Wall clock time and date at job start Sat Apr 11 2020 06:13:22 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 1.52997 * 109.47309 * 2 1 4 4 C 1.52998 * 109.47309 * 180.02562 * 3 2 1 5 5 C 1.52997 * 109.47309 * 180.02562 * 4 3 2 6 6 H 1.09002 * 109.47174 * 305.00121 * 5 4 3 7 7 N 1.46504 * 109.47170 * 65.00200 * 5 4 3 8 8 C 1.34771 * 119.99871 * 59.99930 * 7 5 4 9 9 N 1.34777 * 119.99627 * 180.02562 * 8 7 5 10 10 O 1.21586 * 120.00363 * 0.02562 * 8 7 5 11 11 C 1.50705 * 109.47044 * 184.99997 * 5 4 3 12 12 O 1.21274 * 119.99751 * 259.99885 * 11 5 4 13 13 N 1.34769 * 119.99742 * 79.99874 * 11 5 4 14 14 C 1.46926 * 120.63597 * 354.42152 * 13 11 5 15 15 C 1.53192 * 108.77568 * 126.36522 * 14 13 11 16 16 C 1.53039 * 109.31337 * 54.64262 * 15 14 13 17 17 C 1.53045 * 109.53601 * 298.63009 * 16 15 14 18 18 C 1.46924 * 120.62996 * 174.13903 * 13 11 5 19 19 H 1.09002 * 109.58999 * 113.84532 * 18 13 11 20 20 C 1.53002 * 109.58937 * 353.42223 * 18 13 11 21 21 N 1.46497 * 109.47858 * 181.61827 * 20 18 13 22 22 C 1.36932 * 120.00397 * 184.94536 * 21 20 18 23 23 H 1.07996 * 119.99781 * 0.02562 * 22 21 20 24 24 C 1.38809 * 120.00209 * 179.97438 * 22 21 20 25 25 N 1.31623 * 119.99876 * 0.02562 * 24 22 21 26 26 Si 1.86801 * 120.00271 * 180.02562 * 24 22 21 27 27 H 1.48502 * 109.46940 * 59.99836 * 26 24 22 28 28 H 1.48493 * 109.47228 * 180.02562 * 26 24 22 29 29 H 1.48504 * 109.46809 * 300.00007 * 26 24 22 30 30 H 1.09007 * 109.47445 * 180.02562 * 1 2 3 31 31 H 1.09009 * 109.47395 * 300.00028 * 1 2 3 32 32 H 1.08997 * 109.47358 * 59.99559 * 1 2 3 33 33 H 1.09000 * 109.46850 * 239.99841 * 2 1 3 34 34 H 1.09007 * 109.46644 * 120.00242 * 2 1 3 35 35 H 1.08997 * 109.47015 * 300.00007 * 3 2 1 36 36 H 1.09000 * 109.46834 * 59.99844 * 3 2 1 37 37 H 1.09007 * 109.47095 * 299.99956 * 4 3 2 38 38 H 1.09000 * 109.46850 * 59.99841 * 4 3 2 39 39 H 0.97000 * 119.99236 * 240.00205 * 7 5 4 40 40 H 0.97002 * 120.00305 * 0.02562 * 9 8 7 41 41 H 0.97003 * 119.99703 * 179.97438 * 9 8 7 42 42 H 1.08992 * 109.59362 * 246.15707 * 14 13 11 43 43 H 1.09003 * 109.58727 * 6.44008 * 14 13 11 44 44 H 1.09005 * 109.49963 * 174.58885 * 15 14 13 45 45 H 1.09001 * 109.50331 * 294.68601 * 15 14 13 46 46 H 1.08998 * 109.46549 * 58.65216 * 16 15 14 47 47 H 1.09000 * 109.45932 * 178.62757 * 16 15 14 48 48 H 1.08996 * 109.50020 * 181.32015 * 17 16 15 49 49 H 1.08996 * 109.49980 * 301.38631 * 17 16 15 50 50 H 1.09008 * 109.46848 * 301.62202 * 20 18 13 51 51 H 1.09001 * 109.46787 * 61.61730 * 20 18 13 52 52 H 0.97003 * 119.99603 * 4.95108 * 21 20 18 53 53 H 0.96996 * 119.99780 * 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 2.0400 1.4425 0.0000 4 6 3.5700 1.4425 -0.0006 5 6 4.0800 2.8849 0.0000 6 1 3.6451 3.4245 -0.8413 7 7 3.6931 3.5392 1.2524 8 6 4.1181 3.0430 2.4312 9 7 3.7616 3.6446 3.5833 10 8 4.8231 2.0527 2.4553 11 6 5.5819 2.8867 -0.1245 12 8 6.2718 3.0391 0.8612 13 7 6.1582 2.7190 -1.3311 14 6 5.3428 2.4121 -2.5141 15 6 5.6614 3.4330 -3.6110 16 6 7.1693 3.4414 -3.8721 17 6 7.9072 3.8562 -2.5971 18 6 7.6134 2.8457 -1.4898 19 1 8.0371 1.8784 -1.7599 20 6 8.2322 3.3314 -0.1775 21 7 9.6779 3.4939 -0.3498 22 6 10.4624 3.8244 0.7228 23 1 10.0154 3.9649 1.6958 24 6 11.8323 3.9777 0.5596 25 7 12.3771 3.8060 -0.6262 26 14 12.9026 4.4279 2.0229 27 1 12.7809 3.3786 3.0666 28 1 14.3184 4.5316 1.5873 29 1 12.4592 5.7320 2.5779 30 1 -0.3634 -1.0277 0.0005 31 1 -0.3634 0.5139 0.8900 32 1 -0.3634 0.5139 -0.8899 33 1 1.8933 -0.5139 -0.8900 34 1 1.8933 -0.5139 0.8900 35 1 1.6767 1.9563 -0.8900 36 1 1.6767 1.9563 0.8900 37 1 3.9337 0.9285 0.8892 38 1 3.9329 0.9287 -0.8909 39 1 3.1309 4.3294 1.2331 40 1 3.1989 4.4345 3.5642 41 1 4.0673 3.2873 4.4318 42 1 5.5774 1.4088 -2.8695 43 1 4.2857 2.4697 -2.2543 44 1 5.1353 3.1602 -4.5259 45 1 5.3423 4.4244 -3.2892 46 1 7.4918 2.4438 -4.1701 47 1 7.3958 4.1495 -4.6693 48 1 8.9795 3.8847 -2.7903 49 1 7.5674 4.8437 -2.2851 50 1 7.7896 4.2880 0.1007 51 1 8.0397 2.6001 0.6075 52 1 10.0794 3.3674 -1.2237 53 1 13.3343 3.9135 -0.7402 RHF calculation, no. of doubly occupied orbitals= 66 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 ZINC001700346432.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 06:13:22 Heat of formation + Delta-G solvation = -48.866639 kcal Electronic energy + Delta-G solvation = -32148.019530 eV Core-core repulsion = 28055.231006 eV Total energy + Delta-G solvation = -4092.788524 eV No. of doubly occupied orbitals = 66 Molecular weight (most abundant/longest-lived isotopes) = 340.226 amu Computer time = 0.81 seconds Orbital eigenvalues (eV) -40.82746 -39.35858 -37.09026 -36.39712 -34.70219 -34.13836 -33.46798 -32.66293 -31.87880 -30.49241 -29.61160 -27.28570 -25.77852 -24.29639 -23.24506 -22.82358 -21.76340 -21.09957 -20.96736 -20.14575 -18.85597 -18.44161 -17.27390 -16.94578 -16.45022 -15.98682 -15.64667 -15.10883 -14.75811 -14.60590 -14.38397 -14.34687 -14.06525 -14.02373 -13.89428 -13.43867 -13.30445 -13.22137 -12.86558 -12.83251 -12.59194 -12.55165 -11.98944 -11.91181 -11.47728 -11.39253 -11.25103 -11.10442 -10.92801 -10.85253 -10.80443 -10.71423 -10.62016 -10.45256 -10.28393 -9.96033 -9.83065 -9.56870 -9.47571 -9.36426 -8.74594 -8.27684 -8.18460 -6.67200 -5.58900 -2.84367 2.71489 3.03519 3.23430 3.54355 3.56822 3.59304 3.62661 4.39199 4.49043 4.65244 4.68926 4.75052 4.78212 4.87288 4.89246 4.93313 5.06472 5.12036 5.19479 5.32016 5.44196 5.45702 5.48740 5.51522 5.61379 5.67952 5.69175 5.75833 5.82790 5.87177 5.89828 5.96876 6.05455 6.06406 6.08895 6.23331 6.30002 6.36762 6.37662 6.43918 6.63182 6.69463 6.89297 7.00145 7.22204 7.45125 7.75203 7.92076 8.01358 8.57197 8.66933 8.85794 9.71886 10.32117 10.67277 11.64930 Molecular weight = 340.23amu Principal moments of inertia in cm(-1) A = 0.011961 B = 0.003388 C = 0.002802 Principal moments of inertia in units of 10**(-40)*gram-cm**2 A = 2340.456909 B = 8262.067655 C = 9991.540494 Net atomic charges, atomic populations, and dipole contributions calculated with CM2 Atom NO. Type Charge No. of electrons 1 C -0.151 4.151 2 C -0.125 4.125 3 C -0.111 4.111 4 C -0.138 4.138 5 C 0.154 3.846 6 H 0.104 0.896 7 N -0.733 5.733 8 C 0.710 3.290 9 N -0.872 5.872 10 O -0.559 6.559 11 C 0.493 3.507 12 O -0.478 6.478 13 N -0.610 5.610 14 C 0.106 3.894 15 C -0.134 4.134 16 C -0.120 4.120 17 C -0.126 4.126 18 C 0.142 3.858 19 H 0.068 0.932 20 C 0.162 3.838 21 N -0.737 5.737 22 C -0.221 4.221 23 H 0.068 0.932 24 C -0.021 4.021 25 N -0.941 5.941 26 Si 0.906 3.094 27 H -0.287 1.287 28 H -0.292 1.292 29 H -0.288 1.288 30 H 0.052 0.948 31 H 0.052 0.948 32 H 0.052 0.948 33 H 0.061 0.939 34 H 0.062 0.938 35 H 0.059 0.941 36 H 0.062 0.938 37 H 0.097 0.903 38 H 0.074 0.926 39 H 0.396 0.604 40 H 0.391 0.609 41 H 0.413 0.587 42 H 0.067 0.933 43 H 0.080 0.920 44 H 0.070 0.930 45 H 0.065 0.935 46 H 0.062 0.938 47 H 0.062 0.938 48 H 0.085 0.915 49 H 0.062 0.938 50 H 0.019 0.981 51 H 0.059 0.941 52 H 0.378 0.622 53 H 0.253 0.747 For the charges calculated by CM2: Dipole moment (debyes) X Y Z Total from point charges -28.751 -1.896 -4.553 29.171 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 -0.209 4.209 2 C -0.163 4.163 3 C -0.149 4.149 4 C -0.176 4.176 5 C 0.044 3.956 6 H 0.121 0.879 7 N -0.390 5.390 8 C 0.408 3.592 9 N -0.441 5.441 10 O -0.433 6.433 11 C 0.277 3.723 12 O -0.349 6.349 13 N -0.347 5.347 14 C -0.017 4.017 15 C -0.172 4.172 16 C -0.158 4.158 17 C -0.165 4.165 18 C 0.040 3.960 19 H 0.086 0.914 20 C 0.035 3.965 21 N -0.383 5.383 22 C -0.352 4.352 23 H 0.086 0.914 24 C -0.216 4.216 25 N -0.591 5.591 26 Si 0.737 3.263 27 H -0.214 1.214 28 H -0.218 1.218 29 H -0.215 1.215 30 H 0.071 0.929 31 H 0.071 0.929 32 H 0.072 0.928 33 H 0.080 0.920 34 H 0.081 0.919 35 H 0.077 0.923 36 H 0.080 0.920 37 H 0.115 0.885 38 H 0.092 0.908 39 H 0.230 0.770 40 H 0.218 0.782 41 H 0.245 0.755 42 H 0.086 0.914 43 H 0.098 0.902 44 H 0.089 0.911 45 H 0.083 0.917 46 H 0.081 0.919 47 H 0.081 0.919 48 H 0.103 0.897 49 H 0.081 0.919 50 H 0.037 0.963 51 H 0.077 0.923 52 H 0.212 0.788 53 H 0.062 0.938 Dipole moment (debyes) X Y Z Total from point charges -27.709 -2.657 -3.953 28.116 hybrid contribution 0.385 0.981 0.618 1.222 sum -27.324 -1.675 -3.335 27.578 Atomic orbital electron populations 1.21767 0.96025 1.01479 1.01586 1.21518 0.95579 0.96939 1.02256 1.21543 0.94691 0.96882 1.01764 1.22061 0.95755 0.94780 1.05020 1.20758 0.92961 0.95700 0.86152 0.87871 1.44678 1.56748 1.33343 1.04256 1.15832 0.79554 0.83292 0.80475 1.42967 1.58846 1.34413 1.07830 1.90992 1.39574 1.26990 1.85723 1.20801 0.90222 0.77993 0.83275 1.90882 1.62243 1.45453 1.36292 1.48136 1.07615 1.71626 1.07275 1.21755 0.95053 0.98730 0.86168 1.21928 0.97481 0.99659 0.98175 1.21539 0.94350 1.01742 0.98134 1.21864 1.01665 0.99051 0.93897 1.21437 0.78091 0.98600 0.97898 0.91406 1.21275 0.84137 0.98650 0.92402 1.42584 1.01406 1.84643 1.09706 1.19205 0.88946 1.37462 0.89625 0.91355 1.24684 0.96626 1.03561 0.96693 1.69649 1.10665 1.57634 1.21157 0.86265 0.79605 0.78255 0.82132 1.21389 1.21842 1.21507 0.92902 0.92934 0.92845 0.91973 0.91949 0.92254 0.91973 0.88486 0.90780 0.77034 0.78218 0.75532 0.91427 0.90171 0.91135 0.91665 0.91893 0.91914 0.89687 0.91879 0.96303 0.92347 0.78832 0.93774 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 -0.95 9.91 37.16 0.37 -0.59 16 2 C -0.13 -0.94 5.93 -26.73 -0.16 -1.10 16 3 C -0.11 -0.84 5.10 -26.73 -0.14 -0.98 16 4 C -0.14 -1.42 4.22 -26.73 -0.11 -1.54 16 5 C 0.15 1.70 2.15 -69.08 -0.15 1.55 16 6 H 0.10 0.79 6.83 -51.93 -0.35 0.44 16 7 N -0.73 -7.64 4.66 -59.81 -0.28 -7.92 16 8 C 0.71 9.73 7.59 -86.92 -0.66 9.07 16 9 N -0.87 -8.23 8.88 27.63 0.25 -7.99 16 10 O -0.56 -10.62 13.03 -18.20 -0.24 -10.86 16 11 C 0.49 7.98 6.53 -10.99 -0.07 7.91 16 12 O -0.48 -10.27 9.24 -17.93 -0.17 -10.44 16 13 N -0.61 -9.03 2.98 -165.47 -0.49 -9.52 16 14 C 0.11 1.06 5.53 -3.71 -0.02 1.04 16 15 C -0.13 -1.26 6.08 -26.61 -0.16 -1.43 16 16 C -0.12 -1.44 5.89 -26.69 -0.16 -1.60 16 17 C -0.13 -2.08 5.07 -26.83 -0.14 -2.21 16 18 C 0.14 2.62 3.09 -67.82 -0.21 2.41 16 19 H 0.07 1.29 8.14 -51.93 -0.42 0.87 16 20 C 0.16 3.89 4.14 -4.04 -0.02 3.87 16 21 N -0.74 -20.56 5.38 -59.91 -0.32 -20.88 16 22 C -0.22 -6.81 9.99 -15.06 -0.15 -6.96 16 23 H 0.07 2.12 7.83 -52.49 -0.41 1.71 16 24 C -0.02 -0.65 5.50 -17.43 -0.10 -0.74 16 25 N -0.94 -29.93 13.06 55.49 0.72 -29.20 16 26 Si 0.91 24.13 29.55 -169.99 -5.02 19.11 16 27 H -0.29 -7.58 7.11 56.52 0.40 -7.18 16 28 H -0.29 -7.72 7.11 56.52 0.40 -7.32 16 29 H -0.29 -7.55 7.11 56.52 0.40 -7.15 16 30 H 0.05 0.32 8.14 -51.93 -0.42 -0.11 16 31 H 0.05 0.33 8.14 -51.92 -0.42 -0.09 16 32 H 0.05 0.30 8.14 -51.93 -0.42 -0.12 16 33 H 0.06 0.45 8.14 -51.93 -0.42 0.02 16 34 H 0.06 0.55 8.14 -51.92 -0.42 0.12 16 35 H 0.06 0.35 8.14 -51.93 -0.42 -0.07 16 36 H 0.06 0.49 7.75 -51.93 -0.40 0.09 16 37 H 0.10 1.38 6.04 -51.92 -0.31 1.07 16 38 H 0.07 0.71 6.79 -51.93 -0.35 0.36 16 39 H 0.40 2.66 8.84 -40.82 -0.36 2.30 16 40 H 0.39 2.24 8.84 -40.82 -0.36 1.88 16 41 H 0.41 3.79 8.93 -40.82 -0.36 3.42 16 42 H 0.07 0.64 8.14 -51.93 -0.42 0.22 16 43 H 0.08 0.59 4.95 -51.93 -0.26 0.33 16 44 H 0.07 0.50 8.14 -51.93 -0.42 0.08 16 45 H 0.06 0.63 8.14 -51.93 -0.42 0.21 16 46 H 0.06 0.74 8.14 -51.93 -0.42 0.32 16 47 H 0.06 0.70 8.14 -51.93 -0.42 0.27 16 48 H 0.08 1.60 6.88 -51.93 -0.36 1.24 16 49 H 0.06 1.09 8.14 -51.93 -0.42 0.67 16 50 H 0.02 0.49 7.26 -51.92 -0.38 0.12 16 51 H 0.06 1.59 6.21 -51.93 -0.32 1.27 16 52 H 0.38 10.66 6.35 -40.82 -0.26 10.40 16 53 H 0.25 7.76 8.31 -40.82 -0.34 7.43 16 LS Contribution 402.47 15.07 6.07 6.07 Total: -1.00 -39.67 402.47 -10.48 -50.15 By element: Atomic # 1 Polarization: 21.90 SS G_CDS: -9.12 Total: 12.78 kcal Atomic # 6 Polarization: 10.57 SS G_CDS: -1.87 Total: 8.71 kcal Atomic # 7 Polarization: -75.39 SS G_CDS: -0.12 Total: -75.51 kcal Atomic # 8 Polarization: -20.89 SS G_CDS: -0.40 Total: -21.30 kcal Atomic # 14 Polarization: 24.13 SS G_CDS: -5.02 Total: 19.11 kcal Total LS contribution 6.07 Total: 6.07 kcal Total: -39.67 -10.48 -50.15 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. ZINC001700346432.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 1.281 kcal (2) G-P(sol) polarization free energy of solvation -39.671 kcal (3) G-ENP(sol) elect.-nuc.-pol. free energy of system -38.389 kcal (4) G-CDS(sol) cavity-dispersion-solvent structure free energy -10.477 kcal (5) G-P-CDS(sol) = G-P(sol) + G-CDS(sol) = (2) + (4) -50.148 kcal (6) G-S(sol) free energy of system = (1) + (5) -48.867 kcal 1SCF WAS SPECIFIED, SO GEOMETRY OPTIMIZATION WAS NOT USED Total computer time = 0.82 seconds