Open Access Research article

Quantum chemical assessment of benzimidazole derivatives as corrosion inhibitors

Hasan R Obayes1, Ghadah H Alwan2, Abdul Hameed MJ Alobaidy3, Ahmed A Al-Amiery34*, Abdul Amir H Kadhum4 and Abu Bakar Mohamad4

Author Affiliations

1 Applied Chemistry Division, Applied Science Department, University of Technology, Baghdad, Iraq

2 Ministry of Sciences and Technology, Industrial Research & Development Directorate, Industrial Applications Center, Baghdad, Iraq

3 Environmental Research Center, University of Technology (UOT), Baghdad 10001, Iraq

4 Department of Chemical & Process Engineering, Universiti Kebangsaan Malaysia (UKM), Bangi, Selangor 43000, Malaysia

For all author emails, please log on.

Chemistry Central Journal 2014, 8:21  doi:10.1186/1752-153X-8-21


The electronic version of this article is the complete one and can be found online at: http://journal.chemistrycentral.com/content/8/1/21


Received:18 January 2014
Accepted:21 March 2014
Published:27 March 2014

© 2014 Obayes et al.; licensee Chemistry Central Ltd.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

Abstract

Background

The majority of well-known inhibitors are organic compounds containing multiple bonds and heteroatoms, such as O, N or S, which allow adsorption onto the metal surface. These compounds can adsorb onto the metal surface and block active surface sites, reducing the rate of corrosion.

Results

A comparative theoretical study of three benzimidazole isomers, benzimidazole (BI), 2-methylbenzimidazole (2-CH3-BI), and 2-mercaptobenzimidazole (2-SH-BI), as corrosion inhibitors was performed using density functional theory (DFT) with the B3LYP functional basis set.

Conclusions

Nitro and amino groups were selected for investigation as substituents of the three corrosion inhibitors. Nitration of the corrosion inhibitor molecules led to a decrease in inhibition efficiency, while reduction of the nitro group led to an increase in inhibition efficiency. These aminobenzimidazole isomers represent a significant improvement in the inhibition efficiency of corrosion inhibitor molecules.

Keywords:
Benzimidazole; B3LYP; Corrosion; DFT; Inhibitor

Introduction

Corrosion is an electrochemical process by which metallic structures are destroyed gradually through anodic dissolution [1]. Protection of metallic surfaces can be achieved by the addition of specific compounds known as corrosion inhibitors [2]. Among the numerous corrosion prevention measures available, corrosion inhibitors, which have the advantages of economy, high-efficiency, and facile and feasible use, have been widely applied in various fields. As the importance of environmental protection has become increasingly recognized, the development of new green corrosion inhibitors has received increasing attention [3-5]. A variety of organic compounds containing heteroatoms (N, O, S) that can donate electron pairs have been used to inhibit brass corrosion in various aggressive electrolytes [6-11]. The use of organic inhibitors for preventing corrosion is a promising alternative. These inhibitors are usually adsorbed on the metal surface by the formation of a coordinate covalent bond (chemical adsorption) or an electrostatic interaction between the metal and inhibitor (physical adsorption) [12]. This adsorption produces a uniform film on the metal surface, which reduces or prevents contact with the corrosive medium [13]. Because organic inhibitors act by adsorption on the metal surface, the efficiency of these compounds depends strongly on their ability to form complexes with the metal [14]. Both p electrons and polar groups containing sulfur, oxygen and nitrogen are fundamental characteristics of this type of inhibitor. The polar functional groups serve as the chelation center for chemical adsorption [15]. Considerable effort has been devoted to studying the metallic corrosion inhibition properties of benzimidazole and its derivatives [16-20]. Benzimidazole is a heterocyclic aromatic organic compound with a bicyclic structure comprising fused benzene and imidazole rings [21]. The hydrogen atoms on the rings can be substituted by other groups or atoms. Some derivatives of benzimidazole are excellent corrosion inhibitors for metals and alloys in acidic solution; the level of inhibition varies with substituent groups and substituent positions on the imidazole ring [22-26]. The effects of the molecular structure on chemical reactivity have been studied extensively [27-31]. Density functional theory (DFT) was recently successfully applied to describe the structural importance of corrosion inhibitors and their adsorption efficiency on metal surfaces [32,33]. As part of the development of novel, more efficient organic corrosion inhibitors, several quantum-chemistry studies have been performed that relate inhibition efficiency to the molecular properties of the different types of compounds. The molecular structure and the electronic parameters, which can be obtained from theoretical calculations and include the HOMO (highest occupied molecular orbital) energy, the LUMO (lowest unoccupied molecular orbital) energy, and the energy of the gap, influence the inhibitor activity as well as reactivity, which can be treated by HSAB theory [34-42]. The aim of this work is to elucidate the electron configuration of benzimidazole (BI), 2-methylbenzimidazole (2-CH3-BI) and 2-mercaptobenzimidazole (2-SH-BI) inhibitors using DFT and determine the relationship between molecular structure and inhibition efficiency. The established correlation will facilitate the design and synthesis of new inhibitors with improved inhibition efficiency.

The calculation method

To calculate the ground-state geometries, Gaussian 03, Revision C.01 [43] was optimized to a local minimum without symmetry restrictions using the valence and polarization basis set (6-31G++(d,p)) [44,45]. A combination of the Becke three-parameter hybrid (B3) [46,47] exchange functional and the Lee-Yang-Parr (LYP) [48] correlation functional (B3LYP) [49,50], a version of the (DFT) method [51,52] was used to determine all optimized geometries, HOMO energies (EHOMO), LUMO energies (ELUMO), and physical properties for the molecules in this study.

Results and discussion

Two different groups were chosen as substituents of the corrosion inhibitor molecules BI, 2-CH3-BI, and 2-SH-BI to include the most important electronic effects. The first group (nitro (-NO2)) is a strong acceptor, while the second (amino (-NH2)) is a strong donor. The nitration of corrosion inhibitor molecules yielded four models for each of the corrosion inhibitor molecules, and the same number of models was obtained for the reduced nitro group [53].

Benzimidazole (BI)

The four positions of the nitro group substituent on the benzene ring in BI were C-4, C-5, C-6 and C-7. These positions make the same contribution to both the HUMO and LUMO levels with a small difference, as shown in Figure 1. Figure 1 also shows the structures of the optimized geometries for BI and the models studied. Table 1 presents the EHOMO, ELUMO and energy gap values for (BI) and all models. The ionization potential (I) and the electron affinity (A) were calculated by application of Koopman’s theorem [54]. This theorem establishes a relationship between the energies of the HOMO and the LUMO and the ionization potential and electron affinity, respectively.

thumbnailFigure 1. B3LYP/6-31G++(d,p) optimized geometries, HOMO and LUMO of benzimidazole (BI) and the optimized geometries of the eight models.

Table 1. Quantum-chemical parameters for benzimidazole (BI) and eight models as determined by DFT at the B3LYP/6-31G++ (d,p) level

I = - EHOMO

A = - ELUMO

Table 2 presents the calculated values of inhibition efficiency % for BI and eight models, which were determined using the following formula:

<a onClick="popup('http://journal.chemistrycentral.com/content/8/1/21/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://journal.chemistrycentral.com/content/8/1/21/mathml/M1">View MathML</a>

<a onClick="popup('http://journal.chemistrycentral.com/content/8/1/21/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://journal.chemistrycentral.com/content/8/1/21/mathml/M2">View MathML</a>

<a onClick="popup('http://journal.chemistrycentral.com/content/8/1/21/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://journal.chemistrycentral.com/content/8/1/21/mathml/M3">View MathML</a>

Table 2. The calculated inhibition efficiency % of benzimidazole (BI) and eight models

Where Iadd.% is the percentage ionization potential of the additive for model (x - BI), Ieadd.% is the inhibition efficiency %of the additive, and Ietheor.% is the theoretically calculated percentage inhibition efficiency.

These results demonstrate that the nitration of corrosion inhibitor molecules lead to a decrease in inhibition efficiency; the most efficient inhibitor was model (4-NO2-BI), which displayed an inhibition efficiency of 64.075%. By contrast, reduction of the nitro group led to an increase in inhibition efficiency; the most efficient inhibitor was model (7-NH2-BI), which displayed an inhibition efficiency of 85.609%. The inhibition efficiency of BI was 73.8%. These results represent a significant improvement in the inhibition efficiency of BI.

Methylbenzimidazole (2-CH3-BI)

The nitro group can be substituted at positions C-4, C-5, C-6 and C-7 on the benzene ring in 2- CH3-BI. These positions make the same contributions to the HUMO and LUMO levels, with the exception of position C-7, which is poor in the HUMO level as shown in Figure 2. Figure 2 also presents the structures of the optimized geometries for 2-CH3-BI and the studied models. Table 3 presents the EHOMO, ELUMO and energy gap values for (2-CH3-BI) and all models. Koopmans’ theorem was used to calculate I and A [50].

thumbnailFigure 2. B3LYP/6-31G++(d,p) optimized geometries, HOMO and LUMO of 2-methylbenzimidazole (2-CH3-BI) and the optimized geometries of eight models.

Table 3. Quantum-chemical parameters for 2-methylbenzimidazole (2-CH3-BI) and eight models obtained using DFT at the B3LYP/6-31G++ (d,p) level

Table 4 presents the calculated values of inhibition efficiency % for 2-CH3-BI and eight models, which were determined using the following formula:

<a onClick="popup('http://journal.chemistrycentral.com/content/8/1/21/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://journal.chemistrycentral.com/content/8/1/21/mathml/M4">View MathML</a>

<a onClick="popup('http://journal.chemistrycentral.com/content/8/1/21/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://journal.chemistrycentral.com/content/8/1/21/mathml/M5">View MathML</a>

<a onClick="popup('http://journal.chemistrycentral.com/content/8/1/21/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://journal.chemistrycentral.com/content/8/1/21/mathml/M6">View MathML</a>

Table 4. Calculated inhibition efficiency % for 2-methylbenzimidazole (2-CH3-BI) and eight models

Where Iadd.% is the percentage of ionization potential additive for model (x - 2 - CH3 - BI), Ieadd.% is the percentage of inhibition efficiency additive, and Ietheor.% is the theoretical calculated percentage of inhibition efficiency.

These results demonstrate that the nitration of corrosion inhibitor molecules decreases the inhibition efficiency; the highest inhibition efficiency, 66.001%, was obtained for the model (5-NO2-2-CH3-BI). By contrast, reduction of the nitro group led to an increase in inhibition efficiency; the highest inhibition efficiency, 87.44%, was observed for the model (7-NH2-2-CH3-BI). The inhibition efficiency of 2-CH3-BI was 76.3%. These results represent a significant improvement in the inhibition efficiency of 2-CH3-BI.

Mercaptobenzimidazole (2-SH-BI)

The positions on the benzene ring in 2-SH-BI that were substituted with nitro groups were C-4, C-5, C-6 and C-7. These positions make the same contribution to both the HUMO and LUMO levels, with a small difference as shown in Figure 3. Figure 3 also shows the structures of the optimized geometries for 2-SH-BI and the studied models. Table 5 presents the EHOMO, ELUMO and energy gap values for 2-SH-BI and all models. Koopman’s theorem was used to calculate I and A [50].

thumbnailFigure 3. B3LYP/6-31G++(d,p) optimized geometries, HOMO and LUMO of 2-mercaptobenzimidazole (2-SH-BI) and the optimized geometries of eight models.

Table 5. Quantum-chemical parameters for 2-mercaptobenzimidazole (2-SH-BI) and eight models determined using DFT at the B3LYP/6-31G++ (d,p) level

Table 6 presents the calculated values of inhibition efficiency % for 2-SH-BI and eight models, which were determined using the following formula:

<a onClick="popup('http://journal.chemistrycentral.com/content/8/1/21/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://journal.chemistrycentral.com/content/8/1/21/mathml/M7">View MathML</a>

<a onClick="popup('http://journal.chemistrycentral.com/content/8/1/21/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://journal.chemistrycentral.com/content/8/1/21/mathml/M8">View MathML</a>

<a onClick="popup('http://journal.chemistrycentral.com/content/8/1/21/mathml/M9','MathML',630,470);return false;" target="_blank" href="http://journal.chemistrycentral.com/content/8/1/21/mathml/M9">View MathML</a>

Table 6. Calculated inhibition efficiency % for 2-mercaptobenzimidazole (2-SH-BI) and eight models

Where Iadd.% is the percentage of ionization potential additive for model (x - 2 - SH - BI), Ieadd.% is the percentage of inhibition efficiency additive, and Ietheor.% is the theoretically calculated percentage of inhibition efficiency.

These results demonstrate that the nitration of corrosion inhibitor molecules led to a decrease in inhibition efficiency; the highest inhibition efficiency, 79.217%, was obtained for the model (5-NO2-2-SH-BI). By contrast, reduction of the nitro group led to an increase in inhibition efficiency; the highest inhibition efficiency, 101.382%, was obtained for the model (5-NH2-2-SH-BI). The inhibition efficiency of 2-SH-BI was 90.1%. These results represent a significant improvement in the inhibition efficiency of 2-SH-BI.

Conclusions

DFT quantum-chemical calculations established a correlation between parameters related to electronic structure and the corrosion inhibition potential of the three corrosion inhibitor molecules BI, 2-CH3-BI, and 2-SH-BI, as well as eight models for each inhibitor molecule. Most of the molecular parameters calculated at the B3LYP/6-311G++(d,p) level indicated that the nitration of corrosion inhibitor molecules led to a decrease in inhibition efficiency, while reduction of the nitro group led to an increase in inhibition efficiency. These results represent a significant improvement in inhibition efficiency compared to previously reported corrosion inhibitor molecules. An excellent correlation between inhibition efficiency and the studied models was obtained, confirming the reliability of the method employed.

Competing interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Authors’ contribution

HO carried out DFT studies. GA carried out the screening studies on corrosion. AA carried out the calculation of inhibition efficiency. AA carried out the computational experiments. AK conceived of the study. AM draft the manuscript. All authors read and approved the final manuscript.

References

  1. Uhlig HH, Revie RW: Corrosion and Corrosion Control. 3rd edition. New York: John Wiley & Sons; 1985:1. OpenURL

  2. Sastri VS: Corrosion Inhibitors: principles and applications. New York: John Wiley & Sons Ltd; 1998:25-237. OpenURL

  3. Duda Y, Govea-Rueda R, Galicia M, Beltran HI, Zamudio-Rivera LS: Corrosion inhibitors: design, performance, and computer simulations.

    J Phys Chem 2005, B109:22674-22684. OpenURL

  4. Gَmez B, Likhanova NV, Dominguez Aguilar MA, Olivares O, Hallen JM, Martinez-Magadلn JM: Theoretical study of a new group of corrosion inhibitors.

    J Phys Chem A 2005, 109:8950-8957. PubMed Abstract | Publisher Full Text OpenURL

  5. Rodrيguez-Valdez LM, Martيnez-Villafa˜ne A, Glossman-Mitnik D: Computational simulation of the molecular structure and properties of heterocyclic organic compounds with possible corrosion inhibition properties.

    J. Mol. Struct.-Theochem 2005, 713:65-70. Publisher Full Text OpenURL

  6. Abd El-Maksoud SA:

    Electrochim Acta. 2004, 49:4205. Publisher Full Text OpenURL

  7. Quartarone G, Bellomi T, Zingales A:

    Corros Sci. 2003, 45:715. Publisher Full Text OpenURL

  8. Zucchi F, Trabanelli G, Fonsati M:

    Corros Sci. 1996, 38:2019. Publisher Full Text OpenURL

  9. Wang DX, Li SY, Ying Y, Wang MJ, Xiao HM, Chen ZX:

    Corros Sci. 1999, 41:1911. Publisher Full Text OpenURL

  10. Ravichandran R, Rajendran N:

    Appl Surf Sci. 2005, 241:449. Publisher Full Text OpenURL

  11. Jamil HE, Shriri A, Boulif R, Bastos C, Montemor MF, Ferreira MGS:

    Electrochim Acta. 2004, 49:2753. Publisher Full Text OpenURL

  12. Noor EA: The inhibition of mild steel corrosion in phosphoric acid solutions by some N-heterocyclic compounds in the salt form.

    Corros Sci 2005, 47:33-55. Publisher Full Text OpenURL

  13. Avci G: Inhibitor effect of N, N0-methylenediacrylamide on corrosion behavior of mild steel in 0.5 M HCl.

    Mater Chem Phys 2008, 112:234-238. Publisher Full Text OpenURL

  14. Shukla SK, Quraishi MA: Cefotaxime sodium: a new and efficient corrosion inhibitor for mild steel in hydrochloric acid solution.

    Corros Sci 2009, 51:1007-1011. Publisher Full Text OpenURL

  15. de Souza FS, Spinelli A: Caffeic acid as a green corrosion inhibitor for mild steel.

    Corros Sci 2009, 51:642-649. Publisher Full Text OpenURL

  16. Bentiss F, Traisnel M, Gengembre L, Lagrenee M: A new triazole derivative as inhibitor of the acid corrosion of mild steel: electrochemical studies, weight loss determination, SEM and XPS.

    Appl Surf Sci 1999, 152:237-249. Publisher Full Text OpenURL

  17. Wang L: Evaluation of 2-mercaptobenzimidazole as corrosion inhibitor for mild steel in phosphoric acid.

    Corros Sci 2001, 43:2281-2289. Publisher Full Text OpenURL

  18. Popova M, Christov T: Deligeorgiev, Influence of the molecular structure on the inhibitor properties of benzimidazole derivatives on mild steel corrosion in 1 M hydrochloric acid.

    Corrosion 2003, 59:756-764. Publisher Full Text OpenURL

  19. Khaled KF: The inhibition of benzimidazole derivatives on corrosion of iron in 1 M HCl solutions.

    Electrochim Acta 2003, 48:2493-2503. Publisher Full Text OpenURL

  20. Zhang F, Tang Y, Cao Z, Jing W, Wu Z, Chen Y: Performance and theoretical study on corrosion inhibition of 2-(4-pyridyl)-benzimidazole for mild steel in hydrochloric acid.

    Corros Sci 2012, 61:1-9. OpenURL

  21. Obot IB, Obi-Egbedi NO: Theoretical study of benzimidazole and its derivatives and their potential activity as corrosion inhibitors.

    Corros Sci 2010, 52:657-660. Publisher Full Text OpenURL

  22. Ahamad MA: Quraishi, Bis (benzimidazol-2-yl) disulphide: an efficient water soluble inhibitor for corrosion of mild steel in acid media.

    Corros Sci 2009, 51:2006-2013. Publisher Full Text OpenURL

  23. Ahamad MA: Quraishi, Mebendazole: new and efficient corrosion inhibitor for mild steel in acid medium.

    Corros Sci 2010, 52:651-656. Publisher Full Text OpenURL

  24. Popova M, Christov A: Vasilev, Inhibitive properties of quaternary ammonium bromides of N-containing heterocycles on acid mild steel corrosion. Part II: EIS results.

    Corros Sci 2007, 49:3290-3302. Publisher Full Text OpenURL

  25. Christov M, Popova A: Adsorption characteristics of corrosion inhibitors from corrosion rate measurements.

    Corros Sci 2004, 46:1613-1620. Publisher Full Text OpenURL

  26. Popova M, Christov S, Raicheva E: Sokolova, Adsorption and inhibitive properties of benzimidazole derivatives in acid mild steel corrosion.

    Corros Sci 2004, 46:1333-1350. Publisher Full Text OpenURL

  27. Growcock FB, Lopp VR: The inhibition of steel corrosion in hydrochloric acid with 3-phenyl-2-propyn-1-ol.

    Corrosion Science 1988, 28(4):397-410. Publisher Full Text OpenURL

  28. Khalil N:

    Electrochimica Acta. 2003, 48:2635. Publisher Full Text OpenURL

  29. Lukovits I, Pa’lfi K, Bako’ I, Ka’lma’n E: LKP model of the inhibition mechanism of thiourea compounds.

    Corrosion 53:915-917. OpenURL

  30. Bentiss F, Traisnel M, Vezin H, Lagrene’e M: Linear resistance model of the inhibition mechanism of steel in HCl by triazole and oxadiazole derivatives: structure–activity correlations.

    Corrosion Science 2003, 45(2):371-380. Publisher Full Text OpenURL

  31. Abdul-Ahad PG, Al-Madfai SHF: Elucidation of corrosion inhibition mechanism by means of calculated electronic indexes.

    Corrosion 1989, 45:978-980. Publisher Full Text OpenURL

  32. Cruz J, Pandiyan T, Garc’ıa-Ochoa E:

    J. Electroanal. Chem.. 2005, 583:8. Publisher Full Text OpenURL

  33. Cruz J, Mart’ınez R, Genesca J, Garc’ıa-Ochoa E: Experimental and theoretical study of 1-(2-ethylamino)-2-methylimidazoline as an inhibitor of carbon steel corrosion in acid media.

    J. Electroanal. Chem 2004, 566:111-121. Publisher Full Text OpenURL

  34. Sayo’s R, Gonza’lez M, Costa JM: On the use of quantum chemical methods as an additional tool in studying corrosion inhibitor substances.

    Corrosion Science 1986, 26(11):927-934. Publisher Full Text OpenURL

  35. O¨ G, Mihci B, Bereket G:

    J Mol Struct Theochem. 1999, 488:223. Publisher Full Text OpenURL

  36. Li SL, Wang YG, Chen SH, Yu R, Lei SB, Ma HY, Liu DX: Some aspects of quantum chemical calculations for the study of Schi€ base corrosion inhibitors on copper in NaCl solutions.

    Corrosion Science 1999, 41:1769-1782. Publisher Full Text OpenURL

  37. Lukovits I, Ka’lma’n E, Zucchi F: Corrosion inhibitors—correlation between electronic structure and efficiency.

    Corrosion 2001, 57:3-8. Publisher Full Text OpenURL

  38. Martinez S: Inhibitory mechanism of mimosa tannin using molecular modeling and substitutional adsorption isotherms.

    Materials Chemistry and Physics 2003, 77(1, 2):97-102. OpenURL

  39. Bereket G, Gretir CO¨, Zpahin CO¨:

    Journal of Molecular Structure (Theochem). 2003, 663:39. Publisher Full Text OpenURL

  40. Cruz J, Garcı’a-Ochoa E, Castro M: Experimental and Theoretical Study of the 3-Amino-1,2,4-triazole and 2-Aminothiazole Corrosion Inhibitors in Carbon Steel.

    J. Electrochem. Soc 2003, 150:B26. Publisher Full Text OpenURL

  41. Awad MK:

    J Electroanal Chem. 2004, 567:219. Publisher Full Text OpenURL

  42. Blajiev O, Hubin A:

    Electrochimica Acta. 2004, 49:2761. Publisher Full Text OpenURL

  43. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA: Gaussian 09 series programs–Revision A. Wallingford, CT, USA: Gaussian, Inc; 2009:1. OpenURL

  44. Pietro WJ, Francl MM, Hehre WJ, Defrees DJ, Pople JA, Binkley JS: Self-consistent molecular orbital methods. 24. Supplemented small split-valence basis sets for second-row elements.

    J. Am. Chem. Soc 1982, 104(19):5039-5048. Publisher Full Text OpenURL

  45. Dobbs KD, Hehre WJ: Molecular orbital theory of the properties of inorganic and organometallic compounds 5. Extended basis sets for first-row transition metals.

    J Comput Chem 1987, 861-879. OpenURL

  46. Becke AD: Density-functional exchange-energy approximation with correct asymptotic behavior.

    Phys. Rev 1988, 38:3098-3100. Publisher Full Text OpenURL

  47. Becke AD: Density-functional thermochemistry—III. The role of exact exchange.

    J Chem. Phys 1993, 98(7):5648-5652. Publisher Full Text OpenURL

  48. Lee C, Yang W, Parr RG: Development of the ColleSalvetti correlation-energy formula into a functional of the electron density.

    Phys. Rev 1988, 37:785-789. Publisher Full Text OpenURL

  49. Al-Amiery AA, Jaffar HD, Obayes HR, Musa AY, Kadhum AH, Mohamad A: Thermodynamic studies on 4-aminocoumarin tautomers.

    Int J Electrochem. Sci 2012, 7:8468-8472. OpenURL

  50. Naama JH, Alwan GH, Obayes HR, Al-Amiery A, Al-Temimi A, Kadhum AH, Mohamad A: Curcuminoids as antioxidants and theoretical study of stability of curcumin isomers in gaseous state.

    Res Chem Intermediat 2013, 39(9):4047-4059. Publisher Full Text OpenURL

  51. Obayes HR, Al-Amiery AA, Jaffar HD, Musa AY, Kadhum AH, Mohamad A: ”Theoretical study for the preparation of sub-carbon nano tubes from the cyclic polymerization reaction of two molecules from corannulene, coronene and circulene aromatic compounds”.

    J. Comput. Theor. Nanosci 2013, 10:2459-2463. OpenURL

  52. Obayes HR, Alwan GH, Al-Amiery AA, Kadhum AH, Mohamad A: Thermodynamic and theoretical study of the preparation of new buckyballs from corannulene, coronene, and circulene.

    J Nanomater 2013, 2013:8.

    Article ID 451920

    OpenURL

  53. Fomina L, Porta B, Acosta A, Fomine S: Novel substituted 1-amino-4,5,8-naphthalenetricarboxylic acid-1,8-lactam-4,5-imides: experimental and theoretical study.

    J. Phys. Org. Chem. 2000, 13:705-712. Publisher Full Text OpenURL

  54. Lukovits I, Kalman E, Zucchi F: Corrosion inhibitors—correlation between electronic structure and efficiency.

    Corrosion 2001, 57:3-8. Publisher Full Text OpenURL