Substituent and Solvent Effects on the Absorption Spectra of Cationâ Ï

Article pubs.acs.org/JPCA

Substituent and Solvent Effects on the Absorption Spectra of Cation−π Complexes of Benzene and Borazine: A Theoretical Study Nabajit Sarmah,† Pradip Kr. Bhattacharyya,*,† and Kusum K. Bania*,‡ †

Arya Vidyapeeth College, Guwahati, Assam 781016, India Tezpur University, Napaam, Assam 784028, India

‡

S Supporting Information *

ABSTRACT: Time-dependent density functional theory (TDDFT) has been used to predict the absorption spectra of cation−π complexes of benzene and borazine. Both polarized continuum model (PCM) and discrete solvation model (DSM) and a combined effect of PCM and DSM on the absorption spectra have been elucidated. With decrease in size of the cation, the π → π* transitions of benzene and borazine are found to undergo blue and red shift, respectively. A number of different substituents (both electron-withdrawing and electron-donating) and a range of solvents (nonpolar to polar) have been considered to understand the effect of substituent and solvents on the absorption spectra of the cation−π complexes of benzene and borazine. Red shift in the absorption spectra of benzene cation−π complexes are observed with both electron-donating groups (EDGs) and electronwithdrawing groups (EWGs). The same trend has not been observed in the case of substituted borazine cation−π complexes. The wavelength of the electronic transitions corresponding to cation−π complexes correlates well with the Hammet constants (σp and σm). This correlation indicates that the shifting of spectral lines of the cation−π complexes on substitution is due to both resonance and inductive effect. On incorporation of solvent phases, significant red or blue shifting in the absorption spectra of the complexes has been observed. Kamlet−Taft multiparametric equation has been used to explain the effect of solvent on the absorption spectra of complexes. Polarity and polarizability are observed to play an important role in the solvatochromism of the cation−π complexes.

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and solvent.21−24 However, spectroscopic analysis to understand the cation−π interaction is very limited. Evidence for cation−π interactions has come largely from two sources: mass spectrometry and theoretical calculations.25 Pioneering mass spectrometric studies were reported in 1981 by Sunner, Nishizawa, and Kebarle.26 Electronic predissociation (ultraviolet− visible, UV−vis) studies on Mg+(C2H4) and Ca+(C2H2) cation−π complexes were performed by Kleiber et al.27 and Duncan et al.,28 respectively. Cation−π interactions in aqueous salt solutions were characterized via 2H nuclear magnetic resonance (NMR) spin− lattice relaxation times (T) and calculations of molecular correlation times (τc) for a series of perdeuterated (d6- benzene) benzene cation complexes.29 Few X-ray crystal structure reports for cation−π interactions involving alkali metal cations are present in the literature.30,31 Two structures that have been available for a number of years deserve special note: K+B(C6H5)432 and K+[ dibenzo-18-crown-6].33 Time-dependent density functional theory (TDDFT) found wide application in chemistry and applied physics for calculating the electronic excitations of smaller and larger molecules.34,35 This type of calculation has been well-implemented using the

INTRODUCTION Over the last few decades, the possibility of interactions of alkali metal cations with the aromatic ring systems has proved intriguing and has provoked considerable speculation.1−6 For example, it was proposed that K+−arene interactions might play a critical role in determining the selectivity of potassium protein channels.7 This postulate failed to raise an experimental proof8 but stimulated considerable interest in the subject of cation−π interactions. In recent years, cation−π interaction has been instrumental in explaining the structures, dynamic processes, and functions of microscale and nanoscale materials and also for macroscopic materials.9 A considerable number of experimental and theoretical studies have been devoted to understand the cation−π interaction in aromatic systems.10−18 More recently, the cation−π interaction has been found to play a key role in Li-based energy storage devices.19 Besides benzene, borazine (so-called inorganic benzene) and its derivatives have recently gained considerable interest in the development of optoelectronic and thermally stable materials.20 Because the cation−π interaction can influence the molecular properties, this type of interaction in borazine and its derivative might contribute to the design of new molecular devices. Experimental and theoretical modeling studies involving the cation−π interaction in benzene and borazine have so far focused mainly on the interaction energy, effect of subtituent, © 2014 American Chemical Society

Received: March 4, 2014 Revised: May 6, 2014 Published: May 6, 2014 3760

dx.doi.org/10.1021/jp5021966 | J. Phys. Chem. A 2014, 118, 3760−3774

The Journal of Physical Chemistry A

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verified by the absence of imaginary frequencies. Absorption spectra were computed as vertical excitations from the groundstate structures using the TDDFT39 approach as implemented in Gaussian09.40 In order to estimate the response of the electronic spectra to solvents, single-point calculations were carried out (at the same level of theory) on the gas-phase optimized structures using discrete and polarizable continuum model (PCM).41 We considered a number of solvents ranging from polar to nonpolar, namely, cyclohexane (ε = 2.01), CCl4 (ε = 2.22), chloroform (ε = 4.71), octanol (ε = 9.86), butanol (ε = 17.33), acetone (ε = 20.49), methanol (ε = 32.61), acetonitrile (ε = 35.69), dimethyl sulfoxide (DMSO; ε = 46.83), water (ε = 78.35), and formamide (ε = 108.94).

polarized continuum model (PCM) to understand the phenomenon of solvatochomism in various organic and organometallic systems.36,37 Hence, relying on the TDDFT method, we have implemented this method to evaluate the ground-state electronic transitions of various alkali metal (Li+, Na+, and K+) cation−π complexes of benzene and borazine. We have considered cation−π complexes of benzene and borazine having different substituents at 1, 3, 5 position of benzene and at the boron atoms in borazine (Scheme 1). PCM as well as discrete solvation Scheme 1. Illustration of Cation−π Interaction in Benzene and Borazine. R Represents the Electron-Donating Group and Electron-Withdrawing Group.

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RESULTS AND DISCUSSION Ground- and Excited-State Geometry. The predicted, M+−centroid (X−M), C−C, and B−N distances are reported in Table 1, and the gas-phase optimized ground-state geometries of all the cation−π complexes listed in Table 1 are shown in Figures S1 and S2 of the Supporting Information. The M+−centroid distances exhibit a steady increase as the size of the cation increases in all the complexes. In the case of the cation−π complexes of benzene, all the benzene rings adopt a planar geometry and η6 coordination mode. Our previous studies suggest that all the borazine rings in their cationic complexes adopt a puckered structure and η3 coordination mode.42 The size of the cation as well as the nature of the substituent was also found to effect the binding energy value. As reported by Dougherty et al.,5 we have also obtained a similar trend in binding energy values, i.e., Li+> Na+ > K+, indicating that as the size of the cation increases from Li+ to K+, the binding energy values decreases.42 Most of the things related to structural change, effect of size of cation, and nature of substituent on

model (DSM) and a combination of both are implemented to illustrate the effect of various solvents on the absorption spectra of the cation−π complexes of benzene and borazine.

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COMPUTATIONAL METHODS Ground-state electronic structure of cation−π complexes of benzene and borazine (Scheme 1) were optimized using density functional theory (DFT)38 method at the B3LYP/6-31+G(d) level of theory. The excited-state geometries were obtained using the time-dependent (TD) method as provided in the Gaussian manual. The minima of the optimized structures were

Table 1. Geometrical Parameters of Benzene and Borazine and Their Cationic Complexes Computed at the B3LYP/6-31+G(d) Level of Theorya

a

system

rC−C

rX−M

benzene benzene-Li+ benzene-Na+ benzene-K+ benzene-(CH3)3-Li+ benzene-(CH3)3-Na+ benzene-(CH3)3-K+ benzene-(NH2)3-Li+ benzene-(NH2)3-Na+ benzene-(NH2)3-K+ benzene-(OCH3)3-Li+ benzene-(OCH3)3-Na+ benzene-(OCH3)3-K+ benzene-(OH)3-Li+ benzene-(OH)3-Na+ benzene-(OH)3-K+ benzene-(F)3-Li+ benzene-(F)3-Na+ benzene-(F)3-K+ benzene-(Br)3-Li+ benzene-(Br)3-Na+ benzene-(Br)3-K+ benzene-(CN)3-Li+ benzene-(CN)3-Na+

1.399 1.407 1.405 1.403 1.411 1.408 1.406 1.412 1.408 1.404 1.413 1.412 1.412 1.409 1.409 1.403 1.401 1.398 1.395 1.404 1.401 1.399 1.411 1.408

1.931 2.416 2.887 1.871 2.369 2.822 1.883 2.374 2.776 1.848 2.368 2.885 1.896 1.896 2.966 2.008 2.524 3.111 1.939 2.457 3.108 2.056 2.661

system

rB−N

rX−M

∠NBNB

borazine borazine-Li+ borazine-Na+ borazine-K+ borazine-(CH3)3-Li+ borazine-(CH3)3-Na+ borazine-(CH3)3-K+ borazine-(NH2)3-Li+ borazine-(NH2)3-Na+ borazine-(NH2)3-K+ borazine-(OH)3-Li+ borazine-(OH)3-Na+ borazine-(F)3-Li+ borazine-(F)3-Na+ borazine-(F)3-K+ borazine-(Br)3-Li+ borazine-(Br)3-Na+ borazine-(Br)3-K+ borazine-(CN)3-Li+ borazine-(CN)3-Na+

1.435 1.448 1.445 1.442 1.458 1.460 1.449 1.466 1.460 1.455 1.458 1.452 1.446 1.441 1.437 1.445 1.438 1.433 1.443 1.438

1.940 2.404 2.860 1.833 2.336 2.770 1.808 2.292 2.704 1.827 2.368 1.920 2.466 3.051 1.896 2.440 3.025 1.995 2.618

0.0 18.9 15.3 14.1 22.8 23.6 17.9 30.7 23.7 21.2 24.7 21.8 22.5 16.8 12.1 18.3 12.4 7.85 16.6 16.8

Bond lengths are in angstroms, and angles are in degrees. 3761



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Figure 1. Excited-state geometries of some of the cation−π complexes of benzene and borazine: (a) benzene-Li+, (b) borazine-Li+, (c) benzene (CH3)3-Li+, (d) benzene-Na+, (e) borazine-Na+, (f) borazine (CH3)3-Li+, (g) benzene-K+, (h) borazine-K+, (i) benzene (Br)3-Li+, (j) benzene (NH2)3-Li+, (k) borazine (NH2)3-Li+, and (l) borazine (Br)3-Li+.

differ in bond length and M+−centroid distance from those of the ground-state geometries. In the excited-state geometries of benzene cation−π complexes, C−C bond distances are found to be slightly elongated (∼0.03 Å); however, the planarity of the benzene ring is well-retained. Compared to that in the groundstate geometry (Table 1 and Figure S1 of the Supporting Information), the M+−centroid distances in the excited-states geometries are also found to be slightly increased by few angstroms. For example, in the case of benzene-Li+, benzeneNa+, and benzene-K+ in the ground state, the M+−centroid distances are found to be 1.931, 2.416, and 2.887 Å, respectively. Whereas in the corresponding excited-state geometries, the M+−centroid distances are found to be 1.952, 2.419, and 2.913, respectively, for benzene-Li+, benzene-Na+, and benzene-K+

binding energy, effect of solvent, H-bond cooperativity, reactivity, and thermochemical analysis of such cation−π complexes has already been illustrated in our previous article in a wider sense and also in some other reports.42−45 Hence, herein we shall not focus on such illustration of such complexes. The main objective of the current study is to understand the spectrochemical behavior of cation−π complexes of benzene and borazine and also to understand the effect of substituent and solvent on absorption spectra. To understand the structural change on excitation we have also optimized some of the selected excited geometries of the cation−π complexes of benzene and borazine. The optimized excited-state geometries are shown in Figure 1 along with the selected bond length. The excited-state geometries are found to 3762



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Figure 2. Schematic representation of the orbitals (along with their energy) involved in electronic transition in (a) benzene-Li+, (b) benzene-Na+, (c) benzene-K+, (d) borazine-Li+, (e) borazine-Na+, and (f) borazine-K+.

in borazine is “lumpy” because more electron density is localized on nitrogen atoms (because of high electronegativeity of nitrogen). This partial delocalization weakens the π-bonding in the borzaine ring. Therefore, as the π-electron gets excited, the borazine ring losses its planarity. Absorption Spectra of Cation−π Complexes. Gas-phase TDDFT calculated absorption spectra of benzene and borazine indicates that benzene has one sharp signal at 178 nm due to π → π* transition. Borazine displays a single transition at 165 nm due to π → π* transition. The peak at 178 nm for benzene is due to a transition from the HOMO−1 (−0.257 au) to lowest unoccupied molecular orbital (LUMO; −0.015 au) orbital, and in the case of borazine, the peak at 165 nm corresponds to a transition from highest occupied molecular orbital (HOMO, −0.286 au) to LUMO+2 (0.003 au). The energy difference between the frontier orbitals involved in the electronic

cation−π complexes. This indicates that on excitation, both the C−C bond length and the M+−centroid distances get elongated; this is expected as the π-electron density is involved in the excitation processes. In the case of borazine, in excited states the cation−π complex gets completely deformed loosing the planarity of the ring (Figure 1b,e,h). It is interesting to note that in all three of the borazine-Li+, borazine-Na+, and borazine-K+ cation−π complexes, one of the N atoms moves upward by ∼1.5 Å. Because of this ring deformation in the excited states, the cation moves away from the center and approaches the nitrogen atom of the borzaine moiety. However, in the case of the methyl-substituted borazine-Li+ complex, Figure 1f, the distortion is minimal because of the steric hindrance imposed by the bulkier methyl group. The high distortion in the excited-state geometries of the borazine cation−π complexes is due to the fact that the π-electron cloud 3763



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Figure 3. Absorption spectrum of (a) benzene and respective cation−π complexes showing the blue shift as the size of the cation decreases and b) borazine and respective cation−π complexes showing the red shift as the size of the cation decreases.

Figure 4. Correlation between first ionization potential of alkali metals (Li, Na, K) and wavelength of the corresponding cation−π complexes of (a) benzene and (b) borazine. Panels c and d represent the correlation between wavelength and C−C and B−N distances for benzene and borazine cation−π complexes, respectively.

peaks at ∼174 and 177 nm, respectively. Both these transition are due to transition from a π-orbital of benzene ring to a σ-orbital of metal, ligand-to-metal charge transfer (LMCT) transition (Figure 2). Compared to benzene, these electronic transitions, π → π* as well as the LMCT, are blue-shifted, and the order of shifting is benzene-Li+ > benzene-Na+ > benzene-K+ (Figure 3). Cation−π complexes of borazine show bands at 167, 166, and 165 nm for borazine-Li+, borazine-Na+, and

transitions is 0.242 au and 0.283 au in the case of benzene and borazine, respectively. These results are in accordance with the previously reported values.46 Benzene-Li+ shows a peak at 169 nm mainly due to π → π* transition arising from the transition of π-symmetric benzene-based occupied MO (HOMO−1, 21) to benzene-based unoccupied π* MO (LUMO+1, 24) with an expansion coefficient of 0.5412 for single-electron transitions. Correspondingly, cation−π complexes of Na+ and K+ show 3764



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Table 2. Selected Energies (E), Oscillator Strengths (f), and Expansion Coefficients (ǿ) for Vertical Transitions in Benzene-M+ (M = Li, Na, and K) and Its Substituted Complexes Calculated Using a TDDFT Approacha orbital involved in transition benzene-Li+ benzene-(CH3)3-Li+ benzene-(NH2)3-Li+ benzene-(OCH3)3-Li+ benzene-(OH)3-Li+

benzene-(F)3-Li+ benzene-(Br)3-Li+ benzene-(CN)3-Li+ benzene-Na+ benzene-(CH3)3-Na+ benzene-(NH2)3-Na+ benzene-(OCH3)3-Na+ benzene-(OH)3-Na+ benzene-(F)3-Na+ benzene-(Br)3-Na+ benzene-(CN)3-Na+ benzene-K+ benzene-(CH3)3-K+ benzene-(NH2)3-K+ benzene-(OCH3)3-K+ benzene-(OH)3-K+ benzene-(F)3-K+ benzene-(Br)3-K+ a

HOMO−1 → LUMO+1 HOMO → LUMO+1 HOMO−2 → LUMO+2 HOMO−1 → LUMO+2 HOMO−1 → LUMO+2 HOMO−1 → LUMO+1 HOMO−1 → LUMO+1 HOMO−1 → LUMO+2 HOMO−2 → LUMO+1 HOMO−1 → LUMO+1 HOMO−1 → LUMO+1 HOMO−1 → LUMO+2 HOMO → LUMO+1 HOMO−3 → LUMO+1 HOMO−1 → LUMO+1 HOMO−1 → LUMO+2 HOMO−1 → LUMO+2 HOMO−1 → LUMO+2 HOMO → LUMO+3 HOMO−1 → LUMO+1 HOMO → LUMO+3 HOMO−1 → LUMO+2 HOMO−2 → LUMO+2 HOMO−3 → LUMO+2 HOMO → LUMO+1 HOMO−3 → LUMO HOMO−1 → LUMO+2 HOMO → LUMO+2 HOMO−1 → LUMO+4 HOMO−1 → LUMO+1 HOMO−2 → LUMO+1 HOMO → LUMO+3 HOMO−2 → LUMO+1 HOMO−1 → LUMO+1 HOMO−1 → LUMO+2 HOMO → LUMO+2 HOMO → LUMO+2 HOMO−3 → LUMO+2

transition

wavelength (nm)

f

ǿ

E (eV)

→ → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → → →

169.90 187.86 199.75 223.30 200.86 205.79 195.55 197.48 171.09 177.71 238.97 228.07 233.99 221.79 173.92 192.73 180.03 206.13 211.37 200.69 198.76 180.03 233.85 224.06 229.77 215.93 177.08 196.07 182.99 231.38 201.50 206.81 187.41 198.58 200.73 181.24 230.45 219.12

0.5412 0.5370 0.3775 0.2709 0.3905 0.3710 0.4291 0.3657 0.1879 0.4847 0.1706 0.0852 0.3653 0.1300 0.5615 0.5035 0.4784 0.2378 0.2018 0.2349 0.2073 0.4784 0.1495 0.1418 0.3793 0.0766 0.5375 0.2799 0.2391 0.1901 0.1499 0.2723 0.2129 0.1991 0.1814 0.4518 0.2653 0.1500

0.350 70 0.481 08 0.477 41 0.449 62 0.620 95 0.471 31 0.426 59 0.445 12 0.547 39 0.347 72 0.440 16 0.521 97 0.451 00 0.658 92 0.380 72 0.424 23 0.436 80 0.543 35 0.465 17 0.387 99 0.447 10 0.436 80 0.394 70 0.629 90 0.417 18 0.614 10 0.487 13 0.316 26 0.378 87 0.346 89 0.623 00 0.425 28 0.675 33 0.343 15 0.339 42 0.433 23 0.460 50 0.684 04

7.2976 6.5999 6.2070 5.5523 6.1726 6.0249 6.3403 6.2783 7.2467 6.9769 5.1884 5.4363 5.2987 5.5901 7.1289 6.4331 6.8869 6.0148 5.8659 6.1779 6.2378 6.8869 5.3018 5.5335 5.3959 5.7419 7.0018 6.3233 6.7756 5.3585 6.1532 5.9951 6.6157 6.2436 6.1766 6.8410 5.3801 5.6584

21 34 32 33 45 45 33 33 32 33 72 72 40 37 25 37 37 49 50 37 38 37 75 74 44 41 29 42 41 41 40 54 52 41 41 42 81 78

24 36 37 37 49 48 36 37 36 36 75 76 42 42 28 41 41 53 54 40 42 41 80 80 46 45 33 45 47 44 44 58 56 44 45 45 84 84

The shape of the orbitals are given in Figure S6 of the Supporting Information.

borazine-K+, respectively. All these bands arise because of transition from π-symmetric borazine-based occupied MO to borazine-based unoccupied π* MO (Figure 2). However, in contrast to benzene, cation−π complexes of borazine shows red shifting of the peaks compared to free borazine, and the order of shifting is borazine-Li+> borazine-Na+> borazine-K+. In order, to predict the reason behind the spectral shift, we examined the relationship between the spectral shift and the first ionization potential (IP) of the alkali metal cations.47 In both cases, we observed a very good correlation (r2 > 9) between wavelengths and the first ionization potential of Li, Na, and K (Figure 4). This indicates that ionization potential (IP) of the cations influences the electronic transitions of the cation−π complexes. It is observed from the two plots in Figure 4 that in the case of benzene the slope is negative, whereas in the case of borazine cation−π complex the slope is positive. This indicates that although the nature of the cations is same in both benzene and borazine, still they show an opposite trend in spectral shift. Besides ionization potential,

Figure 5. Effect of substituent on the absorption spectrum of benzeneLi+ complex. 3765



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Table 3. Selected Energies (E), Oscillator Strengths (f), and Expansion Coefficients (ǿ) for Vertical Transitions in Borazine-M+ (M = Li, Na, and K) and Its Substituted Complexes Calculated Using a TDDFT Approacha orbital involved in transition borazine-Li+ bora-(CH3)3-Li+ bora-(NH2)3-Li+ bora-(OH)3-Li+ bora-(F)3-Li+ bora-(Br)3-Li+ bora-(CN)3-Li+ borazine-Na+ bora-(CH3)3-Na+ bora-(NH2)3-Na+ bora-(OH)3-Na+ bora-(F)3-Na+ bora-(Br)3-Na+ bora-(CN)3-Na+ borazine-K+ bora-(CH3)3-K+ bora-(NH2)3-K+ bora-(F)3-K+ bora-(Br)3-K+ a

HOMO−1 → LUMO+1 HOMO−1 → LUMO+1 HOMO−1 → LUMO+5 HOMO → LUMO+5 HOMO → LUMO+2 HOMO−5 → LUMO+2 HOMO−3 → LUMO HOMO−1 → LUMO+2 HOMO−1 → LUMO+1 HOMO−1 → LUMO+9 HOMO → LUMO+5 HOMO−1 → LUMO+5 HOMO−3 → LUMO+1 HOMO−1 → LUMO+2 HOMO−1 → LUMO+1 HOMO → LUMO+5 HOMO−2 → LUMO+5 HOMO → LUMO+5 HOMO−3 → LUMO+1

transition

wavelength

f

ǿ

E

→ → → → → → → → → → → → → → → → → → →

167.15 167.75 161.02 147.81 147.88 193.50 205.21 166.37 167.49 160.70 150.92 143.46 190.25 200.72 165.54 163.69 174.97 146.29 187.03

0.0792 0.0949 0.3277 0.1661 0.1688 0.2474 0.2160 0.1233 0.1170 0.0775 0.1129 0.2622 0.3147 0.3131 0.1753 0.0808 0.0464 0.2736 0.3922

0.193 50 0.394 15 0.414 94 0.590 91 0.457 72 0.327 18 0.371 73 0.300 53 0.313 48 0.458 03 0.430 34 0.363 37 0.486 04 0.319 55 0.371 69 0.330 78 0.390 49 0.376 42 0.464 66

7.4174 7.3911 7.6998 8.3879 8.3843 6.4076 6.0419 7.4523 7.4025 7.7153 8.2150 8.6423 6.5169 6.1771 7.4898 7.5744 7.0858 8.4751 6.6293

21 33 33 34 34 68 37 25 37 38 38 37 74 43 29 42 40 42 78

24 36 40 40 37 76 41 29 40 48 44 44 79 47 32 48 48 47 83

The shape of the orbitals are given in Figure S7 of the Supporting Information.

Figure 6. Pictorial representation of change in energy gap between the frontier orbitals involved in electronic transition of cation−π complexes of (a) benzene-(Br)3-Li+, (b) benzene-(CN)3-Li+, (c) benzene-(OCH3)3-Li+, (d) benzene-(NH2)3-Li+, (e) benzene-(OH)3-Li+, (f) benzene-(CH3)3-Li+, and (g) benzene-(F)3-Li+.

the loss of planarity of aromatic rings plays a vital role in spectral shift. It has been reported that in the case of porphyrin rings, because of the loss of planarity due to ruffled and saddled deformation, there occurs significant red shifting of the absorption spectra.48−50 In the case of the borazine, because of the cation−π interaction, the borazine ring obtains a puckered structure leading to changes in bond length and bond angles. Thus, it is these changes in geometrical parameters known as in-plane nuclear reorganizations (IPNRs) that lead to the red shifting of the spectral line. The plot of C−C bond length and B−N bond length in the case of benzene and borazine, respectively, against wavelength shows excellent correlation (r2 = 1; Figure 4c,d). However, the slopes are found to be opposite: negative in the case of benzene cation−π systems and positive in the case of borazine systems. This further explains that in the case of benzene, as the C−C bond elongates, the wavelengths get blue-shifted whereas

in the case of borazine, as the B−N bond elongates with the decrease in cation-size, the wavelengths get red-shifted. Moreover, because of the in-plane nuclear reorganization, the HOMO−1 orbital in borzaine cation−π complexes are more stabilized in comparison to that of analogous benzene cation−π complexes (Figure 2). This in turn brings a difference in energy gap between the frontier orbitals of cation−π complexes of benzene and borazine. It is observed that the energy gap between the HOMO and LUMO orbitals involved in the electronic transitions decreases in the case of benzene as the size of the cations increases whereas the reverse is observed in the case of borazine (Figure 2). Thus, it is conclusive that because of the in-plane ring deformation due to the cation−π interaction, there occurs a significant change in the frontier orbital energies resulting in opposite trends in the spectral shift in the case of benzene and borazine cation−π complexes. 3766



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Figure 7. Correlation between HOMO energies and wavelengths for cation−π complexes of (a) benzene-Li+ and its substituted complexes, (b) benzene-Na+ and its substituted complexes, (c) benzene-K+ and its substituted complexes, (d) borazine-Li+ and its complexes, (e) borazine-Na+ and its substituted complexes, and (f) borazine-K+ and its substituted complexes.

Effect of Substituent on Absorption Spectra of Cation−π Complexes. Gas-phase spectral analysis of the substituted cation−π complexes of benzene (Table 2) indicates that irrespective of the nature of the substituent (electronwithdrawing or electron-donating), the π → π* and LMCT transition is found to be red-shifted. For example, in the case of benzene-Li+, the maximum shifting (∼69 nm) is observed in the case of the −Br substituted cation−π complex and the least shifting (∼8 nm) is observed in the case of −F substituted complex (Table 2 and Figure 5). The difference that lies between −F and two other EWGs is attributed to the fact that although −F, −Br, and −CN are π-donor, the strong electronwithdrawing ability of fluorine causes σ electrons of the C−C bond to transfer toward the −F substituted carbon atom, thus enhancing the electron-sharing and increasing C−C σ bond strength. −CH3, −Br, and −CN substituted borazine cation−π complexes show red shift, whereas the other −F, −OH, and −NH2 substituted complexes show blue shift (Table 3). The highest red shifting is observed for −CN substituted complexes (more than 28 nm), whereas the highest blue shifting is found in the case of fluorine-substituted complexes (more than 20 nm). This is because, on substitution, the cation−π complexes of borazine lose planarity;42 thus, their electronic behavior deviates from those of benzene. Besides these, substitution also leads to the change in the frontier orbital energy. It can be observed from Figure 6 that the energy gap between the HOMO and LUMO orbitals in benzene-(Br)3-Li+ is much less than that of the benzene-(F)3-Li+complex. This further reflects the shifting

of the spectral line toward higher wavelength in the case of benzene-(Br)3-Li+. The plot of the HOMO energies against the wavelength for the cation−π complexes of benzene and borazine shows very good correlation (Figure 7). It can be observed from Figure 7 that irrespective of the substituent, the HOMO orbitals of the Li+-benzene cation−π complexes shows the highest correlation (r2 ≅ 0.95). Slightly less correlation observed in the case of borazine cation−π complexes might be due to the loss of planarity of the borazine ring in comparison to the benzene ring. However, the existence of very good correlation between the energy of HOMOs involved in electronic transitions and the wavelength suggests that because of the cation−π interaction, the electronic behavior of the aromatic systems changes and leads to the significant changes in the electronic transitions. The C−C and B−N bond length of the substituted benzene and borazine cation−π complexes also shows excellent correlation with the wavelength of the characteristic absorption bands (Figure S3 of the Supporting Information). This further indicates that slight changes in the geometrical parameters will influence absorption spectra of the cation−π complexes. Correlation between Hammet Constants and Wavelength. M+−centroid distances correlate well with respective wavelength of the substituted cation−π complexes of benzene and borazine, panels a and b of Figure 8, respectively. This further suggests that with the change in cation size, the X−M bond distance changes and leads to shifting of the spectral lines. Effect of the substituent in cation−π complexes is better understood in terms of Hammet substituent constants (σm and σp).51 3767



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Figure 8. Panels a and b show the correlation between wavelength and M−X bond length (in angstroms) in different substituted cation−π complexes of benzene and borazine, respectively. Panels c and d represent the correlation between the Hammet constant (σp, of EDG) with wavelength of the corresponding substituted cation−π complexes of benzene and borazine, respectively. Panel e represents the correlation of Hammet constant (σm, of EWG) with the wavelength of substituted cation−π complexes of benzene.

Table 4. α, β, and π Values of Different Solvents Implemented in Present Study solvent no.

solvent

α

β

π*

1 2 3 4 5 6 7 8 9 10 11

cyclohexane carbon tetrachloride (CCl4) chloroform n-octanol 2-butanol acetone methanol acetonitrile dimethylsulfoxide (DMSO) water formamide

0.00 0.00 0.20 0.77 0.69 0.08 0.98 0.19 0.00 1.17 0.71

0.00 0.10 0.10 0.81 0.80 0.43 0.66 0.40 0.76 0.47 0.48

0.00 0.28 0.58 0.40 0.40 0.71 0.60 0.75 1.00 1.05 0.97

electron-withdrawing groups show good correlation (r2 > 9) with only σm, Figure 8e. This implies that the shifting of spectral lines toward lower and/or higher wavelengths is influenced by both the inductive and resonance effects depending on the nature of the substituents. Effect of Solvent on Absorption Spectra. Effect of solvent on the absorption spectra of the cation−π complexes of benzene and borazine has been studied using both PCM and DSM. Different solvents that are considered for the present study are listed in Table 4. The values of α, β, and π* are taken from the literature.52 Considering the PCM model, it is observed that in the presence of both polar and nonpolar solvents, the bands undergo either a red or blue shift. In the presence of both polar and nonpolar solvents, the cation−π complexes of benzene exhibit a red shift. For example, in the case of benzene-Li+ complex, maximum shifting is observed in chloroform (Figure 9a), whereas for benzene-(CH3)3Li+complex, the highest shifting is observed in formamide (Figure 9b). In the case of benzene-(F)3-Li+complex, the highest shifting is observed in chloroform (Figure 9c). The absorption bands of unsubtituted cation−π complexes of borazine are found to be red-shifted in the presence of both polar and nonpolar solvents. In Figure 10a, borazine-Li+ is shown as a representative case. In this case, the maximum red shift is observed in chloroform. Interestingly, similar to the gas phase, substituted borazine complex, irrespective of the presence of the EDG or

Hammet constants are used to understand the nature of noncovalent interactions, viz., arene−arene and cation−π interactions. σm constants provide a measure of the inductive electron withdrawal or donation by the substituent (inductive effect). σp Hammett constant describes the movement of electrons via the σ- and π-framework (inductive and resonance effects). Plot of wavelength associated with the cation−π complexes of both benzene and borazine having electrondonating groups shows very good correlation (r2 > 9) with σp but not with σm (Figure 8c,d). Whereas those containing 3768



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Figure 10. Effect of different solvent on the absorption spectra of (a) borazine-Li+, (b) borazine-(CH3)3-Li+, and (c) borazine-(F)3-Li+.

Figure 9. Effect of different solvent on the absorption spectra of (a) benzene-Li+, (b) benzene-(CH3)3-Li+, and (c) benzene-(F)3-Li+.

that although specific interactions with the solvent, like hydrogen bonding, not accounted for in a polarized continuum solvation model (PCM) still can have a significant impact on the solvatochromism.33 To correlate the effect of solvent on spectral bands of benzene and borazine, the absorption wavelength maxima obtained in various solvents have been analyzed

EWG, shows blue shift. For example, in both the −CH3 and −F substituted borazine-(CH3)3-Li+complexes, blue shift is observed with a maximum shift in chloroform (Figure 10b,c). Cation−π complexes of benzene and borazine show different responses to different solvents. Therefore, it can be considered 3769



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Table 5. Energy (in cm−1) of the Absorption Band of Compounds a−l* in Different Solvents solvent

a

b

c

d

e

f

g

h

i

j

k

l

CCl4 chloroform n-octanol 2-butanol acetone methanol acetonitrile DMSO water formamide

52 031 52 075 51 837 51 915 51 996 52 069 51 837 51 877 52 056 51 810

55 279 55 212 55 386 54 975 55 340 55 460 55 279 55 157 55 245 55 111

59 566 60 168 60 262 60 313 60 240 60 382 60 371 60 320 62 227 60 306

67 727 67 782 68 147 67 967 67 962 67 934 67 911 67 810 67 727 67 746

50 820 50 807 50 779 50 810 50 872 50 919 50 888 50 743 50 900 50 681

54 611 54 740 54 788 54 845 54 923 54 984 54 948 54 788 54 987 54 719

59 830 59 737 60 117 59 973 59 955 59 926 59 916 59 865 59 830 59 830

68 217 68 017 67 948 67 930 67 948 67 953 67 934 67 851 68 217 67 805

50 787 50 976 51 033 51 077 51 132 51 169 51 143 51 033 51 150 50 986

54 395 54 549 54 611 54 677 54 761 54 827 54 791 54 638 54 815 54 576

60 576 60 613 60 720 60 672 60 705 60 642 60 606 60 551 60 580 60 731

67 668 67 649 67 622 67 613 67 645 67 640 67 617 67 994 67 663 67 480

*

a, benzene-(CH3)3-Li+; b, benzene-(F)3-Li+; c, borazine-(CH3)3-Li+; d, borazine-(F)3-Li+; e, benzene-(CH3)3-Na+; f, benzene-(F)3-Na+; g, borazine-(CH3)3-Na+; h, borazine-(F)3-Na+; i, benzene-(CH3)3-K+; j, benzene-(F)3-K+; k, borazine-(CH3)3-K+; l, borazine-(F)3-K+.

Table 6. Values of υ̃0, a, b, and p (in cm−1) and Correlation Coefficients Obtained from Kamlet−Taft Multiparametric Fitting of the Absorption Data compound +

benzene-(CH3)3-Li benzene-(F)3-Li+ benzene-(CH3)3-Na+ benzene-(F)3-Na+ benzene-(CH3)3-K+ benzene-(F)3-K+ borazine-(CH3)3-Li+ borazine-(F)3-Li+ borazine-(CH3)3-Na+ borazine-(CH3)3-Na+ borazine-(CH3)3-K+ borazine-(F)3-K+

υ̃0

a

b

p

R2

solvents excluded

52 132 55 379 50 899 54 494 50 708 54 265 59 607 68 333 59 848 68 285 60 618 67 620

−121 242 −103 326 285 343 228 −88 −15 −82 82 −449

−135 −554 33.5 −128 −41 −95 330 19 332 −150 38 402

−163 245 −148 450 398 502 552 −550 −191 −348 −77 −9

0.83 0.94 0.81 0.80 0.85 0.82 0.83 0.85 0.87 0.91 0.80 0.80

water, metahnol cholroform, CCl4 water, metahnol acetone, formamide acetone, formamide acetone, formamide cholroform, methnol cholroform, CCl4 acetonitrile water acetone, formamide water, metahnol

using the Kamlet and Taft treatment (eq 1).53 This approach separates the dielectric effects of solvents (π*), hydrogen-bond donor ability (α), and hydrogen-bond acceptor ability (β) of the solvents on the spectral properties. υ ̃ = υõ + aα + bβ + p(π * + dδ)

the results obtained usin PCM model system. Nevertheless, such properties of the solvent can affect absorption spectra of the cation−π complexes. However, the plot of the wavelength (λmax) associated with the cation−π complex listed in Table 5 shows very good correlation with the dielectric constants of the solvents (with exclusion of some solvents) Table 7. The presence of a

(1)

In the above equation, υ̃o is the value of absorption and/or emission energies in a reference solvent (cyclohexane; α = β = π* = 0). δ is the polarizability correction for different types of solvent (aliphatic, aromatic, or halogenated). Contribution of δ is often negligible; hence, eq 1 can be simplified to eq 2. Using eq 2, the parameters a, b, and p (corresponding to the responses of the appropriate solute molecular property to the relevant solvent property) can be reacquired through a multiparametric fitting on various solvents. υ ̃ = υõ + aα + bβ + pπ *

Table 7. Correlation between Wavelengths of Selected Compounds and Dielectric Constant of Solvents

(2)

Multiparametric fitting of the Kamlet−Taft equation to the observed absorption energies in reciprocal centimeters (Table 5) of cation−π complexes (benzene-Li+, benzene-(CH3)3-Li+, benzene-(F)3-Li+, and the corresponding borazine complexes) in 11 different solvents have been performed (see list of solvents in Table 4). The solute parameters, υ̃0, a, b, and p and correlation coefficients obtained from the fitting of absorption data are presented in Table 6. Table 6 indicates that the solvatochromic effect is essentially an effect of polarity and polarizability of the solvent (p parameter) and H-bond acceptor (or electron donor) strength of the solvents (b parameter). However, small values of a, b, and p indicate that solute−solvent interactions do not contribute to a great extent, and this is well in accordance with

complex

R2

solvents excluded

benzene-(CH3)3-Li+ benzene-(F)3-Li+ borazine-(CH3)3-Li+ borazine-(F)3-Li+ benzene-(CH3)3-Na+ benzene-(F)3-Na+ borazine-(CH3)3-Na+ borazine-(F)3-Na+ benzene-(CH3)3-K+ benzene-(F)3-K+ borazine -(CH3)3-K+ borazine-(F)3-K+

0.805 0.809 0.877 0.807 0.925 0.856 0.838 0.800 0.823 0.847 0.922 0.883

n-octanol, methanol, water chloroform, 2-butanol, methanol, DMSO DMSO, formamide CCl4, chloroform acetone, methanol, acetonitrile, water DMSO, water, formamide CCl4, chloroform, n-octanol CCl4, water DMSO, water, formamide DMSO, water, formamide CCl4, chloroform, water, formamide CCl4, acetonitrile, DMSO

very good correlation between λ and ε as shown in Figure 11 and Table 7 indicates that although polarity and polarizability and H-bond acceptor (or electron donor) strength of the solvents has little effect on the absorption spectra of the cation−π complexes, the overall electric field surrounding cation−π systems might influence the electronic transitions of such complexes. 3770



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Figure 11. Correlation between wavelength and dielectric constants of the solvents for the cation−π complexes of (a) benzene-(CH3)3-Li+, (b) benzene-(F)3-Li+, (c) borazine-(CH3)3-Li+, (d) borazine-(F)3-Li+, (e) benzene-(CH3)3-Na+, (f) benzene-(F)3-Na+, (g) borazine-(CH3)3-Na+, (h) borazine-(F)3-Na+, (i) benzene-(CH3)3-K+, (j) benzene-(F)3-K+, (k) borazine -(CH3)3-K+, and (l) borazine-(F)3-K+.

calculation, the peaks obtained from DSM are found to be redshifted (Figures 12 and 13. It can be observed from Figure 12 that in the case of benzene-Li+ as well as the substituted benzene cation−π complexes, combination of PCM+DSM leads to red shifts higher than those of individual model systems. However, in the case of borazine, the peaks are blueshifted, but the shifting is less than that obtained by using single PCM and DSM (Figure 13). Thus, on the basis of these results, it can be concluded that solvated cation−π complexes of benzene will result in more red shift in absorption bands; in contrast, the corresponding borazine complexes will result in less blue shift.

Effect of solvent has also been studied via discrete solvation model (DSM). For the discrete solvation model, the considered cation−π complexes were optimized by keeping a single water molecule above the cation. Gas-phase optimized geometries of some of the complexes are presented Figure S4 and Figure S5 of the Supporting Information. As expected, the cation−π bond distance elongates because of direct interaction of cation with the water molecule.54−56 Herein, we shall not emphasize such geometrical changes and interaction energies because they have been well-described in our previous report and also by G.N Sastry.42,43 Therefore, we compare the spectra obtained from the discrete model with those obtained from the PCM model. We have also performed a combined PCM and discrete solvation model effect on the absorption spectra. For these calculations we have considered only the solvents carbon tetrachloride (CCl4), acetone (CH3COCH3), and water (H2O). In Figures 12 and 13, we have compared the gas-phase, PCM, and combined PCM+DSM calculated spectra for a few of the Li+-cation−π complexes of benzene and borazine. Results show that compared to the gas-phase PCM model

■

CONCLUSION Cation−π interaction is now becoming important in various aspects of chemistry and in numerous biological processes. Therefore, characterization of this type of noncovalent interaction bears the utmost importance. In most of the previous reports, this type of interaction is mostly characterized by mass and NMR spectroscopy.25,29 There are only a few reports in 3771



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Figure 12. Comparison of the absorption spectra of (a) benzene-Li+, (b) benzene-(CH3)3-Li+, and (c) benzene-(F)3-Li+ obtained in gas phase, using PCM and PCM+DSM. Figure 13. Comparison the absorption spectra of (a) borazine-Li+, (b) borazine-(CH3)3‑Li+, and (c) borazine-(F)3‑Li+obtained in gas phase, using PCM and PCM+DSM.

which UV−vis techniques have been used to characterize such weaker interaction.27,28 Lucas and co-workers used secondderivative UV−vis analysis to characterize the cation−π intercation for studying the structure and dynamics of proteins.57 Because most of the biological systems involve aromatic sytems, the presence of cation−π interactions can be detected via UV−vis absorption bands. The present study would therefore help the experimental chemist to predict the cation−π interaction in systems involving aromatic rings. Furthermore, nowadays borazine has found application in the design of optoelectronics devices, and cation−π interactions are found to influence optical properties of such materials. Because our theoretical results provide a illustration of absorption bands for a wide range of benzene and borazine cation−π complexes, such studies may help experimental chemists, physicists, and

biologists to understand biological systems as well as aid in the development of new materials. However, our theoretical results predict that most of the absorption band comes below 200 nm (deep UV region). Hence, UV laser techniques would be most beneficial for such characterization. In the present study we have elucidated the absorption spectra of cation−π complexes of aromatic systems in different solvent systems. We analyzed the effect of substituents and solvents on the absorption spectra of alkali metal cation−π complexes of benzene and borazine using TDDFT calculations. The absorption spectra are found to depend on the nature of the substituents on benzene and borazene, polarity of solvent, 3772



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(9) Mahadevi, A. S.; Sastry, G. N. Cation−π Interaction: Its Role and Relevance in Chemistry, Biology, and Material Science. Chem. Rev. (Washington, DC, U.S.) 2013, 113, 2100−2138. (10) Strmcnik, D.; Kodama, K.; van der Vliet, D.; Greeley, J.; Stamenkovic, V. R.; Markovic, N. M. The Role of Non-Covalent Interactions in Electrocatalytic Fuel-Cell Reactions on Platinum. Nat. Chem. 2009, 1, 466−472. (11) Schulze, S.; Koster, S.; Geldmacher, U.; van Scheltinga, A. C. T.; Kuhlbrandt, W. Structural Basis of Na+-Independent and Cooperative Substrate/Product Antiport in CaiT. Nature (London, U.K.) 2010, 467, 233−236. (12) Berl, V.; Huc, I.; Khoury, R. G.; Krische, M. J.; Lehn, J. M. Interconversion of Single and Double Helices Formed From Synthetic Molecular Strands. Nature (London, U.K.) 2000, 407, 720−723. (13) Madueno, R.; Raisanen, M. T.; Silien, C.; Buck, M. Functionalizing Hydrogen-Bonded Surface Networks with SelfAssembled Monolayers. Nature (London, U.K.) 2008, 454, 618−621. (14) Reinhoudt, D. N.; Crego-Calama, M. Synthesis Beyond the Molecule. Science 2002, 295, 2403−2407. (15) Muller, D. K.; Hobza, P. Noncovalent Interactions: A Challenge for Experiment and Theory. Chem. Rev. (Washington, DC, U.S.) 2000, 100, 143−167. (16) Koishi, T.; Yoo, S.; Yasuoka, K.; Zeng, X. C.; Narumi, T.; Susukita, R.; Kawai, A.; Furusawa, H.; Suenaga, A.; Okimoto, N.; et al. Nanoscale Hydrophobic Interaction and Nanobubble Nucleation. Phys. Rev. Lett. 2004, 93, 185701−185704. (17) Zhao, Y.; Truhlar, D. G. Multicoefficient Extrapolated Density Functional Theory Studies of π···π Interactions: The Benzene Dimer. J. Phys. Chem. A 2005, 109, 4209−4212. (18) Rocha, A. R.; Garcia, S. V.; Bailey, S. W.; Lambert, C. J.; Ferrer, J.; Sanvito, S. Towards Molecular Spintronics. Nat. Mater. 2005, 4, 335−339. (19) Song, B.; Yang, J. W.; Zhao, J. J.; Fang, H. P. Intercalation and Diffusion of Lithium Ions in a Carbon Nanotube Bundle by ab initio Molecular Dynamics Simulations. Energy Environ. Sci. 2011, 4, 1379− 1384. (20) Iona, H. T.; Sham, C. C. K.; Chi, M. C.; Nianyong, Z. Borazine Materials for Organic Optoelectronic Applications. Chem. Commun. (Cambridge, U.K.) 2005, 28, 3547−3549. (21) Kim, D.; Hu, S.; Tarakeshwar, P.; Kim, K. S. Cation−π Interactions: A Theoretical Investigation of the Interaction of Metallic and Organic Cations with Alkenes, Arenes, and Heteroarenes. J. Phys. Chem. A 2003, 107, 1228−1238. (22) Lakshminarasimhan, P.; Sunoj, R. B.; Chandrasekhar, J.; Ramamurthy, V. Cation−π Interaction Controlled Selective Geometric Photoisomerization of Diphenylcyclopropane. J. Am. Chem. Soc. 2000, 122, 4815−4816. (23) Sherrill, C. D. Energy Component Analysis of π Interactions. Acc. Chem. Res. 2013, 46, 1020−1028. (24) Vijay, D.; Zipse, H.; Sastry, G. N. On the Cooperativity of Cation−π and Hydrogen Bonding Interactions. J. Phys. Chem. B 2008, 112, 8863−8867. (25) George, W. G.; Leonard, J. B.; Stephen, L. D. W.; Eric, S. M. Macrocyclic Polyethers as Probes to Assess and Understand Alkali Metal Cation-π Interactions. Coord. Chem. Rev. 2001, 222, 127−154. (26) Sunner, J.; Nishizawa, K.; Kebarle, P. Ion−Solvent Molecule Interactions in the Gas Phase. The Potassium Ion and Benzene. J. Phys. Chem. 1981, 85, 1814−1820. (27) Chen, J.; Wong, T. H.; Cheng, Y. C.; Montgomery, K.; Kleiber, P. D. Photodissociation Spectroscopy and Dynamics of MgC2H4+. J. Chem. Phys. 1998, 108, 2285−2296. (28) France, M. R.; Pullins, S. H.; Duncan, M. A. Spectroscopy of the Ca+-Acetylene π Complex. J. Chem. Phys. 1998, 108, 7049−7051. (29) Dongqiang, Z.; Bruce, E. H.; Mark, A. S.; Elizabeth, R. C. Characterization of Cation-π Interactions in Aqueous Solution Using Deuterium Nuclear Magnetic Resonance Spectroscopy. J. Environ. Qual. 2004, 33, 276−284. (30) Wouters, J. Cation-π (Na+-Trp) Interactions in the Crystal Structure of Tetragonal Lysozyme. Protein Sci. 1987, 7, 2472−2475.

and size of the cations. With decreased size of the cation, absorption spectra of benzene are found to be blue-shifted, whereas those of the borazine are red-shifted. The effect of various electron-donating and electron-withdrawing groups on the absorption spectra of such complexes has been determined. Both EDGs and EWGs cause a red shift in the spectral line of benzene cation−π complexes, whereas a similar trend is not observed for borazine cation−π complexes. The wavelength associated with the substituted cation−π complex of benzene correlates well with X−M distances and Hammett constants (σp and σm). This indicates that M+−π distances as well the inductive and resonance effect of the substituentst play a dominating role in the absorption spectra of the cation−π complexes. Comparison of the absorption spectra of the complexes obtained from both the models indicates that DSM leads to high shifting. The multiparametric fitting of Kamlet−Taft equation suggests that solvatochromism is dependent on the dielectric effects of solvents (π*), hydrogen-bond donor ability (α), and hydrogen-bond acceptor ability (β) of the solvents.

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ASSOCIATED CONTENT

S Supporting Information *

Gas-phase optimized geometries of the cation−π complexes, orbitals involved in electronic transition as per Tables 2 and 3, and correlation between HOMO orbitals and C−C and B−N bond length. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (P.K.B.) and [email protected] (K.K.B.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Prof. M. K. Chaudhuri, Vice Chancellor, Tezpur University for his support. Authors also thank UGC, New Delhi for financial support (F. 41-201/2012(SR)).

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