1 Introduction

Piperazine and its derivatives exist in many drug structures such as antipsychotic, antidepressant and anti-tumour activities against colon, prostate, breast and lung tumours [1,2,3,4,5]. These drugs are essential stimulants for the central nervous system that have the reputation of copycat psychoactive effects. Also, these classes of molecules are commonly used to produce some plastics, resins, pesticides, brake fluid and many other industrial materials for several important applications [6, 7]. The biological evaluation of piperazine derivatives has been investigated [8], but the physical assessment of N-(4-methoxyphenyl) piperazine isomers were not examined yet. One of the most important members of this class of molecules is N-(4-methoxyphenyl) piperazine (MeOPP). MeOPP has three isomers called as ortho-, meta- and para-MeOPP. Experimental and theoretical studies both have been carried out for various piperazine derivatives and reported in literature [9,10,11,12]. However, both experimental and theoretical studies on MeOPP molecule are quite insufficient for determination of the physical and chemical properties. The crystal structure of the pMeOPP molecule and its salts have been investigated recently [13]. A detailed theoretical and experimental study of the oMeOPP molecule was carried out by Prabavathi et al. [11]. In this study, FT-IR, FT-Raman, NMR and UV–Vis spectral measurements were experimentally investigated. Theoretically, the density functional theory (DFT) method, using B3LYP functional, with a 6-311++G (d, p) basis set, has been performed for assigning vibrational frequencies of oMeOPP molecule. In addition, molecular electrostatic potential (MEP) and natural bond orbital (NBO), highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO) and nonlinear optical (NLO) properties have been studied. However, a literature search reveals that such a detailed study for pMeOPP and mMeOPP isomers has not been declared so far.

This study aims to obtain the most stable optimized structures of pMeOPP and mMeOPP isomers of molecules and to investigate the physical properties of these structures theoretically. To the best of the authors’ knowledge, a detailed description of the physical properties of these isomers of molecule has been reported using neither experimental nor theoretical methods. It has also been shown how physical properties are affected for isomer structures.

2 Details of Calculation

In this work, firstly, conformer analysis for each isomer of MeOPP molecules was performed with the Spartan 08 package program [14], where conformational analysis was done using Merck molecular force field (MMFF) in the molecular mechanic method. Performance steps followed in the conformer analysis have been given in detail in previous studies [15, 16]. Secondly, a quantum chemical calculation for each isomer of MeOPP molecules was performed using the GAUSSIAN 09 program [17] with density functional theory [18] using the Becke three-parameter Lee–Yang–Parr exchange correlation functional (B3LYP) [19]. In addition, calculations were supplied by the standard 6-311++G (d,p) basis set. The UV–vis spectra of isomers have been computed by courtesy of time-dependent density functional theory (TD-DFT) [20] using the same basis set and exchange correlation functional.

3 Results and Discussion

3.1 Molecular Conformation and Geometrical Structure Analysis

Conformer analysis is an important step in obtaining the most stable structure of the molecule. Conformational analyses of pMeOPP, mMeOPP and oMeOPP isomers were carried out using the Spartan 08 package program with MMFF in the molecular mechanic method. As results of conformer analysis, pMeOPP, mMeOPP and oMeOPP compounds have one, two and five conformers, respectively. The shapes of these structures are shown in Fig. 1.

Fig. 1
figure 1

Possible conformers of pMeOPP, mMeOPP and oMeOPP isomers

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A calculation for geometry optimization is one of the most important steps in the theoretical studies. In order to determine stable conformations of isomers, structure and geometry optimizations of these conformers were performed using the B3LYP method with the 6-311++G(d,p) basis set and the most stable structures were determined. Also, the energy and dipole moments of the optimized structures are given in Table 1.

Table 1 Conformer energies and dipole moment values of pMeOPP, mMeOPP and oMeOPP isomers
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As shown in Table 1, the most stable structures of isomers are conf 1p of pMeOPP, conf 2m of mMeOPP and conf 5o of oMeOPP. Considering dipole moment values among isomers, it can be seen that they have an order of oMeOPP > pMeOPP > mMeOPP, from the largest one to the smallest one, respectively.

The selected geometric parameters (bond lengths, bond angles and dihedral angles) obtained from optimization calculations performed are presented in Table 2. The structural database analysis results specifically show the C–O–C–C dihedral angle which is usually 0° or 180°. The O–C–C angle at the aromatic ring is 115° or 125°. In the study, the O–C–C angle of isomers has been calculated as pMeOPP (116.2°), mMeOPP (124.1°) and oMeOPP (121.2°) respectively, in addition, the C–O–C–C dihedral angle of isomers has been calculated as pMeOPP (−0.29° or 179.7°) and mMeOPP (178.9°). However, this angle of the oMeOPP isomer is −77.06° and nearly orthogonal to the ring system. In addition, the methoxyphenyl group orientation in isomer structures was obtained as either co-planar with the aromatic ring or oriented nearly orthogonal to this ring system.

Table 2 The selected geometric parameters of pMeOPP, mMeOPP and oMeOPP isomers
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In literature, piperazines have been found generally in chair, half chair, boat, twist, boat and envelope forms [21, 22]. In this study, isomer structures of the MeOPP molecule have been obtained as chair conformation and approved by dihedral angles C1-N19-C5-C6. The pMeOPP isomer of the subject molecule has been experimentally studied; X-ray diffraction (XRD) data can be obtained [13] from literature, but XRD data for mMeOPP and oMeOPP isomers are not available yet in literature. Data from the oMeOPP isomer obtained by theoretical studies is also available and obtained from literature. By courtesy of these data, it can be concluded that our results obtained in this present work about molecular structures determined by conformer analysis are quite compatible with theoretical and experimental XRD results from literature.

3.2 HOMO–LUMO and Chemical Reactivity Descriptors

The main orbitals of a molecule are frontier molecular orbitals that are symbolized as highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). HOMO symbolizes the stability to donate an electron of a molecular system, while LUMO symbolizes the stability to obtain an electron. The energy difference between HOMO and LUMO is known as the energy gap. It is an important parameter to assign electrical transport properties of a molecule and a measure of electron conductivity. Also, global chemical reactivity descriptors such as ionization potential (I), electron affinities (A), chemical potential (μ), absolute hardness (η), absolute softness (S), electrophilic index (ω) and electronegativity (χ) of a molecular system have been calculated by using HOMO and LUMO energies. All isomeric structures of high occupied orbital and low unoccupied orbitals of MeOPP molecule are shown in Fig. 2.

Fig. 2
figure 2

HOMO and LUMO for pMeOPP, mMeOPP and oMeOPP isomers

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The red- and green-coloured orbitals in the molecule show positive and negative phases. The obtained results show that LUMO structures in isomers are generally on the benzene ring while HOMO structure is in almost the whole molecule.

The chemical reactivity descriptors have been calculated by courtesy of Koopman’s theorem [23]. In this theorem, I and A are the ionization potential and electron affinity, respectively. Ionization potential has been determined from \(I={-E}_{\mathrm{HOMO}}\) and the electron affinity has been calculated from \(A={-E}_{\mathrm{LUMO}}\). The chemical hardness and softness have been calculated by using \(\eta = \frac{1}{2}\left[{E}_{\mathrm{LUMO}}-{E}_{\mathrm{HOMO}}\right]\) and \(\mathrm{S}= \frac{1}{2\eta }\), respectively. Electronegativity has been determined by using the \(\chi = - \frac{1}{2} \left[{E}_{\mathrm{HOMO}}+{E}_{\mathrm{LUMO}}\right]\) \(\chi = -\frac{1}{2}\left[{E}_{\mathrm{HOMO}}+{E}_{\mathrm{LUMO}}\right]\) formula [24]. The electrophilicity index has been determined by using the \(\omega = \frac{{\mu }^{2}}{2\eta }\) formula [25]. The obtained chemical reactivity descriptors are given in Table 3.

Table 3 Chemical reactivity descriptors of pMeOPP, mMeOPP and oMeOPP isomers
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The results obtained in this work indicate that the oMeOPP isomer is harder than other isomers and the pMeOPP isomer is softer than other isomers. The ionization potentials for oMeOPP, mMeOPP, and pMeOPP are 8.43, 8.32 and 7.94 eV, respectively. The electrochemical potential (μ) is in order of mMeOPP ≈ pMeOPP > oMeOPP. The electrophilicity values for isomers are in order of pMeOPP > oMeOPP ≈ mMeOPP, while the electronegativity values are ranked as oMeOPP > mMeOPP > pMeOPP.

3.3 Nonlinear Optical Properties

The nonlinear optical properties (NLO) of the MeOPP isomer were studied by calculating the dipole moment, the polarizability and the first hyper polarizability using the B3LYP/6-311++G(d,p) level of DFT theory. The dipole moment (μ), the polarizability (α) and the first hyper polarizability (β) have been calculated from the equations given below and are reported in Table 4.

Table 4 The values of calculated dipole moment (µ), polarizability (α), first-order hyper-polarizability (β) components of pMeOPP, mMeOPP and oMeOPP isomers
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The total dipole moment (\({\mu }_{\mathrm{tot}}\)) for the molecule is defined as in Eq. 1:

$${\mu }_{\mathrm{tot}}= {\left({\mu }_{x}+{\mu }_{y}+{\mu }_{z}\right)}^{\raisebox{1ex}{1}\!\left/ \!\raisebox{-1ex}{2}\right.}$$
(1)

Total polarizability (\({\alpha }_{\mathrm{tot}}\)) for the molecule can be evaluated as in Eq. 2:

$${\alpha }_{\mathrm{tot}}=\frac{1}{3} \left({\alpha }_{xx}+{\alpha }_{yy}+{\alpha }_{zz}\right)$$
(2)

The total first hyper polarizability (\({\beta }_{\mathrm{tot}}\)) can be calculated as in Eq. 3:

$${\beta }_{\mathrm{tot}}= {\left({\beta }_{x}^{2}+{\beta }_{y}^{2}+{\beta }_{z}^{2}\right)}^{\raisebox{1ex}{1}\!\left/ \!\raisebox{-1ex}{2}\right.}$$
(3)

were \({\beta }_{x}\), \({\beta }_{y}\) and \({\beta }_{z}\) are defined to be

$${\beta }_{x}= \left({\beta }_{xxx}+{\beta }_{xyy}+{\beta }_{xzz}\right)$$
(4)
$${\beta }_{y}= \left({\beta }_{yyy}+{\beta }_{yzz}+{\beta }_{yxx}\right)$$
(5)
$${\beta }_{z}= \left({\beta }_{zzz}+{\beta }_{zxx}+{\beta }_{zyy}\right)$$
(6)

The total first hyper-polarizability from the Gaussian 09 output is given in Eq. 7.

$$\begin{aligned}{\beta }_{\mathrm{tot}}=& \left[{\left({\beta }_{xxx}+{\beta }_{xyy}+{\beta }_{xzz}\right)}^{2}+{\left({\beta }_{yyy}+{\beta }_{yzz}+{\beta }_{yxx}\right)}^{2}\right.\\&\left.+{\left({\beta }_{zzz}+{\beta }_{zxx}+{\beta }_{zyy}\right)}^{2}\right]^{\raisebox{1ex}{1}\!\left/ \!\raisebox{-1ex}{2}\right.}\end{aligned}$$
(7)

The dipole moment is one of some important results for electronic properties due to the distribution of charges on atoms in a molecule and used to investigate the intermolecular interactions. The higher the dipole moment is, the stronger the intermolecular interactions are. The polarizability and the first hyper-polarizability characterize the response of a molecule in an applied electric field [26]. (The calculated \({\upbeta }_{\mathrm{tot}}\) and \({{\alpha }}_{\mathrm{tot}}\) values in Table 4 were converted into electrostatic units (esu) [1 a.u. = 8.6393 × 10–33 esu] and [1 a.u. = 0.1482 × 10−24 esu], respectively [27, 28].) As seen in Table 4, the polarizability values of the pMeOPP, mMeOPP and oMeOPP isomers have been calculated to be 23.099 × 10–24, 23.056 × 10–24 and 22.391 × 10–24, respectively. Also, the first hyper-polarizability values of pMeOPP, mMeOPP and oMeOPP isomers have been obtained as 1121.59 × 10–33, 3943.84 × 10–33 and 3869.82 × 10–33, respectively. It has been noticed that some very good NLO properties have arisen due to two nitrogen atoms in the structure of isomers [29]. From the obtained results, these isomers are an appealing molecule for future studies of NLO applications.

3.4 Mulliken Population Analysis

Atomic charge calculation has been carried out to show the distribution of positive and negative charges in molecules. This calculation is important to examine some increases or decreases in bond lengths between atoms. Atomic charges can affect many molecular properties such as dipole moment, polarizability and electronic structure. Total atomic charges of Mulliken population analysis are given in Fig. 3.

Fig. 3
figure 3

Mulliken population for pMeOPP, mMeOPP and oMeOPP isomers

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According to Mulliken population analysis, although the oMeOPP isomer has a positive charge for C5, mMeOPP and pMeOPP isomers have negative charges for C5. This situation for the mMeOPP isomer has a positive charge for C8 and C9; they have negative charges for other isomers. In addition, the pMeOPP isomer has a positive charge for C6 and C7 while they have negative charges for other isomers. Another important point is that the pMeOPP isomer has a positive charge distribution at N20 while other isomers have a negative charge distribution. The pMeOPP isomer has a negative charge distribution at N19 while other isomers have a positive charge distribution.

3.5 Molecular Electrostatic Potential Map

The MEP map can be used to distinguish regions where the surface is electron rich or poor. The red and yellow colours on the MEP map correspond to negative electrostatic potential regions and the blue colour corresponds to the positive electrostatic potential region. In addition, it can be employed to investigate the relationship between the molecular structure and physiochemical properties of molecules including bio-molecules and drugs (Fig. 4) [30,31,32,33,34].

Fig. 4
figure 4

MEP map diagram for pMeOPP, mMeOPP, and oMeOPP isomers

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The colour codes of these MEP maps are in the range between −7.981 × 10–2 a.u and 7.981 × 10–2 a.u and −7.429 × 10–2 a.u and 7.429 × 10–2 a.u and −6.865 × 10–2 a.u and 6.865 × 10–2 a.u. mMeOPP, pMeOPP and oMeOPP respectively. In addition, the obtained results show that the negative potential of nitrogen due to the red colour is presented, but the positive potential is shown at hydrogen atoms.

3.6 Thermodynamic Properties

The thermodynamic parameters of the isomer are shown in Table 5. The thermodynamic results obtained can make useful data for further experimental studies on MeOPP isomers, when these were used to investigate the interaction between MeOPP molecule and another molecule [35]. According to thermodynamic results obtained, total energy (thermal) values of isomers varied in only vibrational levels and these values have been obtained in an order of oMeOPP > mMeOPP > pMeOPP from largest to smallest. Heat capacity values are varied at the same level as thermal values. However, the order of heat capacity among isomers has been changed as mMeOPP > pMeOPP > oMeOPP from largest to smallest, whereas the entropy values have shown some differences in both rotational and vibrational levels and, due to these differences, they were ordered from largest to smallest to be pMeOPP > mMeOPP > oMeOPP.

Table 5 The thermodynamic parameters for pMeOPP, mMeOPP and oMeOPP isomers
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3.7 UV–Vis Spectral Analysis

UV–vis spectral analysis of MeOPP isomers has been calculated theoretically. TD-DFT is an important tool used to investigate the static and dynamic properties of any molecule in their exited states [20]. Graphs of data obtained were plotted by GaussSum [36]. The computed absorption bands were obtained for mMeOPP isomers at 296.61 nm, 278.40 nm and 271.73 nm; for oMeOPP isomers at 285.01 nm, 276.64 nm and 268.84 nm; and for pMeOPP isomers at 320.88 nm, 306.99 nm and 294.56 nm. As a result, the absorption wavelength varies for each isomer. However, as seen clearly in Fig. 5, it is prominently different for pMeOPP isomers. In addition, for pMeOPP isomers, the absorption band is found at 275 nm in literature [37]. This difference is due to that theoretical calculations were carried out in gas phase while experimental work was in solution.

Fig. 5
figure 5

UV–Vis spectrum for pMeOPP, mMeOPP and oMeOPP isomers

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Calculated absorption wavelengths, electronic excitation energies, oscillator strength and major contribution values for MeOPP isomers are represented in Table 6. Major contributions for isomers have been observed in HOMO → LUMO with (96%) in 296.61 nm for mMeOPP isomers, in HOMO → L + 2 with (90%) in 268.84 nm for oMeOPP isomers and HOMO → LUMO with (96%) in 320.88 and HOMO → L + 2 with (96%) in 294.56 nm for p MeOPP isomers.

Table 6 Absorption wavelengths, electronic excitation energies, oscillator strength, and major contributions values for pMeOPP, mMeOPP and oMeOPP isomers
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4 Conclusion

In this study, the optimized geometrical parameters, HOMO and LUMO energies, chemical reactivity descriptors, nonlinear optical properties, Mulliken population analysis, molecular electrostatic potential map, thermodynamic properties and UV–Vis spectral analysis of MeOPP isomers have been investigated using DFT and TD-DFT/B3LYP/6-311++G(d,p) method and represented in present work. Structural properties of pMeOPP isomer gathered from XRD analysis in literature have been found to be quite compatible. In addition, in general, results of the bond length, for example, between C–C atoms obtained for other isomers in literature have also been found to be compatible. The band gap values change as in the order of oMeOPP > mMeOPP > pMeOPP according to HOMO and LUMO results obtained for isomers and chemical reactivity descriptors were obtained from these values. MeOPP isomers show some significant dipole moments, polarizability and hyper-polarizability, so these isomers show some good NLO properties; this is due to two nitrogen atoms in the structure of isomers. According to Mulliken results, it can be said that the pMeOPP isomer is found to be different from other isomers. Thermodynamic data provides quite good information for experimental studies on MeOPP isomers. Absorption bands of the pMeOPP isomer as a result of UV–Vis analysis have been observed at 320.88 nm, 306.99 nm and 294.56 nm. In addition, under the scope of obtained theoretical data, we hope that this study will be a guiding study for both experimental and theoretical studies to understand structural isomers for the physics, chemistry and pharmaceutical industries.