The variation in the real and imaginary components of the scattering factor
(Df' and
Df")
of an anomalously scattering atom, when the wavelength of the incident beam
approaches one of its absorption edges, can be exploited to determine the phases for
the native structure; naturally a "tunable" X-ray source such as a synchrotron is
needed for this experiment. The MAD signal is much smaller than the MIR one, so
even more care in collecting, processing and scaling the data is required.
Consequently it is probably advisable to exclude data with
F/s(F) below 3.
The MLPHARE program must be used for phased refinement, and the procedure is
very similar to that for the MIRAS case, with one modification: because in general all
the datasets will have anomalous data, there will be no "native", so one of the
datasets (it doesn't matter which) must serve as both "native" and as one of the
"derivatives". This means that the real scattering factors will actually be differences
between Df' at the different wavelengths,
and hence the real occupancies will also be
differences, and can be positive or negative. Note that the program does not need
input values for Df' and
Df"
(the values shown are for comment only); these are
incorporated in the refined real and anomalous occupancies.
Suppose, for example, that there are 3 datasets, with dataset 1 acting as "native".
Then the sign ambiguity can be resolved by starting the refinement of the real
occupancies of the sites for datasets 2 and 3 with signs equal to the signs of
Df'(2)-Df'(1) and
Df'(3)-Df'(1). In the first stage, only the overall scale and thermal
parameters, and coordinates and real occupancies for datasets 2 and 3 are refined;
dataset 1 is not included as a "derivative" and its parameters are not refined at this
stage.
#
mlphare HKLIN ele-merge3 HKLOUT junk <<EOD
TITLE MAD - Refine real coordinates & occupancies for L2 & L3.
CYCLES 8
LABIN FP=FL1 SIGFP=SIGFL1 FPH1=FL2 SIGFPH1=SIGFL2 FPH2=FL3 SIGFPH2=SIGFL3
LABOUT ALLIN
EXCLUD SIGFP 3
PRINT AVF AVE
THRESH 2.5 0.5
CENTRI
DERIV Se L2 0.9809 f' -8.198 f" 2.058
EXCLUD SIGFPH 3
DCYCLE PHASE ALL REFCYC ALL KBOV ALL
ATOM Se 0.3387 0.1129 -0.0944 -0.1 BFAC 15
ATREF X ALL Y ALL Z ALL OCC ALL
ATOM Se 0.2074 0.0510 0.2426 -0.1 BFAC 15
ATREF X ALL Y ALL Z ALL OCC ALL
DERIV Se L3 0.9795 f' -6.203 f" 3.663
EXCLUD SIGFPH 3
DCYCLE PHASE ALL REFCYC ALL KBOV ALL
ATOM Se 0.3387 0.1129 -0.0944 -0.1 BFAC 15
ATREF X ALL Y ALL Z ALL OCC ALL
ATOM Se 0.2074 0.0510 0.2426 -0.1 BFAC 15
ATREF X ALL Y ALL Z ALL OCC ALL
EOD
Sample of statistics output by MLPHARE
Analysis of Derivative 1 Last Phasing cycle:
<4SSQ/LL>
Resol
Nref_a
DISO_a
LOC_a
PhP_a
CullR_a
Nref_c
DISO_c
LOC_c
PhP_c
CullR_c
0.003
18.93
9
19.7
19.1
1.57
0.97
19
39.7
34.6
0.78
0.87
0.008
10.93
58
18.5
8.6
3.32
0.47
43
25.6
10.6
2.29
0.41
0.017
7.68
145
23.7
12.3
2.18
0.52
67
30.4
12.7
2.05
0.42
0.029
5.92
281
22.7
15.8
1.61
0.70
78
30.5
17.4
1.31
0.57
0.043
4.82
457
24.0
17.2
1.40
0.72
109
32.8
21.5
0.99
0.65
0.061
4.06
678
23.4
18.3
1.16
0.78
134
34.3
23.2
0.90
0.68
0.081
3.51
933
26.6
23.9
0.81
0.90
147
33.6
28.7
0.59
0.85
0.105
3.09
1213
35.5
33.6
0.52
0.95
159
44.5
40.6
0.38
0.91
TOTAL
3774
28.0
23.9
0.86
0.85
756
35.0
25.7
0.78
0.73
Analysis of Derivative 2 Last Phasing cycle:
<4SSQ/LL>
Resol
Nref_a
DISO_a
LOC_a
PhP_a
CullR_a
Nref_c
DISO_c
LOC_c
PhP_c
CullR_c
0.003
18.93
9
15.4
15.8
1.42
1.02
19
39.3
34.9
0.58
0.89
0.008
10.93
58
13.3
7.2
3.01
0.54
43
20.2
9.2
1.99
0.45
0.017
7.68
145
18.3
9.8
2.08
0.53
68
22.7
11.3
1.74
0.50
0.029
5.92
282
18.3
13.2
1.46
0.72
78
22.8
14.3
1.20
0.63
0.043
4.82
458
20.4
15.5
1.16
0.76
109
27.8
21.7
0.74
0.78
0.061
4.06
677
22.3
18.2
0.88
0.82
133
27.3
20.2
0.76
0.74
0.081
3.51
932
26.6
24.3
0.60
0.92
149
35.5
31.8
0.40
0.90
0.105
3.09
1215
33.1
31.6
0.42
0.95
159
35.7
33.2
0.35
0.93
TOTAL
3776
26.0
22.8
0.68
0.88
758
29.8
23.8
0.63
0.80
10.2 Stage 2 - "Real" and "anomalous" refinement against
Df' and
Df"
Next, dataset 1 is included as a "derivative" and its overall parameters, "anomalous"
coordinates and occupancies are refined, together with the overall parameters, real
and anomalous occupancies for datasets 2 and 3. The real occupancies for dataset 1
are never refined from zero, because obviously the difference in the real scattering
factor between it acting as "derivative" and it as "native" is always zero.
#
mlphare HKLIN ele-merge3 HKLOUT ele-phase1 << EOD
TITLE MAD - Refine all anomalous occupancies as well.
CYCLES 8
LABIN FP=FL1 SIGFP=SIGFL1 -
FPH1=FL2 SIGFPH1=SIGFL2 DPH1=DL2 SIGDPH1=SIGDL2 -
FPH2=FL3 SIGFPH2=SIGFL3 DPH2=DL3 SIGDPH2=SIGDL3 -
FPH3=FL1 SIGFPH3=SIGFL1 DPH3=DL1 SIGDPH3=SIGDL1
LABOUT ALLIN
EXCLUD SIGFP 3
PRINT AVF AVE
THRESH 2.5 0.5
DERIV Se L2 0.9809 f' -8.198 f" 2.058
EXCLUD SIGFPH 3
DCYCLE PHASE ALL REFCYC ALL KBOV ALL
SCALE FPH 1.0062 -0.0146
ATOM Se 0.340 0.113 -0.094 -0.174 1 BFAC 15.000
ATREF X ALL Y ALL Z ALL OCC ALL AOCC ALL
ATOM Se 0.206 0.050 0.244 -0.173 1 BFAC 15.000
ATREF X ALL Y ALL Z ALL OCC ALL AOCC ALL
DERIV Se L3 0.9795 f' -6.203 f" 3.663
DCYCLE PHASE ALL REFCYC ALL KBOV ALL
SCALE FPH 1.0082 -0.3268
ATOM Se 0.339 0.113 -0.094 -0.126 1 BFAC 15.000
ATREF X ALL Y ALL Z ALL OCC ALL AOCC ALL
ATOM Se 0.206 0.050 0.241 -0.132 1 BFAC 15.000
ATREF X ALL Y ALL Z ALL OCC ALL AOCC ALL
DERIV Se L1 0.900 f' -1.622 f" 3.285
EXCLUD SIGFPH 3
DCYCLE PHASE ALL REFCYC ALL KBOV ALL
ATOM Se 0.3387 0.1129 -0.0944 0 1 BFAC 15
ATREF AX ALL AY ALL AZ ALL AOCC ALL
ATOM Se 0.2074 0.0510 0.2426 0 1 BFAC 15
ATREF AX ALL AY ALL AZ ALL AOCC ALL
EOD
