Advances in Condensed Matter Physics

Volume 2017, Article ID 3296845, 7 pages

https://doi.org/10.1155/2017/3296845

## Torsional Potential Energy Surfaces of Dinitrobenzene Isomers

Department of Physics, Oklahoma State University, Stillwater, OK 74078, USA

Correspondence should be addressed to Mario F. Borunda; ude.etatsko@adnurob.oiram

Received 1 April 2017; Accepted 4 July 2017; Published 20 August 2017

Academic Editor: Gary Wysin

Copyright © 2017 Paul M. Smith and Mario F. Borunda. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The torsional potential energy surfaces of 1,2-dinitrobenzene, 1,3-dinitrobenzene, and 1,4-dinitrobenzene were calculated using the B3LYP functional with 6-31G(d) basis sets. Three-dimensional energy surfaces were created, allowing each of the two C-N bonds to rotate through 64 positions. Dinitrobenzene was chosen for the study because each of the three different isomers has widely varying steric hindrances and bond hybridization, which affect the energy of each conformation of the isomers as the nitro functional groups rotate. The accuracy of the method is determined by comparison with previous theoretical and experimental results. The surfaces provide valuable insight into the mechanics of conjugated molecules. The computation of potential energy surfaces has powerful application in modeling molecular structures, making the determination of the lowest energy conformations of complex molecules far more computationally accessible.

#### 1. Introduction

Torsional potential energy calculations provide conformational information and allow finding the barriers to the rotations of bonds. Early applications were performed in organic compounds phosphates, 1,3-butadiene, polypeptides, and dimethyl groups [1–4]. These initial works showed that if steric interactions are not strong, a rigid rotor model applies. Furthermore, Bongini and Bottoni used density functional theory (DFT) and found that correlation energy effects are to be taken into account for accurate calculations of the conformal properties of organic compounds [4]. The topologies of the PES in the ground state and a selected excited state are useful in understanding the active site of reactions and photoreactivity [1]. PESs were employed to investigate excited-state reaction mechanisms and proton transfer in a complex molecule (2-(2′-hydroxyphenyl)benzimidazole) and its amino derivatives [2].

The calculations by Bongini and Bottoni compared Hartree-Fock and second-order Møller-Plesset methods [3–5] to DFT results (at the BLYP and B3LYP levels) [6, 7] and determined the structure of the two molecules considered (3,3′-dimethyl-2,2′-bithiophene and 3,4′-dimethyl-2,2′-bithiophene) and to experimental data to quantify the reliability of the models. Both BLYP and B3LYP computations correctly predict both of the rotational minima observed in experiment to an accuracy of 5°. Bongini and Bottoni produced torsional potential energy plots, but their interest was in the nature of the minima, not the characteristics of the energy surface itself [8]. Raman spectra of multiple physical phases of a compound can be used in conjunction with computational ab initio and DFT methods to determine the torsional potential of a two-rotor system and are capable of determining the potential energy surface (PES) with a 3% accuracy [9]. However, this method requires multiple Raman spectra, several single-point energy computations for representative molecular conformations, and theoretical knowledge of the general form of the PES [9]. The PES of ethoxybenzene, a molecule where the coupling between rotors is small, has been calculated using DFT at the B3LYP level for both a one-rotor molecule and a two-rotor molecule. The points on the PES were computed in 15° increments and used to construct a torsional PES with a cosine series least-squares fit to the points and the fit was found to be within 20% of the experimental values and the two-rotor ethoxybenzene molecule has a planar energy minimum [10].

In this manuscript, we explore the use of the torsional PES to determine the geometry of the lowest energy state for molecules, a methodology which might be extended to larger molecules such as proteins. We computationally determine the energy correlation between pairs of rotors on the molecule. These correlations can be reduced to a matrix differential equation, and the eigenvalues and eigenvectors of the equation will specify the lowest energy conformation of the molecule being studied. Since the energy of the system is represented by a differential equation in matrix form, it can be iterated computationally to a convergence at the lowest energy state of the molecule. The knowledge of the correlations between different rotors allows local energy minima distinct from the global minima to be easily identified.

We report the torsional PESs for dinitrobenzene isomers. The two-dimensional PES plots show the potential energy of the molecule as a function of the angles each NO_{2} group makes with respect to the ring. The molecular structure of dinitrobenzene allows for three isomers and thus our calculations explore torsional PESs for modeling conjugated systems with and without steric effects. As shown in Figure 1, the orthoisomer, with the nitro groups at 1 and 2 positions, is characterized by strong steric repulsion. This repulsion is caused by the electrical force between the spatially adjacent oxygen atoms. The 1,3 isomer has attractive intramolecular interactions between the NO_{2} groups and the H atoms. The O atoms have a conjugated negative charge, which is attracted to the conjugated positive charge of the H ions. Finally, the 1,4 isomer has little steric hindrance or attractive forces affecting the rotation of the NO_{2} groups. Thus, these three isomers are useful to determine the roles that steric effects and intermolecular attraction play in the rotation of the NO_{2} groups.