I read the papers about the structure of crystal methanol or ethanol by XRD, the hydrogen bond length was determined by XRD with the precision about 0.01A ~ 0.001A. Can XRD resolve the change of 0.0001A?
You can determine donor-acceptor distance with such estimated standard deviation, but remember that esd is statistically obtained value decreasing with better data:parameter ratio. It is often severely underestimated.
However, for example for such rigid bonds like C(sp3)-C(sp3), the esd of bond lengths can be understood as an indicator of the crystal quality/precision of the refinement. I cannot recall it now but you can look at checkcif help, where the ranges for the alerts are given, but esd of 0.001 A is pretty good, but more than 0.005 A is a signal of some problem.
This is not mechanically applicable to any crystal structure determination - in Organic Letters 12/2014; 16(24):6358-6361. DOI: 10.1021/ol503137p we published the structure severely affected by high thermal motion and diffracting only to 1.1 A resolution, with freely rotating CHCl3 molecules, where higher than 0.01 A esd for C-C distances was OK because of the physical nature of the sample.
Moreover, when considering HYDROGEN bonds, the electron density of the H atoms is not even approximately uniformly distributed around hydrogen nucleus. It is always displaced in the direction of the donor atom, and this displacement is affected by donor and acceptor electronegativity, polarizability, H...A distance, D-H...A angle. This (together with the fact that for X-rays the scattering from hydrogens is often approximately at the noise levels) is the argument for CONSTRAINING the H atoms to geometrically optimised (or idealised) positions. These positions should lead to minimal systematic errors (= F^2(calc) and F^2(obs) are as similar as possible) but the distances are unreal (d(O-H) is constrained to 0.84 A at 100 K, while real value is around 1 A (from neutron diffraction) and is temperature independent) and the angles are also somewhat doubtful.
There are some possibilities for obtaining precise H atoms positions from X-ray data (Hirshfeld refinement or charge density refinement using invarioms/pseudoatoms) but this is by no means routine. Using common Independent Atom Model software like SHELXL, Crystals, olex2, JANA2006 it is possible to obtain precise H atom coordinates only using neutron radiation (OK, JANA is also capable of using multipolar/pseudoatom refinement).
Basically, seeing "hydrogens" using routine X-ray data you in reality see the maxima of bond electron density together with the lone electron pairs.
And finally, there are HARDWARE limitations of the diffractometer construction which are making such resolution only illusory, like position repeatability, backslash, material elasticity, etc. When using not pure cell refinement statistic, but also some kind of diffractometer error model (Bruker has implemented this at some extent) we obtained more realistic and much higher esds for cell parameters...
You can determine donor-acceptor distance with such estimated standard deviation, but remember that esd is statistically obtained value decreasing with better data:parameter ratio. It is often severely underestimated.
However, for example for such rigid bonds like C(sp3)-C(sp3), the esd of bond lengths can be understood as an indicator of the crystal quality/precision of the refinement. I cannot recall it now but you can look at checkcif help, where the ranges for the alerts are given, but esd of 0.001 A is pretty good, but more than 0.005 A is a signal of some problem.
This is not mechanically applicable to any crystal structure determination - in Organic Letters 12/2014; 16(24):6358-6361. DOI: 10.1021/ol503137p we published the structure severely affected by high thermal motion and diffracting only to 1.1 A resolution, with freely rotating CHCl3 molecules, where higher than 0.01 A esd for C-C distances was OK because of the physical nature of the sample.
Moreover, when considering HYDROGEN bonds, the electron density of the H atoms is not even approximately uniformly distributed around hydrogen nucleus. It is always displaced in the direction of the donor atom, and this displacement is affected by donor and acceptor electronegativity, polarizability, H...A distance, D-H...A angle. This (together with the fact that for X-rays the scattering from hydrogens is often approximately at the noise levels) is the argument for CONSTRAINING the H atoms to geometrically optimised (or idealised) positions. These positions should lead to minimal systematic errors (= F^2(calc) and F^2(obs) are as similar as possible) but the distances are unreal (d(O-H) is constrained to 0.84 A at 100 K, while real value is around 1 A (from neutron diffraction) and is temperature independent) and the angles are also somewhat doubtful.
There are some possibilities for obtaining precise H atoms positions from X-ray data (Hirshfeld refinement or charge density refinement using invarioms/pseudoatoms) but this is by no means routine. Using common Independent Atom Model software like SHELXL, Crystals, olex2, JANA2006 it is possible to obtain precise H atom coordinates only using neutron radiation (OK, JANA is also capable of using multipolar/pseudoatom refinement).
Basically, seeing "hydrogens" using routine X-ray data you in reality see the maxima of bond electron density together with the lone electron pairs.
And finally, there are HARDWARE limitations of the diffractometer construction which are making such resolution only illusory, like position repeatability, backslash, material elasticity, etc. When using not pure cell refinement statistic, but also some kind of diffractometer error model (Bruker has implemented this at some extent) we obtained more realistic and much higher esds for cell parameters...
I agree with Erik's analysis. I add that the presence of heavy atoms will decrease the possibility of obtaining reliable H positions. Other aspects are the quality of the collectd diffraction data and of the applied corrections (e.g. absorption).
Because hydrogen do not have core electron, electron density of the H atoms is not uniformly distributed around hydrogen nucleus. So, the position of hydrogen atom can not be accurately refined in X-ray diffraction. Please check this paper for more detail.
Exceptional Steric Congestion in an in,in-Bis(hydrosilane)
http://pubs.acs.org/doi/abs/10.1021/ja407398w
In order to get more accurate measurement, you need to do neutron diffraction.