Chapter 30. Simulated Annealing Search for Multiple Minima (ANNEAL)

Table of Contents

Example I (Floppy system)
Input File (annealing/anneal1.dat):
Archive File (annealing/anneal1.arc):
Output File (annealing/anneal1.out):
Example II (Rigid System)
Input File (annealing/anneal_limit.dat):
Archive File (annealing/anneal_limit.arc):
Output File (annealing/anneal_limit.out):

Example I (Floppy system)

The cyclohexane molecule has been chosen as an example of using simulated annealing on a molecule with relatively low rotational barriers. There are four conformers of the molecule that can be identified (chair, boat (flexible), twist or skew boat, and half-chair) and all of these are located by AMPAC’s annealing protocol, using relaxed constraints and limited penalty functions.

Input File (annealing/anneal1.dat):

  am1 rhf singlet t=auto anneal truste pen2 ncheck=10 noxyz limit
Cyclohexane
Annealing on cyclic system: PEN2, NCHECK, LIMIT
 C              0.000000  0    0.000000  0    0.000000  0    0    0    0
 C              1.520880  0    0.000000  0    0.000000  0    1    0    0
 C              1.520880  0  112.706930  1    0.000000  0    2    1    0
 C              1.520880  0  112.706930  1   -7.376720  1    3    2    1
 C              1.520880  0  112.706930  1  -46.310020  1    1    2    3
 C              1.520880  0  112.706930  1   50.819480  1    5    1    2
 H              1.121200  0  112.384140  1   75.006870  1    1    2    3
 H              1.121200  0  112.384140  1 -167.313050  1    1    2    3
 H              1.121200  0  112.384140  1  121.019560  1    2    3    1
 H              1.121200  0  112.384140  1 -121.144800  1    2    3    1
 H              1.121200  0  112.384140  1  113.455200  1    3    2    1
 H              1.121200  0  112.384140  1 -128.802830  1    3    2    1
 H              1.121200  0  112.384140  1  177.862400  1    4    3    2
 H              1.121200  0  112.384140  1  -63.807980  1    4    3    2
 H              1.121200  0  112.384140  1   57.505850  1    5    4    3
 H              1.121200  0  112.384140  1 -154.797280  1    5    4    3
 H              1.121200  0  112.384140  1  121.566360  1    6    5    4
 H              1.121200  0  112.384140  1 -122.040500  1    6    5    4
 0              0.000000  0    0.000000  0    0.000000  0    0    0    0
$$ limit - annealing boundaries    1
  100 100 -180 100 -180 100 -180 100 -180 100 -180 100 -180 100    2
    -180 100 -180 100 -180 100 -180 100 -180 100 -180 100 -180 
    100 -180 100 -180
  130 130  180 130  180 130  180 130  180 130  180 130  180 130     3
    180 130  180 130  180 130  180 130  180 130  180 130  180 
    130  180 130  180
$$ end of extra data
	

1

This is the extra input section marker for reaction path data. Note, that this marker can be shortened to $$ limit. Details of these markers are found in the section called “Extra Input Data”.

2

These are the lower boundaries of the bond angles and dihedrals (in order as specified) as required for by the annealing keyword LIMIT.

3

These are the upper boundaries of the bond angles and dihedrals (in order as specified) as required for by the annealing keyword LIMIT.

Archive File (annealing/anneal1.arc):

 Timestamp:  2011-08-31-12-30-05-000000059C-win64
 User Info:  John Millam, Nahum, 

                     SUMMARY OF AM1 CALCULATION
                                                       Aug-31-2011
                          AMPAC Version 10.0.1
                             Presented by:
  
                        Semichem, Inc.
                        www.semichem.com
  
 FORMULA: C6H12
 Cyclohexane
 Annealing on cyclic system: PEN2, NCHECK, LIMIT

     GEOMETRY NORMALLY RETURNED BY SIMULATED ANNEALING
     SCF FIELD WAS ACHIEVED
 
          FINAL HEAT OF FORMATION   =       -38.461667 kcal    1
                                    =      -160.962076 kJ
          ELECTRONIC ENERGY         =     -4336.156767 eV
          CORE-CORE REPULSION       =      3401.263230 eV
          TOTAL ENERGY              =      -934.893537 eV
          GRADIENT NORM             =         0.142334 
          RMS GRADIENT NORM         =         0.025564 
          UNSTABLE MODE(S)          =         0 ( ESTIMATE  )
          IONIZATION POTENTIAL      =        10.922850 eV
          HOMO-LUMO GAP             =        14.591989 eV
          DIPOLE                    =         0.001011 debyes
          MOLECULAR WEIGHT          =        84.160800 
          MOLECULAR POINT GROUP     = C2h     0.100000
          NO. OF FILLED LEVELS      =        18 (OCC = 2)
          TOTAL NUMBER OF ORBITALS  =        36
          FINAL GEOMETRY OBTAINED                                       CHARGE
 AM1 RHF SINGLET T=AUTO ANNEAL TRUSTE PEN2 NCHECK=10 NOXYZ LIMIT
 Cyclohexane
 Annealing on cyclic system: PEN2, NCHECK, LIMIT
  C     0.000000  0    0.000000  0    0.000000  0      0     0     0   -0.1551
  C     1.520880  0    0.000000  0    0.000000  0      1     0     0   -0.1551
  C     1.520880  0  111.123665  1    0.000000  0      2     1     0   -0.1552
  C     1.520880  0  111.132186  1   55.517365  1      3     2     1   -0.1547
  C     1.520880  0  111.125824  1  -55.553493  1      1     2     3   -0.1552
  C     1.520880  0  111.136222  1   55.514987  1      5     1     2   -0.1547
  H     1.121200  0  109.556127  1 -176.750967  1      1     2     3    0.0769
  H     1.121200  0  109.417071  1   65.389211  1      1     2     3    0.0782
  H     1.121200  0  109.553009  1  121.190059  1      2     3     1    0.0769
  H     1.121200  0  109.422604  1 -120.947750  1      2     3     1    0.0782
  H     1.121200  0  109.415490  1  -65.433537  1      3     2     1    0.0782
  H     1.121200  0  109.548147  1  176.714592  1      3     2     1    0.0769
  H     1.121200  0  109.447594  1 -176.943500  1      4     3     2    0.0767
  H     1.121200  0  109.309974  1   65.465345  1      4     3     2    0.0781
  H     1.121200  0  143.756993  1 -124.603119  1      5     4     3    0.0769
  H     1.121200  0   93.045319  1  109.416516  1      5     4     3    0.0782
  H     1.121200  0  109.312266  1  121.079425  1      6     5     4    0.0781
  H     1.121200  0  109.449883  1 -121.329555  1      6     5     4    0.0767
  0     0.000000  0    0.000000  0    0.000000  0      0     0     0
 Timestamp:  2011-08-31-12-30-05-000000059C-win64
 User Info:  John Millam, Nahum, 

                     SUMMARY OF AM1 CALCULATION
                                                       Aug-31-2011
                          AMPAC Version 10.0.1
                             Presented by:
  
                        Semichem, Inc.
                        www.semichem.com
  
 FORMULA: C6H12
 Cyclohexane
 Annealing on cyclic system: PEN2, NCHECK, LIMIT

     GEOMETRY NORMALLY RETURNED BY SIMULATED ANNEALING
     SCF FIELD WAS ACHIEVED
 
          FINAL HEAT OF FORMATION   =       -35.291044 kcal
                                    =      -147.693018 kJ
          ELECTRONIC ENERGY         =     -4341.347862 eV
          CORE-CORE REPULSION       =      3406.591814 eV
          TOTAL ENERGY              =      -934.756048 eV
          GRADIENT NORM             =         0.042607 
          RMS GRADIENT NORM         =         0.007653 
          UNSTABLE MODE(S)          =         0 ( ESTIMATE  )
          IONIZATION POTENTIAL      =        10.673743 eV
          HOMO-LUMO GAP             =        14.347769 eV
          DIPOLE                    =         0.000661 debyes
          MOLECULAR WEIGHT          =        84.160800 
          MOLECULAR POINT GROUP     = D2      0.100000
          NO. OF FILLED LEVELS      =        18 (OCC = 2)
          TOTAL NUMBER OF ORBITALS  =        36
          FINAL GEOMETRY OBTAINED                                       CHARGE
 AM1 RHF SINGLET T=AUTO ANNEAL TRUSTE PEN2 NCHECK=10 NOXYZ LIMIT
 Cyclohexane
 Annealing on cyclic system: PEN2, NCHECK, LIMIT
  C     0.000000  0    0.000000  0    0.000000  0      0     0     0   -0.1535
  C     1.520880  0    0.000000  0    0.000000  0      1     0     0   -0.1540
  C     1.520880  0  112.213976  1    0.000000  0      2     1     0   -0.1535
  C     1.520880  0  111.557704  1  -29.939332  1      3     2     1   -0.1532
  C     1.520880  0  111.555172  1  -30.142091  1      1     2     3   -0.1535
  C     1.520880  0  111.567720  1   62.750572  1      5     1     2   -0.1537
  H     1.121200  0  109.547324  1   90.596059  1      1     2     3    0.0780
  H     1.121200  0  109.613700  1 -151.717220  1      1     2     3    0.0766
  H     1.121200  0  109.706537  1  121.281831  1      2     3     1    0.0758
  H     1.121200  0  108.982281  1 -121.704820  1      2     3     1    0.0759
  H     1.121200  0  109.543428  1   90.800513  1      3     2     1    0.0780
  H     1.121200  0  109.613276  1 -151.513979  1      3     2     1    0.0766
  H     1.121200  0  109.524036  1 -175.444429  1      4     3     2    0.0765
  H     1.121200  0  108.888901  1  -58.295232  1      4     3     2    0.0779
  H     1.121200  0  106.591923  1   51.245628  1      5     4     3    0.0780
  H     1.121200  0  137.681082  1 -166.343590  1      5     4     3    0.0766
  H     1.121200  0  109.636356  1  121.386734  1      6     5     4    0.0758
  H     1.121200  0  108.895532  1 -121.788786  1      6     5     4    0.0758
  0     0.000000  0    0.000000  0    0.000000  0      0     0     0
 Timestamp:  2011-08-31-12-30-05-000000059C-win64
 User Info:  John Millam, Nahum, 

                     SUMMARY OF AM1 CALCULATION
                                                       Aug-31-2011
                          AMPAC Version 10.0.1
                             Presented by:
  
                        Semichem, Inc.
                        www.semichem.com
  
 FORMULA: C6H12
 Cyclohexane
 Annealing on cyclic system: PEN2, NCHECK, LIMIT

     GEOMETRY NORMALLY RETURNED BY SIMULATED ANNEALING
     SCF FIELD WAS ACHIEVED
 
          FINAL HEAT OF FORMATION   =        68.531095 kcal
                                    =       286.802633 kJ
          ELECTRONIC ENERGY         =     -4203.135787 eV
          CORE-CORE REPULSION       =      3272.881804 eV
          TOTAL ENERGY              =      -930.253983 eV
          GRADIENT NORM             =         0.084387 
          RMS GRADIENT NORM         =         0.015156 
          UNSTABLE MODE(S)          =         0 ( ESTIMATE  )
          IONIZATION POTENTIAL      =         7.475143 eV
          HOMO-LUMO GAP             =         7.408058 eV
          DIPOLE                    =         0.602974 debyes
          MOLECULAR WEIGHT          =        84.160800 
          MOLECULAR POINT GROUP     = C1      0.100000
          NO. OF FILLED LEVELS      =        18 (OCC = 2)
          TOTAL NUMBER OF ORBITALS  =        36
          FINAL GEOMETRY OBTAINED                                       CHARGE
 AM1 RHF SINGLET T=AUTO ANNEAL TRUSTE PEN2 NCHECK=10 NOXYZ LIMIT
 Cyclohexane
 Annealing on cyclic system: PEN2, NCHECK, LIMIT
  C     0.000000  0    0.000000  0    0.000000  0      0     0     0   -0.1569
  C     1.520880  0    0.000000  0    0.000000  0      1     0     0   -0.1487
  C     1.520880  0  112.136196  1    0.000000  0      2     1     0   -0.1140
  C     1.520880  0  116.144031  1  -91.587285  1      3     2     1   -0.3274
  C     1.520880  0  111.503480  1  -49.763632  1      1     2     3   -0.1524
  C     1.520880  0  109.788080  1   50.544477  1      5     1     2   -0.2933
  H     1.121200  0  109.470583  1 -171.367561  1      1     2     3    0.0805
  H     1.121200  0  109.094858  1   70.946977  1      1     2     3    0.0824
  H     1.121200  0  109.282892  1  121.458833  1      2     3     1    0.0941
  H     1.121200  0  108.735837  1 -121.019887  1      2     3     1    0.0821
  H     1.121200  0  103.633653  1   24.070103  1      3     2     1    0.1761
  H     1.121200  0  115.256379  1  131.780579  1      3     2     1    0.1171
  H     1.121200  0  119.553416  1   23.861674  1      4     3     2    0.1187
  H     1.121200  0  119.257474  1 -164.337223  1      4     3     2    0.1173
  H     1.121200  0  122.158441  1   -0.070768  1      5     4     3    0.0767
  H     1.121200  0  130.053071  1  177.265616  1      5     4     3    0.0810
  H     1.121200  0  113.879260  1 -138.731518  1      6     5     4    0.0821
  H     1.121200  0  113.577996  1   91.432352  1      6     5     4    0.0846
  0     0.000000  0    0.000000  0    0.000000  0      0     0     0
	

1

Each of the located and quenched minima is sequentially listed in the archive file.

Output File (annealing/anneal1.out):

 Timestamp: 2011-08-31-12-30-05-000000059C-win64
 User Info: John Millam, Nahum, 
 *******************************************************************************
                         AM1 CALCULATION RESULTS
 *******************************************************************************
 *                             AMPAC Version 10.0.1
 *                                Presented by:
 *
 *                           Semichem, Inc.
 *                           www.semichem.com
 *
 *  AM1      - THE AM1 HAMILTONIAN TO BE USED
 *  RHF      - RESTRICTED HARTREE-FOCK CALCULATION
 *  ANNE     - SIMULATED ANNEALING ON ENERGY ONLY
 *  TRUSTE   - MINIMIZE ENERGY USING TRUST REGION METHOD
 *  NOXYZ    - CARTESIAN COORDINATES NOT TO BE PRINTED
 *  T=AUTO   - AUTOMATIC DETERMINATION OF ALLOWED TIME
 *  SINGLET  - IS THE REQUIRED SPIN MULTIPLICITY
 *******************************************************************************
 AM1 RHF SINGLET T=AUTO ANNEAL TRUSTE PEN2 NCHECK=10 NOXYZ LIMIT
 Cyclohexane
 Annealing on cyclic system: PEN2, NCHECK, LIMIT
    ATOM    CHEMICAL   BOND LENGTH    BOND ANGLE    TWIST ANGLE
   NUMBER   SYMBOL     (ANGSTROMS)     (DEGREES)     (DEGREES)
    (I)                   NA:I          NB:NA:I      NC:NB:NA:I     NA    NB    NC
      1     C 
      2     C          1.52088                                       1
      3     C          1.52088        112.70693 *                    2     1
      4     C          1.52088        112.70693 *    -7.37672 *      3     2     1
      5     C          1.52088        112.70693 *   -46.31002 *      1     2     3
      6     C          1.52088        112.70693 *    50.81948 *      5     1     2
      7     H          1.12120        112.38414 *    75.00687 *      1     2     3
      8     H          1.12120        112.38414 *  -167.31305 *      1     2     3
      9     H          1.12120        112.38414 *   121.01956 *      2     3     1
     10     H          1.12120        112.38414 *  -121.14480 *      2     3     1
     11     H          1.12120        112.38414 *   113.45520 *      3     2     1
     12     H          1.12120        112.38414 *  -128.80283 *      3     2     1
     13     H          1.12120        112.38414 *   177.86240 *      4     3     2
     14     H          1.12120        112.38414 *   -63.80798 *      4     3     2
     15     H          1.12120        112.38414 *    57.50585 *      5     4     3
     16     H          1.12120        112.38414 *  -154.79728 *      5     4     3
     17     H          1.12120        112.38414 *   121.56636 *      6     5     4
     18     H          1.12120        112.38414 *  -122.04050 *      6     5     4

   MOLECULAR POINT GROUP            SYMMETRY CRITERIA
            C1                          0.10000000

          SINGLET STATE CALCULATION

          RHF CALCULATION, NO. OF DOUBLY OCCUPIED LEVELS =      18

        **  REFERENCES TO PARAMETERS  **

 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).

 *******************************************************************************
 *  KEYWORDS DEDICATED TO SIMULATED ANNEALING SECTION    1
 *
 *  LIMIT    - EXPLICIT PERIODIC CONDITIONS GIVEN
 *  NCHECK=  - SET MARKOV CHAIN IN PIECES OF   10 LONG
 *  PEN2     - SWITCH ON MIN/MAX PENALTY ON INTERATOMIC DISTANCES
 *           - PENALTIES OPERATED BY SKEWED REBOUNDS
 *******************************************************************************
 STANDARD DEVIATION ON ENERGY   (KCAL)       0.00000055521
 STANDARD DEVIATION ON GRADIENT (KCAL/A,RD,RD)  0.00000000 0.00018717 0.00016811

 SIMULATED ANNEALING BY METROPOLIS SCHEME IN   31 VARIABLES    2
     VERSION 2.0 (MAY 2000)
     THERMALIZATION THRESHOLD ON COST FNCT          0.080
     MAXIMUM STEP SIZE                            2.00000
     CONVERGENCE CRITERION ON STEP SIZE           0.06325

 MAXIMUM NUMBER OF STEPS AT EACH TEMPERATURE         1000
     FIRST TEMPERATURE (HOT) SET TO                200.00
     TEMPERATURE EXPONENTIAL DECAY                   0.80
     LAST TEMPERATURE (COLD) SET TO                  2.00
 RANDOM SEQUENCE INITIATOR                       -9876543
     MARKOV CHAIN STUDIED BY PIECES OF                 10
     No OF TEMPERATURES TO DETECT A FROZEN SYSTEM       2
 EQUIVALENCE THRESHOLD IN CLUSTERING ANALYSIS        1.00
     BAND-PASS FILTER NO 1 CENTERED AT               1.40 ANGSTROMS
     HALF BAND-WIDTH                                13.50 %
 CAN HOLD  250 CANDIDATES FOR QUENCHING.
 PENALTIES ACTIVATED:    3
     ON CHEMICAL BONDS, THRESHOLD:                   0.20
 PERIODIC BOUNDARY CONDITIONS (ANGSTROMS, DEGREES)
 LOWER BOUND  100.0000  100.0000 -180.0000  100.0000 -180.0000  100.0000   4
             -180.0000  100.0000 -180.0000  100.0000 -180.0000  100.0000
             -180.0000  100.0000 -180.0000  100.0000 -180.0000  100.0000
             -180.0000  100.0000 -180.0000  100.0000 -180.0000  100.0000
             -180.0000  100.0000 -180.0000  100.0000 -180.0000  100.0000
             -180.0000
 TRIAL COORD  112.7069  112.7069   -7.3767  112.7069  -46.3100  112.7069
               50.8195  112.3841   75.0069  112.3841 -167.3131  112.3841
              121.0196  112.3841 -121.1448  112.3841  113.4552  112.3841
             -128.8028  112.3841  177.8624  112.3841  -63.8080  112.3841
               57.5059  112.3841 -154.7973  112.3841  121.5664  112.3841
             -122.0405
 UPPER BOUND  130.0000  130.0000  180.0000  130.0000  180.0000  130.0000
              180.0000  130.0000  180.0000  130.0000  180.0000  130.0000
              180.0000  130.0000  180.0000  130.0000  180.0000  130.0000
              180.0000  130.0000  180.0000  130.0000  180.0000  130.0000
              180.0000  130.0000  180.0000  130.0000  180.0000  130.0000
              180.0000

 COST FNCT IS ENERGY (KCAL/MOLE)
 PENALTY FUNCTION FOR LOCATION OF BONDS AND DETAILED MINIMUM DISTANCE CHECK     5
 IS INITIALIZED WITH TOLERANCE 0.200
 LOCATED BONDS BETWEEN THE FOLLOWING ATOMS:
    123456789012345678
  1 .*..*.**..........
  2 *.*.....**........
  3 .*.*......**......
  4 ..*..*......**....
  5 *....*........**..
  6 ...**...........**
  7 *.................
  8 *.................
  9 .*................
  0 .*................
  1 ..*...............
  2 ..*...............
  3 ...*..............
  4 ...*..............
  5 ....*.............
  6 ....*.............
  7 .....*............
  8 .....*............

 VISIT OF THE PES BY SIMULATED ANNEALING
 ---------------------------------------
 UNABLE TO HAVE 5 ACCEPTED MOVE-UP AFTER 1001 CALLS
 AT TEMPERATURE   21.4748 WITH STEP    0.0000
 ANNEALING STOPPED AT THIS POINT. EITHER THE SYSTEM IS "FROZEN" OR POOR CHOICE IN STEP/TEMPERATURE
 ELAPSED TIME IN ANNEALING     25.51 SECONDS

 CLUSTERING ANALYSIS OF CONFORMATIONS
 ------------------------------------
 KEEP  83 CONFORMATIONS FROM  91 SELECTED AT PES VISIT

 QUENCHING OF REMAINING CONFORMATIONS
 ------------------------------------
 PERFORMED WITHOUT PERIODIC BOUNDARIES.
 PERFORMED WITHOUT PENALTIES ON INTERATOMIC DISTANCES.
 MINIMIZE ENERGY BY TRUST ALGORITHM

 QUENCHING No  1 -- STAGE 1 OF 1  (   0.27 SECONDS)
 ..................................................
          HEAT OF FORMATION       =   -35.291044 KCAL
          RMS GRADIENT NORM       =     0.007649 KCAL/ANGSTROMS
          CRITICAL POINT INDEX    =            0  ESTIMATE  
 CURRENT COORDINATES (ANGSTROMS, DEGREES)
  112.2140  111.5577  -29.9393  111.5552  -30.1421  111.5677   62.7506  109.5473
   90.5961  109.6137 -151.7172  109.7065  121.2818  108.9823 -121.7048  109.5434
   90.8005  109.6133 -151.5140  109.5240  184.5556  108.8889  -58.2952  106.5919
   51.2456  137.6811 -166.3436  109.6364  121.3867  108.8955 -121.7888

 QUENCHING No  2 -- STAGE 1 OF 1  (   0.41 SECONDS)
 ..................................................
          HEAT OF FORMATION       =   -38.461667 KCAL
          RMS GRADIENT NORM       =     0.025554 KCAL/ANGSTROMS
          CRITICAL POINT INDEX    =            0  ESTIMATE  
 CURRENT COORDINATES (ANGSTROMS, DEGREES)
  111.1237  111.1322   55.5174  111.1258  -55.5535  111.1362   55.5150  109.5561
 -176.7510  109.4171   65.3892  109.5530  121.1901  109.4226 -120.9477  109.4155
  -65.4335  109.5481  176.7146  109.4476 -176.9435  109.3100   65.4653  143.7570
 -124.6031   93.0453  109.4165  109.3123  121.0794  109.4499 -121.3296

 QUENCHING No  3 -- STAGE 1 OF 1  (   0.20 SECONDS)
 ..................................................
          * * * QUENCHING INTERRUPTED: POINT PREVIOUSLY FOUND.

 QUENCHING No  4 -- STAGE 1 OF 1  (   0.17 SECONDS)
 ..................................................
          * * * QUENCHING INTERRUPTED: POINT PREVIOUSLY FOUND.

 QUENCHING No  5 -- STAGE 1 OF 1  (   0.12 SECONDS)
 ..................................................
          * * * QUENCHING INTERRUPTED: POINT PREVIOUSLY FOUND.

 QUENCHING No  6 -- STAGE 1 OF 1  (   0.19 SECONDS)
 ..................................................
          * * * QUENCHING INTERRUPTED: POINT PREVIOUSLY FOUND.

 QUENCHING No  7 -- STAGE 1 OF 1  (   0.12 SECONDS)
 ..................................................
          * * * QUENCHING INTERRUPTED: POINT PREVIOUSLY FOUND.

 QUENCHING No  8 -- STAGE 1 OF 1  (   0.27 SECONDS)
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          HEAT OF FORMATION       =   -35.291035 KCAL
          RMS GRADIENT NORM       =     0.025015 KCAL/ANGSTROMS
          CRITICAL POINT INDEX    =            0  ESTIMATE  
 CURRENT COORDINATES (ANGSTROMS, DEGREES)
  112.2138  111.5576   30.0098  111.5535   30.0724  111.5631  -62.7607  109.5484
  -90.6631  109.6192 -208.3532  108.9777  121.7044  109.6993 -121.2854  109.5442
  -90.7324  109.6102 -208.4130  109.5210  175.4489  108.8859   58.3048  106.5416
  -51.2505  137.7190  166.3915  108.8946  121.7940  109.6349 -121.3897

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          HEAT OF FORMATION       =    68.531095 KCAL
          RMS GRADIENT NORM       =     0.015153 KCAL/ANGSTROMS
          CRITICAL POINT INDEX    =            0  ESTIMATE  
 CURRENT COORDINATES (ANGSTROMS, DEGREES)
  112.1362  116.1440  -91.5873  111.5035  -49.7636  109.7881   50.5445  109.4706
 -171.3676  109.0949   70.9470  109.2829  121.4588  108.7358 -121.0199  103.6337
   24.0701  115.2564  131.7806  119.5534   23.8617  119.2575 -164.3372  122.1584
   -0.0708  130.0531  177.2656  113.8793  221.2685  113.5780   91.4324

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          HEAT OF FORMATION       =    68.531180 KCAL
          RMS GRADIENT NORM       =     0.030797 KCAL/ANGSTROMS
          CRITICAL POINT INDEX    =            0  ESTIMATE  
 CURRENT COORDINATES (ANGSTROMS, DEGREES)
  112.1181  116.1450  -91.5508  111.5093  -49.8453  109.7975   50.4736  109.4799
 -171.4737  109.0840   70.8403  109.2817  121.4621  108.7431 -121.0227  103.6204
   24.1460  115.2582  131.7831  119.5474   23.7629  119.2604 -164.4645  129.9558
  177.1868  122.2623   -0.2062  113.8614  221.4050  113.6011   91.5556

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 TIME CONSUMPTION OF STAGE 1:     21.39 SECONDS
 ON   5 POINTS AT END OF STAGE 1,   3 FULFILL STATIONARITY AND ENERGETIC REQUESTS.

 DETAILS ON NON EQUIVALENT CRITICAL POINTS FOUND (ENERGY SORTED)    6
 ---------------------------------------------------------------

 CRITICAL POINT No  1
 ....................
          HEAT OF FORMATION       =   -38.461667 KCAL
          RMS GRADIENT NORM       =     0.025554 KCAL/ANGSTROMS
          CRITICAL POINT INDEX    =            0  ESTIMATE  
          MOLECULAR POINT GROUP   = C2h   0.100000
    ATOM    CHEMICAL   BOND LENGTH    BOND ANGLE    TWIST ANGLE
   NUMBER   SYMBOL     (ANGSTROMS)     (DEGREES)     (DEGREES)
    (I)                   NA:I          NB:NA:I      NC:NB:NA:I     NA    NB    NC
      1     C 
      2     C          1.52088                                       1
      3     C          1.52088        111.12367 *                    2     1
      4     C          1.52088        111.13219 *    55.51736 *      3     2     1
      5     C          1.52088        111.12582 *   -55.55349 *      1     2     3
      6     C          1.52088        111.13622 *    55.51499 *      5     1     2
      7     H          1.12120        109.55613 *  -176.75097 *      1     2     3
      8     H          1.12120        109.41707 *    65.38921 *      1     2     3
      9     H          1.12120        109.55301 *   121.19006 *      2     3     1
     10     H          1.12120        109.42260 *  -120.94775 *      2     3     1
     11     H          1.12120        109.41549 *   -65.43354 *      3     2     1
     12     H          1.12120        109.54815 *   176.71459 *      3     2     1
     13     H          1.12120        109.44759 *  -176.94350 *      4     3     2
     14     H          1.12120        109.30997 *    65.46534 *      4     3     2
     15     H          1.12120        143.75699 *  -124.60312 *      5     4     3
     16     H          1.12120         93.04532 *   109.41652 *      5     4     3
     17     H          1.12120        109.31227 *   121.07942 *      6     5     4
     18     H          1.12120        109.44988 *  -121.32956 *      6     5     4


 CRITICAL POINT No  2
 ....................
          HEAT OF FORMATION       =   -35.291044 KCAL
          RMS GRADIENT NORM       =     0.007649 KCAL/ANGSTROMS
          CRITICAL POINT INDEX    =            0  ESTIMATE  
          MOLECULAR POINT GROUP   = D2    0.100000
    ATOM    CHEMICAL   BOND LENGTH    BOND ANGLE    TWIST ANGLE
   NUMBER   SYMBOL     (ANGSTROMS)     (DEGREES)     (DEGREES)
    (I)                   NA:I          NB:NA:I      NC:NB:NA:I     NA    NB    NC
      1     C 
      2     C          1.52088                                       1
      3     C          1.52088        112.21398 *                    2     1
      4     C          1.52088        111.55770 *   -29.93933 *      3     2     1
      5     C          1.52088        111.55517 *   -30.14209 *      1     2     3
      6     C          1.52088        111.56772 *    62.75057 *      5     1     2
      7     H          1.12120        109.54732 *    90.59606 *      1     2     3
      8     H          1.12120        109.61370 *  -151.71722 *      1     2     3
      9     H          1.12120        109.70654 *   121.28183 *      2     3     1
     10     H          1.12120        108.98228 *  -121.70482 *      2     3     1
     11     H          1.12120        109.54343 *    90.80051 *      3     2     1
     12     H          1.12120        109.61328 *  -151.51398 *      3     2     1
     13     H          1.12120        109.52404 *   184.55557 *      4     3     2
     14     H          1.12120        108.88890 *   -58.29523 *      4     3     2
     15     H          1.12120        106.59192 *    51.24563 *      5     4     3
     16     H          1.12120        137.68108 *  -166.34359 *      5     4     3
     17     H          1.12120        109.63636 *   121.38673 *      6     5     4
     18     H          1.12120        108.89553 *  -121.78879 *      6     5     4


 CRITICAL POINT No  3
 ....................
          HEAT OF FORMATION       =    68.531095 KCAL
          RMS GRADIENT NORM       =     0.015153 KCAL/ANGSTROMS
          CRITICAL POINT INDEX    =            0  ESTIMATE  
          MOLECULAR POINT GROUP   = C1    0.100000
    ATOM    CHEMICAL   BOND LENGTH    BOND ANGLE    TWIST ANGLE
   NUMBER   SYMBOL     (ANGSTROMS)     (DEGREES)     (DEGREES)
    (I)                   NA:I          NB:NA:I      NC:NB:NA:I     NA    NB    NC
      1     C 
      2     C          1.52088                                       1
      3     C          1.52088        112.13620 *                    2     1
      4     C          1.52088        116.14403 *   -91.58729 *      3     2     1
      5     C          1.52088        111.50348 *   -49.76363 *      1     2     3
      6     C          1.52088        109.78808 *    50.54448 *      5     1     2
      7     H          1.12120        109.47058 *  -171.36756 *      1     2     3
      8     H          1.12120        109.09486 *    70.94698 *      1     2     3
      9     H          1.12120        109.28289 *   121.45883 *      2     3     1
     10     H          1.12120        108.73584 *  -121.01989 *      2     3     1
     11     H          1.12120        103.63365 *    24.07010 *      3     2     1
     12     H          1.12120        115.25638 *   131.78058 *      3     2     1
     13     H          1.12120        119.55342 *    23.86167 *      4     3     2
     14     H          1.12120        119.25747 *  -164.33722 *      4     3     2
     15     H          1.12120        122.15844 *    -0.07077 *      5     4     3
     16     H          1.12120        130.05307 *   177.26562 *      5     4     3
     17     H          1.12120        113.87926 *   221.26848 *      6     5     4
     18     H          1.12120        113.57800 *    91.43235 *      6     5     4

 ELAPSED TIME IN QUENCHING     21.53 SECONDS
 CALLS TO COST FNCT IN QUENCHING: 1633

 ENLARGED CLUSTERING ANALYSIS OF CRITICAL POINTS
 -----------------------------------------------
 TABLE OF NEARLY IDENTICAL CONFIGURATIONS AT THRESHOLD =  1.10 A    7
 ENERGY     ,CONFIGURATIONS    (A "*" MEANS IDENTICAL)
                 2
    -38.4617   1*
    -35.2910   2.*
     68.5311   3..*

 NUMBER OF CONFIGURATIONS KEPT:   3
 
     ELAPSED WALL CLOCK TIME :     12.62 SECONDS
     FULL COMPUTATION TIME :     47.30 SECONDS
	

1

This section lists the dedicated annealing keywords found by the program.

2

Information on the methods and criteria that annealing will use is listed in this section of the output.

3

This section lists the active penalty functions defined by the annealing keywords.

4

The lower bounds, beginning values, and upper bounds for the optimizable parameters are summarized in this table. The user should carefully examine this table to ensure that the proper limits have been defined.

5

For PEN2 or PEN2GRP, a table of located bonded atoms are noted here. This information details which bonds will be enforced during the course of the simulated annealing.

6

These are the coordinates at the end of the annealing configuration search.

7

This table describes the presorted configurations and eliminates identical members from consideration. In this case, the four final candidates are revealed as non-identical and so none are filtered out. The threshold for filtering is controlled by FILTER (default=1.0) and occurs after each major phase of simulated annealing. A smaller value of FILTER can be used to minimize the chance of missing a minima, but this noticeably increases the amount of time required in the quenching process.

Example II (Rigid System)

The following molecule (methyl-N-methyl-amide) has been selected for illustration of the annealing procedure in the case of a relatively rigid system:

Figure 30.1. Example of a Relatively Rigid System


As mentioned in the section called “Strategies for Annealing Searches”, the general strategy to use is to divide the conformational search problem into primary and secondary degrees of freedom. Then a connectivity may be defined which allows an explicit description of the primary degrees of freedom. In this case, three primary degrees of freedom may be identified as the rotation about bonds C1-N3A, C4-N3B, and C5-C1C. The following is a viable (but not necessarily unique) connectivity pattern for this system that produces explicit descriptions of the primary degrees of freedom. (Note that the superscripts A, B, and C above identify below which of the dihedrals are used to specify the rotations.)

 C      0.000000  0    0.000000  0    0.000000  0    0    0    0
 O      1.243077  1    0.000000  0    0.000000  0    1    0    0
 N      1.366966  1  121.946787  1    0.000000  0    1    2    0
 C      1.520000  1  120.615770  1   -0.000067A 1    3    1    2
 C      1.540000  1  123.093733  1 -179.998834  1    1    2    3
 H      0.986177  1  121.170189  1  179.991444  1    3    1    4
 H      1.004440  1  108.958790  1    0.000000B 1    4    3    1
 H      1.004440  1  108.958790  1  120.000000  1    4    3    7
 H      1.000000  1  109.885165  1 -120.000000  1    4    3    7
 H      1.004440  1  108.958790  1  180.000000C 1    5    1    2
 H      1.004440  1  108.958790  1  120.000000  1    5    1   10
 H      1.000000  1  109.885165  1 -120.000000  1    5    1   10

As mentioned in the section called “Geometry Specification”, this modular designation of the hydrogen atoms of a methyl group allows easy manipulation of the orientation of the entire group by altering one dihedral angle. In this example, the master degrees of freedom are defined by the dihedrals of particular atoms: the dihedral on H7for the C4 methyl (C4-N3 rotation), the dihedral on H10 for the C5 methyl (C5-C1 rotation), and the dihedral on C5 for the C1-N3 rotation. The LIMIT keyword can now be used to define boundaries for the search of conformational space. The secondary variables are not important to the annealing procedure and should be limited to about 10% of their original value. (Note that all annealing boundary conditions are ignored during the local quenching of the located minima.) The definition of the problem in these terms requires some chemical knowledge and intuition, but saves enormous computational effort. The final input and results files for the problem is listed below.

Input File (annealing/anneal_limit.dat):

  am1 rhf singlet t=auto anneal truste filter=1.2 noxyz limit    1
methyl-n-methylamide
Annealing on rigid system: LIMIT
 C              0.000000  0    0.000000  0    0.000000  0    0    0    0
 O              1.243077  1    0.000000  0    0.000000  0    1    0    0
 N              1.366966  1  121.946787  1    0.000000  0    1    2    0
 C              1.520000  1  120.615770  1    0.000000  1    3    1    2    2
 C              1.540000  1  123.093733  1 -179.990000  1    1    2    3
 H              0.986177  1  121.170189  1  179.990000  1    3    1    4
 H              1.004440  1  108.958790  1  -60.000000  1    4    3    1    3
 H              1.004440  1  108.958790  1  120.000000  1    4    3    7
 H              1.000000  1  109.885165  1 -120.000000  1    4    3    7
 H              1.004440  1  108.958790  1  120.000000  1    5    1    2    4
 H              1.004440  1  108.958790  1  120.000000  1    5    1   10
 H              1.000000  1  109.885165  1 -120.000000  1    5    1   10
 0              0.000000  0    0.000000  0    0.000000  0    0    0    0
$$ limit - annealing boundaries    5
  1.2  1.3 110   1.5 110 -180   1.5 100 -190   0.9 100  160    6
  0.9 100 -180   0.9 100  100   0.9 100 -140   0.9 100 -180   
  0.9 100  100   0.9 100 -140
  1.3  1.4 130   1.6 130  180   1.6 140 -170   1.1 130  200    7
  1.1 130  180   1.1 130  140   1.1 130 -100   1.1 130  180
  1.1 130  140   1.1 130 -100
$$ end of extra data
	

1

The keyword ANNEAL activates energy-based annealing. LIMIT is used to restrict the range the over which the geometry can vary. The FILTER=n.n keyword loosens the criteria (default =1.0) for elimination of a candidate geometry as already located. For situations such as distinguishing between methyl rotations this value should probably be raised to 1.4.

2 3 4

The dihedrals on these lines comprise the three primary degrees of freedom.

5

This is the extra input section marker for reaction path data. Note, that this marker can be shortened to $$ limit. Details of these markers are found in the section called “Extra Input Data”.

6

These are the lower limits each geometric parameter can assume. Note that most are very close to their initial values but items # 6, 15, and 24 have a lower limit of -180.00.

7

These are the upper limits each geometric parameter can assume. As before, most are very close to their initial values but items # 6, 15, and 24 now have an upper limit of 180.00. The range -180 to +180 represent a full circle rotation about the required bonds.

Archive File (annealing/anneal_limit.arc):

 Timestamp:  2011-09-02-10-31-27-00000008B8-win64
 User Info:  John Millam, Nahum, 

                     SUMMARY OF AM1 CALCULATION
                                                       Sep-02-2011
                          AMPAC Version 10.0.1
                             Presented by:
  
                        Semichem, Inc.
                        www.semichem.com
  
 FORMULA: C3H7N1O1
 methyl-n-methylamide
 Annealing on rigid system: LIMIT

     GEOMETRY NORMALLY RETURNED BY SIMULATED ANNEALING
     SCF FIELD WAS ACHIEVED
 
          FINAL HEAT OF FORMATION   =       -47.273807 kcal    1
                                    =      -197.840883 kJ
          ELECTRONIC ENERGY         =     -3372.707818 eV
          CORE-CORE REPULSION       =      2364.399293 eV
          TOTAL ENERGY              =     -1008.308525 eV
          GRADIENT NORM             =         0.136535 
          RMS GRADIENT NORM         =         0.024928 
          UNSTABLE MODE(S)          =         0 ( ESTIMATE  )
          IONIZATION POTENTIAL      =         9.919350 eV
          HOMO-LUMO GAP             =        11.396568 eV
          DIPOLE                    =         3.512983 debyes
          MOLECULAR WEIGHT          =        73.094400 
          MOLECULAR POINT GROUP     = C1      0.100000
          NO. OF FILLED LEVELS      =        15 (OCC = 2)
          TOTAL NUMBER OF ORBITALS  =        27
          FINAL GEOMETRY OBTAINED                                       CHARGE
 AM1 RHF SINGLET T=AUTO ANNEAL TRUSTE FILTER=1.2 NOXYZ LIMIT
 methyl-n-methylamide
 Annealing on rigid system: LIMIT
  C     0.000000  0    0.000000  0    0.000000  0      0     0     0    0.3005
  O     1.247344  1    0.000000  0    0.000000  0      1     0     0   -0.3707
  N     1.381133  1  121.226528  1    0.000000  0      1     2     0   -0.3919
  C     1.426634  1  123.134683  1    0.930309  1      3     1     2   -0.0753
  C     1.509608  1  121.506124  1 -179.607660  1      1     2     3   -0.2429
  H     0.989975  1  119.083610  1  178.138046  1      3     1     4    0.2203
  H     1.123743  1  110.042025  1 -123.258755  1      4     3     1    0.0657
  H     1.123259  1  110.128295  1  120.142939  1      4     3     7    0.1180
  H     1.123948  1  110.290251  1 -119.663478  1      4     3     7    0.0639
  H     1.117269  1  108.671005  1   -2.926591  1      5     1     2    0.1176
  H     1.116502  1  110.320733  1  119.387121  1      5     1    10    0.0986
  H     1.116278  1  110.774936  1 -119.678593  1      5     1    10    0.0962
  0     0.000000  0    0.000000  0    0.000000  0      0     0     0
 Timestamp:  2011-09-02-10-31-27-00000008B8-win64
 User Info:  John Millam, Nahum, 

                     SUMMARY OF AM1 CALCULATION
                                                       Sep-02-2011
                          AMPAC Version 10.0.1
                             Presented by:
  
                        Semichem, Inc.
                        www.semichem.com
  
 FORMULA: C3H7N1O1
 methyl-n-methylamide
 Annealing on rigid system: LIMIT

     GEOMETRY NORMALLY RETURNED BY SIMULATED ANNEALING
     SCF FIELD WAS ACHIEVED
 
          FINAL HEAT OF FORMATION   =       -47.128097 kcal    2
                                    =      -197.231086 kJ
          ELECTRONIC ENERGY         =     -3381.382435 eV
          CORE-CORE REPULSION       =      2373.080228 eV
          TOTAL ENERGY              =     -1008.302207 eV
          GRADIENT NORM             =         0.146199 
          RMS GRADIENT NORM         =         0.026692 
          UNSTABLE MODE(S)          =         0 ( ESTIMATE  )
          IONIZATION POTENTIAL      =         9.968793 eV
          HOMO-LUMO GAP             =        11.417545 eV
          DIPOLE                    =         3.812818 debyes
          MOLECULAR WEIGHT          =        73.094400 
          MOLECULAR POINT GROUP     = C1      0.100000
          NO. OF FILLED LEVELS      =        15 (OCC = 2)
          TOTAL NUMBER OF ORBITALS  =        27
          FINAL GEOMETRY OBTAINED                                       CHARGE
 AM1 RHF SINGLET T=AUTO ANNEAL TRUSTE FILTER=1.2 NOXYZ LIMIT
 methyl-n-methylamide
 Annealing on rigid system: LIMIT
  C     0.000000  0    0.000000  0    0.000000  0      0     0     0    0.2989
  O     1.247945  1    0.000000  0    0.000000  0      1     0     0   -0.3723
  N     1.382533  1  118.914981  1    0.000000  0      1     2     0   -0.3914
  C     1.424011  1  123.339115  1 -174.380801  1      3     1     2   -0.0691
  C     1.505834  1  121.890796  1  178.881179  1      1     2     3   -0.2367
  H     0.993653  1  117.637889  1  170.185844  1      3     1     4    0.2332
  H     1.123800  1  110.478541  1  -49.571301  1      4     3     1    0.0761
  H     1.125295  1  111.400134  1  120.222450  1      4     3     7    0.0618
  H     1.122051  1  109.493726  1 -119.678278  1      4     3     7    0.0858
  H     1.117092  1  108.802145  1    6.064562  1      5     1     2    0.1159
  H     1.116714  1  110.731439  1  120.021331  1      5     1    10    0.0962
  H     1.117107  1  110.071756  1 -119.390425  1      5     1    10    0.1015
  0     0.000000  0    0.000000  0    0.000000  0      0     0     0
 Timestamp:  2011-09-02-10-31-27-00000008B8-win64
 User Info:  John Millam, Nahum, 

                     SUMMARY OF AM1 CALCULATION
                                                       Sep-02-2011
                          AMPAC Version 10.0.1
                             Presented by:
  
                        Semichem, Inc.
                        www.semichem.com
  
 FORMULA: C3H7N1O1
 methyl-n-methylamide
 Annealing on rigid system: LIMIT

     GEOMETRY NORMALLY RETURNED BY SIMULATED ANNEALING
     SCF FIELD WAS ACHIEVED
 
          FINAL HEAT OF FORMATION   =       -46.479573 kcal
                                    =      -194.517012 kJ
          ELECTRONIC ENERGY         =     -3377.189894 eV
          CORE-CORE REPULSION       =      2368.915810 eV
          TOTAL ENERGY              =     -1008.274084 eV
          GRADIENT NORM             =         0.118537 
          RMS GRADIENT NORM         =         0.021642 
          UNSTABLE MODE(S)          =         0 ( ESTIMATE  )
          IONIZATION POTENTIAL      =         9.953249 eV
          HOMO-LUMO GAP             =        11.428904 eV
          DIPOLE                    =         3.756254 debyes
          MOLECULAR WEIGHT          =        73.094400 
          MOLECULAR POINT GROUP     = Cs      0.100000
          NO. OF FILLED LEVELS      =        15 (OCC = 2)
          TOTAL NUMBER OF ORBITALS  =        27
          FINAL GEOMETRY OBTAINED                                       CHARGE
 AM1 RHF SINGLET T=AUTO ANNEAL TRUSTE FILTER=1.2 NOXYZ LIMIT
 methyl-n-methylamide
 Annealing on rigid system: LIMIT
  C     0.000000  0    0.000000  0    0.000000  0      0     0     0    0.3009
  O     1.249438  1    0.000000  0    0.000000  0      1     0     0   -0.3786
  N     1.380579  1  118.294584  1    0.000000  0      1     2     0   -0.3920
  C     1.423729  1  124.574106  1  179.249337  1      3     1     2   -0.0666
  C     1.505574  1  120.930373  1 -179.925618  1      1     2     3   -0.2349
  H     0.994000  1  117.229073  1 -178.915734  1      3     1     4    0.2338
  H     1.124457  1  111.091737  1  -59.426313  1      4     3     1    0.0687
  H     1.124450  1  111.024190  1  120.524265  1      4     3     7    0.0692
  H     1.122134  1  109.428362  1 -119.763167  1      4     3     7    0.0857
  H     1.117948  1  108.228375  1   57.897759  1      5     1     2    0.1125
  H     1.114605  1  113.737957  1  121.236172  1      5     1    10    0.0891
  H     1.117909  1  108.238855  1 -117.462003  1      5     1    10    0.1121
  0     0.000000  0    0.000000  0    0.000000  0      0     0     0
	

1

This is the data relating to the first minimum located by annealing, and is a refined version of the input structure pictured in Figure 30.2, “Trans-minimum”. This structure happens to be the global minimum on the PES and is referred to as the trans-minimum.

Figure 30.2. Trans-minimum


2

This is the data relating to the second minimum located by annealing. It is referred to as the cis-minimum (Figure 30.3, “Cis-minimum”).

Figure 30.3. Cis-minimum


Output File (annealing/anneal_limit.out):

 Timestamp: 2011-09-02-10-31-27-00000008B8-win64
 User Info: John Millam, Nahum, 
 *******************************************************************************
                         AM1 CALCULATION RESULTS
 *******************************************************************************
 *                             AMPAC Version 10.0.1
 *                                Presented by:
 *
 *                           Semichem, Inc.
 *                           www.semichem.com
 *
 *  AM1      - THE AM1 HAMILTONIAN TO BE USED
 *  RHF      - RESTRICTED HARTREE-FOCK CALCULATION
 *  ANNE     - SIMULATED ANNEALING ON ENERGY ONLY
 *  TRUSTE   - MINIMIZE ENERGY USING TRUST REGION METHOD
 *  NOXYZ    - CARTESIAN COORDINATES NOT TO BE PRINTED
 *  T=AUTO   - AUTOMATIC DETERMINATION OF ALLOWED TIME
 *  SINGLET  - IS THE REQUIRED SPIN MULTIPLICITY
 *******************************************************************************
 AM1 RHF SINGLET T=AUTO ANNEAL TRUSTE FILTER=1.2 NOXYZ LIMIT
 methyl-n-methylamide
 Annealing on rigid system: LIMIT
    ATOM    CHEMICAL   BOND LENGTH    BOND ANGLE    TWIST ANGLE
   NUMBER   SYMBOL     (ANGSTROMS)     (DEGREES)     (DEGREES)
    (I)                   NA:I          NB:NA:I      NC:NB:NA:I     NA    NB    NC
      1     C 
      2     O          1.24308 *                                     1
      3     N          1.36697 *      121.94679 *                    1     2
      4     C          1.52000 *      120.61577 *     0.00000 *      3     1     2
      5     C          1.54000 *      123.09373 *  -179.99000 *      1     2     3
      6     H          0.98618 *      121.17019 *   179.99000 *      3     1     4
      7     H          1.00444 *      108.95879 *   -60.00000 *      4     3     1
      8     H          1.00444 *      108.95879 *   120.00000 *      4     3     7
      9     H          1.00000 *      109.88517 *  -120.00000 *      4     3     7
     10     H          1.00444 *      108.95879 *   120.00000 *      5     1     2
     11     H          1.00444 *      108.95879 *   120.00000 *      5     1    10
     12     H          1.00000 *      109.88517 *  -120.00000 *      5     1    10

   MOLECULAR POINT GROUP            SYMMETRY CRITERIA
            Cs                          0.10000000

          SINGLET STATE CALCULATION

          RHF CALCULATION, NO. OF DOUBLY OCCUPIED LEVELS =      15

        **  REFERENCES TO PARAMETERS  **

 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).

 *******************************************************************************
 *  KEYWORDS DEDICATED TO SIMULATED ANNEALING SECTION
 *
 *  LIMIT    - EXPLICIT PERIODIC CONDITIONS GIVEN
 *  FILTER=  - SET THRESHOLD OF DISTINGUISHED CONFIGURATION TO 1.200
 *******************************************************************************
 STANDARD DEVIATION ON ENERGY   (KCAL)       0.00000055521
 STANDARD DEVIATION ON GRADIENT (KCAL/A,RD,RD)  0.00009841 0.00018732 0.00013159

 SIMULATED ANNEALING BY METROPOLIS SCHEME IN   30 VARIABLES
     VERSION 2.0 (MAY 2000)
     THERMALIZATION THRESHOLD ON COST FNCT          0.080
     MAXIMUM STEP SIZE                            2.00000
     CONVERGENCE CRITERION ON STEP SIZE           0.06325

 MAXIMUM NUMBER OF STEPS AT EACH TEMPERATURE         1000
     FIRST TEMPERATURE (HOT) SET TO                 50.00
     TEMPERATURE EXPONENTIAL DECAY                   0.80
     LAST TEMPERATURE (COLD) SET TO                  0.50
 RANDOM SEQUENCE INITIATOR                       -9876566
     MARKOV CHAIN STUDIED BY PIECES OF                 20
     No OF TEMPERATURES TO DETECT A FROZEN SYSTEM       2
 EQUIVALENCE THRESHOLD IN CLUSTERING ANALYSIS        1.20
     BAND-PASS FILTER NO 1 CENTERED AT               1.40 ANGSTROMS
     HALF BAND-WIDTH                                13.50 %
 CAN HOLD  250 CANDIDATES FOR QUENCHING.
 PERIODIC BOUNDARY CONDITIONS (ANGSTROMS, DEGREES)
 LOWER BOUND    1.2000    1.3000  110.0000    1.5000  110.0000 -180.0000    1
                1.5000  100.0000 -190.0000    0.9000  100.0000  160.0000
                0.9000  100.0000 -180.0000    0.9000  100.0000  100.0000
                0.9000  100.0000 -140.0000    0.9000  100.0000 -180.0000
                0.9000  100.0000  100.0000    0.9000  100.0000 -140.0000
 TRIAL COORD    1.2431    1.3670  121.9468    1.5200  120.6158    0.0000
                1.5400  123.0937 -179.9900    0.9862  121.1702  179.9900
                1.0044  108.9588  -60.0000    1.0044  108.9588  120.0000
                1.0000  109.8852 -120.0000    1.0044  108.9588  120.0000
                1.0044  108.9588  120.0000    1.0000  109.8852 -120.0000
 UPPER BOUND    1.3000    1.4000  130.0000    1.6000  130.0000  180.0000
                1.6000  140.0000 -170.0000    1.1000  130.0000  200.0000
                1.1000  130.0000  180.0000    1.1000  130.0000  140.0000
                1.1000  130.0000 -100.0000    1.1000  130.0000  180.0000
                1.1000  130.0000  140.0000    1.1000  130.0000 -100.0000

 COST FNCT IS ENERGY (KCAL/MOLE)

 VISIT OF THE PES BY SIMULATED ANNEALING
 ---------------------------------------

 * * * SYSTEM LOOKS FROZEN AT TEMPERATURE    6.7109 KCAL
 NORMAL END AFTER  1111 CALLS TO COST FNCT
 ELAPSED TIME IN ANNEALING     10.11 SECONDS

 CLUSTERING ANALYSIS OF CONFORMATIONS
 ------------------------------------
 KEEP   5 CONFORMATIONS FROM  28 SELECTED AT PES VISIT

 QUENCHING OF REMAINING CONFORMATIONS
 ------------------------------------
 PERFORMED WITHOUT PERIODIC BOUNDARIES.
 MINIMIZE ENERGY BY TRUST ALGORITHM

 QUENCHING No  1 -- STAGE 1 OF 1  (   0.08 SECONDS)
 ..................................................
          HEAT OF FORMATION       =   -46.479573 KCAL
          RMS GRADIENT NORM       =     0.021643 KCAL/ANGSTROMS
          CRITICAL POINT INDEX    =            0  ESTIMATE  
 CURRENT COORDINATES (ANGSTROMS, DEGREES)
    1.2494    1.3806  118.2946    1.4237  124.5741 -180.7507    1.5056  120.9304
 -179.9256    0.9940  117.2291  181.0843    1.1245  111.0917  -59.4263    1.1244
  111.0242  120.5243    1.1221  109.4284 -119.7632    1.1179  108.2284   57.8978
    1.1146  113.7380  121.2362    1.1179  108.2389 -117.4620

 QUENCHING No  2 -- STAGE 1 OF 1  (   0.14 SECONDS)
 ..................................................
          HEAT OF FORMATION       =   -47.273807 KCAL
          RMS GRADIENT NORM       =     0.024924 KCAL/ANGSTROMS
          CRITICAL POINT INDEX    =            0  ESTIMATE  
 CURRENT COORDINATES (ANGSTROMS, DEGREES)
    1.2473    1.3811  121.2265    1.4266  123.1347    0.9303    1.5096  121.5061
 -179.6077    0.9900  119.0836  178.1380    1.1237  110.0420 -123.2588    1.1233
  110.1283  120.1429    1.1239  110.2903 -119.6635    1.1173  108.6710   -2.9266
    1.1165  110.3207  119.3871    1.1163  110.7749 -119.6786

 QUENCHING No  3 -- STAGE 1 OF 1  (   0.12 SECONDS)
 ..................................................
          HEAT OF FORMATION       =   -47.128097 KCAL
          RMS GRADIENT NORM       =     0.026692 KCAL/ANGSTROMS
          CRITICAL POINT INDEX    =            0  ESTIMATE  
 CURRENT COORDINATES (ANGSTROMS, DEGREES)
    1.2479    1.3825  118.9150    1.4240  123.3391 -174.3808    1.5058  121.8908
 -181.1188    0.9937  117.6379  170.1858    1.1238  110.4785  -49.5713    1.1253
  111.4001  120.2225    1.1221  109.4937 -119.6783    1.1171  108.8021    6.0646
    1.1167  110.7314  120.0213    1.1171  110.0718 -119.3904

 QUENCHING No  4 -- STAGE 1 OF 1  (   0.06 SECONDS)
 ..................................................
          * * * QUENCHING INTERRUPTED: POINT PREVIOUSLY FOUND.

 QUENCHING No  5 -- STAGE 1 OF 1  (   0.11 SECONDS)
 ..................................................
          * * * QUENCHING INTERRUPTED: POINT PREVIOUSLY FOUND.
 TIME CONSUMPTION OF STAGE 1:      0.58 SECONDS
 ON   3 POINTS AT END OF STAGE 1,   3 FULFILL STATIONARITY AND ENERGETIC REQUESTS.

 DETAILS ON NON EQUIVALENT CRITICAL POINTS FOUND (ENERGY SORTED)    2
 ---------------------------------------------------------------

 CRITICAL POINT No  1
 ....................
          HEAT OF FORMATION       =   -47.273807 KCAL    3
          RMS GRADIENT NORM       =     0.024924 KCAL/ANGSTROMS
          CRITICAL POINT INDEX    =            0  ESTIMATE  
          MOLECULAR POINT GROUP   = C1    0.100000
    ATOM    CHEMICAL   BOND LENGTH    BOND ANGLE    TWIST ANGLE
   NUMBER   SYMBOL     (ANGSTROMS)     (DEGREES)     (DEGREES)
    (I)                   NA:I          NB:NA:I      NC:NB:NA:I     NA    NB    NC
      1     C 
      2     O          1.24734 *                                     1
      3     N          1.38113 *      121.22653 *                    1     2
      4     C          1.42663 *      123.13468 *     0.93031 *      3     1     2
      5     C          1.50961 *      121.50612 *  -179.60766 *      1     2     3
      6     H          0.98998 *      119.08361 *   178.13805 *      3     1     4
      7     H          1.12374 *      110.04202 *  -123.25875 *      4     3     1
      8     H          1.12326 *      110.12829 *   120.14294 *      4     3     7
      9     H          1.12395 *      110.29025 *  -119.66348 *      4     3     7
     10     H          1.11727 *      108.67101 *    -2.92659 *      5     1     2
     11     H          1.11650 *      110.32073 *   119.38712 *      5     1    10
     12     H          1.11628 *      110.77494 *  -119.67859 *      5     1    10


 CRITICAL POINT No  2
 ....................
          HEAT OF FORMATION       =   -47.128097 KCAL    4
          RMS GRADIENT NORM       =     0.026692 KCAL/ANGSTROMS
          CRITICAL POINT INDEX    =            0  ESTIMATE  
          MOLECULAR POINT GROUP   = C1    0.100000
    ATOM    CHEMICAL   BOND LENGTH    BOND ANGLE    TWIST ANGLE
   NUMBER   SYMBOL     (ANGSTROMS)     (DEGREES)     (DEGREES)
    (I)                   NA:I          NB:NA:I      NC:NB:NA:I     NA    NB    NC
      1     C 
      2     O          1.24794 *                                     1
      3     N          1.38253 *      118.91498 *                    1     2
      4     C          1.42401 *      123.33912 *  -174.38080 *      3     1     2
      5     C          1.50583 *      121.89080 *  -181.11882 *      1     2     3
      6     H          0.99365 *      117.63789 *   170.18584 *      3     1     4
      7     H          1.12380 *      110.47854 *   -49.57130 *      4     3     1
      8     H          1.12529 *      111.40013 *   120.22245 *      4     3     7
      9     H          1.12205 *      109.49373 *  -119.67828 *      4     3     7
     10     H          1.11709 *      108.80215 *     6.06456 *      5     1     2
     11     H          1.11671 *      110.73144 *   120.02133 *      5     1    10
     12     H          1.11711 *      110.07176 *  -119.39042 *      5     1    10


 CRITICAL POINT No  3
 ....................
          HEAT OF FORMATION       =   -46.479573 KCAL
          RMS GRADIENT NORM       =     0.021643 KCAL/ANGSTROMS
          CRITICAL POINT INDEX    =            0  ESTIMATE  
          MOLECULAR POINT GROUP   = Cs    0.100000
    ATOM    CHEMICAL   BOND LENGTH    BOND ANGLE    TWIST ANGLE
   NUMBER   SYMBOL     (ANGSTROMS)     (DEGREES)     (DEGREES)
    (I)                   NA:I          NB:NA:I      NC:NB:NA:I     NA    NB    NC
      1     C 
      2     O          1.24944 *                                     1
      3     N          1.38058 *      118.29458 *                    1     2
      4     C          1.42373 *      124.57411 *  -180.75066 *      3     1     2
      5     C          1.50557 *      120.93037 *  -179.92562 *      1     2     3
      6     H          0.99400 *      117.22907 *   181.08427 *      3     1     4
      7     H          1.12446 *      111.09174 *   -59.42631 *      4     3     1
      8     H          1.12445 *      111.02419 *   120.52427 *      4     3     7
      9     H          1.12213 *      109.42836 *  -119.76317 *      4     3     7
     10     H          1.11795 *      108.22838 *    57.89776 *      5     1     2
     11     H          1.11460 *      113.73796 *   121.23617 *      5     1    10
     12     H          1.11791 *      108.23885 *  -117.46200 *      5     1    10

 ELAPSED TIME IN QUENCHING      0.66 SECONDS
 CALLS TO COST FNCT IN QUENCHING:   80

 ENLARGED CLUSTERING ANALYSIS OF CRITICAL POINTS    5
 -----------------------------------------------
 TABLE OF NEARLY IDENTICAL CONFIGURATIONS AT THRESHOLD =  1.32 A
 ENERGY     ,CONFIGURATIONS    (A "*" MEANS IDENTICAL)
                 2
    -47.2738   1*
    -47.1281   2.*
    -46.4796   3..*

 NUMBER OF CONFIGURATIONS KEPT:   3
 
     ELAPSED WALL CLOCK TIME :     20.11 SECONDS
     FULL COMPUTATION TIME :     12.82 SECONDS
	

1

These are the upper and lower boundaries along with the initial values for each coordinate.

2

These are the coordinates at the end of the annealing quenching phase.

3

This is the trans-minimum geometry.

4

This is the cis-minimum geometry.

5

This table describes the presorted configurations and eliminates identical members from consideration. The threshold for filtering is controlled by FILTER (default=1.0) and occurs after each major phase of simulated annealing. A smaller value of FILTER can be used to minimize the chance of missing a minimum, but this noticeably increases the amount of time required in the quenching process.