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SUBROUTINE DERI0 (E,N, SCALAR,DIAG,FRACT,NBO)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DIMENSION E(N), SCALAR(*), DIAG(*), NBO(3)
C
C COMPUTE THE DIAGONAL DOMINANT PART OF THE SUPER-MATRIX AND
C DEFINE THE SCALAR COEFFICIENTS APPLIED ON EACH ROW OF THE
C SUPER LINEAR SYSTEM IN ORDER TO REDUCE THE EIGENVALUE SPECTRUM OF
C THE ELECTRONIC HESSIAN,
C THUS SPEEDING CONVERGENCE OF RELAXATION PROCESS IN 'DERI2'.
C INPUT
C E(N) : EIGENVALUES OF FOCK MATRIX.
C N : NUMBER OF M.O.
C NBO(3) : OCCUPANCY BOUNDARIES.
C FRACT : PARTIAL OCCUPANCY OF 'OPEN' SHELLS.
C SCALAR(MINEAR) : SCALE APPLIED ON EACH COLUMN AND ROW OF THE
C SYMMETRIC SUPER SYSTEM.
C
SHIFT=2.36D0
C
C DOMINANT DIAGONAL PART OF THE SUPER-MATRIX.
C -------------------------------------------
NOPEN=NBO(1)+NBO(2)
CONST=1.D-3
L=1
IF(NBO(2).GT.0 .AND. NBO(1).GT.0) THEN
C OPEN-CLOSED
DO 10 J=1,NBO(1)
DO 10 I=NBO(1)+1,NOPEN
DIAG(L)=(E(I)-E(J))/(2.D0-FRACT+CONST)
10 L=L+1
ENDIF
IF(NBO(3).GT.0 .AND. NBO(1).GT.0) THEN
C VIRTUAL-CLOSED
DO 20 J=1,NBO(1)
DO 20 I=NOPEN+1,N
DIAG(L)=(E(I)-E(J))/2.D0
20 L=L+1
ENDIF
IF(NBO(3).NE.0 .AND. NBO(2).NE.0) THEN
C VIRTUAL-OPEN
DO 30 J=NBO(1)+1,NOPEN
DO 30 I=NOPEN+1,N
DIAG(L)=(E(I)-E(J))/(FRACT+CONST)
30 L=L+1
ENDIF
C
C TAKE SCALE FACTORS AS (SHIFT-DIAG)**(-0.5) .
C ------------------------------------------
DO 40 I=1,L-1
40 SCALAR(I)=SQRT(1.D0/MAX(0.3D0*DIAG(I),DIAG(I)-SHIFT))
RETURN
END
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