Theoretical Study of EUXIT 50 KI Epoxy and its Hardener using Hyperchem-8 Program
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1 Asian Journal of Applied Science and Engineering, Volume 5, No 3/2016 ISSN X(p); (e) Theoretical Study of EUXIT 50 KI Epoxy and its Hardener using Hyperchem-8 Program Ahlam Mohammed Farhan 1, Nafeesa Jabbar Kadhim 2*, Harith Ibrahem Jaafer 3 1,2 Department of Chemistry, College of Science for Woman, University of Baghdad, IRAQ 3 Department of Physics, College of Science, University of Baghdad, IRAQ ARTICLE INFO Received: Jan 16, 2017 Accepted: Feb 16, 2017 Published: Feb 26, 2017 *Corresponding Contact nafeesa.j1975@gmail.com ABSTRACT The work includes a theoretical study of the epoxy and its derivative where it was done by the program of hyperchem-8 using molecular mechanics and semi-empirical calculations. The heat of formation (ΔH f), binding energy (ΔE b) and total energy (ΔE tot.) of the epoxy and its derivative were calculated using the PM3 method at 298 K. Also, PM3 was used to evaluate the bond length and vibrational spectra of epoxy (A1) and epoxy with hardener complex (A2).The experimental values were compared with theoretical results that agree with those found experimentally. Key Words: Epoxy, Hardener, Computational chemistry, hyperchem-8 Source of Support: None No Conflict of Interest: Declared How to Cite: Farhan AM, Kadhim NJ and Jaafer HI Theoritical Study of EUXIT 50 KI Epoxy and its Hardener using Hyperchem-8 Program Asian Journal of Applied Science and Engineering, 5, This article is is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Attribution-NonCommercial (CC BY-NC) license lets others remix, tweak, and build upon work noncommercially, and although the new works must also acknowledge & be non-commercial. INTRODUCTION The term computational chemistry is used when a mathematical method is sufficiently well developed that it can be used automatically on a computer. The entire field of computational chemistry is built around approximate solutions. Some of these solutions are very crude but are still more accurate than any experiment that has yet been conducted (David, 2001). Molecular modeling is an aspect of computational chemistry, and a particular molecular system can be modeled with the hope that it could be synthesized in the laboratory, especially for species that are too difficult, dangerous, impossible or too expensive to carry out experimentally. Molecular modeling is a quite accurate method of accounting for properties like geometric and electronic structures, frequencies, chemical shifts, bond distances, bond angles. Semi-empirical PM3 calculations have been the best in predicting the geometric properties and vibrational frequencies of transition and organometallic Copyright CC-BY-NC 2014, Asian Business Consortium AJASE Page 159
2 Farhan et al.: Theoritical Study of EUXIT 50 KI Epoxy and its Hardener using Hyperchem-8 Program ( ) complexes (Warren, 2003). This was further confirmed by this study which also shows that PM3 calculations worked perfectly as it predicts closely the calculated properties with experimental results. The usefulness of the Semi-empirical, PM3 calculations in predicting the vibrational modes (Topacli and Topacli, 2003). Epoxy products are used for paints and other surface coatings, molded and reinforced plastics, electronic component potting resins, and adhesives ranging from spray foams to dental cement. They are often used in jobs where tough, durable coatings or adhesives are needed. This fact sheet is for workers who use epoxy products in a variety of workplaces, including shipyards, auto body shops, and the electronics, aerospace, and construction industries. Epoxy resin systems are made up of an epoxy resin and a curing agent (also called a hardener or catalyst). Epoxy resins are increasingly used as matrices in composite materials for a wide range of automotive and aerospace applications, and for shipbuilding or electronic devices. They serve as casting resins, adhesives, and as high-performance coatings for tribological applications, such as slide bearings and calender roller covers (Amer et al., 2014). They are one of the most important classes of thermosetting polymers which are widely used as materials for fiber reinforced composite materials and as structural adhesives (Mohammed, 2014). EXPERIMENTAL Epoxy (EUXIT 50 KI) [A1] The epoxy resin of a trade mark (Euxit 50 KI) is a liquid of low viscosity resin as compare with other thermosets, which were supplied by Egyptian Swiss Chemical Industries company. The properties of the epoxy resin used in this work shown in (Table 1) according to the properties of a product company. Scheme 1: Structure of epoxy Preparation of (EUXIT 50 KI) with hardener [A2] The epoxy of (Euxit 50 KI) is converted to a solid state by adding with mixing of hardener of (Euxit 50 KII) at the ratio of (1:3). Scheme 2: Structure of epoxy with hardener Page 160 Volume 5, No 3/2016 AJASE
3 Asian Journal of Applied Science and Engineering, Volume 5, No 3/2016 ISSN X(p); (e) Programs Using hyperchem-8 program which is known for its quality, flexibility, and ease of use. It offers ten semi-empirical methods. Some of them have been devised specifically for the description of organic chemistry as well, and good for predicting molecular geometry and energetic. PM3 calculations were carried out on the most stable structure of epoxy and its derivatives to obtain the parameters, such as bond length, bond angle properties, and FT-IR absorption were recorded and compared with experimental results (Stewart, 1996; Cook, 1998). RESULTS AND DISCUSSION General Some properties of epoxy resin that used are shown in Table (1) according to the properties of a product company. Table 1: Properties of (Euxit 50 KII) Percent Modulus Density Viscosity Fracture Tensile Flexural Compression Elongation of (gm / (Poise) at Toughness strength strength Strength at break elasticity cm3) 35 c (MPa-mo.5) (MP) (MPa) (MPa) (%EL) (MPa) < FT-IR Spectra FT-IR of A1 compound: The FTIR spectrum of epoxy compound (A1) revealed a stretching vibration band at (3059 cm-1), (1184cm -1 ), (3498 cm-1) that corresponds to (oxirane ring), (CO), (OH) groups stretching vibrations respectively (Coates, 2000), see (Figure 1 and Table 2). Figure 1: FT-IR spectrum of compound (A1) FT-IR of A2 compound: The FTIR spectra of epoxy mixing with hardener compound (A2) have important characteristic stretching vibration bands that correspond to (oxirane ring) which are disappeared (Coates, 2000), as in (Figures 2 and Table 2) show the interesting stretching vibration bands for this compound. Copyright CC-BY-NC 2014, Asian Business Consortium AJASE Page 161
4 Farhan et al.: Theoritical Study of EUXIT 50 KI Epoxy and its Hardener using Hyperchem-8 Program ( ) Figure 2: FT-IR spectrum of compound (A2) Table 2: Stretching vibrational frequencies in (cm-1) for an important functional group located in the FT-IR spectra of A1 and A2 compounds Comp. νoh νc-o νc-h νc-h νc=c (hydroxy group) (ether group) ( aromatic ring) (aliphatic) ( aromatic ring) A A Electronic Spectra The electronic spectra of A1 compound exhibited two bands. The first absorption band appeared at 276 nm due to internal ligand (π π*) transition located in the group of (C=C) of benzene rings. The electronic spectra of compound (A2) show the band at 277 nm that belong to (π π*) of (C=C) of benzene rings. As shown below in (Figures 3 and 4). Figure 3: UV-Visible spectrum of compound (A1) Page 162 Volume 5, No 3/2016 AJASE
5 Asian Journal of Applied Science and Engineering, Volume 5, No 3/2016 ISSN X(p); (e) Figure 4: UV-Visible spectrum of compound (A2) Theoretical study Program hyperchem-8 was used for calculations of the heat of formation (ΔHfº), and binding energy (ΔEb) for epoxy and epoxy with hardener were calculated by the semi-empirical and molecular mechanics (Table 3). Also, PM3 was used to evaluate the vibrational spectra of (A1 and A2) compounds. It has been found that these obtained frequencies agree well with the experimental results (Figure 5 and Table 4), while the electronic spectra calculation didn't work due to the memory of the computer and the size of molecules. Electrostatic potential, EHOMO and ELUMO as shown in (Figure 6), Bond length and bond angle measurements for the epoxy and its derivatives was calculated (Tables 5-8), and the optimization geometry of structures (Figures 7,8) was obtained the PM3 method. Table 3: Conformation energetic in (Kcal. mol -1 ), HOMO and LUMO energy in (ev) and dipole moment in (Debye) for epoxy and epoxy mixing with hardener. Compd. ΔH o f ΔEb EHomo ELumo µ A A Table 4: Comparison of experimental and theoretical vibrational frequencies for ligands A1 and A2 by HyperChem-8 Comp. νoh νc-o νc-h νc-h νc=c (hydroxy group) (ether group) ( aromatic ring) (aliphatic) (aromatic ring) Experimental A1 Theoretical Error % Experimental A2 Theoretical Error % ** Error % due to main different in the experimental measurements and theoretical treatment of Vibrational frequency Copyright CC-BY-NC 2014, Asian Business Consortium AJASE Page 163
6 Farhan et al.: Theoritical Study of EUXIT 50 KI Epoxy and its Hardener using Hyperchem-8 Program ( ) Groups A1 A2 νc-h ( aromatic ring) νc-o (ether group) νc-h (aliphatic) νoh (hyroxy group) ---- νc=c ( aromatic ring) Figure 5: Show the vibrational mode of compounds A1 and A2 calculated by hyperchem-8 Page 164 Volume 5, No 3/2016 AJASE
7 Asian Journal of Applied Science and Engineering, Volume 5, No 3/2016 ISSN X(p); (e) A1 A2 E.P LUMO HOMO Figure 6: HOMO, LUMO & electrostatic potential for compounds by Hyperchem-8 Copyright CC-BY-NC 2014, Asian Business Consortium AJASE Page 165
8 Farhan et al.: Theoritical Study of EUXIT 50 KI Epoxy and its Hardener using Hyperchem-8 Program ( ) Figure 7a: Serial number of atoms of compound (A1) Figure 7b: The optimization geometry of structure of compound (A1). Page 166 Volume 5, No 3/2016 AJASE
9 Asian Journal of Applied Science and Engineering, Volume 5, No 3/2016 ISSN X(p); (e) Table 5: Generate all bond length of (A1) compound Atoms Actual Optimal Atoms Actual Optimal C(20)-O(22) C(8)-C(11) C(19)-O(21) C(8)-C(10) C(19)-C(20) C(8)-C(9) C(18)-C(19) C(5)-C(8) O(17)-C(18) C(7)-C(2) C(14)-O(17) C(6)-C(7) C(16)-C(11) C(5)-C(6) C(15)-C(16) C(4)-C(5) C(14)-C(15) C(3)-C(4) C(13)-C(14) C(2)-C(3) C(12)-C(13) C(1)-C(2) C(11)-C(12) Table 6: Generate all bond angles of (A1) compound Atoms Actual Optimal Atoms Actual Optimal H(100)-C(9)-H(99) C(6)-C(5)-C(4) H(100)-C(9)-C(8) H(96)-C(4)-C(5) H(99)-C(9)-C(8) H(96)-C(4)-C(3) C(11)-C(8)-C(10) C(5)-C(4)-C(3) C(11)-C(8)-C(9) H(95)-C(3)-C(4) C(11)-C(8)-C(5) H(95)-C(3)-C(2) C(10)-C(8)-C(9) C(4)-C(3)-C(2) C(10)-C(8)-C(5) C(7)-C(2)-C(3) C(9)-C(8)-C(5) C(7)-C(2)-C(1) H(98)-C(7)-C(6) C(3)-C(2)-C(1) H(98)-C(7)-C(2) H(94)-C(1)-H(93) C(6)-C(7)-C(2) H(94)-C(1)-C(85) H(97)-C(6)-C(7) H(94)-C(1)-C(2) H(97)-C(6)-C(5) H(93)-C(1)-C(85) C(7)-C(6)-C(5) H(93)-C(1)-C(2) C(8)-C(5)-C(6) C(85)-C(1)-C(2) C(8)-C(5)-C(4) Figure 8a: Serial number of atoms of compound (A2) Copyright CC-BY-NC 2014, Asian Business Consortium AJASE Page 167
10 Farhan et al.: Theoritical Study of EUXIT 50 KI Epoxy and its Hardener using Hyperchem-8 Program ( ) Figure 8b: The optimization geometry of structure of compound (A2) Table 7: Generate all bond length of (A2) compound. Atoms Actual Optimal Atoms Actual Optimal O(63)-H(125) C(4)-H(65) C(62)-H(124) C(56)-O(63) C(61)-H(123) C(62)-C(57) C(60)-H(122) C(61)-C(62) C(59)-H(121) C(60)-C(61) C(58)-H(120) C(59)-C(60) C(56)-H(119) C(58)-C(59) C(56)-H(118) C(57)-C(58) C(55)-H(117) N(54)-C(57) C(55)-H(116) C(55)-C(56) C(53)-H(115) N(54)-C(55) C(53)-H(114) C(53)-N(54) O(52)-H(113) C(1)-C(53) O(51)-H(112) C(1)-O(52) C(50)-H(111) C(50)-O(51) C(50)-H(110) C(49)-C(50) C(49)-H(109) N(42)-C(49) C(49)-H(108) C(48)-C(43) C(48)-H(107) C(47)-C(48) C(47)-H(106) C(46)-C(47) C(46)-H(105) C(45)-C(46) C(45)-H(104) C(44)-C(45) C(44)-H(103) C(43)-C(44) C(41)-H(102) N(42)-C(43) Page 168 Volume 5, No 3/2016 AJASE
11 Asian Journal of Applied Science and Engineering, Volume 5, No 3/2016 ISSN X(p); (e) C(41)-H(101) C(41)-N(42) O(40)-H(100) C(39)-C(41) C(39)-H(99) C(39)-O(40) C(38)-H(98) C(36)-C(39) C(37)-H(97) C(38)-C(33) C(35)-H(96) C(37)-C(38) C(34)-H(95) C(36)-C(37) C(32)-H(94) C(35)-C(36) C(32)-H(93) C(34)-C(35) C(32)-H(92) C(33)-C(34) C(31)-H(91) C(30)-C(33) C(31)-H(90) C(30)-C(32) C(31)-H(89) C(30)-C(31) C(29)-H(88) C(27)-C(30) C(28)-H(87) C(29)-C(24) C(26)-H(86) C(28)-C(29) C(25)-H(85) C(27)-C(28) C(22)-H(84) C(26)-C(27) C(22)-H(83) C(25)-C(26) O(21)-H(82) C(24)-C(25) C(20)-H(81) O(23)-C(24) C(19)-H(80) C(22)-O(23) C(19)-H(79) C(20)-C(22) C(17)-H(78) C(20)-O(21) C(16)-H(77) C(19)-C(20) C(14)-H(76) O(18)-C(19) C(13)-H(75) C(15)-O(18) C(11)-H(74) C(17)-C(12) C(11)-H(73) C(16)-C(17) C(11)-H(72) C(15)-C(16) C(10)-H(71) C(14)-C(15) C(10)-H(70) C(13)-C(14) O(63)-H(125) C(12)-C(13) C(62)-H(124) C(9)-C(12) C(61)-H(123) C(9)-C(11) C(60)-H(122) C(9)-C(10) C(59)-H(121) C(6)-C(9) C(58)-H(120) C(8)-C(3) C(56)-H(119) C(7)-C(8) C(56)-H(118) C(6)-C(7) C(55)-H(117) C(5)-C(6) C(10)-H(69) C(4)-C(5) C(8)-H(68) C(3)-C(4) C(7)-H(67) O(2)-C(3) C(5)-H(66) C(1)-O(2) Copyright CC-BY-NC 2014, Asian Business Consortium AJASE Page 169
12 Farhan et al.: Theoritical Study of EUXIT 50 KI Epoxy and its Hardener using Hyperchem-8 Program ( ) Table 8: Generate all bond angles of (A2) compound Atoms Actual Optimal Atoms Actual Optimal C(30)-C(32) H(96)-C(35)-C(36) C(30)-C(31) H(96)-C(35)-C(34) C(27)-C(30) H(95)-C(34)-C(35) C(29)-C(24) H(95)-C(34)-C(33) C(28)-C(29) C(38)-C(33)-C(34) C(27)-C(28) C(38)-C(33)-C(30) C(26)-C(27) C(34)-C(33)-C(30) C(25)-C(26) H(94)-C(32)-H(93) C(24)-C(25) H(94)-C(32)-H(92) O(23)-C(24) H(94)-C(32)-C(30) C(22)-O(23) H(93)-C(32)-H(92) C(20)-C(22) H(93)-C(32)-C(30) C(20)-O(21) H(92)-C(32)-C(30) C(19)-C(20) H(91)-C(31)-H(90) O(18)-C(19) H(91)-C(31)-H(89) C(15)-O(18) H(91)-C(31)-C(30) C(17)-C(12) H(90)-C(31)-H(89) C(16)-C(17) H(90)-C(31)-C(30) C(15)-C(16) H(89)-C(31)-C(30) C(14)-C(15) C(33)-C(30)-C(32) C(13)-C(14) C(33)-C(30)-C(31) C(12)-C(13) C(33)-C(30)-C(27) C(9)-C(12) C(32)-C(30)-C(31) C(9)-C(11) C(32)-C(30)-C(27) C(9)-C(10) C(31)-C(30)-C(27) C(6)-C(9) H(88)-C(29)-C(24) C(8)-C(3) H(88)-C(29)-C(28) C(7)-C(8) H(87)-C(28)-C(29) C(6)-C(7) H(87)-C(28)-C(27) C(5)-C(6) C(30)-C(27)-C(28) C(4)-C(5) C(30)-C(27)-C(26) C(3)-C(4) C(28)-C(27)-C(26) O(2)-C(3) H(86)-C(26)-C(27) C(1)-O(2) H(86)-C(26)-C(25) H(125)-O(63)-C(56) H(85)-C(25)-C(26) H(124)-C(62)-C(57) H(85)-C(25)-C(24) H(124)-C(62)-C(61) C(29)-C(24)-C(25) C(57)-C(62)-C(61) C(29)-C(24)-O(23) H(123)-C(61)-C(62) C(25)-C(24)-O(23) H(123)-C(61)-C(60) C(24)-O(23)-C(22) C(62)-C(61)-C(60) H(84)-C(22)-H(83) H(122)-C(60)-C(61) H(84)-C(22)-O(23) H(122)-C(60)-C(59) H(84)-C(22)-C(20) C(61)-C(60)-C(59) H(83)-C(22)-O(23) H(121)-C(59)-C(60) H(83)-C(22)-C(20) H(121)-C(59)-C(58) O(23)-C(22)-C(20) C(60)-C(59)-C(58) H(82)-O(21)-C(20) H(120)-C(58)-C(59) H(81)-C(20)-C(22) Page 170 Volume 5, No 3/2016 AJASE
13 Asian Journal of Applied Science and Engineering, Volume 5, No 3/2016 ISSN X(p); (e) H(120)-C(58)-C(57) H(81)-C(20)-O(21) C(59)-C(58)-C(57) H(81)-C(20)-C(19) C(62)-C(57)-C(58) C(22)-C(20)-O(21) C(62)-C(57)-N(54) C(22)-C(20)-C(19) C(58)-C(57)-N(54) O(21)-C(20)-C(19) H(119)-C(56)-H(118) H(80)-C(19)-H(79) H(119)-C(56)-O(63) H(80)-C(19)-C(20) H(119)-C(56)-C(55) H(80)-C(19)-O(18) H(118)-C(56)-O(63) H(79)-C(19)-C(20) H(118)-C(56)-C(55) H(79)-C(19)-O(18) O(63)-C(56)-C(55) C(20)-C(19)-O(18) H(117)-C(55)-H(116) C(19)-O(18)-C(15) H(117)-C(55)-C(56) H(78)-C(17)-C(12) H(117)-C(55)-N(54) H(78)-C(17)-C(16) H(116)-C(55)-C(56) H(77)-C(16)-C(17) H(116)-C(55)-N(54) H(77)-C(16)-C(15) C(56)-C(55)-N(54) O(18)-C(15)-C(16) C(57)-N(54)-C(55) O(18)-C(15)-C(14) C(57)-N(54)-C(53) C(16)-C(15)-C(14) C(55)-N(54)-C(53) H(76)-C(14)-C(15) H(115)-C(53)-H(114) H(76)-C(14)-C(13) H(115)-C(53)-N(54) H(75)-C(13)-C(14) H(115)-C(53)-C(1) H(75)-C(13)-C(12) H(114)-C(53)-C(1) C(14)-C(13)-C(12) 120 H(113)-O(52)-C(1) C(17)-C(12)-C(13) H(112)-O(51)-C(50) C(17)-C(12)-C(9) H(111)-C(50)-H(110) C(13)-C(12)-C(9) H(111)-C(50)-O(51) H(74)-C(11)-H(73) H(111)-C(50)-C(49) H(74)-C(11)-H(72) H(110)-C(50)-O(51) H(74)-C(11)-C(9) H(110)-C(50)-C(49) H(73)-C(11)-H(72) O(51)-C(50)-C(49) H(73)-C(11)-C(9) H(109)-C(49)-H(108) H(72)-C(11)-C(9) H(109)-C(49)-C(50) H(71)-C(10)-H(70) H(108)-C(49)-C(50) H(71)-C(10)-H(69) H(107)-C(48)-C(43) H(71)-C(10)-C(9) H(107)-C(48)-C(47) H(70)-C(10)-H(69) H(106)-C(47)-C(48) H(70)-C(10)-C(9) H(106)-C(47)-C(46) H(69)-C(10)-C(9) H(105)-C(46)-C(47) C(12)-C(9)-C(11) H(105)-C(46)-C(45) C(12)-C(9)-C(10) H(104)-C(45)-C(46) C(12)-C(9)-C(6) H(104)-C(45)-C(44) C(11)-C(9)-C(10) H(103)-C(44)-C(45) C(11)-C(9)-C(6) H(103)-C(44)-C(43) C(10)-C(9)-C(6) C(48)-C(43)-C(44) H(68)-C(8)-C(3) C(48)-C(43)-N(42) H(68)-C(8)-C(7) C(44)-C(43)-N(42) H(67)-C(7)-C(8) C(49)-N(42)-C(43) H(67)-C(7)-C(6) C(43)-N(42)-C(41) C(9)-C(6)-C(7) Copyright CC-BY-NC 2014, Asian Business Consortium AJASE Page 171
14 Farhan et al.: Theoritical Study of EUXIT 50 KI Epoxy and its Hardener using Hyperchem-8 Program ( ) H(102)-C(41)-H(101) C(9)-C(6)-C(5) H(102)-C(41)-C(39) C(7)-C(6)-C(5) H(101)-C(41)-C(39) H(66)-C(5)-C(6) H(100)-O(40)-C(39) H(66)-C(5)-C(4) H(99)-C(39)-C(41) H(65)-C(4)-C(5) H(99)-C(39)-O(40) H(65)-C(4)-C(3) H(99)-C(39)-C(36) C(8)-C(3)-C(4) C(41)-C(39)-O(40) C(8)-C(3)-O(2) C(41)-C(39)-C(36) C(4)-C(3)-O(2) H(98)-C(38)-C(33) C(3)-O(2)-C(1) H(98)-C(38)-C(37) H(64)-C(1)-C(53) H(97)-C(37)-C(38) H(64)-C(1)-O(52) H(97)-C(37)-C(36) H(64)-C(1)-O(2) C(39)-C(36)-C(37) C(53)-C(1)-O(52) C(39)-C(36)-C(35) C(53)-C(1)-O(2) C(37)-C(36)-C(35) O(52)-C(1)-O(2) CONCLUSION In this study, we tried to establish the characterization of the compounds (Epoxy and Hardener) by PM3 Semi-empirical quantum mechanical calculations. The optimized geometries, dipole moments, geometric parameters and vibrational frequencies were calculated and the data obtained from the calculated parameter are shown to be in good agreement with the experimental data. This good agreement is well within the accuracy of computational results. The modeling and the calculations does not only presented us the opportunity to take a critical look at this epoxy and its derivatives to produce results which were compared with experimental data but has also given us the opportunity to compile fundamental result on properties that cannot be calculated in the laboratory. REFERENCES Amer, H. M.; Mohammed, S. H. and Hayder R. K. (2014). Diyala Journal of Engineering Sciences, 7(1): , Coates, J. (2000). "Interpretation of Infrared Spectra, a Practical Approach." John Wiley & Sons Ltd, Chichester. Cook, D.B. (1998). "Hand Book of Computational Quantum Chemistry", Oxford Univ. Press, New York, pp. 14. David, C. Y. (2001). "Computational Chemistry- A practical guide for applying real world problems." Wiley-interscience. ISBN Mohammed, H. M. (2014). Journal of Thi-Qar Science, 4(3): Stewart, J. (1996). "Reviews in Computational Chemistry, K. B. Lipkowitz, D. B. Boyd (Eds.) ", VCH Publishers, New York, (1) 9, Topacli, C. And Topacli, A. (2003). Journal of Molecular Structure, 654: Warren, J. H. (2003). "A guide to molecular mechanics and Quantum Chemical calculations in Spartan." Wave function, Inc. ISBN X Page 172 Volume 5, No 3/2016 AJASE
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