Wall clock time and date at job start Tue Mar 31 2020 19:46:43 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 1.53010 * 1 3 3 C 1.52998 * 109.46931 * 2 1 4 4 C 1.52993 * 109.47016 * 120.00273 * 2 1 3 5 5 C 1.53001 * 109.46935 * 174.99824 * 4 2 1 6 6 N 1.46505 * 109.47511 * 179.97438 * 5 4 2 7 7 C 1.34776 * 119.99638 * 89.99748 * 6 5 4 8 8 O 1.21346 * 120.00368 * 354.96939 * 7 6 5 9 9 C 1.49455 * 119.99649 * 175.23856 * 7 6 5 10 10 O 1.21344 * 119.99589 * 275.35783 * 9 7 6 11 11 N 1.34767 * 119.99732 * 95.36321 * 9 7 6 12 12 C 1.46926 * 120.63552 * 354.67114 * 11 9 7 13 13 C 1.52762 * 109.01005 * 233.58989 * 12 11 9 14 14 C 1.53043 * 109.38223 * 305.58636 * 13 12 11 15 15 C 1.53044 * 109.54105 * 61.23789 * 14 13 12 16 16 H 1.09001 * 109.49373 * 58.58802 * 15 14 13 17 17 C 1.50697 * 109.49817 * 178.68750 * 15 14 13 18 18 H 1.07994 * 120.00124 * 359.83240 * 17 15 14 19 19 C 1.37875 * 119.99774 * 179.84594 * 17 15 14 20 20 N 1.31517 * 120.00040 * 359.97438 * 19 17 15 21 21 Si 1.86801 * 119.99922 * 179.97438 * 19 17 15 22 22 H 1.48504 * 109.47149 * 89.99677 * 21 19 17 23 23 H 1.48498 * 109.47038 * 209.99387 * 21 19 17 24 24 H 1.48493 * 109.47142 * 329.99437 * 21 19 17 25 25 C 1.46934 * 120.62815 * 174.95442 * 11 9 7 26 26 C 1.46495 * 120.00002 * 270.00366 * 6 5 4 27 27 C 1.53001 * 117.50249 * 13.42865 * 26 6 5 28 28 C 1.53000 * 117.49779 * 304.76552 * 26 6 5 29 29 H 1.09001 * 109.46856 * 299.99474 * 1 2 3 30 30 H 1.08990 * 109.47079 * 59.99674 * 1 2 3 31 31 H 1.08998 * 109.47091 * 180.02562 * 1 2 3 32 32 H 1.09001 * 109.46856 * 240.00526 * 2 1 3 33 33 H 1.09001 * 109.46873 * 179.97438 * 3 2 1 34 34 H 1.09004 * 109.47196 * 300.00551 * 3 2 1 35 35 H 1.09001 * 109.46921 * 60.00565 * 3 2 1 36 36 H 1.08997 * 109.47495 * 55.00421 * 4 2 1 37 37 H 1.08997 * 109.47444 * 294.99863 * 4 2 1 38 38 H 1.09000 * 109.47003 * 59.99806 * 5 4 2 39 39 H 1.09003 * 109.47490 * 300.00358 * 5 4 2 40 40 H 1.09000 * 109.58057 * 353.42154 * 12 11 9 41 41 H 1.08998 * 109.58800 * 113.84938 * 12 11 9 42 42 H 1.08994 * 109.56359 * 185.55071 * 13 12 11 43 43 H 1.08998 * 109.39026 * 65.51155 * 13 12 11 44 44 H 1.09008 * 109.45587 * 301.22021 * 14 13 12 45 45 H 1.08994 * 109.46252 * 181.26611 * 14 13 12 46 46 H 0.97006 * 119.99811 * 180.02562 * 20 19 17 47 47 H 1.08991 * 109.58453 * 246.15444 * 25 11 9 48 48 H 1.08999 * 109.58507 * 6.43339 * 25 11 9 49 49 H 1.09003 * 115.55020 * 159.10102 * 26 6 5 50 50 H 1.08999 * 117.49355 * 359.97438 * 27 26 6 51 51 H 1.08993 * 117.50294 * 145.01795 * 27 26 6 52 52 H 1.09005 * 117.49587 * 214.97649 * 28 26 6 53 53 H 1.08996 * 117.50245 * 359.97438 * 28 26 6 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 1.5301 0.0000 0.0000 3 6 2.0400 1.4425 0.0000 4 6 2.0400 -0.7213 1.2492 5 6 3.5649 -0.8311 1.1878 6 7 4.0534 -1.5212 2.3843 7 6 4.1821 -2.8628 2.3829 8 8 3.8081 -3.5073 1.4252 9 6 4.7799 -3.5573 3.5636 10 8 5.9850 -3.6611 3.6603 11 7 3.9804 -4.0682 4.5207 12 6 2.5280 -3.8502 4.4782 13 6 2.0746 -3.2579 5.8113 14 6 2.5415 -4.1625 6.9541 15 6 4.0699 -4.2407 6.9532 16 1 4.4855 -3.2390 7.0634 17 6 4.5300 -5.1056 8.0983 18 1 3.8052 -5.5527 8.7625 19 6 5.8763 -5.3258 8.2983 20 7 6.7589 -4.7815 7.4893 21 14 6.4466 -6.3974 9.7181 22 1 6.5358 -7.8096 9.2677 23 1 7.7821 -5.9394 10.1785 24 1 5.4754 -6.2949 10.8367 25 6 4.5454 -4.8488 5.6300 26 6 4.4018 -0.7531 3.5820 27 6 3.9469 0.7065 3.6425 28 6 5.4253 0.3735 3.4258 29 1 -0.3633 0.5138 0.8900 30 1 -0.3633 0.5138 -0.8899 31 1 -0.3633 -1.0276 0.0005 32 1 1.8934 -0.5138 -0.8900 33 1 3.1301 1.4425 0.0005 34 1 1.6766 1.9564 -0.8900 35 1 1.6768 1.9563 0.8900 36 1 1.6055 -1.7198 1.2950 37 1 1.7517 -0.1584 2.1369 38 1 3.9995 0.1674 1.1419 39 1 3.8533 -1.3940 0.3000 40 1 2.2860 -3.1585 3.6714 41 1 2.0206 -4.8005 4.3123 42 1 0.9872 -3.1840 5.8269 43 1 2.5084 -2.2654 5.9326 44 1 2.1267 -5.1615 6.8191 45 1 2.1993 -3.7529 7.9044 46 1 7.7061 -4.9368 7.6298 47 1 4.2058 -5.8821 5.5598 48 1 5.6339 -4.8178 5.5814 49 1 4.4118 -1.3162 4.5153 50 1 3.3887 1.0953 2.7908 51 1 3.6579 1.1037 4.6154 52 1 6.1081 0.5518 4.2565 53 1 5.8396 0.5428 2.4320 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 ZINC001261608140.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 19:46:43 Heat of formation + Delta-G solvation = -58.669586 kcal Electronic energy + Delta-G solvation = -31427.666094 eV Core-core repulsion = 27492.615783 eV Total energy + Delta-G solvation = -3935.050311 eV No. of doubly occupied orbitals = 65 Molecular weight (most abundant/longest-lived isotopes) = 336.220 amu Computer time = 0.81 seconds Orbital eigenvalues (eV) -40.73139 -38.89225 -37.59143 -36.76525 -36.56714 -33.44985 -33.36975 -31.88667 -30.05755 -29.64028 -27.44888 -26.03613 -25.08753 -24.05941 -23.05129 -22.51246 -21.91120 -21.34368 -20.19031 -19.33970 -18.60220 -17.57250 -16.71598 -16.30301 -16.10577 -15.66168 -15.24798 -14.86613 -14.60388 -14.44707 -14.13547 -13.94574 -13.83285 -13.73691 -13.50341 -13.13519 -12.93269 -12.69696 -12.55084 -12.50150 -12.22954 -12.18653 -11.98821 -11.66590 -11.52678 -11.36725 -11.13506 -11.07025 -11.01009 -10.94705 -10.85814 -10.77178 -10.57631 -10.54255 -10.43683 -10.30475 -9.97634 -9.26344 -9.19281 -8.87715 -8.60072 -8.50002 -7.92271 -6.04864 -4.13724 2.32820 2.45410 3.05921 3.28572 3.36379 3.38078 3.60687 3.74020 4.38056 4.42991 4.54936 4.60058 4.63707 4.70527 4.82831 4.85399 4.97135 5.20859 5.23117 5.25830 5.35533 5.37539 5.41298 5.42449 5.47396 5.54541 5.59611 5.60881 5.71523 5.73136 5.76403 5.86029 5.93158 5.95859 5.99041 6.07915 6.09189 6.15595 6.23427 6.35194 6.51013 6.56958 6.76378 6.88638 7.00030 7.11580 7.15480 7.53206 7.77197 7.88063 7.93868 8.04846 8.29931 8.51687 8.90097 9.52428 11.00417 Molecular weight = 336.22amu Principal moments of inertia in cm(-1) A = 0.018437 B = 0.003140 C = 0.003042 Principal moments of inertia in units of 10**(-40)*gram-cm**2 A = 1518.283513 B = 8913.701493 C = 9202.278304 Net atomic charges, atomic populations, and dipole contributions calculated with CM2 Atom NO. Type Charge No. of electrons 1 C -0.146 4.146 2 C -0.095 4.095 3 C -0.151 4.151 4 C -0.131 4.131 5 C 0.109 3.891 6 N -0.571 5.571 7 C 0.522 3.478 8 O -0.518 6.518 9 C 0.506 3.494 10 O -0.507 6.507 11 N -0.587 5.587 12 C 0.108 3.892 13 C -0.131 4.131 14 C -0.112 4.112 15 C 0.043 3.957 16 H 0.030 0.970 17 C -0.521 4.521 18 H 0.059 0.941 19 C 0.063 3.937 20 N -0.880 5.880 21 Si 0.893 3.107 22 H -0.280 1.280 23 H -0.286 1.286 24 H -0.274 1.274 25 C 0.110 3.890 26 C 0.067 3.933 27 C -0.182 4.182 28 C -0.186 4.186 29 H 0.054 0.946 30 H 0.053 0.947 31 H 0.055 0.945 32 H 0.071 0.929 33 H 0.055 0.945 34 H 0.054 0.946 35 H 0.055 0.945 36 H 0.070 0.930 37 H 0.069 0.931 38 H 0.081 0.919 39 H 0.084 0.916 40 H 0.065 0.935 41 H 0.068 0.932 42 H 0.063 0.937 43 H 0.060 0.940 44 H 0.051 0.949 45 H 0.054 0.946 46 H 0.264 0.736 47 H 0.048 0.952 48 H 0.125 0.875 49 H 0.136 0.864 50 H 0.102 0.898 51 H 0.106 0.894 52 H 0.106 0.894 53 H 0.097 0.903 For the charges calculated by CM2: Dipole moment (debyes) X Y Z Total from point charges -10.986 13.394 -11.681 20.894 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 -0.203 4.203 2 C -0.114 4.114 3 C -0.208 4.208 4 C -0.169 4.169 5 C -0.012 4.012 6 N -0.304 5.304 7 C 0.306 3.694 8 O -0.392 6.392 9 C 0.286 3.714 10 O -0.381 6.381 11 N -0.321 5.321 12 C -0.015 4.015 13 C -0.169 4.169 14 C -0.149 4.149 15 C 0.024 3.976 16 H 0.048 0.952 17 C -0.560 4.560 18 H 0.078 0.922 19 C -0.140 4.140 20 N -0.517 5.517 21 Si 0.721 3.279 22 H -0.206 1.206 23 H -0.212 1.212 24 H -0.199 1.199 25 C -0.010 4.010 26 C -0.037 4.037 27 C -0.219 4.219 28 C -0.225 4.225 29 H 0.073 0.927 30 H 0.072 0.928 31 H 0.074 0.926 32 H 0.090 0.910 33 H 0.074 0.926 34 H 0.073 0.927 35 H 0.074 0.926 36 H 0.088 0.912 37 H 0.087 0.913 38 H 0.099 0.901 39 H 0.103 0.897 40 H 0.084 0.916 41 H 0.086 0.914 42 H 0.081 0.919 43 H 0.079 0.921 44 H 0.070 0.930 45 H 0.073 0.927 46 H 0.074 0.926 47 H 0.066 0.934 48 H 0.143 0.857 49 H 0.153 0.847 50 H 0.120 0.880 51 H 0.124 0.876 52 H 0.125 0.875 53 H 0.115 0.885 Dipole moment (debyes) X Y Z Total from point charges -10.319 12.952 -12.180 20.557 hybrid contribution 0.354 -0.569 0.712 0.978 sum -9.965 12.383 -11.469 19.600 Atomic orbital electron populations 1.21818 0.95003 1.01880 1.01629 1.21060 0.95956 0.96131 0.98214 1.21926 1.01038 0.96004 1.01818 1.22048 0.95096 1.01532 0.98253 1.21635 0.94394 0.97572 0.87640 1.47477 1.63780 1.05487 1.13668 1.20731 0.77466 0.82196 0.89000 1.90748 1.47672 1.64894 1.35923 1.19975 0.87598 0.80987 0.82800 1.90830 1.13208 1.58518 1.75576 1.48584 1.06801 1.52132 1.24601 1.21604 0.81139 1.00646 0.98139 1.21861 0.99744 1.00048 0.95255 1.21648 0.99490 0.97857 0.95935 1.18956 0.89244 0.97334 0.92102 0.95198 1.21056 0.91780 1.31192 1.11958 0.92250 1.25054 0.96939 0.95698 0.96300 1.69873 1.01752 1.43213 1.36887 0.86581 0.78085 0.80710 0.82566 1.20617 1.21192 1.19925 1.22484 1.03201 0.91924 0.83372 1.21858 1.04005 0.88537 0.89320 1.23428 0.97910 0.96515 1.04086 1.23398 0.92533 1.02639 1.03882 0.92671 0.92769 0.92593 0.91025 0.92567 0.92724 0.92563 0.91172 0.91256 0.90062 0.89732 0.91638 0.91411 0.91865 0.92111 0.92992 0.92748 0.92565 0.93372 0.85720 0.84656 0.88002 0.87579 0.87513 0.88472 Number of geometries 1 Number of calculations of the screened coulomb radii 1 The total number of SCF iterations 12. 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 -1.05 9.19 37.16 0.34 -0.71 16 2 C -0.09 -0.73 2.92 -90.62 -0.26 -1.00 16 3 C -0.15 -0.99 8.95 37.16 0.33 -0.65 16 4 C -0.13 -1.25 4.83 -26.73 -0.13 -1.38 16 5 C 0.11 1.21 4.38 -4.04 -0.02 1.19 16 6 N -0.57 -8.03 2.82 -166.61 -0.47 -8.50 16 7 C 0.52 9.44 5.46 -11.58 -0.06 9.38 16 8 O -0.52 -10.25 16.73 5.50 0.09 -10.15 16 9 C 0.51 10.66 5.74 -11.59 -0.07 10.59 16 10 O -0.51 -12.63 16.51 5.50 0.09 -12.54 16 11 N -0.59 -11.84 2.98 -173.54 -0.52 -12.36 16 12 C 0.11 1.75 6.30 -3.93 -0.02 1.72 16 13 C -0.13 -2.00 6.07 -26.83 -0.16 -2.16 16 14 C -0.11 -2.10 5.11 -26.69 -0.14 -2.24 16 15 C 0.04 1.00 2.25 -91.65 -0.21 0.80 16 16 H 0.03 0.77 8.14 -51.93 -0.42 0.35 16 17 C -0.52 -13.62 8.56 -34.44 -0.29 -13.91 16 18 H 0.06 1.52 7.74 -52.49 -0.41 1.12 16 19 C 0.06 1.70 5.30 -17.82 -0.09 1.60 16 20 N -0.88 -24.90 11.39 55.43 0.63 -24.27 16 21 Si 0.89 20.82 29.54 -169.99 -5.02 15.80 16 22 H -0.28 -6.52 7.11 56.52 0.40 -6.12 16 23 H -0.29 -6.69 7.11 56.52 0.40 -6.29 16 24 H -0.27 -6.28 7.11 56.52 0.40 -5.88 16 25 C 0.11 2.59 5.41 -3.71 -0.02 2.57 16 26 C 0.07 0.88 6.07 -67.93 -0.41 0.47 16 27 C -0.18 -1.71 9.51 -26.69 -0.25 -1.96 16 28 C -0.19 -2.07 10.03 -26.69 -0.27 -2.34 16 29 H 0.05 0.38 8.14 -51.93 -0.42 -0.04 16 30 H 0.05 0.35 8.14 -51.93 -0.42 -0.08 16 31 H 0.05 0.43 8.14 -51.93 -0.42 0.00 16 32 H 0.07 0.59 8.14 -51.93 -0.42 0.16 16 33 H 0.06 0.36 6.56 -51.93 -0.34 0.02 16 34 H 0.05 0.33 8.14 -51.93 -0.42 -0.10 16 35 H 0.06 0.35 8.14 -51.93 -0.42 -0.07 16 36 H 0.07 0.80 8.14 -51.93 -0.42 0.38 16 37 H 0.07 0.63 7.22 -51.93 -0.37 0.25 16 38 H 0.08 0.73 4.67 -51.93 -0.24 0.49 16 39 H 0.08 1.04 7.50 -51.93 -0.39 0.65 16 40 H 0.07 0.97 6.37 -51.93 -0.33 0.64 16 41 H 0.07 1.05 8.14 -51.93 -0.42 0.63 16 42 H 0.06 0.79 8.14 -51.93 -0.42 0.37 16 43 H 0.06 0.92 8.14 -51.93 -0.42 0.50 16 44 H 0.05 0.97 8.14 -51.92 -0.42 0.54 16 45 H 0.05 1.00 8.14 -51.93 -0.42 0.58 16 46 H 0.26 7.24 8.31 -40.82 -0.34 6.90 16 47 H 0.05 1.14 8.14 -51.93 -0.42 0.72 16 48 H 0.12 3.44 5.12 -51.93 -0.27 3.18 16 49 H 0.14 2.10 7.09 -51.93 -0.37 1.73 16 50 H 0.10 0.82 5.85 -51.93 -0.30 0.52 16 51 H 0.11 0.90 8.14 -51.93 -0.42 0.48 16 52 H 0.11 1.19 8.14 -51.93 -0.42 0.77 16 53 H 0.10 1.02 7.84 -51.93 -0.41 0.61 16 LS Contribution 411.91 15.07 6.21 6.21 Total: -1.00 -30.79 411.91 -10.06 -40.84 By element: Atomic # 1 Polarization: 12.32 SS G_CDS: -9.33 Total: 2.99 kcal Atomic # 6 Polarization: 3.72 SS G_CDS: -1.74 Total: 1.97 kcal Atomic # 7 Polarization: -44.77 SS G_CDS: -0.36 Total: -45.13 kcal Atomic # 8 Polarization: -22.88 SS G_CDS: 0.18 Total: -22.69 kcal Atomic # 14 Polarization: 20.82 SS G_CDS: -5.02 Total: 15.80 kcal Total LS contribution 6.21 Total: 6.21 kcal Total: -30.79 -10.06 -40.84 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. ZINC001261608140.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 -17.827 kcal (2) G-P(sol) polarization free energy of solvation -30.787 kcal (3) G-ENP(sol) elect.-nuc.-pol. free energy of system -48.614 kcal (4) G-CDS(sol) cavity-dispersion-solvent structure free energy -10.056 kcal (5) G-P-CDS(sol) = G-P(sol) + G-CDS(sol) = (2) + (4) -40.843 kcal (6) G-S(sol) free energy of system = (1) + (5) -58.670 kcal 1SCF WAS SPECIFIED, SO GEOMETRY OPTIMIZATION WAS NOT USED Total computer time = 0.81 seconds