Small suggestion -- you may want to make the Be RMT rather larger than that for O. You can check in case.outputm for how much charge is leaking out of the core for the states of interest, and adjust. (I suspect that this won't make much difference.)<br>
<br><div class="gmail_quote">2010/4/19 Amlan Ray <span dir="ltr"><<a href="mailto:amlan_ray2005@yahoo.com">amlan_ray2005@yahoo.com</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<table cellspacing="0" cellpadding="0" border="0"><tbody><tr><td valign="top" style="font:inherit"><div>Dear Prof. Blaha,</div>
<div>I am writing in response to your mail on this subject dated April 8, 2010. In the meantime, I have done the calculations you suggested. </div>
<div> </div>
<div>a) The electron capture rate by an electron-capturing nucleus is proportional to the electron density averaged over the volume of the nucleus. The electron capture reaction of 7Be is 7Be+e- goes to 7Li+neutrino. In the case of 7Be decay, 10% of the time 7Li*(478 keV state) is produced and 90% of the time 7Li(g.s) is produced. So 10% of the time a 478 keV gamma ray photon is emitted as a result of the electron capture by 7Be. The intensity of this 478 keV gamma ray line is measured as a function of time to determine the half-life of 7Be (about 53 days). In this way, the electron capture rate of 7BeO was measured in normal condition and under 270 kbar pressure (causing about 9% volume contraction of the lattice) and 0.6% increase of the electron capture rate was found under compression. </div>
<div> </div>
<div>Since the nuclear volume is very small, so the averaging over the nuclear volume should be a very small effect. So if we take electron density at a point within the nuclear volume and compare with the corresponding result under compression, then that should be approximately ok. </div>
<div> </div>
<div>b) As per your suggestion, I changed RT0 in case.struct file and performed both relativistic and non-relativistic calculations for BeO. WIEN2K is considering a point nucleus and so I took points very close and within the beryllium nuclear volume at R0=0.0001BU, 0.00005Bu and 0.00001BU. In the case of non-relativistic calculations, the absolute value of the electron density increased by about 0.15% from R0=0.0001BU to 0.00001BU. In the case of relativistic calculations, the corresponding increase is by 0.28% (as expected). The absolute value of the electron density is about 1% higher for the relativistic calculation compared to non-relativistic calculation. However the increase of the electron density at R0 due to the compression of the lattice volume of BeO by 9% remains about 0.1% for both the relativistic and non-relativistic calculations. </div>
<div> </div>
<div>c) I performed calculations considering (for Be) 1s as core state and 2s as valence state. I also performed calculations considering both 1s and 2s as valence states. I also performed calculations by increasing Muffintin-radius RMT for Be from 1.45 BU to 1.49 BU. If I try to increase RMT further, then I am getting nn-error. Similarly for the compressed case of BeO, I could increase RMT (for Be) from 1.41 BU to 1.45 BU only. </div>
<div> </div>
<div>I find that the electron density decreases by about 0.1% when both 1s and 2s states are treated as valence states (for Be) compared to when 1s state is treated as core and 2s as valence (for Be). However the increase of the electron density at R0 due to the compression of BeO lattice remains about the same (0.1%) irrespective of how 1s and 2s states are treated. </div>
<div> </div>
<div>Regarding the effect of increasing the Muffin-tin radius RMT, I always found that the electron density at R0 increases very slightly as RMT is increased from 1.45 to 1.49 for Be. It happens for both relativistic and non-relativistic cases. I also studied this effect by treating 1s as core and 2s as valence (for Be). I found that 1s electron density at R0 always increases as a result of increasing RMT of Be, but 2s electron density at R0 usually decreases for increasing RMT of Be. The overall effect is dominated by the much larger increase of 1s electron density as a result of increasing RMT of Be. So the total electron density at R0 always increases if we increase RMT of Be (keeping all other things excatly the same). This observation agrees well with our final result from WIEN2K calculation that as a result of the compression of the BeO lattice 2s electron density at R0 increases but 1s electron density at R0 decreases. </div>
<div> </div>
<div>d) The calculated result from WIEN2K (0.1% increase of the electron density at the nucleus as a result of 9% compression of BeO lattice) disagrees with the experimental result of 0.6% increase. If we assume that the 1s electron density at the nucleus would remain unchanged due to the compression and only consider the increase of 2s electron density as calculated by WIEN2K, then the total electron density at R0 increases by about 0.25% (which is about 40% of the experimental result and so a better result). </div>
<div> </div>
<div>e) I think the problem is with the calculation of 1s electron density of Be at the nucleus (at R0). As the RMT of Be is increased, 1s electron density at the nucleus also increases. In the case of valence 2s state electrons, you have the boundary condition that the atomic wave function should match with the interstitial wave function and so it is behaving properly unders compression. However in the case of 1s core state wave function, you are using a free atom model. As I understand 1s electrons are in scf crystal potential, but they are not constrained to stay within the RMT radius and probably there is no other boundary condition also. So when the lattice is compressed, the Hartree potential increases and more of 1s wave function leaks out of RMT radius, thus reducing the 1s electron density at the nucleus. But 1s electrons should be constrained within RMT radius or there hsould be some appropriate boundary condition on them. </div>
<div> </div>
<div>My suggestion is if it is possible to introduce the boundary condition that 1s state Be wave function should be constrained within the RMT radius i.e. 1s wave function must be zero outside the RMT radius. If we put this boundary condition on 1s wave function, then I think the 1s electron density at the nucleus would increase due to the compression of the lattice and the agreement with the electron capture data (under compression) would be much better. </div>
<div> </div>
<div>With best regards</div>
<div> Amlan Ray</div>
<div>Address</div>
<div>Variable Energy Cyclotron Center</div>
<div>1/AF, Bidhan Nagar</div>
<div>Kolkata - 700064</div>
<div>India</div></td></tr></tbody></table><br><br>_______________________________________________<br>
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<br></blockquote></div><br><br clear="all"><br>-- <br>Laurence Marks<br>Department of Materials Science and Engineering<br>MSE Rm 2036 Cook Hall<br>2220 N Campus Drive<br>Northwestern University<br>Evanston, IL 60208, USA<br>
Tel: (847) 491-3996 Fax: (847) 491-7820<br>email: L-marks at northwestern dot edu<br>Web: <a href="http://www.numis.northwestern.edu">www.numis.northwestern.edu</a><br>Chair, Commission on Electron Crystallography of IUCR<br>
<a href="http://www.numis.northwestern.edu/">www.numis.northwestern.edu/</a><br>Electron crystallography is the branch of science that uses electron scattering and imaging to study the structure of matter.<br>