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MIR Tutorial Bath - MAD
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10. Multiwavelength anomalous diffraction (MAD)

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.

10.1. Stage 1 - "Real" refinement against Df'

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
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 19.5 16.1 1.95 0.82 19 39.9 33.7 0.83 0.84
0.008 10.93 58 18.5 8.3 3.57 0.45 43 25.4 10.2 2.46 0.40
0.017 7.68 145 23.7 11.4 2.44 0.48 67 30.3 13.1 2.04 0.43
0.029 5.92 281 22.6 14.4 1.81 0.64 78 30.5 16.9 1.38 0.55
0.043 4.82 457 23.8 16.5 1.47 0.69 109 32.4 21.2 1.01 0.66
0.061 4.06 678 23.0 17.8 1.19 0.77 134 34.4 23.0 0.91 0.67
0.081 3.51 933 26.6 23.7 0.81 0.89 147 33.7 29.0 0.58 0.86
0.105 3.09 1213 35.5 33.2 0.52 0.94 159 44.5 40.6 0.37 0.91
TOTAL 3774 27.9 23.4 0.88 0.84 756 35.0 25.6 0.78 0.73
<4SSQ/LL> Nref_a DANO_obs DANO_calc LOC_ano CullR_ano
0.003 9 14.5 11.7 5.84 0.40
0.008 58 20.5 11.8 12.83 0.63
0.017 145 19.0 9.9 15.52 0.82
0.029 281 21.0 10.2 17.58 0.84
0.043 457 20.0 9.5 17.39 0.87
0.061 678 23.0 8.7 20.15 0.87
0.081 933 29.0 8.1 28.20 0.97
0.105 1213 46.2 7.4 45.89 0.99
TOTAL 3774 31.2 8.4 29.56 0.95 
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 14.6 12.0 1.85 0.82 19 40.7 35.6 0.55 0.88
0.008 10.93 58 12.8 6.2 3.42 0.48 43 19.5 7.8 2.31 0.40
0.017 7.68 145 18.1 9.1 2.22 0.50 68 22.6 12.8 1.52 0.57
0.029 5.92 282 17.9 12.2 1.61 0.68 78 22.7 15.0 1.17 0.66
0.043 4.82 458 20.0 14.9 1.27 0.75 109 27.5 21.2 0.79 0.77
0.061 4.06 677 21.9 17.8 0.98 0.81 133 27.3 20.4 0.82 0.75
0.081 3.51 932 26.6 24.1 0.69 0.90 149 35.5 31.6 0.46 0.89
0.105 3.09 1215 33.2 31.2 0.51 0.94 159 35.7 33.2 0.41 0.93
TOTAL 3776 25.9 22.3 0.77 0.86 758 29.7 23.8 0.68 0.80
<4SSQ/LL> Nref_a DANO_obs DANO_calc LOC_ano CullR_ano
0.003 9 24.1 18.4 12.14 0.50
0.008 58 24.6 18.9 11.62 0.47
0.017 145 24.2 16.1 14.87 0.61
0.029 282 28.6 17.1 19.84 0.69
0.043 458 28.4 16.6 22.24 0.78
0.061 677 29.3 15.9 23.80 0.81
0.081 932 36.0 15.5 33.40 0.93
0.105 1215 42.4 14.9 41.76 0.99
TOTAL 3776 34.7 15.7 30.91 0.89 
Analysis of Derivative  3 Last Phasing cycle:
<4SSQ/LL> Nref_a DANO_obs DANO_calc LOC_ano CullR_ano
0.003 9 12.0 15.3 7.57 0.63
0.008 58 19.5 15.8 9.70 0.50
0.017 145 23.4 13.4 17.25 0.74
0.029 282 24.8 14.0 19.50 0.79
0.043 459 28.6 13.0 24.63 0.86
0.061 680 30.7 12.0 28.25 0.92
0.081 934 42.0 11.2 40.21 0.96
0.105 1224 56.3 10.3 55.80 0.99
TOTAL 3791 40.6 11.6 38.25 0.94
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