        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    *******************************************************************
  