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RSPTFM_Util.f90
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RSPTFM_Util.f90
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!-----------------------------------------------------------------------------------------------
! Subroutine: 'RQSORT' FIRST: 01 Mar 2010 LAST EDIT: 14 Mar 2010
!
! PURPOSE:
! Quick sort of REAL*16 values using "heap sort" algorithm in
!
! ALGORITHM:
! The index array INDEX is produced such that ARRAY(INDEX(i)) gives
! the values of original ARRAY sorted in ascending order.
!
! REFERENCE(S):
! [1] William H. Press, Brian P. Flannery, Saul A. Teukolski,
! William T. Vetterling / Numerical Recipes: The Art of Scientific
! Computing / Cambridge University Press, Cambridge, 1986, 818 p.
! See Page 232.
!
! CALLED: COMPAC (CPTserv.for);
!
! INPUT:
! LENARR -- The dimension of input REAL*16 array;
! ARRAY -- The array of REAL*16 values to be sorted.
!
! OUTPUT:
! INDEX -- The integer array containing indices of sorted values.
!
! NOTE(S):
! The algorithm was tested using internal check, see below.
!-----------------------------------------------------------------------------------------------
SUBROUTINE RQSORT (LENARR,ARRAY,INDEX)
IMPLICIT REAL*16 (A-H,O-Z), INTEGER*4 (I-N)
DIMENSION ARRAY(LENARR)
DIMENSION INDEX(LENARR)
DO 100 J = 1, LENARR
INDEX(J) = J
100 CONTINUE
IF (LENARR .LE. 1) RETURN
L = LENARR / 2 + 1
IR = LENARR
200 CONTINUE
IF (L .GT. 1) THEN
L = L - 1
IND = INDEX(L)
AUX = ARRAY(IND)
ELSE
IND = INDEX(IR)
AUX = ARRAY(IND)
INDEX(IR) = INDEX(1)
IR = IR - 1
IF (IR .EQ. 1) THEN
INDEX(1) = IND
GO TO 400
ENDIF
ENDIF
I = L
J = L + L
300 CONTINUE
IF (J .LE. IR) THEN
IF (J .LT. IR) THEN
IF (ARRAY(INDEX(J)) .LT. ARRAY(INDEX(J+1))) J = J + 1
ENDIF
IF (AUX .LT. ARRAY(INDEX(J))) THEN
INDEX(I) = INDEX(J)
I = J
J = J + J
ELSE
J = IR + 1
ENDIF
GO TO 300
ENDIF
INDEX(I) = IND
GO TO 200
400 CONTINUE
RETURN
END
!-----------------------------------------------------------------------------------------------
! COPYRIGHT (c) 1980 AEA Technology
! Original date 1 December 1993
! Toolpack tool decs employed.
! Arg dimensions changed to *.
! 1/4/99 Size of MARK increased to 100.
! 13/3/02 Cosmetic changes applied to reduce single/double differences
!
! 12th July 2004 Version 1.0.0. Version numbering added.
!-----------------------------------------------------------------------------------------------
SUBROUTINE KB07AD(COUNT,N,INDEX)
!
! KB07AD HANDLES DOUBLE PRECISION VARIABLES
! THE WORK-SPACE 'MARK' OF LENGTH 100 PERMITS UP TO 2**50 NUMBERS
! TO BE SORTED.
! .. Scalar Arguments ..
INTEGER*4 N
! ..
! .. Array Arguments ..
REAL*16 COUNT(*)
INTEGER*4 INDEX(*)
! ..
! .. Local Scalars ..
REAL*16 AV,X
INTEGER*4 I,IF,IFK,IFKA,INT,INTEST,IP,IS,IS1,IY,J,K,K1,LA,LNGTH,M,MLOOP
! ..
! .. Local Arrays ..
INTEGER*4 MARK(100)
! ..
! .. Executable Statements ..
! SET INDEX ARRAY TO ORIGINAL ORDER .
DO 10 I = 1,N
INDEX(I) = I
10 CONTINUE
! CHECK THAT A TRIVIAL CASE HAS NOT BEEN ENTERED .
IF (N.EQ.1) GO TO 200
IF (N.GE.1) GO TO 30
WRITE (6,FMT=20)
20 FORMAT (/,/,/,20X,' ***KB07AD***NO NUMBERS TO BE SORTED ** ', &
& 'RETURN TO CALLING PROGRAM')
GO TO 200
! 'M' IS THE LENGTH OF SEGMENT WHICH IS SHORT ENOUGH TO ENTER
! THE FINAL SORTING ROUTINE. IT MAY BE EASILY CHANGED.
30 M = 12
! SET UP INITIAL VALUES.
LA = 2
IS = 1
IF = N
DO 190 MLOOP = 1,N
! IF SEGMENT IS SHORT ENOUGH SORT WITH FINAL SORTING ROUTINE .
IFKA = IF - IS
IF ((IFKA+1).GT.M) GO TO 70
!********* FINAL SORTING ***
! ( A SIMPLE BUBBLE SORT )
IS1 = IS + 1
DO 60 J = IS1,IF
I = J
40 IF (COUNT(I-1).LT.COUNT(I)) GO TO 60
IF (COUNT(I-1).GT.COUNT(I)) GO TO 50
IF (INDEX(I-1).LT.INDEX(I)) GO TO 60
50 AV = COUNT(I-1)
COUNT(I-1) = COUNT(I)
COUNT(I) = AV
INT = INDEX(I-1)
INDEX(I-1) = INDEX(I)
INDEX(I) = INT
I = I - 1
IF (I.GT.IS) GO TO 40
60 CONTINUE
LA = LA - 2
GO TO 170
! ******* QUICKSORT ********
! SELECT THE NUMBER IN THE CENTRAL POSITION IN THE SEGMENT AS
! THE TEST NUMBER.REPLACE IT WITH THE NUMBER FROM THE SEGMENT'S
! HIGHEST ADDRESS.
70 IY = (IS+IF)/2
X = COUNT(IY)
INTEST = INDEX(IY)
COUNT(IY) = COUNT(IF)
INDEX(IY) = INDEX(IF)
! THE MARKERS 'I' AND 'IFK' ARE USED FOR THE BEGINNING AND END
! OF THE SECTION NOT SO FAR TESTED AGAINST THE PRESENT VALUE
! OF X .
K = 1
IFK = IF
! WE ALTERNATE BETWEEN THE OUTER LOOP THAT INCREASES I AND THE
! INNER LOOP THAT REDUCES IFK, MOVING NUMBERS AND INDICES AS
! NECESSARY, UNTIL THEY MEET .
DO 110 I = IS,IF
IF (X.GT.COUNT(I)) GO TO 110
IF (X.LT.COUNT(I)) GO TO 80
IF (INTEST.GT.INDEX(I)) GO TO 110
80 IF (I.GE.IFK) GO TO 120
COUNT(IFK) = COUNT(I)
INDEX(IFK) = INDEX(I)
K1 = K
DO 100 K = K1,IFKA
IFK = IF - K
IF (COUNT(IFK).GT.X) GO TO 100
IF (COUNT(IFK).LT.X) GO TO 90
IF (INTEST.LE.INDEX(IFK)) GO TO 100
90 IF (I.GE.IFK) GO TO 130
COUNT(I) = COUNT(IFK)
INDEX(I) = INDEX(IFK)
GO TO 110
100 CONTINUE
GO TO 120
110 CONTINUE
! RETURN THE TEST NUMBER TO THE POSITION MARKED BY THE MARKER
! WHICH DID NOT MOVE LAST. IT DIVIDES THE INITIAL SEGMENT INTO
! 2 PARTS. ANY ELEMENT IN THE FIRST PART IS LESS THAN OR EQUAL
! TO ANY ELEMENT IN THE SECOND PART, AND THEY MAY NOW BE SORTED
! INDEPENDENTLY .
120 COUNT(IFK) = X
INDEX(IFK) = INTEST
IP = IFK
GO TO 140
130 COUNT(I) = X
INDEX(I) = INTEST
IP = I
! STORE THE LONGER SUBDIVISION IN WORKSPACE.
140 IF ((IP-IS).GT. (IF-IP)) GO TO 150
MARK(LA) = IF
MARK(LA-1) = IP + 1
IF = IP - 1
GO TO 160
150 MARK(LA) = IP - 1
MARK(LA-1) = IS
IS = IP + 1
! FIND THE LENGTH OF THE SHORTER SUBDIVISION.
160 LNGTH = IF - IS
IF (LNGTH.LE.0) GO TO 180
! IF IT CONTAINS MORE THAN ONE ELEMENT SUPPLY IT WITH WORKSPACE .
LA = LA + 2
GO TO 190
170 IF (LA.LE.0) GO TO 200
! OBTAIN THE ADDRESS OF THE SHORTEST SEGMENT AWAITING QUICKSORT
180 IF = MARK(LA)
IS = MARK(LA-1)
190 CONTINUE
200 RETURN
END
!-----------------------------------------------------------------------------------------------
! Subroutine: 'PSTATE' FIRST: 13 Apr 2012 LAST EDIT: 14 Jun 2020
!
! PURPOSE:
! For a given polyad formula and polyad number value, find all
! possible vibrational states (or basis functions, what is the same)
! Return total number of found states (NSIZE) and write found states
! in a file LUN = LUNPOL.
! It is very important to remember that in order to obtain all
! possible basis functions or vibrational states, it is necessary
! to set MAXEXC = NPOLY, because the minimum polyad coefficient = 1.
! MAXEXC is introduced for the reason that for bigger molecules the
! search of states can take very long time and produce huge numbers.
! The basis functions are grouped by the symmetry.
!
! THEORY: or ALGORITHM:
! N(t) >= 0, N(t) = C1 * v(1) + C2 * v(2) + ... C(NQ) * v(NQ).
! C(i) are non-negative integers.
! NOTE: Zeros in C(i) mean that such modes produce infinite blocks
!
! REFERENCE(S):
! [1] William F. Polik and J. Ruud van Ommen "The Multiresonant
! Hamiltonian Model and Polyad Quantum Numbers for Highly Excited
! Vibrational States" ACS Symp. Ser, 1997, 678, p.51-68.
!
! CALLED: RSPTFM_Proc ().
!
! INPUT:
! NQ -- The number of vibrational degrees of freedom;
! ISYMQ -- Index of Symmetry Species given the index of normal mode
! in spectroscopic order;
! KPOLY -- Polyad formula, i.e. coefficients for vibrational modes;
! NPOLY -- Particular polyad number, for which the set of all
! possible quantum number sets is sought;
! MAXQUA -- Maximum excitation of vibrational modes;
! IMPORTANT: To obtain ALL possible basis functions or
! vibrational states, it is necessary to set MAXQUA=NPOLY;
! MODRUN --
! LIMIT -- Printout truncation.
!
! OUTPUT:
! NSIZE -- The size of polyad block;
! MAXTOT -- Maximum total excitation in generated states;
! (-) NSTSYM -- The number of states per symmetry species;
! <FILE> -- LUN = NSCR, created states are saved to <FILE>.
!
! FILE I/O:
! Created basis set is saved to a file with LUN = NSCR.
!
! NOTES:
! 1. 08-06-2020: Remastered from POLBLK (ANCO/Diag.for).
!-----------------------------------------------------------------------------------------------
SUBROUTINE PSTATE (NQ,WAVNUM,KPOLY,NPOLY,MAXQUA,MODRUN, & !ISYMQ,
& NSIZE,LQUANT,MAXTOT,LIMIT,IOUT)
IMPLICIT REAL*8 (A-H,O-Z), INTEGER*4 (I-N)
COMMON /IOLUN/ LOUT,NLOG,NINP,NOUT,NAUX,NSCR
! CHARACTER* 4 LSYMSP
! COMMON /SYMINF/ NSYMSP,LSYMSP(0:12),MSYMSP(0:12,0:12)
REAL*16 WAVNUM(NQ)
REAL*16 EZERO
INTEGER*4 KPOLY(NQ),LQUANT(NQ,0:*) !ISYMQ(NQ),
REAL*16, ALLOCATABLE :: ENERGY(:)
INTEGER*4, ALLOCATABLE :: IORDER(:)
INTEGER*4 IQUANT(NQ)
INTEGER*4 IUPPER(NQ) ! DO-loop emulation
INTEGER*4 IX(NQ),IQ(NQ)
CHARACTER*80 FILE ! Vibrational states for N(t) are saved here
CHARACTER*48, ALLOCATABLE :: XSTID(:) ! Extended state ID
LOGICAL ZERPOI,UPDATE
!---- External function
! INTEGER*4 ISYMSTAT
IF (MAXQUA .LT. NPOLY .AND. MODRUN .EQ. 0) &
& WRITE (NOUT,1000)
1000 FORMAT (/'Polyad block may be incomplete as maximum excitation ', &
& 'is less than N(T).')
!-----------------------------------------------------------------------------------------------
! Initialize loop counters IQUANT and upper limits for them IUPPER
!-----------------------------------------------------------------------------------------------
IQUANT = 0 ! Array: NQ quantum numbers
DO 100 I = 1, NQ
DO 100 K = 0, MAXQUA
IF (K * KPOLY(I) .LE. NPOLY) IUPPER(I) = K
100 CONTINUE
ZERPOI = .TRUE. ! To skip zero-point state
UPDATE = .FALSE. ! Flag for full update of IPOLY
NSIZE = 0 ! The size of polyad block of states for N(T) = NPOLY
IPOLY = 0 ! Initialize polyad number for the zero-point state
!---- PSTATE () is called in a loop over NPOLY, rewind every time
REWIND (NSCR)
!=========================== NESTED DO-LOOPS ===========================
! DO 300 v(m) = 0, MAXQUA
! ...
! DO 300 v(2) = 0, MAXQUA
! DO 300 v(1) = 0, MAXQUA
!=========================== EMULATION OF DO ===========================
200 CONTINUE ! GO TO
IF (UPDATE) THEN
IPOLY = 0
DO 210 K = 1, NQ
IPOLY = IPOLY + KPOLY(K) * IQUANT(K)
IF (IPOLY .GT. NPOLY) GO TO 220
210 CONTINUE
UPDATE = .FALSE.
ENDIF
IF (IPOLY .EQ. 0 .AND. ZERPOI) THEN
ZERPOI = .FALSE.
GO TO 220
ENDIF
!---- Save the set of quantum numbers to a dedicated file NSCR
IF (IPOLY .EQ. NPOLY) THEN ! NPOLY -- The polyad number N(T)
WRITE (NSCR) IQUANT
NSIZE = NSIZE + 1
ENDIF
!---- Update counters
220 CONTINUE
DO 230 I = 1, NQ
IF (IQUANT(I) .LT. IUPPER(I)) THEN
IQUANT(I) = IQUANT(I) + 1
IPOLY = IPOLY + KPOLY(I)
GO TO 200
ENDIF
IQUANT(I) = 0
UPDATE = .TRUE.
230 CONTINUE
300 CONTINUE ! END-DO
!---- First time only NSIZE is returned
IF (MODRUN .EQ. 0) RETURN
!-----------------------------------------------------------------------------------------------
! Order Vibrational states by energy in ascending order
!-----------------------------------------------------------------------------------------------
IF (NSIZE .EQ. 0) GO TO 900
ALLOCATE (ENERGY(NSIZE),IORDER(NSIZE))
REWIND (NSCR)
DO 320 K = 1, NSIZE
READ (NSCR) IQUANT
DO 310 I = 1, NQ
310 LQUANT(I,K) = IQUANT(I)
CALL ENERHAOS (NQ,WAVNUM,IQUANT, EZERO, ENERGY(K))
ENERGY(K) = ENERGY(K) - EZERO
320 CONTINUE
! CALL RQSORT (NSIZE,ENERGY,IORDER)
CALL KB07AD (ENERGY,NSIZE,IORDER)
REWIND (NSCR)
DO 340 K = 1, NSIZE
L = IORDER(K)
DO 330 I = 1, NQ
330 IQUANT(I) = LQUANT(I,L)
WRITE (NSCR) IQUANT
340 CONTINUE
DEALLOCATE (ENERGY,IORDER)
REWIND (NSCR)
K = 0
IQUANT = 0
DO 420 N = 1, NSIZE
READ (NSCR) IQUANT
K = K + 1
L = 0
DO 410 I = 1, NQ
L = L + IQUANT(I)
LQUANT(I,K) = IQUANT(I)
410 CONTINUE
420 CONTINUE
!-----------------------------------------------------------------------------------------------
! Order Vibrational states by symmetry, write to temporary array
!-----------------------------------------------------------------------------------------------
! K = 0
! MAXTOT = 0
! DO 430 M = 1, NSYMSP
! REWIND (NSCR)
!
! DO 420 N = 1, NSIZE
! READ (NSCR) IQUANT
!---- Define the symmetry type of the vibrational state
! ITOT = ISYMSTAT (NQ,IQUANT,ISYMQ)
! IF (ITOT .NE. M) CYCLE
!
! K = K + 1
! L = 0
! DO 410 I = 1, NQ
! L = L + IQUANT(I)
! LQUANT(I,K) = IQUANT(I)
! 410 CONTINUE
!
! MAXTOT = MAX (MAXTOT, L)
! 420 CONTINUE
! 430 CONTINUE
!-----------------------------------------------------------------------------------------------
! Print generated vibrational states
!-----------------------------------------------------------------------------------------------
IF (IOUT .EQ. 0) GO TO 900
IF (NSIZE .GT. 0) WRITE (NOUT,1100) NSIZE
ALLOCATE (XSTID(NSIZE))
DO 520 K = 1, NSIZE
IF (K .GT. LIMIT) THEN
WRITE (NOUT,1200) LIMIT
EXIT
ENDIF
N = 0
DO 510 I = 1, NQ
IF (LQUANT(I,K) .EQ. 0) CYCLE
N = N + 1
IX(N) = I
IQ(N) = LQUANT(I,K)
510 CONTINUE
N = MIN (6,N)
!---- Char*8 per mode: " 1*( 1), 1*( 2), 1*( 3)";
!---- If N > 6, extra states printout is simply cut
WRITE (FMT = "(6(I1,'*(',I2,')':', '))", &
& UNIT = XSTID(K), IOSTAT = IOS) (IQ(I),IX(I),I=1,N)
IF (N .GT. 6) XSTID(48:48) = '>'
WRITE (NOUT,1120) K,XSTID(K)
520 CONTINUE
DEALLOCATE (XSTID)
900 RETURN
1100 FORMAT (/'Size of the block = ',I6, &
& '. The list of states satisfying this polyad number:')
1120 FORMAT (I4,': ',A48)
1200 FORMAT ('...'/'Output truncated, exceeding the limit of',I6)
END
!-----------------------------------------------------------------------------------------------
SUBROUTINE ENERHAOS (NQ,W,IQUANT,EZERO,ESTATE)
IMPLICIT REAL*16 (A-H,O-Z), INTEGER*4 (I-N)
REAL*16 W(NQ)
REAL*16 EZERO, ESTATE
INTEGER*4 IQUANT(NQ)
EZERO = 0.0D0
SM = 0.0D0
DO 100 R = 1, NQ
SM = SM + W(R) / 2.0D0
100 CONTINUE
EZERO = SM ! Includes ground state energy
ESTATE = 0.0D0
DO 110 I = 1, NQ
ESTATE = ESTATE + W(I) * (REAL (IQUANT(I)) + 0.5D0)
110 CONTINUE
RETURN
END
!-----------------------------------------------------------------------------------------------
! Calculate Harmonic Energy of molecule with Degenerate modes.
! NQEX, NQIN - Number of External and Internal Quantum Number (V, L)
! W(NQEX) - Harmonic Frequencies for External Q.N.
! IQUANT(NQEX) - External Q.N. of Reference State
!-----------------------------------------------------------------------------------------------
SUBROUTINE ENERHARMDEG (NQEX, NQIN, W,IQUANT,EZERO,ESTATE)
IMPLICIT REAL*16 (A-H,O-Z), INTEGER*4 (I-N)
REAL*16 W(NQEX)
REAL*16 EZERO, ESTATE
INTEGER*4 IQUANT(NQEX), NQEX, NQIN
EZERO = 0.0D0
SM = 0.0D0
DO 100 R = 1, NQEX - NQIN
SM = SM + W(R) / 2.0D0
100 CONTINUE
DO 110 R = 1, NQIN
SM = SM + W(NQEX - NQIN + R)
110 CONTINUE
EZERO = SM ! Includes ground state energy
ESTATE = 0.0D0
DO 120 I = 1, NQEX - NQIN
ESTATE = ESTATE + W(I) * (REAL (IQUANT(I)) + 0.5D0)
120 CONTINUE
DO 130 I = 1, NQIN
ESTATE = ESTATE + W(NQEX - NQIN + I) * (REAL (IQUANT(NQEX - NQIN + I)) + 1.0D0)
130 CONTINUE
RETURN
END
!-----------------------------------------------------------------------------------------------
!
! Calculate harmonic anharmonic frequency using constants x(r,s) and
! search for a proper eigenvector.
! E/(hc)[1/Cm] = Y(0,0) + SUM[r=1,M] Omega(r)*(v(r)+1/2) +
! + SUM[r=1,M;s=1,r] X(r,s)*(v(r)+1/2)*(v(s)+1/2).
!
! NOTE(s):
! 1. Similar routine DPENER () exists.
!-----------------------------------------------------------------------------------------------
! SUBROUTINE VIBRENER (MDIM,NQ,IQUANT,WAVNUM,XCON, &
! & EZERO,EHARM,EGROU,EVPT2)
! IMPLICIT REAL*16 (A-H,O-Z), INTEGER*4 (I-N)
! INTEGER*4 IQUANT(NQ)
! REAL*16 WAVNUM(NQ),XCON(MDIM,NQ)
! INTEGER*4 R,S
! REAL*16 QUANT(NQ)
!
! SM = 0.0D0
! DO 100 R = 1, NQ
! SM = SM + WAVNUM(R) / 2.0D0
! 100 CONTINUE
! EZERO = SM ! Includes ground state energy
!
! SM = 0.0D0
! DO 110 R = 1, NQ
! QUANT(R) = REAL (IQUANT(R)) + 0.5D0
! SM = SM + WAVNUM(R) * QUANT(R)
! 110 CONTINUE
! EHARM = SM ! Includes ground state energy
!
! SM = 0.0D0
! DO 200 R = 1, NQ
! SM = SM + WAVNUM(R) * 0.5D0
! DO 200 S = 1, R
! SM = SM + XCON(R,S) * 0.25D0
! 200 CONTINUE
! EGROU = SM ! Identical for all states
!
! SM = 0.0D0
! DO 210 R = 1, NQ
! SM = SM + WAVNUM(R) * QUANT(R)
! DO 210 S = 1, R
! SM = SM + XCON(R,S) * QUANT(R) * QUANT(S)
! 210 CONTINUE
! EVPT2 = SM ! Includes ground state energy
!
! RETURN
! END
!-----------------------------------------------------------------------------------------------
! Function: 'LADDCOEF' FIRST: 07 Apr 2018 LAST EDIT: 21 Apr 2020
!
! PURPOSE:
! Initialize CLADD(m,n,ket) for fast evaluation of matrix elements
! for the system of H.O. orthonormal basis functions:
! CLADD(m,n,ket) = Coefficient ( a(+)^m * a(-)^n |ket> )
!
! THEORY:
! Matrix element for harmonic oscillator wave function basis set:
!
! a^m * b^n | ket > = COEFLAD(m,n,ket) | ket(m-n) >
!
! when preliminary conditions are obeyed:
! (1) bra - ket = m - n,
! (2) ket >= n.
!
! using the rules for creation/annihilation operators:
!
! a | psi(v) > = (v + 1)^(1/2) | psi(v+1) >,
! a* | psi(v) > = (v)^(1/2) | psi(v-1) >.
!
! CALLED: MAINVSCF ().
!
! OUTPUT:
! COEFLAD -- Array of coefficients, /COMMON/.
!
! NOTE(S):
! 1.
!-----------------------------------------------------------------------------------------------
SUBROUTINE LADDCOEF
IMPLICIT REAL*16 (A-H,O-Z), INTEGER*4 (I-N)
COMMON /LADCOE/ COEFLADD
REAL*16 COEFLADD(0:63,0:51) ! COEFLADD(0:7,0:7,0:31)
REAL*16 COEF,ARGU
DO 200 IRIS = 0, 7
DO 200 ILOW = 0, 7
IND = 8 * IRIS + ILOW
DO 200 KET = 0, 51
IF (KET .LT. ILOW) THEN
COEFLADD(IND,KET) = 0.0D0
CYCLE
ENDIF
COEF = 1.0D0
IQUANT = KET
!---- Lowering: a(-) | psi(v) > = (v)^(1/2) | psi(v-1) >
DO 110 I = 1, ILOW
ARGU = REAL (IQUANT)
COEF = COEF * SQRT (ARGU)
IQUANT = IQUANT - 1
110 CONTINUE
!---- Rising: a(+) | psi(v) > = (v + 1)^(1/2) | psi(v+1) >
DO 120 I = 1, IRIS
ARGU = REAL (IQUANT + 1)
COEF = COEF * SQRT (ARGU)
IQUANT = IQUANT + 1
120 CONTINUE
COEFLADD(IND,KET) = COEF
200 CONTINUE
RETURN
END
!-----------------------------------------------------------------------------------------------
! Subroutine: 'HOSELE' FIRST: 09 Feb 2020 LAST EDIT: 10 Feb 2020
!
! PURPOSE:
! Evaluate matrix element of the primitive Hamiltonian term in
! the VSCF wave functions.
!
! THEORY:
!
! tot M (bra) M (ket)
! E = SUM < PRO Psi | H | PRO Psi > .
! s j=1 j s k=1 k
!
!
! CALLED: MAINRSPT (*.for)
!
! INPUT:
! NQ -- The number of vibrational degrees of freedom;
! NTHAM -- The number of terms in the Hamiltonian operator
! polynomial;
! HCOEF -- 1D Array of numerical coefficients of the polynomial;
! LADHAM -- Array [NQ,NOP,NTHAM] of powers of individual operators;
! IMPORTANT: Quantum numbers are increased by 1:--
! IOPBRA -- Array [1..NQ] of quantum number of < bra_j | operator;
! IOPKET -- Array [1..NQ] of quantum number of < ket_j | operator;
!
! OUTPUT:
! HOSELE -- The value of the matrix element SUM(s) <bra| H(s) |ket>.
!
! NOTE(S):
! 1.
!-----------------------------------------------------------------------------------------------
FUNCTION HOSELE (NQ,NTHAM,HCOEF,LADHAM,IOPBRA,IOPKET)
IMPLICIT REAL*16 (A-H,O-Z), INTEGER*4 (I-N)
COMMON /IOLUN/ LOUT,NLOG,NINP,NOUT,NAUX,NSCR
COMMON /LADCOE/ COEFLADD
DIMENSION COEFLADD(0:63,0:51) ! COEFLADD(0:7,0:7,0:31)
INTEGER*1 LADHAM(NQ,2,NTHAM) ! 2 >> NOPER
DIMENSION HCOEF(NTHAM),IOPBRA(NQ),IOPKET(NQ)
INTEGER*4 S,Q
DATA IOPRIS /1/, IOPLOW /2/
DATA ZERO /0.0D0/, ONE /1.0D0/
ELEMAT = ZERO
DO 200 S = 1, NTHAM
PROD = ONE
DO 100 Q = 1, NQ
LADRIS = LADHAM(Q,IOPRIS,S)
LADLOW = LADHAM(Q,IOPLOW,S)
LADIND = 8 * LADRIS + LADLOW
IF (IOPKET(Q) .LT. LADLOW) THEN
PROD = ZERO
EXIT
ENDIF
IF (LADRIS - LADLOW .EQ. IOPBRA(Q) - IOPKET(Q)) THEN
PROD = PROD * COEFLADD(LADIND, IOPKET(Q) - 1)
ELSE
PROD = ZERO
EXIT
ENDIF
100 CONTINUE
IF (PROD .NE. ZERO) ELEMAT = ELEMAT + PROD * HCOEF(S)
200 CONTINUE
HOSELE = ELEMAT
RETURN
END
!-----------------------------------------------------------------------------------------------
! Subroutine: 'LZELE' FIRST: 20 Jul 2021 LAST EDIT: 20 Jul 2021
!
! PURPOSE:
! Evaluate matrix element of the Angular Momentum of Z Component term in
! the Harmonic oscillator wave functions.
!
! THEORY:
!
! tot M (bra) M (ket)
! L_z = SUM < PRO Psi | L_z | PRO Psi > .
! s j=1 j s k=1 k
!
!
! CALLED: RSPT_L (*.f90)
!
! INPUT:
! NQ -- The number of vibrational degrees of freedom;
! NTLZ -- The number of terms in the Lz operator
! polynomial;
! LCOEF -- 1D Array of numerical coefficients of the polynomial, COMPLEX*8
! LADLZ -- Array [NQ,NOP,NTLZ] of powers of individual operators;
! IMPORTANT: Quantum numbers are increased by 1:--
! IOPBRA -- Array [1..NQ] of quantum number of < bra_j | operator;
! IOPKET -- Array [1..NQ] of quantum number of < ket_j | operator;
!
! OUTPUT:
! LZELE -- The value of the matrix element SUM(s) <bra| H(s) |ket>.
!
! NOTE(S):
! 1.
!-----------------------------------------------------------------------------------------------
FUNCTION LZELE (NQ,NTLZ,LCOEF,LADLZ,IOPBRA,IOPKET)
IMPLICIT REAL*16 (A-H,O-Z), INTEGER*4 (I-N)
COMMON /IOLUN/ LOUT,NLOG,NINP,NOUT,NAUX,NSCR
COMMON /LADCOE/ COEFLADD
DIMENSION COEFLADD(0:63,0:51) ! COEFLADD(0:7,0:7,0:31)
INTEGER*1 LADLZ(NQ,2,NTLZ) ! 2 >> NOPER
DIMENSION IOPBRA(NQ),IOPKET(NQ)
COMPLEX*16 LZELE
COMPLEX*16 LCOEF(NTLZ)
COMPLEX*16 ELEMAT, PROD
INTEGER*4 S,Q
DATA IOPRIS /1/, IOPLOW /2/
DATA ZERO /0.0D0/, ONE /1.0D0/
ELEMAT = (0.0D0, 0.0D0)
DO S = 1, NTLZ
PROD = ( 1.0D0, 0.0D0)
DO Q = 1, NQ
LADRIS = LADLZ(Q,IOPRIS,S)
LADLOW = LADLZ(Q,IOPLOW,S)
LADIND = 8 * LADRIS + LADLOW
IF (IOPKET(Q) .LT. LADLOW) THEN
PROD = ZERO
EXIT
ENDIF
IF (LADRIS - LADLOW .EQ. IOPBRA(Q) - IOPKET(Q)) THEN
PROD = PROD * CMPLX(COEFLADD(LADIND, IOPKET(Q) - 1), 0.0D0, KIND = 8)
ELSE
PROD = ZERO
EXIT
ENDIF
ENDDO
IF (PROD .NE. ZERO) ELEMAT = ELEMAT + PROD * LCOEF(S)
ENDDO
LZELE = ELEMAT
RETURN
END
!-----------------------------------------------------------------------------------------------
! Subroutine: 'HAOSMP' FIRST: 09 Feb 2020 LAST EDIT: 27 Apr 2020
!
! PURPOSE:
! Evaluate matrix element of the primitive Hamiltonian term in
! the VSCF wave functions.
!
! THEORY:
!
! tot M (bra) M (ket)
! E = SUM < PRO Psi | H | PRO Psi > .
! s j=1 j s k=1 k
!
! CALLED: MAINRSPT (*.for)
!
! INPUT:
! NQ -- The number of vibrational degrees of freedom;
! NTHAM -- The number of terms in the Hamiltonian operator
! polynomial;
! HCOEF -- 1D Array of numerical coefficients of the polynomial;
! LADHAM -- Array [NQ,NOP,NTHAM] of powers of individual operators;
! IMPORTANT: Quantum numbers are increased by 1:--
! IOPBRA -- Array [1..NQ] of quantum number of < bra_j | operator;
! IOPKET -- Array [1..NQ] of quantum number of < ket_j | operator;
!
! OUTPUT:
! HOSELE -- The value of the matrix element SUM(s) <bra| H(s) |ket>.
!
! NOTE(S):
! (1) 27-Apr-2020
!
!-----------------------------------------------------------------------------------------------
FUNCTION HAOSMP (NQ,NTHAM,HCOEF,LADHAM,IOPBRA,IOPKET)
IMPLICIT REAL*16 (A-H,O-Z), INTEGER*4 (I-N)
INTEGER*1 LADHAM(NQ,2,NTHAM) ! 2 >> NOPER
INTEGER*4 IOPBRA(NQ),IOPKET(NQ)
COMMON /LADCOE/ COEFLADD
DIMENSION COEFLADD(0:63,0:51) ! COEFLADD(0:7,0:7,0:31)
DIMENSION HCOEF(NTHAM)
!---- Local variables must be saved
INTEGER*4 S,Q
DATA IOPRIS /1/, IOPLOW /2/, NDIM /8/
ELEMAT = 0.0D0
DO S = 1, NTHAM
PROD = 1
DO Q = 1, NQ
LADRIS = LADHAM(Q,IOPRIS,S)
LADLOW = LADHAM(Q,IOPLOW,S)
LADIND = NDIM * LADRIS + LADLOW
IF (IOPKET(Q) .LT. LADLOW) THEN
PROD = 0
EXIT
ENDIF
IF (LADRIS - LADLOW .EQ. IOPBRA(Q) - IOPKET(Q)) THEN
PROD = PROD * COEFLADD(LADIND, IOPKET(Q) - 1)
ELSE
PROD = 0
EXIT
ENDIF
ENDDO
IF (PROD .NE. 0) ELEMAT = ELEMAT + PROD * HCOEF(S)
ENDDO
HAOSMP = ELEMAT
RETURN
END
!-----------------------------------------------------------------------------------------------
SUBROUTINE MLOOPASRCSV(NVARS, VMAXS, NTOT, ARRAY2)
IMPLICIT REAL*16 (A-H,O-Z), INTEGER*4 (I-N)
INTEGER*4 NVARS ! Number of Loops
INTEGER*4 VMAXS(NVARS) ! Array of Maxium Values for each Loop (from 1 to VMAXS(NVARS)
INTEGER*4 NTOT ! Total Number of Cycle ( PRODUCT_I ( VMAXS(I) )
INTEGER*4 ARRAY2(NTOT,NVARS) ! Target Array
INTEGER*4 :: ndims,ndim
INTEGER*4 :: i,j,k,ii
INTEGER,ALLOCATABLE ::array(:,:)
!---
ALLOCATE (ARRAY (NTOT, NVARS))
ARRAY = 0
NDIM = 1
DO K = 1, NVARS !将多重循环的所有循环变量的遍历值写入2维数组中，第一维是遍历数，第二维记录对应每一遍历数的训练变量
!一个循环变量一个循环变量的填
IF (K .EQ. 1) THEN !第一个循环变量填入第二维第一个位置
DO I = 1, VMAXS(NVARS)
ARRAY(I,:) = (/(1,II = 2, NVARS), I/)
ENDDO
NDIM = NDIM * VMAXS(NVARS)
ELSE IF (K .LT. NVARS) THEN !接下来的循环变量，填入第二个位置，前面位置的信息采用复制信息
DO J = 1, VMAXS(NVARS - K + 1)
DO I = 1, NDIM
ARRAY((J - 1) * NDIM + I, :) = (/(1, II = K + 1,NVARS), J, ARRAY(I,NVARS - K + 2: NVARS)/)
ENDDO
ENDDO
NDIM = NDIM * VMAXS(NVARS - K + 1)
ELSE
DO J = 1, VMAXS(1)
DO I = 1, NDIM
ARRAY((J - 1) * NDIM + I, :) = (/ J, ARRAY(I,2:NVARS)/)
ENDDO
ENDDO
ENDIF
ENDDO
ARRAY2 = ARRAY
END SUBROUTINE