Wall clock time and date at job start Tue Mar 31 2020 19:53:24 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 1.53003 * 1 3 3 C 1.53001 * 109.46682 * 2 1 4 4 C 1.52993 * 109.47483 * 240.00102 * 2 1 3 5 5 C 1.50698 * 109.46875 * 119.99609 * 2 1 3 6 6 O 1.20756 * 120.00451 * 359.97438 * 5 2 1 7 7 C 1.50712 * 119.99709 * 180.02562 * 5 2 1 8 8 N 1.46898 * 109.46926 * 174.19968 * 7 5 2 9 9 C 1.48049 * 111.00103 * 183.43810 * 8 7 5 10 10 C 1.54252 * 106.83968 * 146.61046 * 9 8 7 11 11 C 1.54366 * 104.82309 * 358.54893 * 10 9 8 12 12 H 1.09008 * 110.04620 * 94.67029 * 11 10 9 13 13 C 1.48927 * 111.00339 * 300.45803 * 8 7 5 14 14 H 1.09002 * 112.07716 * 78.73143 * 13 8 7 15 15 C 1.53116 * 107.98189 * 314.48332 * 13 8 7 16 16 C 1.52920 * 109.18680 * 184.13021 * 15 13 8 17 17 C 1.50307 * 109.42153 * 52.12422 * 16 15 13 18 18 O 1.21287 * 118.67471 * 159.18641 * 17 16 15 19 19 N 1.35158 * 123.18102 * 338.93229 * 17 16 15 20 20 C 1.46502 * 118.77874 * 180.73144 * 19 17 16 21 21 C 1.53001 * 109.47078 * 270.04843 * 20 19 17 22 22 C 1.50694 * 109.47155 * 180.02562 * 21 20 19 23 23 H 1.07996 * 120.00375 * 359.97438 * 22 21 20 24 24 C 1.37885 * 119.99821 * 180.02562 * 22 21 20 25 25 N 1.31512 * 120.00385 * 359.97438 * 24 22 21 26 26 Si 1.86799 * 119.99511 * 179.97438 * 24 22 21 27 27 H 1.48505 * 109.47232 * 90.00132 * 26 24 22 28 28 H 1.48502 * 109.46946 * 209.99985 * 26 24 22 29 29 H 1.48498 * 109.47444 * 329.99745 * 26 24 22 30 30 H 1.08998 * 109.47150 * 300.00018 * 1 2 3 31 31 H 1.08999 * 109.46941 * 60.00022 * 1 2 3 32 32 H 1.08996 * 109.46639 * 179.97438 * 1 2 3 33 33 H 1.09007 * 109.46758 * 179.97438 * 3 2 1 34 34 H 1.08999 * 109.47415 * 299.99688 * 3 2 1 35 35 H 1.08998 * 109.47343 * 60.00100 * 3 2 1 36 36 H 1.09005 * 109.46909 * 300.00136 * 4 2 1 37 37 H 1.08994 * 109.47324 * 59.99533 * 4 2 1 38 38 H 1.08995 * 109.47364 * 180.02562 * 4 2 1 39 39 H 1.08999 * 109.46829 * 54.20165 * 7 5 2 40 40 H 1.08999 * 109.46895 * 294.19837 * 7 5 2 41 41 H 1.08999 * 109.98624 * 27.26686 * 9 8 7 42 42 H 1.09001 * 110.02285 * 265.97902 * 9 8 7 43 43 H 1.09006 * 110.37218 * 239.71833 * 10 9 8 44 44 H 1.08996 * 110.46469 * 117.43133 * 10 9 8 45 45 H 1.09001 * 109.51867 * 304.04336 * 15 13 8 46 46 H 1.08996 * 109.51581 * 64.21843 * 15 13 8 47 47 H 1.09005 * 109.47971 * 172.11286 * 16 15 13 48 48 H 1.09004 * 109.48099 * 292.14048 * 16 15 13 49 49 H 1.08994 * 109.47364 * 30.04970 * 20 19 17 50 50 H 1.09000 * 109.46775 * 150.05265 * 20 19 17 51 51 H 1.09008 * 109.47090 * 300.00500 * 21 20 19 52 52 H 1.09001 * 109.46747 * 60.00040 * 21 20 19 53 53 H 0.96990 * 119.99969 * 179.97438 * 25 24 22 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 1.4425 0.0000 4 6 2.0401 -0.7212 -1.2492 5 6 2.0323 -0.7103 1.2305 6 8 1.2476 -1.1688 2.0257 7 6 3.5140 -0.8475 1.4693 8 7 3.7436 -1.4484 2.7900 9 6 5.1905 -1.5236 3.0944 10 6 5.3375 -1.3256 4.6171 11 6 3.8980 -1.1006 5.1270 12 1 3.4712 -2.0434 5.4693 13 6 3.1526 -0.6085 3.8685 14 1 2.0746 -0.7469 3.9513 15 6 3.5328 0.8492 3.5945 16 6 3.0270 1.7247 4.7417 17 6 3.5002 1.1564 6.0502 18 8 3.5377 1.8830 7.0207 19 7 3.8833 -0.1308 6.2024 20 6 4.3129 -0.5870 7.5266 21 6 5.8213 -0.3773 7.6738 22 6 6.2632 -0.8472 9.0357 23 1 5.5406 -1.2542 9.7273 24 6 7.5902 -0.7565 9.3991 25 7 8.4703 -0.2604 8.5572 26 14 8.1379 -1.3383 11.0876 27 1 8.5119 -2.7738 11.0193 28 1 9.3107 -0.5416 11.5293 29 1 7.0265 -1.1618 12.0566 30 1 -0.3633 0.5138 0.8900 31 1 -0.3633 0.5138 -0.8900 32 1 -0.3632 -1.0277 -0.0005 33 1 3.1300 1.4426 0.0005 34 1 1.6766 1.9564 -0.8900 35 1 1.6766 1.9564 0.8900 36 1 1.6767 -1.7489 -1.2492 37 1 1.6768 -0.2074 -2.1391 38 1 3.1300 -0.7216 -1.2489 39 1 3.9807 0.1368 1.4319 40 1 3.9486 -1.4852 0.6995 41 1 5.7244 -0.7358 2.5631 42 1 5.5824 -2.4989 2.8059 43 1 5.9556 -0.4529 4.8284 44 1 5.7682 -2.2150 5.0772 45 1 4.6169 0.9352 3.5214 46 1 3.0769 1.1748 2.6595 47 1 3.4135 2.7371 4.6239 48 1 1.9373 1.7476 4.7282 49 1 3.7902 -0.0168 8.2946 50 1 4.0806 -1.6460 7.6390 51 1 6.3440 -0.9475 6.9057 52 1 6.0535 0.6817 7.5613 53 1 9.4036 -0.1962 8.8130 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 ZINC001273947795.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 19:53:24 Heat of formation + Delta-G solvation = -70.644255 kcal Electronic energy + Delta-G solvation = -31390.360871 eV Core-core repulsion = 27454.791299 eV Total energy + Delta-G solvation = -3935.569572 eV No. of doubly occupied orbitals = 65 Molecular weight (most abundant/longest-lived isotopes) = 336.220 amu Computer time = 0.87 seconds Orbital eigenvalues (eV) -41.26622 -39.94891 -38.17166 -36.07346 -35.27355 -33.61145 -32.77340 -31.54017 -29.35412 -28.17621 -27.87632 -27.79387 -26.62742 -25.04910 -23.73641 -22.97389 -21.82199 -20.77434 -20.42331 -18.61739 -17.97541 -16.69410 -16.56561 -16.34677 -16.17964 -15.97441 -15.41791 -15.11538 -14.83134 -14.46327 -14.43985 -14.15296 -14.07252 -13.84207 -13.19685 -13.15741 -12.81589 -12.71963 -12.65738 -12.48563 -12.45564 -12.33317 -12.19396 -12.09808 -11.87111 -11.64984 -11.58382 -11.40680 -11.34723 -11.30438 -11.23982 -10.90509 -10.76751 -10.64775 -10.50618 -9.79593 -9.78170 -9.56097 -9.30652 -8.99807 -8.54961 -8.31545 -7.96540 -5.98183 -4.00057 1.73462 3.05608 3.29747 3.33931 3.40078 3.44135 3.52018 3.97210 4.26618 4.40053 4.42724 4.49006 4.50899 4.61879 4.75441 4.84498 4.98953 5.04864 5.06506 5.11645 5.14909 5.20138 5.23111 5.28325 5.29741 5.36913 5.38492 5.40600 5.44714 5.50353 5.50798 5.66485 5.71865 5.74682 5.77946 5.80658 5.87132 5.88977 6.11779 6.21558 6.24536 6.37497 6.60529 6.66435 6.70454 6.93039 7.01916 7.33603 7.67906 7.78140 8.03232 8.07999 8.41190 8.67954 9.06505 9.63235 11.13310 Molecular weight = 336.22amu Principal moments of inertia in cm(-1) A = 0.023375 B = 0.002771 C = 0.002643 Principal moments of inertia in units of 10**(-40)*gram-cm**2 A = 1197.596394 B =10100.799446 C =10589.684502 Net atomic charges, atomic populations, and dipole contributions calculated with CM2 Atom NO. Type Charge No. of electrons 1 C -0.134 4.134 2 C -0.115 4.115 3 C -0.142 4.142 4 C -0.139 4.139 5 C 0.364 3.636 6 O -0.427 6.427 7 C -0.009 4.009 8 N -0.497 5.497 9 C 0.036 3.964 10 C -0.143 4.143 11 C 0.149 3.851 12 H 0.091 0.909 13 C 0.057 3.943 14 H 0.117 0.883 15 C -0.152 4.152 16 C -0.126 4.126 17 C 0.510 3.490 18 O -0.543 6.543 19 N -0.596 5.596 20 C 0.114 3.886 21 C 0.014 3.986 22 C -0.518 4.518 23 H 0.055 0.945 24 C 0.058 3.942 25 N -0.895 5.895 26 Si 0.893 3.107 27 H -0.281 1.281 28 H -0.287 1.287 29 H -0.273 1.273 30 H 0.061 0.939 31 H 0.060 0.940 32 H 0.061 0.939 33 H 0.063 0.937 34 H 0.068 0.932 35 H 0.061 0.939 36 H 0.060 0.940 37 H 0.067 0.933 38 H 0.063 0.937 39 H 0.075 0.925 40 H 0.109 0.891 41 H 0.047 0.953 42 H 0.084 0.916 43 H 0.082 0.918 44 H 0.084 0.916 45 H 0.075 0.925 46 H 0.069 0.931 47 H 0.098 0.902 48 H 0.095 0.905 49 H 0.072 0.928 50 H 0.062 0.938 51 H 0.021 0.979 52 H 0.019 0.981 53 H 0.260 0.740 For the charges calculated by CM2: Dipole moment (debyes) X Y Z Total from point charges -12.463 0.096 -24.129 27.158 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 -0.191 4.191 2 C -0.116 4.116 3 C -0.199 4.199 4 C -0.196 4.196 5 C 0.236 3.764 6 O -0.298 6.298 7 C -0.138 4.138 8 N -0.221 5.221 9 C -0.092 4.092 10 C -0.182 4.182 11 C 0.043 3.957 12 H 0.109 0.891 13 C -0.052 4.052 14 H 0.135 0.865 15 C -0.191 4.191 16 C -0.167 4.167 17 C 0.298 3.702 18 O -0.421 6.421 19 N -0.328 5.328 20 C -0.007 4.007 21 C -0.024 4.024 22 C -0.557 4.557 23 H 0.074 0.926 24 C -0.143 4.143 25 N -0.534 5.534 26 Si 0.721 3.279 27 H -0.207 1.207 28 H -0.213 1.213 29 H -0.198 1.198 30 H 0.080 0.920 31 H 0.079 0.921 32 H 0.080 0.920 33 H 0.082 0.918 34 H 0.087 0.913 35 H 0.080 0.920 36 H 0.079 0.921 37 H 0.086 0.914 38 H 0.082 0.918 39 H 0.093 0.907 40 H 0.127 0.873 41 H 0.065 0.935 42 H 0.102 0.898 43 H 0.101 0.899 44 H 0.103 0.897 45 H 0.094 0.906 46 H 0.088 0.912 47 H 0.116 0.884 48 H 0.113 0.887 49 H 0.091 0.909 50 H 0.080 0.920 51 H 0.040 0.960 52 H 0.037 0.963 53 H 0.069 0.931 Dipole moment (debyes) X Y Z Total from point charges -12.928 -0.261 -23.226 26.583 hybrid contribution 1.038 0.484 0.670 1.327 sum -11.890 0.222 -22.556 25.499 Atomic orbital electron populations 1.21714 0.92478 1.02739 1.02163 1.21192 0.97902 0.97070 0.95428 1.21888 1.01480 0.93517 1.02996 1.21833 1.01479 1.00479 0.95825 1.24480 0.90632 0.75746 0.85512 1.90377 1.58650 1.36903 1.43831 1.22805 0.96105 1.00707 0.94168 1.64941 1.11221 1.45869 1.00031 1.22999 0.87767 1.01766 0.96634 1.22984 0.97511 1.04202 0.93466 1.21326 0.95288 0.92511 0.86534 0.89081 1.23222 1.00970 0.90135 0.90824 0.86495 1.22267 1.02293 0.96033 0.98481 1.21505 1.02641 1.00479 0.92028 1.20469 0.77584 0.81748 0.90384 1.90719 1.54092 1.57115 1.40147 1.47636 1.64961 1.09094 1.11076 1.21898 0.99415 0.98095 0.81326 1.19422 0.88290 0.97673 0.97020 1.21123 0.93261 1.41235 1.00059 0.92633 1.24979 0.96805 0.95316 0.97167 1.69963 1.02371 1.45616 1.35426 0.86583 0.78265 0.78549 0.84541 1.20687 1.21262 1.19833 0.92025 0.92059 0.92032 0.91771 0.91263 0.92032 0.92071 0.91401 0.91772 0.90729 0.87317 0.93486 0.89783 0.89905 0.89746 0.90608 0.91217 0.88367 0.88712 0.90918 0.91954 0.96029 0.96285 0.93073 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 -0.13 -0.93 7.76 37.16 0.29 -0.64 16 2 C -0.11 -0.73 0.87 -155.66 -0.14 -0.87 16 3 C -0.14 -0.74 8.10 37.16 0.30 -0.43 16 4 C -0.14 -0.67 8.28 37.15 0.31 -0.36 16 5 C 0.36 3.28 4.89 -29.03 -0.14 3.14 16 6 O -0.43 -5.33 13.92 6.00 0.08 -5.25 16 7 C -0.01 -0.08 4.07 -4.97 -0.02 -0.10 16 8 N -0.50 -5.61 5.10 -223.76 -1.14 -6.75 16 9 C 0.04 0.41 5.98 -2.54 -0.02 0.39 16 10 C -0.14 -2.11 4.54 -25.36 -0.12 -2.22 16 11 C 0.15 2.27 3.15 -67.43 -0.21 2.06 16 12 H 0.09 1.38 7.98 -51.92 -0.41 0.97 16 13 C 0.06 0.72 2.56 -65.84 -0.17 0.55 16 14 H 0.12 1.61 6.41 -51.93 -0.33 1.28 16 15 C -0.15 -1.73 3.99 -26.71 -0.11 -1.84 16 16 C -0.13 -1.69 6.07 -28.11 -0.17 -1.86 16 17 C 0.51 9.62 7.54 -11.00 -0.08 9.54 16 18 O -0.54 -12.75 16.34 5.55 0.09 -12.66 16 19 N -0.60 -11.02 2.50 -165.77 -0.41 -11.44 16 20 C 0.11 2.49 5.13 -4.04 -0.02 2.47 16 21 C 0.01 0.36 5.03 -27.89 -0.14 0.22 16 22 C -0.52 -14.90 9.11 -34.44 -0.31 -15.22 16 23 H 0.06 1.55 7.74 -52.49 -0.41 1.14 16 24 C 0.06 1.70 5.46 -17.82 -0.10 1.61 16 25 N -0.89 -27.14 13.29 55.43 0.74 -26.40 16 26 Si 0.89 22.05 29.54 -169.99 -5.02 17.03 16 27 H -0.28 -6.76 7.11 56.52 0.40 -6.36 16 28 H -0.29 -7.03 7.11 56.52 0.40 -6.63 16 29 H -0.27 -6.66 7.11 56.52 0.40 -6.26 16 30 H 0.06 0.49 8.10 -51.93 -0.42 0.07 16 31 H 0.06 0.33 8.14 -51.93 -0.42 -0.10 16 32 H 0.06 0.48 8.10 -51.93 -0.42 0.06 16 33 H 0.06 0.29 7.15 -51.92 -0.37 -0.09 16 34 H 0.07 0.29 8.14 -51.93 -0.42 -0.13 16 35 H 0.06 0.36 8.10 -51.93 -0.42 -0.06 16 36 H 0.06 0.33 8.14 -51.93 -0.42 -0.10 16 37 H 0.07 0.26 8.14 -51.93 -0.42 -0.16 16 38 H 0.06 0.25 7.43 -51.93 -0.39 -0.13 16 39 H 0.08 0.54 5.10 -51.93 -0.27 0.28 16 40 H 0.11 0.73 7.65 -51.93 -0.40 0.33 16 41 H 0.05 0.48 7.38 -51.93 -0.38 0.10 16 42 H 0.08 0.88 8.14 -51.93 -0.42 0.46 16 43 H 0.08 1.43 7.49 -51.93 -0.39 1.04 16 44 H 0.08 1.32 8.04 -51.93 -0.42 0.90 16 45 H 0.08 0.92 6.57 -51.93 -0.34 0.58 16 46 H 0.07 0.64 5.77 -51.93 -0.30 0.34 16 47 H 0.10 1.23 8.14 -51.93 -0.42 0.81 16 48 H 0.09 1.12 8.14 -51.93 -0.42 0.70 16 49 H 0.07 1.72 7.26 -51.93 -0.38 1.34 16 50 H 0.06 1.26 7.88 -51.93 -0.41 0.85 16 51 H 0.02 0.57 6.28 -51.92 -0.33 0.24 16 52 H 0.02 0.56 8.14 -51.93 -0.42 0.14 16 53 H 0.26 7.44 8.31 -40.82 -0.34 7.10 16 LS Contribution 398.41 15.07 6.00 6.00 Total: -1.00 -34.54 398.41 -9.80 -44.34 By element: Atomic # 1 Polarization: 7.99 SS G_CDS: -9.29 Total: -1.30 kcal Atomic # 6 Polarization: -2.72 SS G_CDS: -0.84 Total: -3.57 kcal Atomic # 7 Polarization: -43.77 SS G_CDS: -0.82 Total: -44.59 kcal Atomic # 8 Polarization: -18.08 SS G_CDS: 0.17 Total: -17.91 kcal Atomic # 14 Polarization: 22.05 SS G_CDS: -5.02 Total: 17.03 kcal Total LS contribution 6.00 Total: 6.00 kcal Total: -34.54 -9.80 -44.34 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. ZINC001273947795.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 -26.306 kcal (2) G-P(sol) polarization free energy of solvation -34.537 kcal (3) G-ENP(sol) elect.-nuc.-pol. free energy of system -60.843 kcal (4) G-CDS(sol) cavity-dispersion-solvent structure free energy -9.801 kcal (5) G-P-CDS(sol) = G-P(sol) + G-CDS(sol) = (2) + (4) -44.338 kcal (6) G-S(sol) free energy of system = (1) + (5) -70.644 kcal 1SCF WAS SPECIFIED, SO GEOMETRY OPTIMIZATION WAS NOT USED Total computer time = 0.87 seconds