Syntax of the Xrefin Statement

The xrefin statement is used to read structure factors, symmetry operators, atomic-form factors, unit cell parameters, etc. It also branches into several other statements that allow one to manipulate structure factors, refine certain parameters, carry out translation or rotation searches, compute solvent masks, or compute electron density maps.

Manipulations of structure factors are carried out for the selected reflections. The selection of reflections is accomplished by the RESOlution and FWINdow statements. Atoms contributing to the structure factor $F_{calc}$ are selected through the SELEction and SCATter statements.

XREFin { $<$xrefin-statement$>$ } END

is invoked from the main level of XPLOR.

$<$xrefin-statement$>$:==

A=$<$real$>$

specifies $a$ of unit cell (default: 1.0 Å).

ALPHa=$<$real$>$

specifies $\alpha$ of unit cell (default: 90$^{\circ}$).

B=$<$real$>$

specifies $b$ of unit cell (default: 1.0 Å).

BETA=$<$real$>$

specifies $\beta$ of unit cell (default: 90$^{\circ}$).

C=$<$real$>$

specifies $c$ of unit cell (default: 1.0 Å).

DO

$<$xrefin-do-statement$>$ manipulates structure factors (see Section 13.5).

EXPAnd

expands selected reflections to P1; i.e., the crystallographic symmetry operators and the Hermitian symmetry operator (if HERMitian=TRUE) are applied to the selected reflections. Multiple entries that emerge during this process are discarded. Multiple application of EXPAnd is possible. The second time around, it does not have any effect unless new data are added or more symmetry operators are added.

FFK=$<$real$>$

sets $k$ in Eq. 13.1 to the specified value. If FFK is set to 0, $k$ is automatically determined by Eq. 13.6. Automatic scaling also declares symbols ($FFK, $TEST_FFK) that contain the values of $k$ for the working set and the test set, respectively (default: 0, i.e., automatic scaling).

FFT

{ $<$FFT-statement$>$ } END specifies parameters for the FFT method.

FWINdow

$<$real$>$ $<$real$>$ sets $F_{obs}$ amplitude limits for the selection of reflections. One of the $<$real$>$ values is the upper value; the other one is the lower value; it does not matter whether the upper or the lower limit comes first (default: FWINdow 0 100000).

GAMMa=$<$real$>$

specifies $\gamma$ of unit cell (default: 90$^{\circ}$).

GENErate

complements the current reflections to yield a full asymmetric unit of reflections for the specified resolution range. If no current reflections are present, a full asymmetric unit is generated. The new Fobs are set to 1 except for systematic absences, in which case Fobs is set to 0. Fcalc, Fpart are set to 0; weight, sigma, and FOM are set to 1. Action is taken as soon as this statement is issued.

HERMitian=$<$logical$>$

specifies whether Friedel mates are identical (HERMitian=TRUE) or different from each other (HERMitian=FALSE). Thus, for anomalous scattering data, one has to set HERMitian=FALSE and specify the imaginary scattering components for the appropriate atoms (default: TRUE).

LOOKup=$<$logical$>$

is a flag indicating whether to use lookup tables for the direct summation method and the FFT method (default: TRUE). Turn off the lookup tables if problems with minimization procedures are encountered.

MAP

{ $<$xrefin-map-statement$>$ } END computes electron density maps (see Section 16.1).

MBINs=$<$integer$>$

specifies the number of bins for the $R$ value analysis (PRINt R), phase difference analysis (PRINt PHASe), data completeness analysis (PRINt COMPleteness), and computation of normalized structure factors (Es) (default: 8).

METHod=

DIREct $\vert$ FFT specifies choice of method to compute $F_{calc}$ (default: FFT).

NREFlections=$<$integer$>$

is a required parameter that allocates space for the reflections. It has to be greater than or equal to the actual number of reflections (default: 200).

OPTImize

BFACtor { $<$xrefin-optimize-bfactor-statement$>$ } END optimizes individual (restrained) isotropic B-factors (see Section 14.4).

OPTImize

GROUp { $<$xrefin-optimize-group-statement$>$ } END optimizes group B-factors and/or occupancies (see Section 14.3).

OPTImize

OVERall { $<$xrefin-optimize-overall-statement$>$ }
END optimizes an overall isotropic or anisotropic B-factor (see Section 14.2).

PRINt COMPleteness

prints the ratio of the number of observed reflections to the number of theoretically observable reflections (“completeness," printed as a percentage). The analysis is carried out as a function of resolution. The overall completeness is stored in the symbol $COMPLETENESS. If the data are partitioned into a test set and a working set, a completeness analysis is also carried out for the test reflections (see Chapter 17). In this case, the completeness for the test reflections (TEST=1) is stored in the symbol $TEST COMPLETENESS, and the completeness for the working set is stored in $COMPLETENESS. This statement also produces a listing that can be plotted by a Mathematica script.

PRINt PHASe

prints the average phase difference as a function of resolution for the selected reflections and stores the overall phase difference in the symbol $DPHI. Phases differences are weighted with the WEIGht array (see Section 13.5). If a figure-of-merit weighted average is required, the user should issue a “DO (WEIGHT=MAX(0,FOM))" statement; this will overwrite the existing weights. If the data are partitioned into a test set and a working set, a phase difference analysis for the test reflections is also carried out (see Chapter 17). The “free" phase difference is stored in the symbol $TEST DPHI. Note that no prior update of $F_{calc}$ is performed, and thus the user must issue an UPDAte statement if the $F_{calc}$ array is undefined or not well defined. This statement also produces a listing that can be plotted by a Mathematica script.

PRINt R

prints the $R$ value as a function of resolution for the selected reflections and stores the overall $R$ value in the symbol $R. If the data are partitioned into a test set and a working set, a free $R$ value analysis is also carried out (see Chapter 17). The free $R$ value is stored in the symbol $TEST R. Note that no prior update of $F_{calc}$ is performed. Thus, the user must update $F_{calc}$ with the UPDAte statement if the $F_{calc}$ array is undefined or if an energy calculation (e.g., energy minimization or molecular dynamics) was carried out previously. In the latter case, the $F_{calc}$ array is filled with the values of the derivatives of the target function. This statement also produces a listing that can be plotted by a Mathematica script.

PRINt TARGet

prints the value of $E_{XREF}$ (Eq. 13.1). If the residual or the AB vector-residual is chosen, the $R$ value is stored in the symbol $R. If targets are chosen that contain a correlation coefficient, its value is stored in the symbol $CORR. If the data are partitioned into a test and a working set (see Chapter 17), the corresponding values for the test set are stored in the symbols $TEST R and $TEST CORR. Note that no prior update of $F_{calc}$ is performed, and thus the user must issue an UPDAte statement if the $F_{calc}$ array is undefined or not well defined.

PRINt WILSon

makes a Wilson plot (Wilson, 1949; Main, 1975; Rogers, 1965). The overall scale factor and B-factor are obtained by a least-squares fit of $\log(I_{obs}/f^2)$ vs. $s^2$. The result is stored in symbols $BFACTOR, $SCALE, and $TEST_BFACTOR, $TEST_SCALE for the working and test sets, respectively. This statement also produces a listing that can be plotted by a Mathematica script.

REDUce

decreases selected reflections to an asymmetric unit. In the case of multiple entries, the first entry is kept and the duplicates are discarded; i.e., no data averaging is performed.

REFLection

{ $<$xrefin-reflection-statement$>$ } END initiates reading or merging of diffraction data (see Section 13.4).

RESEt

erases the current xrefin database, i.e., the atomic-form factors, symmetry operators, reflections, and unit cell parameters.

RESOLution

$<$real$>$ $<$real$>$ sets resolution limits in Å for the selection of reflections. One of the $<$real$>$ values is the high resolution limit, and the other one is the low resolution limit; it does not matter whether the high or the low resolution limit comes first. One of the limits can be set to the string “INFInity", e.g., “RESOlution INFInity 3". This statement will then include the 0,0,0 reflection in all calculations (default: RESOlution 10. 3. ).

SCATter

$<$selection$>$ $<$real$>$ $<$real$>$ $<$real$>$ $<$real$>$ $<$real$>$
$<$real$>$ $<$real$>$ $<$real$>$ $<$real$>$ [ IMAGinary $<$real$>$ ] adds an atomic-form factor specification to the xrefin database. The statement specifies the coefficients $a_1, b_1, a_2, b_2, a_3, b_3, a_4, b_4, c, d$ (Eq. 13.10) for the selected atoms (default: none). An atom will contribute to the structure factors only if it has been selected in one SCATter statement and if it has been selected in the SELEction statement. Care should be taken not to produce an overlapping definition of atom selections; e.g., if there is a ca ion, one should exclude it from the atomic-form factor definition for carbon atoms. The optional IMAGinary parameter should be used for anomalous scatterers. “SCATter RESEt" will erase the existing atomic form factor entries.

SEARch

ROTAtion { $<$xrefin-search-rotation-statement$>$ } END is a translation search (see Section 19.3).

SEARch

TRANslation { $<$xrefin-search-translation-statement$>$ } END is a rotation search (see Section 19.3).

SELEction=

$<$selection$>$ selects atoms that will be used in the next structure factor calculation (default: (ALL) ). An atom will contribute to the structure factor only if it has been selected in one SCATter statement and has been selected in the SELEction statement. The selection remains active until a new SELEction statement is issued.

SOLMask

{ $<$xrefin-solmask-statement$>$ } END computes a solvent mask (see Section 13.7).

SYMMetry=$<$symmetry-operator$>$

adds a new symmetry operator ( ${\cal O}_s,{\vec t}_s$) to the xrefin database. The notation is the same as in the International Tables for Crystallography (Hahn, 1987), e.g.,

$$(-x,{y+1}/2,-z).$$ (13.11)

Multiple entries specify the space group. A listing of the symmetry operators of all crystallographic space groups is stored in file “symlib.sym" in the “symmetry" directory. In the case of centered space groups, all symmetry operators have to be specified; otherwise symmetry images will be missing for the packing interactions. Normally, this redundant specification of symmetry operators represents only a small increase in CPU time. The option “SYMMetry RESEt" will erase the existing symmetry operators (default: symmetry=(x,y,z)).

TARGet=

RESIdual $\vert$ AB $\vert$ F1F1 $\vert$ F2F2 $\vert$ E1E1 $\vert$ E2E2 $\vert$ PACKing specifies choice of the target function; see Eq. 13.1 (default: RESIdual).

TOLErance=$<$real$>$

specifies the maximum amount $\Delta_{F}$ (in Å) by which any atomic coordinate can deviate from the position when $F_{calc}$ was last computed during molecular dynamics, energy minimization, or energy calculations. If TOLErance is exceeded, $F_{calc}$ and its derivatives with respect to atomic parameters are recomputed (default: 0.5 Å).

UPDAte

computes $F_{calc}$ for selected reflections using the current atomic model and atomic-form factors.

WA=$<$real$>$

specifies the overall weight factor $W_A$ in Eq. 13.1 (default: 1).

WP=$<$real$>$

specifies the overall weight factor $W_P$ for the phase term $E_{XREF}^{P}$ in Eq. 13.1 (default: 0).

WRITe

REFLection { $<$write-reflection-statement$>$ } END writes the specified xrefin properties, such as FOBS or FCALC, of all selected reflections to a specified output file (see Section 13.4).

$<$FFT-statement$>$:==

AVOID=$<$integer$>$

facilitates avoidance of the specified integer as a factor in the $x$ and $y$ physical dimension of the 3-d electron density matrix in order to avoid memory conflicts on certain supercomputers (default: machine dependent, set automatically).

BASE=$<$integer$>$

specifies the minimum prime allowed in FFT dimensions (default: machine dependent, set automatically).

BSCALefactor=$<$real$>$

sets the artificial temperature factor to minimize aliasing effects (default: 20.0 Å$^2$).

ELIMit=$<$real$>$

defines an atomic “radius" for the electron density calculation by specifying the ratio of the atomic-form factor at zero and at the radius of the atom in natural logarithmic units (default: 7.00). The electron density outside the radius is set to zero.

GRIDsize=$<$real$>$

specifies the grid size relative to the high resolution limit (default: 0.33, which corresponds to 1/3 of the high resolution limit).

MEMOry=$<$integer$>$

indirectly determines the factorization of the FFT by specifying the maximum memory allocation allowed for the electron density matrix in units of complex words (default: 500000).

PRIMe=$<$integer$>$

specifies the maximum prime allowed for FFT dimensions (default: machine dependent, set automatically).