10.3 Second Derivatives

The second derivatives are computed during energy determination and they are stored in temporary array that are allocated dynamically. Once obtained, they can be written out, or diagonalized internally for small systems (up to 200 atoms).

The following is from comments in ENERGY;

     IF 'NSECD=.FALSE.' THEN THE SECOND DERIVATIVES OF THE ENERGY
     ARE RETURNED IN THE ARRAYS DD1,DD2,DD3,DD4,IDD4,JDD4,AND NDD4.
     TREIR USAGE CAN BE SUMMARIZED BY;
         ARRAY        SPACE      TYPE         DESCRIPTION
          DD1         6*NATOM    REAL*8       DIAGONAL ELEMENTS
          DD2         6*NNB      REAL*4       NONBONDED INTERACTIONS
          DD3         9*IBLO(NATOM) R*4       EXCLUDED INTERACTIONS
          DD4         9*NND4     REAL*4       EXTRA INTERACTIONS
          IDD4        NDD4       INTEGER*2    FIRST ATOM OF EXTRAS
          JDD4        NDD4       INTEGER*2    SECOND ATOM OF EXTRAS
      IF THE LOGICAL VARIABLE 'NSECD' IS SET TO .FALSE. SECOND
     DERIVATIVES WILL BE GENERATED. 'DIAGSD' IS SET TO .TRUE. IF ONLY
     THE DIAGONAL (DD1) SECOND DERIVATIVES ARE DESIRED.
     FOR DD1 EACH ATOM REQUIRES 6 SEQUENTIAL R*8 LOCATIONS. THE
     SEQUENCE IS XX,XY,YY,XZ,YZ,ZZ  WHERE EACH IS THE PARTIAL SECOND
     DERIVATIVE OF THE ENERGY WRT THE CORRESPONDING MOTIONS OF THE
     PARTICULAR ATOM. DD2 IS STORED IN THE SAME MANNER EXCEPT THAT
     EACH 6 R*4 LOCATIONS CORRESPOND TO A PARTICULAR NONBONDED
     INTERACTION. THE SEQUENCE OF NONBONDED INTERACTIONS IS DEFINED
     BY THE INTEGER ARRAYS 'INBLO' AND 'JNB'. SINCE THE NONBONDED
     INTERACTIONS ONLY INVOLVE RADIAL FORCES, ONLY 6 LOCATIONS ARE
     NEEDED.(IE  XY=YX). DD3 CONTAINS THE SECOND DERIVATIVES FOR ATOMS
     THAT INTERACT THROUGH THE EXCLUDED LIST. SINCE SYMMETRY IS NOT
     PRESENT FOR ANGLES,ETC... 9 LOCATIONS ARE NEEDED GIVEN BY THE
     SEQUENCE  XIXJ,YIXJ,ZIXJ,XIYJ,YIYJ,ZIYJ,XIZJ,YIZJ,ZIZJ. ATOM
     I IS ALWAYS LESS THAN ATOM J. THE SEQUENCE OF EXCLUDED
     INTERACTIONS IS DEFINED BY 'IBLO' AND 'INB'.
     DD4 CONTAINS ALL OTHER INTERACTIONS NOT CONTAINED ABOVE.
     THESE ARE USUALLY 1-4 DIHEDRAL INTERACTIONS AND HYDROGEN BONDS.
     INFORMATION IS STORED AS IT IS IN DD3. SINCE SOME CODE REFERENCES
     BOTH DD3 AND DD4, THE DIFFERENCE OF THEIR BASES IS NEEDED. THIS
     IS STORED IN IDD3AD (IE  IDD3AD=BASE(DD3)-BASE(DD4) ).
     CODE TO CONVERT THIS STORAGE SCHEME TO SIMPLE UPPER TRIANGULAR
     FORM CAN BE FOUND IN 'MINMIZ' UNDER THE NEWTON RAPHSON SECTION.