Wall clock time and date at job start Sat Apr 11 2020 04:53:34 AMSOL-version 7.1 by G. D. Hawkins, D. J. Giesen, G. C. Lynch, C. C. Chambers, I. Rossi, J. W. Storer, J. Li, J. D. Thompson, P. Winget, B. J. Lynch, D. Rinaldi, D. A. Liotard, C. J. Cramer, and D. G. Truhlar Copyright 2004 by Regents of the University of Minnesota. All rights reserved. Notice: recipients of this code are asked to comply with the user agreement in Section 1 of the documentation file. ******************************************************************************* * 1SCF - SCF CALCULATION WITHOUT GEOMETRY OPTIMIZATION * - USE EF ROUTINE FOR MINIMUM SEARCH (DEFAULT) * GEO-OK - OVERRIDE INTERATOMIC DISTANCE CHECK * TLIMIT= - A TIME OF 15. SECONDS REQUESTED * CHARGE - CHARGE ON SYSTEM= -1 * AM1 - THE AM1 HAMILTONIAN TO BE USED * DEV - DEVELOPER OPTIONS ARE ALLOWED * SM5.42R - SM5.42R CALCULATIONS WILL BE PERFORMED * - CHARGE MODEL 2 WILL BE USED (CM2A) * - THE SOLVENT IS USER-SPECIFIED * DIELEC - THE SOLVENT DIELECTRIC CONSTANT IS 2.06 * IOFR - THE SOLVENT INDEX OF REFRACTION IS 1.4345 * ALPHA - THE SOLVENT ALPHA IS 0.00 * BETA - THE SOLVENT BETA IS 0.00 * GAMMA - THE SOLVENT MACROSCOPIC SURFACE TENSION IS * 38.93 CAL MOL^-1 ANGSTROM^-2 * FACARB - THE FRACTION OF AROMATIC CARBONS IS 0.00 * FEHALO - THE FRACTION OF ELECTRONEGATIVE HALOGENS IS 0.00 ******************************************************************************* Atom NO. Chemical Bond length Bond angle Dihedral angle number (k) symbol (angstroms) (degrees) (degrees) (I) NA:I NB:NA:I NC:NB:NA:I NA NB NC 1 1 C 2 2 C 1.52998 * 1 3 3 C 1.53010 * 109.46748 * 2 1 4 4 N 1.46504 * 109.46935 * 179.97438 * 3 2 1 5 5 N 1.39934 * 125.75789 * 269.97753 * 4 3 2 6 6 C 1.30445 * 108.89702 * 179.77652 * 5 4 3 7 7 C 1.41287 * 108.02446 * 0.37682 * 6 5 4 8 8 C 1.47434 * 126.41843 * 179.87802 * 7 6 5 9 9 O 1.21598 * 120.00330 * 179.69331 * 8 7 6 10 10 N 1.34773 * 119.99611 * 359.69409 * 8 7 6 11 11 C 1.46498 * 120.00043 * 179.97438 * 10 8 7 12 12 C 1.53002 * 109.47272 * 179.97438 * 11 10 8 13 13 C 1.53003 * 109.47269 * 180.02562 * 12 11 10 14 14 H 1.09000 * 109.46953 * 305.00936 * 13 12 11 15 15 N 1.46505 * 109.46807 * 65.00478 * 13 12 11 16 16 C 1.36931 * 119.99788 * 205.00000 * 15 13 12 17 17 H 1.08002 * 120.00438 * 0.02562 * 16 15 13 18 18 C 1.38817 * 119.99680 * 179.72358 * 16 15 13 19 19 N 1.31614 * 119.99888 * 0.27479 * 18 16 15 20 20 Si 1.86803 * 119.99862 * 180.27671 * 18 16 15 21 21 H 1.48498 * 109.47174 * 90.00121 * 20 18 16 22 22 H 1.48501 * 109.47062 * 210.00072 * 20 18 16 23 23 H 1.48504 * 109.46913 * 329.99871 * 20 18 16 24 24 C 1.52996 * 109.47332 * 185.00423 * 13 12 11 25 25 C 1.52998 * 109.46903 * 305.00350 * 24 13 12 26 26 C 1.52993 * 109.46923 * 65.00088 * 24 13 12 27 27 C 1.34261 * 125.74997 * 89.99817 * 4 3 2 28 28 C 1.50703 * 126.29281 * 359.96385 * 27 4 3 29 29 H 1.09001 * 109.46703 * 179.97438 * 1 2 3 30 30 H 1.08991 * 109.47895 * 300.00017 * 1 2 3 31 31 H 1.09000 * 109.46667 * 60.00746 * 1 2 3 32 32 H 1.08991 * 109.47895 * 239.99983 * 2 1 3 33 33 H 1.08995 * 109.47197 * 119.99725 * 2 1 3 34 34 H 1.08999 * 109.46758 * 60.00028 * 3 2 1 35 35 H 1.08995 * 109.47048 * 299.99817 * 3 2 1 36 36 H 1.08003 * 125.98578 * 180.26222 * 6 5 4 37 37 H 0.97004 * 120.00109 * 359.97438 * 10 8 7 38 38 H 1.09000 * 109.46784 * 60.00269 * 11 10 8 39 39 H 1.08992 * 109.47427 * 300.00334 * 11 10 8 40 40 H 1.09000 * 109.46766 * 60.00541 * 12 11 10 41 41 H 1.08992 * 109.47398 * 300.00634 * 12 11 10 42 42 H 0.97000 * 119.99792 * 24.99795 * 15 13 12 43 43 H 0.97005 * 119.99715 * 179.97438 * 19 18 16 44 44 H 1.08990 * 109.47060 * 185.00303 * 24 13 12 45 45 H 1.09003 * 109.47634 * 60.00178 * 25 24 13 46 46 H 1.09004 * 109.47209 * 179.97438 * 25 24 13 47 47 H 1.08998 * 109.47363 * 299.99597 * 25 24 13 48 48 H 1.08998 * 109.47742 * 299.99844 * 26 24 13 49 49 H 1.09004 * 109.47296 * 60.00553 * 26 24 13 50 50 H 1.09006 * 109.47144 * 179.97438 * 26 24 13 51 51 H 1.09005 * 109.46696 * 269.99521 * 28 27 4 52 52 H 1.08994 * 109.47086 * 29.99188 * 28 27 4 53 53 H 1.08999 * 109.47130 * 149.99412 * 28 27 4 Note: An asterisk (*) indicates this parameter was or will be optimized. Cartesian coordinates (angstroms) NO. Atom X Y Z 1 6 0.0000 0.0000 0.0000 2 6 1.5300 0.0000 0.0000 3 6 2.0399 1.4426 0.0000 4 7 3.5050 1.4427 0.0006 5 7 4.3222 1.4433 1.1365 6 6 5.5707 1.4383 0.7587 7 6 5.6000 1.4431 -0.6539 8 6 6.8043 1.4425 -1.5043 9 8 6.6936 1.4414 -2.7153 10 7 8.0280 1.4432 -0.9396 11 6 9.2248 1.4421 -1.7846 12 6 10.4734 1.4439 -0.9004 13 6 11.7233 1.4433 -1.7829 14 1 11.6804 0.6007 -2.4730 15 7 11.7849 2.6943 -2.5430 16 6 12.4670 2.7416 -3.7294 17 1 12.9593 1.8568 -4.1050 18 6 12.5205 3.9254 -4.4524 19 7 11.9202 5.0036 -3.9949 20 14 13.4446 3.9881 -6.0747 21 1 12.5204 3.6423 -7.1844 22 1 13.9817 5.3563 -6.2859 23 1 14.5663 3.0154 -6.0433 24 6 12.9688 1.3193 -0.9031 25 6 12.9641 2.4318 0.1472 26 6 12.9661 -0.0417 -0.2044 27 6 4.2898 1.4425 -1.0887 28 6 3.8258 1.4415 -2.5225 29 1 -0.3633 -1.0277 -0.0005 30 1 -0.3634 0.5138 0.8899 31 1 -0.3633 0.5137 -0.8901 32 1 1.8934 -0.5138 -0.8899 33 1 1.8933 -0.5138 0.8900 34 1 1.6765 1.9564 0.8900 35 1 1.6766 1.9564 -0.8900 36 1 6.4312 1.4335 1.4113 37 1 8.1164 1.4445 0.0264 38 1 9.2252 2.3313 -2.4150 39 1 9.2252 0.5514 -2.4127 40 1 10.4732 0.5549 -0.2697 41 1 10.4728 2.3348 -0.2725 42 1 11.3424 3.4889 -2.2058 43 1 11.9579 5.8310 -4.5000 44 1 13.8613 1.4081 -1.5224 45 1 12.0715 2.3430 0.7666 46 1 13.8512 2.3432 0.7744 47 1 12.9660 3.4015 -0.3505 48 1 12.0736 -0.1306 0.4149 49 1 12.9696 -0.8344 -0.9527 50 1 13.8538 -0.1303 0.4221 51 1 3.7146 0.4135 -2.8676 52 1 2.8669 1.9546 -2.5944 53 1 4.5603 1.9554 -3.1425 RHF calculation, no. of doubly occupied orbitals= 65 REFERENCES FOR PARAMETERS IN GAS-PHASE HAMILTONIAN: H: (AM1): M.J.S. DEWAR ET AL, J. AM. CHEM. SOC. 107 3902-3909 (1985) C: (AM1): M.J.S. DEWAR ET AL, J. AM. CHEM. SOC. 107 3902-3909 (1985) N: (AM1): M.J.S. DEWAR ET AL, J. AM. CHEM. SOC. 107 3902-3909 (1985) O: (AM1): M.J.S. DEWAR ET AL, J. AM. CHEM. SOC. 107 3902-3909 (1985) Si: (AM1): M.J.S.DEWAR, C. JIE, ORGANOMETALLICS, 6, 1486-1490 (1987). REFERENCE FOR CHARGE MODEL 2: J. Li, J. Xing, C. J. Cramer, and D. G. Truhlar, J. Chem. Phys. 111 (1999) 885. REFERENCE FOR THE PARAMETERIZATION OF THE SM5.42R SOLVATION MODEL: J. Li, T. Zhu, G. D. Hawkins, P. Winget, D. A. Liotard, C. J. Cramer, and D. G. Truhlar, Theor. Chem. Acc. 103 (1999) 9-63 P. Winget, J. D. Thompson C. J. Cramer,and D. G. Truhlar, J. Phys. Chem. B. submitted. CHARGE=-1 AM1 1SCF TLIMIT=15 GEO-OK SM5.42R & SOLVNT=GENORG IOFR=1.4345 ALPHA=0.00 BETA=0.00 GAMMA=38.93 & DIELEC=2.06 FACARB=0.00 FEHALO=0.00 DEV ZINC001571351970.mol2 53 1SCF WAS SPECIFIED, SO GEOMETRY OPTIMIZATION WAS NOT USED SCF FIELD WAS ACHIEVED Wall clock time and date at job start Sat Apr 11 2020 04:53:34 Heat of formation + Delta-G solvation = 20.823395 kcal Electronic energy + Delta-G solvation = -29174.182956 eV Core-core repulsion = 25274.872470 eV Total energy + Delta-G solvation = -3899.310486 eV No. of doubly occupied orbitals = 65 Molecular weight (most abundant/longest-lived isotopes) = 336.227 amu Computer time = 0.81 seconds Orbital eigenvalues (eV) -41.62597 -38.98190 -37.46034 -35.83064 -34.51589 -33.12983 -32.62818 -31.64064 -30.78322 -29.36463 -27.46294 -26.72157 -26.61955 -24.95874 -23.10478 -22.52127 -22.40719 -21.66557 -20.32891 -19.69984 -18.33357 -17.57578 -17.08445 -16.20939 -15.78281 -15.54380 -15.39025 -15.11484 -14.65134 -14.54813 -14.25141 -13.91918 -13.74332 -13.56671 -13.31130 -13.23247 -12.99784 -12.96915 -12.87266 -12.69716 -12.51139 -12.26641 -12.07935 -11.91070 -11.84423 -11.36252 -11.21721 -11.16187 -10.97322 -10.88954 -10.83912 -10.51943 -10.42867 -10.22438 -10.09098 -9.78707 -9.59601 -9.54541 -9.45719 -8.86121 -8.79119 -8.50926 -6.87008 -5.69614 -2.97343 1.42414 2.08675 2.10994 3.48938 3.54039 3.54906 3.55258 3.65254 4.11975 4.28162 4.39377 4.53059 4.65066 4.65801 4.80293 4.89147 4.96704 5.13410 5.17095 5.31093 5.36254 5.39015 5.44684 5.46140 5.48898 5.52979 5.64146 5.67211 5.73988 5.74579 5.79029 5.92605 5.98237 6.08729 6.13933 6.22289 6.26785 6.31483 6.35705 6.48198 6.50144 6.67466 6.73162 6.82227 6.84942 6.89823 7.08216 7.14950 7.39177 7.77722 7.85404 8.48841 8.58362 9.60424 10.17774 10.52409 11.52889 Molecular weight = 336.23amu Principal moments of inertia in cm(-1) A = 0.014161 B = 0.002302 C = 0.002070 Principal moments of inertia in units of 10**(-40)*gram-cm**2 A = 1976.738599 B =12162.187611 C =13526.063511 Net atomic charges, atomic populations, and dipole contributions calculated with CM2 Atom NO. Type Charge No. of electrons 1 C -0.149 4.149 2 C -0.141 4.141 3 C 0.128 3.872 4 N -0.362 5.362 5 N -0.300 5.300 6 C 0.082 3.918 7 C -0.293 4.293 8 C 0.590 3.410 9 O -0.546 6.546 10 N -0.725 5.725 11 C 0.125 3.875 12 C -0.136 4.136 13 C 0.186 3.814 14 H 0.048 0.952 15 N -0.719 5.719 16 C -0.235 4.235 17 H 0.069 0.931 18 C -0.013 4.013 19 N -0.932 5.932 20 Si 0.903 3.097 21 H -0.291 1.291 22 H -0.293 1.293 23 H -0.283 1.283 24 C -0.115 4.115 25 C -0.137 4.137 26 C -0.145 4.145 27 C 0.156 3.844 28 C -0.100 4.100 29 H 0.062 0.938 30 H 0.059 0.941 31 H 0.059 0.941 32 H 0.070 0.930 33 H 0.073 0.927 34 H 0.098 0.902 35 H 0.096 0.904 36 H 0.189 0.811 37 H 0.393 0.607 38 H 0.083 0.917 39 H 0.062 0.938 40 H 0.064 0.936 41 H 0.068 0.932 42 H 0.384 0.616 43 H 0.254 0.746 44 H 0.070 0.930 45 H 0.044 0.956 46 H 0.035 0.965 47 H 0.064 0.936 48 H 0.049 0.951 49 H 0.048 0.952 50 H 0.042 0.958 51 H 0.085 0.915 52 H 0.068 0.932 53 H 0.109 0.891 For the charges calculated by CM2: Dipole moment (debyes) X Y Z Total from point charges -19.566 -10.225 12.271 25.258 Note: The Mulliken population analysis charges presented below were not used in the solvation calculation but are provided for completeness. The chosen solvation model uses CM2 partial charges for calculating solvation energies. Net atomic charges, atomic populations, and dipole contributions using Mulliken population analysis Atom NO. Type Charge No. of electrons 1 C -0.207 4.207 2 C -0.180 4.180 3 C 0.007 3.993 4 N -0.142 5.142 5 N -0.119 5.119 6 C -0.105 4.105 7 C -0.308 4.308 8 C 0.377 3.623 9 O -0.424 6.424 10 N -0.375 5.375 11 C 0.002 3.998 12 C -0.175 4.175 13 C 0.075 3.925 14 H 0.066 0.934 15 N -0.360 5.360 16 C -0.366 4.366 17 H 0.087 0.913 18 C -0.209 4.209 19 N -0.580 5.580 20 Si 0.735 3.265 21 H -0.218 1.218 22 H -0.220 1.220 23 H -0.209 1.209 24 C -0.136 4.136 25 C -0.195 4.195 26 C -0.203 4.203 27 C 0.024 3.976 28 C -0.158 4.158 29 H 0.082 0.918 30 H 0.078 0.922 31 H 0.078 0.922 32 H 0.088 0.912 33 H 0.092 0.908 34 H 0.116 0.884 35 H 0.114 0.886 36 H 0.205 0.795 37 H 0.227 0.773 38 H 0.102 0.898 39 H 0.080 0.920 40 H 0.083 0.917 41 H 0.087 0.913 42 H 0.218 0.782 43 H 0.064 0.936 44 H 0.088 0.912 45 H 0.063 0.937 46 H 0.054 0.946 47 H 0.083 0.917 48 H 0.068 0.932 49 H 0.067 0.933 50 H 0.061 0.939 51 H 0.104 0.896 52 H 0.087 0.913 53 H 0.128 0.872 Dipole moment (debyes) X Y Z Total from point charges -20.484 -10.227 12.235 25.959 hybrid contribution 1.096 0.393 -0.827 1.428 sum -19.388 -9.835 11.408 24.551 Atomic orbital electron populations 1.21695 0.94094 1.02637 1.02300 1.21932 0.96832 0.95589 1.03618 1.21877 0.73879 0.98775 1.04791 1.48499 1.06570 1.55758 1.03383 1.77140 1.01877 1.25342 1.07565 1.24007 0.95313 0.97284 0.93933 1.20103 0.93113 1.24043 0.93498 1.17166 0.82203 0.76007 0.86940 1.90753 1.86645 1.50945 1.14098 1.45854 1.05835 1.75690 1.10106 1.21425 0.81876 1.03385 0.93100 1.22149 0.94814 1.01811 0.98679 1.20152 0.90055 0.91008 0.91237 0.93374 1.42426 1.63277 1.07555 1.22750 1.19204 1.25092 0.95582 0.96717 0.91290 1.24703 1.01239 0.96006 0.98943 1.69653 1.48240 1.00719 1.39404 0.86247 0.79368 0.76608 0.84314 1.21801 1.21960 1.20891 1.21785 1.01513 0.93208 0.97133 1.21742 0.99519 1.00254 0.97957 1.21896 1.00562 0.97906 0.99945 1.21530 0.90126 0.94853 0.91084 1.20702 1.02474 1.04073 0.88537 0.91847 0.92199 0.92211 0.91164 0.90831 0.88381 0.88633 0.79462 0.77346 0.89823 0.91993 0.91716 0.91314 0.78248 0.93642 0.91185 0.93696 0.94565 0.91670 0.93152 0.93334 0.93853 0.89619 0.91345 0.87226 Number of geometries 1 Number of calculations of the screened coulomb radii 1 The total number of SCF iterations 14. Note: The number of geometries may not correspond to the number of cycles due to rejected geometry changes. In the following table subtotal= G_P + SS G_CDS. Atom Chem. CM2 G_P Area Sigma k SS G_CDS Subtotal M number symbol chg. (kcal) (Ang**2) cal/(Ang**2) (kcal) (kcal) value 1 C -0.15 -0.59 9.91 37.16 0.37 -0.22 16 2 C -0.14 -0.82 6.26 -26.73 -0.17 -0.99 16 3 C 0.13 0.86 6.21 -4.03 -0.03 0.83 16 4 N -0.36 -3.83 3.58 -56.60 -0.20 -4.03 16 5 N -0.30 -3.61 12.50 30.86 0.39 -3.22 16 6 C 0.08 0.93 11.50 -16.98 -0.20 0.74 16 7 C -0.29 -3.90 6.13 -105.06 -0.64 -4.55 16 8 C 0.59 9.37 7.81 -12.52 -0.10 9.27 16 9 O -0.55 -10.62 14.84 5.28 0.08 -10.54 16 10 N -0.72 -10.24 5.55 -61.39 -0.34 -10.58 16 11 C 0.12 2.10 5.56 -4.04 -0.02 2.08 16 12 C -0.14 -2.07 4.07 -26.73 -0.11 -2.18 16 13 C 0.19 3.49 2.06 -67.93 -0.14 3.35 16 14 H 0.05 0.95 8.08 -51.93 -0.42 0.53 16 15 N -0.72 -17.16 4.03 -53.42 -0.22 -17.38 16 16 C -0.23 -6.38 9.93 -15.06 -0.15 -6.53 16 17 H 0.07 1.84 7.83 -52.49 -0.41 1.43 16 18 C -0.01 -0.37 5.50 -17.43 -0.10 -0.47 16 19 N -0.93 -28.09 13.06 55.49 0.72 -27.36 16 20 Si 0.90 22.66 29.55 -169.99 -5.02 17.63 16 21 H -0.29 -7.34 7.11 56.52 0.40 -6.93 16 22 H -0.29 -7.43 7.11 56.52 0.40 -7.03 16 23 H -0.28 -6.91 7.11 56.52 0.40 -6.51 16 24 C -0.11 -1.95 2.88 -90.63 -0.26 -2.21 16 25 C -0.14 -2.24 8.59 37.16 0.32 -1.92 16 26 C -0.15 -1.98 8.95 37.15 0.33 -1.65 16 27 C 0.16 1.86 7.01 -81.60 -0.57 1.29 16 28 C -0.10 -0.99 9.57 36.01 0.34 -0.65 16 29 H 0.06 0.24 8.14 -51.93 -0.42 -0.18 16 30 H 0.06 0.21 8.14 -51.93 -0.42 -0.21 16 31 H 0.06 0.19 8.14 -51.93 -0.42 -0.23 16 32 H 0.07 0.44 8.14 -51.93 -0.42 0.02 16 33 H 0.07 0.52 8.14 -51.93 -0.42 0.10 16 34 H 0.10 0.59 8.14 -51.93 -0.42 0.17 16 35 H 0.10 0.47 7.02 -51.93 -0.36 0.10 16 36 H 0.19 1.49 7.50 -52.48 -0.39 1.10 16 37 H 0.39 4.25 7.43 -40.82 -0.30 3.95 16 38 H 0.08 1.75 7.75 -51.93 -0.40 1.35 16 39 H 0.06 1.10 8.14 -51.93 -0.42 0.68 16 40 H 0.06 0.83 6.35 -51.93 -0.33 0.50 16 41 H 0.07 1.04 6.65 -51.93 -0.35 0.70 16 42 H 0.38 9.85 7.80 -40.82 -0.32 9.53 16 43 H 0.25 7.48 8.31 -40.82 -0.34 7.14 16 44 H 0.07 1.37 8.14 -51.93 -0.42 0.94 16 45 H 0.04 0.64 6.46 -51.93 -0.34 0.31 16 46 H 0.04 0.53 8.14 -51.93 -0.42 0.11 16 47 H 0.06 1.25 7.75 -51.93 -0.40 0.85 16 48 H 0.05 0.61 6.46 -51.93 -0.34 0.28 16 49 H 0.05 0.65 8.14 -51.93 -0.42 0.22 16 50 H 0.04 0.55 8.14 -51.93 -0.42 0.12 16 51 H 0.09 0.77 8.14 -51.93 -0.42 0.35 16 52 H 0.07 0.48 7.05 -51.93 -0.37 0.12 16 53 H 0.11 1.38 6.50 -51.93 -0.34 1.04 16 LS Contribution 423.01 15.07 6.37 6.37 Total: -1.00 -33.78 423.01 -8.60 -42.38 By element: Atomic # 1 Polarization: 19.82 SS G_CDS: -9.27 Total: 10.54 kcal Atomic # 6 Polarization: -2.70 SS G_CDS: -1.11 Total: -3.81 kcal Atomic # 7 Polarization: -62.93 SS G_CDS: 0.35 Total: -62.58 kcal Atomic # 8 Polarization: -10.62 SS G_CDS: 0.08 Total: -10.54 kcal Atomic # 14 Polarization: 22.66 SS G_CDS: -5.02 Total: 17.63 kcal Total LS contribution 6.37 Total: 6.37 kcal Total: -33.78 -8.60 -42.38 kcal The number of atoms in the molecule is 53 The average number of expansion shells was 16.00 The maximum number of expansion shells was 16 The minimum number of expansion shells was 16 **** NOTA BENE **** This is the net solvation energy for this exact molecular structure (nuclear and electronic)! The standard-state solvation energy should be obtained as the difference between the heat of formation plus delta-G solvation for the relaxed solvated system and that for the relaxed gas-phase system. ZINC001571351970.mol2 53 1SCF run This is a breakdown of the solvation energy calculated without geometric relaxation in solution: (1) E-EN(sol) electronic-nuclear energy of solute 63.205 kcal (2) G-P(sol) polarization free energy of solvation -33.777 kcal (3) G-ENP(sol) elect.-nuc.-pol. free energy of system 29.428 kcal (4) G-CDS(sol) cavity-dispersion-solvent structure free energy -8.605 kcal (5) G-P-CDS(sol) = G-P(sol) + G-CDS(sol) = (2) + (4) -42.382 kcal (6) G-S(sol) free energy of system = (1) + (5) 20.823 kcal 1SCF WAS SPECIFIED, SO GEOMETRY OPTIMIZATION WAS NOT USED Total computer time = 0.81 seconds