Performance of Hybrid DFT Compared to MP2 Methods in Calculating

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Performance of Hybrid DFT Compared to MP2 Methods in Calculating NonLinear Optical Properties of Divinylpyrene Derivatives Molecules Mourad Zouaoui-Rabah, Majda Sekkal-Rahal, Fatna DjilaniKobibi, Abdelkader M Elhorri, and Michael Springborg J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b08040 • Publication Date (Web): 17 Oct 2016 Downloaded from http://pubs.acs.org on October 18, 2016

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The Journal of Physical Chemistry

Performance of Hybrid DFT Compared to MP2 Methods in Calculating NonLinear Optical Properties of Divinylpyrene Derivatives Molecules

M. Zouaoui-Rabah1, M. Sekkal-Rahal1*, F. Djilani-Kobibi1, A. M. Elhorri1 and M. Springborg2 1: Laboratoire de Microscopie, Microanalyse et Spectroscopie Moléculaire (L2MSM), Faculty of Sciences. Djillali Liabes University of Sidi-Bel-Abbes, 22000 Sidi-Bel-Abbes. Algeria 2: Physical and Theoretical Chemistry, University of Saarland, 66123 Saarbrücken, Germany

*email: [email protected]

ACS Paragon Plus Environment


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Abstract A series of divinylpyrene derivatives of the form D-vinyl-pyrene-vinyl-A, in which D corresponds to an electron donor group and A to an electron acceptor group, were studied in this work. The first purpose was to determine the optimal HF % exchange as incorporated in a range of hybrid functional (M06HF, M062X,M06L,CAM-B3LYP, PBE0,BMK et B3LYP) capable to produce, reliably and as closest as possible to the those obtained from MP2 calculations, NLO parameters and, in particular, first order static hyperpolarizabilities. The CAM-B3LYP functional was revealed to be the most suitable one. The pair N(CH3)2/ NO2 was then determined as the most efficient pair of groups in producing appreciable NLO responses. The effect of the substitution position on the pyrene moiety was also investigated, whereby aligning the two substituents involving the D and A groups in the direction of the dipole moment as in the (1,6 DVP) derivatives was shown to be most favorable for increasing the NLO parameters.

Introduction Because of their numerous applications in the areas of photonics and optoelectronic1-3, various types of NLO active materials have been developed over the recent years. These materials are used in technical applications like lasers4, optical data storage devices, biological imaging5, signal processing, and in electro-optical modulation as well.6,7 These materials range from being inorganic, organic to organometallic.8-11 In order to identify additional and more efficient materials for further NLO applications, many studies were conducted on organic materials, including, for instance, the polycyclic aromatic hydrocarbons (PAH) or polynuclear aromatic hydrocarbons.12-15 These latter are a series of hydrocarbons in which carbon atoms are arranged in multiple aromatic rings sharing one or more C-C bond. The resulting structures are molecules wherein all carbon and hydrogen atoms are lying in the same plane. Accordingly, their physical and chemical characteristics make them eligible as π-conjugated bridges16 or chromophores in push-pull systems17 which contain a donor (D) and an acceptor (A) groups end-capping the π-conjugated backbone.18-20 Thereby, an enhancement of the intramolecular charge transfer (ICT) is obtained21-23 , which results in a strong NLO response. This latter is closely connected to several factors such as the energy gap (∆EH-L = εLUMO – εHOMO), the occupation quotient π*/π, the central bond length, the bond-length alternation (BLA), the delocalisation energy E(2), the electronic transitions parameters, the polarizability α and, finally, the most important factors: the static first order


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hyperpolarizability β0 and the dipole moment µ024-26 which have been at the center of much interest from theoretical chemists27-34 since a couple of decades. In this field, pure and hybrid DFT methods have been demonstrated to fail in calculating reliable hyperpolarizabilities 35-38 while post-HF methods reproduce hyperpolarizabilities with a good accuracy39 and are considered in the present work as reference. The wrong asymptotic behavior of DFT methods40 has been shown to be at the origin of the resulting inaccurate values.41,42 Therefore, enhancing the incorporated HF exchange (X) fraction in hybrid DFT fuctionals as well as long-range corrections become very important in order to improve results, and many papers have appeared dealing with this goal.43, popularity of the Minnesota M06 functionals,

45,46

44, 37, 38

Despite the

their performance in calculating NLO

responses of push-pull molecules has not been extensively tested. In this work, we focus on calculating NLO responses of various divinylpyrene derivatives that we consider as sufficiently large systems to test at which extend DFT methods can produce satisfactory results. Actually, as a special case of a PAH we have pyrene which consists of four fused benzene rings;47,48 Fig. 1. Since some years, pyrene and its derivatives have attracted considerable attention in the field of NLO because of their remarkable ICT. Actually, they have been frequently used as materials in organic light emitting diodes (OLED), in organic field effect transistors (OFET), and in organic photovoltaic cells.49, 50 So far, some 1-mono-substituted pyrene derivatives have been studied using DFT-B3LYP/631g (d,p) level of theory.51 It was demonstrated that the pyrene structure is strongly affected by the nature of the substituent. These variations are then obviously reflected in appreciable changes in the dipole moments values. Another work using also the B3LYP/6-31g (d,p) and dealing with some 1,3,6,8 tetra-hologeno-substituted pyrenes, has established a direct relationship between the electronegativities of halogens and their average polarizability.52 Moreover, an experimental investigation on the pyrene derivatives 1-mono-substituted, (1,6) di-substituted , (1,6,8) tri-substituted or (1,3,6,8) tetra-substituted by furyl groups, came to the conclusion that there is a relation between the number of substitutions and the charge transfer inside the pyrene.53,54 This latter fact was confirmed by an investigation involving thermodynamic parameters.55 In their paper, Ma et al. have observed, for de 2,7-di-tertbutylpyrene-4, 5, 9,10-tetraone, that the charge transfer increases when the energy gap decreases and the cis-form is converted into the trans-form.56 Other studies have highlighted the connection between the charge transfer, the distance separating the donor group from the attracting group57 and the hyperpolarizability magnitude58.



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According to the information listed above, we can conclude that many and diverse studies have been performed on pyrene because of the physico-chemical characteristics that make pyrene a potentially attractive compound for charge transfer devices. For this reason, we consider in this work the pyrene moiety substituted on each side by a vinyl group at different positions as a chromophore in a push-pull molecule (Figure 1) whereby we expect to obtain information on a possible relation between the substitution and the NLO parameters magnitude.

Computational details: All calculations presented in this work were performed using the Gaussian09 package59 while structures and other results were analyzed using Gaussview5.0.60 The starting geometry of the 1,6-divinylpyrene (1,6 DVP) shown in Figure 1 was initially optimized in the gas phase without any symmetry constraint using the B3LYP method, after which the vinyl group at the position 1 was substituted either by a nitro (-NO2) or a cyano (-CN) attracting group and the vinyl group at the position 6 was substituted by different donor groups such as NH2, N(CH3)2, OCH3, OH, N2H3 which are very often used in order to enhance the charge transfer within push-pull molecules.61,62 Because of this latter, a sensitivity of the resulting structures to the functional may exist and, therefore, we further optimized the ten geometries P1, P2, P3, P4, P5, P’1, P’2, P’3, P’4 and P’5 shown in Fig. 1b using different hybrid density functional methods including

different % HF exchange; M06L63, B3LYP64, PBE065, BMK66,

BHHLYP67, M06-2X47, CAM-B3LYP68, M06-HF48 in which the amount of exact exchange is 0% , 20%, 25%, 42% ,50%, 54%, 65%, 100%.69-73 In each case, the functional was combined with the cc-pvdz (Correlation-Consistent Polarized Valence Double Zeta) basis set. In addition, optimizations were also performed using the second order perturbation Møller Plesset (MP2) method74 which in this work will be used as a reference as recommended in a number of previous studies.24,75-82 After each structure optimization, a further frequency calculation was carried out to verify that there is no imaginary frequencies. Then, using the above-mentioned functionals and the MP2 methods combined with the ccpvdz basis set, calculations of static polarizabilities and static first order hyperpolarizabilities were performed in the gas phase for the ten molecules. Finally, using that hybrid functional which gives the closest NLO parameters to those obtained with MP2, we calculated the NLO parameters including the dipole moments, the polarizabilities and the first order hyperpolarizabilities for different derivatives of the (1,6


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DVP) molecule differing in the position of the substitutions, namely the (1, 3 DVP), (1,4 DVP), (1,5 DVP), (1,6 DVP), (1,7 DVP), (1,8 DVP) and (1,9 DVP), keeping the position of the acceptor group at the position 1 and varying that of the donor group (Fig 1. c) in order to investigate the isomeric effect on the NLO parameters. These latter are calculated using the following equations: -

The dipole moment is obtained as: (1)

-

The polarizability is calculated from its components : (2)

-

The static first hyperpolarizability is calculated from the corresponding tensor (involving 6x3 components which are reduced to 10 after diagonalization using the symmetry properties) 83: (3)

Where:

The charge transfer parameters are defined as the delocalization energy E(2) and describe the interactions between donors (i) – and acceptor (j). They are given by (4) where qi is the occupation number of the donor orbital, εi and εj are diagonal elements and equal to the orbital energies. Finally, F (i,j) is the off-diagonal (off) of the Fock matrix. In addition we also studied the HOMO-LUMO energy gap ∆EH-L.

Results and discussion:

Incorporated HF Exchange amount effect



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In order to identify the most appropriate hybrid functional and thus the most suitable HF exchange amount to produce NLO parameters and particularly the static first hyperpolarizability β0, we considered at first a series of molecules presented here as P1, P2, P3, P4 and P5 (Figure 1b). In the five molecules of this series, the chromophore is the (1,6 DVP) substituted by an NO2 group on the 1-vinyl, as attractor, while the 6-vinyl is substituted successively by five different electron-withdrawing groups, N(CH3)2, N2H3, NH2, OCH3, OH. To calculate the β0 parameters, the cc-pvdz basis set was combined with the hybrid functionals M06-L, B3LYP, PBE0, BMK, BHHLYP, M06-2X, M06-HF including each an HF exchange of 0%, 20%, 25%, 42%, 50%, 54%, and 100%, respectively, or with the longrange-corrected version of B3LYP (CAM-B3LYP) which includes attenuated coulomb terms; from 16-65%. The obtained results are given in table 1 and compared with those obtained from MP2/cc-pvdz calculations that hare are used as reference and from which deviations, i.e., the Mean Absolute Error (MAE), are calculated. Results from HF/cc-pvdz are also reported in table 1 for comparison. From the listed MAE, it appears that incorporating 0%, 20%, 25% or 42% of HF exchange to DFT methods does not improve the hyperpolarizability values since the deviations from those obtained from MP2 methods are quite appreciable (from 26 to 87%). On the other hand, incorporating 100% exchange gives the same trend as the pure HF method and deviates strongly from MP2 with an MAE of nearly 60% for M06-L and 70% for HF. Incorporating an intermediate amount of HF exchange seems to give the closest results to MP2. This is deduced from the low values of MAE, not exceeding 10% obtained from BHHLYP, M06-2X and particularly from CAM-B3LYP in which the HF exchange amount is not constant but varied over 16 to 65% due to the range separation. The MAE obtained with this latter method for the five considered molecules is very satisfactory with an averaged value of just 3.44%. Without experimental data, a more tangible way to confirm the fact that the CAM-B3LYP functional or other functionals including an intermediate amount of HF exchange around 50% lead to comparable hyperpolarizabilities to those obtained with MP2, is to consider larger systems. For this goal, we further considered additional molecules (Figure 2) in which a phenyl spacer was added at each side of the P1, P2, P3, P4 and P5 molecules between the chromophore and the donor or the acceptor groups. The compounds of this series were named Phy1, Phy2, Phy3, Phy4 and Phy5. They were first optimized in the gas phase using B3LYP/cc-pvdz level of theory without any symmetry constraint. Then, the first static hyperpolarizabilities were calculated using those functionals which were shown to be those that deviate the least from MP2, namely B3LYP, PBE0, BMK, BHHLYP, M06-2X and


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CAM-B3LYP , all combined with the cc-pvdz basis. The results were compared with those obtained from MP2/ cc-pvdz calculations (table 2). Here the same trend as in the previous set of calculations is observed. That is to say that the smaller deviation from the MP2 computed hyperpolarizabilities was obtained using the CAM-B3LYP functional followed by that obtained using M06-2X. BHHLYP functional gives also satisfactory results with a deviation of 5.60%. These observations are thus consistent with our previously issued conclusions. According to these conclusions, in the remaining part of this work, only the CAM-B3LYP/ccpvdz is employed.

Selection of the donor/ acceptor groups

After that the optimal method for the static hyperpolarizabilities for substituted pyrene systems has been identified we focus on the effects of the end-capping groups, i.e., the donor/ acceptor groups and their effect on the NLO parameters, with the ultimate purpose of improving the NLO response. In table 3, we report the static hyperpolarizabilities β0 as well as their projections onto the three coordinate axes (βx, βy, βz)as well as the dipole moment μ tot and its three projections (μ x, μ , μ z). Since we expect a close dependency of these parameters on the HOMO-LUMO gap, the

y

values for the latter are given in table 3, too. All these values are calculated for the molecules P1, P2, P3, P4 and P5 and for an analogous series for which the acceptor group NO2 is replaced by a cyano group CN resulting in the five additional molecules; P’1, P’2, P’3, P’4 and P’5. According to the calculated static hyperpolarizabilities β0 for the ten compounds presented in table 3, the following ordering can be extracted: β0 (P1)> β0 (P2)> β0 (P3)> β0 (P4) > β0 (P’1) > β0 (P5)> β0 (P’2)> β0 (P’3)> β0 (P’4) > β0 (P’5). This implies that in most of the cases the β0 value remains more important when the acceptor is the NO2 group compared to the case that the acceptor is the CN group. This is particularly noticeable for the cases that the N(CH3)2 group is the donor. This fact is directly related to the strength of the electronic charge transfer between the donor and the acceptor groups (DA). The most efficient pair of D/A giving the best NLO response for (1, 6 DVP) derivatives are therefore the NO2 group as electron acceptor and N (CH3)2 as electron donor. Equivalently, from table 3, an inverse behavior of the energy gap is observed. Actually, the smallest values of this latter correspond to the largest hyperpolarizabilities.



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The calculated βx, βy and βz values (also reported in table 3) reveal the strongest response along the main axis of the molecule, an observation that is also made for the components of the dipole moments given in table 3, too.

Effect of the multisite substitution on the pyrene aromatic system

So far, we have focused on push-pull systems where the chromophore consists of the (1,6 DVP). Next, we will investigate, in the following section, the effects on the NLO response if one of the vinyl groups is substituted at another position than the C6. Accordingly, six possibilities were considered; keeping the nitro-vinyl group in the position 1 of the pyrene moiety, while the dimethyl-amine-vinyl group position was varied from 3 to 4 to 5 to 7 to 8 and then to 9 resulting in the structures (1,3 DVP), (1,4 DVP), (1, 5DVP), (1,7 DVP), (1,8 DVP), and (1, 9DVP) (Figures 1c and 3). All calculations were performed using the CAM-B3LYP/cc-pvdz level of theory and the results including those concerning the (1,6 DVP) derivative are collected in table 4. According to the calculated values of the static hyperpolarizabilies β0, we observe significant variations from one isomer to another. The magnitude of β0 value increases slightly from the isomer (1,3) to the isomer (1,4), and strongly to isomer (1,5). It acquires its maximum for the isomer (1,6); the difference between the two latter being relatively small. It decreases for the isomer (1,7), then very slightly for (1,8) and finally it decreases significantly for the nitro-1, 9-dimethylamine DVP. The same trend is noticed for the dipole moment µ except for the isomer (1,4 DVP) (Fig. 3b). This deviation can be explained through a possible steric hindrance that leads to larger structural changes. The values of the dipole moment and hyperpolarizability are closely related to the electron delocalization strength as reflected in the E(2) behavior (Fig. 3e). A larger electronic delocalization parameter leads to a higher β0 value. In fact, this latter is directly connected to the distance separating the NO2 acceptor group and the N(CH3)2 donor group and, therefore, to the length of the electron delocalization pathway. For example, when considering the (1,3 DVP) isomer, the length of the electronic delocalization pathway from the acceptor

to the donor through C(2) is small and the

delocalization is weak, while the length through C(9), C(8)… is rather long and the delocalization will be attenuated. The combination of these two phenomena results in a lower value of the hyperpolarizability for this isomer. An intermediate value (as in the 1,6 DVP isomer) of the distance between the donor and the acceptor seems to give an optimal value for the hyperpolarizability.


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On the other hand, the behavior of the energy gap ∆EH-L (gap), does not follow the more common trend of being roughly inversely proportional to the hyperpolarizabiliy (Fig. 3d). In the present case, the gap is almost constant for the three first isomers corresponding to (1,3 DVP), (1,4 DVP) and (1,5 DVP) derivatives after which it decreases for (1, 6 DVP) to 4.76 eV. Thereafter, the values increase for the other derivatives, particularly for that of (1,7 DVP) which reaches a value of 5.05 eV. This large enhancement is attributed to the fact that this isomer is the most stable one (Fig. 3c) with a HOMO energy lower than those of the (1,8 VDP) and (1,9 VDP) derivatives (Figure 4) and this probably reduces the electron delocalization strength (Fig. 3e). Further information can be obtained directly from the HOMO and LUMO orbitals (Figure 4). Here, the charge density of the HOMO is excluded partly from the acceptor group while for that of the LUMO, the donor group including the linked vinyl group does hardly contribute. Here again, the (1,7 VDP) isomer is a particular case, since the charge density is completely excluded from the nitro-vinyl group for the HOMO and seems to be symmetrically distributed on the pyrene moiety and the dimethyl-vinyl group. The π/π* occupancy quotient (Fig. 3f), as expected, evolves in an analog way as the hyperpolarizability, which confirms previous affirmations. Some additional clarifications can be obtained by analysing the Molecular Electrostatic Potential Surfaces, MESP. This describes the potential due to the total charge density of the molecule of interest84 and, therefore, it identifies the molecular polarity. The results, obtained for the gas phase and based on the Mullikan orbital populations, are reported in table 5. We observe from the MESP of the seven isomers that the charge distribution for the (1,6 DVP) derivative (whereby the red color of the electrostatic potential is due to negative charges, the blue one to the positive charges, and the green to the no charge; the iso-density is equal to 0.02 u.a.) is the most regularly one and being polarized in the direction of the dipole moment of the molecule.85 For all molecules, the negative charge is concentrated towards the acceptor group and the positive charge towards the electron donor group, as would be expected. This fact leads to a strong electronic transfer from one side to the other. In the case of the (1,6 DVP) isomer, this is reflected in a larger dipole moment and, simultaneously, in a larger hyperpolarizability magnitude owing to the fact that the D/A groups are both located to the same axis (the direction of the dipole moment). This clearly enhances the charge transfer inside the molecule. The charge distribution indicates that when the positions of the negative and positive charges are not along the dipole moment axis, the hyperpolarizability decreases.



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In this section, we confirmed that the substitution position on the pyrene moiety affects strongly the NLO response and the optimal values are obtained when the donor and acceptor groups are located along the dipole moment axis.

Basis set effect So far, all calculations were carried out using the cc-pvdz basis set. In order to check whether the first hyperpolarizability magnitudes are sensitive to varying the basis set, we performed further calculations using the CAM-B3LYP method for the nitro-1,6- N(CH3)2 combined successively on one hand with a series of double Zeta basis sets adding progressively first polarization and afterwards diffuse functions: 6-31G, 6-31+G, 6-31G(d),6-31+(d), 631G(d,p), 6-31G+G(d,p), 6-31++G(d,p) and cc-pvdz. On the other hand, a second series of triple Zeta basis sets was employed considering the 6-311G, 6-311+G, 6-311G(d), 6311G(d,p), 6-311++G(d,p) and cc-pvtz basis sets. The obtained results including the components βx, βy and βz are collected in table 6. The first observation from these results is that the hyperpolarizabilities β0, is overestimated when neither polarization nor diffuse functions are involved in the basis set such as 6-31G and 6-311G. Adding one diffuse function to these later increases even further the hyperpolazabilities. On the other side, including one or two diffuse functions leads to almost unchanged values for the hyperpolarizabilities. This is the case when 6-31+G(d,p) or 6-311+G(d,p) are used compared to 6-31++G(d,p) or 6-311++G(d,p). However, when no diffuse function is included, adding one (d) or two (d,p) polarization functions yields very close hyperpolarizabilities values, particularly for the double Zeta series even for cc-pvdz. For this later, a smaller contribution to βy is noted compared to those obtained with the 6-31G(d) and 6-31G(d,p) basis sets. Since the electron transfer occurs only in the x direction, it is obvious that the highest contribution to β0 is the component βx. βy

and

βz should be minimal, and this is well reproduced when

including polarization functions, particularly with cc-pvxz (x= d or t). The cc-pvdz is preferred because the calculations then are less time consuming.

Conclusion In this work, we first focused on identifying an optimal hybrid functional among M06-L, B3LYP, PBE0, BMK, BHHLYP, M06-2X, M06-HF in which the HF % exchange amount


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varies from 0% for M06-L to 100% for M06-HF, and the CAM-B3LYP functional including a variable amount from 16 to 65 %. The essential goal was to obtain the closest NLO parameters to those obtained from MP2 calculations on some derivatives of (1,6 VDP). The CAM-B3LYP/cc-pvdz was found as the functional that gives the best agreement. In the subsequent calculations, this approach was selected when we focused on determining that pair of D/A (donor and acceptor groups) in (1, 6 VDP) derivatives that gives the largest NLO responses. Finally, we investigated the effects of varying the position of the substitution on the first hyperpolarizability, i.e., the (1,3 DVP), (1,4 DVP), (1,5 DVP), (1,7 DVP), (1,8 DVP) and (1,9 DVP) for which the donor group equals N(CH3)2 while the acceptor group was a nitro group. In this case, the largest NLO responses were found for those systems that have the best electronic transfer through the chromphore. Actually, the isomer (1,6 DVP) is the one with the largest response and this should accordingly be a promising system for NLO applications. The direction of the dipole moment is consistent with the charge transfer direction in the (1, 6 DVP) derivative which probably is responsible for this optimal consequence. Acknowledgements: The authors thank the Alexander von Humboldt-Stiftung, Bonn, Germany, for supporting grants.

References (1) Maroulis, G. Electric Multipole Moments, Polarizability, and Hyperpolarizability of Xenon Dihydride (HXeH). Theor. Chem. Acc. 2011, 129, 437-445. (2) Lee, Y. O.; Pradhan, T.; No, K.; Kim, J. S. N,N-Dimethylaniline and 1-(Trifluoromethyl) Benzene-Functionalized Tetrakis (ethynyl) Pyrenes: Synthesis, Photophysical, Electrochemical and Computational Studies. Tetrahedron 2012, 68, 1704-1711. (3) Ennaceur, N.; Ledoux , R. I.; Mhiri, T.; Jarraya, K. NLO in Correlation of Phase Transition and the Alkaline Metal Environment Effect on it in KDP Family. Physica B 2013, 428, 106-109. (4) Abd-El-Aziz, A. S.; Dalgakiran, S.; Kucukkaya, I.; Wagnera, B. D. Synthesis, Electrochemistry and Fluorescence Behavior of Thiophene derivatives Decorated with Coumarin, Pyrene and Naphthalene Moieties. Electrochimica Acta 2013, 89, 445-453. (5) Umadevi, V.; Umadevi, P.; Santhanamoorthi, N. ; Senthilkumar , L. Effect of Alkyl Chain on the NLO Property of Nonylphenol Isomers: a DFT Study.Monatsh Chem. 2015, 146, 1983-1994.



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(6) Zyss, J.; Ledoux, I. Nonlinear Optics in Multipolar Media: Theory and Experiments. Chem. Rev. 1994, 94, 77−105. (7) Ma, N. N.; Yang, G. C. ; Sun, S. L.; Liu, C. G. ; Qiu, Y.Q. Computational Study on Second-Order Nonlinear Optical (NLO) Properties of a Novel Class of Two-Dimensional L- and W-shaped Sandwich Metallocarborane-Containing Chromophores. J. Org. Chem. 2011, 696, 2380-2387. (8) Roy, A.L.; Chavarot , M.; Rose , É.; Rose, M.F.; Attias , A.J.; Kréher , D.; Fave , J-L.; Kamierszky, C. Towards new Organometallic Second-Order Nonlinear Optical Materials. C.R.Chimie 2005, 8, 1256-1261. (9) Gentaricson, A.; Persson, I . Structural Studies of Organometallic Compounds in Solution. J. Org. Chem. 1987, 326, 151-158. (10) Osiry , H. ; Cano , A.; Lemus-Santana , A. A.; Rodríguez , A .; Carbonio , R.E.; Reguera, E. Intercalation of Organic Molecules in 2D Copper (II) Nitroprusside: Intermolecular Interactions and Magnetic Properties .J. Solid state chem. 2015, 230, 374-380. (11) Xin, Li. Modeling and Simulation Study of a Metal free Organic–Inorganic Aqueous flow Battery with flow Through Electrode. Electrochimica Acta 2015, 170, 98-109. (12) Jiang, D.; Xin, C.; Li, W.; Chen, J.; Li, F.; Chu, Z.; Xiao, P.; Shao, L. Quantitative Analysis and Health risk Assessment of Polycyclic Aromatic Hydrocarbons in Edible Vegetable oils Marketed in Shandong of China. Food and Chem. Toxico 2015, 83, 61-67. (13) Grotheer, H.; Robert, A. M.; Greenwood, P. F.; Grice, K. Stability and Hydrogenation of Polycyclic Aromatic Hydrocarbons During Hydropyrolysis (HyPy) – Relevance for High Maturity Organic Matter . Organo. Geochem. 2015, 86, 45-54. (14) Cai, Y.; Yan, Z.; NguyenVan, M.; Wang, L.; Cai, Q. Magnetic Solid Phase Extraction and Gas Chromatography–Mass Spectrometrical Analysis of Sixteen Polycyclic Aromatic Hydrocarbons. J. Chromatography A 2015, 1406, 40-47. (15) Raman, A. S.; Chiew, Y. C. Solubility of Polycyclic Aromatic Hydrocarbons in Subcritical Water: a Predictive Approach Using EoS/GE Models. Fluid Phase Equilibria 2015, 399, 22-29. (16) Wang, S.; Kim, S. H. Photophysical and Electrochemical Properties of D–π–A Type Solvatofluorchromic Isophorone Dye for pH Molecular Switch. Curr. Appl. Phys. 2009, 9, 783-787. (17) Kleinpeter, E.; Stamboliyska, B. A. Hyperpolarizability of Donor–Acceptor Azines Subject to Push–Pull Character and Steric Hindrance. Tetrahedron 2009, 65, 9211-9217. (18) Ashraf, M.; Teshome, A.; Kay, A. J.; Gainsford , G. J.; Bhuiyan , M. D. H.; Asselberghs, I.; Clays, K. NLO Chromophores Containing Dihydrobenzothiazolylidene and Dihydroquinolinylidene Donors with an Azo linker: Synthesis and Optical Properties. Dyes pigm. 2013, 98, 82-92.


Page 12 of 30

Page 13 of 30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(19) Derrar, S. N.; Sekkal-Rahal, M.; Derreumaux, P.; Springborg, M. Theoretical Study of the NLO Responses of Some Natural and Unnatural Amino Acids used as Probe Molecules. J. Mol. Model. 2014, 20, 2735-2742. (20) Derrar, S. N.; Sekkal-Rahal, M.; Guemra, K.; Derreumaux, P. Theoretical Study on a Series of Push–Pull Molecules Grafted on Methacrylate Copolymers Serving for Nonlinear Optics. Int. J. Quant. Chem. 2012, 112, 2735-2742. (21) Blanchard-Desce, M.; Alain, V.; Midrier, L.; Wortmann, R.; Lebus, S.; Glania, C.; Kramer, P.; Fort, A.; Muller, J.; Barzoukas, M. Intermolecular Charge Transfer and Enhanced Quadratic Optical Non-Linearities in Push-Pull Polyenes. Photochem. Photobiol A 1997, 105, 115-121. (22) Ravikumar, C.; Joe, I. H.; Jayakumar ,V.S. Charge Transfer Interactions and Nonlinear Optical Properties of Push–Pull Chromophore Benzaldehyde Phenylhydrazone: a Vibrational Approach. Chem. Phys. Lett. 2008, 460, 552-558. (23) Zhao, Y.; Ye, C.; Qiao, Y.; Xu, W.; Song, Y.; Zhu, D. A novel Donor Acceptor Molecule Containing a Cyclic Triphenylamine Dimer: Synthesis, Characterization, and Application in Memory Device. Tetrahedron 2012, 68, 1547-1551. (24) Marcano, E.; Squitieri, E.; Murgich, J.; Soscun, H. Theoretical Investigation of the Static (Dynamic) Polarizability and Second Hyperpolarizability of DAAD Quadrupolar Push– Pull Molecules. A Comparison Among HF (TD-HF), DFT (TD-B3LYP), and MP2 (TD-MP2) Methods. Comput.Theo.Chem. 2012, 985, 72-79. (25) Castet, F.; Pic, A.; Champagne, B. Linear and Nonlinear Optical Properties of Arylvinyldiazine Dyes: A Theoretical Investigation. Dyes and Pigm. 2014, 110, 256-260. (26) Sayin, K.; Karakas, D.; Karakus, N.; Sayin, T. A.; Zaim, Z.; Kariper, S. E. Spectroscopic Investigation, FMOs and NLO Analyses of Zn(II) and Ni(II) Phenanthroline Complexes: A DFT Approach. Polyhedron 2015, 90, 139-146. (27) Cheng, L.T.; Tam, W.; Meridith, G. R. Nonresonant EFISH And THG Studies Of Nonlinear Optical Property And Molecular Structure Relations Of Benzene, Stilbene, And Other Arene Derivatives. NLO prop. Orga. Mater. 1989, 1147, 61-67. (28) Suslick, K. S.; Chen, C-T.; Meredith, G. R.; Cheng, L-T. Push-Pull Porphyrins as Nonlinear Optical Materials. J. Am. Chem. Soc. 1992, 114, 6928-6930. (29) Suponitsky, K. Y.; Timofeeva, T.V.; Antipin, M. Y. Molecular and Crystal design of Nonlinear Optical Organic Materials. Russ. Chem. Rev. 2006, 75, 457-496. (30) Zhang, M. Y.; Ma, N. N.; Sun, S. L.; Qiu, Y-Q.; Chen, B. Quantum Chemical Study on First Hyperpolarizabilities of Mono- and Bimetal Pt(II) Diimine Complexes. J. Org. Chem. 2012, 718, 1-7.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(31) Liu, C. G.; Qiu, Y. Q.; Sun, S. L.; Chen, H.; Li, N.; Su, Z. M. DFT Study on SecondOrder Nonlinear Optical Properties of a Series of Mono Schiff-Base M(II) (M = Ni, Pd, Pt) Complexes. Chem. Phys. Lett. 2006, 429, 570-574. (32) Zhang, Y.; Castet, F.; Champagne, B. Theoretical Investigation of the First Hyperpolarizability Redox-Switching in a Ruthenium Complex. Chem. Phys. Lett. 2013, 574, 42-46. (33) de Wergifosse, M.; Castet, F.; Champagne, B. Frequency Dispersion of the First Hyperpolarizabilities of Reference Molecules for Nonlinear Optics. J. Chem. Phys. 2015, 142, 1-7. (34) Champagne, B.; Perpete, E. A.; van Gisbergen, S. J. A.; Baerends, E.J.; SoubraGhaoui, C.; Robins, K. A.; Kirtman, B. Assessment of Conventional Density Functional Schemes for Computing the Polarizabilities and Hyperpolarizabilities of Conjugated Oligomers: An ab initio Investigation of Polyacetylene Chains. J. Chem. Phys. 1998, 109, 10489-10498. (35) Champagne, B.; Perpète, E. A.; Jacquemin, D.; van Gisbergen, S. J. A.; Baerends, E. J.; Soubra-Ghaoui, C.; Robins, K.A.; Kirtman, B. Assessment of Conventional Density Functional Schemes for Computing the Dipole Moment and (Hyper) Polarizabilities of PushPull π-Conjugated Systems. J. Phys. Chem. A. 2000, 104, 4755-4763. (36) Gruning, M.; Gritsenko, O.V.; van Gisbergen, S.J.A.; Baerends, E.J. On the Required Shape Corrections to the Local Density and Generalized Gradient Approximations to the Kohn–Sham Potentials for Molecular Response Calculations of (Hyper) Polarizabilities and Excitation Energies. J. Chem. Phys. 2002, 116, 9591-9601. (37) Rohrdanz M. A.; Martins, K. M.; Herbert, J. H. A long-Range-Corrected Density Functional that Performs Well for Both Ground-State Properties and Time-Dependent Density Functional Theory Excitation Energies, Including Charge-Transfer Excited States. J. Chem. Phys. 2009, 130, 1-8. (38) Garza, A. J.; Wazzan, N. A.; Asiri, A.M.; Scuseria, G. E. Can Short- and Middle-Range Hybrids Describe the Hyperpolarizabilities of Long-Range Charge-Transfer Compounds. J. Phys.Chem. A 2014, 118, 11787-11796. (39) Shelton, D. P.; Rice, J. E. Measurements and Calculations of the Hyperpolarkabilities of Atoms and Small Molecules in the Gas Phase. Chem. Rev. 1994, 94, 3-29. (40) de Wergifosse, M.; Champagne, B . Electron Correlation Effects on the First Hyperpolarizability of Push-Pull π-Conjugated Systems. J. Chem. Phys. 2011, 134, 7-13. (41) Karton, A.; Martin, J. M. L. Comment on “Estimating the Hartree-Fock Limit From Finite Basis Set Calculations”. Theor. Chem. Acc. 2006, 115, 330-333. (42) Tozer, D. J.; Handy, N. C. Improving virtual Kohn–Sham Orbitals and Eigenvalues: Application to Excitation Energies and Static Polarizabilities. J. Chem. Phys. 1998, 109, 10180-10189.


Page 14 of 30

Page 15 of 30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(43) Tozer, D. J.; Handy, N. C. Relationship Between Long-Range Charge-Transfer Excitation Energy error and Integer Discontinuity in Kohn–Sham Theory. J. Chem. Phys. 2003, 119, 12697-12699. (44) Alipour, M.; Parisa Fallahzadeh, P. First Principles Optimally Tuned Range-Separated Density Functional Theory for Prediction of Phosphorus–Hydrogen Spin–Spin Coupling Constants . Phys. Chem. Chem. Phys. 2016, 18, 18431-18440. (45) Zhao, Y.; Truhlar, D. G. Density Functionals with Broad Applicability in Chemistry. Acc.Chem. Res. 2008, 41, 157-167. (46) Zhao, Y.; Truhlar, D. G. DensityFunctional for Spectroscopy: No Long-Range SelfInteraction Error, Good Performance for Rydberg and Charge-Transfer States, and Better Performance onAverage than B3LYP for Ground States. J. Phys. Chem. 2006, 110, 1312613130. (47) Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two new Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215-241. (48) Wang, B. C.; Chang, J. C.; Tso, H. C.; Hsu, H. F.; Cheng, C. Y. Theoretical Investigation The Electroluminescence Characteristics of Pyrene and Its Derivatives. J. Mol. Struct:THEOCHEM 2003, 629, 11-20. (49) Kanai, M.; Hirano , T.; Azumaya, I.; Okamoto, I.; Kagechika, H.; Tanatani, A. Solvent-Dependent Conformational and Fluorescence Change of an NPhenylbenzohydroxamic Acid derivative Bearing two Pyrene Moieties. Tetrahedron 2012, 68, 2778-2783. (50) Moorthy , J. N.; Natarajan, P.; Venkatakrishnan, P.; Huang, D. F.; Chow, T. J. Steric Inhibition of π-Stacking: 1, 3, 6, 8-Tetraarylpyrenes as Efficient blue Emitters in Organic Light Emitting Diodes (OLEDs). Org. Lett. 2007, 09, 5215-5218. (51) Rodríguez-Alba, E.; Ortíz-Palacios, J.; Morales-Espinoza, E. G.; Vonlanthen, M.; Valderrama, B. X.; Rivera, E. Synthesis, Characterization and Optical Properties of Novel Oligothiophenes Bearing pyrene Units Attached via Well defined Oligo (ethylene glycol) Spacers. Synthetic.Met. 2015, 206, 92-105. (52) Fort, A.; Boeglin, A; Mager, L.; Amyot, C.; Combellas, C.; Thiébault, A.; Rodriguez, V. Geometry and Quadratic Optical Propertises of Push-Pull Biphenyls Twisted Synthetic.Met. 2001, 124, 209-211. (53) Orucu, H.; Acar, N. Effects of Substituent Groups and Solvent Media on Pyrene in Ground and Excited States: A DFT and TDDFT study. Comput. Theo. Chem. 2015, 1056, 1118. (54) Mohi, A. T .Theoretical Study of Substituent Effects on Electronic and Structural Properties and IR Spectrum of 1,3,6,8-Tetrahalogens Pyrene Compounds via Density Functional Theory . IJAIEM. 2013, 2, 228-234.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(55) Ledwon, P.; Lapkowski, M.; Licha, T.; Frydel, J.; Idzik, K. R. The role of Furyl Substituents of Pyrene on Monomer and Polymerproperties .Synthetic. Met. 2014, 191, 74-82. (56) Qiao, Y.; Zhang, J.; Xu,W.; Zhu, D. Novel 2,7-Substituted Pyrene derivatives: Syntheses, Solid-State Structures, and Properties. Tetrahedron 2014, 191, 74-82. (57) Xinf, F.; Jian-Young, H.; Xian-Fu, W.; Carl, R.;Takehiko, Y. Influence of Substituent Position on Thermal Properties Photoluminescence and Morphology of Pyrene–Fluorene derivatives .J.Mol.Struct :THEOCHEM 2015, 1086, 216-222. (58) Ma, B. B. ; Peng, Y. X; Zhao, P. C.; Huang , W. Cis and Trans Isomers Distinguished by Imidazole N-alkylation after Debus-Radziszewski Reaction Starting From 2,7-di-TertButylpyrene-4,5,9,10-Tetraone.Tetrahedron 2015, 71, 3195-3202. (59) Rujkorakarn, R. ; Tanaka, F. Three-Dimensional Representations of Photo-Induced Electron Transfer Rates in Pyrene-(CH2)n-N,N0-dimethylaniline Systems Obtained by Three Electron Transfer Theories. J. Mol.Graph. Model. 2009, 27, 571-577. (60) Makowska, J. M.; Kajzar, F.; Miniewicz, A.; Mydlova, L.; Rau, I. First Principle Calculations of the Electronic and Vibrational Properties of the 3‑(1,1-dicyanoethenyl)-1phenyl-4,5-dihydro-1Hpyrazole Molecule. J. Phys. Chem A. 2015, 119, 1347−1358. (61) Frisch, M .J.; Trucks, G. W. ; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B. G.; Petersson, A.; et al. Gaussian Inc, Wallingford CT, 2009. (62) Gaussview 05 , Dennington, R. ; Keith, T.; Millam, J.; Semichem Inc, Shawnee Mission KS, 2009. (63) Benkova, Z.; Cernusak, I.; Zahradnık, P. Theoretical Study of Static Electric Properties of Benzothiazole Containing Push–Pull Systems as Potential Candidates for NLO Materials. J.Struct .Chem . 2006, 17, 287–300. (64) Labidi, N. S.; Djebaili, A.; Rouina, I. Substitution Effects on the Polarizability (Α) and First Hyperpolarizability (β) of All-Trans Hexatriene. Saudi Chemical Society 2011, 15, 2937. (65) Xiao, H.; Yin, H.; Zhang, X. Improved Nonlinearity–Transparency–Thermal Stability Trade-Off with Spirobifluorene-Bridged Donor-π-Acceptor Chromophores. J.org.lett. 2012, 14, 82-85. (66) Cariati, F.; Caruso, U. ; Centore, R.; De Maria, A.; Fusco, M. ; Panunzi, B. ; Roviello, A., Tuzi , A .Optical Second Order Nonlinearities in New Chromophores Obtained by Selective Mono-Reduction of Dinitro Precursors. Optical Materials 2004, 27, 91-97. (67) Zhao, Y.; Truhlar, D. G. A new Local Density Functional for Main-Group Thermochemistry, Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent Interactions. J. Chem. Phys. 2006, 125, 94-101.


Page 16 of 30

Page 17 of 30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(68) Stephens, P. J.; Devlin, F. J. ; Chabalowski ,C. F.; Frisc,M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J. Phys. Chem. 1998, 45, 11623–11627. (69) Carlo, A.; Vincenzo, B . Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model. J.Chem. Physi. 2013, 110, 6158–6170. (70) Boese, A. D.; Martin, J. M, Development of Density Functionals for Thermochemical Kinetics. J. Chem. Phys. 2004, 121, 3405-16. (71) Becke, A. D. A new Mixing of Hartree-Fock and Local Density-Functional Theories. J. Chem. Phys. 1993, 98, 72-77. (72) Yanai, T.; Tew, D.; Handy, N. A New Hybrid Exchange-Correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP).Chem. Phys. Lett. 2004, 393, 51-57. (73) Adamo, C.; Cossi, M.; Barone, V. An Accurate Density Functional Method for the Study of Magnetic Properties: the PBE0 Model. J.Mol. Struct : THEOCHEM 1999, 493, 145157. (74) Michael Peach, J. G.; Tellgren, E.; Sałek, P.; Helgaker, T.; David Tozer, J. Structural and Electronic Properties of Polyacetylene and Polyyne from Hybrid and CoulombAttenuated. Density Functionals. J. Phys. Chem A. 2007, 111, 11930-11935. (75) Jacquemin, D.; Perpète, E. A.; Ciofini, I.; Adamo, C.; Valero, R.; Zhao, Y.; Truhlar, D. G. On the Performances of the M06 Family of Density Functionals for Electronic Excitation Energies. J. Chem. Theory Comput. 2010, 6, 2071–2085. (76) Head-Gordon, M.; Head-Gordon, T. Analytic MP2 Frequencies Without Fifth Order Storage: Theory and Application to Bifurcated Hydrogen Bonds in the Water Hexamer. Chem. Phys. Lett. 1994 , 220, 122-28. (77) de Wergifosse, M.; Wautelet, F.; Champagne, B.; Kishi, R.; Fukuda, K.; Matsui, H.; Nakano, M. Challenging Compounds for Calculating Hyperpolarizabilities: pQuinodimethane Derivatives. J. Phys. Chem. A. 2013, 117, 4709-4715. (78) Medved, M.; Budzak, S.; Cernušak, I. High Second-Order NLO Responses of Dehydrogenated Hydrogen Cyanide Borane(1) Oligomers. J.Mol. Struct : THEOCHEM 2010, 961, 66-72. (79) Alparone, A. Linear and Nonlinear Optical Properties of Nucleic Acid Bases.Chem. Phys. 2013, 410, 90-98. (80) Medved, M.; Jacquemin, D. Tuning the NLO Properties of Polymethineimine Chains by Chemical Substitution.Chem. Phys. 2013, 415, 196-206. (81) Pereira Silva, P. S. ; El Ouazzani, H.; Pranaitis, M.; Ramos Silva, M.; Arranja, C. T.; Abilio Sobral , J. F. N. ; Sahraoui, B.; Paixao, J. A. Experimental and theoretical studies of the Second- and Third-Order NLO Properties of a Semi-Organic Compound: 6Aminoquinolinium iodide Monohydrate. Chem. Phys. 2014, 428, 67-74. (82) Sinha, L.; Prasad, O.; Karabacak, M.; Mishra, H. N.; Narayan, V.; Asiri, A. M. Quantum-Chemical (DFT, MP2) and Spectroscopic Studies (FT-IR and UV) of Monomeric



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

and Dimeric Structures of 2(3H)-Benzothiazolone. Spectrochimica. Acta Part A 2014, 120, 126-136. (83) Nandi, P. K.; Mandal,K.; Kar, T. Ab Initio SCRF Study of Solvent Effect on the Nonlinear Polarizabilities of Different Intramolecular Charge-Transfer Molecules. Theo. Chem. Acc. 2005, 114, 200-207. (84) Seshadri, S.; Rasheed .M.P.; Sangeetha, R. Vibrational Spectroscopic (FT-IR and FTRaman) Studies, HOMO LUMO Analysis and Electrostatic Potential Surface of 2-Amino-4, 5-Dimethyl-3-Furancarbonitrile. IOSR J.Applied Chem .2015, 15, 87-100. (85) Michielan, L.; Bacilieri,M.; Kaseda, C. ;Moro, S. Prediction of the Aqueous Solvation Free Energy of Organic Compounds by Using Autocorrelation of Molecular Electrostatic Potential Surface Properties Combined with Response Surface Analysis .Bioorg. Med. Chem. 2008, 16, 33-42.

Table. 1. Static hyperpolarizabilities (in units of 10-30 esu) obtained for P1, P2, P3, P4 and P5 compounds from different hybrid functionals incorporating a given HF exchange amount (%X) and Pure HF method compared with those obtained with MP2 as reference. Mean Absolute Error (MAE %) is calculated for each method compared to MP2.


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Page 19 of 30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Method

M06-L

B3LYP

PBE0

BMK

BHHLYP

MO6-2X

CAMB3LYP

MO6-HF

HF

MP2

%X

0

20

25

42

50

54

65

100

-

-

P1

217.28

189.20

172.55

148.06

101.37

103.99

107.16

42.87

30.79

105.72

P2

163.17

144.09

131.01

111.70

82.36

83.3

86.96

36.33

26.98

88.91

P3

151.93

136.28

123.39

10.01

78.68

79.46

83.39

34.2

25.65

85.62

P4

139.77

114.54

102.37

88.02

63.89

64.27

67.32

25.74

20.77

71.89

P5

118.68

100.64

90.27

79.22

58.86

57.82

61.69

22.93

20.21

66.65

MAE

87.79

62.10

46.50

26.39

8.48

7.79

3.44

61.68

70.27

-

.

Table. 2. Static hyperpolarizabilities (in units of 10-30 esu) obtained for Phy1, Phy2, Phy3, Phy4 and Phy5 compounds from different hybrid functionals incorporating a given HF exchange amount (%X) compared with those obtained with MP2 as reference. Mean Absolute Error (MAE %) is calculated for each method compared to MP2.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 30

Method

PBE0

BMK

BHHLYP

MO62X

CAM-B3LYP

MP2

%X

25

42

50

54

65

-

Phy1

600.63

411.73

318.63

319.66

288.63

278.15

Phy2

469.92

322.90

258.57

253.34

233.43

253.16

Phy3

453.41

313.40

253.70

246.12

228.14

247.55

Phy4

363.65

253.95

207.11

197.41

185.86

187.12

Phy5

335.62

233.97

175.90

184.62

173.17

179.15

MAE %

75.14

33.69

5.60

4.59

3.17

-

Table. 3. Static hyperpolarizabilities β0 (in units of 10-30 esu) and their projections on the three axes, dipole moments µ (Debye) and their projections on the three axes, energy gaps ∆EH-L (eV) obtained with CAM-B3LYP/cc-pvdz level of theory for compounds P1, P2, P3, P4, P5, P’1, P’2, P’3, P’4 and P’5. Molécules

βX

βY

βZ

β0

μx

μy


μz

μ tot

(gap)

Page 21 of 30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


P1

105.62

18.10

0.62

107.16

10.28

1.65

0.39

10.42

4.76

P2

86.14

11.83

1.34

86.96

-8.33

2.03

-0.16

8.58

4.88

P3

82.30

14.89

0.75

83.39

9.52

2.16

0.88

9.80

5.10

P4

66.46

10.70

0.16

67.32

8.33

0.74

0.82

8.41

5.02

P5

60.79

10.53

0.25

61.69

8.16

0.44

1.02

8.24

5.05

P’1

72.51

11.84

0.62

70.73

9.43

1.68

0.26

9.58

4.78

P’2

57.46

7.29

1.17

57.77

-7.56

1.92

-0.06

7.80

4.88

P’3

54.06

7.99

0.77

52.62

8.71

2.23

0.75

9.20

4.88

P’4

40.80

5.99

0.20

39.71

7.60

0.80

0.74

7.68

5.02

P’5

36.76

5.82

0.20

35.83

7.45

0.50

0.93

7.53

5.05

Table. 4. Polarizabilities α (in units of 10-24esu), Static hyperpolarizabilities β0 (in units of 1030 esu), Dipole moments µ (Debye), D distance the N atom belonging to (NO2) group and that belonging to N(CH3)2 group (Å), Energy gaps ∆EH-L (eV), π */π quotients, delocalization energy E(2) (kcal/mol), ∆E Electronic relative energy (kcal/mol), obtained with CAMB3LYP/cc-pvdz for different position isomers.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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*

Isomers

α

β0

μ

D

Gap

π /π

E(2)

ΔE

1.3DVP

46.15

39.00

7.80

8.63

4.923

0.107

45.81

3.67

1.4 DVP

45.81

43.21

7.46

9.76

4.947

0.105

44.29

4.14

1.5 DVP

48.19

98.11

10.09

12.59

4.936

0.109

46.87

3.52

1.6 DVP

49.96

107.16

10.56

13.57

4.780

0.116

54.28

1.33

1.7 DVP

48.64

66.29

9.59

13.66

5.048

0.115

52.97

0.00

1.8 DVP

47.85

65.88

7.34

9.84

4.811

0.114

53.92

2.71

1.9 DVP

46.52

46.36

7.18

8.68

4.931

0.110

47.10

3.42

Table. 5. Static hyperpolarizabilities β0 (in units of 10-30 esu), Dipole moments µ (Debye) and total density surfaces tds (a.u.) represented according to MESP values.

position

β0, µ, tds

MESP


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1.3 DVP

39.00, 7.80, ±5.34x10-2

1.4 DVP

43.21, 7.46, ±5.30x10-2

1.5 DVP

98.11, 10.09, ±5.52x10-2

1.6 DVP

107.16, 10.56, ±5.55x10-2

1.7 DVP

66.29, 9.59, ±5.41x10-2

1.8 DVP

65.88, 7.34, ±5.45x10-2

1.9 DVP

46.36, 7.18, ±5.47x10-2

Table 6. Static first hyperpolarisabilities (β0; in units of10-30 esu) obtained for Nitro 1,6 N(CH3)2 DVP using CAM-B3LYP method combined with different basis sets. Bases 6-31G

βX 161.76

βY 28.84

βZ 0.01


β0 164.31


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

6-31+G 6-31G(d) 6-31+G (d) 6-31G (d.p) 6-31+G (d. p) 6-31++G (d. p) cc-pvdz 6-311G 6-311+G 6-311G (d) 6-311G (d. p) 6-311+G (d. p) 6-311++G (d. p) cc-pvtz

191.87 106.55 123.74 106.55 124.35 124.03 105.62 160.38 184.97 98.38 101.38 115.90 115.70 103.46

33.89 18.33 20.68 18.41 20.90 20.32 18.10 30.84 32.89 16.64 17.31 20.35 19.09 17.66

0.94 0.52 1.48 0.51 1.52 1.81 0.62 0.41 0.80 0.96 1.00 1.42 1.69 0.88

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194.25 108.12 125.47 108.13 126.11 125.70 107.16 163.21 187.87 99.78 102.78 117.68 117.28 104.96

Fig. 1. Schematic representation of the considered compounds


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 2. Schematic representation of the Phn molecules (n= 1, 2, 3, 4, 5)


Page 26 of 30

Page 27 of 30

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Fig.3. (a) Evolution of first hyperpolarizability β0 ,(b) µ (Debye), (c) ∆E Electronic relative energy (kcal/mol), (d) gaps ΔEH-L (eV),(e) E2 (kcal/mol) and (f) π*/π quotient with respect to the substitution positions (1,3), (1,4), (1,5), (1,6), (1,7), (1,8) and (1,9).



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position

structure

HOMO

∆E H-L (eV)

1.3 DVP

4.92 (eV)

1.4 DVP

4.94 (eV)

1.5 DVP

4.93 (eV)

1.6 DVP

4.78 (eV)

1.7 DVP

5.04 (eV)

1.8 DVP

4.81 (eV)


Page 28 of 30

LUMO

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1.9DVP

4.93 (eV)

Figure 4. HOMO & LUMO calculated with CAM-B3LYP/cc-pvdz for DVP derivatives isomers



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Table of Contents Graphic


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Performance of Hybrid DFT Compared to MP2 Methods in Calculating

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