# CORRECT.LP

## Space group determination

The approach to space group determination is well explained in CORRECT.LP :

XDS adopts the following approach. (1) it looks for possible symmetries of the crystal lattice (2) it computes a redundancy independent R-factor for all enantiomorphous point groups compatible with the observed lattice symmetry. (3) it selects the group which explains the intensity data at an acceptable, redundancy-independent R-factor (Rmeas, Rrim) using a minimum number of unique reflections. This approach does not test for the presence of screw axes. Consequently, orthorhombic cell axes will be specified in increasing length (following conventions), despite the possibility that different assignments for the cell axes could become necessary for space groups P222(1) and P2(1)2(1)2 containing one or two screw axes, respectively. The user can always override the automatic decisions by specifying the correct space group number and unit cell constants in XDS.INP and repeating the CORRECT step of XDS. This provides a simple way to rename orthorhombic cell constants if screw axes are present. In addition, the user has the option to specify in XDS.INP (a) a reference data set or (b) a reindexing transformation or (c) the three basis vectors (if known from processing a previous data set taken at the same crystal orientation in a multi-wavelength experiment). These features of XDS are useful for resolving the issue of alternative settings of polar or rhombohedral cells (like P4, P6, R3).

Please note the sentence: **This approach does not test for the presence of screw axes.** The information about those reflections that may indicate screw axes is actually given in the table **"REFLECTIONS OF TYPE H,0,0 0,K,0 0,0,L OR EXPECTED TO BE ABSENT (*)"** (near the end of CORRECT.LP) but there is no automatic evaluation of that table that would result in screw axis assignment.

Therefore, the **space group determination of XDS only results in evaluation of the possible point groups that are compatible with the lattice symmetry**. Space group determination of XDS only suggests one representative for each point group - the other possible space groups belonging to its point group are possibilities as well, but are not listed! For example, if XDS suggest space group 89 (P422), then any other space group of point group PG422, like 90, 91, 92, 93, 94, 95 and 96 is equally possible.

If the user wants more automatic determination, it is suggested to run

echo SETTING SYMMETRY-BASED | pointless XDS_ASCII.HKL

Please note that SETTING SYMMETRY-BASED overrides a pointless default that would lead to ambiguity between space group numbers and space group symbols for space group numbers 5, 17 and 18. The mapping of numbers and names is:

****** LATTICE SYMMETRY IMPLICATED BY SPACE GROUP SYMMETRY ****** BRAVAIS- POSSIBLE SPACE-GROUPS FOR PROTEIN CRYSTALS TYPE [SPACE GROUP NUMBER,SYMBOL] aP [1,P1] mP [3,P2] [4,P2(1)] mC,mI [5,C2] oP [16,P222] [17,P222(1)] [18,P2(1)2(1)2] [19,P2(1)2(1)2(1)] oC [21,C222] [20,C222(1)] oF [22,F222] oI [23,I222] [24,I2(1)2(1)2(1)] tP [75,P4] [76,P4(1)] [77,P4(2)] [78,P4(3)] [89,P422] [90,P42(1)2] [91,P4(1)22] [92,P4(1)2(1)2] [93,P4(2)22] [94,P4(2)2(1)2] [95,P4(3)22] [96,P4(3)2(1)2] tI [79,I4] [80,I4(1)] [97,I422] [98,I4(1)22] hP [143,P3] [144,P3(1)] [145,P3(2)] [149,P312] [150,P321] [151,P3(1)12] [152,P3(1)21] [153,P3(2)12] [154,P3(2)21] [168,P6] [169,P6(1)] [170,P6(5)] [171,P6(2)] [172,P6(4)] [173,P6(3)] [177,P622] [178,P6(1)22] [179,P6(5)22] [180,P6(2)22] [181,P6(4)22] [182,P6(3)22] hR [146,R3] [155,R32] cP [195,P23] [198,P2(1)3] [207,P432] [208,P4(2)32] [212,P4(3)32] [213,P4(1)32] cF [196,F23] [209,F432] [210,F4(1)32] cI [197,I23] [199,I2(1)3] [211,I432] [214,I4(1)32]

## Cell parameter refinement

This may look like

****************************************************************************** REFINEMENT OF DIFFRACTION PARAMETERS USING ALL IMAGES ****************************************************************************** REFINED VALUES OF DIFFRACTION PARAMETERS DERIVED FROM 197690 INDEXED SPOTS REFINED PARAMETERS: POSITION BEAM AXIS ORIENTATION CELL STANDARD DEVIATION OF SPOT POSITION (PIXELS) 0.50 STANDARD DEVIATION OF SPINDLE POSITION (DEGREES) 0.03 SPACE GROUP NUMBER 199 UNIT CELL PARAMETERS 77.443 77.443 77.443 90.000 90.000 90.000 E.S.D. OF CELL PARAMETERS 1.8E-02 1.8E-02 1.8E-02 0.0E+00 0.0E+00 0.0E+00 REC. CELL PARAMETERS 0.012913 0.012913 0.012913 90.000 90.000 90.000 COORDINATES OF UNIT CELL A-AXIS 45.490 47.263 -41.162 COORDINATES OF UNIT CELL B-AXIS -45.887 59.759 17.904 COORDINATES OF UNIT CELL C-AXIS 42.690 13.873 63.107 CRYSTAL MOSAICITY (DEGREES) 0.048 LAB COORDINATES OF ROTATION AXIS 0.999999 0.001525 -0.000039 DIRECT BEAM COORDINATES (REC. ANGSTROEM) -0.003439 0.001125 0.999994 DETECTOR COORDINATES (PIXELS) OF DIRECT BEAM 2299.53 2261.76 DETECTOR ORIGIN (PIXELS) AT 2308.69 2258.76 CRYSTAL TO DETECTOR DISTANCE (mm) 199.65 LAB COORDINATES OF DETECTOR X-AXIS 1.000000 0.000000 0.000000 LAB COORDINATES OF DETECTOR Y-AXIS 0.000000 1.000000 0.000000 THE DATA COLLECTION STATISTICS REPORTED BELOW ASSUMES: SPACE_GROUP_NUMBER= 199 UNIT_CELL_CONSTANTS= 77.44 77.44 77.44 90.000 90.000 90.000

## Scaling information

****************************************************************************** CORRECTION FACTORS AS FUNCTION OF IMAGE NUMBER & RESOLUTION ****************************************************************************** RECIPROCAL CORRECTION FACTORS FOR INPUT DATA SETS MERGED TO OUTPUT FILE: XDS_ASCII.HKL THE CALCULATIONS ASSUME FRIEDEL'S_LAW= TRUE TOTAL NUMBER OF CORRECTION FACTORS DEFINED 40 DEGREES OF FREEDOM OF CHI^2 FIT 2649.6 CHI^2-VALUE OF FIT OF CORRECTION FACTORS 1.557 NUMBER OF CYCLES CARRIED OUT 3 CORRECTION FACTORS for visual inspection by XDS-Viewer DECAY.cbf XMIN= 0.2 XMAX= 99.7 NXBIN= 2 YMIN= 0.00100 YMAX= 0.50246 NYBIN= 20 NUMBER OF REFLECTIONS USED FOR DETERMINING CORRECTION FACTORS 4832 ****************************************************************************** CORRECTION FACTORS AS FUNCTION OF X (fast) & Y(slow) IN THE DETECTOR PLANE ****************************************************************************** RECIPROCAL CORRECTION FACTORS FOR INPUT DATA SETS MERGED TO OUTPUT FILE: XDS_ASCII.HKL THE CALCULATIONS ASSUME FRIEDEL'S_LAW= TRUE TOTAL NUMBER OF CORRECTION FACTORS DEFINED 90 DEGREES OF FREEDOM OF CHI^2 FIT 2640.3 CHI^2-VALUE OF FIT OF CORRECTION FACTORS 1.456 NUMBER OF CYCLES CARRIED OUT 4 CORRECTION FACTORS for visual inspection by XDS-Viewer MODPIX.cbf XMIN= 232.6 XMAX= 3623.4 NXBIN= 9 YMIN= 313.3 YMAX= 4064.2 NYBIN= 10 NUMBER OF REFLECTIONS USED FOR DETERMINING CORRECTION FACTORS 4832 ****************************************************************************** CORRECTION FACTORS AS FUNCTION OF IMAGE NUMBER & DETECTOR SURFACE POSITION ****************************************************************************** RECIPROCAL CORRECTION FACTORS FOR INPUT DATA SETS MERGED TO OUTPUT FILE: XDS_ASCII.HKL THE CALCULATIONS ASSUME FRIEDEL'S_LAW= TRUE TOTAL NUMBER OF CORRECTION FACTORS DEFINED 26 DEGREES OF FREEDOM OF CHI^2 FIT 2652.0 CHI^2-VALUE OF FIT OF CORRECTION FACTORS 1.418 NUMBER OF CYCLES CARRIED OUT 3 CORRECTION FACTORS for visual inspection by XDS-Viewer ABSORP.cbf XMIN= 0.2 XMAX= 99.7 NXBIN= 2 DETECTOR_SURFACE_POSITION= 1928 2189 DETECTOR_SURFACE_POSITION= 2504 2826 DETECTOR_SURFACE_POSITION= 1352 2826 DETECTOR_SURFACE_POSITION= 1352 1552 DETECTOR_SURFACE_POSITION= 2504 1552 DETECTOR_SURFACE_POSITION= 3231 2786 DETECTOR_SURFACE_POSITION= 2468 3630 DETECTOR_SURFACE_POSITION= 1388 3630 DETECTOR_SURFACE_POSITION= 625 2786 DETECTOR_SURFACE_POSITION= 625 1592 DETECTOR_SURFACE_POSITION= 1388 747 DETECTOR_SURFACE_POSITION= 2468 747 DETECTOR_SURFACE_POSITION= 3231 1592 NUMBER OF REFLECTIONS USED FOR DETERMINING CORRECTION FACTORS 4832

### Details about the error model

****************************************************************************** CORRECTION PARAMETERS FOR THE STANDARD ERROR OF REFLECTION INTENSITIES ****************************************************************************** The variance v0(I) of the intensity I obtained from counting statistics is replaced by v(I)=a*(v0(I)+b*I^2). The model parameters a, b are chosen to minimize the discrepancies between v(I) and the variance estimated from sample statistics of symmetry related reflections. This model implicates an asymptotic limit ISa=1/SQRT(a*b) for the highest I/Sigma(I) that the experimental setup can produce (Diederichs (2010) Acta Cryst D66, 733-740). a b ISa 1.042E+00 2.177E-04 66.41

## Statistics of reflections

Near the top of CORRECT.LP we find:

531781 REFLECTIONS ON FILE "INTEGRATE.HKL" 0 CORRUPTED REFLECTION RECORDS (IGNORED) 0 REFLECTIONS INCOMPLETE OR OUTSIDE IMAGE RANGE 1 ... 1799 0 OVERLOADED REFLECTIONS (IGNORED) 81 REFLECTIONS OUTSIDE ACCEPTED RESOLUTION RANGES OR TOO CLOSE TO ROTATION AXIS (IGNORED) 531700 REFLECTIONS ACCEPTED

## Statistics of observations

XDS, like e.g. SCALA/aimless and d*TREK, gives statistics about unaveraged (individual observations) and averaged ("merged") quantities, but in different tables. The unaveraged values are in a table that is fine-grained in terms of resolution, at the beginning of CORRECT.LP. The Sigma values in that table are corrected to match the RMS scatter.

The table that has information about the averaged data (suitably weighted) is repeated several times. It is less fine-grained in resolution (9 shells, and overall). [if a user wants this table in fine-grained form, s/he can use XSCALE].

The way the tables are printed is the same for both types of tables: at first the definitions of the quantities in the table are given, and then the table itself is printed.

Specifically, the heading of the table which talks about the unaveraged data ("observations") looks like this:

I/Sigma = mean intensity/Sigma of a reflection in shell Chi2 = goodness of fit between sample variances of symmetry-related intensities and their errors (Chi2 = 1 for perfect agreement) R-FACTOR observed = (SUM(ABS(I(h,i)-I(h))))/(SUM(I(h,i))) expected = expected R-FACTOR derived from Sigma(I) NUMBER = number of reflections in resolution shell used for calculation of R-FACTOR ACCEPTED = number of accepted reflections REJECTED = number of rejected reflections (MISFITS), recognized by comparison with symmetry-related reflections.

and then the table itself is:

RESOLUTION RANGE I/Sigma Chi2 R-FACTOR R-FACTOR NUMBER ACCEPTED REJECTED observed expected 48.268 17.853 9.63 0.97 5.06 6.10 865 868 44 17.853 13.079 10.02 0.97 5.22 6.14 1301 1305 81 13.079 10.812 9.83 1.10 5.56 5.94 1374 1388 99 10.812 9.423 9.88 1.09 5.32 6.03 1820 1825 108 9.423 8.460 9.56 1.07 6.03 6.21 2087 2101 167 .... (many resolution shells deleted for brevity)

## Statistics of unique reflections

Later tables talk about the averaged ("merged") intensities. Please note that I/SIGMA means "average of I/SIGMA", not "average of I" / "average of SIGMA".

R-FACTOR observed = (SUM(ABS(I(h,i)-I(h))))/(SUM(I(h,i))) expected = expected R-FACTOR derived from Sigma(I) COMPARED = number of reflections used for calculating R-FACTOR I/SIGMA = mean of intensity/Sigma(I) of unique reflections (after merging symmetry-related observations) Sigma(I) = standard deviation of reflection intensity I estimated from sample statistics R-meas = redundancy independent R-factor (intensities) Diederichs & Karplus (1997), Nature Struct. Biol. 4, 269-275. CC(1/2) = percentage of correlation between intensities from random half-datasets. Correlation significant at the 0.1% level is marked by an asterisk. Karplus & Diederichs (2012), Science 336, 1030-33 Anomal = percentage of correlation between random half-sets Corr of anomalous intensity differences. Correlation significant at the 0.1% level is marked. SigAno = mean anomalous difference in units of its estimated standard deviation (|F(+)-F(-)|/Sigma). F(+), F(-) are structure factor estimates obtained from the merged intensity observations in each parity class. Nano = Number of unique reflections used to calculate Anomal_Corr & SigAno. At least two observations for each (+ and -) parity are required.

and the table itself is

NOTE: Friedel pairs are treated as different reflections. SUBSET OF INTENSITY DATA WITH SIGNAL/NOISE >= -3.0 AS FUNCTION OF RESOLUTION RESOLUTION NUMBER OF REFLECTIONS COMPLETENESS R-FACTOR R-FACTOR COMPARED I/SIGMA R-meas CC(1/2) Anomal SigAno Nano LIMIT OBSERVED UNIQUE POSSIBLE OF DATA observed expected Corr 5.72 23750 7284 7488 97.3% 6.6% 6.6% 23666 14.59 7.9% 99.3* 33* 1.043 3033 4.06 41574 12997 13384 97.1% 10.0% 8.3% 41476 11.40 12.1% 98.3* 45* 1.341 5775 3.32 56679 16961 17336 97.8% 16.8% 15.4% 56494 6.49 20.1% 97.9* 31* 1.079 7697 2.88 67173 20272 20497 98.9% 38.4% 39.0% 66875 2.91 45.9% 93.1* 19* 0.840 9333 2.57 79365 23100 23197 99.6% 77.6% 85.3% 79063 1.46 92.1% 75.3* 5 0.701 10761 2.35 86431 25554 25631 99.7% 128.9% 146.7% 86014 0.86 153.2% 54.7* 3 0.633 11894 2.18 83863 27529 27946 98.5% 197.0% 230.0% 81669 0.49 237.7% 31.6* -1 0.575 11422 2.04 51338 23815 29966 79.5% 286.2% 343.0% 43478 0.26 361.1% 15.1* 0 0.526 5523 1.92 25803 15877 31898 49.8% 483.3% 577.5% 17026 0.12 635.3% 3.8 2 0.519 1856 total 515976 173389 197343 87.9% 27.8% 29.3% 495761 2.89 33.5% 98.2* 19* 0.781 67294 NUMBER OF REFLECTIONS IN SELECTED SUBSET OF IMAGES 531700 NUMBER OF REJECTED MISFITS 15698 NUMBER OF SYSTEMATIC ABSENT REFLECTIONS 0 NUMBER OF ACCEPTED OBSERVATIONS 516002 NUMBER OF UNIQUE ACCEPTED REFLECTIONS 173398

Why is there a discrepancy between "total 515976 173389" *versus* "NUMBER OF ACCEPTED OBSERVATIONS 516002", and "NUMBER OF UNIQUE ACCEPTED REFLECTIONS 173398" ?? The reason is that the (higher) numbers *below* the table *include* observations (and unique reflections) with I < -3*sigma(I), whereas the numbers *in* the table refer only to those reflections which should be used downstream (for phasing and refinement). Indeed, XDSCONV filters out those unique reflections which have I<-3*sigma(I).

It should also be noted that the alien rejection controlled by REJECT_ALIEN= (default 20) will be performed *after* making this table. So the number of reflections which you will get from XDSCONV is not the same as reported here. If you want to see the statistics of reflections which will be converted by XDSCONV (thus will be used for further process), you should prepare REMOVE.HKL to explicitly specify the reflections which will be thrown away and run CORRECT step again.

At the bottom of CORRECT.LP we find:

NUMBER OF UNIQUE ALIEN REFLECTIONS WITH A Z-SCORE ABOVE LIMIT 162 (ALIENS ABOVE LIMIT (REJECT_ALIEN= 20.0) ARE MARKED INVALID) NUMBER OF REFLECTION RECORDS ON OUTPUT FILE "XDS_ASCII.HKL" 531700 NUMBER OF ACCEPTED OBSERVATIONS (INCLUDING SYSTEMATIC ABSENCES) 515712 NUMBER OF REJECTED MISFITS & ALIENS (marked by -1*SIGMA(IOBS)) 15988

The file XDS_ASCII.HKL actually has all 531700 reflections.