Wall clock time and date at job start Sat Apr 11 2020 06:09:55 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 1.52996 * 1 3 3 C 1.53001 * 109.47323 * 2 1 4 4 C 1.52996 * 109.47354 * 239.99852 * 2 1 3 5 5 O 1.45202 * 109.47082 * 119.99714 * 2 1 3 6 6 C 1.34634 * 117.00070 * 60.00008 * 5 2 1 7 7 O 1.21515 * 119.99613 * 0.02562 * 6 5 2 8 8 N 1.34773 * 120.00369 * 179.97438 * 6 5 2 9 9 C 1.47237 * 121.71469 * 359.97438 * 8 6 5 10 10 C 1.53097 * 109.39805 * 131.47816 * 9 8 6 11 11 N 1.47454 * 109.77912 * 48.44632 * 10 9 8 12 12 C 1.48071 * 109.71574 * 49.00175 * 11 10 9 13 13 C 1.54096 * 106.82736 * 269.94347 * 12 11 10 14 14 H 1.09003 * 110.42005 * 119.45607 * 13 12 11 15 15 O 1.42900 * 110.42262 * 241.92577 * 13 12 11 16 16 C 1.42896 * 113.99947 * 268.54547 * 15 13 12 17 17 C 1.53000 * 109.47124 * 180.02562 * 16 15 13 18 18 C 1.52996 * 109.47490 * 180.02562 * 17 16 15 19 19 C 1.50701 * 109.47520 * 180.02562 * 18 17 16 20 20 H 1.08003 * 119.99795 * 359.97438 * 19 18 17 21 21 C 1.37878 * 120.00286 * 179.97438 * 19 18 17 22 22 N 1.31515 * 119.99944 * 0.02562 * 21 19 18 23 23 Si 1.86797 * 120.00104 * 179.97438 * 21 19 18 24 24 H 1.48500 * 109.47332 * 59.99988 * 23 21 19 25 25 H 1.48497 * 109.47316 * 180.02562 * 23 21 19 26 26 H 1.48502 * 109.46996 * 300.00121 * 23 21 19 27 27 C 1.48379 * 121.71639 * 179.97438 * 8 6 5 28 28 H 1.08995 * 114.47457 * 5.47119 * 27 8 6 29 29 C 1.48794 * 108.53247 * 294.46400 * 11 10 9 30 30 H 1.09004 * 109.46969 * 299.99913 * 1 2 3 31 31 H 1.09003 * 109.47130 * 59.99606 * 1 2 3 32 32 H 1.08993 * 109.47310 * 180.02562 * 1 2 3 33 33 H 1.08998 * 109.47253 * 180.02562 * 3 2 1 34 34 H 1.09003 * 109.47339 * 300.00266 * 3 2 1 35 35 H 1.09001 * 109.47103 * 59.99357 * 3 2 1 36 36 H 1.09004 * 109.47163 * 300.00556 * 4 2 1 37 37 H 1.09002 * 109.47394 * 59.99813 * 4 2 1 38 38 H 1.08998 * 109.47473 * 180.02562 * 4 2 1 39 39 H 1.09000 * 109.48283 * 11.49729 * 9 8 6 40 40 H 1.09005 * 109.49151 * 251.46728 * 9 8 6 41 41 H 1.08995 * 109.41883 * 288.34743 * 10 9 8 42 42 H 1.09000 * 109.36749 * 168.51078 * 10 9 8 43 43 H 1.09004 * 109.98908 * 150.60397 * 12 11 10 44 44 H 1.09005 * 109.99376 * 29.28665 * 12 11 10 45 45 H 1.08995 * 109.47448 * 300.00070 * 16 15 13 46 46 H 1.09008 * 109.47268 * 60.00336 * 16 15 13 47 47 H 1.09002 * 109.47338 * 300.00443 * 17 16 15 48 48 H 1.09003 * 109.47092 * 60.00400 * 17 16 15 49 49 H 1.09009 * 109.46953 * 299.99995 * 18 17 16 50 50 H 1.09000 * 109.47554 * 59.99952 * 18 17 16 51 51 H 0.96997 * 120.00218 * 180.02562 * 22 21 19 52 52 H 1.09007 * 110.97790 * 316.41481 * 29 11 10 53 53 H 1.08998 * 110.98116 * 192.62552 * 29 11 10 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 2.0400 -0.7213 -1.2492 5 8 2.0140 -0.6844 1.1856 6 6 1.6522 -1.9722 1.3384 7 8 0.9516 -2.5096 0.5036 8 7 2.0680 -2.6656 2.4167 9 6 2.9189 -2.0527 3.4502 10 6 2.3352 -2.3528 4.8333 11 7 2.0229 -3.7898 4.9420 12 6 3.1861 -4.5890 4.4942 13 6 3.0116 -4.8214 2.9809 14 1 3.8483 -4.3904 2.4309 15 8 2.8959 -6.2179 2.7009 16 6 4.1412 -6.8590 2.4176 17 6 3.8980 -8.3427 2.1339 18 6 5.2314 -9.0293 1.8312 19 6 4.9918 -10.4906 1.5511 20 1 3.9888 -10.8897 1.5859 21 6 6.0530 -11.3179 1.2504 22 7 7.2743 -10.8320 1.2085 23 14 5.7561 -13.1293 0.9039 24 1 4.8507 -13.2678 -0.2650 25 1 7.0501 -13.7957 0.6100 26 1 5.1312 -13.7646 2.0919 27 6 1.6917 -4.0859 2.6235 28 1 1.1415 -4.5324 1.7953 29 6 0.9332 -4.1109 3.9810 30 1 -0.3633 0.5138 0.8900 31 1 -0.3633 0.5139 -0.8900 32 1 -0.3633 -1.0276 0.0005 33 1 3.1300 1.4425 -0.0005 34 1 1.6767 1.9564 -0.8900 35 1 1.6766 1.9564 0.8899 36 1 1.6766 -1.7489 -1.2492 37 1 1.6767 -0.2075 -2.1392 38 1 3.1300 -0.7217 -1.2490 39 1 2.9564 -0.9740 3.2976 40 1 3.9260 -2.4644 3.3834 41 1 1.4239 -1.7720 4.9758 42 1 3.0616 -2.0808 5.5991 43 1 3.2055 -5.5447 5.0181 44 1 4.1095 -4.0414 4.6830 45 1 4.5997 -6.3931 1.5455 46 1 4.8059 -6.7570 3.2756 47 1 3.4393 -8.8090 3.0058 48 1 3.2336 -8.4444 1.2758 49 1 5.6905 -8.5631 0.9594 50 1 5.8955 -8.9277 2.6895 51 1 8.0208 -11.4139 0.9966 52 1 0.1535 -3.3496 4.0064 53 1 0.5180 -5.0993 4.1779 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 ZINC001205656461.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 06:09:55 Heat of formation + Delta-G solvation = -111.361621 kcal Electronic energy + Delta-G solvation = -31152.342793 eV Core-core repulsion = 27024.551532 eV Total energy + Delta-G solvation = -4127.791261 eV No. of doubly occupied orbitals = 66 Molecular weight (most abundant/longest-lived isotopes) = 340.220 amu Computer time = 0.94 seconds Orbital eigenvalues (eV) -41.63527 -40.39593 -37.54501 -37.03189 -34.83060 -33.90760 -33.71791 -32.10764 -31.20383 -28.83185 -27.75470 -27.67681 -27.46123 -26.47067 -24.01068 -23.23237 -22.73616 -21.12752 -20.72956 -20.11895 -19.37688 -18.34187 -17.19764 -16.77073 -16.43315 -16.13570 -16.02303 -15.48276 -15.09815 -15.02502 -14.84085 -14.61210 -14.43013 -14.30137 -13.99066 -13.73354 -13.29301 -12.97828 -12.80031 -12.56824 -12.49763 -12.25524 -12.22691 -12.19140 -12.03707 -11.88739 -11.68834 -11.58922 -11.55701 -11.51538 -11.31738 -11.11732 -10.87170 -10.66939 -10.58935 -10.42956 -10.27052 -9.92486 -9.70124 -9.44142 -9.38908 -9.12312 -8.43223 -8.35619 -6.01091 -4.03367 1.70970 2.56229 3.34452 3.37288 3.38259 3.41410 3.65730 3.81701 4.36473 4.38105 4.39543 4.43055 4.47422 4.57066 4.60107 4.64050 4.70105 4.88819 5.07522 5.11586 5.12984 5.21070 5.27810 5.30107 5.34914 5.35428 5.38654 5.43435 5.49028 5.53551 5.54169 5.62860 5.65394 5.68273 5.79128 5.87429 5.95229 5.99064 6.06715 6.14418 6.17403 6.38709 6.59387 6.65774 6.69624 7.05448 7.07252 7.45526 7.64560 7.76857 7.98097 8.05805 8.40825 9.02949 9.60696 11.10431 Molecular weight = 340.22amu Principal moments of inertia in cm(-1) A = 0.014735 B = 0.002228 C = 0.002049 Principal moments of inertia in units of 10**(-40)*gram-cm**2 A = 1899.827555 B =12565.021173 C =13664.169473 Net atomic charges, atomic populations, and dipole contributions calculated with CM2 Atom NO. Type Charge No. of electrons 1 C -0.183 4.183 2 C 0.135 3.865 3 C -0.140 4.140 4 C -0.184 4.184 5 O -0.364 6.364 6 C 0.658 3.342 7 O -0.562 6.562 8 N -0.596 5.596 9 C 0.074 3.926 10 C 0.022 3.978 11 N -0.493 5.493 12 C 0.006 3.994 13 C 0.051 3.949 14 H 0.072 0.928 15 O -0.372 6.372 16 C 0.063 3.937 17 C -0.107 4.107 18 C 0.024 3.976 19 C -0.520 4.520 20 H 0.056 0.944 21 C 0.056 3.944 22 N -0.897 5.897 23 Si 0.895 3.105 24 H -0.276 1.276 25 H -0.287 1.287 26 H -0.276 1.276 27 C 0.130 3.870 28 H 0.137 0.863 29 C 0.025 3.975 30 H 0.058 0.942 31 H 0.070 0.930 32 H 0.088 0.912 33 H 0.066 0.934 34 H 0.080 0.920 35 H 0.066 0.934 36 H 0.088 0.912 37 H 0.070 0.930 38 H 0.060 0.940 39 H 0.097 0.903 40 H 0.072 0.928 41 H 0.082 0.918 42 H 0.093 0.907 43 H 0.100 0.900 44 H 0.078 0.922 45 H 0.043 0.957 46 H 0.045 0.955 47 H 0.057 0.943 48 H 0.056 0.944 49 H 0.016 0.984 50 H 0.017 0.983 51 H 0.261 0.739 52 H 0.085 0.915 53 H 0.104 0.896 For the charges calculated by CM2: Dipole moment (debyes) X Y Z Total from point charges -11.323 27.811 3.559 30.238 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 -0.240 4.240 2 C 0.099 3.901 3 C -0.197 4.197 4 C -0.242 4.242 5 O -0.278 6.278 6 C 0.413 3.587 7 O -0.451 6.451 8 N -0.339 5.339 9 C -0.049 4.049 10 C -0.107 4.107 11 N -0.215 5.215 12 C -0.123 4.123 13 C -0.010 4.010 14 H 0.090 0.910 15 O -0.290 6.290 16 C -0.013 4.013 17 C -0.145 4.145 18 C -0.013 4.013 19 C -0.558 4.558 20 H 0.075 0.925 21 C -0.145 4.145 22 N -0.536 5.536 23 Si 0.722 3.278 24 H -0.202 1.202 25 H -0.213 1.213 26 H -0.202 1.202 27 C 0.027 3.973 28 H 0.155 0.845 29 C -0.104 4.104 30 H 0.077 0.923 31 H 0.089 0.911 32 H 0.107 0.893 33 H 0.085 0.915 34 H 0.099 0.901 35 H 0.085 0.915 36 H 0.107 0.893 37 H 0.089 0.911 38 H 0.079 0.921 39 H 0.115 0.885 40 H 0.091 0.909 41 H 0.100 0.900 42 H 0.112 0.888 43 H 0.118 0.882 44 H 0.096 0.904 45 H 0.062 0.938 46 H 0.064 0.936 47 H 0.076 0.924 48 H 0.075 0.925 49 H 0.034 0.966 50 H 0.035 0.965 51 H 0.071 0.929 52 H 0.103 0.897 53 H 0.123 0.877 Dipole moment (debyes) X Y Z Total from point charges -11.675 27.455 3.804 30.075 hybrid contribution 0.627 -0.550 -1.170 1.437 sum -11.047 26.905 2.634 29.204 Atomic orbital electron populations 1.22510 0.93950 1.05117 1.02417 1.22090 0.94393 0.91486 0.82143 1.21856 1.02280 0.92473 1.03090 1.22522 1.01649 1.03609 0.96384 1.86280 1.71548 1.23566 1.46452 1.17860 0.78754 0.80513 0.81535 1.90920 1.41123 1.70316 1.42706 1.47451 1.53540 1.11604 1.21266 1.22440 0.94205 0.99971 0.88333 1.22919 1.02163 0.90664 0.94999 1.66008 1.05711 1.03810 1.45941 1.23738 0.93950 1.00254 0.94361 1.23736 0.97110 0.84422 0.95710 0.91029 1.87934 1.32229 1.18595 1.90286 1.22886 0.84411 0.95406 0.98563 1.21659 1.01593 0.90073 1.01154 1.19038 0.90443 0.94916 0.96882 1.21176 0.93470 0.93778 1.47377 0.92545 1.25028 0.95157 0.98839 0.95484 1.69952 0.98676 1.35780 1.49201 0.86617 0.77316 0.84979 0.78863 1.20193 1.21303 1.20174 1.23405 0.95727 0.77557 1.00625 0.84546 1.23921 0.94464 1.03623 0.88375 0.92267 0.91099 0.89346 0.91457 0.90095 0.91531 0.89293 0.91074 0.92131 0.88506 0.90937 0.89958 0.88842 0.88194 0.90386 0.93840 0.93618 0.92426 0.92517 0.96558 0.96480 0.92923 0.89690 0.87733 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 -0.18 -1.57 8.37 37.16 0.31 -1.26 16 2 C 0.14 1.21 1.13 -90.62 -0.10 1.11 16 3 C -0.14 -0.86 8.85 37.16 0.33 -0.53 16 4 C -0.18 -1.74 8.37 37.16 0.31 -1.43 16 5 O -0.36 -3.91 8.66 -40.31 -0.35 -4.25 16 6 C 0.66 8.19 7.79 54.05 0.42 8.62 16 7 O -0.56 -8.28 11.60 -19.28 -0.22 -8.50 16 8 N -0.60 -6.58 2.70 -166.92 -0.45 -7.03 16 9 C 0.07 0.62 5.76 -3.59 -0.02 0.60 16 10 C 0.02 0.17 5.91 -3.47 -0.02 0.15 16 11 N -0.49 -4.96 5.97 -229.08 -1.37 -6.33 16 12 C 0.01 0.06 6.03 -2.61 -0.02 0.05 16 13 C 0.05 0.65 2.46 -24.96 -0.06 0.59 16 14 H 0.07 0.93 7.20 -51.93 -0.37 0.56 16 15 O -0.37 -6.02 9.99 -35.23 -0.35 -6.37 16 16 C 0.06 1.11 5.80 37.16 0.22 1.33 16 17 C -0.11 -2.28 5.52 -26.73 -0.15 -2.42 16 18 C 0.02 0.63 4.97 -27.88 -0.14 0.49 16 19 C -0.52 -14.88 9.11 -34.44 -0.31 -15.19 16 20 H 0.06 1.57 7.74 -52.48 -0.41 1.16 16 21 C 0.06 1.62 5.46 -17.82 -0.10 1.52 16 22 N -0.90 -27.04 13.29 55.43 0.74 -26.30 16 23 Si 0.89 21.84 29.54 -169.99 -5.02 16.82 16 24 H -0.28 -6.64 7.11 56.52 0.40 -6.24 16 25 H -0.29 -6.92 7.11 56.52 0.40 -6.52 16 26 H -0.28 -6.61 7.11 56.52 0.40 -6.21 16 27 C 0.13 1.55 4.15 -64.35 -0.27 1.29 16 28 H 0.14 1.86 7.48 -51.93 -0.39 1.48 16 29 C 0.03 0.26 6.53 -1.43 -0.01 0.25 16 30 H 0.06 0.47 8.14 -51.93 -0.42 0.05 16 31 H 0.07 0.48 8.14 -51.93 -0.42 0.06 16 32 H 0.09 0.99 5.88 -51.93 -0.31 0.68 16 33 H 0.07 0.41 8.14 -51.93 -0.42 -0.02 16 34 H 0.08 0.37 8.14 -51.93 -0.42 -0.06 16 35 H 0.07 0.38 8.14 -51.93 -0.42 -0.05 16 36 H 0.09 1.08 5.88 -51.93 -0.31 0.78 16 37 H 0.07 0.53 8.14 -51.93 -0.42 0.11 16 38 H 0.06 0.56 8.14 -51.93 -0.42 0.14 16 39 H 0.10 0.72 7.09 -51.93 -0.37 0.35 16 40 H 0.07 0.60 6.25 -51.93 -0.32 0.28 16 41 H 0.08 0.60 7.91 -51.93 -0.41 0.19 16 42 H 0.09 0.58 8.14 -51.93 -0.42 0.16 16 43 H 0.10 1.23 7.97 -51.93 -0.41 0.82 16 44 H 0.08 0.73 7.02 -51.93 -0.36 0.37 16 45 H 0.04 0.76 8.10 -51.93 -0.42 0.34 16 46 H 0.05 0.76 8.14 -51.92 -0.42 0.34 16 47 H 0.06 1.22 8.14 -51.93 -0.42 0.79 16 48 H 0.06 1.22 8.14 -51.93 -0.42 0.80 16 49 H 0.02 0.44 8.14 -51.92 -0.42 0.02 16 50 H 0.02 0.46 8.14 -51.93 -0.42 0.04 16 51 H 0.26 7.43 8.31 -40.82 -0.34 7.09 16 52 H 0.08 0.82 7.84 -51.93 -0.41 0.41 16 53 H 0.10 1.12 8.14 -51.93 -0.42 0.69 16 LS Contribution 407.95 15.07 6.15 6.15 Total: -1.00 -32.01 407.95 -10.03 -42.04 By element: Atomic # 1 Polarization: 8.15 SS G_CDS: -9.54 Total: -1.39 kcal Atomic # 6 Polarization: -5.23 SS G_CDS: 0.39 Total: -4.83 kcal Atomic # 7 Polarization: -38.58 SS G_CDS: -1.08 Total: -39.66 kcal Atomic # 8 Polarization: -18.20 SS G_CDS: -0.92 Total: -19.12 kcal Atomic # 14 Polarization: 21.84 SS G_CDS: -5.02 Total: 16.82 kcal Total LS contribution 6.15 Total: 6.15 kcal Total: -32.01 -10.03 -42.04 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. ZINC001205656461.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 -69.318 kcal (2) G-P(sol) polarization free energy of solvation -32.014 kcal (3) G-ENP(sol) elect.-nuc.-pol. free energy of system -101.333 kcal (4) G-CDS(sol) cavity-dispersion-solvent structure free energy -10.029 kcal (5) G-P-CDS(sol) = G-P(sol) + G-CDS(sol) = (2) + (4) -42.043 kcal (6) G-S(sol) free energy of system = (1) + (5) -111.362 kcal 1SCF WAS SPECIFIED, SO GEOMETRY OPTIMIZATION WAS NOT USED Total computer time = 0.94 seconds