Density Function Theory and Hartree-Fock Study on the Electronic Structure of β-Sitosterol

Research Article

Austin Biochem. 2017; 2(1): 1010.

Density Function Theory and Hartree-Fock Study on the Electronic Structure of β-Sitosterol

Joginipelli S¹, Melapu VK¹ and Darsey J²*

¹Department of Computer Science, Jackson State University, USA

²Department of Chemistry, University of Arkansas at Little Rock, USA

*Corresponding author: Darsey J, Department of Chemistry, University of Arkansas at Little Rock, 2801 South University Avenue, Little Rock, AR, 72204, USA

Received: January 24, 2017; Accepted: May 17, 2017; Published: May 24, 2017


In this study, a comparative Density Functional Theory (DFT) and Hartree- Fock (HF) calculations were preformed to understand the dynamic behaviour and bioactivity of β-Sitosterol (beta-Sitosterol) to gain insights about its electronic structural properties, and reactivity. This research article deals with theoretical study of structural and electronic properties such as Highest Occupied Molecular Orbitals (HOMO) and Lowest Unoccupied Molecular Orbitals (LUMO), molecular structure, energy surfaces, orbital energies, energy gap, electron affinity, ionization potential, vibrational spectra, of β-Sitosterol; a well-known natural product from medicinal plants. HOMO, LUMO of β-Sitosterol were generated and interpreted with Density Functional Theory (DFT) and Hartree-Fock (HF) calculations following full structure optimization. HOMO, LUMO generated with DFT and HF calculations were compared and a detailed visualization of orbitals and their energies were presented. Contour plots and energy maps were also generated, analyzed and interpreted for potential activity. The similarities and differences between the DFT and HF calculations for β-Sitosterol were studied and highlighted. Thermodynamic calculations were performed with the DFT methods using B3LYP/6-31G: PM3 level of theory.

Keywords: β-Sitosterol; Quantum mechanical calculations; ab-initio; Density Function Theory (DFT); Highest Occupied Molecular Orbitals (HOMO); Lowest Unoccupied Molecular Orbitals (LUMO); B3LYP; 6-31G; Hartree-Fock (HF)


DFT: Density Functional Theory; HOMO: Highest Occupied Molecular Orbitals; LUMO: Lowest Unoccupied Molecular Orbitals; HF: Hartree-Fock

Introduction & Background

Throughout the ages, humans have relied on nature for their basic needs such as food, shelter, clothing, and medicines [1]. Due to the natural ability of plants to synthesize a wide variety of compounds, they have traditionally been used as source of medicines to cure a variety of ailments and to prevent disease. Countries with ancient civilization such as India, China, and Egypt historically used plants as remedies for various conditions and ailments [2]. Although many approved and clinical-trial drugs have been derived from natural products, the last 20 years has shifted the emphasis from natural products to less expensive synthetic products [3]. Many of these compounds have served as predecessors for modern drug therapies [3]. Advances in medicinal chemistry, in combination with multidisciplinary research, have expanded our understanding regarding the specifics of individual chemical constituents. Armed with this information, it has become possible to analyze and evaluate the active principles in natural products and plants that possess better drug properties, less toxicity, and better pharmacokinetics [4].

Chemical constituents such as β-Sitosterol, Sitosterol, Stigmasterol, Tectoquinone, Kaempferol, and Lygiodinolide found in Lygodium flexuosum plant have been linked to the prevention and delaying onset of symptoms Alzheimer’s disease. β-Sitosterol is one of the several phytosterols found in Lygodium flexuosum plant and is an anabolic precursor of Boldenone steroid. Lygodium flexuosum plant has high content of β-Sitosterol and the plant extract is used in the treatment of Alzheimer’s disease [5]. Phytosterols are a subgroup of the steroids, and are important class of bio-organic molecules widespread in plants, animals, marines and fungi. Pharmaceutical products and certain food materials have these compounds and are generally recognized as safe without undesirable side effects. Among phytosterols, β-Sitosterol is usually used for heart diseases, hypercholesterolemia, modulating immune system, prevention of cancer, as well as relieving symptoms of rheumatoid arthritis, tuberculosis, cervical cancer, and benign prostate hyperplasia. Due to the diverse biological activities β-Sitosterol was considered as one of the most important natural product that need to be analyzed to confirm its efficacy and safety [6]. β-Sitosterol was chosen to perform Quantum Mechanical calculations to gain insights about reactivity and electronic structural properties and β-Sitosterol molecule used in this study is not purified from Lygodium flexuosum plant. Quantum Mechanics (QM) stands out as a powerful computational approach to characterize the structure, dynamics, and reactivity of bio-molecules [7]. QM calculations to identify potent inhibitors are extremely attractive approaches mainly because of high accuracy (relative) to estimate structural properties [8]. The increasing popularity of quantum mechanical methods in Computer Aided Drug Design (CADD) is not just a consequence of growing computational power, but is due to the first principle nature of QM that provides highest accuracy [8]. Over the last two decades powerful molecular modeling tools have been developed that are capable of accurately predicting structural energetics, reactivity’s, and other electronic properties of molecules. These developments are due to dramatic increases in computer speed and design of efficient quantum chemical algorithms [9]. Quantum Mechanical studies particularly DFT and HF studies can evaluate a vast range of structural, chemical, optical, spectroscopic, elastic, vibrational and thermodynamic phenomena. The ability of DFT and HF calculations to predict structure-property relationships have improved and revolutionized experimental studies [10]. DFT and ab-initio quantum chemistry has become an essential tool in the study of atoms, molecules and complex systems. The underlying technology in DFT and HF study is providing a computational solution of the electronic Schrodinger equation; given the position of atomic nuclei and total number of electrons in the system, DFT and HF calculations will calculate the electronic energy, electron density, HOMO (Highest Occupied Molecular Orbitals), LUMO (Lowest Unoccupied Molecular Orbitals), electrostatic potential maps and other properties [11]. Graphical models from quantum mechanical studies, electrostatic potential maps, HOMO (Highest Occupied Molecular Orbitals), and LUMO (Lowest Unoccupied Molecular Orbitals) maps have proven of considerable value not only to rationalize trends in molecular structure, stability, chemical reactivity, and selectivity, but also as tools with which to carry out chemical investigations [12]. Electrons and their distribution in molecular orbitals are considered the most important factor to determine the reactivity of the molecule. For example, p surface of benzene with high electron density indicate electrophilic attack that occurs on Benzene at p face [12]. Chirality of potential drug molecules is essential to current pharmaceutical development process [13]. The physiological effects of different enantiomers are not often equivalent; in some cases, they have different physiological effects [13]. Sometimes two enantiomers of the same compound can be used to treat two separate medical conditions. For example, the (R, R) enantiomer of Ritalin is used to treat Attention Deficit Disorder (ADD) while the (S, S) enantiomer is an antidepressant [13]. Ab-initio quantum mechanical calculations including Density Functional Theory (DFT) calculations are computationally intensive but regarded as the most accurate approaches to theoretically calculate the structural properties of molecules [11].Quantum mechanical studies of chemical constituents from medicinal plants will provide insights into electronic structural properties, electron density, molecular orbitals, vibrational spectra, and chirality of the molecule.

The classes Density Functional Theory (DFT) formalism introduced by Hohenber, Kohn, and Sham in mid 1960’s is based on the idea of replacing complicated N-electron wave function with simpler 1-electron charge density in electronic structural calculations of the ground stationary states [14]. In this study, theoretical DFT calculations were performed on β-Sitosterol to gain insights into electronic structural properties. Density Function Theory is presently useful tool for extracting electronic energy states of molecules and is considered as one of the useful tools in quantum chemistry to calculate electronic structural properties. The electronic strucutral properties calculated with DFT is combination with B3LYP hybrid functional and the 6-31G basis set has been shown to provide accurate energies for excited states [14].

Materials and Methods

Quantum mechanical calculations

The molecular geometries of β-Sitosterol in their ground and excited states were optimized using the Gaussian 09 program package. DFT calculations were performed with optimized structures using B3LYP exchange correlation functional and 6-31G basis set. The calculations were used to evaluate electronic structural properties, chemical reactivity, and selectivity of molecules. Calculations were performed on the University of Arkansas at Little Rock (UALR) High Performance Computer Cluster servers; Argon, Erbium, and Boron using Gaussian 09 program [15]. DFT calculations were performed with 6-31G basis set and HOMO (Highest Occupied Molecular Orbitals), LUMO (Lowest Unoccupied Molecular Orbitals), density, electrostatic potential, Laplacian, and spin density cube files for surfaces were generated. The graphical models generated for HOMO and LUMO were visualized with Gauss-View 5 program [16]. Abinitio level calculations were performed with HF method, used to solve the time-independent Schrodinger equation for a multi-electron atom or molecule using 6-31G basis set. Calculations to calculate the total energy and dipole moment were also performed. The output file generated from Gaussian09 was used to visualize the electron density, electrostatic potential map, and HOMO, LUMO orbitals using GaussView5. The results of β-Sitosterol were visualized with Gauss view and were presented to analyze and interpret the potential medicinal activity.

By using HOMO and LUMO energy values for a molecule, chemical potential, electronegativity and chemical hardness can be calculated as follows [17]

Chemical Potential of the molecule given by

μ = (EHOMO + ELUMO) / 2

Chemical hardness of the molecule is given by

η = (ELUMO - EHOMO) / 2

Electronegativity of the molecule is given by

Χ = - (EHOMO + ELUMO) / 2

Results and Discussion

Quantum mechanical calculations for β-Sitosterol were carried out using the DFT method at the B3LYP/6-31G level of approximation. The optimized structure parameters of β-Sitosterol allowing the relaxation of all parameters, the calculations converge to optimized geometries, which correspond to the true energy minima, as revealed by the lack of imaginary frequencies in the vibrational mode. Quantum mechanical studies such as DFT and HF calculations were performed on chemical constituents obtained from Lygodium flexuosum with emphasis on β-Sitosterol. The HOMO, LUMO orbitals, mapped surfaces, contour plots, electro static potential surfaces, were calculated. Global chemical reactivity indices of all phytochemicals obtained were also compiled and archived. The calculated global chemical reactivity indices for each chemical compound include the HOMO, LUMO, energy gap, ionization potential, electron affinity, electro negativity, electrochemical potential, hardness, softness, electrophilicity in eV, total energy in A.U units, and dipole moment in Debye units. Frontier molecular orbital theory of explaining HOMO and LUMO surfaces was visualized with Gauss-view program using DFT calculations. Chemical structures of β-Sitosterol obtained from Lygodium flexuosum plant was shown with Gaussview. Figure 1 shows β-Sitosterol optimized chemical structure. From the structure, β-Sitosterol appears non-planar in the middle, all the energy contributions are positive and dominant contributions are due to dihedral, Van der waals, and angle interactions. The remaining contributions are relatively small. There is only one double bond in β-Sitosterol molecule, located in the middle of the ring. The c=c double bond is 1.34 Å, whereas the C-C single bonds vary between 1.48 and 1.55 Å. There is one oxygen atom in the present system; the C-O single bond length is 1.41 Å. C-H bonds are almost the same, ~1.11 Å, and the O-H bond is ~0.95 Å.