1 Introduction

Every organism takes place cells in the world; all multicellular organisms have a cell and a cell nucleus. This nucleus includes the DNA, the hereditary material. DNA is short for deoxyribonucleic acid. In every nucleus of an organism the DNA is exactly the same in all cells. DNA consists of four different bases (nucleotides) adenine, thymine, guanine, and cytosine. Ribonucleic acid (RNA) is synthesized in the nucleus and is very similar to DNA. The synthesis of RNA also involves the use of bases, but in RNA synthesis no thymine is used but uracil is used instead.

Corrosion is a major problem in today’s industry. Corrosion is an erosion of the surface of metal or metal alloys by oxidation or other chemical effects. Many methods are used to inhibit corrosion in industry. The corrosion inhibitors adsorbed on metal surfaces are p-conjugated systems and heterocyclic organic compounds [1, 2]. Many of the organic and inorganic inhibitors containing nitrogen, oxygen, sulfur, and an aromatic ring are widely used against corrosion in recently studies.

In the Density Functional Theory, quantum chemical parameters such as highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), electrophilicity, electronegativity, chemical potential, chemical hardness, and nucleophilicity are a very important for reactivity [3,4,5,6,7,8,9,10,11]. In this study, we have studied in detail the inhibition performance of five compounds, adenine, thymine, guanine, cytosine, and uracil.

The hard and soft acid–base (HSAB) method [12, 13] is a very important method in corrosion. According to HSAB method, Pearson says that “hard acids prefer to coordinate to hard bases and soft acids prefer to coordinate to soft bases”. The non-polarized chemical species is described by the hard concept. As it is well-known that hetero atom-containing structures give electrons easily to metals [14]. The molecular structures of studied molecules are given in Fig. 1.

Fig. 1
figure 1

The structure and schematic representation of molecules of DNA and RNA

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2 Computational Details

Density functional theory (DFT) is absolutely the most widely used method for the prediction of chemical reactivity of studied molecules. In this study, the input files of studied molecules were prepared with GausView 5.0.8 programs [15]. Calculations were performed by using Gaussian IA32W-G09RevA.02 and Gaussian AS64L-G09RevD.01 programs [16, 17]. A full optimization was applied using the HF and DFT/B3lyp methods with sdd, 6-31g and 6-31++g basis sets in gas and aqueous phase. With the help of this theory, the evaluation of chemical reactivity of molecules has existed a very popular in the theoretical method. Chemical reactivity descriptors include EHOMO, ELUMO, ΔE (HOMO–LUMO energy gap), electronegativity (χ), chemical potential (µ), chemical hardness (η), electrophilicity (ω), nucleophilicity (ε), global softness (σ), and proton affinity (PA).

$$\mu = - \chi ={\left( {\frac{{\partial E}}{{\partial N}}} \right)_{\upsilon (r)}}$$
(1)
$$\eta =\frac{1}{2}{\left( {\frac{{{\partial ^2}E}}{{\partial {N^2}}}} \right)_{\upsilon (r)}}=\frac{1}{2}\left( {\frac{{\partial \mu }}{{\partial N}}} \right)$$
(2)

Electronegativity, global softness, and chemical hardness have pertained to ionization energy (I) and electron affinity (A) values of chemical molecules obtaining the following equations.

$$\chi = - \mu =\left( {\frac{{I+A}}{2}} \right)$$
(3)
$$\eta =\frac{{I - A}}{2}$$
(4)

It is well-known that the negative value of the highest occupied molecular orbital energy and the negative value of the lowest unoccupied molecular orbital energy were attached to the ionization energy and electron affinity, respectively (− EHOMO = I and − ELUMO = A). on the other hand, the global softness is described as the inverse of the chemical hardness.

$$\sigma =1/\eta$$
(5)
$$\chi = - \mu =\left( {\frac{{ - {E_{{\text{HOMO}}}} - {E_{{\text{LUMO}}}}}}{2}} \right)$$
(6)
$$\eta =\left( {\frac{{{E_{{\text{LUMO}}}} - {E_{{\text{HOMO}}}}}}{2}} \right)$$
(7)

The global electrophilicity index (ω) presented by Parr et al. [18] is the inverse of nucleophilicity and is expressed as in Eq. (8). Electrophilicity power of studied molecules is interrelated with its global softness and electronegativity. Nucleophilicity (ε) is described as the inverse of the electrophilicity in Eq. (9).

$$\omega ={{{\mu ^2}} \mathord{\left/ {\vphantom {{{\mu ^2}} {2\eta }}} \right. \kern-0pt} {2\eta }}={{{\chi ^2}} \mathord{\left/ {\vphantom {{{\chi ^2}} {2\eta }}} \right. \kern-0pt} {2\eta }}$$
(8)
$$\varepsilon =1/\omega$$
(9)

3 Result and Discussion

3.1 Quantum Chemical Calculation

The corrosion inhibitor efficiencies of the DNA–RNA molecules were investigated by molecular docking and quantum chemical. The result obtained of these molecules indicated that studied molecules are good inhibitors. Molecular docking and quantum chemical calculations were performed and these molecules are very active against corrosion. The obtained result of molecules is given in detail below.

In this study, quantum chemical parameters, for example, EHOMO, ELUMO, ΔE (HOMO–LUMO energy gap), global softness, chemical hardness, electrophilicity, nucleophilicity, proton affinity, and electronegativity are very important parameters to compare the of performances of inhibition molecules [19]. The studied molecules for protonated and non-protonated forms were investigated by quantum chemical calculation in both gas and aqueous phase and are presented in Tables 1, 2, 3, and 4.

Table 1 All parameter for neutral forms of inhibitor molecules in gas phase (eV)
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Table 2 All parameters for neutral forms inhibitor molecules in aqueous phase (eV)
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Table 3 All parameter for protonated molecules in gas phase (eV)
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Table 4 All parameter for protonated molecules in aqueous phase (eV)
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The prediction of chemical reactivity of molecules was compared by frontier molecular orbital of studied molecules. The energy of HOMO has expressed the electron donating ability of studied molecules in Fig. 2. The molecule that has high values of energy of HOMO shows the tendency to donate the electrons of the molecule to appropriate acceptor molecules [20,21,22,23,24,25,26,27]. As a result of this theorem that the inhibition efficiencies to HOMO energy value follow the order: guanine > adenine > cytosine > thymine > uracil in all basis set. In consideration of previous explanation, energy levels of LUMO orbital of molecules are demonstrating electron accepting abilities of inhibitor molecules in Fig. 2. If the molecule has lower values of energy of LUMO, this molecule has more electron accepting ability. On the basis of the calculated LUMO energy level value given in Tables 1 and 2, the corrosion inhibition efficiency ranking of DNA-RNA molecules can be written as: guanine > adenine > cytosine > thymine > uracil.

Fig. 2
figure 2

Structures of HOMO, LUMO, and ESPs of molecules of DNA and RNA

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The energy gap (ΔE) is a very important parameter for chemical reactivity of corrosion inhibitor molecules. As it is well-known, molecule that has a small energy gap value is a good corrosion inhibitor. Because the energy gap value demonstrates the binding ability of studied molecules on metal surfaces. In consideration of previous explanations, one of the studied molecules that have a high energy gap is harder compared to other molecules [20,21,22,23,24]. We can be seen from Tables 1 and 2, Guanine has the smallest energy gap in HF/6-31++G basis set.

Chemical hardness is described that the resistance to electron cloud polarization or deformation of chemical species. This parameter is a very important both experimental and theoretical chemistry. A chemical species tends to achieve maximum hardness. In addition, it is a measure of the stability of the chemical hardness. In quantum chemical calculations, chemical hardness, ΔE, and global softness are very important parameters that are attached to each other. According to Koopman’s theorem [28], both chemical hardness value and global softness value have occurred HOMO and LUMO energy value. Soft molecules that have low HOMO–LUMO energy gap can be good corrosion inhibitor in view of the fact that soft molecules can very readily give electron of HOMO to metals [20,21,22,23,24]. From the light of the result given in Tables 1 and 2, we can write the corrosion inhibitor ranking of three parameter that is chemical hardness, global softness, and HOMO–LUMO energy gap value as: guanine > adenine > cytosine > thymine > uracil in HF/6-31++G basis set.

Electronegativity is a very important parameter that is a numerical value that is considered to predict the electron transfer between the metal and inhibitor [4]. Molecules having high electronegativity can’t act as good corrosion inhibitor. If the molecule has a high electronegativity value, the molecule cannot be a good corrosion inhibitor [20,21,22,23,24]. We have calculated the value of electrons transferred from corrosion inhibitor molecule to metal (ΔN) via the following equation by Sanderson’s electronegativity equalization principle [29, 30].

$$\Delta N=\frac{{{\chi _{\text{M}}} - {\chi _{{\text{inh}}}}}}{{2({\eta _{\text{M}}}+{\eta _{{\text{inh}}}})}}$$
(10)

where \({\chi _{\text{M}}}\) and \({\chi _{{\text{inh}}}}\) are electronegativity of metal and electronegativity of corrosion inhibitor molecule, respectively.\(~{\eta _{\text{M}}}\) and \({\eta _{{\text{inh}}}}\) are the chemical hardness of metal and chemical hardness of corrosion inhibitor molecule, respectively. From the light of the result given in Tables 1 and 2, we have seen that guanine has the lowest electronegativity value in all basis set. Electronegativity value of corrosion inhibitor ranking follows the order: guanine > adenine > cytosine > thymine > Uracil.

In all parameters of quantum chemical calculation, we can see that guanine is the best corrosion inhibitor. On the other hand, A similar ranking was obtained in the experimental study conducted by Kassou et al. [31] who make the comparative study of low carbon steel corrosion inhibition by amino acid compounds.

3.2 Molecular Docking Calculation

The interaction between studied molecules and B-DNA dodecamer d(CGCCAATTCGCG)2 (PDB code:1BNA) is examined to find the activity of studied molecules by DockingServer. In Fig. 3, molecules of guanine, adenine, cytosine, thymine, and uracil aree interacting with B-DNA dodecamer. Obtained results give information about this interaction. Many studies have been carried out on the biological activities of molecules [32, 33]. Many programs are used to study biological activities [34, 35]. Highly biologically active molecules are used as a good corrosion inhibitor. Studied DNA–RNA molecules are compared to activity using the molecular docking program.

Fig. 3
figure 3

Interactions between protein and adenine (a), guanine (b), cytosine (c), thymine (d), and uracil (e)

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Molecular docking is a very useful tool for obtaining an information of ligand–receptor interactions. Studied molecules are interacted with generally the upper region of 1BNA. These interactions are almost dipole–dipole interactions. For each interaction, heteroatoms increase the biological reactivity of these molecules.

In Table 5, we can see that interaction energies are formed when molecules bind to the protein. According to obtained results for molecules, inhibition constant is 1.70, 2.90, 10.21, 11.37, and 11.29 for guanine, adenine, thymine, cytosine, and uracil, respectively. Value of Ki gives information that both molecules can inhibit an enzyme and molecules can interact with a substrate for the enzyme. If Ki has bigger value, the extra drug is needed to inhibit the enzyme activity. The vdW, hydrogen bond, and dissolved energy are the numerical value of the position the molecule receives relative to the target protein. vdW, hydrogen bond, and dissolved energy have negative value, the molecule is well-bonded to an active site on the protein. In addition, the electrostatic energy has a negative value, and this value shows that the molecule is linked to a protein [25].

Table 5 Molecular docking energy data for studies molecule
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4 Conclusions

From the light of the the result given in this paper, quantum chemical parameters and results of molecular docking give information about inhibition of studied molecule. Parameters such as HOMO, LUMO, and ΔE (HOMO–LUMO energy gap) demonstrate which molecule is the better inhibitor. Results of molecular docking give information about molecular activity. The molecule with the higher molecular activity is the better inhibitor. in quantum chemical calculation, studied molecules are investigated in different basis sets that show how molecule activity is affected. Results of molecular docking give six parameters that offer knowledge about molecular inhibition. In quantum chemical calculations, the neutral and protonated forms are studied in gas and aqueous phases. In this study, following obtained results are presented.

  1. 1.

    The results of quantum chemical calculation and molecular docking calculations showed that the corrosion inhibition ranking of DNA–RNA molecules can be presented as: guanine > adenine > cytosine > thymine > uracil.

  2. 2.

    The obtained different parameters of molecular docking software show that guanine is good activity molecule against B-DNA dodecamer d(CGCCAATTCGCG)2 (PDB code:1BNA).

  3. 3.

    In this study, the theoretical results obtained are very important towards rational designing of new molecules as a corrosion inhibitor.