Wall clock time and date at job start Sat Apr 11 2020 06:12:03 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 1.50699 * 109.47370 * 2 1 4 4 N 1.30294 * 126.35002 * 87.22610 * 3 2 1 5 5 N 1.28532 * 110.05491 * 180.02562 * 4 3 2 6 6 C 1.31216 * 109.85970 * 0.02562 * 5 4 3 7 7 N 1.38576 * 126.47195 * 179.97438 * 6 5 4 8 8 C 1.46899 * 111.00152 * 256.53466 * 7 6 5 9 9 C 1.46899 * 111.00001 * 20.49183 * 7 6 5 10 10 H 1.08994 * 109.46892 * 299.99624 * 9 7 6 11 11 C 1.52998 * 109.47179 * 59.99737 * 9 7 6 12 12 C 1.50699 * 109.47092 * 179.97438 * 9 7 6 13 13 H 1.08004 * 120.00530 * 0.02562 * 12 9 7 14 14 C 1.37876 * 120.00052 * 179.97438 * 12 9 7 15 15 N 1.31514 * 119.99932 * 0.02562 * 14 12 9 16 16 Si 1.86798 * 120.00237 * 180.02562 * 14 12 9 17 17 H 1.48495 * 109.47433 * 59.99796 * 16 14 12 18 18 H 1.48498 * 109.47465 * 180.02562 * 16 14 12 19 19 H 1.48508 * 109.46769 * 299.99777 * 16 14 12 20 20 N 1.36457 * 107.05626 * 0.02562 * 6 5 4 21 21 C 1.46502 * 127.13873 * 180.02562 * 20 6 5 22 22 C 1.52994 * 109.47170 * 89.34199 * 21 20 6 23 23 C 1.53002 * 109.47320 * 299.99887 * 22 21 20 24 24 O 1.42901 * 109.47358 * 60.00084 * 22 21 20 25 25 C 1.53003 * 109.46826 * 179.97438 * 22 21 20 26 26 C 1.53004 * 109.46828 * 179.97438 * 25 22 21 27 27 O 1.42904 * 109.46613 * 180.02562 * 26 25 22 28 28 C 1.42901 * 113.99730 * 180.02562 * 27 26 25 29 29 H 1.08999 * 109.47297 * 184.80371 * 1 2 3 30 30 H 1.08998 * 109.46693 * 304.80828 * 1 2 3 31 31 H 1.08998 * 109.46565 * 64.80052 * 1 2 3 32 32 H 1.08995 * 109.47324 * 239.99627 * 2 1 3 33 33 H 1.09000 * 109.46937 * 119.99710 * 2 1 3 34 34 H 1.08999 * 109.47132 * 65.67653 * 8 7 6 35 35 H 1.09004 * 109.47020 * 185.67666 * 8 7 6 36 36 H 1.09001 * 109.47419 * 305.67343 * 8 7 6 37 37 H 1.09002 * 109.47253 * 300.00511 * 11 9 7 38 38 H 1.09011 * 109.46965 * 60.00105 * 11 9 7 39 39 H 1.09002 * 109.47387 * 179.97438 * 11 9 7 40 40 H 0.97002 * 120.00101 * 180.02562 * 15 14 12 41 41 H 1.09002 * 109.46833 * 209.34355 * 21 20 6 42 42 H 1.08997 * 109.46415 * 329.33889 * 21 20 6 43 43 H 1.08999 * 109.47121 * 62.42979 * 23 22 21 44 44 H 1.08997 * 109.46998 * 182.42953 * 23 22 21 45 45 H 1.09000 * 109.46960 * 302.42534 * 23 22 21 46 46 H 0.96698 * 113.99574 * 65.17594 * 24 22 21 47 47 H 1.09002 * 109.47110 * 300.00115 * 25 22 21 48 48 H 1.09004 * 109.46838 * 60.00444 * 25 22 21 49 49 H 1.09002 * 109.47387 * 299.99967 * 26 25 22 50 50 H 1.08994 * 109.47182 * 60.00631 * 26 25 22 51 51 H 1.08997 * 109.46986 * 300.00124 * 28 27 26 52 52 H 1.08999 * 109.47336 * 59.99921 * 28 27 26 53 53 H 1.09005 * 109.47051 * 180.02562 * 28 27 26 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 2.0324 1.4208 0.0000 4 7 2.2420 2.1658 1.0482 5 7 2.6692 3.3233 0.6879 6 6 2.7553 3.3794 -0.6202 7 7 3.1763 4.4645 -1.3722 8 6 2.0343 5.1522 -1.9894 9 6 3.9721 5.3925 -0.5578 10 1 3.3679 5.7565 0.2731 11 6 5.2034 4.6658 -0.0130 12 6 4.4117 6.5567 -1.4077 13 1 4.1278 6.6030 -2.4488 14 6 5.1753 7.5635 -0.8561 15 7 5.5205 7.5076 0.4117 16 14 5.7195 9.0070 -1.9094 17 1 4.5246 9.7121 -2.4386 18 1 6.5241 9.9451 -1.0862 19 1 6.5432 8.5110 -3.0412 20 7 2.3509 2.1677 -1.1002 21 6 2.2756 1.7526 -2.5032 22 6 3.6129 1.1422 -2.9269 23 6 4.7233 2.1818 -2.7616 24 8 3.8986 0.0060 -2.1087 25 6 3.5340 0.7080 -4.3919 26 6 4.8716 0.0982 -4.8159 27 8 4.7980 -0.3068 -6.1844 28 6 6.0022 -0.8931 -6.6825 29 1 -0.3634 -1.0240 0.0861 30 1 -0.3632 0.5866 0.8438 31 1 -0.3632 0.4376 -0.9299 32 1 1.8934 -0.5139 -0.8899 33 1 1.8933 -0.5138 0.8900 34 1 1.4126 5.5945 -1.2110 35 1 2.3980 5.9365 -2.6534 36 1 1.4449 4.4359 -2.5619 37 1 4.8859 3.8235 0.6016 38 1 5.8077 4.3018 -0.8441 39 1 5.7942 5.3545 0.5910 40 1 6.0575 8.2161 0.7999 41 1 1.4845 1.0120 -2.6209 42 1 2.0577 2.6193 -3.1272 43 1 4.8082 2.4588 -1.7109 44 1 5.6687 1.7611 -3.1040 45 1 4.4839 3.0660 -3.3524 46 1 3.2780 -0.7268 -2.2227 47 1 2.7430 -0.0327 -4.5092 48 1 3.3160 1.5745 -5.0164 49 1 5.6623 0.8393 -4.6986 50 1 5.0901 -0.7682 -4.1916 51 1 6.8167 -0.1731 -6.6035 52 1 6.2436 -1.7803 -6.0971 53 1 5.8651 -1.1728 -7.7271 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 ZINC001401445798.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 06:12:03 Heat of formation + Delta-G solvation = -6.268721 kcal Electronic energy + Delta-G solvation = -32678.838240 eV Core-core repulsion = 28587.896901 eV Total energy + Delta-G solvation = -4090.941340 eV No. of doubly occupied orbitals = 66 Molecular weight (most abundant/longest-lived isotopes) = 340.226 amu Computer time = 0.78 seconds Orbital eigenvalues (eV) -42.50890 -39.17502 -37.66097 -37.12030 -34.47397 -33.83185 -32.87824 -32.45624 -29.44098 -29.09183 -28.70650 -27.28921 -26.51180 -25.50062 -24.46047 -23.75557 -23.43869 -21.74828 -20.71959 -19.88951 -19.39394 -17.41242 -16.97392 -16.37305 -16.34876 -16.05084 -15.66485 -15.35861 -15.07134 -14.98519 -14.67979 -14.49283 -14.24955 -13.96749 -13.66611 -13.50579 -13.19311 -12.53065 -12.52283 -12.29200 -12.21764 -12.02868 -11.94155 -11.81558 -11.67619 -11.55847 -11.44753 -11.25616 -11.13915 -10.97174 -10.93097 -10.87670 -10.64898 -10.52520 -10.29961 -10.16799 -10.03611 -9.85766 -9.82285 -9.41391 -9.16974 -8.57002 -8.41438 -7.41240 -6.03210 -4.10895 2.27165 2.67529 3.29364 3.35053 3.35804 3.44492 3.48508 4.00828 4.32445 4.44694 4.46836 4.54820 4.62713 4.75687 4.77130 4.92204 4.98342 5.08267 5.17100 5.17781 5.21968 5.28626 5.30773 5.32300 5.39881 5.41564 5.62230 5.65200 5.69066 5.72020 5.79276 5.99408 6.02560 6.06658 6.12326 6.15025 6.30308 6.42478 6.52142 6.63745 6.89546 6.96389 6.99661 7.16290 7.27018 7.43494 7.47612 7.72986 7.76109 7.98829 8.26968 8.48111 8.91238 9.42898 9.53962 11.03060 Molecular weight = 340.23amu Principal moments of inertia in cm(-1) A = 0.008826 B = 0.004326 C = 0.003169 Principal moments of inertia in units of 10**(-40)*gram-cm**2 A = 3171.732920 B = 6471.651819 C = 8834.408852 Net atomic charges, atomic populations, and dipole contributions calculated with CM2 Atom NO. Type Charge No. of electrons 1 C -0.148 4.148 2 C -0.024 4.024 3 C 0.164 3.836 4 N -0.292 5.292 5 N -0.316 5.316 6 C 0.383 3.617 7 N -0.459 5.459 8 C 0.042 3.958 9 C 0.231 3.769 10 H 0.023 0.977 11 C -0.132 4.132 12 C -0.516 4.516 13 H 0.063 0.937 14 C 0.065 3.935 15 N -0.883 5.883 16 Si 0.898 3.102 17 H -0.277 1.277 18 H -0.287 1.287 19 H -0.277 1.277 20 N -0.472 5.472 21 C 0.092 3.908 22 C 0.124 3.876 23 C -0.139 4.139 24 O -0.545 6.545 25 C -0.140 4.140 26 C 0.064 3.936 27 O -0.396 6.396 28 C 0.033 3.967 29 H 0.063 0.937 30 H 0.063 0.937 31 H 0.050 0.950 32 H 0.073 0.927 33 H 0.094 0.906 34 H 0.031 0.969 35 H 0.093 0.907 36 H 0.041 0.959 37 H 0.021 0.979 38 H 0.026 0.974 39 H 0.087 0.913 40 H 0.263 0.737 41 H 0.088 0.912 42 H 0.105 0.895 43 H 0.077 0.923 44 H 0.057 0.943 45 H 0.084 0.916 46 H 0.367 0.633 47 H 0.073 0.927 48 H 0.086 0.914 49 H 0.057 0.943 50 H 0.055 0.945 51 H 0.042 0.958 52 H 0.040 0.960 53 H 0.084 0.916 For the charges calculated by CM2: Dipole moment (debyes) X Y Z Total from point charges -6.290 -18.083 -11.443 22.305 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 -0.206 4.206 2 C -0.064 4.064 3 C -0.103 4.103 4 N -0.131 5.131 5 N -0.159 5.159 6 C 0.027 3.973 7 N -0.185 5.185 8 C -0.105 4.105 9 C 0.127 3.873 10 H 0.041 0.959 11 C -0.191 4.191 12 C -0.554 4.554 13 H 0.082 0.918 14 C -0.138 4.138 15 N -0.521 5.521 16 Si 0.726 3.274 17 H -0.203 1.203 18 H -0.213 1.213 19 H -0.203 1.203 20 N -0.167 5.167 21 C -0.033 4.033 22 C 0.082 3.918 23 C -0.196 4.196 24 O -0.351 6.351 25 C -0.178 4.178 26 C -0.012 4.012 27 O -0.315 6.315 28 C -0.064 4.064 29 H 0.082 0.918 30 H 0.082 0.918 31 H 0.069 0.931 32 H 0.092 0.908 33 H 0.112 0.888 34 H 0.050 0.950 35 H 0.112 0.888 36 H 0.060 0.940 37 H 0.040 0.960 38 H 0.045 0.955 39 H 0.106 0.894 40 H 0.073 0.927 41 H 0.106 0.894 42 H 0.123 0.877 43 H 0.096 0.904 44 H 0.076 0.924 45 H 0.103 0.897 46 H 0.214 0.786 47 H 0.092 0.908 48 H 0.105 0.895 49 H 0.076 0.924 50 H 0.073 0.927 51 H 0.061 0.939 52 H 0.059 0.941 53 H 0.103 0.897 Dipole moment (debyes) X Y Z Total from point charges -5.461 -17.251 -10.126 20.735 hybrid contribution -0.252 0.313 -1.506 1.559 sum -5.714 -16.938 -11.632 21.327 Atomic orbital electron populations 1.21774 0.94360 1.02057 1.02406 1.19826 0.95679 0.87176 1.03740 1.24400 1.05786 0.97344 0.82786 1.73943 1.15650 0.99318 1.24209 1.74792 1.20359 1.12697 1.08098 1.22991 0.97377 0.87611 0.89305 1.59270 1.19086 1.07897 1.32261 1.22289 0.91039 0.98141 0.99058 1.19304 0.89776 0.87322 0.90895 0.95901 1.21825 0.99173 0.98860 0.99198 1.21009 1.33657 1.04160 0.96613 0.91848 1.24890 0.95803 0.98124 0.94994 1.69913 1.37149 1.33380 1.11680 0.86567 0.78685 0.82026 0.80125 1.20289 1.21284 1.20255 1.45981 1.52147 1.11404 1.07195 1.22429 0.98429 1.02022 0.80419 1.21578 0.94959 0.87174 0.88087 1.21876 0.95929 0.96463 1.05288 1.86752 1.56335 1.26168 1.65818 1.22108 0.97632 1.02224 0.95886 1.22499 0.97760 0.98829 0.82144 1.87826 1.35879 1.80736 1.27093 1.22721 0.87193 0.96885 0.99593 0.91756 0.91760 0.93109 0.90817 0.88785 0.95042 0.88822 0.94017 0.96043 0.95479 0.89397 0.92709 0.89358 0.87709 0.90373 0.92414 0.89695 0.78571 0.90818 0.89542 0.92436 0.92652 0.93942 0.94133 0.89731 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 -1.34 9.90 37.16 0.37 -0.97 16 2 C -0.02 -0.26 6.15 -27.88 -0.17 -0.43 16 3 C 0.16 2.66 7.06 -154.01 -1.09 1.57 16 4 N -0.29 -6.08 12.18 32.99 0.40 -5.68 16 5 N -0.32 -7.36 10.01 30.31 0.30 -7.05 16 6 C 0.38 7.77 4.45 -318.88 -1.42 6.35 16 7 N -0.46 -9.55 3.86 -176.09 -0.68 -10.23 16 8 C 0.04 0.77 9.07 60.06 0.54 1.32 16 9 C 0.23 5.85 1.73 -68.87 -0.12 5.73 16 10 H 0.02 0.67 7.91 -51.93 -0.41 0.26 16 11 C -0.13 -3.42 8.49 37.16 0.32 -3.10 16 12 C -0.52 -13.52 7.95 -34.44 -0.27 -13.79 16 13 H 0.06 1.59 6.40 -52.48 -0.34 1.26 16 14 C 0.06 1.74 5.30 -17.82 -0.09 1.65 16 15 N -0.88 -25.18 11.32 55.43 0.63 -24.55 16 16 Si 0.90 20.75 29.54 -169.99 -5.02 15.73 16 17 H -0.28 -6.29 7.11 56.52 0.40 -5.89 16 18 H -0.29 -6.67 7.11 56.52 0.40 -6.26 16 19 H -0.28 -6.32 7.11 56.52 0.40 -5.92 16 20 N -0.47 -7.50 2.43 -114.09 -0.28 -7.78 16 21 C 0.09 1.04 5.03 -4.04 -0.02 1.02 16 22 C 0.12 1.37 0.85 -90.62 -0.08 1.30 16 23 C -0.14 -2.05 7.54 37.16 0.28 -1.77 16 24 O -0.55 -6.04 11.28 -35.23 -0.40 -6.44 16 25 C -0.14 -1.26 4.78 -26.73 -0.13 -1.39 16 26 C 0.06 0.64 5.44 37.16 0.20 0.84 16 27 O -0.40 -4.21 10.70 -35.23 -0.38 -4.59 16 28 C 0.03 0.26 11.01 101.05 1.11 1.37 16 29 H 0.06 0.43 8.14 -51.93 -0.42 0.01 16 30 H 0.06 0.70 8.14 -51.93 -0.42 0.28 16 31 H 0.05 0.44 8.14 -51.93 -0.42 0.02 16 32 H 0.07 0.59 5.57 -51.93 -0.29 0.30 16 33 H 0.09 1.00 8.14 -51.93 -0.42 0.57 16 34 H 0.03 0.61 8.14 -51.93 -0.42 0.19 16 35 H 0.09 1.72 6.30 -51.93 -0.33 1.39 16 36 H 0.04 0.62 6.63 -51.93 -0.34 0.27 16 37 H 0.02 0.54 6.23 -51.93 -0.32 0.22 16 38 H 0.03 0.66 7.70 -51.92 -0.40 0.27 16 39 H 0.09 2.48 6.07 -51.93 -0.32 2.16 16 40 H 0.26 7.17 8.31 -40.82 -0.34 6.83 16 41 H 0.09 0.73 7.77 -51.93 -0.40 0.33 16 42 H 0.10 1.19 6.58 -51.93 -0.34 0.85 16 43 H 0.08 1.49 5.63 -51.93 -0.29 1.19 16 44 H 0.06 0.80 6.30 -51.93 -0.33 0.47 16 45 H 0.08 1.29 8.14 -51.93 -0.42 0.87 16 46 H 0.37 2.55 7.60 45.56 0.35 2.89 16 47 H 0.07 0.54 8.14 -51.93 -0.42 0.12 16 48 H 0.09 0.80 8.14 -51.93 -0.42 0.37 16 49 H 0.06 0.62 6.38 -51.93 -0.33 0.29 16 50 H 0.06 0.53 7.68 -51.93 -0.40 0.13 16 51 H 0.04 0.32 8.14 -51.93 -0.42 -0.10 16 52 H 0.04 0.28 8.14 -51.93 -0.42 -0.14 16 53 H 0.08 0.53 8.14 -51.93 -0.42 0.11 16 LS Contribution 406.01 15.07 6.12 6.12 Total: -1.00 -33.32 406.01 -8.15 -41.46 By element: Atomic # 1 Polarization: 11.60 SS G_CDS: -8.28 Total: 3.32 kcal Atomic # 6 Polarization: 0.25 SS G_CDS: -0.57 Total: -0.31 kcal Atomic # 7 Polarization: -55.67 SS G_CDS: 0.38 Total: -55.29 kcal Atomic # 8 Polarization: -10.25 SS G_CDS: -0.77 Total: -11.03 kcal Atomic # 14 Polarization: 20.75 SS G_CDS: -5.02 Total: 15.73 kcal Total LS contribution 6.12 Total: 6.12 kcal Total: -33.32 -8.15 -41.46 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. ZINC001401445798.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 35.195 kcal (2) G-P(sol) polarization free energy of solvation -33.316 kcal (3) G-ENP(sol) elect.-nuc.-pol. free energy of system 1.879 kcal (4) G-CDS(sol) cavity-dispersion-solvent structure free energy -8.148 kcal (5) G-P-CDS(sol) = G-P(sol) + G-CDS(sol) = (2) + (4) -41.463 kcal (6) G-S(sol) free energy of system = (1) + (5) -6.269 kcal 1SCF WAS SPECIFIED, SO GEOMETRY OPTIMIZATION WAS NOT USED Total computer time = 0.78 seconds