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Theoretical Diagnostics of Second and Third-order Hyperpolarizabilities of Several Acid Derivatives

  • A. Karakas , Y. Ceylan , M. Karakaya , M. Taser , B. B. Terlemez , N. Eren EMAIL logo , Y. El Kouari , M. Lougdali , A. K. Arof and B. Sahraoui
Published/Copyright: April 10, 2019
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Open Chemistry
From the journal Open Chemistry Volume 17 Issue 1

Abstract

The density functional theory (DFT) at B3LYP/6-31G(d) level has been utilized to achieve the electric dipole moment (μ),static dipole polarizability (α)and first hyperpolarizability (β)values for ferulic acid (1) and chenodeoxycholic acid (2). The time-dependent Hartree-Fock (TDHF) technique as a powerful quantum chemical method has been implemented to reveal the dynamic α, βand third-order hyperpolarizabilities (γ)of the examined compounds. Our computational conclusions have been compared with the results of similar materials in the literature. The first and second frontier molecular orbitals (MOs) and their band gaps have also been investigated by means of DFT.

Graphical Abstract

Keywords: Electric dipole moment; Second-order nonlinear optic; Third-order nonlinear optic
PACS: 42.65.−k; 42.65.An

1 Introduction

To determine the magnitudes of first hyperpolarizabilities is quite important for the devices provided the second-harmonic generation (SHG) and quadratic electro-optic responses. So, the push-pull type π-electronarrangements associated with aromatic chains and unsaturated bonds and also unsymmetrically substituted donors and acceptors have been especially designed to obtain the SHG processes [1]. It has been also shown that the molecules with octupolar symmetries are among the efficient molecular materials [2]. The third-order macroscopic NLO susceptibilities are directly related to their corresponding microscopic cubic responses. The images of biological structures are provided by the third-harmonic generation (THG) technique indicating the variations on the third-order NLO susceptibilities [3].

In this work, one of our aims is to focus on theoretically evaluating the second and third-order NLO behaviour of the title molecules in Figure 1. The μ ,dispersion-free αand β values have been produced using DFT calculations. The dynamic dipole polarizabilities, quadratic and cubic hyperpolarizabilities have been also computed by means of ab-initio quantum mechanical approach (TDHF). Besides, the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) have been defined by DFT/B3LYP.

Figure 1 Bond-line formulas of Ferulic acid (1) and Chenodeoxycholic acid (2).
Figure 1

Bond-line formulas of Ferulic acid (1) and Chenodeoxycholic acid (2).

2 Theoretical Calculations

We have firstly performed the optimization studies on the examined structures. After the geometry optimizations, we have calculated the μ,static α and βfor 1-2 utilizing the finite field (FF) procedure [4]. The GAUSSIAN03W [5] package program using DFT method at B3LYP/ 6-31G(d) level has carried out the computations of optimization, μ ,static α and β.To build the molecular models of examined compounds shown in Figure 2, GaussView [6] program has been utilized as the interface program for GAUSSIAN03W [5]. The total electric dipole moments in terms of electric dipole moment components (μx,μy,μz),the orientationally averaged (isotropic) dipole polarizabilities 〈α〉and the magnitudes of βtot (total first static hyperpolarizability) are evaluated as follows, respectively [7,8]:

(1)μ=[μx2+μy2+μz2]1/2
(2)〈α〉=(αxx+αyy+αzz)/3
(3)βtot=[(βxxx+βxyy+βxzz)2+(βyyy+βyzz+     +βyxx)2+(βzzz+βzxx+βzyy)2]1/2

The TDHF procedure of the GAMESS [9] package program has obtained the γ(0;0,0,0)at ω=0  and  α(−ω;ω),β(−2ω;ω,ω),     γ(−3ω;ω,ω,ω)values at ω=0.04282atomic units (a.u.) (λ = 1064 nm) with 6-31G(d) basis set. The dispersion-free second hyperpolarizabilities are expressed as γ(0;0,0,0).The SHG and THG groups, respectively, in TDHF method have generated the β(−2ω;ω,ω)and γ(−3ω;ω,ω,ω)calculations at the studied ω frequencies.

Figure 2 Molecular models of Ferulic acid (1) and Chenodeoxycholic acid (2).Ethical approval: The conducted research is not related to either human or animal use.
Figure 2

Molecular models of Ferulic acid (1) and Chenodeoxycholic acid (2).

Ethical approval: The conducted research is not related to either human or animal use.

Using the following equations, we have computed the β−V(β vector)which is the vector part of the second-order hyperpolarizability and the averaged (isotropic) second hyperpolarizability γ :

(4)β−V=(βx2+βy2+βz2)1/2                           

where βi(i=x,y,z)is given by:

(5)βi=(1/3)∑j=x,y,z (βijj+βjij+βjji)
(6)〈γ〉=(1/5)[γxxxx+γyyyy+γzzzz+2(γxxyy+γxxzz+γyyzz)]

The GAUSSIAN03W [5] package program at DFT/ B3LYP level with 6-31G(d) basis set has also derived the HOMOs, LUMOs and HOMO-LUMO energy band gaps. The HOMO-LUMO energy gaps ( Eg ) are achieved by the following expression:

(7)Eg=ELUMO−EHOMO

3 Computational Results And Discussion

Table 1 lists the electric dipole moments of the title molecules. It has been found that the μ values of 1-2 are almost same for both studied acids (Table 1). The μ value for 1 has been calculated (μ=4.583D)by Sebastian et al. utilizing ab-initio quantum mechanical techniques [10]. Our computed data on μ of 1 (Table 1) is almost 1.6 times lower than the estimated value in Ref. [10]. The μ value of 1 was calculated utilizing DFT technique by Kumar et al. as μ =3.22 D [11]. The reported μ of 3.22 D by Ref. [11] is in good agreement with our calculated value of 2.807 D (Table 1). Calaminici et al. calculated the dipole moment ( μ =3 D) with DFT method of a phosphonic acid stilbene derivative containing the conjugated stilbene backbone, which is p-substituted by a methoxy electron donor group and p′ -substituted by a phosphonic acid electron acceptor moiety [12]. Our computed data on μ for 1-2 (Table 1) are quite close to the evaluated result by Ref. [12]. It has been found that the DFT results on μ values of 1-2 have given rather consistent results with the computed DFT data for similar structures in Refs. [11,12], while the other technique (ab-initio method) used in Ref. [10] yield a numerical diversity.

Table 1

The calculated electric dipole moments μ (Debye) and dipole moment components for 1-2 using DFT method at B3LYP/6-31G(d) level.

Compoundμxμyμzμ
12.5591.1550.0002.807
2-1.642-1.5631.5072.722

Tables 2-4, respectively, show a few important computed components for the static dipole polarizabilities, first and second hyperpolarizabilities of 1-2. The dispersion-free 〈α〉 values in Table 2 have an apparent reduction in sort order 2 > 1. The static 〈α〉 value of a

Table 2

Some selected components of the static α(0;0)  and  〈α〉  (0;0)(× 10−24esu)values for 1-2 computed by DFT method at B3LYP/6-31G(d) level.

Compoundαxαyαz〈α〉
133.40118.6617.08419.715
247.73334.70930.25337.565
Table 3

Some selected components of the static β(0;00) and βtot(0;00)(×10-30esu)values for 1-2 computed by DFT method at B3LYP/ 6-31G(d) level.

Compoundβxxxβyyyβyyzβxzzβzzzβtot
1-20.295-0.423-0.008-0.014-0.004 21.272
20.567-0.045-0.105-0.2390.380 0.709
Table 4

All static γ(0;0,0,0)components and 〈γ〉(0;0,0,0)(×10-37esu)values for 1-2 computed by TDHF method with 6-31G(d) basis set.

γxxxxγyyyyγzzzzγxxyyγxxzzγvvzz〈γ〉
1407.4204.716-0.23311.5921.4430.76187.899
233.0032.9670.3233.8580.5980.1069.084

phosphonic acid stilbene derivative with a conjugated stilbene backbone was computed by DFT with a triple zeta valence basis set (TZVP) to be 41.854× 10-24 esu [12]. The calculated static 〈α〉value reported by Calaminici et al. [12] are about 2 and 1.1 times, respectively, higher than that of 1 and 2 in Table 2. The static first hyperpolarizability of a phosphonic acid stilbene derivative containing a conjugated stilbene backbone was reported at DFT/TZVP level to be 44.075× 10-30 esu by Ref. [12]. Our result on βtotfor 1 (Table 3) is almost a factor of 2 lower than the presented data by Calaminici et al. [12]. To change the basis sets (TZVP) in the same method (DFT) for a similar acid reported by Ref. [12] has found out numerically discrepancies with the static 〈α〉    and  βresults of 1-2 (DFT method and 6-31G(d) basis set). It is seen from Table 4 that the dispersion-free 〈γ〉values show a reduction in sort order 1>2.

Tables 5-7, respectively, give a few important calculated components for dynamic dipole polarizabilities, second and third-order hyperpolarizabilities of 1-2. The dynamic 〈α〉  and  〈γ〉values display the same reduction in sort order 2 > 1 (for 〈α〉values) and 1 > 2 (for 〈γ〉values) as their corresponding static ones (see Tables 2,4,5,7). Song et al obtained the dynamic βvalue of 35×10-30esu using Hyper-Rayleigh scattering (HRS) technique at 532 nm for 5-(3,4-dimethoxybenzylidene) barbituric acid [13]. The quadratic hyperpolarizability of non-aromatic amino acid lysine was measured by means of HRS at 800 nm to be 0.3×10-30 esu [14]. The theoretical β−Vvalues for 1(β−V=32.428×10-30 esu)and 2(β−V=0.196×10-30 esu),respectively, in Table 6 are in accordance with the experimental results of similar acids in the literature reported by Refs. [13,14]. Our computed results on dynamic first hyperpolarizabilities could be compared with the result of urea which is well-known an efficiency standard in order to find out second-order NLO characterization. The β−Vvalues for 1 and 2, respectively, have been obtained 72 times higher (for 1) and 2.3 times lower (for

Table 5

Some selected components of the frequency-dependent α(−ω;ω)and absolute values of 〈α〉(−ω;ω)(×10-24 esu)at ω =0.04282 a.u. for 1-2 computed by TDHF method with 6-31G(d) basis set.

Compoundαxxαyyαzz〈α〉
121.93612.3182.39212.215
225.93320.37417.62821.311
Table 6

Some selected components of the frequency-dependent β(−2ω;ω,ω) and β−V(×10-30 esu)values at ω=0.04282  a.u.  for1-2 computed by TDHF method with 6-31G(d) basis set.

Compoundβxxxβyyyβzzzβxβyβzβ-  V
110.401-0.4210.00031.7186.746-0.00032.428
20.0360.0210.0710.023-0.1440.1300.196
Table 7

Some selected components of the frequency-dependent γ(−3ω;ω,ω,ω)and absolute values of 〈γ〉(−3ω;ω,ω,ω)(×10-35esu) at ω=0.04282a.u. for 1-2 computed by TDHF method with 6-31G(d) basis set.

Compoundγxxxxγyyyyγzzzzγxxyyγxxzzγyyzz〈γ〉
17.5090.062-0.0020.1450.0200.0081.601
20.3590.0320.0040.0410.0060.0010.099

2) than the quadratic hyperpolarizability of urea (βurea=0.45× 10-30 esu) reported by Ledoux et al. [15]. The dynamic 〈γ〉values for the title molecules are about factors of 1.25 higher (for 1) and factors of 12.8 lower (for 2) than the cubic hyperpolarizability of para-nitroaniline (p-NA) (γp-NA=1.271×10-35 esu)given in [16] which is one of the reference materials utilized in third-order NLO area. Since the NLO parameters, their magnitudes and frequency dependences for 1-2 are determined by ab-initio and DFT levels of theory, these levels of understanding and such theoretical insights make viable computer-aided molecular design of new NLO materials in the future. It is shown that the non-zero μvalues for 1-2 might cause microscopic quadratic and cubic hyperpolarizabilities with non-zero values derived by the numerical second-derivatives of the electric dipole moments to extent the implemented field. The presented data on dynamic β−V    and   〈γ〉with non-zero values predict that the title compounds might acquire microscopic second and third-order NLO responses. As was to be expected from the comparisons with the urea standard, compound 1 might also possess macroscopic second-order NLO responses with non-zero

values in NLO measurements. So, compound 1 could be a promising material having quadratic electro-optic responses in second-order NLO applications, such as SHG experiments. Hence, compared with compound 2, compound 1 may fulfill many of quadratic optical nonlinearity requirements and could have potential applications in NLO and electro-optic devices.

Table 8 presents the computed first and second frontier MO energies and also band gaps for 1-2. Figure 3 shows the first and second frontier MOs. Since the charge transfer stimulations containing HOMO and LUMO affect the second and third-order optical nonlinearities, the lower HOMO-LUMO energy band gaps should generate the higher first and second hyperpolarizability values. In this work, the HOMO-LUMO and (HOMO-1)-(LUMO+1) energy band gaps have a reduction in sort order 2 > 1, while the calculated values of dynamic β−V   and   〈γ〉show an inverse reduction in sort order 1 > 2 (see Tables 6-8). It is obvious that the HOMO-LUMO energy band gaps and hyperpolarizabilities introduce an opposite correlation [17]. The LUMO for 1 is localized on almost the whole molecule, while the HOMO is mainly localized on methoxy and hydroxyl groups, consequently the HOMO ➝ LUMO transition implies an electron density transfer to aromatic part and propenoic acid of π -conjugated system from methoxy and hydroxyl group (Figure 3). The HOMO, HOMO-1, LUMO+1 for 2 are located over the benzene rings. By contrast, the LUMO of 2 is mainly located over the side chain (Figure 3).

Table 8

The calculated HOMO-LUMO energy (a.u.) and HOMO-LUMO band gap Eg values for 1-2 using DFT method at B3LYP/ 6-31G(d) level.

12
HOMO-0.20926-0.25174
LUMO-0.058590.01445
Eg[HOMO–LUMO]0.150670.26619
HOMO–1-0.24793-0.25346
LUMO +1-0.002070.06196
Eg[(HOMO–1)–(LUMO+1)]0.245860.31542
Figure 3 The frontier and second frontier molecular orbitals of Ferulic acid (1) and Chenodeoxycholic acid (2).
Figure 3

The frontier and second frontier molecular orbitals of Ferulic acid (1) and Chenodeoxycholic acid (2).

4 Conclusions

We have determined the dispersion-free and frequency-dependent dipole polarizabilities, quadratic and cubic hyperpolarizabilities utilizing DFT and TDHF approaches, respectively. The microscopic second and third-order optical nonlinearity behaviour for 1-2 have been confirmed by the non-zero hyperpolarizability values computed in this work. We have also made the comparisons for μ ,static and dynamic α, β, γresults of the title compounds with the corresponding NLO parameters of similar structures previously reported in the literature. The applied computational techniques (DFT and TDHF) in this paper presented quite comparable results with the reported data in the literature. It has been shown that some numerical discrepancies between our results and the obtained data in the literature for similar acid derivatives could originate from different methods or basis sets preferred in the computations. One can also see from the comparisons on NLO efficiencies of 1-2 related to reference compounds (urea and p-NA) that compound 1 with quite high β−Vresult offers a successful quadratic NLO behaviour. Both various chemical reactions and also resonance phenomena belonging to the structural properties for 1-2 could be understood with information of the HOMOs, LUMOs and HOMO-LUMO band gaps. To investigate the charge transfer properties of the examined structures, the HOMO and LUMO energies have been found out by means of DFT. One can benefit from the first and second frontier MOs determined here for the title compounds to explain their molecular structures and reactivities. Besides, since the better hyperpolarizability responses are attained by the systems with rather low HOMO-LUMO band gaps, in this work, HOMOs, LUMOs and HOMO-LUMO band gaps for 1-2 have been obtained to define their NLO properties. Our computational results on first and second frontier MOs for 1-2 justify the relationship between HOMO-LUMO band gaps and NLO responses, supporting an inverse behaviour.

  1. Conflict of interest: Authors declare no conflict of interest.

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Received: 2018-01-25
Accepted: 2018-09-21
Published Online: 2019-04-10

© 2019 A. Karakas et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 Public License.

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  75. Increasing the activity of DNAzyme based on the telomeric sequence: 2’-OMe-RNA and LNA modifications
  76. Exploring the optoelectronic properties of a chromene-appended pyrimidone derivative for photovoltaic applications
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  79. Greener synthesis of dimethyl carbonate from carbon dioxide and methanol using a tunable ionic liquid catalyst
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  81. Enhanced adsorption of sulfonamide antibiotics in water by modified biochar derived from bagasse
  82. Study on the Mechanism of Shugan Xiaozhi Fang on Cells with Non-alcoholic Fatty Liver Disease
  83. Comparative Effects of Salt and Alkali Stress on Antioxidant System in Cotton (Gossypium Hirsutum L.) Leaves
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  87. Phytochemistry and toxicological assessment of Bryonia dioica roots used in north-African alternative medicine
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  100. Generators of Maximal Subgroups of Harada-Norton and some Linear Groups
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  103. Effects of Supercritical Carbon Dioxide Extraction (SC-CO2) on the content of tiliroside in the extracts from Tilia L. flowers
  104. Impact of xanthan gum addition on phenolic acids composition and selected properties of new gluten-free maize-field bean pasta
  105. Impact of storage temperature and time on Moldavian dragonhead oil – spectroscopic and chemometric analysis
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  116. Determination of Gamma Rays Efficiency Against Rhizoctonia solani in Potatoes
  117. Studies On Compatibilization Of Recycled Polyethylene/Thermoplastic Starch Blends By Using Different Compatibilizer
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  119. Synthesis of Graphene Oxide Through Ultrasonic Assisted Electrochemical Exfoliation
  120. Special Issue on ISCMP 2018
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  123. Electrochemical modification of platinum and glassy carbon surfaces with pyridine layers and their use as complexing agents for copper (II) ions
  124. Effect of Electrospinning Process on Total Antioxidant Activity of Electrospun Nanofibers Containing Grape Seed Extract
  125. Effect Of Thermal Treatment Of Trepel At Temperature Range 800-1200˚C
  126. Topical Issue on Agriculture
  127. The effect of Cladophora glomerata exudates on the amino acid composition of Cladophora fracta and Rhizoclonium sp.
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  130. The use of microorganisms as bio-fertilizers in the cultivation of white lupine
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  133. Human health risk assessment of potential toxic elements in paddy soil and rice (Oryza sativa) from Ugbawka fields, Enugu, Nigeria
  134. Recovery of phosphates(V) from wastewaters of different chemical composition
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  145. Photocatalytic activity of NiFe2O4 and Zn0.5Ni0.5Fe2O4 modified by Eu(III) and Tb(III) for decomposition of Malachite Green
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  148. Special Issue on Monitoring, Risk Assessment and Sustainable Management for the Exposure to Environmental Toxins
  149. Soil organic carbon mineralization in relation to microbial dynamics in subtropical red soils dominated by differently sized aggregates
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  151. Special Issue on 13th JCC 2018
  152. Fluorescence study of 5-nitroisatin Schiff base immobilized on SBA-15 for sensing Fe3+
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  161. The Study of the Optical Properties of C60 Fullerene in Different Organic Solvents
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  163. Topical Issue on Environmental Chemistry
  164. Ionic liquids modified cobalt/ZSM-5 as a highly efficient catalyst for enhancing the selectivity towards KA oil in the aerobic oxidation of cyclohexane
  165. Application of Thermal Resistant Gemini Surfactants in Highly Thixotropic Water-in-oil Drilling Fluid System
  166. Screening Study on Rheological Behavior and Phase Transition Point of Polymer-containing Fluids produced under the Oil Freezing Point Temperature
  167. The Chemical Softening Effect and Mechanism of Low Rank Coal Soaked in Alkaline Solution
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  170. Design of SiO2/TiO2 that Synergistically Increases The Hydrophobicity of Methyltrimethoxysilane Coated Glass
  171. Antidiabetes and Antioxidant agents from Clausena excavata root as medicinal plant of Myanmar
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  173. Special Issue on Applied Biochemistry and Biotechnology 2019
  174. Adsorption of copper ions on Magnolia officinalis residues after solid-phase fermentation with Phanerochaete chrysosporium
  175. Erratum
  176. Erratum to: Sand Dune Characterization For Preparing Metallurgical Grade Silicon
https://doi.org/10.1515/chem-2019-0020
Keywords for this article
Electric dipole moment; Second-order nonlinear optic; Third-order nonlinear optic
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  124. Effect of Electrospinning Process on Total Antioxidant Activity of Electrospun Nanofibers Containing Grape Seed Extract
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  133. Human health risk assessment of potential toxic elements in paddy soil and rice (Oryza sativa) from Ugbawka fields, Enugu, Nigeria
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  145. Photocatalytic activity of NiFe2O4 and Zn0.5Ni0.5Fe2O4 modified by Eu(III) and Tb(III) for decomposition of Malachite Green
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  148. Special Issue on Monitoring, Risk Assessment and Sustainable Management for the Exposure to Environmental Toxins
  149. Soil organic carbon mineralization in relation to microbial dynamics in subtropical red soils dominated by differently sized aggregates
  150. A potential reusable fluorescent aptasensor based on magnetic nanoparticles for ochratoxin A analysis
  151. Special Issue on 13th JCC 2018
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  153. Thermal and Morphology Properties of Cellulose Nanofiber from TEMPO-oxidized Lower part of Empty Fruit Bunches (LEFB)
  154. Encapsulation of Vitamin C in Sesame Liposomes: Computational and Experimental Studies
  155. A comparative study of the utilization of synthetic foaming agent and aluminum powder as pore-forming agents in lightweight geopolymer synthesis
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  161. The Study of the Optical Properties of C60 Fullerene in Different Organic Solvents
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  163. Topical Issue on Environmental Chemistry
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  165. Application of Thermal Resistant Gemini Surfactants in Highly Thixotropic Water-in-oil Drilling Fluid System
  166. Screening Study on Rheological Behavior and Phase Transition Point of Polymer-containing Fluids produced under the Oil Freezing Point Temperature
  167. The Chemical Softening Effect and Mechanism of Low Rank Coal Soaked in Alkaline Solution
  168. The Influence Of NO/O2 On The NOx Storage Properties Over A Pt-Ba-Ce/γ-Al2O3 Catalyst
  169. Special Issue on the International conference CosCI 2018
  170. Design of SiO2/TiO2 that Synergistically Increases The Hydrophobicity of Methyltrimethoxysilane Coated Glass
  171. Antidiabetes and Antioxidant agents from Clausena excavata root as medicinal plant of Myanmar
  172. Development of a Gold Immunochromatographic Assay Method Using Candida Biofilm Antigen as a Bioreceptor for Candidiasis in Rats
  173. Special Issue on Applied Biochemistry and Biotechnology 2019
  174. Adsorption of copper ions on Magnolia officinalis residues after solid-phase fermentation with Phanerochaete chrysosporium
  175. Erratum
  176. Erratum to: Sand Dune Characterization For Preparing Metallurgical Grade Silicon
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