All statistics and lots of useful information about the behaviour of the program are printed out to the standard output file called .log file.

The .log file contains information about:

- input script
- input and default parameters
- geometric statistics
- NCS operators
- X-ray statistics
- scale and sigmaA parameters
- TLS parameters
- rigid body parameters

Information on input and default parameters is always written to the .log file in a set order.

If there is a comment line, the program prints out:

Comment line--- # Comment line--- ##### Makecif parameters Comment line--- #

This means there are 3 comment lines.

Keywords are written as ` Data line`. For example:

Data line--- NONX NCHAIns 6 CHNID A B C D E F NSPANS 1 12 72 5

This means there is a command line describing NONX which is for non-crystallographic restraints parameters. If there is an error in the command line, the program prints out a warning message describing the nature of the error.

If there is a reflection file (MTZ), the program prints out information about MTZ (this is done by CCP4 library routines).

Input and default parameters describing those used for refinement or idealisation or other refinement modes used. For example:

**** Make restraint parameters ***** Dictionary files for restraints : /usr/o4/people/garib/refmac/ftncheck/linux/newdic/add_dict/dic/mon*cif Parameters for new entry and VDW: /usr/o4/people/garib/refmac/ftncheck/linux/newdic/add_dict/dic/ener_lib.cif Cis peptides will be found and used automatically

Form factors of the atoms in a psuedo CIF form:

loop_ _atom_type_symbol _atom_type_scat_Cromer_Mann_a1 _atom_type_scat_Cromer_Mann_b1 _atom_type_scat_Cromer_Mann_a2 _atom_type_scat_Cromer_Mann_b2 _atom_type_scat_Cromer_Mann_a3 _atom_type_scat_Cromer_Mann_b3 _atom_type_scat_Cromer_Mann_a4 _atom_type_scat_Cromer_Mann_b4 _atom_type_scat_Cromer_Mann_c N 12.2126 0.0057 3.1322 9.8933 2.0125 28.9975 1.1663 0.5826 -11.5290 C 2.3100 20.8439 1.0200 10.2075 1.5886 0.5687 0.8650 51.6512 0.2156 O 3.0485 13.2771 2.2868 5.7011 1.5463 0.3239 0.8670 32.9089 0.2508 S 6.2915 2.4386 3.0353 32.3337 1.9891 0.6785 1.5410 81.6937 1.1407

This information could be checked to see if the program has correctly interpreted all the scattering atom types present in the input coordinate file.

The program prints out outliers of the geometric restraints, overall statistics about the geometry and NCS operators if there are any. For more information about geometry see geometric part of the Description of the program.

Outliers will be printed out at every cycle if

has been specifed. IfMONItor MANY

has been specified, they will be printed out only at the first and last cycles. IfMONItor MEDium

has been specified, no outliers will be printed out.MONItor FEW

By default if the value of restrained parameters deviates from the ideal by more than 10 sigma (for non-bonding interactions this is 3 sigma), these restraints are printed out. These parameters can be changed using the MONItor keyword. Sigmas of most restraints (apart from sigmas for non-bonded interactions and non-crystallographic symmetry) are taken from the dictionary file.

If at least one bond length deviates from the ideal value by more than alpha*sigma (alpha is defined by MONItor DISTance alpha, default 10), then the following message is printed:

**** Bond distance outliers **** Bond distance deviations from the ideal > 3.000Sigma will be monitored A 15 ARG C . - A 15 ARG O . mod.= 1.295 id.= 1.231 dev= -0.064 sig.= 0.020

This means that the distance between C of Arg15 of chain A and O of Arg15 of chain A is 1.295, the expected value is 1.231, the deviation from "ideal" value is 0.064, and the sigma for this bond distance restraint is 0.020.

If at least one bond angle deviates from the ideal by more than alpha*sigma (alpha is defined by MONItor ANGLE alpha, default 10), then the following message is printed out:

**** Bond angle outliers **** Bond angle deviations from the ideal >10.000Sigma will be monitored A 50 GLU O B - A 51 LEU N mod.= 100.81 id.= 123.00 dev= 22.193 sig.= 1.600

This means that the angle corresponding to the B conformation of main chain atom O of Glu50 of chain A and N of Leu51 of chain A is 100.81, the expected "ideal" value is 123, the deviation is 22.193 and the sigma is 1.6. Only the first and last atoms of the angle are printed. Middle atom is not printed.

If at least one torsion angle deviates from the "ideal" value by more than alpha*sigma (alpha is defined by MONItor TORSion alpha, default 10), then the following message is printed out:

**** Torsion angle outliers **** Torsion angle deviations from the ideal > 3.000Sigma will be monitored A 11 ASN CA - A 12 LEU CA mod.=-167.65 id.= 180.00 per.= 1 dev=-12.352 sig.= 3.000

This means that the torsion angle with end atoms CA of Asn11 of chain A and CA of Leu12 of chain A is -167.65, the "ideal" value is expected to be 180.0, this torsion angle has periodicity 360/1 = 360, it deviates from the ideal by -12.352, and the sigma for this torsion angle is 3.0. Middle atoms of the torsion angle are not printed.

If at least one chiral volume deviates from the "ideal" by more than alpha*sigma (alpha is defined using MONItor CHIRal alpha, default 10), then the following message is printed out:

**** Chiral volume outliers **** Chiral volume deviations from the ideal >10.000Sigma will be monitored A 51 LEU CG mod.= 2.79 id.= -2.59 dev= -5.375 sig.= 0.200

This means that the chiral volume with centre at CG of Leu51 of chain A is 2.79, the expected value is -2.59, the deviation is -5.375, and the sigma for this chiral volume is 0.2. In this case CD1 and CD2 of LEU should be changed.

If at least one atom in one planar group deviates from planarity more than alpha*sigma (alpha is defined by MONItor PLANe alpha, default 10), then the following message is printed out:

**** Large deviation of atoms from planarity **** Deviations from the planarity >10.000Sigma will be monitored Atom: A 59 ASP C B deviation= 0.31 sigma.= 0.02

The program first calculates the plane for the given set of atoms which are supposed to be in one plane and then calculates the deviation of each atom from this plane. Here C of Asp59 chain A deviates from the plane by 0.31Å, the sigma for this plane is 0.02

If at least one of the distances for non-bonding repulsions (vdw, hydrogen bond, metal-ion) deviates from the ideal by more than alpha*sigma (alpha is defined by MONItor VDWR alpha, default 3), the program prints out the following message:

**** VDW outliers **** VDW deviations from the ideal > 2.000Sigma will be monitored A 26 CYS SG A - A 75 ILE CD1 . mod.= 2.812 id.= 3.820 dev= -1.008 sig.= 0.300

This means the distance between SG of Cys26 of chain A, A conformer and CD1 of Ile75 of chain A is 2.812, the expected "ideal" value is 3.82, the deviation from the "ideal" value is -1.008, and the sigma for this interaction is 0.3.

If the difference between the B-values of bonded atoms or angle-related atoms is more than alpha*sigma (alpha is defined by MONItor BFACtors alpha, default is 10), the following message is printed out:

**** B-value outliers **** B-value differences > 10.00Sigma will be monitored B 5 PHE N - B 4 GLN C ABS(DELTA)= 15.990 Sigma= 1.500

This means that the difference between B-values of the atoms N Phe5 of chain B and C of Gln4 chain B is 15.9, and the sigma for this B-value restraint is 1.5.

If, after transformation of positional or thermal parameters, the difference between NCS-related atoms deviates from 0.0 by more than alpha*sigma (alpha is defined by MONItor NCSR alpha, default is 10), the following message is printed out:

**** NCS restraint outliers **** Deviations from the average position > 3.000Sigma will be monitored Positional: A 12 LEU N . deviation = 0.544 sigma= 0.050 B-value : B 50 ASN CA . deviation =20.000 sigma= 1.500

This means that the position of atom N of Leu12 of chain A deviates from the average position by 0.544Å; the sigma for this NCS-related atoms is 0.05. The B-value of CA Asn50 of chain B deviates from the average B-value by 20.00; the sigma for this B-value is 1.5.

If at least one anisotropic U-value of one atom deviates from the sphere by more than alpha*sigma (alpha is defined by MONItor BSPHere alpha, default 10), the following message is printed out:

**** Sphericity outliers **** U-values different from sphere > 2.00Sigma will be monitored A 26 CYS SG B U-value= 0.2014 0.2329 0.2399 0.0179 0.0227-0.0064 Delta= 0.051 Sigma= 0.025

This means the B conformer of atom SG of Cys26 of chain B deviates from sphericty by more
than 2sigma, the U-value for this atom is U11 = 0.2014, U22= 0.2329, U33=0.2399,
U12=0.0179, U13=0.0227 U14=-0.0064, the Delta of U-values is 0.051 and the sigma is
0.025. The isotropic equivalent of the U-value is calculated as U_{iso} = (U11+U22+U33)/3.
In this case U_{iso} = 0.2247. The B-value equivalent of U_{iso} is 17.74.

If at least for one pair of bonded atoms the rigid bond restraint deviates from 0 by more than alpha*sigma (alpha is defined by MONItor RBONd alpha, default 10), the following message is printed out

**** Rigid bond outliers **** Rigid bond differences > 2.00Sigma will be monitored A 12 LEU N - A 11 ASN C Delta = 4.625 Sigma= 2.000

This means the rigid bond restraint between atoms N of Leu12 chain A and C of Leu12 of chain A deviate from 0 by 4.625, the sigma for the rigid bond restraint in terms of B values is 2.0.

An example:

------------------------------------------------------------------------------- Restraint type N restraints Rms Delta Av(Sigma) Bond distances: refined atoms 3167 0.017 0.022 Bond distances: others 2000 0.006 0.020 Bond angles : refined atoms 4217 1.560 2.007 Torsion angles, period 1. refined 377 4.740 3.000 Torsion angles, period 3. refined 703 20.175 15.000 Chiral centers: refined atoms 503 0.110 0.200 Planar groups: refined atoms 2186 0.006 0.020 VDW restraints: refined atoms 4658 0.397 0.431 VDW restraints: refined atoms 190 0.197 0.363 VDW restraints: refined atoms 106 0.285 0.300 VDW restraints: refined atoms 9 0.227 0.300 M. chain bond B-values: refined atoms 1900 0.335 1.500 M. chain angle B-values: refined atoms 3076 0.617 2.000 S. chain Bond B-values: refined atoms 1267 1.307 3.000 S. chain angle B-values: refined atoms 1141 1.956 4.500 NCS: tight positional, group 1 chain A 26 0.081 0.050 NCS: medium positional, group 1 chain A 170 0.420 0.500 NCS: loose positional, group 1 chain A 171 1.031 5.000 NCS: tight thermal, group 1 chain A 26 0.068 0.500 NCS: medium thermal, group 1 chain A 170 0.626 2.000 NCS: loose thermal, group 1 chain A 171 2.339 10.000 -------------------------------------------------------------------------------

Where

`N restraints`- Number of restraints for this particular geometric value.
`Rms Delta`- Root mean square deviation of model values of geometric paramters from
ideal ones. It is calculated as:
Rms Delta = sqrt(sum(Geom

_{ideal}-Geom_{model})^{2}/N_{restraints})`Geom`_{ideal}- ideal value for the geometric parameter (bond distance, bond angle
*etc.*), taken from the dictionary. `Geom`_{model}- value of the geometric parameter calculated from the current model.
`N`_{restraints}- number of restraints for this particular geometric parameter, over which the summation runs.

`Av(Sigma)`- Average sigma for this restraint type. Each restraint has its own sigma value. Most of them are stored in the dictionary file.
`refined atoms`- Restraints corresponding to the atoms included in the geometric and X-ray gradient and second derivative calculations.
`others`- Restraints corresponding to the atoms included in the geometric calculation, gradients, and structure factor calculations but not included in the X-ray gradient and second derivative calculations. By default hydrogens are dealt with in this way.

Statistics about the following restraints are printed out: bond lengths, bond angles, torsion angles, chiral volumes, planar groups, non-bonding interactions, B-value, NCS, sphericity, rigid bond.

Details should be in the description of the program and theory behind the program. But they are not ready yet.

Root mean square deviation of covalent bond lengths from the "ideal" ones. For example:

Bond distances: refined atoms 3167 0.017 0.022

The first number is the number of covalent bond lengths, the second is the root mean square deviation of the bond lengths from the dictionary values and the third is the average sigma for this restraint type. Bond lengths are calculated in Ås.

Statistics about agreement of the bond angles calculated from the current refined model and corresponding ideal angles from the dictionary. For example:

Bond angles : refined atoms 4217 1.560 2.007

The first value is the number of restraints, the second is the root mean square deviation of the bond angles from dictionary values and the third is the average sigma. Bond angles are given in degrees (°).

Root mean square deviation of the model torsion angles from the "ideal" values. For example:

Torsion angles, period 1. refined 677 4.874 3.000 Torsion angles, period 3. refined 950 18.910 15.000

This means that there are 677 torsion angles with period 1, the root mean square deviation from the ideal value for them is 4.874 and the average sigma for these torsion angles is 3.0. There are 950 torsion angles with period 3 and the root mean square deviation from the ideal value for them is 18.91 and the average sigma for these torsion angles is 15.0.

The first line gives statistics for the torsion angles with period 1 and the second line for the torsion angles with period 3. The period of a torsion angle means: if the ideal value of a torsion angle is alpha then alpha + n*360/period values are also ideal values (here n is integer). For example if the ideal value of a torsion angle is 60° and the period is 3, then 60 + 1*360/3 = 60 + 120 = 180 and 60 - 1*360/3 = 60 - 120 = -60 are also ideal values. All other possibilities (for example 60 + 2*360/3 = 60 + 240 = 300 is equivalent to -60) are equivalent to one of these values.

This gives statistics about chiral volumes. For example:

Chiral centres: refined atoms 816 0.355 0.200

This means that there are 816 chiral volumes, the root mean square deviation of these chiral volumes from the dictionary values is 0.355 and the average sigma for them is 0.2.

Chiral volumes are defined with four atoms. The volume of a pyramid formed by these four atoms is calculated and compared with the "ideal" value from dictionary. Chiral volumes could be positive or negative. If two atoms have changed their positions, the chiral volume changes its sign. For example consider Val CB. Three other atoms involved are CA, CG1 and CG2. If CG1 and CG2 have swapped their positions, the chiral volume changes its sign.

Statistics about the deviation of the atoms from the planes in planar groups like the rings of histidine residues. For example:

Planar groups: refined atoms 4016 0.019 0.020

This means in total there are 4016 atoms in planar groups. The root mean square deviation of these atoms from the planes is 0.019 and the average sigma for the planar groups is 0.020.

Four types of non-bonding interactions are considered:

- The atoms can form a hydrogen bond. Acceptor-donor repulsion.
- One of the atoms is acceptor and the other atom is hydrogen from donor.
- One of the atoms is a metal and the other is an ion.
- None of above. VDW repulsion.

If the interacting atoms are related through symmetry, they are considered separately. If the VDW repulsion is between atoms related by one torsion angle, they are considered separately. Sigma and "ideal" distance for them is different from other VDW pairs.

Statistics for above interactions; an example:

VDW repulsions: refined atoms 2697 0.265 0.300 VDW; torsion: refined atoms 488 0.154 0.500 HBOND: refined atoms 451 0.160 0.500 VDW repulsions; symmetry: refined atoms 215 0.263 0.300 HBOND; symmetry: refined atoms 50 0.266 0.500

Here the first number is the number of restraints for this repulsion type, the second is
the root mean square deviation from the "ideal" value. The last number is the
average sigma for this restraint type. Note that only repulsions are considered, *i.e.*
if atoms are separated by more than the "ideal" distance they are not considered as
interacting atoms.

This statistic is about differences in B-values between atoms related by one covalent bond or bond angle. Side chains and main chains of the amino acids are considered separately. In other entries all bonds and angles are considered to be equivalent. The sigma and root mean square deviation of B-value differences from 0 are given in terms of B-values not U-values. Example of B-value restraint statistics:

M. chain bond B-values: refined atoms 3365 3.464 1.500 M. chain angle B-values: refined atoms 5393 4.960 2.000 S. chain Bond B-values: refined atoms 1900 3.839 3.000 S. chain angle B-values: refined atoms 1755 5.312 4.500

The first line states that there are 3365 pairs of atoms in main chain related by covalent bonds. The root mean square deviation from 0 of the B-value differences of these atoms is 3.465 and the average sigma for these pairs of atoms is 1.5. The second line is for main chain angle related atoms, the third line is for side chain bond related atoms and the fourth line is for side chain angle related atoms.

The program prints out the agreement between NCS-related atoms. First transformation matrices for all chains are calculated and average positions for each atom after applying corresponding transformation matrices are calculated. Then the difference between transformed and average positions is calculated and used for statistics calculations.

NCS: tight positional, group 1 chain A 26 0.081 0.050 NCS: medium positional, group 1 chain A 170 0.420 0.500 NCS: loose positional, group 1 chain A 171 1.031 5.000 NCS: tight thermal, group 1 chain A 26 0.068 0.500 NCS: medium thermal, group 1 chain A 170 0.626 2.000 NCS: loose thermal, group 1 chain A 171 2.339 10.000

The first number is the number of atoms from this group (chain or part of chain), the second number is the root mean square deviation of transformed atoms from the average positions of NCS-related atoms and the third number is the sigma used for this restraint type.

REFMAC prints out statistics about tight, medium and loose NCS restraints. The difference between these restraint types is the weight used for restraints. Statistics about positional as well as thermal parameters are printed out. If NCS-related atoms have anisotropic thermal parameters then the transformation matrix corresponding to anisotropic U-values is calculated and used to compare NCS-related atomic U-values. All statistics about thermal parameters are given in B-value units.

Positional parameters are in Å and thermal parameters are in Å².

The program prints out the root mean square deviation from a sphere, for
anisotropic B-values. For each anisotropic atom their isotropic equivalent
(B_{iso}=(B11+B22+B33)/3) and the deviation of the anisotropic B-value
from the isotropic equivalent is calculated. Then the root mean square is
calculated and printed out. For example:

Sphericity. Free atoms 388 4.689 2.000 Sphericity. Bonded atoms 5184 0.825 2.000

The program prints out statistics for free atoms (like water) and bonded atoms separately. For example the first line states that there are 388 free atoms, the root mean square deviation of these atoms' B-values from a sphere is 4.689 and the average sigma used for this restraint type is 2.0. Deviation of the anisotropic B-value from sphericity for bonded atoms is smaller than that for free atoms as expected. In general there are more restraints for bonded atoms (B-value restraints, rigid bond restraints and sphericity restraints) than for free atoms (only sphericity restraints).

For bonded atoms REFMAC calculates projections of the anisotropic B-values onto the bond for both atoms and then calculates the difference between these projections. The root mean square of these differences then printed out. For example:

Rigid bond restraints 5265 3.054 2.000

This states that there are 5265 covalent bonds, the root mean square value of differences of the projections of anisotropic B-values onto the bond between them is 3.054, and the sigma used for these restraints is 2.0.

REFMAC calculates transformation matrices for all chains specified to be related by NCS. The first chain (or group) is taken as reference so it has identity matrix of rotation and 0 translation vector. For all other chains the transformation matrix to this chain is calculated. The program prints out (if MONItor MANY has been specified) the transformation matrices, translations as well as rotation angles in polar coordinate system. For example (only one chain is considered):

Transformation from chain B to chain A -0.9988 0.2784E-01 -0.4056E-01 R = 0.2855E-01 0.9994 -0.1693E-01 0.4006E-01 -0.1807E-01 -0.9990 T = 2.848 -25.48 76.07 DET(R) = 1.000 Phi = 89.50 Psi(or Omega) = -90.81 Chi(or Kapppa) = 177.69

Where R is the transformation matrix, T is the translation vector, Phi and Psi
show the position of a vector around which the rotation takes place and Chi(or Kappa)
is the amount of rotation around this vector. This NCS rotation is nearly
180°, *i.e.* nearly a 2-fold axis. For a 3-fold axis Chi would be 120, for
a four-fold it would be 90 *etc.*

To get the transformed position, first the rotation matrix and after that the
translation is applied (x_{new} = R x_{old} + T, x_{new}
is transformed position and x_{old} is original position.).

If NCS-related atoms have anisotropic B-values, the corresponding matrix for anisotropic B-values is calculated. See reference [3].

The determinant of the rotation matrices should be 1. If the transformation includes inversion, then the determinant is equal to -1.

For more information about X-ray contribution to refinement and statistics see X-ray part of the Description of the program.

If MONItor MANY is specified, the program will print overall X-ray statistics as well as a distribution of X-ray statistics over resolution. It is a good idea to check if the behaviour of statistics is as expected. If MONItor MEDIum is specified, the program will print the behaviour of statistics over resolution only in the first and last cycles. In all other cycles only the minimum of overall statistics, namely "overall R-factor", "overall free R-factor" and "overall figure of merit" will be printed out. If MONItor FEW is specified, the program will print out only a minimum of statistics about X-ray.

The behaviour of the X-ray statistics over resolution is printed out so that they can be utilised using loggraph. For example:

**** Things for loggraph, R factor and others **** $TABLE: Rfactor analysis, F distribution v resln : $GRAPHS:<rfactor> v. resln :N:1,6,7,11,12: :<fobs> and <fc> v. resln :N:1,4,5,9,10: :% observed v. resln :N:1,3: $$ M(4SSQ/LL) NR_used %_obs M(Fo_used) M(Fc_used) Rf_used WR_used NR_free M(Fo_free) M(Fc_free) Rf_free WR_free $$ $$ 0.008 369 89.38 901.7 828.2 0.21 0.25 18 1013.0 905.9 0.25 0.28 0.020 635 100.00 537.3 532.3 0.27 0.29 29 576.0 617.2 0.30 0.36 0.032 769 99.88 423.7 457.2 0.27 0.28 52 407.6 403.0 0.32 0.32 0.044 906 99.90 562.7 563.9 0.19 0.21 49 514.0 523.8 0.24 0.26 0.055 1053 99.64 604.7 572.5 0.19 0.21 45 539.9 499.8 0.23 0.25 0.067 1096 99.74 544.1 501.4 0.18 0.19 65 496.5 443.8 0.22 0.23 0.079 1223 100.00 476.1 440.5 0.18 0.19 68 438.4 390.2 0.23 0.24 0.091 1312 99.78 366.6 347.5 0.19 0.18 66 359.7 357.0 0.26 0.25 0.103 1376 99.93 308.8 300.1 0.19 0.17 72 316.9 293.6 0.25 0.24 0.114 1432 99.21 249.4 257.0 0.21 0.19 81 253.0 261.6 0.27 0.24 0.126 1534 99.69 217.4 225.6 0.21 0.18 77 227.1 234.7 0.31 0.28 0.138 1570 99.76 195.0 197.0 0.21 0.19 98 181.5 180.8 0.35 0.30 0.150 1696 99.83 179.9 187.0 0.22 0.18 90 176.1 182.4 0.22 0.19 0.161 1691 99.61 162.2 166.9 0.22 0.18 91 171.9 171.3 0.25 0.22 0.173 1775 99.26 152.1 152.4 0.21 0.18 91 148.8 144.5 0.31 0.25 0.185 1819 98.35 144.5 138.3 0.22 0.18 84 133.0 131.9 0.30 0.25 0.197 1858 97.70 131.8 126.8 0.23 0.19 98 129.2 125.1 0.33 0.30 0.209 1895 97.19 135.5 121.1 0.22 0.19 109 137.1 116.6 0.30 0.27 0.220 1942 99.71 118.1 102.0 0.25 0.23 101 127.1 110.7 0.28 0.27 0.232 1939 100.00 139.4 92.3 0.36 0.35 96 129.5 85.2 0.38 0.38 $$

Where (all statistics are for resolution bins):

- M(4SSQ/LL)
- Middle of resolution bins in 4 sin²(theta)/lambda²
- NR_used
- Number of reflections included in the refinement.
- %_obs
- Percentage observed reflections.
- M(Fo_used)
- Average value of the observed reflections used in the refinement.
- M(Fc_used)
- Average value of the amplitudes of the calculated structure factors.
- Rf_used
- R-factors corresponding to the reflections used in the refinement.
- WR_used
- Weighted (with weights 1/sigma
_{Fo}) R-factor corresponding to the reflections included in the refinement. - NR_free
- Number of reflections used for free R-factor calculation and likelihood parameters estimation.
- M(Fo_free)
- Average value of the amplitudes of the observed
*"free"*reflections. - M(Fc_free)
- Average value of the amplitudes of the calculated
*"free"*reflections. - Rf_free
- R-factor corresponding to the
*"free"*reflections. - WR_free
- Weighted R-factors corresponding to the
*"free"*reflections.

Another example:

**** Fom and SigmaA vs resolution **** $TABLE: Fom(<cos(DelPhi)>-acentric, centric, overall v resln: $GRAPHS:<Fom> v. resln :N:1,3,5,7,8: $$ <4SSQ/LL> NREFa FOMa NREFc FOMc NREFall FOMall SigmaA_Fc1 $$ $$ 0.0084 313 0.808 56 0.727 369 0.796 0.884 0.0202 568 0.810 67 0.758 635 0.805 0.884 0.0319 704 0.809 65 0.744 769 0.803 0.885 0.0437 838 0.812 68 0.788 906 0.811 0.885 0.0555 985 0.809 68 0.792 1053 0.808 0.885 0.0673 1029 0.808 67 0.771 1096 0.806 0.885 0.0790 1158 0.811 65 0.769 1223 0.809 0.885 0.0908 1243 0.800 69 0.659 1312 0.792 0.885 0.1026 1310 0.809 66 0.722 1376 0.805 0.885 0.1143 1368 0.801 64 0.735 1432 0.798 0.885 0.1261 1468 0.799 66 0.596 1534 0.790 0.885 0.1379 1501 0.793 69 0.678 1570 0.788 0.885 0.1497 1628 0.796 68 0.685 1696 0.791 0.885 0.1614 1625 0.793 66 0.624 1691 0.787 0.885 0.1732 1719 0.787 56 0.640 1775 0.782 0.885 0.1850 1756 0.792 63 0.694 1819 0.789 0.885 0.1967 1802 0.783 56 0.607 1858 0.777 0.885 0.2085 1840 0.795 55 0.679 1895 0.792 0.885 0.2203 1883 0.776 59 0.629 1942 0.772 0.885 0.2321 1884 0.830 55 0.800 1939 0.829 0.885 $$

Where:

- <4SSQ/LL>
- Middle of resolution bins in 4 sin²(theta)/lambda²
- NREFa
- Number of acentric reflections
- FOMa
- Figure of merit of the phases for the acentric reflections
- NREFc
- Number of centric reflections
- FOMc
- Figure of merit of the phases for the centric reflections
- NREFall
- Number of all reflections
- FOMall
- Figure of merit of the phases for all reflections

An example:

Resolution limits = 19.920 2.050 Number of used reflections = 27890 Percentage observed = 99.1694 Percentage of free reflections = 5.0392 Overall R factor = 0.2142 Free R factor = 0.2722 Overall weighted R factor = 0.2076 Free weighted R factor = 0.2630 Overall correlation coefficient = 0.9403 Free correlation coefficient = 0.9030 Cruickshank's DPI for coordinate error= 0.2245 DPI based on free R facotr = 0.2019 Overall figure of merit = 0.7948 ML based su of positional parameters = 0.1576 ML based su of thermal parameters = 5.7279

Where:

- Resolution limits
- Resolution limits used for refinement (in Å)
- Number of used reflections
- Number of all reflections used for the refinement
- Percentage observed
- Fraction of the observed reflections in %. If uniqueify has been run before using REFMAC, this value will be calculated correctly. Otherwise it will be 100.0%.
- Percentage of free reflections
- Percentage of reflections observed but not included in refinement and used for purpose of free R-factor calculation and estimation of the overall maximum likelihood parameters
- Overall R-factor
- Overall R-factor. It is calculated as:

whereR-factor = sum||F

_{o}-|F_{c}||/sum|F_{o}|`sum`is over all reflections included in the refinement,`|F`is observed amplitude of the structure factor,_{o}|`|F`is amplitude of the calculated structure factor._{c}| - Before calculating an "R-factor", the observed and calculated structure factors are scaled to each other. Scale values (isotropic and anisotropic) are applied to the calculated structure factors. If bulk solvent is used then this is also taken into account. See scaling part of Description of program for details of scaling.
- Free R factor
- As "Overall R-factor" described above, except the summation is
over the reflections
*not*included in the refinement. - Overall weighted R-factor
- Overall weighted R-factor. It is calculated as:

whereweighted R factor = sum w ||F

_{o}-|F_{c}||/sum w |F_{o}|`w`is 1/sigma_{Fo},`sigma`is the uncertainty of the observed amplitudes of the structure factor._{Fo} - Free weighted R factor
- As "Overall weighted R-factor" except the summation is over the reflections not included in the refinement.
- Overall correlation coefficient
- Correlation between observed and calculated structure factor amplitudes.
It is calculated as:

whereCorrel = (sum(|F

_{o}||F_{c}|)-<|F_{o}|><|F_{c}|>)/((sum(|F_{o}|²)-<|F_{o}|>²)(sum(|F_{c}|²)-<|F_{c}|>²))^{1/2}`<|F`,_{o}|>=sum(|F_{o}|)/N_{used}`<|F`, summation is over the reflections included in the refinement,_{c}|>=sum(|F_{c}|)/N_{used}`N`is number of reflections included in the summation._{used} - Free correlation coefficient
- Same as "Overall correlation coefficient" except summation is over the reflections not included in the refinement.
- Cruickshank's DPI for coordinate error
- It is calculated using R-factor, number of the reflections,
number of parameters and number of observables. Completeness of the data
is also taken into account:

whereDPI = sqrt(N

_{atom}/(N_{refl}-N_{param})) R_{factor}D_{max}compl^{-1/3}`N`is the number of the atoms included in the refinement,_{atom}`N`is the number of reflections included in the refinement,_{refl}`R`is the overall R-factor,_{factor}`D`is the maximum resolution of reflections included in the refinement,_{max}`compl`is the completeness of the observed data. - DPI based on free R-factor
- It gives some idea about precision of the positional parameters. It is
calculated using the free R-factor:

whereDPI = sqrt(N

_{atom}/N_{free}) R_{free}D_{max}compl^{-1/3}`N`is the number of atoms included in the refinement,_{atom}`N`is the number of reflections included in the free R-factor calculation,_{free}`R`is the free R-factor,_{free}`D`is the maximum resolution in Å,_{max}`compl`is the completeness of the reflection data. - Overall figure of merit
- Overall figure of merit of the phases. It is calculated as:
- ML based su of positional parameters
- Overall standard uncertainties of the positional parameters based on the likelihood function
- ML based su of the thermal parameters
- Overall standard uncertainties of the thermal parameters (B-values) based on the likelihood function.

REFMAC prints out the scale and sigmaA parameters at every cycle. However, if anisotropic scale is used it is estimated at the first cycle only. For example:

----------------------------------------------------------------------------- Overall : scale = 0.604, B = -0.050 Babinet's bulk solvent: scale = 0.299, B = 200.000 Partial structure 1: scale = 0.727, B = 13.532 Overall anisotropic scale factors B11 = 0.98 B22 = -0.91 B33 = 0.21 B12 = 0.00 B13 = 0.31 B23 = 0.00 Overall sigmaA parameters : sigmaA0 = 0.930, B_sigmaA = 2.136 Babinet's scale for sigmaA : scale = -0.191, B = 150.000 SigmaA fo partial structure 1: scale = 0.304, B = 56.473 -----------------------------------------------------------------------------

Scale factors are estimated using the following equation:

sum(|F_{o}|-Sc_{ov}exp(-s^{T}B_{an}s)(1-Sc_{b}exp(-B_{b}|S|^{2}))|F_{c}exp(-B_{ov}|S|^{2})+F_{s}Sc_{s}exp(-B_{s}|S|^{2})|)^{2}

where

Sc_{ov} |
overall scale factor. |

B_{an} |
overall anisotropic B tensor. It is calculated so that it obeys crystal symmetry and in orthogonal system its trace is 0 (B11+B22+B33=0). |

Sc and _{b}B_{b} |
scale and B-values for bulk solvent, based on Babinet's principle. |

B_{ov} |
overall B-value applied to the structure factors calculated from the coordinates. |

Sc and _{s}B _{s} |
scale and B-values applied to the structure factors calculated from Fourier transformation of the solvent region. |

|F_{o}| |
observed amplitude of the structure factor. |

F_{c} |
structure factor (complex) calculated from the coordinates. |

F_{s} |
structure factor (complex) calculated from the solvent region |

s |
vector (h a*, k b*, l c*);
a*, b*, c* are reciprocal space cell dimensions,
(h,k,l) are the Miller indices of a reflection. |

|S| |
length of reciprocal space vector or sin(theta)/lambda). |

The summation in the above equation is over all reflections included in the refinement.

SigmaA parameters are estimated using the likelihood function. Reflections
not included in the refinement are used for SigmaA estimations.
**This part should be completed or refer to description, theory whatever**

If one of the following keywords has been specified:

or# # Refine TLS parameters before individual atomic refinement # REFI TLSCcycle ncycle

# # Refine TLS parameters # TLSCcycle ncycle

then REFMAC prints out the TLS parameters at each TLS refinement cycle. If TLSIN does not contain information about origin, T, L or S parameters then they are initialised to 0. For details of TLS parameters see, description whatever.

The program prints out information about TLS parameters into the .log file in the following form:

TLS group 1: From REFMAC T tensor ( 1) = 0.072 0.171 0.105 -0.064 0.034 -0.030 L tensor ( 1) = 4.809 8.514 2.917 4.601 -1.762 -1.277 S tensor ( 1) = -0.751 0.397 -0.344 0.006 0.263 0.683 -0.012 -0.038 ... TLS group 6: chain F T tensor ( 6) = 0.160 0.295 0.304 0.034 -0.119 0.071 L tensor ( 6) = 9.227 8.425 11.079 3.739 3.652 3.743 S tensor ( 6) = -0.167 0.090 -0.829 -0.203 -0.566 0.744 0.676 0.432

where numbers for the T-tensor correspond to T_{11}, T_{22},
T_{33}, T_{12}, T_{13}, T_{23}. Note that the T-tensor
is symmetric. The same is true for the L-tensor. The S-tensor is printed out as
S_{22}-S_{11}, S_{11}-S_{33}, S_{12},
S_{13}, S_{23}, S_{21}, S_{31}, S_{32}.
The number inside the brackets show the domain (TLS group) number.

The unit for T is Å², for L it is degree², and for S it is Å*degree.

Note that by inspecting the L-tensor, one can make inference about the degree of order of specific domains. In the above example, the L parameter for domain 6 (rigid group 6) has a larger value than for domain 1. Electron density before and after TLS refinement shows that domain 6 is less ordered.

If either

# # Do rigid body refinement # MODE RIGId_body

or

# # Do rigid body refinement # REFInement TYPE RIGId_body

has been specified, then REFMAC prints out information about the progress of the rigid body refinement. In the case of rigid body refinement refmac prints out information about X-ray statistics, scale parameters and the parameters of the rigid body (or bodies).

If

# # Print out full refinement statistics. In case of the rigid body refinement # print out full x-ray statistics and parameters of the rigid bodies # at every cycle. # MONItor MANY

then the program prints out rigid body statistics at every cycle. If either:

# # Print out minimum information. In case of rigid body refinement # print out only minimum x-ray statistics (scale parameters, R factor, # free R factor, figure of merit) at every cycle and parameters of the # rigid body only in the last cycle. # MONItor FEW

or

# # Print out medium number statistics. In case of the rigid body # it means that print out rigid body parameters only at the last cycle, # full x-ray statistics at the first and last cycles. In all other cycles # only minimum information about x-ray (scale parameters, R factor, free R # factor and fom) # MONItor MEDIum

has been specified, then REFMAC prints out rigid body statistics only at
the last cycle of refinement, *i.e.* only total rotation and translation.

After giving information about the input script in the "Input and default parameters" section, the program prints out information about rigid body groups. For example:

Refinement type : Rigid Body **** Domain Definition **** Group: 1: No. of pieces: 1 Chain: A Span: 1 600 ** All atoms ** Group: 2: No. of pieces: 1 Chain: B Span: 1 600 ** All atoms **

This means that the program will perform rigid body refinement. The number of rigid body groups is 2. The first group contains residues from 1 to 600 of chain A, the second group contains residues from 1 to 600 of chain B. All atoms in all residues will be used for refinement and structure factor calculations.

At the end the program prints out a message about rigid body movement. For example:

---------------------------------------------------------- Rigid body parameters will be applied to coordinates as following Xnew = Rot*Xold - Rot*Tg + Tg +deltaTg Where Xnew and Xold are new and old coordinates of atoms in this domain Rot is rotation matrix derived from Euler angles Tg is centre of mass of this domain deltaTg is shift of centre of mass ---------------------------------------------------------- Domain 1 Centre of mass: 62.077 15.442 64.907 Euler angles and deltaTg: -0.22 0.57 -0.08 -0.05 -0.09 -0.09 Matrix and deltaTg 1.000 0.005 0.010 -0.005 1.000 0.000 -0.010 0.000 1.000 -0.045 -0.093 -0.087 Polar angles: PHI, PSI(or Omega), CHI(or Kappa), deltaTg: 117.27 89.93 0.64 -0.05 -0.09 -0.09 Domain 2 Centre of mass: 89.665 19.770 4.975 Euler angles and deltaTg: -0.21 -0.50 -0.06 0.15 0.11 -0.14 Matrix and deltaTg 1.000 0.005 -0.009 -0.005 1.000 0.000 0.009 0.000 1.000 0.152 0.113 -0.144 Polar angles: PHI, PSI(or Omega), CHI(or Kappa), deltaTg: 118.88 -90.07 0.57 0.15 0.11 -0.14

Important numbers to look at are deltaTg, *i.e.* the domain's centre of mass's shift,
and CHI (or Kappa), which gives the amount of rotation. For example:

Shift of the first domain in Å is ( -0.045,-0.093,-0.087) and rotation is 0.64°.

Output coordinates correspond to the new rotated and shifted atoms.