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CCL orfee.ins | |||
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SUBROUTINE INSTRU
C ******************************************************************
C
C OR FFE3 DATA INPUT
C
C 1) TITLE CARD
C COLS
C 1-72 TITLE, ANY 72 HOLLERITH CHARACTERS
C
C 2) CONTROL CARD
C COLS
C 1- 3 INCD, (0) INPUT OF PARAMETERS, ETC., FROM XFLS TAPE.
C (1) ALL INPUT FROM CARDS.
C
C 4- 6 IPM, (1) VARIANCE-COVARIANCE MATRIX READ FROM OR XFLS3
C TAPE. (USE ONLY IF INCD=0)
C (0) NO PARAMETER ERRORS USED.
C (-1) STANDARD ERRORS (WITHOUT COVARIANCES) READ
C FROM CARDS. (USE ONLY IF INCD=1)
C
C 7- 9 IAM, CELL PARAMETER ERRORS ARE
C (0) NOT TO BE USED
C (1) TO BE READ IN THE FORM OF STANDARD ERRORS
C (2) TO BE READ IN THE FORM OF A VARIANCE-
C COVARIANCE MATRIX
C
C 10-12 NS, THE NUMBER OF SYMMETRY CARDS TO BE READ. NS MAY TAKE
C ON VALUES FROM 1 TO 48.
C
C 13-15 NA, THE NUMBER OF ATOMS WHOSE PARAMETERS ARE TO BE READ.
C IRRELEVANT IF INCD=0
C
C 16-18 ITF, THE TEMPERATURE FACTOR INDICATOR.
C IRRELEVANT IF INCD=0
C (0) POSITION PARAMETERS ONLY WILL BE READ.
C (1) POSITION AND ISOTROPIC THERMAL PARAMETERS WILL
C BE READ.
C (2) POSITION AND ANISOTROPIC THERMAL PARAMETERS
C WILL BE READ.
C IF ITC(I) IS NON-ZERO FOR AN INDIVIDUAL ATOM
C (SEE BELOW), IT OVERRIDES ITF.
C
C 3) ATOM PARAMETERS. OMIT IF INCD=0. OTHERWISE 1, 2, OR 4 CARDS
C ARE INCLUDED FOR EACH OF NA ATOMS. CARDS FROM XFLS MAY BE USED
C COLS
C 1- 6 ANY 6 HOLLERITH CHARACTERS IDENTIFYING ATOM I.
C
C 7-27 WILL BE IGNORED
C
C 28-36 THE COORDINATE X(I) FOR ATOM I
C 37-45 THE COORDINATE Y(I) FOR ATOM I
C 46-54 THE COORDINATE Z(I) FOR ATOM I
C
C SECOND CARD. TEMPERATURE FACTORS. OMIT IF ITF=0.
03/12/
C COLS
C 1- 9 BETA(1,1) OR B FOR ANISOTROPIC OR ISOTROPIC TEMP FACTOR
C 10-18 BETA(2,2) (OR IRRELEVANT IF ISOTROPIC)
C 19-27 BETA(3,3)
C 28-36 BETA(1,2)
C 37-45 BETA(1,3)
C 46-54 BETA(2,3)
C
C 55-63 IRRELEVANT
C
C 64-66 ITC(I), TEMPERATURE FACTOR INDICATOR FOR ATOM I
C (0) TEMPERATURE FACTOR AS SPECIFIED BY ITF
C (1) ISOTROPIC TEMPERATURE FACTOR FOR THIS ATOM
C (2) ANISOTROPIC TEMPERATURE FACTOR FOR THIS ATOM
C
67-69 IGM(I), GAMMA TENSOR INDICATOR
C (0) NO GAMMA TENSOR FOR THIS ATOM
C (1) GAMMA TENSOR FOLLOWS
C
C THIRD AND FOURTH CARDS. GAMMA TENSOR. OMIT IF IGM(I)=0
C OR ITF=0. FORMAT(5F14.10)
C
C 4) STANDARD ERRORS OF ATOM PARAMETERS. OMIT IF INCD=0 OR IPM=0.
C OTHERWISE THE CARDS INCLUDED ARE ANALOGOUS TO THE ATOM
C PARAMETER CARDS.
C FIRST CARD
C COLS
C 1-27 IRRELEVANT
C 28-36 STANDARD ERROR OF X(I)
C 37-45 STANDARD ERROR OF Y(I)
C 46-54 STANDARD ERROR OF Z(I)
C
C SECOND CARD. OMIT IF ITF=0
C COLS
C 1- 9 STANDARD ERROR OF B OR BETA(1,1)
C 10-18 STANDARD ERROR OF BETA(2,2)
C 19-27 STANDARD ERROR OF BETA(3,3)
C 28-36 STANDARD ERROR OF BETA(1,2)
C 37-45 STANDARD ERROR OF BETA(1,3)
C 46-54 STANDARD ERROR OF BETA(2,3)
C
C THIRD AND FOURTH CARDS. OMIT IF IGM(I)=0 OR ITF=0.
C STANDARD ERRORS OF GAMMA TENSOR. FORMAT(5F14.10)
C
C 5) LATTICE PARAMETERS.
C COLS
C 1- 9 A, ANGSTROM UNITS
C 10-18 B
03/12/
C 19-27 C
C 28-36 COS(ALPHA)
C 37-45 COS(BETA)
C 46-54 COS(GAMMA)
C
C 6) STANDARD ERRORS OF LATTICE PARAMETERS. INCLUDE IF IAM=1
C COLS
C 1- 9 STANDARD ERROR OF A
C 10-18 STANDARD ERROR OF B
C 19-27 STANDARD ERROR OF C
C 28-36 STANDARD ERROR OF COS(ALPHA)
C 37-45 STANDARD ERROR OF COS(BETA)
C 46-54 STANDARD ERROR OF COS(GAMMA)
C
C 7) VARIANCE-COVARIANCE MATRIX FOR LATTICE PARAMETERS. USE IF IAM=2
C FIRST CARD
C COLS
C 1- 9 VARIANCE OF A
C 10-18 COVARIANCE OF A AND B
C 19-27 COVARIANCE OF A AND C
C 28-36 COVARIANCE OF A AND COS(ALPHA)
C 37-45 COVARIANCE OF A AND COS(BETA)
C 46-54 COVARIANCE OF A AND COS(GAMMA)
C 55-63 VARIANCE OF B
C 64-72 COVARIANCE OF B AND C
C
C SECOND CARD
C 1- 9 COVARIANCE OF B AND COS(ALPHA)
C 10-18 COVARIANCE OF B AND COS(BETA)
C 19-27 COVARIANCE OF B AND COS(GAMMA)
C 28-36 VARIANCE OF C
C 37-45 COVARIANCE OF C AND COS(ALPHA)
C 46-54 COVARIANCE OF C AND COS(BETA)
C 55-63 COVARIANCE OF C AND COS(GAMMA)
C 64-72 VARIANCE OF COS(ALPHA)
C
C THIRD CARD
C 1- 9 COVARIANCE OF COS(ALPHA) AND COS(BETA)
C 10-18 COVARIANCE OF COS(ALPHA) AND COS(GAMMA)
C 19-27 VARIANCE OF COS(BETA)
C 28-36 COVARIANCE OF COS(BETA) AND COS(GAMMA)
C 37-45 VARIANCE OF COS(GAMMA)
C
C 8) SYMMETRY INFORMATION. NS CARDS EACH OF WHICH DESCRIBES ONE
C SYMMETRY TRANSFORMATION. IF ALL DISTANCES ARE TO BE COMPUTED
C READ IN ALL EQUIVALENT POSITIONS INCLUDING THE BASIC POSITION
C X,Y,Z AND THOSE RELATED CENTROSYMMETRICALLY OR BY CENTERING.
03/12/
C
C THE TRANSFORMED COORDINATES ARE IN THE FORM
C X(NEW)=T(X)+M(XX)*X+M(XY)*Y+M(XZ)*Z
C Y(NEW)=T(Y)+M(YX)*X+M(YY)*Y+M(YZ)*Z
C Z(NEW)=T(Z)+M(ZX)*X+M(ZY)*Y+M(ZZ)*Z
C
C FORMAT(3(F15.10,3F3.0))
C
C COLS
C 1-15 T(X)
C 16-18 M(XX)
C 19-21 M(XY)
C 22-24 M(XZ)
C 25-39 T(Y)
C 40-42 M(YX)
C 43-45 M(YY)
C 46-48 M(YZ)
C 49-63 T(Z)
C 64-66 M(ZX)
C 67-69 M(ZY)
C 70-72 M(ZZ)
C
C 9) INSTRUCTION CARDS AS DESCRIBED BELOW. INCLUDE AS MANY AS
C NEEDED TO DEFINE THE QUANTITIES TO BE COMPUTED.
C
C 10) TERMINATION CARD
C COLS
C 1- 5 (0) TERMINATE JOB
C (-1) START NEW JOB READING NEW TITLE CARD, ETC.
C
C ******************************************************************
C
C INSTRUCTION INPUT
C
C EACH FUNCTION TO BE COMPUTED IS SPECIFIED BY A SEQUENCE OF
C INTEGERS, IN, WHICH ARE READ FROM ONE OR MORE INSTRUCTION
C CARDS. THE FIRST INTEGER IN THIS SEQUENCE, IN(1), DEFINES THE
C TYPE OF FUNCTION TO BE COMPUTED, AND THE INTERPRETATION OF
C THE REMAINING INSTRUCTION INTEGERS WILL BE DIFFERENT FOR
C DIFFERENT TYPES OF FUNCTIONS. DETAILS OF THE INSTRUCTION
C INTEGERS FOR EACH TYPE OF FUNCTION ARE GIVEN BELOW.
C
C EACH INSTRUCTION CARD IS READ WITH FORMAT(14I5). OF THE 14
C INTEGERS ON THIS CARD ONLY THE FIRST 13 ARE CONSIDERED TO BE
C PART OF THE INSTRUCTION. IF A FUNCTION REQUIRES MORE THAN 13
03/12/
C INTEGERS TO DEFINE IT THEN PUNCHING A ONE IN COLUMN 70 INDICATES
C THAT THE INSTRUCTION IS CONTINUED ON THE NEXT CARD.
C
C ATOM DESCRIPTION
C
C IN THE INSTRUCTIONS DESCRIBED BELOW EACH ATOM I IS DESIGNATED
C BY TWO INTEGERS, AI AND SI, DEFINED AS FOLLOWS-
C
C AI IS THE NUMBER OF THE ATOM IN THE PARAMETER LIST. THE UNIT
C CELL ORIGIN MAY BE DESIGNATED BY SETTING AI AT ZERO.
C
C SI IS A FIVE-DIGIT NUMBER, THE TWO LOW-ORDER DIGITS OF WHICH
C SPECIFY THE NUMBER OF THE SYMMETRY OPERATION (THE NUMBER OF
C THE SYMMETRY CARD) TO BE APPLIED. ZERO MAY BE USED TO REFER TO
C THE REFERENCE ASYMMETRIC UNIT TRANSFORMATION X, Y, Z EVEN
C THOUGH THIS IDENTITY TRANSFORMATION SHOULD BE PRESENT SOMEWHERE
C IN THE SYMMETRY CARDS.
C
C THE THREE HIGH-ORDER DIGITS OF SI SPECIFY UNIT CELL TRANSLATIONS
C ALONG A, B, AND C, RESPECTIVELY, WITH 5 ADDED TO EACH DIGIT.
C THUS 655 IMPLIES A TRANSLATION OF ONE UNIT CELL IN THE X
C DIRECTION. AN EXCEPTION IS THAT THE REFERENCE CELL MAY BE
C REFERRED TO AS 000 AS WELL AS 555.
C
C NOTE THAT AN ATOM IN THE BASIC ASYMMETRIC UNIT MAY BE
C SPECIFIED BY LEAVING SI BLANK.
C
C
C INSTRUCTION CARDS
C ------------------------------------------------------------------
C 1) DISTANCE BETWEEN ATOMS 1 AND 2
C
C COL 5 10 15 20 25
C 1 A1 S1 A2 S2
C ------------------------------------------------------------------
C 101) ALL DISTANCES LESS THAN MAX/100 BETWEEN ORIGIN ATOMS WITH
C NUMBERS A1 TO A2 AND TARGET ATOMS WITH NUMBERS A3 TO A4
C
C COL 5 10 15 20 25 30
C 101 A1 A2 A3 A4 MAX
C ------------------------------------------------------------------
C 201) SAME AS 101 BUT ALSO COMPUTES ANGLES WITH ORIGIN ATOMS AS
C VERTICES. IF MAX IS LARGE THEN THE NUMBER OF ANGLES WILL
C ALSO BE LARGE.
C
C COL 5 10 15 20 25 30
C 201 A1 A2 A3 A4 MAX
C ------------------------------------------------------------------
03/12/
C 2) ANGLE DEFINED BY THREE ATOMS. ATOM 2 IS VERTEX.
C
C COL 5 10 15 20 25 30 35
C 2 A1 S1 A2 S2 A3 S3
C ------------------------------------------------------------------
C 3) ANGLE BETWEEN NORMALS TO PLANES DEFINED BY ATOMS 1, 2, AND 3,
C AND ATOMS 4, 5, AND 6, RESPECTIVELY. IF RIGHT-HAND FINGERS
MODE IS 9 TRACK 1600 BPI RING=OUT BLOCK 118 DATA 1600
C ARE CURVED SO THAT THEY CAN PASS SUCCESSIVELY
C THROUGH ATOMS 1, 2, AND 3 THEN THUMB IS IN DIRECTION OF NORMAL.
C SIGN OF ANGLE WILL BE POSITIVE IF THIS NORMAL MAKES AN ACUTE
C ANGLE WITH VECTOR FROM ATOM 4 TO ATOM 6.
C
C COL 5 10 15 20 25 30 35 40 45 50 55 60 65
C 3 A1 S1 A2 S2 A3 S3 A4 S4 A5 S5 A6 S6
C ------------------------------------------------------------------
C 4) DISTANCE BETWEEN ATOMS 1 AND 2 LESS THAT BETWEEN ATOMS 3 AND 4.
C
C COL 5 10 15 20 25 30 35 40 45
C 4 A1 S1 A2 S2 A3 S3 A4 S4
C ------------------------------------------------------------------
C 5) ANGLE DEFINED BY ATOMS 1, 2, AND 3 LESS THAT DEFINED BY ATOMS
C 4, 5, AND 6. ATOMS 2 AND 5 ARE VERTICES.
C
C COL 5 10 15 20 25 30 35 40 45 50 55 60 65
C 5 A1 S1 A2 S2 A3 S3 A4 S4 A5 S5 A6 S6
C ------------------------------------------------------------------
C 6) SUM OF N ANGLES EACH DEFINED BY THREE ATOMS.
C
C COL 5 10 15 20 25 30 35 40 45 50 55 60 65 70
C 6 N A1 S1 A2 S2 A3 S3 A4 S4 A5 S5 A6 1
C S6 A7 S7 A8 S8 A9 S9 ETC.
C ------------------------------------------------------------------
C 7) RMS COMPONENT OF THERMAL DISPLACEMENT OF ATOM 1 ALONG ITS
C PRINCIPAL AXIS R. R=1, 2, OR 3.
C
C COL 5 10 15 20
C 7 A1 S1 R
C ------------------------------------------------------------------
C 107) RMS COMPONENTS OF THERMAL DISPLACEMENT OF ATOM 1 ALONG ITS
C THREE PRINCIPAL AXES.
C
C COL 5 10 15 20
C 107 A1 S1 -
C ------------------------------------------------------------------
C 207) RMS COMPONENTS OF THERMAL DISPLACEMENT OF ALL NA ATOMS, EACH
C ALONG ITS THREE PRINCIPAL AXES.
C
03/12/
C COL 5 10 15 20
C 207 NA S1 -
C ------------------------------------------------------------------
C 8) ANGLE BETWEEN PRINCIPAL AXIS R OF ATOM 1 AND A VECTOR FROM
C ATOM 2 TO ATOM 3.
C
C COL 5 10 15 20 25 30 35 40
C 8 A1 S1 R A2 S2 A3 S3
C ------------------------------------------------------------------
C 108) ANGLE BETWEEN EACH OF THE THREE PRINCIPAL AXES OF ATOM 1
C AND A VECTOR FROM ATOM 2 TO ATOM 3.
C
C COL 5 10 15 20 25 30 35 40
C 108 A1 S1 - A2 S2 A3 S3
C ------------------------------------------------------------------
C 208) ANGLE BETWEEN EACH OF THE THREE PRINCIPAL AXES OF ALL NA ATOMS
C AND A VECTOR FROM ATOM 2 TO ATOM 3.
C
C COL 5 10 15 20 25 30 35 40
C 208 NA S1 - A2 S2 A3 S3
C ------------------------------------------------------------------
C 9) RMS COMPONENT OF THERMAL DISPLACEMENT OF ATOM 1 ALONG ITS
C PRINCIPAL AXIS R, PROJECTED ON A VECTOR FROM ATOM 2 TO ATOM 3.
C
C COL 5 10 15 20 25 30 35 40
C 9 A1 S1 R A2 S2 A3 S3
C ------------------------------------------------------------------
C 109) RMS COMPONENTS OF THERMAL DISPLACEMENT OF ATOM 1 ALONG ITS
C THREE PRINCIPAL AXES, EACH PROJECTED ON A VECTOR FROM ATOM 2
C TO ATOM 3.
C
C COL 5 10 15 20 25 30 35 40
C 109 A1 S1 - A2 S2 A3 S3
C ------------------------------------------------------------------
C 209) RMS COMPONENTS OF THERMAL DISPLACEMENT OF ALL NA ATOMS, EACH
C ALONG ITS THREE PRINCIPAL AXES, AND EACH PROJECTED ON A VECTOR
C FROM ATOM 2 TO ATOM 3.
C
C COL 5 10 15 20 25 30 35 40
C 209 NA S1 - A2 S2 A3 S3
C ------------------------------------------------------------------
C 10) ANGLE BETWEEN PRINCIPAL AXIS R OF ATOM 1 AND AXIS I OF A
C CARTESIAN COORDINATE SYSTEM DEFINED BY ATOMS 2, 3, 4, AND 5.
C AXIS 1 IS DIRECTED FROM ATOM 2 TO ATOM 3. AXIS 2 IS DIRECTED
C ALONG THE CROSS PRODUCT OF AXIS 1 WITH THE VECTOR FROM ATOM 4
03/12/
C TO ATOM 5. AXIS 3 IS THE CROSS PRODUCT OF AXIS 1 WITH AXIS 2.
C
C COL 5 10 15 20 25 30 35 40 45 50 55 60 65
C 10 A1 S1 R I A2 S2 A3 S3 A4 S4 A5 S5
C ------------------------------------------------------------------
C 110) ANGLE BETWEEN EACH OF THE THREE PRINCIPAL AXES R OF ATOM 1 AND
C EACH OF THREE AXES I OF A CARTESIAN COORDINATE SYSTEM DEFINED
C BY ATOMS 2, 3, 4, AND 5 AS DESCRIBED FOR (10) ABOVE.
C
C COL 5 10 15 20 25 30 35 40 45 50 55 60 65
C 110 A1 S1 - - A2 S2 A3 S3 A4 S4 A5 S5
C ------------------------------------------------------------------
C 210) ANGLE BETWEEN EACH OF THE THREE PRINCIPAL AXES R OF ALL NA
C ATOMS AND EACH OF THREE AXES I OF A CARTESIAN COORDINATE
C SYSTEM DEFINED BY ATOMS 2, 3, 4, AND 5 AS DESCRIBED FOR
C (10) ABOVE.
C
C COL 5 10 15 20 25 30 35 40 45 50 55 60 65
C 210 NA S1 - - A2 S2 A3 S3 A4 S4 A5 S5
C ------------------------------------------------------------------
C 11) RMS COMPONENT OF THERMAL DISPLACEMENT OF ATOM 1 ALONG ITS
C PRINCIPAL AXIS R, PROJECTED ON AXIS I OF A CARTESIAN
C COORDINATE SYSTEM DEFINED BY ATOMS 2, 3, 4, AND 5 AS
C DESCRIBED FOR (10) ABOVE.
C
C COL 5 10 15 20 25 30 35 40 45 50 55 60 65
C 11 A1 S1 R I A2 S2 A3 S3 A4 S4 A5 S5
C ------------------------------------------------------------------
C 111) RMS COMPONENTS OF THERMAL DISPLACEMENT OF ATOM 1 ALONG ITS
C THREE PRINCIPAL AXES R, EACH PROJECTED ON EACH OF THREE AXES I
C OF A CARTESIAN COORDINATE SYSTEM DEFINED BY ATOMS 2, 3, 4,
C AND 5 AS DESCRIBED FOR (10) ABOVE.
C
C COL 5 10 15 20 25 30 35 40 45 50 55 60 65
C 111 A1 S1 - - A2 S2 A3 S3 A4 S4 A5 S5
C ------------------------------------------------------------------
C 211) RMS COMPONENTS OF THERMAL DISPLACEMENT OF ALL NA ATOMS, EACH
C ALONG ITS THREE PRINCIPAL AXES R, AND EACH PROJECTED ON THE
C AXES I OF A CARTESIAN COORDINATE SYSTEM DEFINED BY ATOMS
C 2, 3, 4, AND 5 AS DESCRIBED FOR (10) ABOVE.
C
C COL 5 10 15 20 25 30 35 40 45 50 55 60 65
C 211 NA S1 - - A2 S2 A3 S3 A4 S4 A5 S5
C ------------------------------------------------------------------
C 12) RMS COMPONENT OF THERMAL DISPLACEMENT OF ATOM 1 IN A DIRECTION
C DEFINED BY ATOMS 2 AND 3.
C
C COL 5 10 15 20 25 30 35
03/12/
C 12 A1 S1 A2 S2 A3 S3
C ------------------------------------------------------------------
C 13) RMS RADIAL THERMAL DISPLACEMENT OF ATOM 1.
C
C COL 5 10 15
C 13 A1 S1
C ------------------------------------------------------------------
C 14) INTERATOMIC DISTANCE AVERAGED OVER THERMAL MOTION. ATOM 2 IS
C ASSUMED TO RIDE ON ATOM 1.
C
C COL 5 10 15 20 25
C 14 A1 S1 A2 S2
C ------------------------------------------------------------------
C 15) INTERATOMIC DISTANCE AVERAGED OVER THERMAL MOTION. ATOMS 1
C AND 2 ARE ASSUMED TO MOVE INDEPENDENTLY.
C
C COL 5 10 15 20 25
C 15 A1 S1 A2 S2
C ------------------------------------------------------------------
C 16) DISTANCE OF ATOM 1 FROM THE PLANE DEFINED BY ATOMS 2, 3, AND 4.
C IF RIGHT-HAND FINGERS ARE CURVED SO THAT THEY CAN PASS
C SUCCESSIVELY THROUGH ATOMS 2, 3, AND 4 THEN
C THE THUMB POINTS IN A POSITIVE DIRECTION.
C
C COL 5 10 15 20 25 30 35 40 45
C 16 A1 S1 A2 S2 A3 S3 A4 S4
C ------------------------------------------------------------------
C 17) CONFORMATION OR TORSION ANGLE OF A CHAIN OF ATOMS 1, 2, 3
C AND 4. SIGN IS POSITIVE IF WHEN LOOKING FROM 2 TO 3 A CLOCKWISE
C MOTION OF ATOM 1 WOULD SUPERIMPOSE IT ON ATOM 4.
C
C COL 5 10 15 20 25 30 35 40 45
C 17 A1 S1 A2 S2 A3 S3 A4 S4
C ------------------------------------------------------------------
C 18) ANGLE BETWEEN VECTOR FROM ATOM 1 TO ATOM 2 AND THAT FROM
C ATOM 3 TO ATOM 4.
C
C COL 5 10 15 20 25 30 35 40 45
C 18 A1 S1 A2 S2 A3 S3 A4 S4
C
C *******************************************************************
C
C FUNCTIONS ADDED TO SPARE BY W. BERNHARD
C
C
C ------------------------------------------------------------------
C 20) ANGLES BETWEEN A VECTOR FROM A1 TO A2 AND THREE AXES DEFINED BY
03/12/
C THE FIRST FOUR NA ATOMS NA1, NA2, NA3, NA4. THE AXES ARE:
C NA1-NA2, NA1-NA3, NA1-NA4.
C
C COL 5 10 15 20 25
C 20 A1 S1 A2 S2
C
C ___________________________________________________________________
C
21) USING THE AXES AS DEFINED IN 20 THE ORIENTATION OF THE FOLLOWING
C THREE ORTHOGONAL VECTORS ARE FOUND.
C V3= NORMAL TO THE PLANE OF ATOMS A1, A2, A3
C V4= BISECTOR OF THE ANGLE A1-A2-A3 WHICH LIES IN THE ANGLES PLANE
C V5= NORMAL TO THE ABOVE TWO VECTORS
C
C THE BISECTOR (V4) IS FOUND BY SOLVING SIMULTANIOUSLY
C V1.AA.V4 = V2.AA.V4
C V3.AA.V4 = 0.0
C WHERE
C V1 = A2 TO A1
C V2 = A2 TO A3
C V3 = V1XV2
C AA IS A 3X3 MATRIX DETERMINED BY THE UNIT CELL AXES
C
C COL 5 10 15 20 25 30 35
C 21 A1 S1 A2 S2 A3 S3
C
C ___________________________________________________________________
C
C 22) TORSION ANGLE BETWEEN THE NORMAL TO THE PLANE OF ATOMS 1,2, AND
C 3 AND THE VECTOR FROM ATOM 3 TO ATOM 4
C
C COL 5 10 15 20 25 30 35 40 45
C 22 A1 S1 A2 S2 A3 S3 A4 S4
C
C *******************************************************************
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