Molecular Structure and Theoretical Thermodynamic Study of Folic Acid Based on the Computational Approach

Shhl Hmedni Hossein Aghie

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Molecular Structure and Theoretical Thermodynamic Study of Folic Acid Based on the Computational Approach

Shahla Hamedania①Hossein Aghaiea

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In our previous work, we studied the interaction of folic acid, FA, molecule with single-walled carbon nanotube and the related binding energies with other related parameters. Now, in order to extend our study with respect to the other structural properties offolic acid molecule and its thermodynamic properties, we optimized the structures of bothneutral and zwitteronic forms of this molecule by using the DFT/B3LYP method in the gas phase and then in different solvents. In addition, the electronic properties, such as the molecular orbital study (HOMO, LUMO, PDOS, and TDOS) and geometrical structure,were investigated by the above-mentioned method with 6-31G(d) basis set. The thermodynamic properties of both neutral and zwitterionic forms of the FA molecule at different temperaturehave been calculated. Natural bond orbital (NBO) analysis has been done to study the stability of the molecule arising from charge delocalization.

folic acid, thermodynamic properties, DFT, NBO;

1 INTRODUCTION

Folic acid, N-[-{[(2-amino-4-hydroxy-t-pteridinyl) methyl] amino}benzoyl]-l-glutamic acid[1-3], is a water-soluble essential vitamin B and is necessary for the metabolism of amino acids and biosynthesis of DNA and RNA (Fig. 1). For reducing the risk of birth defects of the brain and spina (such as brain anencephaly), folic acid or its salt is used mainly as part of a healthy diet. It may also be used for the prevention of Alzheimer's disease, high blood pressure, protecting against neoplasia in ulcerative colitis and some psychiatric disorders. According to the research that was done in 1945, this drug is an effective material in the treatment of Gilbert's syndrome that is a common hereditary disorder, and the cause of Gilbert's syndrome is the high concentration of bilirubin. The folic acid deficiency is one of the causes of certain types of anemia, which is called macrocytic anemia[4].

Fig. 1. Molecular structure of neutral form of folic acid

The present research is an extend of our previous work related to theoretical study of folic acid properties[5-7].Now, the ground state properties of both zwitterionic and neutral forms of FA molecule have been investigated by using the DFT/B3LYP level of theory with 6-31G(d) basis set. Along with this investigation, molecular polarizability, energy gap, charge transfer within the molecule,thermodynamic parameter of FA molecule and so on were estimated respect to the ground state of studied molecule. Moreover, natural bonding orbital (NBO) calculations have been performed at the same level of theory in order to investigate the intramolecular charge transfer interactions and the delocalization of electron density within the molecule[8].

2 COMPUTATIONAL METHODS

In the first step, the molecular geometry optimiza-tion and electronic property calculations of both zwitterionic and neutral forms of FA without any symmetry constraints were performed on the basis of Gaussian 03 quantum chemistry package[9]and the results were visualized by Gauss View 5.0.8 graphical program[10](Fig.2).The geometry optimizationwas performed at the DFT level of theory, according to hybrid Becke’s three parameters and the Lee-Yang-Parr correlation functional (B3LYP)[11-14], with the 6-31G(d) basis set. NBO calculations are important for understanding the delocalization of the electron density between the lone pair (Lewis donor) NBO orbitals and anti-bonding (non-Lewis acceptor) NBO orbitals. For each donor (i) and acceptor (j), the stabilization energy E(2)related to the delocalization→is estimated using the second-order perturbation theory as:

where niis the donor orbital occupancy,iandjare diagonal elements (orbital energies) and F(i,j) is the off diagonal NBO Fock or Kohn-Sham matrix element[15].The larger E(2)value depicts the stronger interaction between electron donors and acceptors i.e., the more donation tendency from electron donors to electron acceptors and the higher the amount of conjugation of the whole system.

(a)

(b)

Fig. 2. Optimized geometries of (a) neutral form, and (b) zwitterionic form of folic acid molecule estimated upon the B3LYP/6-31G (d) approach

In order to investigate the solvent effect on the geometries of studied molecule, the structures of it were optimized in methanol, DMSO and in water as a high polar solvent. From the optimized geometries parameters, the global molecular descriptors such as energy gap,atomic charges,dipole moment () andpolarizability () of FA molecule were evaluated based on the finite field method by using DFT methods[16, 17]. Also, frequency calculations were performed using the B3LYP/6-31G(d) optimized geometries to achieve the thermodynamic values such as zero point vibrational energy, thermal energy (E), entropy (), and Gibbs free energy () of FA molecule. These calculations were done at the temperature range of 150 to 600 K at1atm.

3 RESULTS AND DISCUSSION

3.1 Geometrical parameters

The final optimized geometries of both neutral and zwitterionic forms of folic acid molecule were investigated at the B3LYP/6-31G(d) level by using the Gaussian 03 program, with the resultsshown in Fig. 2 and the optimized parameterslisted in Table 1. The two C=O bond lengths in the zwitterionic form are different (1.227 ? and 1.246 ?) due to the charge delocalization as compared to the neutral form having one single and one double C=O bonds which form hydrogen bonding between the carboxyl and amino groups of neighboring molecules.

Table 1. Selected Geometric Parameters of the Neutral and Zwitterionic Forms of Folic Acid Molecule upon the B3LYP/6-31G(d) Level

3.2 Electronic properties

Fully optimized ground state structures of FA mole-cule were used to estimate the total energies, HOMO and LUMO energies, the dipole moment () and the polarizability ()in the gas phase andthe solution media. The results are listed in Table 2 and Fig. 3 showthe related HOMO and LUMO energies and their difference. The HOMO energy characterizes the ability of electron giving, the LUMO energy charac-terizes the ability of electron accepting, and the gap between HOMO and LUMO specifies the molecular chemical stability[18-22].

Based on the B3LYP/6-31G(d) calculation, the energy gap (transition from the ground state to the first excited state) for the neutral form of FA molecule in the gas phase is about 3.154 eV. This low value of the energy gap confirms charge transfer within the molecule. GaussSum 2.2 program[23]was used to calculate the molecular orbital HOMO and LUMO energies and evaluate the total density of the states (TDOS) and partial density of states (PDOS) plots, as shown in Fig. 4. The TDOS plot represents population analysis per orbital and a makeup of the molecular orbital in a special energy range, and also indicates that electrons transfer from the lone pair orbitals to*or*orbitals, while PDOS plot shows the percent contribution of a group to each molecular orbital.

Fig. 3. HOMO and LUMO presentation for the neutral and zwitterionic forms of FA molecule in the gas phase at the B3LYP/6-31G(d) level of theory

Fig. 4. TDOS and PDOS plots of the folic acid molecule

Table 2. Calculated Total Energies, HOMO and LUMO Energies, Dipole Moment and Polarizability in the Gas Phase and in the Solution of the Neutral and Zwitterionic Forms of Folic Acid Molecule

3.3 Molecular electrostatic potential

Another important local descriptor for charge determining is the molecular electrostatic potential (MEP), which includes the potential of all nuclei and electrons in a molecule and is a very useful property for analyzing and predicting the molecular reactivity behavior. The different values of the electrostatic potentials are shown by different colors. In the majority ofMEPs, the negative electrostatic potential (red color) is related to the attraction ofproton toward the region where the rich electron density exists (subject to electrophilic attack). In turn, the positive electrostatic potential (blue color) corresponds to the repulsion of proton (subject to nucleophilic attack)[24-26].

The MEP mesh and transparent plots of the folic acid moleculeclearly suggest that O6,O10andO31atoms have maximum negative electrostatic potential (electron rich region), whereas the other surfaces with maximum positive electrostatic potential may be suitable sites for nucleophilic reactions (Fig. 5). In addition, the calculated charges such as NBO and Mulliken were compared with MEP and the distribution of positive and negative charge values with color change was investigated (Fig. 6).

Mesh

Transparent

Fig. 5. Molecular electrostatic potential plot of the FA molecule

Fig. 6. Histogram of different atomic charges on FA molecule at the B3LYP/6-31G(d) level

3.4 Polarizability descriptor

The polarizability of a molecule is a measure of tendency of an electronic cloud of that molecule for distorting the molecule from normal shape by a weak external electric field[27]. The mean polarizability,, and the total electric dipole moment,, for both forms of FA molecule were calculated at the DFT level using the following equation:

(3)

whereα,αandαare diagonal components of the polarizability tensor. The average values of polarizabilities for neutral and zwitterionic forms of the FA molecule in the gas phase are286.7766 and 259.6588 a.u. respectively and in water solvent with the maximum amounts of polarization are 363.5177 and 387.2013 a.u. (see Table 2).

3.5 Natural bond orbital analysis

The NBO analysis was performed on the folic acid molecule (neutral and zwitterionic) to determine intermolecular charge transfer (ICT), delocalization of electron density and the direction and magnitude of donor-acceptor interactions. The energy gap between bonding (occupied Lewis) and anti-bonding (unoccupied non-Lewis) NBO’s determines the feasibility of interactions between the filled and vacant orbitals. The calculations were done according to a stabilizing donor-acceptor interactionon the basis of DFT level with the B3LYP/6-31G(d) basis set. The calculations of the second order interaction energies(2)between Lewis and non-Lewis orbitals, occupation numbers, stabilization energy and the valence space energy splittingE–E(a.u.) of the interacting NBO’s are reported in Tables 3 and 4. The intramolecular interactions are formed by the orbitals’ overlap between the bonding(C–C),(C–H) and(C–N) with the anti-bonding*(C–C) and*(C–H) orbitals which resultin intramolecular charge transfer (ICT) causing stabilization of the system.

As can be seen from Tables 3 and 4, the interaction (→*), related to the resonance in the molecule, is electron donation from LP (3) O6atom of the electron donating group to the anti-bonding acceptor*(C5–O7) and leads to a high stabilization energy 77.97 kcal/mol. Also, there is a strong intramolecular interaction of electrons from LP (3)O6atom with*(N24–H45) band of the pterin ring leading to the stabilization energy of 16.78 kcal/mol. Table 4 indicates the strong intramo-lecular interactions ofelectrons of (C11–C12) with*(C13–C16),*(C9–O10) and*(C14–C15), and(C13–C16) with*(C11–C12) and*(C14–C15) of the ring. From the NBO analysis, we could conclude that the maximum occupancies of 1.99668 and 1.99478 are obtained for C5–O7and C5–O6, respectively.

3.6 Thermodynamic properties

The calculationvibrational frequencies were performed in order to insure that the correct geometry optimization has been done. If all the studied structures correspond to the minima of the potential energy surface, the vibrational frequencies would not be imaginary and that is a reason for the stability of optimized structure. The results of these calculations revealed that the optimized geometries were stable. So, we attempted to calculate the thermodynamic properties of the studied molecule such as zero point energy, heat capacity at constant volume (C), enthalpy (), Gibbs free energy (), entropy (),. for FA molecule in the zwitterionic and neutral forms at various temperature. The computed values in the range of 150～600 K at 1atm are given in Table 5. The results show that the energy of neutral folic acid molecule is lower than zwitterionic form with an amount of 0.5334 Hartree. This clearly indicates that in zwitterion form the charge separation is not sta-bilized in the gas phase. Generally, observation thermo-dynamic parameters show the molecular vibrational intensities increase with the temperature[28, 29].

Table 3. Occupation Numbers of the Interacting NBOs with Their Associated Energies

a(2) means the energy of a hyper-conjugative interactions; cf. Eq. (1)

bEnergy difference between donor and acceptorandNBO orbitals

Table 5. Calculated Values of Thermodynamic Parameters at Different Temperature at 1 atm for Neutral and Zwitterionic Forms of FA Molecule in the Gas Phase

4 CONCLUSION

In the present investigation, molecular structures, bond lengths, bond angles, dihedral angles, thermodynamic parameters, energy gap, NBO and other important properties of FA molecule were studied by using ab initio DFT (B3LYP/6-31G(d)) calculations. The high value of energy gap for zwitterionic and neutral forms of FA molecule showed the FA molecule is more stable in water media. The possible electrophilic and nucleophilic sites in FA molecule were identified by MEP. In addition, the atomic charge analysis, such as NBO and Mulliken methods, strengthened the results of MEP. In turn, the NBO analysis showed that the important interactions related to the resonance in FA molecule involveelectron density transfer from lone pair LP(3) O6to anti-bonding*(C5–O7), resulting in the stability of 77.97 kcal/mol and also a strong intramolecular interaction of lone pair LP(3) O6to anti-bonding*(N24–H45) of the pterin ring,thus leading to the stabilization energy of 16.78 kcal/mol. Further, thermodynamic parameters like SCF energies, zero point vibrational energy, total thermal energies, entropies, enthalpies, Gibbs free energies and heat capacities were estimated at different temperaturefor both two forms of FA molecule. It was observed that the magnitude of thermodynamic functions increases with the temperature increasing because the intensity of the molecular vibration increases as the temperature rises.

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① Corresponding author. E-mail: sh_hamedani2004@yahoo.com (S. Hamedani)

10.14102/j.cnki.0254-5861.2011-0688

14 February 2015; accepted 10 August 2015