Solvent effect on the interaction of C20 and N2H2: A theoretical study
Reza Ghiasi*,1, Hanieh Alavi2
 
Abstract:
In this work, the interaction of C20 and N2H2 fragment was investigated in the M062X/6-311G(d,p) level of theory in both gas and solution phases. The influence of solvent on the interaction energy, structural parameters, frontier orbital energies and hyperpolarizability of C20…N2H2 complex has been explored. The interaction energies obtained with standard method were corrected by basis set superposition error (BSSE) during the geometry optimization for all complexes at the same levels of theory. The thermodynamic properties of the C20…N2H2 molecule at vacuum phase and different solvents have been calculated.
Keywords: C20 cage, C20…N2H2 molecules, Frontier orbitals, solvent effect, hyperpolarizability.
Introduction
C20 molecule is potentially the smallest fullerene, and its structure has been investigated theoretically and experimentally [1-6]. This molecules has been generated and characterized in the gas phase [7]. Owing to its attractive structure, this ambiguous molecule has been the subject of many theoretical investigations [8, 9]. Fullerenes are considered as promising candidates for basic elements in nanoscale devices, and several examples of fullerene-based devices have been already investigated both experimentally and theoretically [10, 11]. Modification of C20 is a matter of general interest for experimentalists as well theoreticians to look into the structural as well as electronic properties. As a recent research, for instant, structure and properties of fullerene C20 and its derivatives C20(C2H2)n and C20(C2H4)n (n=1–4) have been studied [12]. These calculations showed that the most stable fullerene C20 and its derivatives C20(C2H2)n and C20(C2H4)n (n=1–3) reveal significant aromaticity, while C20(C2H2)4 and C20(C2H4)4 have no spherical aromaticity. Also, heteroatom impacts on structure, stability and aromaticity of XnC20-n fullerenes have been explored [13]. The interaction of C20 with N2X2 (X=H, F, Cl, Br, Me) have been investigated theoretically [14]. Structure, aromaticity, frontier orbital analysis and the natural bond analysis of C20…N2X2 complexes have been explored, and the influence of the basis set and methods on the structure and interaction energies of these complexes have been explored.
In the present work, extensive theoretical calculations on fullerene C20 and their interactions with N2H2 have been performed in both gas and solution phases. The Structure, frontier orbital analysis and hyperpolarizability of the C20…N2H2 have been explored. We also discuss the influence of the solvent on the structure properties of C20…N2H2 molecule.
Computational Methods
All calculations were carried out with the Gaussian 09 suite of program [15]. The calculations of systems contain C, and N described by the standard 6-311G(d,p) basis set [16-19]. Geometry optimization was performed utilizing with the hybrid functional of Truhlar and Zhao (M062X) [20].
A vibrational analysis was performed at each stationary point found, that confirm its identity as an energy minimum.
The interaction energy, IE, can be evaluated from the difference between energy of the complex and sum of the energies of the C20 and N2H2:
I.E = E(complex) – [E (C20)+ E(N2H2)]
The calculated interaction energies were corrected for basis set superposition errors (BSSE), which were computed for all calculations using the counterpoise correction method of Boys and Bernardi [21].
Geometries were optimized at this level of theory without any symmetry constraints followed by the calculations of the first order hyperpolarizabilities. The total static first hyperpolarizability  was obtained from the following relation:

upon calculating the individual static components

Due to the Kleinman symmetry [22]:
xyy =  yxy =  yyx ; yyz =  yzy =  zyy,…
one finally obtains the equation that has been employed:

We have studied the solvation effects by using self-consistent reaction field (SCRF) approach, in particular using the polarizable continuum model (PCM) [23]. Using this method, the geometry of the studied complex was re-optimized and the hyperpolarizability was calculated by the same functionals and basis sets.
Results and discussion

Energetic

The computed interaction energies (I.E) and the corrected interaction energies (I.E corrected) for the C20…N2H2 complex (Figure 1) in gas phase and various solvents have been gathered in Table 1. It can be expected interaction between C20 and N2H2 increases in the presence of more polar solvents. Figure 2 presents a good correlation between interaction energies values and dielectric constants of solvents. On the other hand, the comparison of interaction energy value in gas phase and solution phase show more interaction between C20 and N2H2 in solution phase.

Thermochemical Analysis

Thermochemical analysis is studied for all complexes. The values of H, G and K are reported in Table 2 in which the individual terms are referred to a temperature of 298 K. The reaction can be considered as:
C20 + N2H2ï‚® C20…N2H2
As can be verified, the G values increase in solution phase. The equilibrium constants of the all complexes are given in Table 2. This shows that the equilibrium constant is most vacuum phase.

Dipole moments

The dipole moments of C20…N2H2 complex in gas phase and different solvents have been listed in Table 3. As seen in Table 3, C20…N2H2 complex has less dipole moment in gas phase. In the solution phase, dipole moments increase with increasing of polarity of the solvents. Also, these values show a good relationship with interaction energies values (Figure 3).

Polarizability

The isotropic and anisotropic polarizability values of C20…N2H2 complex in gas phase and different solvents have been gathered in Table 3. As seen in Table 3, C20…N2H2 complex has less polarizability in gas phase. There is good correlation between isotropic polarzability values and dielectric constants of solvent (R2=0.948).

Bond distances

The NN and C..N bond distances of C20…N2H2 complex in gas phase and different solvents have been collected in Table 1. As seen from Table 1, the bond lengths increase in solution phase. There is minor dependence between bond distances and dielectric constants values. The comparison NN bond distances of free N2H2 and complexed molecule show the rising of this bond in C20…N2H2 complex.

Molecular orbital analysis

The energies of the frontier orbitals (HOMO, LUMO) along with the corresponding HOMO–LUMO energy gaps for of C20…N2H2 complex in gas phase and different solvents are given in Table 4.
Inclusion of solvation effects leads also to changes on the molecular orbital energies (Table 4). In solution, HOMO and LUMO are destabilized, with respect to the corresponding values in vacuum. Also, HOMO-LUMO gap and hardness of C20…N2H2 complex in solution phase is more than gas phase. A good relationship between HOMO-LUMO gap and polarity of solvents (R2=0.954). The variations in this property may be illustrated by considering the fact that neutral or charged species enhance their effective radii in solution phase. This signifies that the electrostatic potential q/r will forever diminish from gas phase to solution phase. As a result, solvated species will reduce their effective hardness and subsequently become softer in the solution phase [24].
On the other hand, when the interaction between C20 and N2H2 increases, then the most hardness values have observed. There is a good linear correlation between interaction energies and hardness values (R2=0.949).
Electrophilic charge transfer (ECT) of C20…N2H2 complex in gas and various solvents has been reported in Table 4. ECT is defined as the difference between Nmax values of interacting molecules:
ECT = Nmax(N2H2) – Nmax(C20)
In this equation Nmax is defined as:

The positive values of ECT reveal charge flow from C20 to N2H2. On the other hand, these values show the decreasing of charge transfer with increasing of solvent polarity.

Hyperpolarizability

It is illustrated that solvent polarity participate an important role on the first hyperpolarizabilities in dipolar molecules. The tot , x, y, z values of C20…N2H2 complex in different solvents have been listed in Table 5. These values indicate tot values decrease from vacuum to solution phase (total=0.0 for C20). The dependence of the first hyperpolarizability of the studied compound both on the dielectric constant of the media and the Onsager function has been investigated [25]. Figure 4 is typical for a dipolar reaction field interaction in the salvation process [25-28]. Therefore, the electronic reorganization in solution for C20…N2H2 complex acts an important effect on the resulting first hyperpolarizabilities.
Conclusion:
We showed in paper:

The interaction energies values increase from vacuum to different solvents.
In solution, HOMO and LUMO energies, hardness and chemical potential values are increased, with respect to the corresponding values in vacuum. On the other hand, electrophilicty values have been decreased in solution phase.
The largest tot values have been found in more polartity, and these values increase from vacuum to different solvents.

References:
[1]J. C. Grossman, L. Mitas, K. Raghavachari, Phys. Rev. Lett., 750, 3870 (1995).
[2]E. J. Bylaska, P. R. Taylor, R. Kawai, J. H. Weare, J. Phys. Chem. A, 100, 6966 (1996).
[3]R. Taylor, E. Bylaska, J. H. Weare, R. Kawai, Chem. Phys. Lett, 235, 558 (1995).
[4]Z. Wang, P. Day, R. Pachte, Chem. Phys. Lett., 248, 121 (1996).
[5]M. L. M. Jan, J. El-Yazal, J. Francois, Chem. Phys. Lett. , 248, 345 (1996).
[6]S. Sokolova, A. Luchow, J. B. Anderson, Chem. Phys. Lett. , 323, 229 (2000).
[7]H. Prinzbach, A. Weiler, P. Landenberger, F. Wahl, J. Worth, L. T. Scott, M. D. Gelmont, D. Olevano, B. V. Issendorff, Nature, 60, 407 (2000).
[8]J. Luo, L. M. Peng, Z. Q. Xue, J. L. Wu, J. Chem. Phys, 120, 7998 (2004).
[9]Z. Chen, T. Heine, H. Jiao, A. Hirsch, W. Thiel, P. v. R. Schleyer, Chem. Eur. J. , 10, 963 (2004).
[10]J. Taylor, H. Guo, J. Wang, Phys. Rev. B 63, 121104 (2001).
[11]D. Zeng, H. Wang, B. Wang, J. G. Hou, Appl. Phys. Lett, 77, 3595 (2000).
[12]C. Zhanga, W. Sun, Z. Caob, J. Chem. Physics, 126, 144306 (2007).
[13]M. Z. Kassaee, F. Buazar, M. Koohi, Journal of Molecular Structure: THEOCHEM, 940, 19 (2010).
[14]R. Ghiasi, M. Z. Fashami, J. Theo.Comput. Chem (2014).
[15]M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalman, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, D. J. Fox, Revision A.02 ed., Gaussian, Inc., Wallingford CT, 2009.
[16]R. Krishnan, J. S. Binkley, R. Seeger, J. A. Pople, J. Chem. Phys. , 72, 650 (1980).
[17]A. J. H. Wachters, J. Chem. Phys., 52, 1033 (1970).
[18]P. J. Hay, J. Chem. Phys. , 66, 4377 (1977).
[19]A. D. McLean, G. S. Chandler, J. Chem. Phys., 72, 5639 (1980).
[20]Y. Zhao, D. G. Truhla, J. Phys. Chem, 110, 5121 (2006).
[21]S. F. Boys, F. Bernardi, Mol. Phys., 19, 553 (1970).
[22]D. A. Keleiman, Phy. Rev., 126, 1977 (1962).
[23]J. Tomasi, B. Mennucci, R. Cammi, Chem. Rev., 105, 2999- (2005).
[24]R. Pearson, J. Am. Chem. Soc. , 108, 6109 (1986).
[25]L. Onsager, J. Am. Chem. Soc., 58, 1486 (1936).
[26]K. Clays, A. Persoons, Phys. Rev. Lett. , 66, 2980 (1991).
[27]H. Lee, S.-Y. An, M. Cho, J. Phys. Chem. B, 103, 4992 (1999).
[28]P. C. Ray, J. Leszczynski, Chem. Phys. Lett., 399, 162 (2004).
1