75 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 © Global Society of Scientific Research and Researchers http://asrjetsjournal.org/ Computational Determination of Reactivity Descriptors, Vibrational Analysis and Nuclear Magnetic Resonance of (E)-5-oxo-1-phenyl-4-(2-phenylhydrazono)-4,5-dihydro- 1H-pyrazole-3-carbaldehyde Nagwa M. M. Hamada a* , Mohamed A. El Sekily b , Sohila H. Mancy c a,c Department of Physics and Chemistry, Faculty of Education, University of Alexandria, 21526 Alexandria, Egypt b Department of Chemistry, Faculty of Science, University of Alexandria, 21321 Alexandria, Egypt . a Email: sohaylamansy@gmail.com b Email: prof_dr_m_a_elsekily@yahoo.com Abstract The title compound, pyrazole carbaldehyde have been optimized using Gaussian 9 software program, via density functional theory framework (DFT/B3LYP) by 6-311G (d, p) basis set, the output file was visualize using Gaussian view program, geometric properties, thermochemical and reactivity descriptors such as ionization potential (IP), electron affinity (EA), electronegativity (χ), chemical potential (μ), hardness (η), softness (σ), electrophilicity index (ω) and nucleophilicity index (N) were calculated. Mapping of electrostatic surface potential (MESP) allow us to establish trends that enable making predictions about the reactive sites of the studied compound. Besides, the optimized structure is subjected to frequency analysis at the same level of theory to obtain thermodynamic correction values. Vibrational assignments and nuclear magnetic resonance ( 1 H- & 13 C-NMR) chemical shifts of the molecule were calculated by gauge independent atomic orbital (GIAO) method using the CPCM model, and mapping of current density shielding of proton and carbon nucleus of the aldehyde group shied light on the molecular properties and reactivity of 5-oxo-1-phenyl-4-(2-phenylhydrazono)- 4,5- dihydro-1H-pyrazole-3-carbaldehyde . Keywords: Pyrazole carbaldehyde; DFT; Chemical potential; Hardness; Shielding density. ------------------------------------------------------------------------ * Corresponding author American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 75-91 76 1. Introduction At the end of the 1980s of the twentieth century, ab initio Hartree-Fock (HF) calculations [1], enabled the study of the molecular mechanism of many organic reactions by characterizing the stationary points involved in a reaction. The electron density is more attractive and effective in explaining properties where it is measurable depends only on the Cartesian axes, x, y, and z. The fact that the ground state properties are functionals of the electron density ρ (r) was introduced by Hohenberg and Kohn [2] and it is the basic framework for modern Density functional (DF) methods [3], where the total ground state energy of an electron system can be written as a functional of the electronic density. At the end of the 20th century, a new theory based on the studying of the electronic structure of the matter was developed, known as Density Functional Theory (DFT), after its applications [4-7] a few decades ago, DFT has been recognized as a powerful tool to provide theoretical insights into chemical reactivity and how this influences the synthesis of different heterocyclic compounds, [8-15]. The split-valence basis sets were introduced by John Pople and his group in the late 1970s. There are an expansion of basis sets to make the total function more accurate and reliable. In general, polarization functions significantly improve the description of molecular geometries (bond lengths and angles) as well as molecular relative energies. The use of the density functional theory (DFT) calculations for predicting the molecular structure, as well as spectroscopic properties of organic compounds, are of great interest, and the selection of the proper basis set for the optimization of the studied molecule is very important. [16-19]. It has been reported that a large number of interesting pharmaceutical heterocyclic derivatives have been synthesized using the title compound 5-oxo-1-phenyl-4-(2-phenylhydrazone)-4,5-dihydro-1H-pyrazol-3-yl)-3-carbaldehyde, this attract our attention to study theoretically the activity of the pyrazole-aldehyde as a reaction intermediate in organic synthesis [20-22]. From this point of view, DFT calculations have been applied on the title aldehyde computed at The Lee, Yang, and Parr Correlation Energy Functional DFT/B3LYP at the triply split valence basis set 6311G (d,p) to generate quantum mechanical descriptors used in quantitative structure-activity relationship (QSAR) to explain its geometrical and energetic properties. Experimentally obtained physical and spectroscopic properties will be presented and validated by theoretical parameters related to the molecular reactivities such as electronegativity, dipole moment, electrophilicity, chemical potential, softness and hardness which are obtained by quantum chemical computations using DFT approximations [14,15, 23-27]. The electrostatic surface potential maps (ESP) maps of the energetically optimized molecules will also be reported [28,29]. 2. Materials and Methods Computations were performed using, ab initio/ DFT /B3LYP [30,31] from Gaussian 09 program package, GaussView 05 program [32-34]. was used to get the graphical presentations of calculated IR and 1 H-NMR spectra. Harmonic vibrational frequencies of the optimized geometries were calculated by employing the widely used B3LYP /6-311G (d,p) model, in order to verify that they are true minima (with zero imaginary frequencies). The calculation of 1 H NMR chemical shifts was performed by Gauge Induced atomic orbital (GIAO) method at the same level of theory. 3. Results and Discussion 3.1. Optimization calculations American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 75-91 77 The aim of the present work was to describe and characterize the molecular structure, vibrational frequencies and chemical shifts of the starting pyrazole carbaldehyde. The title compound was computed using DFT/B3LYP 6311 G (d,p) in gas phase and in acetonitrile as aprotic solvent, the results showed that there is no significant difference between the data obtained from both media, and this reflects that there is no solvent effect by acetonitrile, so we herein discuss the results obtained from the study in the gas phase only. The optimized structure with Mulliken charge numbers of the computed compound is shown in Figure 1. Figure 1: Optimized structure of the title compound calculated The plots display the total energy of the optimized structure is shown in Figure 2. Figure 2: Total energy optimization of the title compound American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 75-91 78 3.2. Mulliken Charges and Geometrical Parameters The Mulliken atomic charges of the studied compound are shown in Table 1. The charges at all the carbon atoms have negative values except that at C-3 (0.295150), C-20 (0.213292), C-32 (0.205287), C-2 (0.136294) and C-6 (0.086755), which can be responsible for nucleophilic attack centers. The large negatively charged atoms are O-17(-0.415732), N-19 (- 0.322440), N-5(-0.320278), O-33(-0.264034), N-18 (-0.155118), N-4(- 0.152470). It is interesting to note the difference in distances of the two oxygen atoms of the carbonyl groups, the bond length of the carbonyl of the pyrazole ring (C3-O17) appeared to be 1.43 Aº which is longer than that of the carbonyl of the aldehyde group (C32-O33) which appeared to be 1.2273 Aº , There is one kind of intermolecular hydrogen bonding interaction, hydrogen bonding interactions between the oxygen atom of the pyrazole ring and the hydrogen 12 of the aromatic ring [3C=O17………..H12]; ( 1.4731 Aº), bond lengths, and the average angles within the molecule are in a good agreement with those reported in the literature [35, 36]. Selected bond distances and related angles are collected in Table 1. Table 1: Mulliken Charge, bond lengths (Aº) and selected bond angles(º) of the title compound calculated at DFT/B3LYP/6-311G (d,p) Mulliken Charges Bond lengths (Aº) Bond angles (º) C-1 -0.026303 C-2 0.136294 C-3 0.295150 N-4 -0.152470 N-5 -0.320278 C-6 0.086755 C-7 -0.031808 C-8 -0.109997 C-9 -0.098779 H-10 0.132139 C-11 -0.101914 H -12 0.137239 C-13 -0.081483 H -14 0.099857 H -15 0.097334 H -16 0.095330 O -17 -0.415732 N-18 -0.155118 N-19 -0.322440 C -20 0.213292 C-21 -0.077706 C -22 -0.105951 C-23 -0.095728 H-24 0.123691 C-25 -0.094613 H -26 0.110329 C-27 -0.083064 H-28 0.105762 H-29 0.104745 H-30 0.103329 H-31 0.263615 C-32 0.205287 O-33 -0.264034 H-34 0.081261 (C-1, C-2) 1.5219 (C-1, N-4) 1.5222 (C-1, C-32) 1.54 (C-2, C-3) 1.5219 (C-2, N-18) 1.47 (C-3, N-5) 1.522 (C-3, O-17) 1.43 (N-4, N-5) 1.522 (N-5, N-6) 1.47 (C-6, C-7) 1.3952 (C-6, C-8) 1.3948 (C-7, C-9) 1.3947 (C-7, H-10) 1.0997 (C-8, C-11) 1.3951 (C-8, H-12) 1.0996 (C-9, C-13) 1.3954 (C-9, H-14) 1.0997 (C-11, C-13) 1.3948 (C-11, H-15) 1.0998 (H-12, O-17) 1.4731 (C-13, H-16) 1.0997 (N-18, N-19) 1.232 (N-19, C-20) 1.47 (N-19, H-31) 1.2566 (C-20, C-21) 1.3952 (C-20, C-22) 1.3948 (C-21, C-23) 1.3947 (C-21, H-24) 1.0997 (C-22 ,C-25) 1.3951 ( (C-22, H-26) 1.0996 (C-23, C-27) 1.3954 (C-23, H-28) 1.0997 (C-25, C-27) 1.3948 (C-25, H-29) 1.0998 (C-27, H-30) 1.0997 (C-32, O-33) 1.2273 (C-32, H-34) 1.1105 (C-2,C-1,N-4) 107.954 (C-2,C-1,C-32) 110.507 (N-4,C-1,C3-2) 110.534 (C-1,C-2,C-3) 107.940 (C-1,C-2,N-18) 110.317 (C-3,C-2,N-18) 110.332 (C-2,C-3,N-5) 107.914 (C-2,C-3,O-17) 110.333 (N-5,C-3,N-17) 110.327 (C-1,N-4,N-5) 107.974 (C-3,N-5,N-4) 107.959 (C-3,N-5,C-6) 110.507 (N-4,N-5,C-6) 110.547 (N-5,C-6,C-7) 119.997 (N-5,C-6,C-8) 120.004 (C-7,C-6,C-8) 119.999 (C-6,C-7,C-9) 120.009 (C-6,C-7,H-10) 119.981 (C-9,C-7,H-10) 120.011 (C-6,C-8,C-11) 120.0 (C-6,C-8,H-12) 120.008 (C-11,C-8, H-12) 119.992 (C-7, C-9, C-13) 119.994 (C-7, C-9, H-14) 120.013 (C-13, C-9, H-14) 119.993 (C-8, C-11,C-13) 120.005 (C-8,C-11,H-15) 119.984 (C13,C11,H15) 120.011 (C-9,C-13,C-11) 119.994 (C-9,C-13,H-16) 119.981 (C-11,C-13,H-16) 120.025 (N-18,N-19,H-31) 96.975 (C-20,N-19,H-31) 83.025 (N-19,C-20,C-21) 119.997 (N-19,C-20,C-22) 120.004 (C-21,C-20,C-22) 119.999 (C-20,C-21,C-23) 120.009 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 75-91 79 3.3. eactivity descriptors of the title compound. The quantum chemical descriptors of the title compound were calculated using DFT/B3LYP /6311 G (d,p) in gas phase, all the calculated descriptors [37-40] depends mainly on the energy of the frontier molecular orbitals EHOMO (High occupied molecular orbital) and ELUMO (Low unoccupied molecular orbital) , the ground state plot for the frontier molecular orbitals of the title compound is shown in Figure 3. Figure 3: The ground state plots for the frontier molecular orbitals of the title compound . In general chemical potential is the link between structure and reactivity as the greater chemical potential of studied compounds the greater its reactivity, the defined index of chemical potential (μ) is depends on the value of the electronegativity index (χ) which is the mean value of EHOMO and ELUMO, defined in terms of ionization energy (IP) and electron affinity (EA) as follows: χ = (IP +EA)/2 and consequently the chemical potential (μ) = - χ , the hardness is given by: η = 0.5 (ELUMO - EHOMO), softness (σ) =1/ η . As electrophilicity/nucleophilicity are useful concepts to explain electronic aspects of reactivity, selectivity, substituent effects, solvent effects, etc., the development of such scales becomes strongly justified. Within this point of view, the electrophilicity index ( ω = μ 2 /2η) which measures the total ability to attract electrons, shows the tendency of an electrophile to acquire an extra amount of electron density, and the resistance of a molecule to exchange electron density with the environment given by the chemical hardness (η ) & softness (σ) has shown to be a powerful tool. Furthermore, there are many attempts to define a nucleophilicity index, simple index was chosen for the nucleophilicity (N) which explain the maximum number of electrons that an electrophile can acquire, based on the HOMO energy, within DFT calculations, explain the reactivity of the organic material towards electrophiles [11,37,38] . The simple nucleophilicity index (N) is defined as N = EHOMO (ev) + 9.12 (ev), where -9.12 is the energy of the HOMO of tetracyano ethylene (TCE), this nucleophilicity scale is referred to TCE and taken as a reference because TCE exhibits the lowest HOMO energy (= -9.12 eV). For instance, Roy and his colleagues [39] proposed the local hardness and softness based on DFT reactivity descriptors predict both intramolecular and intermolecular nucleophilic attacks on carbonyl compounds. On the other hand, Chattaraj and his colleagues suggested that the inverse of electrophilicity (x) can also be a valid measure of nucleophilicity [40]. The American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 75-91 80 activation parameters of the starting pyrazol-carbaldehyde has been calculated according to the previous equations. From the results depicted in Table 2 we can conclude that, the target molecule with high electrophilicity index (ω)= 7.241eV and small value of nucleophilicity index = 2.86 is considered to be more likely attacked by a nucleophile, which is in agreement with the suggested mechanisms for the synthesized of heterocyclic compounds from the target compound in our recent article [22]. Also, the high value of the chemical potential (-4.721 eV) confirm our conclusion. Table 2: Reactivity descriptors of the studied compound 3.4. Molecular electrostatic potential Molecular electrostatic potential (MESP) diagram has been also used to predict the reactive sites for electrophilic and nucleophilic attack, as well as hydrogen bonding interaction [41-43], the MEP of the studied compound 1 calculated using B3LYP method with 6‒311G (d,p) basis set is shown in Figure 4. This figure provides a visual representation of the chemically active sites and comparative reactivity of atoms. Potential increases in the order red < orange < yellow < green < blue. The map represents that the region of maximum negative electrostatic potential is situated around the aldehyde group with MEP value around -6.822 a.u and the most positive region is found at phenyl hydrazone moiety & with a value of +6.822 a.u. Parameter Value Homo energy (eV) Lumo energy (eV) Energy gap (eV) Ionization potential IP (-EHOMO) Electron affinity EA (-ELUMO ) Electronegativity χ = (IP +EA)/2 Chemical potential μ = -χ Hardness η = (IP-EA)/2 softness (σ)=1/ η Electrophlicity index (ω) = μ2/ 2η Nucleophilicity = EHOMO + 9.12 -6.260 -3.182 3.078 6.260 3.182 4.721 -4.721 1.539 0.650 7.241 2.86 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 75-91 81 Figure 4: Electron density from total SCF density mapped with (ESP) of title compound (isovalue =0.0004). 3.5. Thermochemistry analysis Table 3: Thermodynamic parameters of the title compound calculated using B3LYP/6-311G(d,p) The computed vibration frequency of the pyrazole carbaldehyde, using DFT-B3LYP/6-311G (d.p) method , show some thermodynamic parameter values reflecting molecular polarities and the stability of the molecule.the target compound is asymmetric polar molecule, the computed total energy and thermodynamic parameters reflect the stability of the molecule. Table 3 shows different thermodynamic parameters of target molecule and the dipole moment calculation value. Standard enthalpies of formation are evaluated using calculated energies, zero point vibration energy (ZPVE), plus thermal contributions (to 298K) the calculated total energy is corrected by the ZPVE. 3.6. Vibrational analysis Computed harmonic frequencies of pyrazole carbaldehyde, shown in Figure 5. Table 4 contains experimental and scaled calculated wave numbers, correlation between the experimental and Parameters B3LYP/6-311 G(d,p) Rotational temperatures (Kelvin) 0.02741 0.00632 0.00513 Rotational constants (GHZ) 0.57121 0.13162 0.10697 X Y Z Zero-point vibrational energy (Kcal/mol) 160.38587 Total Energy ( Hartree ) -986.573 Dipole moment 5.173 Electronic and zero-point Energies (Hartree ) -986.317637 Electronic and thermal Energies (Hartree ) -986.299956 Electronic and thermal Enthalpies (Hartree ) -986.299012 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 75-91 82 theoretical wave numbers at B3LYP/6311G basis set, showed a good linear correlation (Figure 6) with a regression coefficient of R² = 0.9979. Figure 5: Computed harmonic frequencies of title compound. Table 4: Experimental FT-IR and calculated vibrational frequencies in cm -1 for the title compound Experimental Calculated Vibrational assignment 3250 3335 -N19-H31 stretching 3210 3217 Symmetric C-H stretching Aromatic 2825 2924 Symmetric C32-H34 1760 1789 Symmetric C32=O33 stretching 1638 1713 Symmetric C3=O17 stretching 1548 1553 C2=N18 stretching 1536 1540 C1=N4 stretching American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 75-91 83 Figure 6: Correlation graph between experimental and calculated wave numbers. 3.7. Nuclear Magnetic Resonance studies The optimized file of the studied compound was computed as NMR job at the same level of theory using The gauge-including atomic orbital (GIAO/ CPCM) method, and DMSO as solvent as shown in the screenshot of the out put wordPad file . Figure 7 Figure 7: Screenshot of the out put wordPad file From the output file of the NMR job, the results showed that the calculated chemical shift for the studied compound (Figure 8 & 9) for both 1 H-NMR and 13 C-NMR were in good correlation with the experimental one (Table 5) with a regression coefficient of R² = 0.9785 & 0.9549 for 1 H-NMR and 13 C-NMR respectively. (Figure 10 & 11). y = 1.021x - 3.973 R² = 0.9979 0 500 1000 1500 2000 2500 3000 3500 4000 0 500 1000 1500 2000 2500 3000 3500 C al cu la te d w av e n u m b e r cm -1 Experimental wave number cm-1 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 75-91 84 Figure 8: Optimized structure of the title compound with calculated 1 H-NMR chemical shift (ppm). Figure 9: Optimized structure of the title compound with 13 C-NMR chemical shift (ppm). American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 75-91 85 Table 5: Experimental and calculated 13 C-NMR & 1 H-NMR chemical shift (ppm). Carbon atom Experimental 13 C-NMR chemical shift (ppm) Calculated 13 C-NMR chemical shift (ppm) Hydrogen atom Experimental 1 H-NMR chemical shift(ppm) Calculated 1 H -NMR chemical shift (ppm) C-32 C-3 C-20 C-6 C-1 C-2 C-23 C-25 C-9 C-11 C-13 C-27 C-22 C-7 C-8 C-21 194.000 157.500 143.000 140.300 136.800 136.800 129.500 129.500 128.900 128.900 128.000 122.400 113.900 118.500 118.500 113.900 185.241 160.974 145.576 144.637 144.544 130.711 134.423 133.936 133.176 133.075 129.793 131.860 122.094 120.091 120.065 117.371 H-31 H-34 H-12 H-10 H-24 H-28 H-14 H-29 H-15 H-30 H-16 H-26 - - - - 11.700 9.500 8.900 8.060 7.793 7.550 7.231 7.220 7.200 7.130 7.120 7.100 - - - - 13.528 10.540 9.096 8.179 8.100 7.722 7.673 7.660 7.642 7.493 7.440 7.320 - - - - American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 75-91 86 Figure 10: Correlation graph between experimental and calculated 1 H-NMR chemical shift. Figure 11: Correlation graph between experimental and calculated 13 C-NMR chemical shift. In practice, NMR experiments do not measure the shielding directly, instead the common practice is to measure the chemical shifts as the change of resonance frequency of a nucleus relative to a given standard. Moreover, for historic reasons it is normally to reverse the frequency scale, i.e. nuclei more shielded than the standard are considered to have positive chemical shifts and those less shielded negative ones. The formal relation between the chemical shift and shielding tensors is given by: δ = 1σiso − σ, where δ is the chemical shift tensor, σ is the shielding tensor, 1 is the unit matrix and σiso is the isotropic value or trace of the shielding tensor of the standard reference used in the NMR experiments. Magnetic shielding tensors are given in units of ppm, and the J- coupling tensors are given in reduced SI units. This choice of units has been made so quantities given are independent of the isotope of the nucleus. The calculation of nuclear magnetic anisotropy shielding tensors via y = 1.2969x - 1.9109 R² = 0.9785 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 C al cu la te d 1 H -N M R c h e m ic al s h if t (p p m ) Experimental 1H-NMR chemical shift (ppm) y = 1.1215x - 19.554 R² = 0.9549 0 50 100 150 200 250 0 50 100 150 200 C al cu la te d 13 C -N M R c h e m ic al s h if t (p p m ) Experimental 13C-NMR chemical shift (ppm) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 75-91 87 gauge-including atomic orbital for nuclei C-1, H-31, C-32, H-34, is shown in Figure 12. Figure 12: Screen shot of the out put wordPad file with the anisotropy shielding tensor From the check point file of the GIAO calculations, shielding density maps are computed at shielding tensor (XX), diffuse functions of H-31, C-32, H-34 , which may be related to the fact that polar systems with lone pairs in general require diffuse functions for a competent description, is well suited for the conception and interpretation of the H-31 of the hydrazone moiety and C-32& H-34 of the aldehyde group (Figures 13, 14 and 15). Maps showing streamlines and modulus of the current density yield valuable tools for interpreting the large out-of plane component of the magnetic susceptibility and the proton deshielding. [15, 44, 45]. The electron density yield valuable tools for interpreting component of the magnetic susceptibility and the proton, carbon deshielding. This is in good agreement with the ESP map of the molecule (Figure 4) which describes the active sites at the hydrazine moiety and the aldehyde group. Figure 13: Shielding density as seen by nucleus H-31 in the XX directionmapped between the values of -2.632 to 2.632 on the current density isosurface at a value of 0.0004 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 75-91 88 Figure 14: Shielding density as seen by nucleus C-32 in the XX direction mapped between the values of -2.631 to 2.631on the current density isosurface at a value of 0.0004. Figure 15: Shielding density as seen by nucleus H-34 in the XX direction mapped between the values of -2.631 to 2.631on the current density isosurface at a value of 0.0004. 4. Conclusion In the present work, The B3LYP/ 6-311G (d, p) model within the DFT is used to optimize the structure of 5- oxo-1-phenyl-4-(2-phenylhydrazono)-4,5-dihydro-1H-pyrazol-3-yl)-1H-pyrazole-3-carbaldehyde and predict the American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2019) Volume 61, No 1, pp 75-91 89 structure-properties relationships. Reactivity parameters calculated from the frontier orbitals help in prediction of chemical potential, hardness, softness, electrophilicity as well as nucleophilicity of the pyrazol-carbaldehyde molecule. Moreover, thermodynamic parameters verify the conclusions drawn from the molecular polarity. Computed and visualized MESP map surfaces enable exploration of molecular reactive sites (hydrazone moiety and the aldehyde group), which confirmed by mapping of shielding density by nuclei H-31, C-31, H-34 in the XX direction mapped on the current density. References [1]. W.J. Hehre, L. Radom, P. v. R. 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