審稿意見-晶體數(shù)據(jù)的“真實(shí)分辨率”
審稿意見-晶體數(shù)據(jù)的“真實(shí)分辨率”
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最近遇到不少小伙伴的審稿意見是關(guān)于晶體數(shù)據(jù)的“真實(shí)分辨率”的，本文以實(shí)際文獻(xiàn)案例展示如何判斷晶體數(shù)據(jù)的真實(shí)分辨率以及在平常的數(shù)據(jù)處理中應(yīng)當(dāng)如何處理這一問題。
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案例文獻(xiàn)：Dalton Trans., 2023, DOI: 10.1039/D3DT02460A
論文主頁：https://pubs.rsc.org/en/content/articlelanding/2023/DT/D3DT02460A
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具體審稿意見如下：
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Structure 4 (CCDC 2262742): C23 H32 Cl2 Co N2
- The I/sigma drops below 3 at ~2theta = 45. The data should be truncated here and a note added to the experimental.
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Structure 230222d-iPr-NH (CCDC 2262744): C30 H46 Cl4 Co N2
- Looking at the HKLF instruction it seems that the cell has been changed after the initial integration, the data should really be reintegrated in the correct cell. This may also help to improve the Rint. Again the I/sigma drops below 3 at ~2theta = 45, if this remains the case after reintegration the data should be truncated here and a note added to the experimental.
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上述有關(guān)兩個晶體數(shù)據(jù)的審稿意見紅色部分均為有關(guān)晶體數(shù)據(jù)真實(shí)分辨率的部分。大意是信噪比（I/sigma，或表示為I/σ）在2theta = 45時低于3（即2θ角大于等于45°時信噪比開始小于3）。有關(guān)2θ角與分辨率（?）之間的關(guān)系可查看推文“單晶X射線的分辨率”。
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關(guān)于信噪比分布，在Olex2[1]中可按圖1或圖2方式查看I/sigma vs resolution圖（橫軸為2θ角，縱軸為信噪比I/σ(I)），如圖3所示（CCDC 2262744投稿時的數(shù)據(jù)）。
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圖3中有一條紅色橫線（信噪比閾值線）“3 sigma line (noise below, data above)”，高于該線的為數(shù)據(jù)（data）——即圖中的綠色方塊，低于該線的為噪音（noise）——即圖中紅色方塊。從圖中可以看出，2θ角從大約46.602°開始到55.1°（圖1）范圍均為噪音，也就是審稿人說的“The I/sigma drops below 3 at ~2theta = 45.”。
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另外也可以查看xprep中的統(tǒng)計(jì)結(jié)果，如圖4所示。
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從圖4可以看出，分辨率殼層（resolution shell）0.91?0.89的平均信噪比（mean I/s）為3.25，而0.89?0.87則以將為2.80。若以信噪比3為閾值，則分辨率可截斷到0.89 ?；若以信噪比2為閾值，則分辨率可截斷到0.83 ?。
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這部分內(nèi)容亦可參考推文“晶體日記（十四）-真實(shí)的數(shù)據(jù)質(zhì)量（1）”。
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在精修階段分辨率可以使用OMIT指令（見推文“SHELXL指令之OMIT”）或SHEL指令（見推文“SHELXL指令之SFAC和SHEL”）進(jìn)行截斷，如圖5和圖6所示。
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從圖5–6可以看出，雖然用OMIT或SHEL指令截斷了分辨率（0.84 ?，即2θ角為50°），但I/sigma vs resolution圖中仍然能夠顯示到55.1°的2θ角范圍，這是因?yàn)榫拗羞@兩個指令只是從精修中排除了指定范圍的數(shù)據(jù)，而不是對hkl文件進(jìn)行編輯。采用這種指令截斷分辨率的方法不知是否可以滿足審稿人的要求。
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不過審稿人明確要求重新還原數(shù)據(jù)的時候?qū)⒎直媛式財嗟胶线m的值。
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Structure 230222d-iPr-NH (CCDC 2262744): C30 H46 Cl4 Co N2
- Looking at the HKLF instruction it seems that the cell has been changed after the initial integration, the data should really be reintegrated in the correct cell. This may also help to improve the Rint. Again the I/sigma drops below 3 at ~2theta = 45, if this remains the case after reintegration the data should be truncated here and a note added to the experimental.
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在APEX4中[2]，在Reduce Data>>Integrate Images中Resolution Limit [?]處將分辨率截斷到合適值，如圖7所示。完整數(shù)據(jù)還原過程參見推文“布魯克單晶數(shù)據(jù)還原操作步驟”。
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在APEX4中重新還原數(shù)據(jù)并截斷分辨率（0.84 ?，2θ = 45°，采取的是信噪比大于2的閾值）后，各項(xiàng)參數(shù)如圖8所示。
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審稿意見回復(fù)：
Structure 4 (CCDC 2262742): C23 H32 Cl2 Co N2
- The I/sigma drops below 3 at ~2theta = 45. The data should be truncated here and a note added to the experimental.
Answer: Effective data standards (I/sigma above 2) were applied to the new data integration process, thus the data were truncated by 0.84 ? (2θ = 50°). The new cif file have been updated in CCDC.
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CCDC 2262744則截斷至0.91 ?（2θ = 45.8°，采取的是信噪比大于2的閾值），如圖9所示。
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相關(guān)審稿意見回復(fù)：
Structure 230222d-iPr-NH (CCDC 2262744): C30 H46 Cl4 Co N2 （對應(yīng)編號230222d-ok）
- Looking at the HKLF instruction it seems that the cell has been changed after the initial integration, the data should really be reintegrated in the correct cell. This may also help to improve the Rint. Again the I/sigma drops below 3 at ~2theta = 45, if this remains the case after reintegration the data should be truncated here and a note added to the experimental.
Answer: Effective data standards (I/sigma above 2) were applied to the new data integration process, thus the data were truncated by 0.91 ? (2θ = 45°). The new cif file have been updated in CCDC.
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當(dāng)然，分辨率截斷后，可能會出現(xiàn)相關(guān)的AB類警報。例如CCDC 2262744就出現(xiàn)了如圖10所示的A類警報。
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有AB類警報并不意味著數(shù)據(jù)無法發(fā)表，只要能對相應(yīng)警報給出合理解釋即可。例如本例中圖10所示A類警報是因?yàn)榫w在測試條件下的極限分辨率只有0.93 ?左右，所以在數(shù)據(jù)還原時將數(shù)據(jù)分辨率截斷至0.93 ?，此時theta_max為22.907（如圖11所示），代入sin(theta_max)/wavelength = sin(22.907)/0.71073 = 0.5477，該值小于0.550，所以引起圖10所示警報。
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在進(jìn)行數(shù)據(jù)還原的時候，可能被教的是：鉬靶數(shù)據(jù)分辨率截斷至0.77 ?，銅靶數(shù)據(jù)分辨率截斷至0.83 ?這樣的一刀切策略。然而，實(shí)際上每個晶體的衍射分辨率極限是千差萬別的，有些晶體可能衍射分辨率根本達(dá)不到0.77 ?這么高，例如本例中的CCDC 2262744極限分辨率只能到0.93 ?左右，而CCDC 2262742極限分辨率勉強(qiáng)能到0.84 ?，如果這兩個數(shù)據(jù)都按照0.77 ?的分辨率進(jìn)行截斷，那么數(shù)據(jù)就包含很多噪音，從而降低其真實(shí)性，或者說使數(shù)據(jù)的可靠性大打折扣。而有些晶體的極限分辨率明明可以高于0.77 ?（鉬靶最高分辨率為0.71073/2 = 0.36 ?），但卻截斷至0.77 ?，那也不太合適，畢竟人們追求的就是盡可能高的分辨率。
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參考文獻(xiàn)：
[1] Dolomanov, O. V.; Bourhis, L. J.; Gildea, R. J.; Howard, J. A. K.; Puschmann, H. OLEX2: A complete structure solution, refinement and analysis program. J. Appl. Cryst. 2009, 42, 339–341.
[2] Bruker (2016). APEX4. Bruker AXS Inc., Madison, Wisconsin, USA.
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視頻見：https://www.bilibili.com/video/BV1mm4y1T7Tq/?spm_id_from=333.999.0.0
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