Startseite    

 

HINT (Hilderbrandt INTernal Coordinates)

 

Diese Art von internen Koordinaten ist extrem schwierig zu verstehen. Es nutzt dabei auch nicht viel, die empfohlene Literaturstelle zu lesen (R. L. Hilderbrandt, Cartesian Coordinates of Molecular Models, J. Chem. Phys. 51, 1654 (1969)). Da die nichtanalytische Geometrieoptimierung angeregter Zustände nur mit diesen Koordinaten funktioniert, ist es aber notwendig, damit arbeiten zu können. Ich versuche es anhand einiger Beispiele.

 

COORD=HINT: only symmetry unique atoms will be given, in Hilderbrandt style internals

 

!

!     H2O

!

 $CONTRL SCFTYP=RHF MULT=1 RUNTYP=TRUDGE CITYP=GUGA COORD=HINT $END

 $SYSTEM TIMLIM=100 MEMORY=5000000 $END

 $BASIS  GBASIS=N31 NGAUSS=6 NDFUNC=1 $END

 $GUESS  GUESS=HUCKEL $END

 $TRUDGE OPTMIZ=GEOMETRY NPAR=2 IEX(1)=21,22 P(1)=0.96 $END

 $CIDRT GROUP=C2V SOCI=.TRUE. NFZC=1 NDOC=4 NVAL=14 NEXT=-1 $END

 $DATA

Water CI-SD Geometry Optimization

CNV 2

 

O   8.0   LC   0.0     0.0    0.0   -   O   K

H   1.0   PCC  0.94   53.0    0.0   +   O   K   I

 $END

ändert man die Koordinatenzeilen wie folgt:

O   8.0   LC   0.0     0.0    0.0   -   O  

H   1.0   PCC  0.94   53.0    0.0   +   O   K  
kommt aber das Gleiche heraus.

 

NAME, ZNUC, CONX, R, ALPHA, BETA, SIGN, POINT1, POINT2, POINT3

NAME: 10 character atomic name (used only for print out).

ZNUC: nuclear charge.

CONX: connection type, choose from:

            LC: linear connection: 0.0: O-Atom ist am Koordinaten-Ursprung; keine Winkel

            PCC: planar central connection: 0.94:  H-Atom ist 0.94 A vom O-Atom entfernt und bildet mit der
            Drehachse einen Winkel von 53°, 0.0: die eingeschlossene Fläche ist nicht verdrillt?

            NPCC: non-planar central connection

            PTC : planar terminal connection

            CCPA : central connection with polar atom

            TCT: terminal connection with torsion

R: connection distance

ALPHA: first connection angle

BETA: second connection angle

SIGN: connection sign “+” or “-“: spielt im obigen Fall keine Rolle.

POINT1, POINT2, POINT3: connection points, a serial number of a previously input atom, or one of 4 standard points: O, I, J, K (origin and unit points on axes of master frame). Default: POINT1=O, POINT2=I, POINT3=J

 

Am besten geht es durch probieren. Z. B. das N2O4-Molekül 

!
! N2O4-Molekuel
!
!
 $CONTRL SCFTYP=RHF MULT=1 RUNTYP=OPTIMIZE COORD=HINT $END
 $SYSTEM TIMLIM=1000 MEMORY=5000000 $END
 $BASIS GBASIS=STO NGAUSS=6 $END
 $GUESS GUESS=HUCKEL $END
 $DATA
N2O4-Molekuel
CNH 2

N    7.0    LC       0.90       0.0      0.0    -    O
O    8.0    PCC      1.20     112.0      0.0    +    1
O    8.0    PCC      1.20    -112.0      0.0    +    1
 $END

 

ergibt:

ATOM ATOMIC               COORDINATES (BOHR)
     CHARGE         X             Y                Z
N     7.0    -1.7007533889   0.0000000000    0.0000000000
N     7.0     1.7007533889   0.0000000000    0.0000000000
O     8.0    -0.8512688112  -2.1025481104    0.0000000000
O     8.0     0.8512688112   2.1025481104    0.0000000000
O     8.0    -0.8512688112   2.1025481104    0.0000000000
O     8.0     0.8512688112  -2.1025481104    0.0000000000

Man sieht, dass die beiden N-Atome auf der x-Achse liegen, die O-Atome liegen aber näher zum Ursprung, d. h. folgende Struktur liegt vor:

                                   O     O
                             N                 N
                                  O      O


Man muss also die Eingabe ändern.

 N  7.0   LC   0.90    0.0   0.0  + O
 O  8.0   PCC  1.20  112.0   0.0  + 1
 O  8.0   PCC  1.20 -112.0   0.0  + 1

Das ist die Lösung:

 N  7.0    1.7007533889   0.0000000000   0.0000000000
 N  7.0   -1.7007533889   0.0000000000   0.0000000000
 O  8.0    2.5502379666  -2.1025481104   0.0000000000
 O  8.0   -2.5502379666   2.1025481104   0.0000000000
 O  8.0    2.5502379666   2.1025481104   0.0000000000
 O  8.0   -2.5502379666  -2.1025481104   0.0000000000

INTERNUCLEAR DISTANCES (ANGS.)
------------------------------
N N O O

 1  N   0.0000000     1.8000000 *    1.2000000 *    2.5096415 *
 2  N   1.8000000 *   0.0000000      2.5096415 *    1.2000000 *
 3  O   1.2000000 *   2.5096415 *    0.0000000      3.4980853
 4  O   2.5096415 *   1.2000000 *    3.4980853      0.0000000
 5  O   1.2000000 *   2.5096415 *    2.2252413 *    2.6990558 *
 6  O   2.5096415 *   1.2000000 *    2.6990558 *    2.2252413 *
 

Nach der Geometrieoptimierung:

 ***** EQUILIBRIUM GEOMETRY LOCATED *****

N2O4-Molekuel
COORDINATES OF SYMMETRY UNIQUE ATOMS (ANGS)
ATOM CHARGE         X                 Y                Z
------------------------------------------------------------
 N    7.0      1.4182942123      0.0000000002      0.0000000000
 O    8.0      0.6801493554      1.1710604612      0.0000000000
 O    8.0      0.6801493560     -1.1710604626      0.0000000000

COORDINATES OF ALL ATOMS ARE (ANGS)
ATOM CHARGE X Y Z
------------------------------------------------------------
N 7.0 -1.4182942123 -0.0000000002 0.0000000000
N 7.0 1.4182942123 0.0000000002 0.0000000000
O 8.0 -0.6801493554 -1.1710604612 0.0000000000
O 8.0 0.6801493554 1.1710604612 0.0000000000
O 8.0 -0.6801493560 1.1710604626 0.0000000000
O 8.0 0.6801493560 -1.1710604626 0.0000000000

INTERNUCLEAR DISTANCES (ANGS.)
------------------------------

N N O O

1 N 0.0000000 2.8365884 * 1.3842834 * 2.4030913 *
2 N 2.8365884 * 0.0000000 2.4030913 * 1.3842834 *
3 O 1.3842834 * 2.4030913 * 0.0000000 2.7084946 *
4 O 2.4030913 * 1.3842834 * 2.7084946 * 0.0000000
5 O 1.3842834 * 2.4030913 * 2.3421209 * 1.3602987 *
6 O 2.4030913 * 1.3842834 * 1.3602987 * 2.3421209 *


INTERNUCLEAR DISTANCES (ANGS.)
------------------------------

                      N                   N                         O                      O

1    N     0.0000000       1.8000000       * 1.2000000       * 1.7497713 *
2    N     1.8000000    * 0.0000000          1.7497713       * 1.2000000 *
3    O     1.2000000    * 1.7497713       * 0.0000000          2.4007080 *
4    O     1.7497713    * 1.2000000       * 2.4007080       * 0.0000000
5    O     1.2000000    * 1.7497713       * 2.2252413       * 0.9009442 *
6    O     1.7497713    * 1.2000000       * 0.9009442       * 2.2252413 *

* ... LESS THAN 3.000


Obige Logik funktioniert aber nicht, wenn im Koordinatenursprung ein Atom steht, z. B. NO2:
 

 N  7.0   LC   0.00    0.0   0.0  + O
 O  8.0   PCC  1.20   56.0   0.0  + 1
 

ATOM ATOMIC COORDINATES (BOHR)
CHARGE X Y Z
 N  7.0    0.0000000000    0.0000000000   0.0000000000
 O  8.0   -1.2680656342   -1.8799846148   0.0000000000
 O  8.0    1.2680656342   -1.8799846148   0.0000000000
 O  8.0   -1.2680656342    1.8799846148   0.0000000000
 O  8.0    1.2680656342    1.8799846148   0.0000000000
 

Man muss wie oben im ersten Beispiel (H2O) verfahren:

 N  7.0   LC    0.00    0.0   0.0  - O K

 O  8.0   PCC   1.20   56.0   0.0  + O K I

und erhält dann:

ATOM ATOMIC              COORDINATES (BOHR)
     CHARGE      X              Y              Z
 N   7.0    0.0000000000   0.0000000000   0.0000000000
 O   8.0   -1.8799846148   0.0000000000   1.2680656342
 O   8.0    1.8799846148   0.0000000000   1.2680656342

 

Bicyclopropylium

Bicyclopropylium-Molekuel
CNH 2

C  6.0   LC   0.75    0.0   0.0  + O
C  6.0   PCC  1.40  150.0   0.0  + 1
C  6.0   PCC  1.40 -150.0   0.0  + 1
H  1.0   LC   1.00    0.0   0.0  + 2
H  1.0   LC   1.00    0.0   0.0  + 3

ergibt:

ATOM ATOMIC COORDINATES (BOHR)
  CHARGE      X              Y               Z
C  6.0   1.4172944908   0.0000000000   0.0000000000
C  6.0  -1.4172944908   0.0000000000   0.0000000000
C  6.0   3.7084654870  -1.3228081914   0.0000000000
C  6.0  -3.7084654870   1.3228081914   0.0000000000
C  6.0   3.7084654870   1.3228081914   0.0000000000
C  6.0  -3.7084654870  -1.3228081914   0.0000000000
H  1.0   5.5475472041  -1.7573685974   0.0000000000
H  1.0  -5.5475472041   1.7573685974   0.0000000000
H  1.0   5.5475472041   1.7573685974   0.0000000000
H  1.0  -5.5475472041  -1.7573685974   0.0000000000

    Bild ist allerdings verdreht!

INTERNUCLEAR DISTANCES (ANGS.)
------------------------------

C C C C

1 C 0.0000000 1.5000000 * 1.4000000 * 2.8013045 *
2 C 1.5000000 * 0.0000000 2.8013045 * 1.4000000 *
3 C 1.4000000 * 2.8013045 * 0.0000000 4.1670869
4 C 2.8013045 * 1.4000000 * 4.1670869 0.0000000
5 C 1.4000000 * 2.8013045 * 1.4000000 * 3.9248711
6 C 2.8013045 * 1.4000000 * 3.9248711 1.4000000 *
7 H 2.3752533 * 3.8011493 1.0000000 * 5.1621576
8 H 3.8011493 2.3752533 * 5.1621576 1.0000000 *
9 H 2.3752533 * 3.8011493 1.8983905 * 4.9034665
10 H 3.8011493 2.3752533 * 4.9034665 1.8983905 *
 

 

$TRUDGE: non-gradient optimization

 

NPAR= number of parametres to be optimized

IEX= defines the parameters to be optimized. Pointers to the HINT internal coordinates which will be optimized. The pointers to the internal coordinates are defined as: (the number of atom in the input list)*10 + (the number of internal coordinate for that atom). For each atom, the HINT internal coordinates are numbered as 1, 2, and 3 for BOND, ALPHA, and BETA, respectively.

 

P= Defines the initial values of the parameters to be optimized. If omitted, the $DATA values are used.

 

-----------------------------------------------------------

 INTERNAL COORDINATES (ANGSTROMS/DEGREE)

  I   BOND     ALPHA      BETA    SIGN ICONX   IATCON INATOM

  1 0.0000000   0.00000   0.00000 -1.0     1501504503      1

  2 0.9600000  53.00000   0.00000  1.0     2501504502      3

 -----------------------------------------------------------

 ----- TRUDGE RESTART DATA AT NSTEP   0 --------

 $TRUDGE OPTIMIZE=GEOMETRY  NPAR= 2

         IEX(1)= 21, 22,

         P(1)=  0.960000, 53.000000,

 $END

TRUDGE ENERGY VALUE AT NSTEP=   0 IS      -76.0103894679

 -----------------------------------------------------------

 INTERNAL COORDINATES (ANGSTROMS/DEGREE)

  I   BOND     ALPHA      BETA    SIGN ICONX   IATCON INATOM

  1 0.0000000   0.00000   0.00000 -1.0     1501504503      1

  2 0.9600000  58.57406   0.00000  1.0     2501504502      3

 -----------------------------------------------------------

 ----- TRUDGE RESTART DATA AT NSTEP   1 --------

 $TRUDGE OPTIMIZE=GEOMETRY  NPAR= 2

         IEX(1)= 21, 22,

         P(1)=  0.960000, 58.574059,

 $END

TRUDGE ENERGY VALUE AT NSTEP=   1 IS      -76.0064779202

 LOOKS =  1 ALF =  0.1000 FUNC =   -76.006477920 AMIN =  0.0000 FMIN =   -76.010389468 ANEXT =  0.1000 FNEXT =   -76.006477920

 -----------------------------------------------------------

 INTERNAL COORDINATES (ANGSTROMS/DEGREE)

  I   BOND     ALPHA      BETA    SIGN ICONX   IATCON INATOM

  1 0.0000000   0.00000   0.00000 -1.0     1501504503      1

  2 0.9600000  47.95638   0.00000  1.0     2501504502      3

 -----------------------------------------------------------

 ----- TRUDGE RESTART DATA AT NSTEP   2 --------

 $TRUDGE OPTIMIZE=GEOMETRY  NPAR= 2

         IEX(1)= 21, 22,

         P(1)=  0.960000, 47.956383,

 $END

TRUDGE ENERGY VALUE AT NSTEP=   2 IS      -76.0078393859

 LOOKS =  2 ALF = -0.1000 FUNC =   -76.007839386 AMIN =  0.0000 FMIN =   -76.010389468 ANEXT = -0.1000 FNEXT =   -76.007839386

 -----------------------------------------------------------

 INTERNAL COORDINATES (ANGSTROMS/DEGREE)

  I   BOND     ALPHA      BETA    SIGN ICONX   IATCON INATOM

  1 0.0000000   0.00000   0.00000 -1.0     1501504503      1

  2 0.9600000  52.44458   0.00000  1.0     2501504502      3

 -----------------------------------------------------------

 ----- TRUDGE RESTART DATA AT NSTEP   3 --------

 $TRUDGE OPTIMIZE=GEOMETRY  NPAR= 2

         IEX(1)= 21, 22,

         P(1)=  0.960000, 52.444576,

 $END

 

TRUDGE ENERGY VALUE AT NSTEP=  16 IS      -76.0107457254

 

 NON-GRADIENT ENERGY MINIMIZATION  ...  CONVERGED

 

 CONJUGATE DIRECTION =     0

 PARAMETER =     1

 VALUE OF THE FUNCTION =       -76.0107457254

                  FNOT =       -76.0107457254

 $TRURST KSTART= 0  JSTART= 1  TOLF=  0.001000 TOLR=  0.050000

         FNOISE=  0.000500  FNOT= -76.010745725

         RNOT(1)=  0.007667 -0.006251

         CURV(1)=  1.901800  0.321617

         ALPH(1)=  0.012500  0.012500

            V(1)=  1.000000  0.000000

                   0.000000  1.000000

 $END

 -----------------------------------------------------------

 INTERNAL COORDINATES (ANGSTROMS/DEGREE)

  I   BOND     ALPHA      BETA    SIGN ICONX   IATCON INATOM

  1 0.0000000   0.00000   0.00000 -1.0     1501504503      1

  2 0.9472348  52.66973   0.00000  1.0     2501504502      3

 -----------------------------------------------------------

 

 COORDINATES OF ALL ATOMS ARE (ANGS)

   ATOM   CHARGE       X              Y              Z

 ------------------------------------------------------------

 O           8.0   0.0000000000   0.0000000000   0.0000000000

 H           1.0  -0.7531968076   0.0000000000   0.5744113322

 H           1.0   0.7531968076   0.0000000000   0.5744113322

 

          INTERNUCLEAR DISTANCES (ANGS.)

          ------------------------------

 

                    O              H              H        

 

  1  O               0.0000000      0.9472348 *    0.9472348 * 

  2  H               0.9472348 *    0.0000000      1.5063936 * 

  3  H               0.9472348 *    1.5063936 *    0.0000000   

 

 

Benzol

 

!

!    Benzol, HINT

!

 $CONTRL SCFTYP=RHF MULT=1 RUNTYP=TRUDGE COORD=HINT $END

 $TRUDGE OPTMIZ=GEOMETRY NPAR=2 IEX(1)=11,21 $END

 $SYSTEM TIMLIM=10 MEMORY=6000000 $END

 $BASIS  GBASIS=N31 NGAUSS=6 $END

 $GUESS  GUESS=HUCKEL $END

 $DATA

Benzene

Dnh  6

         

C   6.0    LC   1.390   0.0  0.0   +   O 

H   1.0    LC   2.470   0.0  0.0   +   O

 $END

 

Man erkennt, dass sich Linear Connection (LC) auf den Abstand zum Ursprung (O, Origin) bezieht. Das Vorzeichen spielt hier keine Rolle.