****************************************************************************** SURVIBTM ANL/STEVENS TECH SURFACE FITTING AND VIBRATIONAL ANALYSIS PROGRAM ****************************************************************************** AUTHORS : LAWRENCE B. HARDING AND WALTER C. ERMLER REFERENCES : L.B. HARDING AND W.C. ERMLER J. COMPUT. CHEM. VOL. 6, P. 13 (1985) W.C. Ermler, H.C. Hsieh, L.B. Harding Computer Physics Communications 51, 257-284 (1988) DESCRIPTION : THE FUNCTIONS OF THIS PROGRAM ARE 1) TO LEAST SQUARES FIT AN N-DIMENSIONAL ENERGY OR PROPERTY SURFACE BY SINGLE-VALUED DECOMPOSITION 2) TO PERFORM A NORMAL MODE ANALYSIS USING THE POLYNOMIAL FIT TO THE SURFACE 3) TO CALCULATE ANHARMONICITY AND CORIOLIS CORRECTIONS 4) TO CALCULATE EXPECTATION VALUES OF PROPERTIES LAST REVISION : October 1991 LANGUAGE : FORTRAN NOTE : VAX USERS SHOULD COMPILE SURVIB USING THE G_FLOATING OPTION ****************************************************************************** INPUT DATA ****************************************************************************** 1) TITLE 2) NPERT,NPROP,NSMOFF,NOVIB,NREEXP,NPRINT,NPUNCH,NVIBTM,NSUM 3) NREORD,NEVAL,NGUESS,NSCALE,NSHIFT,NMEPS,NMEVALI,NMEVALN,NEQUIV 4) NPTS,NINTERM,NVAR,NATOMS,NDEG,N4DEF,NROOT,NUSER,NCRD 5) IF(NPTS.EQ.0) GO TO 16 IF(NPROP.NE.0) read cfact 6) IF(NEQUIV .ne. 0) read (IEQUIV(I),I=1,NVAR) 7) IF(NSCALE .EQ. 0) read (INTYP(I), I=1,NVAR) IF(NSCALE .GT. 0) read (SCALE(I), I=1,NVAR) 8) IF(NSHIFT .GT. 0) read (SHIF(I), I=1,NVAR) 9) IF(NREORD .NE. 0) read (IREORD(I),I=1,NVAR) 10) IF(NCRD .NE. 0) read ((TCRD(I,J),I=1,NVAR),J=1,NVAR) 11) IF(NMEPS .EQ. 0) read epsn 12) (X(J,1),J=1,NVAR),E(1),WTMAX,WTR,SVDTOL,ITMXSVD,NPRSVD DO I=2,NPTS (X(J,I),J=1,NVAR),E(I),WT(I) 13) IF(NINTERM.NE.0) THEN DO I=1,NINTERM (N(J,I),J=1,NVAR),FK(I) ENDIF IF(NPROP.NE.0) GO TO 25 IF (NATOMS .EQ. 0) GO TO 21 17) ATOM(1), ATMNO(1), ATMWT(1), ICOORD(1) 18) IPM(1),ATOM(2), ATMNO(2), ATMWT(2), ICOORD(2) 19) IF(ICOORD(2).NE.1) THEN IAT2, IAT3, IPM(2), IPM(3), ATOM(3), ATMNO(3), ATMWT(3), ICOORD(3) ELSE IPM(2),IPM(3),ATOM(3),ATMNO(3),ATMWT(3),ICOORD(3) ENDIF 20) DO I=4,NATOMS J0=3*(I-3) IAT2,IAT3,IAT4,IPM(J0+1),IPM(J0+2),IPM(J0+3),ATOM(I),ATMNO(I), ATMWT(I),ICOORD(I) ENDDO 21) IF(NGUESS .LE. 0) GO TO 24 ITMAX, CONVG 22) EPS(I), I=1,NVAR 23) DO I=1,NGUESS (F(J),J=1,NVAR),NROOT 24) IF(NEVAL .EQ. 0) GO TO 25 DO I=1,NEVAL (XEVAL(J,I),J=1,NVAR) 25) IF(NATOMS .EQ. 0 .OR. NOVIB .NE. 0) GO TO 1 IF(NMEVALI .EQ. 0) GO TO 26 DO I=1,NMEVALI (XEVAL(J,I),J=1,NVAR) 26) IF (NPERT .EQ. 0) GO TO 1 NKADD,NDEG,N4DEF,EPS 27) IF (NKADD.EQ.0) GO TO 28 DO I=1,NKADD (N2(J,I),J=1,NVAR) 28) IF(NMEVALN .EQ.0) GO TO 29 DO I=1,NMEVALN (XEVAL(J,I),J=1,NVAR) 29) NQADD,NDEG,N4DEF,NIISKP,NIJSKP,ICRES 30) IF(NIISKP.EQ.0) GO TO 31 DO I=1,NIISKP NI,NJ 31) IF(NIJSKP.EQ.0) GO TO 32 DO I=1,NIJSKP NI,NJ,NK 32) IF(NQADD.EQ.0) GO T0 33 DO I=N4DEF+1,N4DEF+NQADD (NV(I,J),J=1,NVAR) 33) IF(ICRES.EQ.0) GO TO 34 IAX,I,J (SETS UNTIL LIST IS TERMINATED BY IAX=-1) 34) GO TO 1 ****************************************************************************** EXPLANATION OF DATA ****************************************************************************** 1) TITLE TITLE FOR THIS RUN (AN EOF TERMINATES THE JOB). 2) NPERT .EQ. 0 STOP AFTER NORMAL MODE ANALYSIS NPERT .EQ. 1 RE-EXPAND THE SURFACE AS A POWER SERIES IN NORMAL COORDINATES AND CARRY OUT A SECOND-ORDER PERTURBATION THEORY CALCULATION OF ANHARMONICITY CORRECTIONS. NPERT .GT. 1 RE-EXPAND THE SURFACE AS A POWER IN NORMAL COORDINATES BUT DO NOT CARRY OUT PERTURBATION SERIES ANALYSIS. NPROP .NE. 0 THE DATA THAT FOLLOWS IS FOR A PROPERTY (DIPOLE MOMENT, FIELD GRADIENT, ETC.). THESE DATA REQUIRE ONLY DATA SETS 5-11 AND 25-32 (AS APPROPRIATE). NSMOFF CONTROLS WHETHER OR NOT THE POLYNOMIAL EXPANSION WILL BE ANALYZED FOR TERMS THAT ARE EQUIVALENT BY SYMMETRY. THIS ANALYSIS IS CARRIED OUT RELATIVE TO THE FIRST POINT IN DATA SET 10. THEREFORE THIS POINT SHOULD REFLECT THE FULL SYMMETRY OF THE MOLECULE. IF THIS ANALYSIS IS EMPLOYED THEN ONLY THOSE POINTS NECCESSARY TO DEFINE THE SYMMETRY UNIQUE TERMS NEED BE INPUT. USE OF THIS OPTION REQUIRES THE DEFINITION OF THE INTERNAL COORDINATES IN TERMS OF BOND LENGTHS, BOND ANGLES, ETC. THERFORE NATOMS MUST BE NONZERO AND DATA SETS 12-15 MUST BE SUPPLIED. NSMOFF .NE. 0 DO NOT USE THE FIRST ENERGY OR PROPERTY POINT TO DETERMINE THE MOST COMPACT FORM FOR THE INTERNAL COORDINATE EXPANSION BASED ON ITS SYMMETRY. (DEFAULT=0) NOVIB .NE. 0 A NORMAL MODE ANALYSIS IS NOT TO BE PERFORMED, BUT SYMMETRY WAS USED TO DEFINE THE INTERNAL COORDINATES EXPANSION. (I.E. NATOMS .NE. 0 .AND. NOSYM .EQ. 0) (DEFAULT=0) NREEXP DETERMINES WHETHER OR NOT THE POLYNOMIAL EXPRESSION FOR THE ENERGY IS TO BE RE-EXPANDED ABOUT A CALCULATED STATIONARY POINT. USE OF THIS OPTION REQUIRES, OF COURSE, THAT A STATIONARY POINT BE LOCATED (SEE THE NGUESS PARAMETER) NREEXP.EQ. 0 RE-EXPAND POLYNOMIAL NREEXP.GT. 0 DO NOT RE-EXPAND POLYNOMIAL (DEFAULT=0) NPRINT FIVE DIGIT NUMBER CONTROLING DEBUG PRINT NPRINT=IJKLM I.NE.0 DEBUG PRINTING TURNED ON IN PERTURBATION THEORY J.NE.0 DEBUG PRINTING TURNED ON IN NMDEXP K.NE.0 DEBUG PRINTING TURNED ON IN NMODES L.NE.0 DEBUG PRINTING TURNED ON IN NEWT M.NE.0 DEBUG PRINTING TURNED ON IN INTSYM (DEFAULT=00000) NPUNCH.EQ.1 THE NORMAL MODE VECTORS IN MASS WEIGHTED ATOMIC CARTESIAN COORDINATE FORM ARE WRITTEN TO UNIT 7. NPUNCH.GE.2 THE ENERGY EXPRESSION (IN INTERNAL COORDINATES) ARE WRITTEN TO UNIT 7. NPUNCH.GE.3 THE ENERGY EXPRESSION (IN NORMAL MODE COORDINATES) IS WRITTEN TO UNIT 7. (DEFAULT=0) NSUM.GT.0 SUMMARY FILE CONTAINING ENERGY,GEOMETRY AND FREQUENCIES OF ALL STATIONARY POINTS FOUND, CREATED ON UNIT 3. (DEFAULT=0) 3) NREORD .NE. 0 READ ARRAY IREORD(I),I=1,NVAR THAT OVERRIDES THE DEFAULT ORDERING OF NORMAL MODE EIGENVALUES AND EIGENVECTORS (USEFUL FOR MAKING OUTPUT ORDER CONSISTENT WITH THAT USED BY SPECTROSCOPISTS) NEVAL NUMBER OF POINTS AT WHICH THE ENERGY EXPRESSION IS TO BE EVALUATED (THE COORDINATES OF THESE POINTS ARE READ IN 19) (DEFAULT=0) NGUESS .GT. 0 CAUSES STARTING GUESSES FOR STATIONARY POINT SEARCH TO BE READ IN (NGUESS = -1 RESULTS IN NO SEARCH FOR A MINIMUM) NSCALE SPECIFIES WHETHER OR NOT THE COORDINATES ARE TO BE SCALED IF A NORMAL MODE ANALYSIS IS TO BE CARRIED OUT THE INTERNAL COORDINATES MUST BE SCALED TO BOHR AND RADIANS. NSCALE .EQ. 0 SCALE FACTORS ARE SET TO STANDARD VALUES BASED ON THE TYPE OF PARAMETER AS DEFINED BY INTYPE (DATA SET 7) NSCALE .GT. 0 SCALE FACTORS ARE READ IN DATA SET 8 (DEFAULT=0) NSHIFT SPECIFIES WHETHER OR NOT THE INTERNAL COORDINATES ARE TO BE SHIFTED TO SOME NEW ORIGIN. NSHIFT .EQ. 0 USE THE FIRST GEOMETRY AS A REFERENCE VALUE. NSHIFT .GT. 0 READ THE SHIFTS FOR EACH INTERNAL COORDINATE IN DATA SET 9 NSHIFT .LT. 0 DO NOT SHIFT THE INTERNAL COORDINATES (DEFAULT=0) NMEPS .EQ. 0 THE NORMAL COORDINATE ANALYSIS STEP SIZE IS DEFAULTED TO 0.0001 AU. NMEPS .NE. 0 READ IT ACCORDING TO 11) BELOW. (DEFAULT=0) NMEVALI NUMBER OF POINTS (IN TERMS OF NORMAL COORDINATES) AT WHICH THE INTERNAL COORDINATE ENERGY EXPRESSION WILL BE EVALUATED (DEFAULT=0) NMEVALN NUMBER OF POINTS (IN TERMS OF NORMAL COORDINATES) AT WHICH THE NORMAL COORDINATE ENERGY EXPRESSION WILL BE EVALUATED. (DEFAULT=0) NEQUIV .NE. 0 READ IN THE EFFECT OF A SYMMETRY OPERATION ON THE INTERNAL COORDINATES 4) NPTS NUMBER OF POINTS TO BE INPUT IF NPTS.EQ.0 THE INTERNAL COORDINATE ENERGY EXPRESSION IS READ FROM UNIT 4 NINTERM NUMBER OF TERMS IN THE POLYNOMIAL TO BE READ IN EXPLICITLY. IF NDEG .NE. 0 THESE TERMS WILL BE ADDED TO THOSE DEFINED INTERNALY WITH THE NDEG PARAMETER. NVAR NUMBER OF INDEPENDENT VARIABLES (I.E. THE DIMENSIONALITY) NATOMS NUMBER OF ATOMS (APPLICABLE ONLY IF NORMAL MODE ANALYSIS IS DESIRED OR IF A SYMMETRY ADAPTED EXPANSION IN INTERNAL COORDINATES IS DESIRED.) NATOMS .EQ. 0 NO NORMAL MODE ANALYSIS NDEG THE DEGREE OF THE POLYNOMIAL. THIS CAN BE USED TO HAVE THE ARRAY N(J,I) GENERATED INTERNALLY FOR ALL POWERS UP TO NDEG. (DEFAULT=0) N4DEF .NE. 0 THIS PARAMETER DEFAULTS THE FOURTH DEGREE TERMS TO THOSE INVOLVING THE POWERS 4 OR COMBINATIONS 2 2 FOR ALL COORDINATES. (DEFAULT=0) NROOT ONE PLUS THE NUMBER OF NEGATIVE EIGENVALUES OF THE HESSIAN MATRIX DESIRED I.E. NROOT=1 MINIMUM NROOT=2 SADDLE POINT NROOT=0 CLOSEST STATIONARY POINT OF ANY KIND (DEFAULT NROOT=0) NUSER.NE.0 INDICATES A USER-SUPPLIED POTENTIAL FUNCTION ROUTINE WILL BE USED. USER MUST LINK THE ROUTINES USERIN AND USERSUB INTO THE SURVIB EXECUTABLE. 5) CFACT CONVERSION FACTOR BY WHICH PROPERTIES WILL BE MULTIPLIED TO OBTAIN THE DESIRED UNITS (DEFAULT 1.0). 6) IEQUIV(I) IEQUIV(I)=J, IMPLIES THAT VARIABLES I AND J ARE EQUIVALENT AND THIS EQUIVALENCE WILL BE IMPOSED ON THE COEFFICIENTS OF THE POLYNOMIAL. NOTE, IN MOST CASES THIS IS HANDLED AUTOMATICALLY BY THE PROGRAM CHECKING FOR EQUIVALENCES BETWEEN THE VARIOUS TERMS IN THE POLYNOMIAL. THE AUTOMATIC HANDLING OF SYMMETRY CAN ONLY BE DONE WHEN THE INTERNAL COORDINATES ARE DEFINED IN TERMS OF BOND LENGTHS AND BOND ANGLES, ETC (NATOMS>0) AND THE FIRST POINT MUST RELFECT THE FULL SYMMETRY OF THE SYSTEM. THE IEQUIV ARRAY IS USED IN THOSE CASES WHERE THIS AUTOMATIC PROCEDURE DOESN'T WORK. 8) INTYP(I) DEFINE EACH INTERNAL COORDINATE I AS FOLLOWS: 0 - BOND LENGTH IN AU OR BOND ANGLE IN RADIANS -1 - BOND LENGTH IN ANGSTROMS 1 - BOND ANGLE IN DEGREES 2 - NEGATIVE BOND ANGLE IN DEGREES THESE DEFINITIONS ARE USED TO SET STANDARD SCALE FACTORS FOR EACH OF THE COORDINATES. 9) SCALE(I) SCALE PARAMETER FOR THE ITH VARIABLE 10) SHIF(I) SHIFT PARAMETER FOR THE ITH VARIABLE (DEFAULT = 0.0) NOTE: THE SCALE AND SHIFT PARAMETERS ARE APPLIED AS FOLLOWS X(J,I) = (X(J,I)-SHIF(I))/SCALE(I) 11) IREORD(I) ARRAY TO SPECIFY ORDER OF NORMAL MODE EIGENVALUES AND EIGENVECTORS (DEFAULT IS HIGHEST TO LOWEST FREQUENCY WITH IMAGINARY FREQUENCIES PRECEDING ZERO (SMALL) FREQUENCIES CORRESPONDING TO ROTATIONS AND TRANSLATIONS 12) TCRD(I,J) OPTIONAL TRANSFORMATION MATRIX RELATING INTERNAL COORDINATES TO FITTING COORDINATES. THIS TRANSFORMATION IS APPLIED TO ALL INPUT COORDINATES BEFORE ANY FITTING IS DONE 13) EPSN CARTESIAN COORDINATE STEPSIZE USED TO DETERMINE DERIVATIVES FOR NORMAL MODE ANALYSIS (READ IN SUBROUTINE NMODES) (DEFAULT = 0.0005) 14) X(J,I) VALUE OF THE JTH INDEPENDENT VARIABLE AT THE ITH POINT E(I) VALUE OF THE ENERGY OR PROPERTY AT THE ITH INPUT POINT WTMAX MAXIMUM WEIGHTING FACTOR FOR ANY POINT (DEFAULT = 1.0E+08) WTR RANGE PARAMETER FOR WEIGHTING OF POINTS (DEFAULT = 10.0) THE WEIGHT FOR THE I-TH POINT, WT(I), IS CALCULATED WITH THE FOLLOWING FORMULA, WT(I) = WTMAX * WTR ** (-ABS( (E(I)-E(1))/ETR ) ) WHERE, ETR IS CHOSEN SUCH THE THE EXPONENT RANGES FROM 0 TO -1. NOTES: THE MINIMUM WEIGHT WILL BE WTMAX/WTR. TO ACHEIVE EQUAL WEIGHTING OF ALL POINTS SET WTR=1.0. SVDTOL THRESHOLD AT WHICH EIGENVALUES IN THE SINGLE-VALUED DECOMPOSITION ARE ZEROED. (DEFAULT = 1.0E-14) ITMXSVD MAXIMUM NUMBER OF ITERATIONS IN SVDCMP (DEFAULT = 30) NPRSVD DEBUG PRINTING IN SVDCMP (DEFAULT = 0) WT(I) THE WEIGHTING FACTOR FOR THE ITH INPUT POINT IN THE FIT (IF NONZERO, THIS OVERRIDES THE WEIGHT CALCULATED ABOVE. 15) N(J,I) Four digit number that defines the functional dependence of the i-th term in the expansion on the j-th independent variable: M = First two digits of N(J,I) N = Second two digits of N(J,I) X(J) = j-th independent variable (scaled but unshifted) R(J) = X(J) - SHIF(J) M = 11 -> R(J)**N (Taylor Series) M = 12 -> (1/R(J))**N M = 13 -> R(J) * X(J)**N M = 14 -> R(J) * (1/X(J))**N M = 21 -> (R(J)/X(J))**N (Simons-Parr-Finlan) M = 22 -> (R(J)/X(J)+SHIF(J))**N (Ogilvie) M = 31 -> SIN(N * R(J)) M = 32 -> (SIN(N * R(J)))**2 M = 33 -> (SIN(N * R(J)))**3 M = 41 -> COS(N * R(J)) M = 42 -> (COS(N * R(J)))**2 M = 43 -> (COS(N * R(J)))**3 M = 51 -> SIN( R(J)) * COS(N * R(J)) M = 52 -> SIN(2*R(J)) * COS(N * R(J)) M = 53 -> SIN(3*R(J)) * COS(N * R(J)) M = 54 -> SIN(4*R(J)) * COS(N * R(J)) M = 61 -> (SIN( R(J)))**2 * COS(N * R(J)) M = 62 -> (SIN(2*R(J)))**2 * COS(N * R(J)) M = 63 -> (SIN(3*R(J)))**2 * COS(N * R(J)) M = 64 -> (SIN(4*R(J)))**2 * COS(N * R(J)) M = 80 -> Associated Legendre Polynomial [Plm(X(J))] N=1 -> l=1, m=0 N=2 -> l=1, m=1 N=3 -> l=2, m=0 N=4 -> l=2, m=1 N=5 -> l=2, m=2 N=6 -> l=3, m=0 N=7 -> l=3, m=1 N=8 -> l=3, m=2 N=9 -> l=3, m=3 (etc) M = 90 -> Plm(COS(X(J))) FK(I) COEFFICIENT OF THE ITH TERM OF THE POLYNOMIAL IF ZERO, THE COEFICIENT IS VARIED TO FIT THE POINTS IF NONZERO, THE COEFFICIENT IS KEPT FIXED AT THE INPUT VALUE 16-20) DATA SETS 15-19 SPECIFY THE ATOMS AND DEFINE THE INTERNAL COORDINATES IN TERMS OF THESE ATOMS (THESE DATA ARE READ IN SUBROUTINE INTDEF) IN WHAT FOLLOWS THE INDEX I REFERS TO THE I-TH ATOM IAT2,IAT3,IAT4 REFER TO SEQUENCE NUMBERS OF PREVIOUSLY INPUT ATOMS ATOM(I) ATOMIC SYMBOL FOR THE ITH ATOM ATMNO(I) ATOMIC NUMBER FOR THE ITH ATOM (DEFAULTS TO THE MOST ABUNDANT ISOTOPE OF ATOM(I) ) ATMWT(I) ATOMIC MASS OF ATOM I (AMU) (DEFAULTS TO THE CORRECT VALUE FOR ALL COMMON ISOTOPES) IPM THERE IS BOTH A "NATURAL" ORDERING OF THE INTERNAL COORDINATES, WHICH IS DETERMINED BY THE ORDER IN WHICH THE ATOMS ARE INPUT, AND THERE IS A USER SPECIFIED ORDER WHICH IS CHOSEN BY THE USER, FOR HIS/HER CONVENIENCE. THE INDICES J AND K WILL REFER TO THE NATURAL AND USER SPECIFIED ORDERINGS RESPECTIVELY (J AND K BOTH RUN FROM 1 TO 3*NATOM-6). THE "NATURAL" ORDERING OF INTERNAL COORINATES IS DETERMINED BY THE ORDER IN WHICH THE ATOMS ARE INPUT, AS SHOWN BELOW. IPM IS THE MAPPING BETWEEN THE NATURAL AND USER ORDERINGS OF INTERNAL COORDINATES, SUCH THAT K = IPM(J), IMPLIES THAT THE J-TH INTERNAL COORDINATE IN THE "NATURAL" ORDERING WILL BE MAPPED INTO THE K-TH INTERNAL COORDINATE IN THE USER ORDERING. ICOORD(I) SPECIFIES THE KIND OF INTERNAL COORDINATES USED TO SPECIFY THE POSITION OF THE I-TH ATOM. FOR THE FIRST ATOM, NO INTERNAL COORDINATES ARE SPECIFIED, FOR THE SECOND ATOM, ONE INTERNAL COORDINATE IS DEFINED, FOR THE THIRD ATOM, TWO ARE DEFINED AND FOR THE FOURTH AND SUBSEQUENT ATOMS THREE INTERNAL COORDINATES ARE DEFINED PER ATOM. THE FOLLOWING IS A DESCRIPTION OF THE INTERNAL COORDINATES COORESPONDING TO EACH ICOORD, IN THEIR "NATURAL" ORDERING. ICOORD(1) NOT USED (FIRST ATOM ALWAYS PLACED AT ORIGIN, RESULTING IN NO INTERNAL COORDINATES) ICOORD(2)=0 J=1, BOND LENGTH BETWEEM ATOMS 1 AND 2 ICOORD(2)=1 J=1, DISTANCE BETWEEN ATOM 1 AND MIDPOINT OF ATOMS 2 AND 3 J=2, DISTANCE BETWEEN ATOMS 2 AND 3 J=3, ANGLE BETWEEN ATOM 1 - MIDPOINT OF (2,3) - ATOM 2 (NOTE IN THIS CASE ICOORD(3) IS IGNORED) ICOORD(3)=0 J=2, BOND LENGTH BETWEEN ATOMS 3 AND IAT2 J=3, BOND ANGLE BETWEEN ATOMS 3 - IAT2 - IAT3 ICOORD(3)=2 J=2, BOND LENGTH BETWEEN ATOMS 3 AND IAT2 J=3, BOND LENGTH BETWEEN ATOMS 3 AND IAT3 ICOORD(I)=4 THE COORDINATES OF THE I-TH ATOM ARE DEFINED WITH RESPECT TO THE CENTER OF MASS AND THE PRINCIPLE AXES OF INERTIA OF THE FIRST TWO ATOMS. (THIS OPTION IS NOT RECOMMENDED FOR THE NOVICE USER) J=3*(I-3)+1, DISTANCE BETWEEN ATOM I AND THE CENTER OF MASS OF ATOMS 1 THROUGH I-1. J=3*(I-3)+2, POLAR ANGLE WITH PRINCIPLE AXIS J=3*(I-3)+3, AZIMUTHAL ANGLE FOR I>3 ICOORD(I)=0 J=3*(I-3)+1, BOND LENGTH BETWEEN ATOMS I AND IAT2 J=3*(I-3)+2, BOND ANGLE (I - IAT2 - IAT3) J=3*(I-3)+3, DIHEDRAL ANGLE (I - IAT2 - IAT3 - IAT4) ICOORD(I)=1 J=3*(I-3)+1, BOND LENGTH BETWEEN ATOMS I AND IAT2 J=3*(I-3)+2, BOND ANGLE (I - IAT2 - MIDPOINT(IAT3,IAT4)) J=3*(I-3)+3, DIHEDRAL ANGLE (I - IAT2 - MIDPOINT(IAT3,IAT4) - IAT3) ABS(ICOORD(I))=3 J=3*(I-3)+1, BOND LENGTH BETWEEN ATOMS I AND IAT2 J=3*(I-3)+2, BOND ANGLE (I - IAT2 - IAT3) J=3*(I-3)+3, BOND ANGLE (I - IAT2 - IAT4) IN THIS CASE THE SIGN OF ICOORD CONTROLS WHETHER ATOM I IS PLACE ABOVE OR BELOW THE PLANE DEFINED BY ATOMS IAT2, IAT3, AND IAT4. ICOORD(I)=4 THE COORDINATES OF THE I-TH ATOM ARE DEFINED WITH RESPECT TO THE CENTER OF MASS AND THE PRINCIPLE AXES OF INERTIA OF THE PREVIOUS (I-1) ATOMS. (THIS OPTION IS NOT RECOMMENDED FOR THE NOVICE USER) J=3*(I-3)+1, DISTANCE BETWEEN ATOM I AND THE CENTER OF MASS OF ATOMS 1 THROUGH I-1. J=3*(I-3)+2, POLAR ANGLE WITH PRINCIPLE AXIS J=3*(I-3)+3, AZIMUTHAL ANGLE 21) ITMAX MAXIMUM NUMBER OF ITERATIONS IN THE NEWTON RAPHESON SEARCH( (DEFAULT = 20 ) CONVG CONVERGENCE CRITERION FOR THE NEWTON-RAPHESON SEARCH(S) THIS IS COMPARED TO THE NORM OF THE GRADIENT, IN SCALED UNITS. (DEFAULT = 1.0D-10 ) 22) EPS(I) STEPSIZE FOR THE ITH VARIABLE USED TO OBTAIN DERIVATIVES IN THE NEWTON-RAPHESON SEARCH (DEFAULT = 0.001) 23) F(J) STARTING GUESS FOR THE JTH VARIABLE IN THE STATIONARY POINT SEARCH(S) 24) XEVAL(J,I) VALUE OF THE JTH INDEPENDENT VARIABLE AT THE ITH POINT FOR ENERGY EVALUATION (INTERNAL COORDINATE EXPANSION) 25) XEVAL(J,I) VALUE OF THE JTH INDEPENDENT VARIABLE AT THE ITH POINT FOR ENERGY EVALUATION (NORMAL COORDINATES, INTERNAL COORDINATE EXPANSION) 26-27) PARAMETERS DEFINING THE RE-EXPANSION OF THE SURFACE IN TERMS OF THE NORMAL COORDINATES. (THESE ARE READ IN SUBROUTINE NMDEXP) 26) NKADD NUMBER OF TERMS IN THE POLYNOMIAL EXPANSION IN NORMAL COORDINATES TO BE READ IN EXPLICITLY. THESE WILL BE ADDED TO ANY GENERATED INTERNALLY USING NDEG. NDEG,N4DEF SAME AS DESCRIBED IN 4) ABOVE IF NKADD.EQ.0 AND NDEG.EQ.0 THEN THE ENERGY EXPRESSION IN NORMAL COORDINATES IS READ FROM UNIT 4. EPS NORMAL COORDINATE STEPSIZE ( DEFAULT = 0.0005 ) 27) N2(J,I) EXPONENT OF JTH THE NORMAL COORDINATE IN THE ITH TERM OF THE POLYNOMIAL 28) XEVAL(J,I) VALUE OF THE JTH INDEPENDENT VARIABLE AT THE ITH POINT FOR ENERGY EVALUATION (NORMAL COORDINATES, NORMAL COORDINATE EXPANSION) 29-33) PARAMETERS DEFINING THE VALUES OF THE VIBRATIONAL QUANTUM NUMBERS FOR THE CALCULATION OF THE VALUE OF THE VIBRATIONAL ENERGY OR THE EXPECTATION VALUE OF A PROPERTY IN CHOOSEN VIBRATIONAL STATES AND OTHER DATA RELATED TO THE PERTURBATION THEORY ANALYSIS. (THESE ARE READ IN SUBROUTINE VIBPT) 29) NQADD NUMBER OF STATES DESIRED FOR WHICH QUANTUM NUMBERS WILL BE READ IN EXPLICITLY. THESE WILL BE ADDED TO THOSE GENERATED INTERNALLY USING THE NDEG PARAMETER. (DEFAULT=0) NDEG THE LEVEL OF VIBRATIONAL EXCITATION. ALL STATES FROM THE GROUND THROUGH ALL POWERS ADDING TO NDEG ARE SET INTERNALLY. (DEFAULT = 1, .I.E. ZERO-POINT PLUS FUNDAMENTALS) N4DEF.NE.0 SETS THE POWERS OF 4 TO ONLY THE 4 0 0 0 ETC. AND 2 2 0 0 ETC. TYPE (SEE DATA SET 4 ABOVE) NIISKP THE NUMBER OF SETS OF MODES THAT LEAD TO FERMI RESONANCES OF THE TYPE 2*W(I)=W(J) NIJSKP THE NUMBER OF SETS OF MODES THAT LEAD TO FERMI RESONACES OF THE TYPE W(J)+W(K)=W(I) ICRES FLAG THAT INDICATES CORIOLIS RESONANCE DATA IS TO BE READ IN 32 BELOW 30) NI,NJ INDICES OF MODES INVOLVED IN FERMI RESONANCES (NIISKP) 31) NI,NJ,NK INDICES OF MODES INVOLVED IN FERMI RESONANCES (NIJSKP) 32) NV(J,I) QUANTUM NUMBER OF J'TH THE NORMAL MODE IN THE I'TH STATE FOR WHICH ENERGIES, AND/OR PROPERTY EXPECTATION VALUES ARE TO BE CALCULATED. 33) IAX,I,J SETS OF INTEGERS (TERMINATED BY IAX=-1) THAT DEFINE A CORIOLIS RESONANCE FOR AXIS IAX INVOLVING MODES I AND J ****************************************************************************** DIMENSIONING LIMITATIONS ****************************************************************************** MAXIMUM NUMBER OF POINTS : NPTS = 2000 MAXIMUM NUMBER OF TERMS IN POLYNOMIAL : 700 MAXIMUM NUMBER OF ATOMS : NATOMS = 7 MAXIMUM NUMBER OF INDEPENDENT VARIABLES : NVAR = 21 ****************************************************************************** PROGRAM LIMITATIONS ****************************************************************************** NONLINEAR POLYATOMIC SYSTEMS ONLY HIGH DEGREE EXPANSIONS MAY RESULT IN PRECISION LOSS AND SURVIB MAY HAVE TO BE EXTENDED TO QUADRUPLE PRECISION FOR CERTAIN APPLICATIONS. (THIS HAS BEEN NOTED FOR AN EIGHTH DEGREE NORMAL MODE EXPANSION FOR WATER. SEE B. MAESSEN, M. WOLFSBERG, AND L.B. HARDING, J. PHYS. CHEM. 89, 3324(1985) ). SYMMETRIC TOP SYSTEMS CAN BE TREATED, BUT FORMULAS FOR ANHARMONICITY CONSTANTS X(I,J) HAVE NOT BEEN AS THOROUGHLY TESTED AS THOSE FOR THE ASYMMETRIC TOP. SPECTROSCOPIC CONSTANT FORMULAS FOR SPHERICAL TOPS HAVE NOT BEEN IMPLEMENTED. FERMI RESONANCES (DEFINED IN TERMS OF HARMONIC FREQUENCIES) WILL RESULT IN INACCURATE SPECTROSCOPIC CONSTANTS. THE OUTPUT PAGE THAT SHOWS THIS ANALYSIS SHOULD BE CONSULTED. (SEE ALSO, INPUT DATA SET NO. 28.) ISOTOPIC SUBSTITUTION CAN ALSO BE USEFUL IN ADDRESSING THIS PROBLEM. ****************************************************************************** SAMPLE DATA SETS ****************************************************************************** **************** SAMPLE INPUT SET NUMBER 1 ********************************* CHF Variables: R[C-F], R[C-H], Angle F-C-H 0 0 0 0 1 0 4 / NPERT,NPROP,NSMOFF,NOVIB,NREEXP,NPRINT,NPUNCH 0 0 1 0 1 / NREORDR, NEVAL, NGUESS, NSCALE, NSHIFT 42 0 3 3 4 / NPTS, NINTERM, NVAR, NATOMS, NDEG 0 0 1 / iscale 2.50 2.150 100.00 / shifts 2.500 2.150 100.000 -0.82503801 / geometries and energies 2.200 2.150 100.000 -0.79639403 / 2.300 2.150 100.000 -0.81342935 / 2.400 2.100 95.000 -0.81840460 / 2.400 2.100 100.000 -0.82161574 / 2.400 2.100 105.000 -0.82206190 / 2.400 2.150 95.000 -0.81906703 / 2.400 2.150 100.000 -0.82219825 / 2.400 2.150 105.000 -0.82259033 / 2.400 2.200 95.000 -0.81904558 / 2.400 2.200 100.000 -0.82209508 / 2.400 2.200 105.000 -0.82243338 / 2.500 2.000 100.000 -0.82108041 / 2.500 2.050 100.000 -0.82330380 / 2.500 2.100 95.000 -0.82225177 / 2.500 2.100 100.000 -0.82457688 / 2.500 2.100 105.000 -0.82435085 / 2.500 2.150 80.000 -0.79757849 / 2.500 2.150 85.000 -0.80940808 / 2.500 2.150 90.000 -0.81767186 / 2.500 2.150 95.000 -0.82276639 / 2.500 2.150 100.000 -0.82503801 / 2.500 2.150 105.000 -0.82477840 / 2.500 2.150 110.000 -0.82223052 / 2.500 2.150 115.000 -0.81760029 / 2.500 2.150 120.000 -0.81107002 / 2.500 2.200 95.000 -0.82259161 / 2.500 2.200 100.000 -0.82480802 / 2.500 2.200 105.000 -0.82451501 / 2.500 2.250 100.000 -0.82399238 / 2.500 2.300 100.000 -0.82268308 / 2.600 2.100 95.000 -0.82175121 / 2.600 2.100 100.000 -0.82329413 / 2.600 2.100 105.000 -0.82248236 / 2.600 2.150 95.000 -0.82215974 / 2.600 2.150 100.000 -0.82367053 / 2.600 2.150 105.000 -0.82284155 / 2.600 2.200 95.000 -0.82187357 / 2.600 2.200 100.000 -0.82335062 / 2.600 2.200 105.000 -0.82250454 / 2.700 2.150 100.000 -0.81936708 / 2.800 2.150 100.000 -0.81306692 / 'C' / 1 'F' / 1 2 2 3 'H' / / / 2.50 2.150 100.0 0 / starting guess for minimum **************** SAMPLE INPUT SET NUMBER 2 ********************************* CH3Cl RCI+1+2+qc2 / (5s,4p,2d,1f/4s,3p,2d,1f/3s,2p,1d) 0 0 1 0 1 / 0 0 0 0 1 / 39 30 9 5 0 0 0 0 1 / 0 0 0 0 1 1 1 1 1 / scales 3.400 2.100 2.100 2.100 110.0 110.0 110.0 120.0 240.0 / shifts 1.0d0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0d0 0.5773502691 0.5773502691 0.5773502691 0.0 0.0 0.0 0.0 0.0 0.0d0 0.0 0.7071067811 -0.7071067811 0.0 0.0 0.0 0.0 0.0 0.0d0 0.8164965808 -0.4082482903 -0.4082482903 0.0 0.0 0.0 0.0 0.0 0.0d0 0.0 0.0 0.0 0.5773502691 0.5773502691 0.5773502691 0.0 0.0 0.0d0 0.0 0.0 0.0 0.0 0.7071067811 -0.7071067811 0.0 0.0 0.0d0 0.0 0.0 0.0 0.8164965808 -0.4082482903 -0.4082482903 0.0 0.0 0.0d0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0d0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 / tcrd 3.40 2.08 2.08 2.08 109. 109. 109. 120. 240. -0.56077226 / 3.30 2.05 2.10 2.10 110. 110. 110. 120. 240. -0.55962721 / 3.30 2.10 2.05 2.10 110. 110. 110. 120. 240. -0.55962721 / 3.30 2.10 2.10 2.05 110. 110. 110. 120. 240. -0.55962721 / 3.30 2.10 2.10 2.10 105. 110. 110. 120. 240. -0.55860058 / 3.30 2.10 2.10 2.10 110. 105. 110. 120. 240. -0.55860058 / 3.30 2.10 2.10 2.10 110. 110. 105. 120. 240. -0.55860058 / 3.30 2.10 2.10 2.10 110. 110. 110. 120. 240. -0.55924846 / 3.40 2.00 2.05 2.05 110. 110. 110. 120. 240. -0.56040425 / 3.40 2.05 2.00 2.05 110. 110. 110. 120. 240. -0.56040425 / 3.40 2.05 2.05 2.00 110. 110. 110. 120. 240. -0.56040425 / 3.40 2.05 2.05 2.05 110. 110. 110. 120. 240. -0.56090180 / 3.40 2.05 2.05 2.10 110. 110. 110. 120. 240. -0.56051428 / 3.40 2.05 2.10 2.05 110. 110. 110. 120. 240. -0.56051428 / 3.40 2.05 2.10 2.10 110. 110. 110. 120. 240. -0.56012025 / 3.40 2.08 2.08 2.08 109. 109. 109. 120. 240. -0.56077226 / 3.40 2.10 2.05 2.05 110. 110. 110. 120. 240. -0.56051428 / 3.40 2.10 2.05 2.10 110. 110. 110. 120. 240. -0.56012025 / 3.40 2.10 2.10 2.05 110. 110. 110. 120. 240. -0.56012025 / 3.40 2.10 2.10 2.10 105. 105. 110. 120. 240. -0.55913187 / 3.40 2.10 2.10 2.10 105. 110. 105. 120. 240. -0.55913187 / 3.40 2.10 2.10 2.10 105. 110. 110. 120. 240. -0.55952803 / 3.40 2.10 2.10 2.10 110. 105. 105. 120. 240. -0.55913187 / 3.40 2.10 2.10 2.10 110. 105. 110. 120. 240. -0.55952803 / 3.40 2.10 2.10 2.10 110. 110. 105. 120. 240. -0.55952803 / 3.40 2.10 2.10 2.10 110. 110. 110. 120. 240. -0.55971960 / 3.40 2.10 2.10 2.10 110. 110. 115. 120. 240. -0.55825994 / 3.40 2.10 2.10 2.10 110. 115. 110. 120. 240. -0.55825994 / 3.40 2.10 2.10 2.10 115. 110. 110. 120. 240. -0.55825994 / 3.40 2.10 2.10 2.15 110. 110. 110. 120. 240. -0.55856028 / 3.40 2.10 2.15 2.10 110. 110. 110. 120. 240. -0.55856028 / 3.40 2.15 2.10 2.10 110. 110. 110. 120. 240. -0.55856028 / 3.50 2.10 2.10 2.10 110. 110. 110. 120. 240. -0.55806107 / 3.40 2.10 2.10 2.10 110. 110. 110. 125. 240. -0.55906028 / 3.40 2.10 2.10 2.10 110. 110. 110. 120. 235. -0.55906028 / 3.40 2.10 2.10 2.10 110. 110. 110. 125. 245. -0.55906028 / 3.40 2.10 2.10 2.10 110. 110. 110. 115. 235. -0.55906028 / 3.40 2.10 2.10 2.10 110. 110. 110. 120. 245. -0.55906028 / 3.40 2.10 2.10 2.10 110. 110. 110. 115. 240. -0.55906028 / 0 0 0 0 0 0 0 0 0 / 1101 0 0 0 0 0 0 0 0 / 0 1101 0 0 0 0 0 0 0 / 0 0 0 0 1101 0 0 0 0 / 1102 0 0 0 0 0 0 0 0 / 1101 1101 0 0 0 0 0 0 0 / 1101 0 0 0 1101 0 0 0 0 / 0 1102 0 0 0 0 0 0 0 / 0 1101 0 0 1101 0 0 0 0 / 0 0 1102 0 0 0 0 0 0 / 0 0 1101 0 0 1101 0 0 0 / 0 0 1101 0 0 0 0 1101 0 / 0 0 1101 0 0 0 0 0 1101 / 0 0 0 1102 0 0 0 0 0 / 0 0 0 1101 0 0 1101 0 0 / 0 0 0 1101 0 0 0 1101 0 / 0 0 0 1101 0 0 0 0 1101 / 0 0 0 0 1102 0 0 0 0 / 0 0 0 0 0 1102 0 0 0 / 0 0 0 0 0 1101 0 1101 0 / 0 0 0 0 0 1101 0 0 1101 / 0 0 0 0 0 0 1102 0 0 / 0 0 0 0 0 0 1101 1101 0 / 0 0 0 0 0 0 1101 0 1101 / 0 0 0 0 0 0 0 1102 0 / 0 0 0 0 0 0 0 1101 1101 / 0 0 0 0 0 0 0 0 1102 / 0 1103 0 0 0 0 0 0 0 / 0 1101 1102 0 0 0 0 0 0 / 0 1101 0 1102 0 0 0 0 0 / 'C' / 1 'CL' / 1 2 2 5 'H' / 1 2 3 3 6 8 'H' / 1 2 3 4 7 9 'H' /