Wall clock time and date at job start Sat Apr 11 2020 06:10:31 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 1.53006 * 1 3 3 C 1.52998 * 109.46807 * 2 1 4 4 H 1.08997 * 109.52790 * 54.92136 * 3 2 1 5 5 C 1.53197 * 109.49817 * 294.83632 * 3 2 1 6 6 N 1.46921 * 108.77527 * 185.41482 * 5 3 2 7 7 C 1.34782 * 120.63202 * 233.63490 * 6 5 3 8 8 O 1.21274 * 120.00016 * 0.02562 * 7 6 5 9 9 C 1.50703 * 119.99632 * 180.02562 * 7 6 5 10 10 O 1.42907 * 109.46483 * 179.97438 * 9 7 6 11 11 C 1.42902 * 113.99356 * 179.97438 * 10 9 7 12 12 C 1.53181 * 109.54522 * 269.82098 * 11 10 9 13 13 C 1.53100 * 109.15761 * 183.24561 * 12 11 10 14 14 O 1.42902 * 109.48767 * 57.47356 * 13 12 11 15 15 C 1.42901 * 114.10196 * 298.89071 * 14 13 12 16 16 C 1.53095 * 109.41161 * 61.15368 * 15 14 13 17 17 C 1.46927 * 118.73848 * 53.61343 * 6 5 3 18 18 C 1.53192 * 108.77485 * 306.39105 * 17 6 5 19 19 C 1.53036 * 109.31556 * 54.63581 * 18 17 6 20 20 H 1.08997 * 109.45248 * 178.62583 * 19 18 17 21 21 N 1.46500 * 109.46251 * 58.65158 * 19 18 17 22 22 C 1.36935 * 119.99795 * 84.93172 * 21 19 18 23 23 H 1.08006 * 119.99956 * 0.02562 * 22 21 19 24 24 C 1.38809 * 120.00104 * 180.02562 * 22 21 19 25 25 N 1.31615 * 120.00002 * 0.02562 * 24 22 21 26 26 Si 1.86798 * 120.00116 * 180.02562 * 24 22 21 27 27 H 1.48506 * 109.47297 * 359.97438 * 26 24 22 28 28 H 1.48503 * 109.47261 * 239.99934 * 26 24 22 29 29 H 1.48500 * 109.47454 * 119.99927 * 26 24 22 30 30 H 1.09001 * 109.47048 * 180.02562 * 1 2 3 31 31 H 1.09004 * 109.46509 * 299.99921 * 1 2 3 32 32 H 1.08994 * 109.47229 * 59.99775 * 1 2 3 33 33 H 1.09004 * 109.46509 * 240.00079 * 2 1 3 34 34 H 1.08994 * 109.47229 * 120.00224 * 2 1 3 35 35 H 1.08995 * 109.58660 * 305.20366 * 5 3 2 36 36 H 1.08999 * 109.58011 * 65.48984 * 5 3 2 37 37 H 1.08993 * 109.47265 * 299.99750 * 9 7 6 38 38 H 1.09001 * 109.47346 * 60.00123 * 9 7 6 39 39 H 1.08999 * 109.54569 * 30.00238 * 11 10 9 40 40 H 1.08997 * 109.52032 * 303.06328 * 12 11 10 41 41 H 1.09000 * 109.51891 * 63.25136 * 12 11 10 42 42 H 1.09006 * 109.40931 * 297.49270 * 13 12 11 43 43 H 1.08997 * 109.49186 * 177.50877 * 13 12 11 44 44 H 1.08999 * 109.47650 * 301.17634 * 15 14 13 45 45 H 1.09001 * 109.49148 * 181.14351 * 15 14 13 46 46 H 1.09002 * 109.51711 * 182.48691 * 16 15 14 47 47 H 1.09001 * 109.57470 * 62.33371 * 16 15 14 48 48 H 1.08998 * 109.58977 * 66.17988 * 17 6 5 49 49 H 1.09002 * 109.59192 * 186.46007 * 17 6 5 50 50 H 1.09003 * 109.49985 * 294.68205 * 18 17 6 51 51 H 1.09003 * 109.49799 * 174.58853 * 18 17 6 52 52 H 0.96997 * 120.00022 * 264.93646 * 21 19 18 53 53 H 0.97004 * 120.00335 * 0.02562 * 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 1.5301 0.0000 0.0000 3 6 2.0400 1.4425 0.0000 4 1 1.6048 1.9828 0.8407 5 6 1.6385 2.1268 -1.3106 6 7 2.2450 3.4643 -1.3507 7 6 1.4855 4.5565 -1.5673 8 8 0.2894 4.4407 -1.7307 9 6 2.1227 5.9217 -1.6062 10 8 1.1186 6.9091 -1.8489 11 6 1.6199 8.2462 -1.9045 12 6 1.5868 8.8645 -0.5034 13 6 2.0488 10.3218 -0.5863 14 8 1.2120 11.0360 -1.4983 15 6 1.2411 10.5311 -2.8348 16 6 0.7446 9.0829 -2.8425 17 6 3.6952 3.5888 -1.1500 18 6 4.0736 2.8881 0.1587 19 6 3.5653 1.4450 0.1256 20 1 3.8546 0.9371 1.0456 21 7 4.1507 0.7475 -1.0220 22 6 5.3885 0.1718 -0.9147 23 1 5.9331 0.2317 0.0161 24 6 5.9434 -0.4886 -2.0022 25 7 5.2800 -0.5612 -3.1366 26 14 7.6317 -1.2745 -1.8556 27 1 8.1637 -1.0531 -0.4869 28 1 8.5507 -0.6621 -2.8484 29 1 7.5232 -2.7326 -2.1151 30 1 -0.3633 -1.0277 0.0005 31 1 -0.3632 0.5139 0.8901 32 1 -0.3633 0.5138 -0.8899 33 1 1.8933 -0.5139 -0.8901 34 1 1.8934 -0.5138 0.8899 35 1 1.9965 1.5377 -2.1549 36 1 0.5531 2.2138 -1.3596 37 1 2.6080 6.1235 -0.6514 38 1 2.8641 5.9540 -2.4046 39 1 2.6451 8.2362 -2.2745 40 1 0.5699 8.8277 -0.1130 41 1 2.2517 8.3071 0.1565 42 1 3.0804 10.3554 -0.9369 43 1 1.9853 10.7802 0.4006 44 1 2.2621 10.5674 -3.2148 45 1 0.5957 11.1401 -3.4678 46 1 0.8077 8.6818 -3.8541 47 1 -0.2901 9.0498 -2.5014 48 1 4.2208 3.1190 -1.9812 49 1 3.9674 4.6428 -1.0945 50 1 3.6193 3.4147 0.9980 51 1 5.1578 2.8894 0.2717 52 1 3.6614 0.6935 -1.8578 53 1 4.4035 -0.1528 -3.2129 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 ZINC001037928314.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 06:10:31 Heat of formation + Delta-G solvation = -124.396888 kcal Electronic energy + Delta-G solvation = -31274.079489 eV Core-core repulsion = 27145.722977 eV Total energy + Delta-G solvation = -4128.356512 eV No. of doubly occupied orbitals = 66 Molecular weight (most abundant/longest-lived isotopes) = 340.220 amu Computer time = 0.88 seconds Orbital eigenvalues (eV) -40.35032 -39.78773 -38.20008 -37.18439 -34.60864 -34.01690 -32.82730 -31.85137 -31.52941 -29.66953 -28.99542 -27.59660 -24.93233 -24.32329 -23.95518 -23.79288 -23.46146 -20.97728 -20.79080 -19.82518 -18.48806 -17.70029 -17.36258 -16.65781 -16.54319 -16.45298 -16.03156 -15.57159 -15.20019 -15.11068 -14.73974 -14.52391 -14.10744 -13.85167 -13.74307 -13.68917 -13.41741 -13.32232 -13.07004 -12.87294 -12.73321 -12.52300 -12.30922 -11.83059 -11.77524 -11.67487 -11.55165 -11.27386 -11.21051 -11.01834 -10.78150 -10.73487 -10.60553 -10.36672 -10.24043 -10.09562 -10.08430 -9.92799 -9.83459 -9.54607 -9.21179 -8.97336 -8.35881 -7.09053 -6.15072 -3.15842 2.69249 2.72078 3.46188 3.47369 3.53113 3.62315 3.66401 4.33553 4.37052 4.55746 4.57873 4.61360 4.71263 4.80414 4.86000 4.99333 5.01781 5.03114 5.10050 5.16203 5.21219 5.23804 5.28014 5.34588 5.40577 5.44577 5.56669 5.59552 5.61620 5.64874 5.68738 5.76918 5.79819 5.83735 5.91150 6.04006 6.06238 6.21578 6.25968 6.30603 6.44097 6.49113 6.55795 6.64501 6.77367 6.78886 6.82926 6.92785 7.56600 7.76715 8.29058 8.69642 9.15973 10.02448 10.17922 11.32628 Molecular weight = 340.22amu Principal moments of inertia in cm(-1) A = 0.013876 B = 0.002560 C = 0.002317 Principal moments of inertia in units of 10**(-40)*gram-cm**2 A = 2017.333734 B =10935.468156 C =12079.850722 Net atomic charges, atomic populations, and dipole contributions calculated with CM2 Atom NO. Type Charge No. of electrons 1 C -0.154 4.154 2 C -0.109 4.109 3 C -0.105 4.105 4 H 0.068 0.932 5 C 0.121 3.879 6 N -0.602 5.602 7 C 0.514 3.486 8 O -0.531 6.531 9 C 0.046 3.954 10 O -0.353 6.353 11 C 0.087 3.913 12 C -0.180 4.180 13 C 0.064 3.936 14 O -0.383 6.383 15 C 0.065 3.935 16 C -0.153 4.153 17 C 0.113 3.887 18 C -0.150 4.150 19 C 0.184 3.816 20 H 0.052 0.948 21 N -0.730 5.730 22 C -0.329 4.329 23 H 0.064 0.936 24 C -0.044 4.044 25 N -0.944 5.944 26 Si 1.083 2.917 27 H -0.295 1.295 28 H -0.294 1.294 29 H -0.294 1.294 30 H 0.050 0.950 31 H 0.048 0.952 32 H 0.053 0.947 33 H 0.072 0.928 34 H 0.062 0.938 35 H 0.070 0.930 36 H 0.088 0.912 37 H 0.078 0.922 38 H 0.079 0.921 39 H 0.063 0.937 40 H 0.083 0.917 41 H 0.076 0.924 42 H 0.052 0.948 43 H 0.098 0.902 44 H 0.052 0.948 45 H 0.100 0.900 46 H 0.082 0.918 47 H 0.083 0.917 48 H 0.083 0.917 49 H 0.067 0.933 50 H 0.050 0.950 51 H 0.076 0.924 52 H 0.367 0.633 53 H 0.255 0.745 For the charges calculated by CM2: Dipole moment (debyes) X Y Z Total from point charges -5.847 18.321 4.979 19.865 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 -0.211 4.211 2 C -0.147 4.147 3 C -0.125 4.125 4 H 0.086 0.914 5 C -0.001 4.001 6 N -0.336 5.336 7 C 0.301 3.699 8 O -0.407 6.407 9 C -0.034 4.034 10 O -0.271 6.271 11 C 0.029 3.971 12 C -0.218 4.218 13 C -0.013 4.013 14 O -0.301 6.301 15 C -0.012 4.012 16 C -0.191 4.191 17 C -0.009 4.009 18 C -0.191 4.191 19 C 0.074 3.926 20 H 0.070 0.930 21 N -0.373 5.373 22 C -0.460 4.460 23 H 0.082 0.918 24 C -0.242 4.242 25 N -0.589 5.589 26 Si 0.914 3.086 27 H -0.222 1.222 28 H -0.221 1.221 29 H -0.221 1.221 30 H 0.070 0.930 31 H 0.068 0.932 32 H 0.072 0.928 33 H 0.091 0.909 34 H 0.081 0.919 35 H 0.088 0.912 36 H 0.106 0.894 37 H 0.095 0.905 38 H 0.097 0.903 39 H 0.081 0.919 40 H 0.101 0.899 41 H 0.094 0.906 42 H 0.070 0.930 43 H 0.116 0.884 44 H 0.071 0.929 45 H 0.118 0.882 46 H 0.101 0.899 47 H 0.102 0.898 48 H 0.102 0.898 49 H 0.086 0.914 50 H 0.068 0.932 51 H 0.094 0.906 52 H 0.201 0.799 53 H 0.066 0.934 Dipole moment (debyes) X Y Z Total from point charges -5.492 17.497 4.298 18.835 hybrid contribution -0.583 0.576 0.646 1.043 sum -6.074 18.073 4.944 19.697 Atomic orbital electron populations 1.21858 0.96623 1.01158 1.01465 1.21403 0.94441 0.95615 1.03222 1.21784 0.97398 0.96209 0.97092 0.91372 1.21660 0.99002 0.81308 0.98091 1.48072 1.08640 1.06367 1.70509 1.20095 0.87076 0.85445 0.77289 1.90689 1.14668 1.86266 1.49119 1.22306 0.91360 0.87935 1.01811 1.88068 1.32366 1.13945 1.92752 1.22157 0.97490 0.82516 0.94977 1.22757 1.04075 0.96851 0.98140 1.22558 0.93426 0.91065 0.94222 1.87945 1.67333 1.55713 1.19126 1.22593 1.00968 0.93511 0.84161 1.22289 1.01443 0.94902 1.00467 1.21745 0.79137 0.99866 1.00198 1.22515 1.01948 0.99306 0.95308 1.20145 0.89538 0.90498 0.92410 0.92974 1.42488 1.19433 1.65164 1.10260 1.20068 0.94613 1.31632 0.99641 0.91763 1.25688 1.05571 1.00152 0.92743 1.70834 1.14524 1.47666 1.25900 0.83179 0.74721 0.76309 0.74373 1.22202 1.22148 1.22102 0.93044 0.93247 0.92763 0.90898 0.91899 0.91192 0.89361 0.90451 0.90307 0.91868 0.89852 0.90560 0.93015 0.88427 0.92937 0.88163 0.89949 0.89828 0.89833 0.91428 0.93168 0.90586 0.79880 0.93416 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 -2.08 9.67 37.16 0.36 -1.72 16 2 C -0.11 -1.72 5.19 -26.73 -0.14 -1.85 16 3 C -0.10 -1.67 2.14 -90.49 -0.19 -1.87 16 4 H 0.07 1.04 8.14 -51.93 -0.42 0.62 16 5 C 0.12 2.02 5.03 -3.71 -0.02 2.00 16 6 N -0.60 -9.47 2.97 -172.77 -0.51 -9.99 16 7 C 0.51 8.32 7.78 -10.98 -0.09 8.24 16 8 O -0.53 -10.54 15.92 -14.35 -0.23 -10.77 16 9 C 0.05 0.56 4.58 36.01 0.16 0.73 16 10 O -0.35 -4.75 9.53 -55.14 -0.53 -5.28 16 11 C 0.09 0.85 2.69 -26.55 -0.07 0.77 16 12 C -0.18 -1.56 5.77 -26.59 -0.15 -1.71 16 13 C 0.06 0.48 6.84 37.21 0.25 0.73 16 14 O -0.38 -3.57 10.77 -35.23 -0.38 -3.95 16 15 C 0.06 0.48 6.84 37.21 0.25 0.73 16 16 C -0.15 -1.36 5.79 -26.59 -0.15 -1.51 16 17 C 0.11 1.68 6.08 -3.71 -0.02 1.66 16 18 C -0.15 -2.35 5.78 -26.61 -0.15 -2.50 16 19 C 0.18 3.34 2.53 -67.89 -0.17 3.17 16 20 H 0.05 1.00 8.08 -51.93 -0.42 0.58 16 21 N -0.73 -16.26 3.72 -53.38 -0.20 -16.46 16 22 C -0.33 -8.47 9.93 -15.06 -0.15 -8.62 16 23 H 0.06 1.66 7.83 -52.48 -0.41 1.25 16 24 C -0.04 -1.20 5.50 -17.43 -0.10 -1.29 16 25 N -0.94 -27.79 13.70 55.49 0.76 -27.03 16 26 Si 1.08 24.97 29.92 -169.99 -5.09 19.89 16 27 H -0.30 -6.41 7.11 56.52 0.40 -6.00 16 28 H -0.29 -6.79 7.11 56.52 0.40 -6.39 16 29 H -0.29 -6.83 7.11 56.52 0.40 -6.43 16 30 H 0.05 0.64 8.14 -51.93 -0.42 0.22 16 31 H 0.05 0.62 8.14 -51.93 -0.42 0.20 16 32 H 0.05 0.74 6.70 -51.93 -0.35 0.39 16 33 H 0.07 1.33 7.70 -51.93 -0.40 0.93 16 34 H 0.06 0.99 8.14 -51.93 -0.42 0.57 16 35 H 0.07 1.27 6.64 -51.93 -0.34 0.92 16 36 H 0.09 1.50 5.73 -51.93 -0.30 1.20 16 37 H 0.08 0.79 7.52 -51.93 -0.39 0.40 16 38 H 0.08 0.84 7.89 -51.93 -0.41 0.43 16 39 H 0.06 0.52 7.79 -51.93 -0.40 0.12 16 40 H 0.08 0.83 8.14 -51.93 -0.42 0.41 16 41 H 0.08 0.59 7.97 -51.93 -0.41 0.18 16 42 H 0.05 0.32 8.14 -51.93 -0.42 -0.10 16 43 H 0.10 0.60 8.14 -51.93 -0.42 0.18 16 44 H 0.05 0.33 8.14 -51.93 -0.42 -0.10 16 45 H 0.10 0.60 8.14 -51.93 -0.42 0.18 16 46 H 0.08 0.69 8.14 -51.93 -0.42 0.27 16 47 H 0.08 0.84 8.14 -51.93 -0.42 0.42 16 48 H 0.08 1.47 7.74 -51.93 -0.40 1.07 16 49 H 0.07 0.79 5.93 -51.93 -0.31 0.48 16 50 H 0.05 0.70 8.14 -51.93 -0.42 0.27 16 51 H 0.08 1.26 8.14 -51.93 -0.42 0.84 16 52 H 0.37 8.60 4.77 -40.82 -0.19 8.41 16 53 H 0.25 7.38 6.78 -40.82 -0.28 7.11 16 LS Contribution 404.89 15.07 6.10 6.10 Total: -1.00 -32.17 404.89 -9.76 -41.93 By element: Atomic # 1 Polarization: 17.93 SS G_CDS: -9.31 Total: 8.62 kcal Atomic # 6 Polarization: -2.68 SS G_CDS: -0.37 Total: -3.06 kcal Atomic # 7 Polarization: -53.52 SS G_CDS: 0.05 Total: -53.47 kcal Atomic # 8 Polarization: -18.87 SS G_CDS: -1.13 Total: -20.00 kcal Atomic # 14 Polarization: 24.97 SS G_CDS: -5.09 Total: 19.89 kcal Total LS contribution 6.10 Total: 6.10 kcal Total: -32.17 -9.76 -41.93 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. ZINC001037928314.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 -82.468 kcal (2) G-P(sol) polarization free energy of solvation -32.173 kcal (3) G-ENP(sol) elect.-nuc.-pol. free energy of system -114.641 kcal (4) G-CDS(sol) cavity-dispersion-solvent structure free energy -9.756 kcal (5) G-P-CDS(sol) = G-P(sol) + G-CDS(sol) = (2) + (4) -41.929 kcal (6) G-S(sol) free energy of system = (1) + (5) -124.397 kcal 1SCF WAS SPECIFIED, SO GEOMETRY OPTIMIZATION WAS NOT USED Total computer time = 0.88 seconds