Wall clock time and date at job start Tue Mar 31 2020 21:00:23 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 1.53001 * 1 3 3 C 1.52993 * 109.47456 * 2 1 4 4 C 1.53008 * 109.46467 * 119.99740 * 2 1 3 5 5 H 1.09000 * 112.81300 * 310.03037 * 4 2 1 6 6 N 1.45838 * 113.50267 * 179.12091 * 4 2 1 7 7 C 1.46493 * 133.17929 * 65.32403 * 6 4 2 8 8 N 1.46895 * 109.47292 * 97.16426 * 7 6 4 9 9 C 1.46851 * 111.00213 * 204.88960 * 8 7 6 10 10 C 1.53036 * 109.52736 * 174.16223 * 9 8 7 11 11 C 1.53118 * 109.27756 * 59.17565 * 10 9 8 12 12 C 1.50699 * 109.52188 * 182.37899 * 11 10 9 13 13 H 1.08005 * 119.99965 * 359.87679 * 12 11 10 14 14 C 1.37880 * 120.00162 * 179.87085 * 12 11 10 15 15 N 1.31514 * 119.99690 * 0.02562 * 14 12 11 16 16 Si 1.86800 * 120.00187 * 180.02562 * 14 12 11 17 17 H 1.48492 * 109.47053 * 90.00100 * 16 14 12 18 18 H 1.48500 * 109.47145 * 210.00554 * 16 14 12 19 19 H 1.48501 * 109.46939 * 330.00169 * 16 14 12 20 20 C 1.53117 * 109.21292 * 302.31373 * 11 10 9 21 21 C 1.46847 * 111.00329 * 80.67840 * 8 7 6 22 22 C 1.33988 * 93.64395 * 245.06174 * 6 4 2 23 23 O 1.21281 * 133.35818 * 180.22329 * 22 6 4 24 24 C 1.49458 * 93.28261 * 0.22252 * 22 6 4 25 25 C 1.53627 * 115.52892 * 115.99994 * 24 22 6 26 26 C 1.54938 * 103.95174 * 133.28198 * 25 24 22 27 27 C 1.55026 * 102.11922 * 20.84708 * 26 25 24 28 28 O 1.43206 * 115.85817 * 243.59927 * 24 22 6 29 29 H 1.08994 * 109.47309 * 295.41208 * 1 2 3 30 30 H 1.09006 * 109.46812 * 55.41275 * 1 2 3 31 31 H 1.08997 * 109.47291 * 175.40606 * 1 2 3 32 32 H 1.08998 * 109.47070 * 239.99187 * 2 1 3 33 33 H 1.09006 * 109.47352 * 68.32717 * 3 2 1 34 34 H 1.08998 * 109.47109 * 188.33062 * 3 2 1 35 35 H 1.09004 * 109.46762 * 308.32790 * 3 2 1 36 36 H 1.09004 * 109.46694 * 337.16431 * 7 6 4 37 37 H 1.09003 * 109.47098 * 217.16817 * 7 6 4 38 38 H 1.08998 * 109.46671 * 54.14017 * 9 8 7 39 39 H 1.09008 * 109.46053 * 294.17724 * 9 8 7 40 40 H 1.08999 * 109.49912 * 299.23520 * 10 9 8 41 41 H 1.08992 * 109.53645 * 179.14052 * 10 9 8 42 42 H 1.08998 * 109.52179 * 62.25431 * 11 10 9 43 43 H 0.97002 * 119.99692 * 180.02562 * 15 14 12 44 44 H 1.08999 * 109.50194 * 177.62463 * 20 11 10 45 45 H 1.08998 * 109.50871 * 297.74547 * 20 11 10 46 46 H 1.09003 * 109.46147 * 305.85627 * 21 8 7 47 47 H 1.09001 * 109.46288 * 65.82050 * 21 8 7 48 48 H 1.09003 * 110.53131 * 251.89730 * 25 24 22 49 49 H 1.08996 * 110.53728 * 14.65739 * 25 24 22 50 50 H 1.08996 * 110.87522 * 139.00755 * 26 25 24 51 51 H 1.09008 * 110.86967 * 262.69360 * 26 25 24 52 52 H 1.09008 * 110.60007 * 81.81061 * 27 26 25 53 53 H 1.08998 * 110.60085 * 204.75952 * 27 26 25 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 2.0401 1.4424 0.0000 4 6 2.0399 -0.7213 1.2494 5 1 1.5714 -0.3619 2.1656 6 7 3.4945 -0.7904 1.3281 7 6 4.5397 0.2252 1.4765 8 7 4.9302 0.3232 2.8893 9 6 5.4905 1.6469 3.1898 10 6 5.7499 1.7632 4.6935 11 6 6.7263 0.6652 5.1244 12 6 6.9404 0.7381 6.6144 13 1 6.4330 1.4931 7.1966 14 6 7.7839 -0.1592 7.2343 15 7 8.4021 -1.0784 6.5253 16 14 8.0488 -0.0694 9.0813 17 1 7.0439 -0.9204 9.7674 18 1 9.4140 -0.5528 9.4097 19 1 7.8993 1.3367 9.5349 20 6 6.1413 -0.7015 4.7578 21 6 5.8699 -0.7457 3.2510 22 6 3.5222 -2.1257 1.2207 23 8 4.4194 -2.9417 1.2096 24 6 2.0350 -2.2343 1.1198 25 6 1.5002 -2.7853 -0.2108 26 6 0.4517 -3.8427 0.2171 27 6 0.1178 -3.4024 1.6655 28 8 1.3870 -2.9431 2.1821 29 1 -0.3633 0.4410 0.9282 30 1 -0.3633 0.5834 -0.8461 31 1 -0.3634 -1.0243 -0.0823 32 1 1.8933 -0.5140 -0.8899 33 1 1.8034 1.9115 0.9551 34 1 3.1198 1.4460 -0.1489 35 1 1.5603 1.9974 -0.8062 36 1 4.1607 1.1890 1.1366 37 1 5.4068 -0.0557 0.8786 38 1 4.7847 2.4185 2.8823 39 1 6.4278 1.7760 2.6485 40 1 4.8108 1.6481 5.2347 41 1 6.1800 2.7399 4.9148 42 1 7.6786 0.8031 4.6124 43 1 8.9952 -1.7099 6.9615 44 1 6.8512 -1.4845 5.0243 45 1 5.2084 -0.8555 5.3001 46 1 5.4395 -1.7120 2.9880 47 1 6.8054 -0.6055 2.7095 48 1 1.0284 -1.9921 -0.7910 49 1 2.3029 -3.2519 -0.7817 50 1 -0.4327 -3.7918 -0.4179 51 1 0.8828 -4.8439 0.2051 52 1 -0.6106 -2.5914 1.6616 53 1 -0.2502 -4.2470 2.2479 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 ZINC000840043693.mol2 53 1SCF WAS SPECIFIED, SO GEOMETRY OPTIMIZATION WAS NOT USED SCF FIELD WAS ACHIEVED Wall clock time and date at job start Tue Mar 31 2020 21:00:23 Heat of formation + Delta-G solvation = -39.250621 kcal Electronic energy + Delta-G solvation = -31518.590391 eV Core-core repulsion = 27584.382149 eV Total energy + Delta-G solvation = -3934.208242 eV No. of doubly occupied orbitals = 65 Molecular weight (most abundant/longest-lived isotopes) = 336.220 amu Computer time = 0.86 seconds Orbital eigenvalues (eV) -42.08159 -38.65871 -37.80749 -37.03431 -34.67134 -33.75771 -32.38663 -31.55496 -29.76354 -29.56963 -27.38868 -26.88924 -25.34979 -24.52118 -22.65636 -22.26243 -22.04580 -21.23605 -20.49844 -18.60094 -18.37267 -17.54997 -17.12913 -16.47718 -16.36231 -15.90472 -15.36469 -14.92112 -14.62547 -14.51134 -14.35203 -14.11812 -13.86074 -13.68177 -13.17932 -13.00572 -12.91268 -12.77333 -12.46954 -12.41304 -12.27335 -12.16012 -12.02066 -11.85353 -11.71899 -11.49458 -11.37878 -11.10655 -11.04085 -10.93136 -10.88132 -10.65993 -10.47325 -10.26005 -10.17511 -9.93435 -9.47818 -9.40386 -8.99411 -8.83586 -8.63462 -8.22849 -7.81526 -5.90526 -3.96395 2.31914 2.93161 3.36093 3.42502 3.45156 3.62333 3.83347 4.05857 4.23610 4.44791 4.50366 4.51942 4.58877 4.65236 4.77658 4.90766 4.98146 5.06612 5.14028 5.25530 5.33279 5.33880 5.36127 5.39472 5.44189 5.47370 5.52956 5.60103 5.62061 5.67951 5.72851 5.79941 5.85796 5.96751 6.01037 6.08943 6.24355 6.28984 6.55884 6.61900 6.65178 6.71592 6.74308 6.88229 7.10192 7.19060 7.47796 7.62175 7.68581 7.87524 8.10451 8.22954 8.29197 8.54206 9.07111 9.67778 11.15498 Molecular weight = 336.22amu Principal moments of inertia in cm(-1) A = 0.016248 B = 0.003096 C = 0.002852 Principal moments of inertia in units of 10**(-40)*gram-cm**2 A = 1722.853347 B = 9043.025192 C = 9815.670830 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 -0.101 4.101 3 C -0.151 4.151 4 C 0.123 3.877 5 H 0.105 0.895 6 N -0.597 5.597 7 C 0.288 3.712 8 N -0.550 5.550 9 C 0.066 3.934 10 C -0.105 4.105 11 C 0.048 3.952 12 C -0.511 4.511 13 H 0.054 0.946 14 C 0.060 3.940 15 N -0.890 5.890 16 Si 0.890 3.110 17 H -0.281 1.281 18 H -0.288 1.288 19 H -0.275 1.275 20 C -0.101 4.101 21 C 0.056 3.944 22 C 0.534 3.466 23 O -0.496 6.496 24 C 0.054 3.946 25 C -0.139 4.139 26 C -0.152 4.152 27 C 0.042 3.958 28 O -0.333 6.333 29 H 0.061 0.939 30 H 0.061 0.939 31 H 0.059 0.941 32 H 0.081 0.919 33 H 0.061 0.939 34 H 0.059 0.941 35 H 0.059 0.941 36 H 0.096 0.904 37 H 0.054 0.946 38 H 0.058 0.942 39 H 0.027 0.973 40 H 0.056 0.944 41 H 0.051 0.949 42 H 0.020 0.980 43 H 0.259 0.741 44 H 0.092 0.908 45 H 0.041 0.959 46 H 0.062 0.938 47 H 0.022 0.978 48 H 0.100 0.900 49 H 0.086 0.914 50 H 0.084 0.916 51 H 0.081 0.919 52 H 0.066 0.934 53 H 0.098 0.902 For the charges calculated by CM2: Dipole moment (debyes) X Y Z Total from point charges -19.549 1.035 -18.496 26.932 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 -0.121 4.121 3 C -0.208 4.208 4 C 0.019 3.981 5 H 0.123 0.877 6 N -0.333 5.333 7 C 0.078 3.922 8 N -0.277 5.277 9 C -0.062 4.062 10 C -0.143 4.143 11 C 0.030 3.970 12 C -0.549 4.549 13 H 0.072 0.928 14 C -0.141 4.141 15 N -0.529 5.529 16 Si 0.718 3.282 17 H -0.207 1.207 18 H -0.213 1.213 19 H -0.200 1.200 20 C -0.139 4.139 21 C -0.070 4.070 22 C 0.317 3.683 23 O -0.368 6.368 24 C 0.009 3.991 25 C -0.176 4.176 26 C -0.190 4.190 27 C -0.034 4.034 28 O -0.250 6.250 29 H 0.081 0.919 30 H 0.080 0.920 31 H 0.078 0.922 32 H 0.099 0.901 33 H 0.080 0.920 34 H 0.078 0.922 35 H 0.078 0.922 36 H 0.114 0.886 37 H 0.071 0.929 38 H 0.076 0.924 39 H 0.045 0.955 40 H 0.075 0.925 41 H 0.070 0.930 42 H 0.038 0.962 43 H 0.069 0.931 44 H 0.111 0.889 45 H 0.060 0.940 46 H 0.080 0.920 47 H 0.041 0.959 48 H 0.119 0.881 49 H 0.104 0.896 50 H 0.103 0.897 51 H 0.100 0.900 52 H 0.085 0.915 53 H 0.116 0.884 Dipole moment (debyes) X Y Z Total from point charges -19.061 0.497 -17.943 26.182 hybrid contribution 0.870 0.146 0.524 1.026 sum -18.191 0.643 -17.419 25.194 Atomic orbital electron populations 1.21907 0.93993 1.02165 1.02648 1.21433 0.96428 0.97004 0.97203 1.21939 1.01357 0.95072 1.02395 1.22511 0.81508 0.94547 0.99538 0.87714 1.49778 1.06618 1.06802 1.70081 1.21937 0.88806 0.90818 0.90603 1.61741 1.43957 1.04539 1.17464 1.22073 0.96472 0.88431 0.99193 1.21667 1.00767 1.00013 0.91817 1.18686 0.92710 0.89960 0.95687 1.21187 1.26106 1.14972 0.92676 0.92792 1.24981 0.95721 0.95455 0.97894 1.69885 1.29751 1.18177 1.35126 0.86632 0.77317 0.78183 0.86077 1.20736 1.21347 1.20018 1.21664 1.00337 1.02434 0.89507 1.22382 0.91911 0.92704 1.00051 1.21162 0.89263 0.82473 0.75359 1.90733 1.46353 1.49733 1.49959 1.23335 0.93670 0.92357 0.89689 1.22893 0.99712 0.99486 0.95558 1.23178 0.99095 0.99907 0.96810 1.23739 0.86333 0.99312 0.94060 1.88966 1.31210 1.71793 1.32994 0.91946 0.91955 0.92161 0.90117 0.92027 0.92181 0.92231 0.88588 0.92864 0.92359 0.95492 0.92489 0.93027 0.96176 0.93089 0.88933 0.94008 0.91980 0.95927 0.88141 0.89570 0.89691 0.90021 0.91536 0.88356 Number of geometries 1 Number of calculations of the screened coulomb radii 1 The total number of SCF iterations 13. 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 -0.84 8.75 37.16 0.33 -0.52 16 2 C -0.10 -0.77 2.22 -90.62 -0.20 -0.97 16 3 C -0.15 -1.13 8.31 37.15 0.31 -0.82 16 4 C 0.12 1.38 3.61 -73.73 -0.27 1.11 16 5 H 0.11 1.26 8.14 -51.93 -0.42 0.84 16 6 N -0.60 -8.64 3.21 -187.75 -0.60 -9.24 16 7 C 0.29 4.29 6.03 -63.33 -0.38 3.91 16 8 N -0.55 -10.20 4.75 -238.49 -1.13 -11.33 16 9 C 0.07 1.17 5.40 -3.83 -0.02 1.15 16 10 C -0.10 -2.22 5.32 -26.65 -0.14 -2.36 16 11 C 0.05 1.24 2.16 -91.65 -0.20 1.04 16 12 C -0.51 -14.47 8.56 -34.44 -0.29 -14.76 16 13 H 0.05 1.50 7.75 -52.48 -0.41 1.10 16 14 C 0.06 1.73 5.30 -17.82 -0.09 1.63 16 15 N -0.89 -26.41 11.36 55.43 0.63 -25.78 16 16 Si 0.89 21.96 29.54 -169.99 -5.02 16.94 16 17 H -0.28 -6.92 7.11 56.52 0.40 -6.51 16 18 H -0.29 -7.05 7.11 56.52 0.40 -6.65 16 19 H -0.28 -6.66 7.11 56.52 0.40 -6.26 16 20 C -0.10 -2.59 5.13 -26.58 -0.14 -2.72 16 21 C 0.06 1.25 5.31 -3.77 -0.02 1.23 16 22 C 0.53 8.92 8.04 -16.80 -0.14 8.79 16 23 O -0.50 -10.29 16.94 5.56 0.09 -10.19 16 24 C 0.05 0.67 1.62 -92.66 -0.15 0.52 16 25 C -0.14 -1.20 5.40 -25.38 -0.14 -1.33 16 26 C -0.15 -1.08 7.16 -24.64 -0.18 -1.25 16 27 C 0.04 0.36 7.72 38.23 0.30 0.65 16 28 O -0.33 -4.56 11.29 -35.23 -0.40 -4.95 16 29 H 0.06 0.37 8.14 -51.93 -0.42 -0.05 16 30 H 0.06 0.29 8.14 -51.93 -0.42 -0.14 16 31 H 0.06 0.30 6.29 -51.93 -0.33 -0.03 16 32 H 0.08 0.59 6.37 -51.93 -0.33 0.26 16 33 H 0.06 0.50 8.13 -51.93 -0.42 0.07 16 34 H 0.06 0.49 5.68 -51.93 -0.29 0.20 16 35 H 0.06 0.36 8.12 -51.93 -0.42 -0.06 16 36 H 0.10 1.14 4.91 -51.93 -0.26 0.89 16 37 H 0.05 0.82 7.92 -51.93 -0.41 0.41 16 38 H 0.06 0.86 7.91 -51.93 -0.41 0.45 16 39 H 0.03 0.47 8.14 -51.92 -0.42 0.05 16 40 H 0.06 1.24 8.14 -51.93 -0.42 0.82 16 41 H 0.05 1.04 8.14 -51.93 -0.42 0.62 16 42 H 0.02 0.56 8.14 -51.93 -0.42 0.14 16 43 H 0.26 7.36 8.31 -40.82 -0.34 7.02 16 44 H 0.09 2.65 6.16 -51.93 -0.32 2.33 16 45 H 0.04 1.11 8.14 -51.93 -0.42 0.68 16 46 H 0.06 1.45 6.14 -51.93 -0.32 1.13 16 47 H 0.02 0.51 8.14 -51.93 -0.42 0.08 16 48 H 0.10 0.63 3.97 -51.93 -0.21 0.43 16 49 H 0.09 0.81 7.97 -51.93 -0.41 0.40 16 50 H 0.08 0.38 8.14 -51.93 -0.42 -0.04 16 51 H 0.08 0.62 8.14 -51.92 -0.42 0.20 16 52 H 0.07 0.44 7.98 -51.92 -0.41 0.02 16 53 H 0.10 0.72 8.14 -51.93 -0.42 0.29 16 LS Contribution 395.78 15.07 5.96 5.96 Total: -1.00 -33.57 395.78 -11.05 -44.62 By element: Atomic # 1 Polarization: 7.85 SS G_CDS: -9.16 Total: -1.31 kcal Atomic # 6 Polarization: -3.29 SS G_CDS: -1.42 Total: -4.72 kcal Atomic # 7 Polarization: -45.25 SS G_CDS: -1.11 Total: -46.36 kcal Atomic # 8 Polarization: -14.84 SS G_CDS: -0.30 Total: -15.15 kcal Atomic # 14 Polarization: 21.96 SS G_CDS: -5.02 Total: 16.94 kcal Total LS contribution 5.96 Total: 5.96 kcal Total: -33.57 -11.05 -44.62 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. ZINC000840043693.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 5.371 kcal (2) G-P(sol) polarization free energy of solvation -33.569 kcal (3) G-ENP(sol) elect.-nuc.-pol. free energy of system -28.198 kcal (4) G-CDS(sol) cavity-dispersion-solvent structure free energy -11.052 kcal (5) G-P-CDS(sol) = G-P(sol) + G-CDS(sol) = (2) + (4) -44.621 kcal (6) G-S(sol) free energy of system = (1) + (5) -39.251 kcal 1SCF WAS SPECIFIED, SO GEOMETRY OPTIMIZATION WAS NOT USED Total computer time = 0.87 seconds