Article pubs.acs.org/JPCA
Exploring Cation−π Interaction in the Complexes with BB Triple Bond: A DFT Study Pradip K. Bhattacharyya* Department of Chemistry, Arya Vidyapeeth College, Guwahati, Assam 781016, India S Supporting Information *
ABSTRACT: Density functional theory calculations on metal ion−π interactions in cation−π complexes of diboryne and sandwiches of diboryne and benzene formed via metal ions were performed to understand the strength of interaction in these complexes. Results suggest that apart from the smaller metal ions (Li+, Be2+), larger ions (Na+, Mg2+, Ca2+, and Al3+) can also form cation−π complexes with BB triple bond and interaction energies of the complexes with larger metal ions (possessing same charges) are less than those obtained with smaller ions. Cations with higher charge lead to stronger interaction with the BB triple bonds. The calculated interaction energy further reveals that the sandwiches are more stable than their corresponding cation−π complexes. Stability of the complexes is measured in terms of global hardness (using Koopmans’ theorem and ΔSCF method), and the values obtained using ΔSCF method corroborate with the stability trend predicted by interaction energy values. Negative solvent-phase interaction energy for most of the chosen complexes indicates their stability in polar solvents too.
1. INTRODUCTION Cation−π interaction, a noncovalent interaction,1−4 is known to play an important role in biological systems especially in sodium and potassium channels.2−6 Although the existence of cation−π interaction was unravelled in biological contexts, in recent past, this interaction has been recognized for its prominent role in supramolecular chemistry, macromolecular structure, drug−receptor interactions, catalytic systems, crystal packing, and material chemistry.1−18 This type of interaction changes molecular properties to a significant level.18 With the pioneering work of Dougherty,4 a large number of theoretical studies has been devoted to illustrate the cation−π interaction in benzene and other aromatic systems.6,7 Cation−π interactions in benzene and borazine and the effect of substituent and solvent on such interactions were studied using density functional theory (DFT) calculation.19 Time-dependent density functional theory (TDDFT) calculations were also performed to predict electronic spectra of cation−π complexes of benzene and substituted benzenes.20 Recently, the possibility of cation−π interaction in cofacial dyads or molecular tweezers has been explored.21 Although a good number of theoretical studies has been devoted into the understanding of cation−π interaction in neutral aromatic compounds,6,7,19−21 very few experimentally authenticated compounds have so far been reported.22−28 Only the mass-spectrometric data are available for binding of alkali metal ions via cation−π interaction with neutral molecules.29,30 In addition to aromatic systems, alkenes and alkynes also form cation−π complexes.31−34 The BB triple bond is expected to be similar to that of a CC triple bond, and accordingly interaction of BB triple bond with metal ions can © 2017 American Chemical Society
be presumed to take place. The group of H. Braunschweig reported an interesting diboryne compound with NHC ligand substituted with 2,6-diisopropylphenyl to exhibit such kind of cation−π interaction.35 Earlier, there were very few reports predicting the existence of diboryne molecule. Zhou et al.36 identified B2 molecule in an argon matrix at 8 K stabilized by two CO molecules. Although existence of molecules with BB triple bond was proposed theoretically beforehand,37−39 until the report of the crystal structure of the cation−π complex of diboryne with Li+ and Na+ by Bertermann et al.,35 there was no experimental evidence for the existence of cation−π interaction in triply bonded boron compounds. Recently, on the basis of molecular orbital description, Frenking et al.39 proposed that the B−B bond order in diboryne should be ∼2.34, which is fairly equivalent to a triple bond.39 With the help of experimental Raman spectroscopy and theoretical measurement of relaxed force constants, Braunschweig and his coworkers,40 however, proved that the vibrational frequencies and force constant of the BB bond is in agreement with the trends established for CC and NN bonds. In comparison to a significant number of studies dealing with cation−π interactions with aromatic systems, alkenes, or alkynes, only a few reports on cation−π interaction with B B triple bond are available. To the best of my knowledge no extensive theoretical studies have been made on the cation−π complexes and sandwiches of diboryne except one by Bertermann et al. and another by our group.35,41 Therefore, Received: February 10, 2017 Revised: April 10, 2017 Published: April 12, 2017 3287
DOI: 10.1021/acs.jpca.7b01326 J. Phys. Chem. A 2017, 121, 3287−3298
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The Journal of Physical Chemistry A
Figure 1. (a) Shape of HOMO of the Dby molecule, (b) optimized structure of the Dby molecule, (c) cation−π complex of Dby, and (d) sandwich complexes of Dby.
performed using B3LYP/6-311++G(d,p) level of theory in different solvents ranging from nonpolar to a polar one via cyclohexane (ε = 2.02), tetrahydrofuran (THF; ε = 7.43), acetone (ε = 20.49), ethanol (ε = 24.85), and water (ε = 78.35). Global hardness (η) is defined as the second derivative of energy with respect to the number of electrons.48,49 Use of finite difference approximation and Koopmans’ theorem50 leads to the working formulas for η as, η = (ELUMO − EHOMO)/2, where EHOMO is the energy of the highest occupied molecular orbital (HOMO), and ELUMO is the energy of the lowest unoccupied molecular orbital (LUMO). The electron affinity (EA) obtained from Koopmans’ theorem is sometimes not reliable, and hence the global hardness of the chosen systems are recalculated using ΔSCF method,51 and the stability pattern predicted by this method is compared with stability trend inferred from interaction energy. In ΔSCF method, EA and ionization potential (IP) are defined as EA = EN − EN+1 and IP = EN‑1 − EN, where EN−1, EN, and EN+1 are energies of the N − 1, N, and N + 1 electron systems. This leads to the formula for global hardness as, η = (EN+1 + EN−1 − 2EN)/2.
in an attempt to gain insights about the strength of cation−π interaction, as well as the nature of the electronic transitions involved therein, DFT and TDDFT calculations are performed on cation−π complexes and sandwiches (with benzene) of modeled diboryne molecule with mono-, di-, and trivalent cations (Li+, Na+, K+, Be2+, Mg2+, Ca2+, and Al3+).
2. COMPUTATIONAL DETAILS The optimized geometry of the complexes are obtained using B3LYP/6-311++G(d,p) level of theory without any symmetry constraints using Gaussian 09.42 The B3LYP functional has earlier been used to study the cation−π interactions in a number of occasions.2,7 To check the consistency in results obtained using B3LYP/6-311++G(d,p) level of theory, singlepoint calculations are performed using ωB97X-D/6-311+ +G(d,p) level of theory. Absorption spectra are computed as vertical excitations from the ground-state structures using TDDFT43 (using N = 20) approach as implemented in Gaussian09.42 Interaction energies (ΔE) are calculated using supermolecular model [for A + B → AB, ΔE = (EAB) − (EA + EB), where E is the total electronic energy of the respective species]. While the interaction energies are calculated, basis set super position error (BSSE) is taken into account. Similar protocol was considered in calculating enthalpy and free energy of complexation, ΔH = (HAB) − (HA + HB) and ΔG = (GAB) − (GA + GB), where H and G are the enthalpy and free energy of the species. Of the different models for accounting the solvation energies, dielectric continuum solvation models have been widely and successfully applied.44 In the self-consistent model the solvent is considered as a continuous dielectric medium that is polarized by the solute. Polarizability continuum model (PCM) is a popular way to implement the SCRF (selfconsistent reaction field) approach, which describes the solvent polarization in terms of the electrostatic potential.45 This model was developed by Tomasi’s group, and a wealth of documented literature shows its applicability in different molecular systems.44,46,47 To assess the impact of dielectric of the solvent media on the interaction energies, single-point calculations are
3. RESULTS AND DISCUSSION The cation−π complex considered by Bertermann et al.35 contains additional cation−π interactions with aromatic rings apart from cation−π interaction with the BB triple bond. Therefore, in modeling the association geometries of the complexes, the aromatic wings are replaced by H atoms so that it contains only M+···BB interaction only. Earlier it was reported that this type of substitution does not lead to any significant variation in the geometrical parameters around the B2 unit,40,52 and thus this modeling of the geometry is expected to be reliable. 3.1. Geometries of the Complexes. Referring to Figure 1a, the modeled molecule (abbreviated as Dby), major portion of the HOMO lies on the BB bond, enticing the cation to indulge in cation−π interactions. The shape of the HOMO also infers that it bears π character. It is evident from Figure 1b that in Dby, the pyrazole rings are perpendicular to each other with 3288
DOI: 10.1021/acs.jpca.7b01326 J. Phys. Chem. A 2017, 121, 3287−3298
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The Journal of Physical Chemistry A Table 1. Important Structural Parameters of the Cation−π Complexes and Their Corresponding Sandwichesa Obtained Using B3LYP/6-311++G(d,p) Level of Theory system
RB−Bb
Δq
RX−Mb
Dby Dby@Li+ Dby@Na+ Dby@K+ Dby@Be2+ Dby@Mg2+ Dby@Ca2+ Dby@Al3+ Dby-Ben@Li+ Dby-Ben@Na+ Dby-Ben@K+ Dby-Ben@Be2+ Dby-Ben@Mg2+ Dby-Ben@Ca2+
1.45 1.44 1.45 1.45 1.47 1.47 1.46 1.51 1.44 1.45 1.45 1.44 1.45 1.45
0.12 0.09 0.04 0.83 0.69 0.33 1.72 0.36 0.22 0.11 1.04 0.75 0.47
2.15 2.51 2.93 1.75 2.21 2.47 2.25 2.20 2.54 2.30 1.78 2.23 2.53
a
Dby-Ben@Al3+ could not be optimized. angstroms.
b
RX′−Mb
RB−Mb
2.08 2.59 3.05 2.08 2.23 2.58
2.27 2.61 3.02 1.89 2.33 2.58 2.37 2.31 2.64 3.07 1.91 2.34 2.65
Figure 2. Plot of magnitude of interaction energy (Dby@Na+, Dby@ Mg2+, and Dby@Al3+ complexes are considered for the comparison) vs charge on the cation (charge of the bare ions are considered; charges are 1, 2, and 3 for Na+, Mg2+, and Al3+, respectively).
bond distances in
complex). For example, BB bond in Dby@Li+ is 1.44 Å, and in case of Dby@Na+ and Dby@K+ it is 1.45 Å. This bond length is slightly elongated in case of Dby@Be2+, Dby@Mg2+, and Dby@Ca2+ (1.47, 1.47, and 1.46 Å, respectively). The B B bond distances do not get affected much in case of complexes with monovalent and divalent ions (the change is divalent ions > monovalent ions. A smaller
∠N1C2C3N4 = 89.9°. Interestingly during complex formation (cation−π and sandwiches) the rings become perfectly parallel to each other (∠N1C2C3N4 = 0.0°). The distance of the metal ion from the midpoint of the BB bond, RX−M, and the distance of the cation from the B atom, RB−M, along with the BB distances, RB−B (obtained using B3LYP/6-311++G(d,p) level of theory) are presented in Table 1. The RB−B distance in absence of the cation (i.e in the Dby molecule) is calculated to be 1.45 Å. This is in line with the earlier report by Braunschweig et al.53 They used Amsterdam Density Functional (ADF) program at the OLYP/DZP level of theory for the calculation. The B−B distances in Dby are in close agreement with those calculated distances (1.46 Å) in bis(carbene) and bis(phosphene) stabilized diborynes.39,54 The B−B distance increases due to BB···cation interaction; the RB−B distance in the complexes (cation−π and sandwiches) with monovalent ions are in the range of 1.44− 1.45 Å. In case of complexes with divalent ions, there is slight elongation of the BB bonds and is within the range of 1.46− 1.47 Å. Elongation of the BB bonds is more pronounced in case of complexes with trivalent ions (1.51 Å in Dby@Al3+
Table 2. BSSE-Corrected Interaction Energy for Cation−π Complexes and Sandwiches at Four Different Levels of Theory level of theory system
B3LYP/6-311++G(d,p)a
B3LYP/6-311++G(2d,2p)a
ωB97X-D/6-311++G(d,p)a
ωB97X-D/6-311++G(2d,2p)a
−72.1 −56.0 −38.2 −354.8 −242.4 −160.8 −645.0 −87.4 −67.2 −47.3 −408.0 −277.7 −194.9
−72.5 −56.6 −38.8 −355.5 −243.5 −163.4 −646.6 −88.1 −67.7 −47.7 −409.1 −279.7 −197.5
−73.2 −56.0 −40.9 −343.6 −231.4 −161.4 −619.1 −94.4 −71.8 −53.2 −405.0 −277.3 −200.9
−72.7 −55.3 −40.2 −342.5 −229.9 −158.3 −616.7 −93.6 −71.0 −52.7 −403.5 −274.8 −198.0
+
Dby@Li Dby@Na+ Dby@K+ Dby@Be2+ Dby@Mg2+ Dby@Ca2+ Dby@Al3+ Dby-Ben@Li+ Dby-Ben@Na+ Dby-Ben@K+ Dby-Ben@Be2+ Dby-Ben@Mg2+ Dby-Ben@Ca2+ a
ΔE, in kilocalories per mole. 3289
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Figure 3. Plot of magnitude of interaction energy (gas phase) vs charge transfer during complexation (Δq) in (a) cation−π complexes and (b) sandwiches.
Table 3. Interaction Energies (ΔE, in kcal mol−1) in Different Solvent Media Obtained Using B3LYP/6-311++G(d,p) Level of Theory solvents system
gas phase
cyclohexane
THF
acetone
ethanol
water
Dby@Li+ Dby@Na+ Dby@K+ Dby@Be2+ Dby@Mg2+ Dby@Ca2+ Dby@Al3+ Dby-Ben@Li+ Dby-Ben@Na+ Dby-Ben@K+ Dby-Ben@Be2+ Dby-Ben@Mg2+ Dby-Ben@Ca2+
−72.1 −56.0 −38.2 −354.7 −242.4 −160.7 −645.0 −208.0 −187.7 −167.9 −528.5 −398.2 −315.4
−35.3 −28.4 −19.3 −215.1 −128.5 −75.1 −506.0 −41.6 −33.5 −23.8 −252.3 −144.8 −89.1
−9.8 −8.9 −5.7 −118.5 −53.4 −21.2 −404.1 −7.2 −8.6 −6.7 −137.7 −50.3 −18.4
−4.1 −3.8 −2.4 −96.6 −37.4 −10.1 −379.4 1.0 −2.9 −2.8 −110.1 −29.0 −3.7
−3.5 −3.2 −2.1 −94.5 −35.9 −9.0 −376.9 1.8 −2.4 −2.4 −107.4 −26.9 −2.3
−1.7 −1.3 −1.1 −87.7 −31.1 −5.7 −368.9 4.3 −0.6 −1.2 −98.5 −20.4 2.1
cation imposes more charge transfer compared to a larger one. For example, Δq values (in au) for Li+, Na+, and K+ (in cation−π complexes) are 0.12, 0.09, and 0.04, respectively. A larger charge transfer during complexation imparts more covalency to the interaction between the moieties, and therefore higher interaction energy in case of such complexes is expected. In case of sandwiches, similar charge transfer is also observed. Further, because of charge transfer from the BB bond to the metal ion, the absorption spectra of the Dby@Mn+ and Dby-Ben@Mn+ complexes also are to be affected. The distance of the cation from the geometric mean of the BB bond (RX−M) depends on the size of the cation, and reflecting this size dependence, these distances for Dby@Li+, Dby@Na+, and Dby@K+ are 2.15, 2.51, and 2.93 Å, respectively, Table 1. Yang et al. performed MP2/6311+G(2d) level of calculation on HCCH···Na+ complex and showed that the CH···Na+ distance is 2.63 Å.33 This is close to that obtained for Dby@Na+ complex in the present
Table 4. Enthalpy (ΔH) and Free Energy (ΔG) Involved in the Formation of the Complexes Obtained Using B3LYP/6311++G(d,p) Level of Theory system
ΔH (kcal mol−1)
ΔG (kcal mol−1)
−70.4 −54.9 −37.1 −352.7 −240.4 −158.9 −643.0 −85.2 −65.5 −45.4 −404.5 −274.9 −192.7
−63.3 −48.0 −30.4 −342.3 −232.0 −151.2 −634.5 −68.4 −49.8 −30.9 −385.8 −256.8 −173.6
+
Dby@Li Dby@Na+ Dby@K+ Dby@Be2+ Dby@Mg2+ Dby@Ca2+ Dby@Al3+ Dby-Ben@Li+ Dby-Ben@Na+ Dby-Ben@K+ Dby-Ben@Be2+ Dby-Ben@Mg2+ Dby-Ben@Ca2+
Table 5. B−B Stretching Frequency in the Cation−π Complexes and Sandwiches (in cm−1) system Dby Dby@Li+ Dby@Na+ Dby@K+
B−B (νsym) 1733 1713 1707 1712
system 2+
Dby@Be Dby@Mg2+ Dby@Ca2+ Dby@Al3+
B−B (νsym)
system
B−B (νsym)
system
B−B (νsym)
1673 1680 1668 1662
Dby-Ben@Li+ Dby-Ben@Na+ Dby-Ben@K+
1717 1711 1714
Dby-Ben@Be2+ Dby-Ben@Mg2+ Dby-Ben@Ca2+
1701 1692 1688
3290
DOI: 10.1021/acs.jpca.7b01326 J. Phys. Chem. A 2017, 121, 3287−3298
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Figure 4. Comparison of the UV−vis spectra of (a) Dby@M+ complexes, (b) Dby@M2+ and Dby@M3+ complexes, (c) Dby-Ben@M+ complexes, and (d) Dby-Ben@M2+ complexes.
study. They also showed that HCCH···Na+ distance depends on the nature of the substituent on the carbon atom. For example, the cation−π distances in CH3CCCH3···Na+ and FCCF···Na+ are 2.54 and 2.77 Å, respectively.33 However, the distances in the chosen cation−π complexes are longer as compared to those obtained in case of benzene−M complexes (where M = Li+, Na+, and K+); at MP2/6-31+G(d) level of theory, the benzene···M distances were measured to be 1.93, 2.42, and 2.89 Å for M = Li+, Na+, and K+ cation−π complexes, respectively.19 The RX−M distances in case of cation−π complexes with divalent cations are comparatively shorter. For example, RX−M distances in Dby@Be2+, Dby@Ca2+, and Dby@Mg2+ complexes are 1.75, 2.21, and 2.47 Å, respectively. Such complexes of borazine possess slightly shorter bonds.19 In case of aromatic rings, the π clouds are delocalized over the ring, which allows a shorter cation−π distance as compared to a CC, CC, or BB bond, where the π cloud is confined within the two sites. The RX−M distances in the sandwiches are calculated to be 2.20, 2.54, and 2.30 Å, respectively, for DbyBen@Li+, Dby-Ben@Na+, and Dby-Ben@K+ complexes. The distance of the cation from the geometric mean of the benzene ring (RX′−M) (Figure 1 and Table 1) in the sandwiches also exhibits little variation as compared to that observed in case of respective cation−π complexes; slightly longer RX′−M distances are observed, Table 1. These distances are measured to be 2.08, 2.59, 3.05, 2.08, 2.23, and 2.58 Å for Dby-Ben@Li+, Dby-Ben@
Na+, Dby-Ben@K+, Dby-Ben@Be2+, Dby-Ben@Mg2+, and Dby-Ben@Ca2+, respectively. As in Dby-Ben@Be2+ complex, the benzene ring is not situated perfectly perpendicular to the BB···M moiety; comparison of RX−M and RX′−M distances is not to be made. Optimized structures of the complexes are provided in Supplement Figures S1a,b. Similar to RX−M distances, the RB−M distances also depend on the size of the cation. 3.2. Interaction Energy. The gas-phase BSSE-corrected interaction energy of the considered cation−π complexes and the sandwiches are presented in Table 2. As can be seen from Table 2, the interaction energies in cation−π complexes with BB triple bond are very high in comparison to those calculated for benzene and borazine cation−π complexes.19 The gas-phase interaction energies calculated using B3LYP/6-311+ +G(d,p) level of theory for Dby@Li+, Dby@Na+, and Dby@K+ are are −72.1, −56.0, and −38.2 kcal mol−1 respectively. The interaction energies for the complexes with divalent cations are even higher. For Dby@Be2+, interaction energy is −354.8 kcal mol−1, while for Dby@Mg2+ and Dby@Ca2+ complexes, the interaction energies are −242.4 and −160.8 kcal mol−1 respectively. Dby@Al3+ complex possesses even much higher interaction energy and is calculated to be −645.0 kcal mol−1. Results demonstrate that interaction energy decreases with the increase in size of the cation and increases with the increase in charge of the cation. It is not that the strength of the cation−π 3291
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The Journal of Physical Chemistry A Table 6. λmax of Transition, Oscillator Strength, Molecular Orbitals, and Their Contributions in Few Selected Electronic Transitions of Cation−π Complexes and Sandwiches Obtained Using B3LYP/6-311++G(d,p) Level of Theory systems
(nm)
oscillator strength ( f)
molecular orbitals (MO) involved
orbital contribution
HOMO−1→LUMO +1 HOMO→LUMO+2 HOMO→LUMO HOMO→LUMO+8 HOMO−1→LUMO +1 HOMO→LUMO HOMO→LUMO+4 HOMO−1→LUMO HOMO→LUMO HOMO→LUMO+4 HOMO−1→LUMO HOMO→LUMO HOMO→LUMO+5 HOMO−1→LUMO +1 HOMO→LUMO HOMO−3→LUMO +1 HOMO−1→LUMO +1 HOMO→LUMO HOMO−1→LUMO +5 HOMO−1→LUMO +1 HOMO→LUMO HOMO−3→LUMO HOMO−1→LUMO +1 HOMO−2→LUMO HOMO→LUMO HOMO→LUMO+5
0.33
0.60
0.44 0.52
Dby
335.9
0.6
Dby@Li+
494.0 273.3 485.4
0.02 0.4 0.3
835.9 318.1 485.9 753.9 326.3 520.0 784.2 206.5 444.7
0 0.3 0.2 0.0008 0.5 0.1 0.0008 0.6 0.3
748.3 257.1
0.0077 0.3
384.5
0.2
961.0 361.0
0.0036 0.2
573.8
0.1
774.1 240.0 340.2
0.0074 0.3 0.7
462.8 1929.7 336.7
0.2 0.0005 0.3348
499.8
0.1409
301.6
0.3129
316.7
0.2083
349.2 328.3
0.1913 0.3951
HOMO−1→LUMO +1 HOMO→LUMO +10 HOMO−3→LUMO +6 HOMO→LUMO+4 HOMO→LUMO+6
272.3
0.2227
HOMO−3→LUMO
0.69
337.9
0.1699
0.68
487.2 244.5
0.1520 0.5043
407.4
0.322
306.8 521.9
0.1524 0.2405
HOMO−1→LUMO +3 HOMO−1→LUMO HOMO−1→LUMO +4 HOMO−1→LUMO +5 HOMO→LUMO+9 HOMO−1→LUMO +2
Dby@Na+
Dby@K+
Dby@Be2+
Dby@ Mg2+
Dby@Ca2+
Dby@Al3+
Dby-Ben@ Li+
Dby-Ben@ Na+
Dby-Ben@ K+ Dby-Ben@ Be2+
Dby-Ben@ Mg2+ Dby-Ben@ Ca2+
interaction.34 Sharma et al.56 have shown that this size dependency exists in cation−π complexes of transition-metal ions too. Along the same line with the previous reports of other cation−π complexes, interaction energy is found to be higher with smaller cations.19−21 For instance, cation−π complexes of Li+ are more stabilized (by ∼34 kcal mol−1) than the corresponding cation−π complexes of K+. Similarly, Dby@ Be2+ complex is more stable than Dby@Ca2+ by 194 kcal mol−1. The ratio of interaction energies for complexes with monovalent/divalent/trivalent ions is 1:4.3:11.4 (interaction energies in Dby@Na+, Dby@Mg2+, and Dby@Al3+ complexes are compared). The ratio further clarifies that interaction energy is not simply additive in nature, that is, does not increase linearly with the charge of the metal ion; in fact, an exponential relationship between interaction energy and charge of the bare cation is observed (with R2 = 0.9871), Figure 2. The corresponding sandwiches exhibit higher gas-phase interaction energies (obtained using B3LYP/6-311++G(Dd,p) level of theory) as compared to their corresponding cation−π complexes. The interaction energies for Dby-Ben@Li+, DbyBen@Na+, and Dby-Ben@K+ are −87.4, −67.2, and −47.3 kcal mol−1 respectively. Sandwiches of divalent metal ions exhibit interaction energies, −408.0, −277.7, and −194.9 kcal mol−1, respectively for Dby-Ben@Be2+, Dby-Ben@Mg2+, and DbyBen@Ca2+ sandwiches. In case of sandwiches too, smaller ions yield larger interaction energies. Even though the sandwiches involve two cation−π interactions (one with the BB bond and the other with the benzene ring), on account of sharing of the charge of the cation by the two moieties (BB bond and benzene ring) the interaction energy does not show proportionate increase in case of sandwiches. For example, Dby@Li+ shows interaction energy of −72.1 kcal mol−1, whereas, in its corresponding sandwich, Dby-Ben@Li+ the same is −87.4 kcal mol−1 (obtained using B3LYP/6-311++G(d,p) level of theory). Referring to Table 1, smaller cations impose more charge transfer during complexation (cation−π complexes) and consequently impart more covalency to the interaction between metal ion and the BB triple bond. Conclusively, there exists a relationship between interaction energy and charge transfer during complexation. To verify the statement further, these two parameters in the chosen complexes are plotted, and it is interesting to see that in both cases (cation−π complex and sandwiches) excellent linear relationship is observed with R2 = 0.9907 for cation−π complexes and R2 = 0.9735 for sandwiches, Figure 3. It is important to note that at B3LYP/6-311++G(d,p) level of theory, the interaction energies for benzene−Li+, benzene−Na+, and benzene−K+ complexes were calculated to be −37.8, −23.2, and −15.9 kcal mol−1 respectively.19 The results in the present study thus suggest that interaction of the metal ion with the BB bond is much stronger as compared to benzene−M+ interactions. The BSSE corrections are provided in Supplement Table S1; note that the BSSE corrections in the chosen complexes are negligible. However, in other cation−π interactions, BSSE corrections were shown to be quite significant, and it can be as large as 15% of the raw interaction energies (interaction energy without BSSE correction), and use of a triple-ζ basis set can reduce the BSSE corrections substantially.19 Interaction energies calculated at ωB97X-D/6-311++G(d,p) and B3LYP/6-311++G(d,p) level of theories are close to each other, Table 2. Herein, close resemblance of the values obtained with two different functionals reveals that B3LYP is a better choice over ωB97X-D, as the latter is computationally
0.34 0.65 0.64 0.67 0.71 0.47 0.62 0.70 0.53 0.61 0.70 0.62 0.68 0.71 0.56 0.65 0.71 0.62 0.65 0.70 0.52 0.66 0.67 0.71 0.52
0.60 0.60
0.69 0.50 0.66 0.62 0.66
interaction depends on the size of the cation only; it does depend on the size of the aromatic system too.32,55 Earlier works also point toward such size dependency in alkane−cation 3292
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Figure 5. Shape of HOMO, HOMO−1, LUMO, and LUMO+1 orbitals of Dby@Li+, Dby@Al3+, and Dby-Ben@Li+.
interaction energy in water only (2.1 kcal mol−1). All the other sandwiches exhibit negative interaction energies in chosen solvents. The bare ions are more solvated in solvent phases. In cation−π complexes, the charge is dispersed over a larger sphere, and hence the complexes are less solvated, which leads to a drop of interaction energies in cation−π complexes in solvent phases. As dielectric of the solvent medium increases the interaction between the metal ion and the solvent phase increases, and hence interaction energy drops with the increase in solvent dielectric. Drop in interaction energies in case of complexes with smaller ions is more pronounced as compared to larger ions. A noticeable change in the cation−π interaction energy in case of smaller ions with respect to the solvent polarity can be attributed to the fact that smaller ions bind strongly to π systems, but at the same time, smaller ions are highly solvated in polar solvents. A stronger cation−π interaction compensates the high desolvation penalty for smaller ions to provide negative interaction energy even in polar medium. It is to be noted that the benzene−Li+ interaction is repulsive in water phase,19 whereas, in the present study, a negative interaction energy (−1.7 kcal mol−1 for Dby@Li+ complex) in water phase is significant. This predicts the feasibility of formation of Dby@M+ complexes even in polar medium also. Earlier, Dougherty found that the order of cation−π interaction energy in the gas phase was Li+ > Na+ > K+ > Rb+.5 The gas-phase results in this study do agree with the trend observed by Dougherty. Earlier Sastry and his co-workers57 have made extensive study on the effect of solvent on Li+−benzene, K+−benzene, and Mg2+−benzene systems and showed that the strength of the cation−π interactions in these systems depend on the site of solvation of the complex. They also observed that when the solvent molecules (water) interact from the side of the cation, interaction energy drops, and the reverse is observed when water molecules interact from the side of the benzene molecule.
demanding. The interaction energies obtained using 6-311+ +G(2d,2p) basis set is also close to that obtained using 6-311+ +G(d,p) basis set, Table 2, which indicates that use of more polarize basis sets is not necessary for estimating interaction energies in this type of complexes. Effect of Solvent on Interaction Energy. As witnessed in earlier studies, interaction energy in cation−π complexes is highly influenced by the dielectric of the medium.19 To understand the effect of solvents on the interaction energy in the considered cation−π complexes and the sandwiches, five different solvent systems are chosen, and the solvent-phase interaction energies are calculated using B3LYP/6-311++G(d,p) level of theory; results are summarized in Table 3. It is worthwhile to note that interaction energies exhibit a spiky fall as the solvent medium is incorporated and in polar solvent (water) interaction energies fall significantly as compared to gas-phase interaction energies. For example, gas-phase interaction energy in Dby@Li+ complex is −72.1 kcal mol−1, which reduces to −35.3 kcal mol−1 in cyclohexane, and −9.8 kcal mol−1 is estimated in THF. In acetone and ethanol, interaction energy drops further (−4.1 and −3.5 kcal mol−1, respectively), and in water as solvent, interaction energy is very small (−1.7 kcal mol−1). For all the chosen cation−π complexes, reduction in interaction energies is observed in solvent phases. However, the trend of solvent-phase interaction energy is identical to the gas-phase one. For instance, interaction energies of the chosen complexes in water are in order: Dby@Li+ (−1.7) > Dby@Na+ (−1.3) > Dby@K+ (−1.1); Dby@Be2+ (−87.7) > Dby@Mg2+ (−31.1) > Dby@Ca2+ (−5.7). And Dby@Al3+ (−368.9) > Dby@Mg2+ (−31.1) > Dby@Na+ (−1.3) (values shown within brackets are in kcal mol−1; more negative values imply higher interaction energy). Significantly, all the cation−π complexes exhibit negative interaction energies in water. Among the sandwiches, Dby-Ben@Li+ possesses positive interaction energies in acetone, ethanol, and water (1.0, 1.8, and 4.3 kcal mol−1, respectively), and Dby-Ben@Ca2+ exhibits positive 3293
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Figure 6. (a) Variation of gas-phase HOMO energy of the complexes, (b) plot of interaction energy (gas phase) vs HOMO energy of the cation−π and sandwiches of monovalent cations. (c) plot of interaction energy (gas phase) vs HOMO energy of the cation−π and sandwiches of divalent cations. (d) plot of interaction energy (gas phase) vs global hardness (obtained with ΔSCF method).
Reorganization Energy. It is seen that during formation of the complexes, the Dby molecule undergoes reorientation, and hence the reorganization energy for the chosen complexes has been computed (at B3LYP/6-311++G(d,p) level of theory). The reorganization energy is calculated as the difference in the total energy of the Dby molecule in its free state and in the complexes (cation−π and sandwiches). The reorganization energy for Li+, Na+, and K+ complexes are 4.9, 4.0, and 3.7 kcal mol−1, respectively. For complexes with divalent ions, reorganization energies are calculated to be higher as compared to that observed in case of complexes with monovalent ions and are in the range from 7.6 to 7.9 kcal mol−1. The complexes with trivalent ion exhibit much higher reorganization energies compared to mono-or divalent ions; it is recorded to be 12.4 kcal mol−1 (for Dby@Al3+). Reorganization energy depends on the size of the cation as well as on the size of the molecule that undergoes reorientation. Earlier, for ethane molecule the reorganization energy with monovalent ions Li+, Na+, and K+ are reported to be 0.41, 0.38, and 0.28 kcal mol−1.32 Also, the reorganization energy decreases with an increase in the size of the monovalent cation. This is due to the decrease in the charge transfer observed for larger metal ions, Table 1. A comparison of interaction energy (provided in Table 2) and reorganization energy (mentioned above) of complexes with monovalent cations indicates that higher the reorganization energy of a complex, the greater is its interaction energy. However, in case
of complexes with divalent metal ions no such relationship could be established, which might be due to the different reorganization energies in the complexes. 3.3. Thermochemical Analysis. To examine thermodynamic driving forces involved in cation−π complex and sandwich formation, change in enthalpy (ΔH), and free energy (ΔG) during the complex formation is analyzed. The results obtained using B3LYP/6-311++G(d,p) level of theory are presented in Table 4. A more negative ΔH value in gas phase indicates a strong thermodynamic driving force concomitant with the complex formation. Calculated ΔH values (in kcal mol−1) for cation−π complexes with monovalent ions follow the order −70.4 (Li+) > −54.9 (Na+) > −37.1 (K+) (values are in kcal mol−1), which reflects a strong inverse dependence of ΔH on the size of the cation, (Table 4) similar to that observed in case of interaction energy. Similarly, cation−π complexes of Be2+, Mg2+, and Ca2+ follow the order −352.7 (Be2+) > −240.4 (Mg2+) > −158.9 (Ca2+) (values are in kcal mol−1). Similar to the interaction energy, among the chosen set of complexes, ΔH for Dby@Al3+ complex is maximum. This trend can be related to the polarizing power of the cation and polarizability of the anion (here the π-electron cloud). Comparatively smaller ions polarize the π-electron cloud more, leading to a more negative value of ΔH. An earlier work reported that in cation−π complexes of benzene, gas-phase ΔH values follow the order −36.9 (Li+) > −24.1 (Na+) > −17.5 (K+) (in kcal mol−1).19 It 3294
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The Journal of Physical Chemistry A was also reported that the ΔH values (in kcal mol−1) for thiophene−M+ complexes follow the order −58.43 (Li+) > −40.39 (Na+) > −26.49 (K+).58 Results thus point at the exothermic nature of cation−π complexation or sandwich formation in gas phase, irrespective of the size of cations. ΔH values for the sandwiches are higher as compared to their corresponding interaction energies. In practice, ΔG is a more suitable parameter to predict the thermodynamic feasibility of a process, as it encompasses the contribution of both enthalpy and entropy factor concomitant with the process. Usually, complexation is accompanied by a decrease in entropy, which opposes a negative ΔG value. In the considered systems, the ΔG values follow the same order as that by ΔH, Table 4. As can be observed in Table 4, with the increase in charge of the cation and decrease in their sizes, ΔG becomes progressively more negative. For example, ΔG values for Dby@Na+, Dby@Mg2+, and Dby@Al3+ are −48.0, −232.0, and −634.5 kcal mol−1, respectively. Similar inverse dependence of ΔG values on the size of cation is observed in case of cation−π complexes of benzene also.2 Experimental and theoretical ΔG values of alkali metal ion−benzene complexes (theoretical values are shown in parentheses) suggests a trend as Li+(−38.3 and (−43.8)) > Na+(−28.0 and (−29.5)) > K+(−19.2 and (−19.2) (in kcal mol−1)).59 Both ΔH and ΔG values support the fact that the cation−π complex and sandwich formation are enthalpy- as well as free energy-driven processes. 3.4. Spectroscopic Analysis of the Complexes. IR Analysis. Interaction of the cation with the BB bond might have an impact on the B−B stretching frequencies. A comparison of the B−B symmetric stretching frequency (obtained using B3LYP/6-311++G(d,p) level of theory) of Dby molecule with its corresponding cation−π complexes and sandwiches are shown in Table 5. Referring to Table 5, the B− B stretching frequency in the Dby molecule appears at 1733 cm−1, which is shifted to 1713, 1707, and 1712 cm−1 in Dby@ Li+, Dby@Na+, and Dby@K+ complexes, respectively. Similar decrease in B−B stretching frequencies in the cation−π complexes was also observed experimentally.35 For cation−π complexes with divalent ions, these frequencies even decrease further; for example, the B−B stretching frequencies for Dby@ Be2+, Dby@Mg2+, and Dby@Ca2+ complexes appear at 1673, 1680, and 1668 cm−1, respectively. For Dby@Al3+ complex the B−B stretching frequency is even less and appears at 1662 cm−1. Decrease in B−B stretching frequencies in the cation−π complexes clearly indicates weakening of BB bond due to cation−π interaction. This is in accordance with the interaction energy values. As expected stronger interaction with the divalent ions further lowers the B−B stretching frequencies in Dby@M2+ complexes, and accordingly least B−B stretching frequency is recorded in Dby@Al3+ complex. Despite the fact that the interaction energies are higher for the sandwiches as compared to the cation−π complexes, the B−B stretching frequencies in the sandwiches are recorded to be in higher range. UV−Vis Analysis. To gain an insight into the involvement of the molecular orbitals involved in the transition of the UV−vis spectra, TDDFT calculations were performed on the optimized structures of the chosen complexes and also on the Dby molecule. The calculated UV−vis spectra are shown in Figure 4, and the results of TDDFT calculation are presented in Table 6. The main peak of Dby molecule appears at 335.9 nm, which is mostly contributed by HOMO−1 → LUMO+1 and HOMO
→ LUMO+2 transitions. This peak is shifted (blue) upon interaction with the cations; for example, in Dby@Li+, Dby@ Na+, and Dby@K+ complexes the peak appears at 273.3, 318.1, and 326.3 nm, respectively, Table 6. As the strength of the interaction between BB bond and the cation decreases with the increase in the size of the cation, Li+ ion shifts the peak to a larger extent (63 nm) as compared to Na+ (18 nm) or K+ (10 nm) ions. Interestingly, the broad peak for Dby molecule that appears at ∼494 nm becomes sharp in cation−π complexes. This peak is observed at 485 nm for Dby@Li+ and Dby@Na+ complexes and at 520 nm in case of Dby@K+ complex, Table 6. Similarly, in case of Dby@M2+ and Dby@M3+ complexes blue shift in the main absorption peak is observed, Figure 4. Like smaller monovalent cation, a smaller divalent cation also produces maximum shift in the absorption spectra. The shift in the peaks is much more prominent in Dby@Be2+ complex (129 nm), followed by Dby@Al3+ complex (96 nm) and Dby@Mg2+ complex (79 nm). Contrarily, Dby@Ca2+ complex exhibits a different spectral shift. In case of the sandwich complexes, the maxima of the absorption peak appear at 336.7, 301.6, and 328.3 nm for DbyBen@Li+, Dby-Ben@Na+, and Dby-Ben@K+ complexes respectively. Similar to that observed in case of cation−π complexes, the broad peak of the Dby molecules sharpens in sandwiches, Figure 4. The sandwiches with the divalent cations experience significant shift in the absorption peaks. In DbyBen@Be2+, Dby-Ben@Mg2+, and Dby-Ben@Ca2+ peaks are at 272.3, 244.5, and 306.8 nm, respectively. It is seen that most of the transitions are associated with the transition from HOMO or HOMO−1 orbital to LUMO+n (n = 1−8). Since the HOMO and HOMO−1 orbitals are mostly concentrated in the B2 unit of the complexes (Figure 5, few MOs of Dby@Li+, Dby@Al3+, and Dby-Ben@Li+ are shown as a representative case), it is conclusive to comment that the sharp and intense signal of the complexes are characteristic of BB unit. Importantly, the absorption peaks due to HOMO → LUMO transition appears at higher wavelength, and in many cases, they are dark states ( f = 0). 3.5. Stability of the Complexes. Reactivity descriptors like HOMO energy, global hardness, and chemical potential have been some back-of-an-envelop tool for rationalizing the chemical stability as well as the donor−acceptor properties of a system.60,61 As the interaction between the two moieties is essentially a cation−π in nature, it is expected that the cation interacts with the HOMO of the Dby molecule resulting in a drop in the HOMO energy (more negative), Figure 6a. Drop in HOMO energies in case of cation−π complexes with monovalent cations is minimal as compared to the complexes with divalent cations. Interestingly, in case of the sandwiches, drop in HOMO energy is slightly less than in case of cation−π complexes. This is obvious, as in case of sandwiches, the cation interacts with two π orbitals, one in BB bond and the other in the aromatic ring. A lower HOMO (more negative HOMO energy) imparts stability to the system. Moreover, a negative interaction energy also points toward the stability of the complex. Therefore, to check the consistency of stability trend obtained from both the parameters, plot of interaction energy and HOMO energy are obtained, Figures 6b,c. It is interesting to see that in all the cases (cation−π complexes and sandwiches) excellent linear relationships are observed with R2 > 0.90. Results thus advocate for the excellence of HOMO energy to predict the stability of a 3295
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The Journal of Physical Chemistry A complex. In contrast, no such relationship could be drawn between the global hardness (obtained using Koopmans’ approximation) and interaction energy; values are shown in Supporting Information Table S2. Maximum hardness principle (MHP) was proposed long ago, and despite controversies,62,63 it has been applied in number of cases.64−77 Also there are reported cases where this principle failed to prove its validity.78−84 Applicability of global hardness and also its efficacy as a measure of stability of complexes has been highlighted in recent literature also.58,75−77,85−91 According to MHP, a harder species is more stable. However, in this study global hardness obtained using Koopmans’ approximation fails to predict the stability pattern of the complexes. To examine the consistency of global hardness obtained using ΔSCF method in explaning the stability of the complexes, similar plot of global hardness versus gas-phase interaction energies is obtained. Importantly, it gives excellent agreement (R2 = 0.9436); plot is shown in Figure 6d. The results thus prove the reliability ΔSCF method over the use of Koopmans’ approximation in predicting the stability of complexes (in terms of global hardness). In Figure 6d only the cation−π complexes of monovalent ions are considered, as many of the N − 1 or N + 1 systems could not be optimized.
ACKNOWLEDGMENTS
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REFERENCES
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b01326. Optimized structures of the chosen complexes obtained using B3LYP/6311++G(d,p) level of theory, BSSE corrections obtained at different level of theories, interaction energy and global hardness (using Koopmans’ theorem) obtained at B3LYP/6-311++G(d,p) level of theory (PDF)
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Authors thank Department of Science and Technology (DST), India, for the financial grant (No. SB/S1/PC-17/2014).
4. CONCLUSION In summary, the present theoretical study predicts the feasibility of formation of cation−π complexes as well as sandwiches between BB triple bond and benzene moiety via monovalent, divalent, and trivalent cations. The gas-phase interaction energies are measured to be quite high for all the complexes, and solvents impart significant impact on the interaction energies. In most of the cases the interaction energies are negative and remain so even in water. Interaction energies with smaller cations are significantly higher compared to the larger cations. The order of interaction energies in the cation−π complexes and sandwiches is monovalent > divalent > trivalent. Analysis of the IR spectra supports the weakening of the BB bond upon cation−π interaction. Because of the interaction between the BB bond and the cations, the maxima in the absorption spectra of the complexes are shifted. Information gleaned from thermochemical study supports the existence of thermodynamic driving force for complexation.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Pradip K. Bhattacharyya: 0000-0002-5935-508X Notes
The author declares no competing financial interest. 3296
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