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Binding of Alkali Metal Ions With 1,3,5- Tri(phenyl)benzene and 1,3,5-Tri(naphthyl)benzene: The Effect of Phenyl and Naphthyl Rings Substitution on Cation–# Interactions Revealed by DFT Study Ali Mirchi, Natalia Sizochenko, Tandabany Dinadayalane, and Jerzy Leszczynski J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b08725 • Publication Date (Web): 25 Oct 2017 Downloaded from http://pubs.acs.org on October 28, 2017

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The Journal of Physical Chemistry

Binding of Alkali Metal Ions with 1,3,5Tri(phenyl)benzene and 1,3,5-Tri(naphthyl)benzene: The Effect of Phenyl and Naphthyl Rings Substitution on Cation–π Interactions Revealed by DFT Study Ali Mirchi1, Natalia Sizochenko1, Tandabany Dinadayalane*2, Jerzy Leszczynski*1

1

Interdisciplinary Center for Nanotoxicity, Department of Chemistry and Biochemistry, Jackson State

University, 1400 J. R. Lynch Street, Jackson, Mississippi 39217 2

Department of Chemistry, Clark Atlanta University, 223 James P. Brawley Drive, S.W., Atlanta,

Georgia 30314

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Abstract: The effect of substitution of phenyl and naphthyl rings to benzene was examined to elucidate the cation-π interactions involving alkali metal ions with 1,3,5-tri(phenyl)benzene (TPB) and 1,3,5tri(naphthyl)benzene (TNB). Benzene, TPB and four TNB isomers (with ααα, ααβ, αββ, βββ type of fusion) and their complexes with Li+, Na+, K+, Rb+ and Cs+ were optimized using DFT approach with B3LYP and M06-2X functionals in conjunction with def2-QZVP basis set. Higher relative stability of βββ-TNB over ααα-TNB can be attributed to peri repulsion, which is defined as the non-bonding repulsive interaction between substituents in the 1- and the 8-positions on the naphthalene core. Binding energies, distances between ring centroid and the metal ions and the distance to metal ions from the center of other six-membered rings were compared for all complexes. Our computational study reveals that the binding affinity of alkali metal cations increases significantly with the 1,3,5-trisubstituion of phenyl and naphthyl rings to benzene. The detailed computational analyses of geometries, partial charges, binding energies and ligand organization energies reveal the possibility of favorable C−H…M+ interactions when α-naphthyl group exists in complexes of TNB structures. Like benzene-alkali metal ion complexes, the binding affinity of metal ions follows the order: Li+ > Na+ > K+ > Rb+ > Cs+ for any considered 1,3,5-tri-substituted benzene systems. In case of TNB, we found that the strength of interactions increases as the fusion point change from α to β position of naphthalene.


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Introduction: Cation-π interaction is now well recognized by chemical and biological sciences community as an important contributor of non-bonding interactions in macromolecular structures, drug-receptor interactions, protein-protein interactions and neurobiology.1-5 It plays an important role in catalysis,6,7 protein structure determination8-11 and molecular recognition processes within ion channels and enzymes.12-18 In-depth knowledge on the сation-π interactions will certainly also benefit environmental science and mineral surface chemistry.19 Cation-π interactions mainly include electrostatic, inductive and charge transfer effects.20 The existence of cation-π interactions in both inter- and intra-molecular processes of proteins was clearly demonstrated by experimental results published in 2001.21 It was an outstanding breakthrough in experimental chemistry, which stimulated computational studies of such phenomena.22 Earlier studies have shown that not only the unique structure of the π-system, but also the nature of the cation affects the strength of cation-π interactions.23-29 Remarkable progress has been achieved on the understanding of C−H…π, N−H…π and O−H…π interactions through investigations of these interactions using benzene and substituted benzene systems.30-36 Among various cations, alkali and alkaline metal ions are widely used to design ionophores for capturing the cationic species.37-39 Cation-π interactions were known to be influenced by the substitutions to π-systems. Scientists focused to understand the origin of stabilization of cation-π complexes.40-46 Multiple weak cation-π interactions inside cage or cup-shaped host ligands increase the strength of the overall interaction.47,48 Ring annelated benzene systems have been studied both experimentally and computationally.47-59 We investigated the cation-π interactions with tri-substituted and ring-annelated benzene systems.47,26-29 Earlier computational studies reported that modification of benzene by annelation of mono- or bi-cyclic (or mixture of these two kinds of rings) significantly strengthens the binding affinity of both alkali and alkaline earth metal cations. Moreover, the strained 3 ACS Paragon Plus Environment


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bicyclo[2.1.1]hexene ring annelation was reported to have substantially larger effect on the strength of cation-π interactions than the monocyclic ring fusion due to the π-electron localization at the central six-membered ring.27,28 The binding energy data at the B3LYP/6-311+G(2d,2p) level revealed that triannelation of bicyclo[2.1.1]hexene to benzene yields a strong binding between benzene and alkali metal cations.26

Scheme 1. Structures of benzene and tri-substituted benzene systems

Structures of π-aromatic systems considered in our study are presented in Scheme 1. All of the π-aromatic systems considered in this computational investigation have already been synthesized.60-65 4 ACS Paragon Plus Environment

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Experimental approaches have been reported recently for obtaining the 1,3,5-triphenylbenzene and its thermodynamic properties were also studied experimentally.61-65 Sirilaksanapong and co-workers reported that 1,3,5-triphenylbenzene has application as Cu2+ sensor in aqueous media.66 TPB corresponds to 1,3,5-triphenylbenzene and TNB corresponds to 1,3,5-tri-(naphthyl)benzene. Depending on the position (α or β) in which the substitution occurs, four structures could be generated for TNB namely, ααα−, ααβ−, αββ−, βββ−ΤΝΒ. In this paper, total of six π-systems including benzene were considered to understand the effect of ring fusion on the cation-π interactions involving alkali metal ions (Li+, Na+, K+, Rb+ and Cs+). Computational Details: All π-systems (1–6) and their complexes with Li+, Na+, K+, Rb+ and Cs+ cations were fully optimized using hybrid density functional theory (DFT) approach employing B3LYP functional67,68 and hybrid meta exchange-correlation functional M06-2X69 developed by Truhlar's group with def2QZVP basis set. Quantum chemical calculations at B3LYP/def2-QZVP and M06-2X/def2-QZVP levels are computationally expensive because of the large quadruple-ζ basis set. In all complexes, the metal ion was placed above the central benzene ring. When the substituted π-system is highly symmetric, the cation resides directly above the center of the ring; otherwise, the cation is slightly displaced from the center.70 We calculated the binding energies using the following equation: ∆E = −[E(complex) − E(π-system) − E(cation)]

……(1)

The binding energies calculated for all complexes were corrected for basis set superposition error (BSSE). The calculations for BSSE were carried out using counterpoise technique proposed by Boys and Bernardi.71 All geometry optimizations and BSSE corrections were performed using Gaussian 09 program package.72 Mulliken charges obtained at the B3LYP/def2-QZVP and M062X/def2-QZVP levels were used to determine the amount of electron charge that transferred from the 5 ACS Paragon Plus Environment


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aromatic moieties to the cations. The values of electron charge transfer from π-system to cation were calculated by subtracting the residual charge on the cation in the complex from its initial charge of +1 for alkali metal cations. Molecular electrostatic potential (MEP) surfaces were generated for all trisubstituted benzene systems considered in the study using the electron density obtained at the B3LYP/6-311G(d,p) level on the B3LYP/def2-QZVP optimized geometries. GaussView 5.0 was used for generating the pictures of MEP surfaces.73 Results and Discussion: Based on the molecular electrostatic potential maps shown in Figure 1, electron density on the central six-membered ring of 2 and 6 seems to be comparable to that of benzene (1). It should be mentioned that substitution of three naphthyl functional groups has significant influence on the electron density of benzene ring. Figure 1 shows that the electron density at the central six-membered ring of structures 3-5 is lower than that of benzene (1). Increasing the number of substitution of naphthyl group at β-position increases the electron density at the central six-membered ring (Figure 1). In case of naphthyl substitution, one has to take into account the so called peri repulsion, which is defined as the non-bonding repulsive interaction between substituents in the 1- and the 8-positions on the naphthalene core.74,75 As shown in Scheme 1, four isomers exist for TNB. The relative energies of these four isomers are listed in Table 1. Both B3LYP and M06-2X functionals produce the same trend of their relative stabilities. The structure α,α,α-TNB (3) is the least stable among the four isomers. As the number of β-substitution of naphthyl group increases, the relative energy of the isomer decreases. The structure α,α,α-TNB (3) is about 8 and 5 kcal/mol less stable than β,β,β-TNB (6) at the B3LYP/def2-QZVP and M06-2X/def2-QZVP levels, respectively. The peri repulsion plays a key factor for higher relative energy of α,α,α-TNB (3) compared to β,β,β-TNB (6). Previously, the experimental study has been reported the attractive and repulsive effects in the interactions of different 6 ACS Paragon Plus Environment

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functional groups in peri-disubstituted naphthalene.76 Scheme 2 shows the pictorial representation of the steric hindrance between the central aromatic six-membered ring and the phenyl or naphthyl substitutions. Steric repulsions for triphenyl benzene (Scheme 2a) and trinaphthyl substitution at βposition to benzene (Scheme 2b) are less compared to trinaphthyl substitution at α-position to benzene (Scheme 2c).

Figure 1. Molecular electrostatic potential (MEP) maps obtained at the B3LYP/6311G(d,p)//B3LYP/def2-QZVP level. The red surface corresponds to a negative region of the electrostatic potential (-0.06 au), whereas the blue color corresponds to the region of positive potential (+0.06 au). Table 1. Relative energies (in kcal/mol) of different positional isomers of 1,3,5-tri(naphthyl)benzene (TNB)

∆EB3LYP/def2-QZVP

α,α,α-TNB (3) 8.2

∆EM06-2X/def2-QZVP

5.4

Ligand α,α,β-TNB (4) α,β,β-TNB (5) 5.4 2.8 3.5 7

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1.6

β,β,β-TNB (6) 0.0 0.0


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Scheme 2. Steric hindrance showed between central benzene with phenyl (a) and naphthyl substitutions (b, c). Less repulsion highlighted for (a) and (b) is relative to the structure (c).

At the next step, complexes with ions were constructed and the geometries were fully optimized using two different density functionals. Selected distances between the ligands and ions were measured as shown in Scheme 3. Phenyl, α−naphthyl, and β−naphthyl substituted benzene systems are displayed in Scheme 3a, 3b and 3c, respectively. Distances between the metal ion and the center of central six-membered ring are denoted as R┴. Distances to substituted/fused rings were designated as R in case of system 2. However, distances between the metal ion and the center of farther and nearer rings of naphthyl in complexes 3-6 are denoted as RF and RN, respectively (see Scheme 3b and 3c).

Scheme 3. The model complex pictures showing the distances measured between the metal ion and the center of phenyl (a), α−naphthyl (b) and β−naphthyl (c) positions. For RN and RF, the letters N and F indicate correspondingly the nearer and farther six-membered rings, and the R┴ is the distance of the metal ion from the center of the central six-membered ring. 8 ACS Paragon Plus Environment

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Figure 2. Variation of the distance between the metal ion and the centroid of central six-membered ring (R┴, in Å) of considered ligands calculated at (a) B3LYP/def2-QZVP level and (b) M06-2X/def2QZVP level. The non-bonding distances obtained at both computational levels are listed in Tables 2 and 3. Figure 2 shows the variation of distances between the metal ion and the center of central six-membered ring, R┴ as the metal ion changes for different π-systems. Because of the absence of C3 symmetry, the metal ions are not located exactly above the center of the central six-membered ring in case of 4-M+ and 5-M+. The complexes of 1-M+ possess six-fold axis of symmetry while those of 2-M+, 3-M+, and 6-M+ have C3 symmetry. Thus, the metal ions in these complexes stay above the center of the central six-membered ring. Table 2. Distances (in Å) measured between the metal ion and centers of six-membered rings for cation-π complexes of 1 and 2 at the B3LYP/def2-QZVP and M06-2X/def2-QZVP (in parentheses) levels. System

1

M+ +

Li

Na K

+

+

Rb

+

+

Cs

R┴, Å 1.84 (1.80)

System

2

M+ +

Li

R, Å 4.68 (4.66)

R┴, Å 1.79 (1.76)

2.39 (2.33)

Na

+

4.93 (4.89)

2.34 (2.29)

2.89 (2.79)

+

5.15 (5.05)

2.81 (2.70)

+

5.28 (5.16)

3.05 (2.93)

+

5.39 (5.22)

3.23 (3.10)

K

3.14 (3.01)

Rb

3.34 (3.19)

Cs



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The geometrical trends produced by B3LYP/def2-QZVP (Figure 2a) and M06-2X/def2-QZVP (Figure 2b) levels for the distances of R┴ are very similar. Expectedly, the distance between metal ion and the ring center (R┴) is shown to constantly increase as the size of the alkali metal cations increases for the complexes formed by each ligand (the radii of cations 0.60, 0.95, 1.33, 1.48 and 1.67 (in Å) correspondingly for Li+, Na+, K+, Rb+ and Cs+). Thus, the complexes having the smallest cation, Li+, have the shortest R┴ distances compared to those involving other cations. It is important to note that R┴ distances for Li+ metal binding with ligands 2-6 are always shorter compared to 1-Li+ complex. However, an oscillating trend of the R┴ distances is obtained in case of other alkali metal ions when we go from 1 to 6, irrespective of the computational level employed. For all the ligands 1-6, one can notice a significant change in R┴ distances while moving from Li+ to Na+, then to K+ compared to going from K+ to Rb+, then to Cs+. Interestingly, the complexes of TPB (2-M+) and those of β,β,βTNB (6-M+) exhibit insignificant difference in R┴ distances (within 0.01 Å) for the corresponding metal ions. The data given in Table 2 indicate that R┴ distances for 1-M+ increase in the following order: 1.84 (Li+) < 2.39 (Na+) < 2.89 (K+) < 3.14 (Rb+) < 3.34 (Cs+) Å at the B3LYP/def2-QZVP level. Although the same trend is retained between B3LYP (Figure 2a) and M06-2X (Figure 2b) functionals, the later one predicts shorter distance (0.04 to 0.15 Å) compared to the former functional. Indeed, substitution of three phenyl groups to benzene decreases the R┴ distances at both levels for each of the alkali metal ion. The distance between the metal ion and the center of the substituted phenyl rings ranges from 4.7 to 5.4 Å depending on the size of the metal ion.


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Table 3. Distances (in Å) measured between the metal ion and centers of six-membered rings for cation-π complexes involving 3-6 at the B3LYP/def2-QZVP and M06-2X/def2-QZVP (in parentheses) levels.a System 3

M+ +

RF1(α), Å 4.81 (4.46)

RN1(α), Å 4.76 (4.58)

RF2(α), Å 4.81 (4.46)

RN2(α), Å 4.76 (4.58)

RF3(α), Å 4.81 (4.46)

RN3(α), Å 4.76 (4.58)

R┴, Å 1.79 (1.80)

Li

+

4.62 (4.39)

4.92 (4.78)

4.62 (4.39)

4.92 (4.78)

4.62 (4.39)

4.92 (4.78)

2.41 (2.38)

+

4.88 (4.51)

5.25 (5.01)

4.88 (4.51)

5.25 (5.01)

4.88 (4.51)

5.25 (5.01)

2.89 (2.84)

+

4.97 (4.62)

5.44 (5.15)

4.97 (4.62)

5.44 (5.15)

4.97 (4.62)

5.44 (5.15)

3.16 (3.04)

+

5.10 (4.70)

5.59 (5.28)

5.10 (4.70)

5.59 (5.28)

5.10 (4.70)

5.59 (5.28)

3.36 (3.22)

+

RF1(α), Å 4.75 (4.72)

RN1(α), Å 4.72 (4.69)

RF2(α), Å 4.77 (4.68)

RN2(α), Å 4.74 (4.66)

RF(β) 6.67 (6.95)

RN(β), Å 4.70 (4.64)

R┴, Å 1.79 (1.78)

+

4.54 (4.57)

4.84 (4.81)

4.71 (4.72)

4.97 (4.93)

6.87 (6.79)

5.04 (4.95)

2.39 (2.32)

+

4.73 (4.87)

5.12 (5.23)

4.93 (4.62)

5.32 (4.99)

6.88 (6.83)

5.19 (5.12)

2.86 (2.77)

Na K

Rb Cs

4

Li

Na K

+

5.11 (4.74)

5.55 (5.16)

4.85 (4.93)

5.28 (5.35)

6.87 (6.84)

5.26 (5.21)

3.11 (2.99)

+

5.02 (4.77)

5.45 (5.21)

5.32 (4.90)

5.80 (5.41)

6.75 (6.72)

5.22 (5.20)

3.32 (3.17)

+

RF(α), Å 4.73 (4.71)

RN(α), Å 4.71 (4.68)

RF1(β), Å 6.98 (6.95)

RN1(β), Å 4.67 (4.63)

RF2(β), Å 7.02 (6.98)

RN2(β), Å 4.72 (4.67)

R┴, Å

Rb Cs

5

Li

4.37 (4.43)

4.70 (4.72)

7.15 (7.15)

4.88 (4.87)

7.51 (7.29)

5.18 (4.99)

2.40 (2.33)

+

4.69 (4.60)

5.06 (4.97)

7.21 (7.13)

4.99 (4.92)

7.71 (7.55)

5.44 (5.27)

2.86 (2.76)

+

4.83 (4.68)

5.25 (5.08)

7.18 (7.65)

5.02 (5.40)

7.93 (7.16)

5.69 (4.97)

3.12 (2.96)

+

5.06 (4.85)

5.47 (5.27)

7.15 (7.18)

5.01 (5.02)

8.04 (7.67)

5.82 (5.45)

3.32 (3.13)

+

RF1(β), Å 6.99 (6.95)

RN1(β), Å 4.68 (4.63)

RF2(β), Å 6.99 (6.95)

RN2(β), Å 4.68 (4.63)

RF3(β), Å 6.99 (6.95)

RN3(β), Å 4.68 (4.63)

R┴, Å 1.78 (1.76)

+

7.20 (7.14)

4.91 (4.84)

7.20 (7.14)

4.91 (4.84)

7.20 (7.14)

4.91 (4.84)

2.33 (2.29)

+

7.40 (7.33)

5.13 (5.04)

7.40 (7.33)

5.13 (5.04)

7.40 (7.33)

5.13 (5.04)

2.80 (2.69)

+

7.50 (7.32)

5.24 (5.10)

7.50 (7.32)

5.24 (5.10)

7.50 (7.32)

5.24 (5.10)

3.03 (2.93)

+

7.59 (7.40)

5.36 (5.19)

7.59 (7.40)

5.36 (5.19)

7.59 (7.40)

5.36 (5.19)

3.22 (3.10)

Na K

Rb Cs

6

Li

Na K

Rb Cs a

1.79 (1.77)

+

See Scheme 3 for pictorial representation of distances.

Interestingly, for all metal ions except Li+, the distance between M+ and the center of farther ring (RF) is shorter than that of M+ and the center of nearer ring (RN) where the α-position of naphthyl group is attached to the six-membered rings (see 3-5 systems in Table 3). In contrast to the situation of α-substituted naphthyl rings, the M+…RF distances are significantly longer (1.5 – 2.3 Å longer) than 11 ACS Paragon Plus Environment


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M+…RN for β-substituted naphthyl rings (see 4-6 systems in Table 3) because of the orientation of the substituted rings. The M+…RN and M+…RF distances for 4-M+ and 5-M+ confirm that the metal ion does not lie exactly above the center of the central six-membered ring. We also measured the distances between M+ and the hydrogen atoms closer to the metal ion in the complexes of 3-M+, 4-M+, 5-M+ and 6-M+, and provided the corresponding values in the Supporting Information (Table S1). These values reveal that M+…H(α) distances are notably shorter than M+…H(β) distances. These distances suggest the possible interactions between M+ and the hydrogen atoms of naphthyl groups that are connected via α-position to the central six-membered ring. Earlier computational studies also highlighted the influence of M+…H interactions on different class of cation-π complexes.26-28 The R┴ distances indicate that strong cation-π interactions exist between alkali metal ions and the central six-membered aromatic ring for both TPB and TNB complexes. Occurrence of these interactions has impacts on other bond distances. Therefore, we analyzed bond distances between central benzene and phenyl groups, [C(1,3,5)−C], and naphthyl groups C1−C, C3−C and C5−C for α and β positions attached to central six-membered ring. The pictorial representations of the measured bond distances for complexes are depicted in Scheme 4. The values of selected distances obtained at both levels are listed in Tables 4 and 5 along with the values of partial charges of metal ions and hydrogen atoms closer to the metal ions (δ+M+ and δ±H). Partial charges were obtained based on Mulliken population analysis. Although the absolute values of the charges obtained using population analysis are questionable, we just focus on the trends of their changes for various molecular systems considered here. The symbol δ±H is used because the charges for hydrogen atoms are negative in some cases. From Tables 4 and 5, we found insignificant change in the lengths of C−C bonds, which connect benzene ring to the phenyl or naphthyl functional groups, upon complex formation with metal ions. The bond length between central six-membered ring and naphthyl group decreases by changing 12 ACS Paragon Plus Environment

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α−position to β-position of naphthyl group in TNBs and their complexes. Measured C−C bond lengths are around 1.48 or 1.49 Å.

Scheme 4: Selected C−C bond distances and partial charges of specific hydrogen atoms (δ±H) and M+ in the complexes formed with π-systems of 1-6 (M+ = Li+, Na+, K+, Rb+ and Cs+). 13 ACS Paragon Plus Environment


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Table 4. Bond distances (in Å) and partial charges (in electron unit) obtained at the B3LYP/def2QZVP and M06-2X/def2-QZVP (in parentheses) levels for the complexes with ligands 1 and 2. System

+

δ+M

---

---

M

δ± H

System

0.053 (0.222)

M

1.482 (1.482)

0.774 (0.775)

0.036 (0.190)

+

1.484 (1.483)

0.937 (0.983)

0.040 (0.190)

+

1.484 (1.483)

0.906 (0.971)

0.044 (0.201)

+

1.484 (1.482)

0.886 (0.982)

0.047 (0.189)

Li

+

Na

K

0.903 (0.900)

0.104 (0.273)

+

0.919 (0.923)

0.097 (0.268)

0.917 (0.937)

K

Rb

0.096 (0.271)

0.041 (0.190)

0.053 (0.204)

1.484 (1.483)

0.104 (0.259) 0.102 (0.262)

Cs

1.483 (1.481)

+

0.493 (0.497) 0.769 (0.741)

+

δ± H

δ+M

--0.560 (0.478)

+

2

+

C(1,3,5)− −C

+

Na

Rb

+

---

+

Li

1

+

Cs

Data from Table 5 illustrates that in case of systems 3-6, the hydrogen atoms closest to the metal ions have significantly smaller partial charges using B3LYP than M06-2X functional. In particular, the hydrogen atoms of α-naphthyl groups interacting to metal ions have negative partial charges in case of Li+, Rb+ and Cs+-TNB complexes of 3, 4 and 5 (as found by B3LYP method). Although M06-2X functional predicts lower partial charges for α-naphthyl hydrogens for the abovementioned complexes, the values are not negative like those obtained using B3LYP functional. It is worthwhile to mention that in case of the naphthyl group fused at β position, the partial charges of the hydrogen atoms closest to M+ do not significantly reduce by complex formation for systems 3-6. This strongly supports the argument of M+…H stabilizing interactions when naphthyl group is fused at α position. This is due to the orientation of the α-substituted naphthyl rings and the farthest rings moved δ+ δ+ closer to the metal ion to form homopolar interactions of M … H type, where the H atom comes from

the naphthyl ring. Such homopolar interactions have been reported in earlier studies.77 Density functional theory calculations at both levels reflect the electron charge transfer from π-system to the metal ion in the complexes as evidenced by the decrease in the value of metal ion charge from its original charge of +1.


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Table 5. Bond distances (in Å) and partial charges (in electron unit) obtained at the B3LYP/def2QZVP and M06-2X/def2-QZVP (in parentheses) levels for complexes with ligands 3-6. System

3

System

C1− −C(α1)

C3− −C(α2)

C5− −C(α3)

δ+M

--Li+

1.489 (1.485) 1.486 (1.484)

1.489 (1.485) 1.486 (1.484)

1.489 (1.485) 1.486 (1.484)

Na+ K+

1.488 (1.485) 1.489 (1.486)

1.488 (1.485) 1.489 (1.486)

1.488 (1.485) 1.489 (1.486)

--0.646 (0.455) 0.637 (0.573)

Rb+ Cs+

1.489 (1.487) 1.490 (1.487)

1.489 (1.487) 1.490 (1.487)

1.489 (1.487) 1.490 (1.487)

M+

C1− −C(α1)

C3− −C(α2)

C5− −C(β1)

δ+M

---

1.489 (1.485)

1.489 (1.485)

1.483 (1.481)

+

1.487 (1.483)

1.486 (1.483)

Na+

1.488 (1.485)

1.488 (1.485)

Li

4

System

5

+

6

δ±H (α1)

δ±H (α2)

δ±H (α3)

0.053 (0.230) -0.013 (0.209)

0.053 (0.230) -0.013 (0.209)

0.053 (0.230) -0.013 (0.209)

0.033 (0.251) 0.016 (0.249)

0.033 (0.251) 0.016 (0.249)

0.033 (0.251) 0.016 (0.249)

-0.052 (0.182) -0.070 (0.162)

-0.052 (0.182) -0.070 (0.162)

-0.052 (0.182) -0.070 (0.162)

δ±H (α1)

δ±H (α2)

δ±H (β1)

---

0.052 (0.232)

0.060 (0.237)

0.055 (0.184)

1.480 (1.478)

0.625 (0.462)

-0.016 (0.210)

-0.006 (0.174)

0.044 (0.203)

1.482 (1.481)

0.694 (0.691)

0.001 (0.239)

0.039 (0.236)

0.042 (0.164)

0.858 (0.856) 0.835 (0.852) 0.868 (0.966) +

K

1.489 (1.485)

1.489 (1.486)

1.483 (1.481)

0.887 (0.960)

0.008 (0.215)

0.021 (0.230)

0.039 (0.159)

Rb+

1.489 (1.486)

1.489 (1.486)

1.484 (1.482)

0.857 (0.927)

-0.058 (0.135)

-0.034 (0.159)

0.040 (0.165)

Cs+

1.489 (1.487)

1.489 (1.486)

1.484 (1.482)

0.871 (0.973)

-0.070 (0.148)

-0.044 (0.163)

0.044 (0.146)

M+

C1− −C(α1)

C3− −C(β1)

C5− −C(β2)

δ+M

δ±H (α1)

δ±H (β1)

δ±H (β2)

---

1.489 (1.485)

1.483 (1.481)

1.483 (1.481)

---

0.057 (0.234)

0.058 (0.207)

0.055 (0.217)

Li+

1.487 (1.483)

1.480 (1.479)

1.480 (1.478)

0.599 (0.449)

-0.016 (0.186)

0.047 (0.204)

0.048 (0.212)

+

Na+

1.489 (1.485)

1.482 (1.481)

1.481 (1.480)

0.722 (0.725)

0.007 (0.185)

0.047 (0.220)

0.049 (0.206)

K+

1.489 (1.485)

1.483 (1.481)

1.482 (1.480)

0.914 (0.965)

0.016 (0.177)

0.051 (0.195)

0.053 (0.222)

+

1.489 (1.486)

1.482 (1.480)

1.484 (1.482)

0.882 (0.945)

-0.052 (0.098)

0.051 (0.202)

0.058 (0.230)

Cs+

1.489 (1.486)

1.482 (1.481)

1.484 (1.480)

0.878 (0.972)

-0.060 (0.088)

0.052 (0.196)

0.063 (0.222)

M+

C1− −C(β1)

C3− −C(β2)

C5− −C(β3)

δ+M

δ±H (β1)

δ±H (β2)

δ±H (β3)

---

1.483 (1.481)

1.483 (1.481)

1.483 (1.481)

---

0.055 (0.219)

0.055 (0.219)

0.055 (0.219)

Li+

1.480 (1.479)

1.480 (1.479)

1.480 (1.479)

0.561 (0.466)

0.047 (0.214)

0.047 (0.214)

0.047 (0.214)

Rb

System

+

M+

+

Na+

1.482 (1.481)

1.482 (1.481)

1.482 (1.481)

0.770 (0.772)

0.044 (0.218)

0.044 (0.218)

0.044 (0.218)

K+

1.483 (1.481)

1.483 (1.481)

1.483 (1.481)

0.937 (0.989)

0.008 (0.219)

0.048 (0.219)

0.048 (0.219)

1.483 (1.482) 1.483 (1.481)

1.483 (1.482) 1.483 (1.481)

1.483 (1.482) 1.483 (1.481)

0.901 (0.966) 0.877 (0.978)

0.052 (0.230) 0.055 (0.221)

0.052 (0.230) 0.055 (0.221)

0.052 (0.230) 0.055 (0.221)

+

Rb Cs+

The data in Table 5 also indicates that both levels predict lower positive charge for Li+ and Na+ compared to K+, Rb+ and Cs+ for complexes of all the systems (1-6). The extent of electron charge transfer (qCT, e-) from ligand to metal is calculated by subtracting the partial charge of metal ion in the complex from the actual value of +1. The calculated values for all the complexes were plotted in Figure 3. One can notice a dissimilar trend between B3LYP (Figure 3a) and M06-2X (Figure 3b) for 15 ACS Paragon Plus Environment


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Li+ ion in case of qCT. The extent of electron charge transfer from ligand to metal ion varies by changing the size of the metal ion in the complexes. In general, the large size metal ions namely Cs+, Rb+ and K+ exhibit smaller qCT values than Li+ and Na+ for each π-system. It should be noted that system 3 (α,α,α-TNB) shows considerably higher value of electron transfer from ligand to metal ions (Na+, K+ and Rb+) compared to the prototype benzene system (1). Moreover, the electron density at the central six-membered ring is not as high as in systems 2 and 6 (Figure 1). Thus, the higher values of qCT observed for the above metal ions in case of α,α,α-TNB could be attributed to the electron transfer not only from the central six-membered rings but also from the neighboring substituted naphthyl rings through the hydrogen atoms that are closer to cations. The qCT values gradually decrease while going from 3 to 6 for those metal ions. This represents the impact of changing the α-naphthyl substitution to β-naphthyl substitution. As shown in Figure 1, the presence of comparable electron density at the central six-membered rings of ligands 2 and 6 justifies for having same values of electron transfer for specific alkali metal ions with those two ligands, especially at the B3LYP/def2-QZVP level.

Figure 3: Changes in the values of the extent of electron charge transfer (qCT, e-) from ligand to metal ions based on Mulliken charges for different complexes obtained at the (a) B3LYP/def2-QZVP level and (b) M06-2X/def2-QZVP level. 16 ACS Paragon Plus Environment

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The values of binding energies (∆E), BSSE corrected binding energies (∆EBSSE), the ligand reorganization energies (∆Er) and π-cloud thickness for all of the complexes at the B3LYP/def2-QZVP and M06-2X/def2-QZVP levels are provided in Table 6. The ligand reorganization energy is defined as the energy of the ligand in the complex (means that the metal was removed and the single-point energy calculation was done for the ligand) subtracted from the energy of optimized free ligand. The π-cloud thickness was calculated by subtracting the radii of different cations (0.60, 0.95, 1.33, 1.48 and 1.67 (in Å) correspondingly for Li+, Na+, K+, Rb+ and Cs+) from the R┴ distance and this procedure was reported elsewhere.27,48,78 In general, the BSSE correction is not significant (within 1.3 kcal/mol) at both levels and their values range from 0.0 to 0.3 kcal/mol for majority of the complexes. All our discussions are based on the BSSE corrected binding energies. The binding energies obtained at B3LYP (M06-2X) for the prototype benzene-cation systems (1-Li+, 1-Na+, 1-K+, 1-Rb+ and 1-Cs+) are 38.6 (41.4), 23.8 (26.5), 16.0 (19.8), 13.1 (17.4) and 11.4 (16.3) kcal/mol, respectively. The corresponding experimental values are 38.5±3.2, 22.1±1.4, 17.5±1.0, 16.4±1.0 and 15.4±1.2 kcal/mol.79 The trends obtained at both computational levels are same for the prototype system. Although B3LYP functional yields binding energies that are in good agreement with the experimental results for 1-Li+, 1-Na+ and 1-K+, it underestimates (3-4 kcal/mol) binding for 1-Rb+ and 1-Cs+. Although M06-2X/def2-QZVP level overestimates the binding energies for 1-Li+, 1-Na+ and 1-K+ complexes, it produces the values that are very close to the experimental values for 1-Rb+ and 1-Cs+ complexes. Thus, B3LYP/def2-QZVP level is predicted to be suitable for cation-π interactions involving Li+, Na+ and K+ but M06-2X/def2-QZVP level could be a better choice for the complexes involving Rb+ and Cs+. Overall, both levels in general produce the same trend for various analyses including the binding energies. Therefore, for the consistency, the binding energy values obtained at the M06-2X/def2-QZVP level are considered for discussion unless otherwise stated. 17 ACS Paragon Plus Environment


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Table 6: Binding energies (∆E, in kcal/mol), BSSE corrected binding energies (∆EBSSE, in kcal/mol) and ligand reorganization energies (∆Er, in kcal/mol) along with the values of π-cloud thickness (in Å) obtained at the B3LYP/def2-QZVP and M06-2X/def2-QZVP (in parentheses) levels. +

System

+

K

+

Rb

+

+

Li

Na

Cs

∆E ∆EBSSE a Expt π-cloud thickness

37.8 (40.3) 38.6 (41.4) 38.5 ± 3.2 1.24 (1.20)

22.9 (25.3) 23.8 (26.5) 22.1 ± 1.4 1.44 (1.38)

15.1 (18.5) 16.0 (19.8) 17.5 ± 1.0 1.56 (1.46)

13.2 (17.4) 13.1 (17.4) 16.4 ± 1.0 1.66 (1.53)

11.4 (16.4) 11.4 (16.3) 15.4 ± 1.2 1.67 (1.52)

∆E ∆EBSSE ∆Er π-cloud thickness

47.5 47.4 0.71 1.19

(50.0) (49.9) (0.77) (1.16)

30.2 30.1 0.51 1.39

(33.2) (33.2) (0.56) (1.34)

21.5 21.2 0.37 1.48

(26.0) (25.9) (0.47) (1.37)

17.9 17.8 0.36 1.57

(23.5) (23.5) (0.57) (1.45)

16.0 15.9 0.41 1.56

(22.8) (22.7) (0.58) (1.43)


47.7 47.6 1.14 1.19

(50.0) (49.9) (2.60) (1.20)

31.3 31.1 2.33 1.46

(34.7) (34.6) (4.58) (1.42)

22.0 21.7 1.92 1.56

(27.3) (27.2) (4.67) (1.51)

18.0 18.0 2.15 1.68

(25.4) (25.3) (4.69) (1.56)

15.5 15.4 2.23 1.69

(24.2) (24.1) (5.02) (1.55)


48.3 48.3 1.06 1.19

(51.4) (51.3) (0.79) (1.18)

31.6 31.4 1.70 1.43

(35.0) (34.9) (1.42) (1.37)

22.3 22.0 1.66 1.53

(27.7) (27.6) (1.63) (1.44)

18.3 18.3 1.57 1.63

(25.1) (25.0) (1.67) (1.51)

16.0 16.0 1.40 1.65

(24.1) (24.0) (2.31) (1.50)


49.4 49.4 0.96 1.19

(51.6) (51.6) (0.97) (1.17)

32.3 32.2 1.54 1.45

(35.1) (35.0) (1.61) (1.38)

23.1 22.8 1.14 1.53

(27.8) (27.7) (1.40) (1.43)

19.3 19.2 0.97 1.64

(25.1) (25.1) (1.41) (1.47)

17.1 17.1 0.80 1.65

(24.2) (24.1) (1.36) (1.46)


50.2 50.1 0.85 1.18

(52.1) (52.1) (1.00) (1.16)

32.4 32.3 0.60 1.38

(34.8) (34.8) (0.81) (1.34)

23.3 23.1 0.44 1.47

(27.3) (27.2) (0.63) (1.36)

19.5 19.4 0.42 1.55

(24.8) (24.8) (0.83) (1.45)

17.6 17.5 0.44 1.54

(24.0) (23.9) (0.85) (1.44)

1

2

3

4

5

6

a

Experimental ∆H values taken from Ref. 79.

The variations of binding energies for all the complexes at both levels are depicted in Figure 4 that exhibits very similar trend between B3LYP (Figure 4a) and M06-2X (Figure 4b) for all systems. Expectedly, the strength of binding of the alkali metal cations with each of the ligands follows the 18 ACS Paragon Plus Environment

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classical electrostatic trend: Li+ > Na+ > K+ > Rb+ > Cs+. The binding strengths of later two metal ions are approximately 35-45 % that of Li+ binding affinity with ligands. Distance between the metal ion and ring center (R┴) is shown to constantly increase as the size of the alkali metal cations increases and this trend explains the varying binding strengths of the metal ions with ligands. Although a sharp increase of binding energy is shown from system 1 to 2 for each of the metal ions, the increase of binding strength is not very high while moving from 2 to 6. Our computational study reveals that phenyl- and naphthyl-substitutions to benzene strongly influence the cation-π interactions. The change in binding energy from phenyl- to naphthyl-substitution varies depending on the metal ion that involves in binding. The binding energy for Li+ with 3 is almost same as that of with 2. However, other metal ions show minor increase in binding strength when we move from 2 to 3. Although the complexes of TPB (2-M+) and β,β,β-TNB (6-M+) exhibit almost same values of R┴ distances for corresponding metal ions, the binding strength for later complexes are higher than that of the former systems. By gradual replacement of α−naphthyl by β-naphthyl in TNB (3-6), the total electron density at central six-membered ring increases (Figure 1). This is reflected by the gradual minor increase of binding affinity of metal ion by moving from 3 to 6 using the B3LYP functional (Figure 4a). However, such straightforward increasing trend is not shown by the M06-2X (Figure 4b). As shown in Figure 1, the electron density at the central six-membered ring of structure 3 is lower than that of 6, but the former ligand exhibits slightly lower or comparable binding energies for metal ions (of Na+ to Cs+) than the later. This could be attributed to the geometrical differences of the ligands in the presence of cations that enjoy favorable C−H…M+ interactions. Notable values of ligand reorganization energies obtained for the system 3 could strongly support the considerable geometrical change of ligand 3 in the complexes. The values of ligand reorganization energy indicate that the α-naphthyl groups reorganize 19 ACS Paragon Plus Environment


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more than β-naphthyl groups. Smaller values (below 1 kcal/mol) of reorganization energies obtained for systems 2 and 6 reveal that those ligands are less perturbed by metal ion binding compared to systems 3-5.

Figure 4. The variation of BSSE corrected binding energies (in kcal/mol) for complexes of different alkali metal ions with ligands (1-6) at the (a) B3LYP/def2-QZVP level and (b) M06-2X/def2-QZVP level. Each carbon atom of central six-membered ring donates an electron into the delocalized ring above and below the ring. It is the side-on overlap of π-orbitals that produce the π-clouds. The distance between the plane of six-membered ring and the edge of π-cloud above or below the ring is called the π-cloud thickness. The values of π-cloud thickness indicate the ability of each cation to polarize the six-membered aromatic rings. They were calculated by the side in which the metal ion binds. The πcloud thickness steadily increases by changing the size of the cation from Li+ to Rb+ while it is almost the same for the complexes involving Rb+ and Cs+. For all the π-systems, the values of π-cloud thickness range from 1.0 to 1.7 Å by using the B3LYP functional. As mentioned earlier, tri-phenyl and tri-naphthyl benzene systems were experimentally reported. Cation-π interactions involving alkali metal ions and the influence of substituents on those interactions have been investigated earlier by


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experimentalists.40-43,79 Thus, our computational study is expected to stimulate experimental interests on the cation-π interactions of alkali metal ions with tri-phenyl and tri-naphthyl benzene systems. Conclusions: The results from DFT calculations performed at the B3LYP and M06-2X functionals with def2-QZVP basis set clearly show that the nature of the metal ion as well as the nature of the π-ligand does affect the binding strength of cation-π interactions. In case of geometrical parameters, B3LYP and M06-2X do not show significant variations. However, some differences were noticed between these two functionals in case of partial charges and the binding energies. Our study suggests, based on the comparison of binding energies with available experimental data, that B3LYP/def2-QZVP level is suitable for cation-π interactions involving Li+, Na+ and K+ ions, and M06-2X/def2-QZVP level could be a better choice for the complexes involving Rb+ and Cs+. The relative stability of β,β,β-TNB is higher than α,α,α-TNB (by > 5 kcal/mol). The lower stability of α,α,α-TNB could be attributed to peri repulsion. The binding energies of all cation-π complexes are large indicating a strong favorable interaction. The distance between metal ion and the ring center (R┴) is shown to constantly increase as the size of the alkali metal cations increases. In line with the trend of the R┴ distances, the binding strength of the cation with any given ligand follows the order Li+ > Na+ > K+ > Rb+ > Cs+. We observed slightly high values of electron transfer from ligand to metal ions for Na+, K+ and Rb+ in case of α,α,α-TNB (3). This could be attributed to the electron transfer not only from the central sixmembered rings but also from the neighboring substituted naphthyl rings through the hydrogen atoms that are closest to cations. A sharp increase in magnitude of binding energy is observed from benzene (1) to TPB (2) for each of the metal ion. However, the increase of binding strength is not very high while moving from TPB (2) to TNB structures (3-6). Our computational study concludes that phenyl- and naphthyl21 ACS Paragon Plus Environment


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substitutions to benzene strongly influence the cation-π interactions. Although the complexes of TPB (2-M+) and β,β,β-TNB (6-M+) exhibit almost same values of R┴ distances for corresponding metal ions, the binding strength for later complexes are higher than that of the former systems. The data of reorganization energies of ligands reveal that α,α,α-TNB (3) experiences considerable geometrical change in the formation of cation-π complexes due to favorable C−H…M+ interactions. By gradual replacement of α−naphthyl by β-naphthyl in TNB (3-6), the total electron density of central sixmembered ring increases. The π-cloud thickness increases by changing the size of the cation from Li+ to Rb+ while it is almost the same for the complexes involving Rb+ and Cs+. This computational study is expected to stimulate experimental interests on the cation-π interactions of alkali metal ions with triphenyl and tri-naphthyl benzene systems that were reported experimentally. Supporting Information Available: The scheme showing selected M+...H distances in the complexes involving π-systems of 3-6 and the corresponding values obtained at the B3LYP/def2-QZVP and M062X/def2-QZVP levels listed in the Table. See DOI:

Contact information: *Corresponding authors. Prof. Tandabany Dinadayalane, email: [email protected] Prof. Jerzy Leszczynski, email: [email protected] Notes The authors declare no competing financial interests.


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Acknowledgments: J.L. acknowledges the National Science Foundation (NSF) for funding of the CREST Interdisciplinary Center for Nanotoxicity, Grant # HRD-1547754. He also thanks the Department of Defense (DoD) High Performance Computing Modernization Program (HPCMP) and ONR for providing computational facilities. Mississippi Center for Supercomputing Research (MCSR) is acknowledged for generous computational facilities. T.D. thanks the National Science Foundation (NSF) for funding of HBCU-UP Research Initiation Award (Grant # HRD-1601071). XSEDE is acknowledged for the computational resources. References: (1) (2) (3) (4) (5) (6) (7)

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