceptor NBO, Uj, respectively. The results of NBO analysis for both the molecular systems are depicted in Fig. 5 which shows that the hyperconjugative stabilization interaction (DE2) between Na lone pair (LP) and the r(OdAH1) orbital is sharply diminished with elongation of the Na  H1 IMHB, justifying the presence of IMHB in the molecules. This is again substantiated from the contour plot showing the overlap between the Na lone pair orbital and the r(OdAH1) orbital (cf. Fig. S2 in Section S2). The presence of a finite, nonzero overlap between the orbitals obviously manifests the presence of a finite, nonzero stabilization interaction (DE2) due to the hyperconjugative charge transfer interaction from Na lone pair to the r(OdAH1) orbital resulting in the formation of the IMHB interaction. Also a good extent of overlap advocates for a strong IMHB in the studied molecular systems, in corroboration to other findings (as discussed above).

Fig. 4. Relationship between the electronic energy density properties (G(r) (– s –) and V(r) (– d –)) of BCP and the intramolecular H-bond distance (Na  H1) in (a) 2T2YP and (b) 2B2YP. The solid lines only provide a visual guide to the pattern of variation.

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The perusal of the variation of population (occupation number as calculated from NBO analysis) of the respective LP and r orbitals, as elaborated in the Supporting Information (cf. Fig. S3 in Section S2), is also attuned with the concept of formation of IMHB in 2T2YP and 2B2YP as discussed under the NBO perspectives. Another major factor that needs to be addressed in the present context is the rehybridization which accompanying repolarization of the XAH bond (in a XAH  Y hydrogen bonding system) upon Hbond formation makes hydrogen more electropositive such that the ‘s’ character of the X-hybrid atomic orbital of XAH bond increases leading to contraction and hence imparts a shortening effect on the XAH bond. Hyperconjugation and rehybridization thus act in opposite directions so that the net outcome in terms of a red or blue-shift of the XAH bond is governed by a balance of the two effects. The variation of percentage ‘s’-character of Odhybrid atomic orbital of the OdAH1 bond in the studied molecular systems is seen to exhibit that the percentage s-character on Od attains the minimum value at the equilibrium geometry of the molecule in all cases while it increases with elongation of the IMHB distance (cf. Fig. S4 in Section S2). This result strongly substantiates the instrumental role of hyperconjugation rather than rehybridization in the studied IMHB systems which thereby leads to a redshift of the OdAH1 stretching frequency in the H-bonded C-form compared to that in the O-form (vide Section ‘Excited-State Proton Transfer (ESIPT) process in 2T2YP and 2B2YP’, Fig. 1) [27–29,53]. Resonance-Assisted Hydrogen Bond (RAHB) Interplay between IMHB and aromaticity. Assistance from additional effects is well known to augment the strength of H-bond, e.g., resonance or charge-assisted H-bonding. The concept of Resonance-Assisted Hydrogen Bond (RAHB) was coined by Gilli and coworkers [4,31]. Usually RAHBs are classified as p-conjugated ring or chain motifs, for which characteristic changes in geometrical or electronic properties are observed, i.e., elongation of formally double bonds and shortening of formally single bonds, together with elongation of the XAH bond and shortening of the H  Y bond within the H-bridge: XAH  Y [27,28,52,53]. The comparison of optimized geometry parameters between the closed and open conformations of the studied molecular systems (vide Section ‘Intramolecular H-bond (IMHB) in 2T2YP and 2B2YP’, Table 1) led to the initial indications for the occurrence of RAHB in the systems (Scheme 3a). Herein, we endeavor to delve into an interplay between the resonance assistance in the IMHB interaction and the aromaticity of the benzene nucleus. The descriptors of aromaticity used in the work and relevant discussions regarding their calculations are presented in Section ‘Computational details’ and the results are compiled in Table 3.

(a)

H

O C

N C

(b)

H

O

N S

H C

C

C

O C

N

C

C

C

S

Scheme 3. Schematic paradigm for (a) general structure of the studied molecules at the IMHB ring site and electronic movement in the cyclic Resonance-Assisted Hydrogen Bonding interaction; (b) tautomeric equilibrium and the structure of the tautomers involving the benzene and thiazole aromatic nuclei.

Here we attempt to explore the operation of RAHB in the studied systems in analogy to reported literatures [27,28,52,53]. Three simultaneous p-electron delocalization effects can be considered within the analyzed systems. The first one refers to the global pelectron delocalization effect occurring within the aromatic nucleus, leading to stabilization of the aromatic species. In the Clar’s model [54,55], an aromatic p-sextet in a Kekulé resonance structure is defined as six p-electrons localized in a single benzene ring separated from adjacent rings by formal CC single bonds. In a general sense, this model refers to the Kekulé resonance structure with the largest number of disjoint aromatic p-sextets to be the socalled Clar structure [54,55]. However, our investigated systems are devoid of additional complexities by the presence of only one ring in the molecule and the p-sextet of electrons has to be localized within this ring. The second effect is concerned about the interaction between the substituents present in the aromatic ring. A schematic of the effect is shown in a general manner for both the studied molecules in Scheme 3b. It is obvious that the communication between substituents (the mesomeric effect) engages the p-electrons of the aromatic nucleus. It is thus conventionally argued that the effect of interaction between the substituents proceeds in a direction that resists the process of p-electron delocalization within the ring, whereby perturbing the uniform electronic distribution within the aromatic ring [27,54,55]. Therefore, the global p-electron delocalization effect and the substituent effect can be described to be mutually competitive. The operation of the substituent effect should thus lead to a decrement of the aromaticity of the ring compared to the unsubstituted counterpart. Indeed, all aromaticity indices used in this work are found to substantiate this postulation through a comparison between the closed and open forms of both the studied systems (Table 3). Therefore, it is logical at this stage to argue that the mutually competitive global p-electron delocalization effect and the substituent effect are present in both the investigated systems and the IMHB interaction plays a role in determining the local aromaticity of the systems. In fact, the last effect to be discussed in the series is strictly associated with the intramolecular RAHB and is applicable to closed conformations only. As can be seen in Scheme 3a, the effect of resonance within the additional pseudoaromatic ring formed from the RAHB interaction proceeds in the same direction as it is for the substituent effect (Scheme 3b). Therefore, these two effects should mutually cooperate. Even it is postulated that both the effect of communication between the substituents and the resonance accompanying H-bonding are in fact the same phenomenon which can be considered as a mesomeric effect amplified with the process of formation of the extra pseudoaromatic RAHB ring [27,53–57]. These results corroborating to the formation of RAHB in the studied molecular systems probably evinces that determination of IMHB energy simply by calculating the energy difference between the intramolecularly hydrogen bonded closed form (Cform) and the non-hydrogen bonded open form (O-form) is not a rational method to apply (it may even be misleading), at least for the presently investigated molecules and within the present computational window. A basic pitfall of this method may veil in the assumption of ignoring the interactions of the lone pair electrons

Table 3 Comparison of different aromaticity indices for the benzene aromatic nucleus of 2T2YP and 2B2YP (closed form vs. open form). Molecular HOMA system 2T2YP 2B2YP

NICS(0)

NICS(1)

0.92459 vs. 0.96614 7.7045 vs. 8.6219 8. 0266 vs. 9.3654 0.91948 vs. 0.96377 7.6191 vs. 8.0928 8.1640 vs. 9.2642

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on the oxygen atom of the OH functional moiety with the pelectron system of the aromatic nucleus via C3@C4 bond which could be manifested as resonance interaction energy differences. This apparently simple strategy also ignores other geometry parameters and their subsequent effect on the molecular optimized energies during rotation of the OdAH1 functional moiety to produce the non-hydrogen bonded open conformer [27,53].

p-Delocalization effect in RAHB in the context of ellipticity of bonds. The ellipticity (e) at the BCP can be interpreted as a measure of the anisotropy of the curvature of the electron density in the directions normal to the bond, in which a zero value signatures the absence of anisotropy. Thus ellipticity is often regarded to reflect a sensitive index to monitor the p-character of bonds. The ellipticity at the BCP is a direct measure of the degree to which the electron density is unequally distorted in perpendicular directions away from the bond axis [29]. The ellipticity values at the respective BCPs for the bonds surrounding the IMHB framework in 2T2YP and 2B2YP at the equilibrium geometries are comprised in Table 4. Pure single, double, and triple bonds have been found to have ellipticity values equal to 0.014, 0.298, and 0.000 in butane, ethene and ethyne, respectively [29]. Thus a direct comparison with the studied molecular systems reveals discernible increase of ellipticity for the formally single CAC bond, while the same for formally double C@C bonds decreases at the IMHB ring site of both 2T2YP and 2B2YP (cf. Table 4). These findings thus comply with the notion of the absence of pure single and pure double bond characters across the bonds concerned and are hence attuned with the p-electron delocalization concept relating to ResonanceAssisted Hydrogen Bonds. The analysis of isoelectronic molecular electrostatic potential surfaces (MEPS) for 2T2YP and 2B2YP (cf. Fig. S5 in Section S3) also substantiates the argument of p-electron delocalization within the contiguous IMHB circuit. Excited-State Proton Transfer (ESIPT) process in 2T2YP and 2B2YP Structural parameters The photo-induced proton transfer process in 2T2YP and 2B2YP involves structural rearrangement associated with cleavage of the OdH1 bond. The initial glimpse of the ESIPT process in 2T2YP and 2B2YP is thus obtained from assessment of the changes in optimized geometry parameters of the molecules following photoexcitation from the ground-state to the S1-state, and then the changes due to conversion into the PT-form. The relevant geometry parameters are summarized in Table S1 of the Supporting Information. Elongation of C2@Na and C3@C4 bonds following photo-excitation from S0 to S1-state is consistent with the notion of reduction in double bond character of the bonds. Simultaneously, shortening of the C4Od and C2@C3 bonds evinces enhancement of multiple character after photo-excitation. The interchange in H-bond (Na  H1) and covalent bond (OdH1) character across the H-bonded network, Na  H1Od, as a result of occurrence of ESIPT is also evident from significant shortening and lengthening of

Table 4 Ellipticity (e) parameters at the BCPs of the bonds involved in Resonance-Assisted Hydrogen Bond formation in 2T2YP and 2B2YP. Bonds

Ellipticity (e) 2T2YP

2B2YP

OdAH1 OdAC4 C3@C4 C2AC3 C2ANa

0.01784 0.01004 0.2327 0.1421 0.2184

0.01767 0.00829 0.2298 0.1423 0.2142

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respectively the NaH1 and OdH1 distances upon photo-excitation. The structural changes along these directions juxtapose well with the concept of ESIPT. For the sake of completeness, the optimized geometry parameters of the PT-form are compared concurrently (cf. Table S1). It is worth noting that the C2C3 and C4Od linkages are even shorter in the PT-form compared to that in the S1-state geometry. Similarly, the N2Ca and C3C4 linkages are longer in PT-geometry than in the photo-excited C-form (S1-state). GSIPT vs. ESIPT potential energy surfaces (PESs) A critical evaluation of the ESIPT process from the perspective of potential energy surface (PES) is of huge diagnostic importance. Apart from helping one to delve into the energetics of the process, this approach hints valuable information regarding the mechanistic details also. Herein, the PES for ESIPT reaction in the studied molecular systems has been constructed according to the method described in Section ‘Elucidation of potential energy curve (PEC)’. The minimum-energy paths (MEPs) connecting the two concerned structures in each electronic state have been calculated to identify the major coordinates involved in the PT process and the results are displayed in Fig. 6. The excited-state potential energy surfaces (PESs) has been constructed by TD-DFT optimization method as discussed in Section ‘Elucidation of potential energy curve (PEC)’. Fig. 6 reveals that the C-form constitutes the global minimum structure on the ground-state PESs (S0-surface) for both the molecules. The high instability of the PT-form in the ground state PES coupled with the high energy barrier for C-form ? PT-form transformation dictates the non-viability of ground state intramolecular proton transfer (GSIPT) process in 2T2YP and 2B2YP. As seen in Fig. 6, the S1-surface reflects remarkable reduction of the barrier across the proton transfer coordinate following photoexcitation from the S0-state. This signals not only the inoperativeness of a GSIPT process, but also the feasibility of an ESIPT process in 2T2YP and 2B2YP. It is obvious that a meaningful description of the ultrafast photoinduced PT process should require the surfaces to be large enough so as to include both the closed and PT geometries in both the electronic states (S0 and S1). Therefore, for construction of the PESs, energy variation is observed as a function of the OdANa distance apart from the PT reaction coordinates (OdAH1 distance). Several other coordinates were examined during the MEP analysis over the molecular skeleton for their relevance in describing the PT dynamics, but many of them were found to vary insignificantly or only monotonically (ca. Fig. 7) with the PT reaction coordinate. Hence, the OdAH1 and OdANa coordinates were finally selected for describing the ultrafast dynamics and construction of these PESs of the ESIPT process in 2T2YP and 2B2YP [17,27]. This calculation accounts for the possibility of a facile proton transfer reaction in the S1-state of 2T2YP and 2B2YP. The calculated PESs for 2T2YP and 2B2YP show a back proton transfer in the ground-state to produce the stable C-form. It is relevant at this stage to highlight the characteristic four-level photophysical scheme of ESIPT reaction of 2T2YP and 2B2YP (Fig. 6), which allows almost complete exclusion of self-absorption and thus accounts for the observed large Stokes shifted emission [14–16]. Also an almost barrierless ‘C ? PT’ transition (ESIPT) on the S1state PES and an exothermic nature of the S1-state PES should conform to an ultrafast nature of the ESIPT process in 2T2YP and 2B2YP in corroboration to experimental reports [14–16]. Fig. 7 illustrates the variation of OdANa distance and angle \OdAH1ANa as a function of the PT coordinate (i.e. OdAH1 bond axis) to show that the occurrence of PT involves significant deformation of the entire molecular architecture. As seen in the figure, the OdANa distance contracts to a minimum and \OdAH1ANa angle increases to a maximum before relaxing to the PT-form. This may be a corroboration of the fact that the S0 and S1 surfaces are

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Fig. 6. Ground-state (GS) and excited-state (ES) potential energy surfaces (PESs) for the ESIPT reaction in (a) 2T2YP and (b) 2B2YP plotted in terms of variation of energy as a function of OdAH1 and OdAOa distances.

Fig. 7. Variation of OdAOa distance (open markers) and angle \OdAH1AOa (solid markers) with PT reaction coordinate, OdAH1 distance, in (a) 2T2YP and 2B2YP.

quite distinct with respect to their gross appearances and also the S1-surface minima are relatively shallow and located at a larger OH distance than S0-surface minimum (Fig. 6). A crossover point between C- and PT-forms is obtained at ROH  1.3 Å. This mirror image plot indicates towards the unavoidable errors that would have been incorporated in results for a frozen calculation (unrelaxed/rigid scan) [17,27]. Fig. 7 shows that the PT is dominated by a large change of distance between the two heteroatoms (Od and Na). The transfer mechanism can be described in three consecutive phases associated with the three regions, viz., E minimum, barrier, PT minimum in the S1 MEP energetics (Fig. 7). In the first phase the OdANa distance decreases (from 2.638 to 2.427 Å for 2T2YP and 2.635 to 2.425 Å for 2B2YP) along with a shortening of the NaAH1 distance (from 1.757 to 1.144 Å for 2T2YP and 1.754 to 1.141 Å for 2B2YP), while the OdAH1 bond is elongated by 0.3 Å. At the barrier, the OdANa distance attains a minimum and the OdAH1 bond character is exchanged to NaAH1 bond character. Finally, the heteroatoms separate again and the proton remains with Na atom. When the system passes by the E geometry, it has already gained considerable momentum, which is sufficient to carry over the small barrier for the transformation to PT

and thus allows ESIPT [17,27]. Additionally, the variation of optimized geometry parameters in the course of photoinduced PT process as presented in Fig. 7 can be critically assayed to conceptually visualize the movement of the H1-atom in course of the process. Fig. 7 evinces that attainment of the crossover point at ROH  1.3 Å requires the OdANa distance to contract to a minimum and the angle \OdAH1ANa to increase to a maximum value before relaxing to the PT-form. While concurrently the NaAH1 distance has been shortened considerably (Fig. 7) at the crossover point of ROH  1.3 Å. Again the co-planarity of the atoms at the IMHB site (comprising the atoms at the IMHB framework) is another significant criterion to sustain the appreciably strong IMHB in the molecules, given the directional nature of IMHB interaction. Such geometric constraints describing the process of translocation from C-form ? PT-form can be satisfied if we assume the movement of the H1-atom in a manner that during attainment of the crossover point (at ROH  1.3 Å) it moves a bit upward on the plane (comprising the atoms at the IMHB framework) in a direction that justifies shortening of the NaAH1 distance. If the H1-atom moves a little downward or does not change its coordinate on the crossover point, the condition of shortening of the OdANa distance would

B.K. Paul et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 131 (2014) 72–81

entail contraction of angle \OdAH1ANa. Therefore, the only possibility for motion of the H1-atom that can juxtapose with the necessary geometric modification in the course of PT process as presented in Fig. 7 is as argued above. Concluding remarks The present work articulates a computational investigation on the photophysics of two quintessential heterocyclic ESIPT probes 2T2YP and 2B2YP with major emphasis being driven toward delineating the IMHB interaction in the molecular systems and a mechanistic assay of the ESIPT process within the presently employed computational window. Calculation of IMHB energy predicts a strong IMHB interaction in the studied molecular systems. In order to fathom deeper into the nature of the H-bonding interaction it has been characterized in terms of the effects arising from the electron distribution under the provision of AIM theory. The present results, within the AIM framework, appear to indicate that only electrostatic consideration may not be adequate to account for the interaction in the equilibrium geometries as covalent bond characteristic, mainly Hc < 0, is found to exist in the presently investigated IMHB systems. But surprisingly, the description provided by quantum calculations clearly differs from that of a typical covalent bond. So, it is perhaps not improbable to state that the overall interaction is partially ionic and partially covalent. This is fairly supported from IMHB–aromaticity inter-correlation under the concept of resonance-assistance in the IMHB interaction. Also the critical perusal of the interplay between aromaticity and IMHB interaction in 2T2YP and 2B2YP unveils that the substituent effect and the effect of resonance assistance of the H-bond are mutually cooperating. Furthermore, it is noted that some important properties of the IMHB interactions in the studied molecules e.g., directional nature, presence of partial covalency are fruitfully assessed from the quantum chemical parameters, while the inadequacy of only geometrical criteria are also evident in this respect. In another aspect of the work emphasis is given on the photoinduced proton transfer reaction. Within our computational window, the non-viability of GSIPT reaction and feasibility of ESIPT process in both the studied molecular systems has been critically addressed from an analysis of the potential energy surface (PES) for the reaction. The characteristic four-level photophysical scheme of ESIPT process in 2T2YP and 2B2YP is found to be well manifested through the as-constructed PES. Acknowledgment A research fellowship for AG from the Council of Scientific and Industrial Research (CSIR), Government of India is gratefully acknowledged. NG likes to thank UPE and CRNN of CU for financial assistance. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.saa.2014.03.124. References [1] G. Jeffrey, An Introduction to Hydrogen Bonding, Oxford University Press, New York, 1997. [2] S. Scheiner, Hydrogen Bonding: A Theoretical Perspective, Oxford University Press, New York, 1997. [3] G. Desiraju, T. Steiner, The weak hydrogen bond, in: Structural Chemistry and Biology, Oxford University Press, Oxford, 1999.

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[4] G. Gilli, P. Gilli, J. Mol. Struct. 552 (2000) 1–15. [5] A.H. Weller, Z. Elektrochem. 60 (1956) 1144–1147. [6] J. Zhao, S. Ji, Y. Chen, H. Guo, P. Yang, Phys. Chem. Chem. Phys. 14 (2012) 8803– 8817. [7] J.E. Kwon, S.Y. Park, Adv. Mater. 23 (2011) 3615–3642. [8] K.C. Tang, M.J. Chang, T.Y. Lin, H.A. Pan, T.C. Fang, K.Y. Chen, W.Y. Hung, Y.H. Hsu, P.T. Chou, J. Am. Chem. Soc. 133 (2011) 17738–17745. [9] B.K. Paul, N. Guchhait, J. Phys. Chem. B 114 (2010) 12528–12540. [10] B.K. Paul, A. Samanta, N. Guchhait, Langmuir 26 (2010) 3214–3224. [11] B.K. Paul, N. Guchhait, J. Phys. Chem. B 115 (2011) 10322–10334. [12] J.S. Wu, W.M. Liu, J.C. Ge, H.Y. Zhang, P.F. Wang, Chem. Soc. Rev. 40 (2011) 3483–3495. [13] J.R. Lakowicz, Principles of Fluorescence Spectroscopy, Plenum, New York, 1999. [14] T. Iijima, A. Momotake, Y. Shinohara, T. Sato, Y. Nishimura, T. Arai, J. Phys. Chem. A 114 (2010) 1603–1609. [15] J.S. Stephan, K.H. Grellmann, J. Phys. Chem. 99 (1995) 10066–10068. [16] A.P. Fluegge, F. Waiblinger, M. Stein, J. Keck, H.E.A. Kramer, P. Fischer, M.G. Wood, A.D. DeBellis, R. Ravichandran, D. Leppard, J. Phys. Chem. A 111 (2007) 9733–9744. [17] M. Fores, M. Duran, M. Sola, M. Orozco, F.J. Luque, J. Phys. Chem. A 103 (1999) 4525–4532. [18] A. Kamal, K.S. Reddy, M. Naseer, A. Khan, R.V.C.R.N.C. Shetti, M. Janaki Ramaiah, S.N.C.V.L. Pushpavalli, C. Srinivas, M. Pal-Bhadra, M. Chourasia, G.N. Sastry, A. Juvekar, S. Zingde, M. Barkume, Bioorg. Med. Chem. 18 (2010) 4747– 4761. [19] I.A. Mikhailov, M.V. Bondar, K.D. Belfield, A.E. Masunov, J. Phys. Chem. C 113 (2009) 20719–20724. [20] A.R. Morales, K.J. Schafer-Hales, C.O. Yanez, M.V. Bondar, O.V. Przhonska, A.I. Marcus, K.D. Belfield, ChemPhysChem 10 (2009) 2073–2081. [21] M. Santra, B. Roy, K.H. Ahn, Org. Lett. 13 (2011) 3422–3425. [22] M.E. Noble, J.A. Endicott, L.N. Johnson, Science 303 (2004) 1800–1805. [23] M.J. Evans, B.F. Cravatt, Chem. Rev. 106 (2006) 3279–3301. [24] S. Kumar, B. Zhou, F. Liang, W.-Q. Wang, Z. Huang, Z.-Y. Zhang, Proc. Natl. Acad. Sci. USA 101 (2004) 7943–7948. [25] F. Delmas, A. Avellaneda, C.D. Giorgio, M. Robin, E.D. Clercq, P. Timon-David, J.P. Galy, Eur. J. Med. Chem. 39 (2004) 685–690. [26] L.G. Arnaut, S.J. Formosinho, J. Photochem. Photobiol., A 75 (1993) 1–20. [27] A. Ganguly, B.K. Paul, S. Ghosh, N. Guchhait, Comput. Theor. Chem. 1018 (2013) 102–114. [28] S.J. Grabowski, J. Phys. Org. Chem. 17 (2004) 18. [29] R.F.W. Bader, Atoms in Molecules, A Quantum Theory, Oxford University Press, New York, 1990. [30] A.E. Reed, L.A. Curtiss, F.A. Weinhold, Chem. Rev. 88 (1988) 899–926. [31] G. Gilli, V. Bertolasi, in: Z. Rappoport (Ed.), The Chemistry of Enols, Wiley, Chichester, UK, 1990 (Chapter 13). [32] Gaussian 03, M.J. Frisch et al., Gaussian Inc., Pittsburgh, PA, 2003. [33] A.D. Becke, J. Chem. Phys. 98 (1993) 5648–5652. [34] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785–789. [35] W.J. Hehre, L. Radom, P.v.R. Schleyer, J.A. Pople, Ab Initio Molecular Orbital Theory, Wiley, New York, 1986. [36] E.D. Glendening, A.E. Reed, J.E. Carpenter, F.A. Weinhold, NBO, Version 3.1, 1995. [37] J. Kruszewski, T.M. Krygowski, Tetrahedron Lett. 13 (1972) 3839–3842. [38] T.M. Krygowski, M.K. Cyranski, Chem. Rev. 101 (2001) 1385–1419. [39] P.V.R. Schleyer, C. Maerker, A. Dransfeld, H. Jiao, N.J.R. Hommes, J. Am. Chem. Soc. 118 (1996) 6317–6318. [40] P. Lazzeretti, Phys. Chem. Chem. Phys. 6 (2004) 217–223. [41] J. Aihara, Chem. Phys. Lett. 365 (2002) 34–39. [42] M.J. Frisch et al., Gaussian 09, Revision A.02-SMP, Gaussian Inc., Wallingford, CT, 2009. [43] P. Schuster, in: P. Schuster, G. Zundel, C. Sandorfy (Eds.), The Hydrogen Bond, vol. 1, North Holland, Amsterdam, The Netherlands, 1976. [44] R.N. Musin, Y.H. Mariam, J. Phys. Org. Chem. 19 (2006) 425–444. [45] M. Jablonski, A. Kaczmarek, A.J. Sadlej, J. Phys. Chem. A 110 (2006) 10890– 10898. [46] E. Espinosa, E. Molins, J. Chem. Phys. 113 (2000) 5686–5694. [47] U. Koch, P.L.A. Popelier, J. Phys. Chem. 99 (1995) 9747–9754. [48] P.L.A. Popelier, J. Phys. Chem. A 102 (1998) 1873–1878. [49] J. Cioslowski, S.T. Mixon, J. Am. Chem. Soc. 114 (1992) 4382–4387. [50] C.F. Guerra, J.-W. Handgraaf, E.J. Baerends, F.M. Bickelhaupt, Voronoi Deformation Density (VDD) Charges: Assessment of the Mulliken Bader Hirshfeld Weinhold and VDD Methods for Charge Analysis. [51] R.F.W. Bader, J. Phys. Chem. A 102 (1998) 7314–7323. [52] J.N. Woodford, J. Phys. Chem. A 111 (2007) 8519–8530. [53] S.J. Grabowski, Chem. Rev. 111 (2011) 2597–2625. [54] E. Clar, In The Aromatic Sextet, Wiley, London, 1972. [55] M. Randic, A.T. Balaban, J. Chem. Inf. Model. 46 (2006) 57–64. [56] S. Wojtulewski, S.J. Grabowski, Chem. Phys. 309 (2005) 183–188. [57] B.K. Paul, N. Guchhait, Chem. Phys. 412 (2013) 58–67.