Exploring alkali metal cation⋯hydrogen interaction in the formation half sandwich complexes with cycloalkanes: a DFT approach

Bapan Saha; Pradip Kumar Bhattacharyya

doi:10.1515/pac-2022-1111

Article Publicly Available

Exploring alkali metal cation⋯hydrogen interaction in the formation half sandwich complexes with cycloalkanes: a DFT approach

Bapan Saha and Pradip Kumar Bhattacharyya

Published/Copyright: February 15, 2023

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From the journal Pure and Applied Chemistry Volume 95 Issue 3

Abstract

Gas and solvent phase stability of half sandwich complexes between cycloalkanes viz. cyclopropane, cyclobutane, cyclopentane, cyclohexane, bicyclo[2.2.2]octane and adamantane with alkali metal cations (Li⁺, Na⁺ and K⁺) are analysed using density functional theory (DFT). M06-2X/6-31++G(d,p) level is primarily used for the study. The studied half sandwich complexes are stable in gas phase (stabilization energy upto 26.55 kcal mol⁻¹). Presence of solvent phase irrespective of its dielectric, imparts negative impact on the stability of the chosen complexes. The formation of the complexes is exothermic in nature. The process of complexation is both enthalpy (ΔH) and free energy (ΔG) driven. Variation in HOMO (highest occupied molecular orbital) energy also indicates towards the chemical stability of complexes. The interaction is non-covalent with primary contribution from induction component. NBO analysis indicates that C–H bond is the donor and antibonding metal orbital is the acceptor site in the process of complexation. Stability of the complexes depends on the size of the interacting monomers.

Keywords: Alkali metal cation; cycloalkane; DFT; enthalpy; free energy; NBO; solvent dielectric; stabilization energy; VCCA-2022

Introduction

Noncovalent interactions, although generalized as weak, have drawn remarkable interest of scientific community owing to their wide range of applications in areas like material science, medicine, biology and many more [1], [2], [3]. Amongst these, studies based on hydrogen bonding interaction has been very popular [4]. However, presence of interactions such as cation⋯π, anion⋯π, π⋯π stacking, X-H⋯π (X = N, O, F, etc.) interactions, halogen bonding has also been recognized in material design, supramolecular assembly, molecular recognition, catalysis and many more [1, 5], [6], [7]. Generally, non-covalent interactions are non-additive in nature and thereby associated with remarkable cooperative or anticooperative effects [8]. Strength and nature of non-covalent interactions like hydrogen bonding, cation⋯π, π⋯π stacking depends on the size and shapes of interacting units along with solvation [9], [10], [11], [12]. Interaction of metal ions with saturated π-analogue viz. cation⋯alkane interaction proved to be quite significant from the view point of cation passage through lipid bilayer and C–H activation [12], [13], [14], [15]. C–H activation reactions are important in transforming alkanes to more reactive or different unsaturated compounds leading to development of new synthetic strategies. Recently, transition metal ion complexes have been explored in C–H activation reactions such as aromatization of n-alkanes [16]. Studies also validated the crucial role of cation⋯alkane interaction in such transformation (C–H activation) [17]. Although expected to be weak, Hill et al., have suggested a competitive binding of alkane and alkene with metal ions [18]. Computational study has also suggested the presence of hydrogen bonding interaction between hydronium ion and alkane [19]. Even though, cation⋯alkane interaction is recognized few decades back, its physical origin and nature have been elucidated recently by Sastry et al. [20] They have also suggested that such interaction is reasonably strong, comparable to that of cation⋯π interaction.

Non-covalent interactions especially interactions with π-systems are widely used in crystal engineering and designing new materials [1, 21, 22]. For example, metal⋯π, π⋯π and cation⋯π interactions are explored in the formation of sandwich and multidecker complexes [23], [24], [25], [26], [27]. Some of these complexes exhibit useful optoelectronic properties [24, 27]. Multidecker complexes of V with benzene has been reported to possess interesting non-linear optical (NLO) properties [24]. Similarly, molecular and thin film properties of half sandwich complexes of Co for its optoelectronic application has been reported by Robertson et al. [26] Recently, we have also reported the formation of sandwich complexes of alkali metal ions with aromatic inorganic linker pentazolate ( N 5 − ) ion computationally [28].

Sandwich and multidecker complexes have been known to be stabilized by both weak and strong non-covalent interactions, presence stronger interaction like cation⋯π leads to the formation of more stable complexes [11, 23, 29], [30], [31]. Since, cation⋯alkane interaction is reasonably strong and in some cases is even comparable to cation⋯π interaction, such interaction might be suitably explored in the formation of sandwich and multidecker complexes. This prompted us to explore cation⋯alkane interaction more precisely cation⋯hydrogen interaction (since the interaction is expected to be between the metal ion and hydrogen atom of alkane) between alkali metal ion, M⁺ (M = Li, Na and K) and cycloalkanes (shown in Scheme 1). Other than fluorocyclohexane, no prior attempt has been made to explore cation⋯alkane interaction from the view point of sandwich and multidecker complexes [31]. Amongst cycloalkane, interaction between metal ion and cyclohexane (only) along with other linear alkanes (C_nH_2n + 2) are reported by Sastry et al. [20] In the present study, density functional (DFT) study has been performed in the formation of half sandwich complexes between alkali metal ions M⁺ (M = Li, Na and K) and cycloalkanes viz. cyclopropane (CPro), cyclobutane (CBut), cyclopentane (CPent), cyclohexane (CHex), bicyclo[2.2.2]octane (CBicy) and adamantane (Ada). Moreover, feasibility of complexation and solvent phase stability of the complexes have also been scrutinized.

Scheme 1:

Chosen cycloalkanes.

Theoretical and computational details

The use of quantum chemical methods has become quite common in studying different aspects of non-covalent interactions [23, 29], [30], [31], [32], [33]. For weaker non-covalent interactions, second order Moller-Plesset (MP2) and coupled cluster theory with perturbative triples (CCSD(T)) methods have been known to yield satisfactory results while for stronger counterparts, DFT methods are preferably used [34], [35], [36]. Compared to MP2 and CCSD(T), DFT methods are computationally less expensive and known to produce reasonably accurate results especially in case of stronger interactions [37, 38]. Since earlier literatures have suggested that the chosen interaction is reasonably strong, DFT method is exclusively used for the study. Sastry et al. have also suggested that for interaction between metal ion and alkane, MP2 method and DFT method produce comparable results [20]. The geometries are optimized at M06-2X/6-31++G(d,p) level and hessian calculation is performed to ensure the real geometrical minima. To validate the consistency of the obtained results, single point calculations are performed at ωB97-XD/6-31++G(d,p), B3LYP/6-31++G(d,p), M06-2X/6-31+G(d,p) and M06-2X/6-311++G(d,p) levels. Similar protocol has also been adopted in several recent literatures [39, 40].

Stability of the complexes are estimated in terms of stabilization energy (SE) calculated adopting supermolecular approach. SE is defined as magnitude of difference between the energy of complex and sum of energies of the interacting units. Higher the SE values (positive) higher is the stability of the complexes. For the process, M⁺ + Cycloalkane → M⁺⋯Cycloalkane, SE = −[E_{M+⋯Cycloalkane} − (E_M+ + E_Cycloalkane)] where, E_{M+⋯Cycloalkane}, E_M+ and E_Cycloalkane are the energies of the complex, metal ion and chosen cycloalkane respectively. Counterpoise correction method (N route, N is number of monomers in the complex) is used to encounter basis set superposition error (BSSE) [41]. Similar approach (supermolecular) is also used in estimating enthalpy change (∆H) and free energy change (∆G) for the process of complexation (magnitude is not considered). Polarizable continuum model (PCM) is used for scrutinizing the solvent phase stability of the complexes [42]. For the process single point calculation is done at M06-2X/6-31++G(d,p) level in cyclohexane, ethanol, DMSO and water. Natural bond orbital (NBO) analysis is performed to predict the donor-acceptor orbitals and estimate second order perturbation energy at M06-2X/6-31++G(d,p) level [43]. For topological analysis, quantum theory of atoms in molecules (QTAIM) is used using Multiwfn programme code [44, 45]. All these quantum chemical calculations are accomplished using Gaussian09 programme [46].

Results and discussions

In this manuscript, the half sandwich between M⁺ (M = Li, Na and K) and cycloalkanes are represented as M⁺-CPro, M⁺-CBut, M⁺-CPent, M⁺-CHex, M⁺-Bicy and M⁺-Ada for complexes with cyclopropane, cyclobutane, cyclopentane, cyclohexane, bicyclo[2.2.2]octane and adamantane respectively.

Geometry of the complexes

The conformational analysis was performed considering all the three possible modes of interaction of Li⁺ ion (η¹-Li⁺-CPro, η²-Li⁺-CPro and η³-Li⁺-CPro), minimum to maximum number of C–H bond interactions using cyclopropane as representative case. The geometry of η¹-Li⁺-CPro and η²-Li⁺-CPro complexes could not be optimized to real minima. Sastry et al. have also echoed similarly and suggested that η¹ and η² mode of interaction of Li⁺ ion with methane to get collapsed into η³ mode [20]. Therefore, interaction of M⁺ ion with maximum number of C–H bond is considered in this study. The optimized geometries of complexes of Li⁺ ion with the chosen alkanes is shown in Fig. 1a–f (as representative cases) and all the obtained M⁺⋯H distances are shown in Table 1. The optimized geometries suggested that Li⁺ ion can coordinate either by η³-mode or by η⁴-mode with the chosen alkanes, Fig. 1a–f. η³ mode of coordination is observed with CPro, CBut, CHex, and Ada while η⁴-mode of coordination is observed with CPent and Bicy, Fig. 1a–f. Similar modes of coordination are also observed for the complexes of Na⁺ and K⁺ ion with respective alkane systems. Moreover, the Li⁺ ion is almost situated over the centroid of the interacting hydrogen atom for CPro, CHex, Bicy and Ada, Fig. 1a, d–f. On the other hand, Li⁺ ion is significantly tilted towards the interacting hydrogen atoms in case of CBut and CPent, Fig. 1a, b. This is due to the unsymmetrical shape of the involved alkane moiety for which one of the hydrogen atoms (Li⁺⋯H distances >3.49 Å) is reluctant to interact with the Li⁺ ion. Like these, complexes of Na⁺ and K⁺ ions also possess similar variation in shape with respect to the nature of the interacting alkane moiety.

Fig. 1:

Geometry of (a) η³-Li⁺-CPro, (b) η³-Li⁺-CBut, (c) η⁴-Li⁺-CPent, (d) η³-Li⁺-CHex, (e) η⁴-Li⁺-Bicy, (f) η³-Li⁺-Ada, (g) (Li⁺-(CPro)₂, (h) Li⁺-(CBut)₂, (i) Li⁺-(CPent₂, (j) Li⁺-(CHex)₂ and (k) Li⁺-(Bicy)₂ complexes obtained at M06-2X/6-31++G(d,p) level.

Table 1:

M⁺⋯H distances (Å) in the complexes obtained at M06-2X/6-31++G(d,p) level.

Complexes	M⁺⋯H distances	Complexes	M⁺⋯H distances
Li⁺-CPro	1.99–2.00	Li⁺-CHex	1.88–1.89
Na⁺-CPro	2.31–2.36	Na⁺-CHex	2.22–2.23
K⁺-CPro	2.70–2.73	K⁺-CHex	2.70–2.71
Li⁺-CBut	1.90–1.99	Li⁺-Bicy	1.97–1.98
Na⁺-CBut	2.24–2.32	Na⁺-Bicy	2.25–2.26
K⁺-CBut	2.60–2.74	K⁺-Bicy	2.63–2.64
Li⁺-CPent	2.06–2.09	Li⁺-Ada	1.83–1.85
Na⁺-CPent	2.35–2.37	Na⁺-Ada	2.20–2.21
K⁺-CPent	2.71–2.73	K⁺-Ada	2.66–2.67

The observed M⁺⋯H distances for Li⁺ complexes are within the range 1.83–2.09 Å, Table 1. The said distance is minimum for η³-Li⁺-Ada complex (1.83–1.85 Å) while the maximum Li⁺⋯H distance is observed in η⁴-Li⁺-CPent complex (2.06–2.09 Å). Other than η⁴-Li⁺-CPent and η⁴-Li⁺-CBicy (1.97–1.98 Å) complexes, Li⁺⋯H distance decreased with the increase in size of the chosen alkanes i.e., the distance decreased in the order Li⁺-CPro (1.99–2.00 Å) > Li⁺-CBut (1.90–1.99 Å) > Li⁺-CHex (1.88–1.89 Å) > Li⁺-Ada (1.83–1.85 Å). Thus, stronger interaction is expected for the complexes with larger alkanes. For the complexes of Na⁺ and K⁺ ion, the M⁺⋯H distances are within the range 2.20–2.37 Å and 2.60–2.73 Å respectively. As expected, the observed M⁺⋯H distances increased parallely with the size of the involved metal cations. Recent literature on cation-alkane interaction also reported similar variation in M⁺⋯H distances with the size of involved metal ions [20]. Like the Li⁺ ion complexes, the M⁺⋯H distances also decreased with the increase in size of the chosen alkanes and follows similar trends for complexes of Na⁺ and K⁺ ions, Table 1. It is to be mentioned that all the Li⁺⋯H distances in a particular complex are not equal. For most of the complexes, the variation in said distance is nominal (<0.05 Å). However, notable variation in Li⁺⋯H distance is observed in case of Li⁺-CBut complex (upto 0.1 Å). Thus, it can be concluded that all the individual Li⁺⋯H interaction would contribute unequally to the stability of the complex. Similar variations are also observed in complexes of Na⁺ and K⁺ ions, Table 1. Bhattacharyya et al. have studied the complexation of Na⁺ ion with trifluoro- and hexafluoro-cyclohexane and suggested the dependence of M⁺⋯F distances on the individual bond and/or dipole moments [31]. Moreover, the C–C bond lengths of chosen alkanes are unresponsive to any change while a nominal change is observed in C–H (<0.06 Å) bond length upon complexation. This suggests the presence of M⁺⋯H interaction in the process of complexation. Besides, the consistency in C–C and C–H bond lengths upon complexation also reveals the non-covalent nature of interaction between M⁺ ions and alkanes.

Besides, possibility of sandwich formation is also scrutinized by considering the complexation of Li⁺ ion as representative case and the optimized geometries are shown in Fig. 1g–k. Sandwich formation by Li⁺ ion via η³-mode of interaction is possible with CPro (Li⁺-(CPro)₂), CBut (Li⁺-(CBut)₂) and CHex (Li⁺-(CHex)₂), Fig. 1g, h, j. The corresponding Li⁺⋯H distances are found to be 1.97–1.98 Å, 1.92–1.99 Å and 1.91–1.92 Å respectively. The (Li⁺-(CPro)₂) and (Li⁺-(CBut)₂) complexes are saddle point structures with imaginary frequencies of 47i and 16i respectively while the complex (Li⁺-(CHex)₂) is a real geometrical minimum. The sandwich complex of adamanatane, (Li⁺-(ada)₂) could not be optimized. Also, sandwich complexes of CPent (Li⁺-(CPent)₂) and Bicy (Li⁺-(Bicy)₂) via η⁴-mode of interaction are observed with real geometrical minima, Fig. 1i, k. The respective Li⁺⋯H distances are found to be 2.11–2.13 Å and 2.03–2.04 Å. In sandwich complexes, the two alkane moieties are almost staggard to each other, Fig. 1g–k. Like half sandwiches, the (Li⁺-(CBut)₂) and (Li⁺-(CPent)₂) sandwich complexes are significantly tilted with respect to Li⁺ ion, Fig. 1h, i. The Li⁺⋯H distances in for Li⁺-(CPent)₂, (Li⁺-(CHex)₂ and Li⁺-(Bicy)₂ complexes are a bit longer than that of half sandwich complexes and is due to the dissipation of charge of Li⁺ ion with two cycloalkane units simultaneously. The Na⁺-(CPent)₂, K⁺-(CPent)₂ complexes are found to exhibit saddle point geometries with imaginary frequencies of 26i and 29i respectively. Real geometrical minimum is obtained for Na⁺-(Bicy)₂ complex (M⁺⋯H distances is within 2.24–2.26 Å) while K⁺-(Bicy)₂ complex could not be optimized. Moreover, real minima for Na⁺-(CHex)₂ and K⁺-(CHex)₂ complexes are obtained with M⁺⋯H distances in the range 2.25–2.30 Å and 2.71–2.78 Å respectively. As expected, the said distances are also longer than the corresponding distances for half sandwich complexes.

Stabilization energy (SE) and change in enthalpy (ΔH) and free energy (ΔG) of complexation

SE is of paramount importance in interpreting the extent of interaction and therefore a focused look into the SEs is essential in predicting the stability of the complexes. The estimated BSSE corrected SE values obtained at M06-2X/6-31++G(d,p) level in gas phase are presented in Table 2. Higher the SE values higher is the extent of interaction and hence higher is the stability of the complexes. The chosen half sandwich complexes are found to be weak to moderately strong in gas phase with SE values within the range 3.03–26.55 kcal mol⁻¹, Table 2. As expected, the SE values for these half sandwich complexes with a particular alkane decreased with increase in size of the metal cation, Table 2. For example, SE values for Li⁺-CPro, Na⁺-CPro and K⁺-CPro complexes are 12.63, 6.28 and 3.03 kcal mol⁻¹ respectively. The observed trend can be attributed to the size or ionic radii of the involved alkali metal ions. Similar trends in SE values are also reported in number of occasions for the interaction of metal ions with alkanes, alkenes and arenes [11, 12, 21, 31, 32]. The estimated SE values are comparable with the SE values reported for cation-alkane interaction [20]. For example, the SE value obtained for Na⁺-CPro complex at M06-2x/6–31++G(d,p) level is 6.28 kcal mol⁻¹ while the reported SE values for Na⁺-Methane via η³-mode is 5.95 kcal mol⁻¹ at MP2/cc-pVTZ level of theory [20]. Although earlier reports have suggested comparable strength of cation-alkane and cation-π interaction, the obtained results are contradiction to this. For example, the estimated SE values for Li⁺-CHex, Na⁺-CHex and K⁺-CHex complexes are 21.47, 12.19 and 6.62 kcal mol⁻¹ respectively. In contrast to this, the reported SE values at B3LYP/6-31+G(d) level for Li⁺-Ben, Na⁺-Ben and K⁺-Ben complexes are 36.84, 23.78 and 15.14 kcal mol⁻¹ respectively [11]. Sastry et al. have performed DFT-SAPT analysis for Li⁺-CHex and Na⁺-CHex complexes and reported their respective SE values of 24.97 and 11.28 kcal mol⁻¹, which is also comparable with the obtained results [20]. Thus, it can be concluded that cation-hydrogen interaction of cycloalkane is weaker than cation- π interaction for hydrocarbons with identical number of C-atoms. This is possibly due to the distribution of lower charge density (compared to corresponding π-systems) around the interacting hydrogen atoms of cycloalkanes. Significant role of charge density in stabilizing the complex is also well indicated in earlier literatures [11, 28]. Moreover, SE values obtained for complexes with CPent and Bicy are relatively higher than the others, Table 2. For example, SE values for Li⁺-CPent and Li⁺-Bicy are 22.39 and 26.55 kcal mol⁻¹ respectively. On the other hand, the SE values for Li⁺-CHex and Li⁺-Ada complexes are 21.47 and 23.26 kcal mol⁻¹ respectively. This is due to presence of η⁴-mode of coordination with the metal ion. Although earlier literature has suggested that stability of the complexes depends on the number of C-atoms, the results obtained herein also indicate the crucial role of mode of co-ordination with the metal ion. Again, for rest of the complexes i.e., for complexes formed via η³-mode of coordination, SE values increased with increase in size or number of C-atoms in the chosen alkanes. For example, SE values for the complexes with Li⁺ ion are in the order; Li⁺-CPro (12.63) < Li⁺-CBut (18.86) < Li⁺-CHex (21.47) < Li⁺-Ada (23.26), values are in kcal mol⁻¹. The observed trends for are similar for the complexes of Na⁺ and K⁺ ion. To validate the role of size of the alkanes or number of C-atom, the SE values for the complexes formed via η³-mode of coordination are plotted against the number of C-atoms and the results indicate moderate linear relationship between the SE values and number of C-atoms for Li⁺ (R² = 0.70), Na⁺ (R² = 0.71) and K⁺ (R² = 0.72) complexes. The stability of the studied complexes not only depends on mode of coordination but also on the nature of the cycloalkane involved. Thus, larger the cycloalkane higher is the stability and hence lower is the corresponding cation mobility in cycloalkane.

Table 2:

SE, ΔH and ΔG values (kcal mol⁻¹) values for the complexes in gas phase and SE values in solvent phase (kcal mol⁻¹) obtained at M06-2X/6-31++G(d,p) level.

Complexes	SE_Gas	ΔH	ΔG	SE_Cyclohexane	SE_Ethanol	SE_DMSO	SE_Water
Li⁺-CPro	12.63	−12.52	−5.44	−6.64	−17.81	−18.04	−18.29
Na⁺-CPro	6.28	−6.41	−0.44	−4.24	−9.28	−9.33	−9.41
K⁺-CPro	3.03	−2.93	2.81	−2.18	−4.43	−4.45	−4.49
Li⁺-CBut	18.86	−18.72	−12.03	−2.89	−15.84	−16.12	−16.41
Na⁺-CBut	10.59	−10.95	−4.72	−1.89	−8.47	−8.59	−8.84
K⁺-CBut	5.78	−5.86	−0.34	−0.62	−3.63	−3.67	−3.75
Li⁺-CPent	22.39	−22.26	−14.39	−2.25	−18.35	−18.79	−19.19
Na⁺-CPent	13.43	−13.56	−5.84	−1.48	−9.73	−9.87	−10.01
K⁺-CPent	7.86	−7.87	−1.08	0.02	−3.92	−3.97	−4.08
Li⁺-CHex	21.47	−20.89	−13.66	−6.26	−24.65	−25.12	−25.54
Na⁺-CHex	12.19	−12.43	−5.52	−2.45	−10.31	−10.44	−10.61
K⁺-CHex	6.62	−6.64	−0.76	−0.77	−4.15	−4.17	−4.26
Li⁺-Bicy	26.55	−25.42	−18.44	−2.53	−22.02	−22.56	−23.03
Na⁺-Bicy	15.17	−14.80	−8.11	−1.40	−11.41	−11.65	−12.01
K⁺-Bicy	8.57	−7.81	−1.41	−0.52	−5.20	−5.27	−5.43
Li⁺-Ada	23.26	−22.77	−15.32	−6.30	−25.97	−26.50	−26.97
Na⁺-Ada	13.35	−13.81	−6.74	−2.34	−10.43	−10.55	−10.81
K⁺-Ada	7.58	−7.72	−1.48	−0.57	−4.32	−4.35	−4.50

SE values for the sandwich complexes with real geometrical minima are calculated. The obtained SE values for Li⁺-(CPent)₂, Li⁺-(CHex)₂, Na⁺-(CHex)₂, K⁺-(CHex)₂, Li⁺-(Bicy)₂, and Na⁺-(Bicy)₂ sandwich complexes are found to be 41.83, 38.74, 23.19, 12.46, 45.71 and 28.32 kcal mol⁻¹ respectively. The calculated SE values suggests that these complexes are also stable in gas phase. There also exists an inverse relationship between the SE values and size of the M⁺ ion. The SE values for the sandwich complexes are non-additive in nature. For example, the SE value for Li⁺-(CPent)₂ is 41.83 kcal mol⁻¹ and that for Li⁺-CPent is 22.39 kcal mol⁻¹, which is more than half of the SE value for corresponding sandwich complex. Moreover, obtained SE values are significantly high and therefore it can be concluded that sandwich complexes are possible for the aforesaid complexes and multidecker complexes might also be stable especially with cyclohexane (the geometry of these complexes are not tilted, three H-atoms are free to interact with one more M⁺ ions and therefore further interactions are likely to occur).

The ΔH values play decisive role in predicting stability of complexes [23, 28, 31]. Moreover, to predict the thermodynamic driving forces, estimation of ΔH and ΔG values is imperative. Thus, these parameters are estimated in gas phase and the results are presented in Table 2. The ΔH (−2.93 to −25.42 kcal mol⁻¹) and ΔG (−0.34 to −18.44 kcal mol⁻¹) values are found to be both negative. Thus, the process of complexation is exothermic and spontaneous in nature. Both these parameters possess similar trends i.e., ΔH and ΔG values follows the order Li⁺-complexes > Na⁺-complexes > K⁺-complexes (in terms of magnitude), Table 2. More negative ΔH values reveal higher is the exothermic nature and more negative ΔG values correspond to higher feasibility of the process. Therefore, complexes formed by Li⁺ ion is more favourable (thermodynamically more stable) than that of Na⁺ ion which in turn more favourable than complexes of K⁺ ion. SE values also predicted similar trends in the stability of the complexes. Besides, the process of complexation is enthalpy driven. However, positive ΔG value (2.81 kcal mol⁻¹) for K⁺-CPro complex questions the thermodynamic feasibility of its formation.

In addition to gas phase, solvent phase stability of the complexes is scrutinized with cyclohexane, ethane, dimethyl sulfoxide (DMSO) and water as solvent dielectric. For the purpose, SE values are calculated by single point calculation in solvent with varying dielectric using PCM model and the obtained results are presented in Table 2. It is seen that SE values for the complexes are all negative, irrespective of solvent dielectric, Table 2. Thus, the complexes are unstable in solvent phase. With increase in solvent dielectrics, the SE values are found to be more negative (Table 2) and thereby questions on the existence of these complexes in solvent phase. Negative SE values of M⁺ complexes with aromatic pentazolate ion in solvent phase are also reported in literature [28].

To validate the suitability of adopted DFT method, SE values are further estimated at ωB97X-D/6-31++G(d,p) and B3LYP/6-31++G(d,p) levels and the results are compared and plotted, shown in Fig. 2a. The SE values obtained at ωB97X-D functional is comparable with the results obtained from M06-2X functional, the results differ upto 0.53 kcal mol⁻¹ (SE values are lower as well as higher), Fig. 2a. However, the SE values obtained from B3LYP functional differ from that obtained from M06-2X functional. The SE values obtained with B3LYP functional is lower, upto 2.74 kcal mol⁻¹, Fig. 2a. The observed results might be due to contribution from dispersion component (M06-2X and ωB97X-D encounter dispersion contribution to some extent while B3LYP functional fails to do so). Moreover, SE values are also calculated using 6-31+G(d,p) and 6-311++G(d,p) basis set with M06-2X functional and the compared results are shown in Fig. 2b. Referring to Fig. 2b, it is obvious that addition of extra diffused basis set imparts nominal impact in SE values, varies upto 0.35 kcal mol⁻¹ (except very few). Close resemblance of the SE values obtained with ωB97X-D and M06-2X functional and with different basis sets suggest the suitability of the M06-2X/6-31++G(d,p) level for the study.

Fig. 2:

Variation of SE values obtained with (a) different functionals and (b) different basis sets in gas phase.

HOMO-LUMO perspective

HOMO-LUMO shapes of a system is imperative from the view point of predicting the donor and acceptor site between two interacting moieties. Therefore, shapes of HOMOs and LUMOs of M⁺ complexes with Ada are studied (as representative case) and are presented in Fig. 3. Referring to this, it is seen that HOMOs of all the complexes viz. Li⁺-Ada, Na⁺-Ada and K⁺-Ada are primarily located over the Ada unit (Fig. 3a–c) while LUMOs for the same complexes are predominantly located over the M⁺ ion (Fig. 3d–e). Thus, it can be inferred that in the interaction between M⁺ ion and Ada (cycloalkane) former is the acceptor while the latter is the donor moiety.

Fig. 3:

Shapes of HOMO of (a) Li⁺-Ada, (b) Na⁺-Ada, (c) K⁺-Ada and LUMO of (d) Li⁺-Ada, (e) Na⁺-Ada, (f) K⁺-Ada complexes (as representative case) obtained at M06-2X/6-31++G(d,p) level.

Moreover, the HOMO energy of the system is also important from the perspective of chemical stability along with electron donating ability. Therefore, HOMO energies are calculated for the cycloalkanes and their corresponding complexes, the results are presented in Table 3. The HOMO energies for the cycloalkanes dropped substantially (become more negative) upon complexation, Table 3. Drop in HOMO energy is inversely related to the ionic radii of the involved metal ions. For example, the HOMO energy for CPro is −219.77 kcal mol⁻¹ while in the corresponding complexes with Li⁺, Na⁺ and K⁺ ions are −350.70, −333.06 and −318.83 kcal mol⁻¹ respectively. Larger the drop (more negative) on HOMO energy upon complexation higher is the stability. Thus, complexes with Li⁺ ion is expected to be more stable than that with Na⁺ ion which in turn more stable than that of K⁺ ion. Similar observation was also predicted from the corresponding SE values.

Table 3:

HOMO energy (in kcal mol⁻¹) for cycloalkanes and their corresponding complexes in gas phase obtained at M06-2X/6-31++G(d,p) level.

Complexes	HOMO energy of free cycloalkanes	HOMO energy of complexes	Complexes	HOMO energy of free cycloalkanes	HOMO energy of complexes
Li⁺-CPro	−219.77	−350.70	Li⁺-CHex	−220.00	−333.89
Na⁺-CPro		−333.06	Na⁺-CHex		−317.52
K⁺-CPro		−318.83	K⁺-CHex		−303.93
Li⁺-CBut	−226.00	−348.32	Li⁺-Bicy	−210.09	−315.44
Na⁺-CBut		−333.69	Na⁺-Bicy		−304.20
K⁺-CBut		−320.26	K⁺-Bicy		−293.54
Li⁺-CPent	−232.30	−353.29	Li⁺-Ada	−207.29	−304.49
Na⁺-CPent		−340.59	Na⁺-Ada		−291.51
K⁺-CPent		−327.94	K⁺-Ada		−281.34

To scrutinize the relationship between HOMO energy and SE values i.e., stability of the complexes, the two parameters are plotted against each other and the obtained results are depicted in Fig. 4a–f. There exists strong linear relationship between the said parameters for all the complexes with R² values within the range 0.98–0.99. Thus, the stability of the complexes predicted from HOMO values are exactly like that from SE values. Suitability of HOMO energy in predicting the stability of stronger (cation⋯π) interaction is well established in literature [30]. Since, HOMO energy and SE values are linearly related, it would be wise to expect similar relationship between charge transfer and SE values. This would also indicate whether the interaction is charge controlled or orbital controlled. Generally covalent interaction is orbital controlled and ionic and/or non-covalent interaction is charge controlled. Therefore, charge transfer of the involved M⁺ ion is calculated by NBO analysis and the obtained plots for charge transfer vs. SE values are shown in Fig. 4g–l. As expected, strong linear relationships also exist between charge transfer and SE values with R² values within the range 0.97–0.99. The extent of charge transfer of M⁺ ion is also suitable in predicting the stability of the complexes and thereby indicating the existence of charge-controlled interaction (possibly non-covalent) between the interacting units.

Fig. 4:

HOMO energy vs. SE plot for (a) M⁺-CPro, (b) M⁺-CBut, (c) M⁺-CPent, (d) M⁺-CHex, (e) M⁺-Bicy, (f) M⁺-Ada complexes and charge transfer vs. SE plot for (g) M⁺-CPro, (h) M⁺-CBut, (i) M⁺-CPent, (j) M⁺-CHex, (k) M⁺-Bicy, (l) M⁺-Ada obtained at M06-2X/6-31++G(d,p) level.

Electron topological analysis and nature of interaction

To validate the nature of interaction, electron topological analysis is performed using quantum theory of atoms in molecules (QTAIM) that ascribes the concept of interaction with the help of bond path and bond critical point (BCP) [44]. The topological parameters like electron density at BCP (ρ), laplacian of electron density (∇²ρ) and local electronic energy density (H(r)) provide reliable information form the view point of nature of interaction [47]. Usually for an orbital controlled interaction, ρ is large (>0.2 a.u.) and ∇²ρ values are large negative while for a charge-controlled interaction, ρ is small (<0.1 a.u.) and ∇²ρ values are positive [48]. However, to derive more specific information, H(r) values are calculated according to which for an orbital controlled interaction H(r) < 0 and for charge-controlled interaction H(r) > 0 [49]. Electron localization function (ELF) is another popular topological parameter that reflects the quantitative localization of electron density at critical point. An ELF value > 0.5 is indicative of orbital controlled interaction and ELF < 0.5 corresponds to charge-controlled interaction [50]. Hence, these parameters are studied for the process of complexation with CPro and Ada as representative cases and the obtained results are presented in Table 4. Moreover, Fig. 5 the molecular graph containing bond path obtained from the QTAIM analysis for these complexes are also shown in Fig. 5. Referring to Table 4, the ρ values are within the range 0.0075–0.0182, ∇²ρ values are all positive and are within the range 0.0319–0.1126, H(r) values are all positive and are within the range 0.0017–0.0061 and ELF values are all positive and are within the range 0.0127–0.0259 (values are in a.u.). Results thus validate the presence of non-covalent interaction. Sastry et al. also advocated in favour of non-covalent interaction between metal ion and linear alkane [20].

Table 4:

Electron density (ρ), laplacian of electron density (∇²ρ), local electronic energy density (H(r)) and electron localization function (ELF) values (in a.u.) for the half sandwiches with cyclopropane and adamantane (as representative cases) at the bond critical point obtained at M06-2X/6-31++G(d,p) level.

Complexes	ρ	∇²ρ	H(r)	ELF
Li⁺-CPro	0.0134	0.0889	0.0048	0.0154
Na⁺-CPro	0.0093	0.0519	0.0027	0.0127
K⁺-CPro	0.0075	0.0348	0.0020	0.0152
Li⁺-Ada	0.0182	0.1126	0.0061	0.0259
Na⁺-Ada	0.0111	0.0561	0.0025	0.0189
K⁺-Ada	0.0079	0.0319	0.0017	0.0198

Fig. 5:

Molecular graph containing bond path obtained from the QTAIM analysis for (a) Li⁺-CPro, (b) Na⁺-CPro, (c) K⁺-CPro, (d) Li⁺-Ada, (e) Na⁺-Ada and (f) K⁺-Ada complexes.

To scrutinize the role of different forces in stabilizing the studied interaction, simple energy decomposition analysis (EDA) have been performed on the M06-2X/6-31++G(d,p) geometries. The contribution from each component can be decomposed as

E t o t a l = E e l e c + E e x + E o r b = E s t e r + E i n d ;

where E_elec is electrostatic component E_ex is exchange repulsion component, and for convenience, these two terms combined as steric (E_ster) component, E_ind is the induction component, (also known as orbital, E_orb or polarization, E_pol). The contribution from the dispersion component (E_disp) is obtained from the difference between SE and E_total (estimated from HF calculation). The obtained results are compared (total SE, E_ster, E_ind and E_disp) and plotted as bar diagram, shown in Fig. 6. Referring to Fig. 6, it is seen that contribution from E_ster is repulsive in nature i.e., E_elec and E_ex in combination destabilize the interaction (green). The expected attractive, E_elec interaction (as indicated from HOMO and charge transfer analysis) is offset by the repulsive, E_ex component in all the complexes. On the other hand, E_ind contributes predominantly (blue) towards the stabilization of the complexes in addition to nominal contribution from E_disp (cyano). Thus, it can be concluded that induction component i.e., polarization or the orbital component is the major contributor in stabilizing these half sandwich complexes. Although small, contribution from dispersion component is relatively larger for complexes with larger cations. Density functional theory-symmetry adapted perturbation theory (DFT-SAPT) calculations performed by Sastry et al. also revealed the crucial role of induction component in stabilizing cation alkane interaction [20].

Fig. 6:

Comparison of contribution from different components (forces) in stabilizing the half sandwich complexes.

NBO analysis and second order perturbation energy

NBO analysis is also carried out to establish most favourable donor-acceptor interactions [43] and strength of such interactions are calculated in terms of second-order perturbation energy E(2) (larger the E(2) value more favourable is the interaction) [51], the obtained results are shown in Table 5. Referring to Table 5, the C–H bonds are the primary donors while the antibonding 2s (Li⁺), 3s (Na⁺) and 4s (K⁺) orbitals acts as the acceptor orbitals. As expected from SE values, E(2) values for the complexes are also size dependent and increased with decrease in size metal ions, Tables 2 and 5. For example, E(2) values for the complexes decreases in the order: Li⁺-CPro (2.45) > Na⁺-CPro (0.64) > K⁺-CPro (0.26), values are in kcal mol⁻¹. To scrutinize the relationship between SE and E(2) values, the two parameters are plotted against each other for complexation with CPro and Ada as representative cases, shown in Fig. 7. There exist strong linear relationship between SE and E(2) values with R² values of 0.97 and 0.95 for complexes with CPro and Ada respectively. Hence, E(2) values are also suitable in estimating the stability of the complexes. Similar results are also reported for interaction between the lone pair of N atom of pentazolate ion and metal ion in recent literature [28].

Table 5:

The donor acceptor orbitals and E(2) values (in kcal mol⁻¹) for the complexes obtained at M06-2X/6-31++G(d,p) level (LP = lone pair, * = antibonding).

Complexes	Donor(i)→Acceptor(j)	E(2)	Complexes	Donor(i)→Acceptor(j)	E(2)
Li⁺-CPro	BD C–H→ LP* Li	2.45	Li⁺-CHex	BD C–H→ LP* Li	6.60
	BD C–H→ LP* Li	2.16		BD C–H→ LP* Li	5.68
	BD C–H→ LP* Li	1.70		BD C–H→ LP* Li	5.58
Na⁺-CPro	BD C–H → LP* Na	0.64	Na⁺-CHex	BD C–H → LP* Na	1.63
	BD C–H → LP* Na	0.60		BD C–H → LP* Na	1.62
	BD C–H → LP* Na	0.57		BD C–H → LP* Na	1.62
K⁺-CPro	BD C–H → LP* K	0.26	K⁺-CHex	BD C–H → LP* K	0.13
	BD C–H → LP* K	0.25		BD C–H → LP* K	0.13
	BD C–H → LP* K	0.24		BD C–H → LP* K	0.13
Li⁺-CBut	BD C–H→ LP* Li	4.79	Li⁺-CBicy	BD C–H→ LP* Li	4.13
	BD C–H→ LP* Li	2.80		BD C–H→ LP* Li	4.12
	BD C–H→ LP* Li	2.70		BD C–H→ LP* Li	3.95
				BD C–H → LP* Li	3.95
Na⁺-CBut	BD C–H → LP* Na	1.34	Na⁺-CBicy	BD C–H → LP* Na	1.58
	BD C–H → LP* Na	1.18		BD C–H → LP* Na	1.58
	BD C–H → LP* Na	1.18		BD C–H → LP* Na	1.57
				BD C–H → LP* Na	1.57
K⁺-CBut	BD C–H → LP* K	0.53	K⁺-CBicy	BD C–H → LP* K	0.46
	BD C–H → LP* K	0.34		BD C–H → LP* K	0.46
	BD C–H → LP* K	0.33		BD C–H → LP* K	0.46
				BD C–H → LP* K	0.46
Li⁺-CPent	BD C–H→ LP* Li	4.82	Li⁺-Ada	BD C–H → LP* Li	7.21
	BD C–H→ LP* Li	4.78		BD C–H → LP* Li	6.10
	BD C–H→ LP* Li	4.23		BD C–H → LP* Li	5.53
	BD C–H → LP* Li	4.10
Na⁺-CPent	BD C–H → LP* Na	2.01	Na⁺-Ada	BD C–H → LP* Na	1.27
	BD C–H → LP* Na	2.00		BD C–H → LP* Na	1.27
	BD C–H → LP* Na	1.37		BD C–H → LP* Na	1.27
	BD C–H → LP* Na	1.36
K⁺-CPent	BD C–H → LP* K	0.54	K⁺-Ada	BD C–H → LP* K	0.08
	BD C–H → LP* K	0.54		BD C–H → LP* K	0.07
	BD C–H → LP* K	0.51		BD C–H → LP* K	0.07
	BD C–H → LP* K	0.51

Fig. 7:

SE and E(2) plot for (a) M⁺-CPro and (b) M⁺-Ada complexes obtained at M06-2X/6-31++G(d,p) level.

Effect of complexation on C–H stretching frequencies

Since the chosen interaction is reasonably strong, there would be some impact on the C–H stretching frequencies and therefore symmetric (υ_sym) and asymmetric (υ_asym) C–H stretching for the free cycloalkane and cycloalkane upon complexation are studied, the results are shown in Table 6. Red shifts (lower wave number) in corresponding stretching frequencies (upto 26 cm⁻¹) are observed upon complexation, Table 6. For example, the υ_sym and υ_asym for C–H stretching frequencies for free CPro is obtained at 3175 and 3248 cm⁻¹ respectively. Upon complexation, the corresponding stretching frequencies are red shifted and appeared at 3097 and 3083 cm⁻¹ respectively. Besides, an antiparallel relationship between the extent of shift and the size of the metal cation is also observed upon complexation, Table 6. For example, υ_sym and υ_asym for the complexes decreases in the order: Li⁺-CPro (3097 and 3083) > Na⁺-CPro (3134 and 3117) > K⁺-CPro (3154 and 3141), values are in cm⁻¹. Thus, stronger interaction leads to larger shift in υ_sym and υ_asym C–H stretching frequencies, Tables 2 and 6. Similar trends in stretching frequencies are also reported theoretically and experimentally for cation⋯π and cation⋯lone pair interactions [28, 30, 52]. Thus, it can be concluded that the complexes are primarily stabilized by M⁺⋯H interaction between the interacting monomers.

Table 6:

Symmetric (υ_sym) and asymmetric (υ_asym) C–H stretching (in cm⁻¹) for the free cycloalkane and cycloalkane upon complexation obtained at M06-2X/6-31++G(d,p) level.

Complexes	ν_symC−H in free alkane	ν_symC−H in complexes	ν_asymC−H in free alkane	ν_asymC−H in complexes
Li⁺-CPro	3175	3097	3248	3083
Na⁺-CPro	–	3134		3117
K⁺-CPro	–	3154		3141
Li⁺-CBut	3099	2973	3152	2951
Na⁺-CBut	–	3009		2986
K⁺-CBut	–	3041		3028
Li⁺-CPent	3069	3026	3114	2929
Na⁺-CPent	–	3048		2959
K⁺-CPent	–	3057		2994
Li⁺-CHex	3036	2906	3097	2890
Na⁺-CHex	–	2936		2915
K⁺-CHex	–	2965		2947
Li⁺-Bicy	3060	2965	3094	2939
Na⁺-Bicy	–	2989		2977
K⁺-Bicy	–	3019		3007
Li⁺-Ada	3072	2907	3092	2892
Na⁺-Ada	–	2944		2918
K⁺-Ada	–	2970		2950

Conclusion

The current study delves into the formation of half sandwich complexes of alkali metal ion with cycloalkanes. In summary, the interaction is reasonably strong, leading to the formation of stable half sandwich complexes in gas phase. Besides, sandwich complexes with CPro, CHex and Bicy are also stable in gas phase. Stability of the complex is inversely related to size of the metal ion and directly related to the size of cycloalkane. Presence of solvent phase exert remarkable impact on the stability of the complexes, complexes are unstable irrespective of solvent dielectric. Energy decomposition analysis suggests the major role of induction forces in between the interacting units. The complexation is exothermic and spontaneous in nature. C–H bond is the donor and antibonding metal orbital (2s for Li, 3s for Na and 4s for K) is acceptor site for interaction. Red shift in C–H stretching frequencies is observed upon complexation. Nonetheless, experimental investigations are required to further validate our results.

Corresponding author: Bapan Saha, Department of Chemistry, Handique Girls’ College, Gauhati University, Guwahati 781001, India, e-mail: bapan.chem@gmail.com

Article note: A collection of invited papers based on presentations at the Virtual Conference on Chemistry and its Applications 2022 (VCCA-2022) held on-line, 8–12 August 2022.

Funding source: Department of Science and Technology, New Delhi

Award Identifier / Grant number: Grant No. SB/S1/PC-17/2014

Acknowledgements

Authors sincerely acknowledge the Department of Science and Technology, New Delhi, (Grant No. SB/S1/PC-17/2014) India for providing computational set-up required for the study.

Research funding: This work was funded by Department of Science and Technology, New Delhi (Grant No. SB/S1/PC-17/2014).

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Published Online: 2023-02-15

Published in Print: 2023-03-28

© 2023 IUPAC & De Gruyter. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. For more information, please visit: http://creativecommons.org/licenses/by-nc-nd/4.0/

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https://doi.org/10.1515/pac-2022-1111

Keywords for this article

Alkali metal cation; cycloalkane; DFT; enthalpy; free energy; NBO; solvent dielectric; stabilization energy; VCCA-2022