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<div>Dear L. D. Ding:
<BR>
In my opinion, this kind of thing also can be understood from group theory for quantum mechanics: the "carrier space" of the eigen-function of bulk materials are not consistent with the one of the atomic wavefunctions, although both of them form orthogonal and complete basis sets. So the projection operation between the two spaces will miss some information. To some extent, this is the same as Duy Le's comment.
<BR>
Best Regards
<BR>
L. F. Huang
<BR>
Institute of Solid State Physics of China
<BR>
</FONT><FONT color=#444444>> 1. Lowdin charge problem (loc duong ding)
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</FONT><FONT color=#444444>> 2. Re: Lowdin charge problem (Duy Le)
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> ----------------------------------------------------------------------
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</FONT><FONT color=#444444>>
<BR>
</FONT><FONT color=#444444>> Message: 1
<BR>
</FONT><FONT color=#444444>> Date: Fri, 4 Sep 2009 18:59:30 -0700 (PDT)
<BR>
</FONT><FONT color=#444444>> From: loc duong ding
<BR>
</FONT><FONT color=#444444>> Subject: [Pw_forum] Lowdin charge problem
<BR>
</FONT><FONT color=#444444>> To: PWscf forum
<BR>
</FONT><FONT color=#444444>> Message-ID:
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</FONT><FONT color=#444444>> Content-Type: text/plain; charset=iso-8859-1
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> Dear QE users,
<BR>
</FONT><FONT color=#444444>>
<BR>
</FONT><FONT color=#444444>> I try to analysis the atomic charge. I found that Lowdin charge analysis can be implemeted by QE. I dod a test with NO2. I get the the result as following:
<BR>
</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> Lowdin Charges:
<BR>
</FONT><FONT color=#444444>> ???? Atom #?? 1: total charge =?? 4.5377, s =? 1.2595, p =? 3.2782,
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</FONT><FONT color=#444444>> ???????????????? spin up????? =?? 2.4718, s =? 0.7016, p =? 1.7701,
<BR>
</FONT><FONT color=#444444>> ???????????????? spin down??? =?? 2.0659, s =? 0.5578, p =? 1.5081,
<BR>
</FONT><FONT color=#444444>> ???????????????? polarization =?? 0.4058, s =? 0.1438, p =? 0.2620,
<BR>
</FONT><FONT color=#444444>> ???? Atom #?? 2: total charge =?? 6.1075, s =? 1.7256, p =? 4.3818,
<BR>
</FONT><FONT color=#444444>> ???????????????? spin up????? =?? 3.1926, s =? 0.8642, p =? 2.3284,
<BR>
</FONT><FONT color=#444444>> ???????????????? spin down??? =?? 2.9149, s =? 0.8614, p =? 2.0534,
<BR>
</FONT><FONT color=#444444>> ???????????????? polarization =?? 0.2777, s =? 0.0027, p =? 0.2749,
<BR>
</FONT><FONT color=#444444>> ???? Atom #?? 3: total charge =?? 6.1113, s =? 1.7254, p =? 4.3859,
<BR>
</FONT><FONT color=#444444>> ???????????????? spin up????? =?? 3.1939, s =? 0.8641, p =? 2.3298,
<BR>
</FONT><FONT color=#444444>> ???????????????? spin down??? =?? 2.9174, s =? 0.8613, p =? 2.0561,
<BR>
</FONT><FONT color=#444444>> ???????????????? polarization =?? 0.2765, s =? 0.0028, p =? 0.2737,
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> The strange thing is that the total charge of all atom is ~16.7 instead of 17 in NO2 molecules.
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> Can you give me some instructions or explanation to fix this problem?
<BR>
</FONT><FONT color=#444444>>
<BR>
</FONT><FONT color=#444444>> I great appreciate your help.
<BR>
</FONT><FONT color=#444444>>
<BR>
</FONT><FONT color=#444444>> Sincerely,?-----------------------------------------------
<BR>
</FONT><FONT color=#444444>> Loc Duong Dinh
<BR>
</FONT><FONT color=#444444>> Ms-Ph.D Student
<BR>
</FONT><FONT color=#444444>> Sungkyunkwan Advanced Institute of Nanotechnology,
<BR>
</FONT><FONT color=#444444>> Sungkyunkwan University,
<BR>
</FONT><FONT color=#444444>> Suwon, 440-746, Korea
<BR>
</FONT><FONT color=#444444>> Email: <A href=mailto:mambom1902@yahoo.com>mambom1902@yahoo.com</A>, <A href=mailto:ddloc@skku.edu>ddloc@skku.edu</A</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> ------------------------------
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</FONT><FONT color=#444444>>
<BR>
</FONT><FONT color=#444444>> Message: 2
<BR>
</FONT><FONT color=#444444>> Date: Fri, 4 Sep 2009 22:31:06 -0400
<BR>
</FONT><FONT color=#444444>> From: Duy Le
<BR>
</FONT><FONT color=#444444>> Subject: Re: [Pw_forum] Lowdin charge problem
<BR>
</FONT><FONT color=#444444>> To: PWSCF Forum
<BR>
</FONT><FONT color=#444444>> Message-ID:
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> Content-Type: text/plain; charset="iso-8859-1"
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> Hi,I don't think you can get 17e for not only Lowdin charge but also others.
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</FONT><FONT color=#444444>> This estimated charge does not follow the sum rule. I believe the "error"
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</FONT><FONT color=#444444>> comes from the delocolized charge which can not be well estimated or taken
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</FONT><FONT color=#444444>> in to account.
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</FONT><FONT color=#444444>>
<BR>
</FONT><FONT color=#444444>> D.
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</FONT><FONT color=#444444>>
<BR>
</FONT><FONT color=#444444>> On Fri, Sep 4, 2009 at 9:59 PM, loc duong ding wrote:
<BR>
</FONT><FONT color=#444444>>
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> Dear QE users,
<BR>
</FONT><FONT color=#444444>> >
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> I try to analysis the atomic charge. I found that Lowdin charge analysis
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> can be implemeted by QE. I dod a test with NO2. I get the the result as
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> following:
<BR>
</FONT><FONT color=#444444>> >
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> Lowdin Charges:
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> Atom # 1: total charge = 4.5377, s = 1.2595, p = 3.2782,
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> spin up = 2.4718, s = 0.7016, p = 1.7701,
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> spin down = 2.0659, s = 0.5578, p = 1.5081,
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> polarization = 0.4058, s = 0.1438, p = 0.2620,
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> Atom # 2: total charge = 6.1075, s = 1.7256, p = 4.3818,
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> spin up = 3.1926, s = 0.8642, p = 2.3284,
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> spin down = 2.9149, s = 0.8614, p = 2.0534,
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> polarization = 0.2777, s = 0.0027, p = 0.2749,
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> Atom # 3: total charge = 6.1113, s = 1.7254, p = 4.3859,
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> spin up = 3.1939, s = 0.8641, p = 2.3298,
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> spin down = 2.9174, s = 0.8613, p = 2.0561,
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> polarization = 0.2765, s = 0.0028, p = 0.2737,
<BR>
</FONT><FONT color=#444444>> >
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> The strange thing is that the total charge of all atom is ~16.7 instead of
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> 17 in NO2 molecules.
<BR>
</FONT><FONT color=#444444>> >
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> Can you give me some instructions or explanation to fix this problem?
<BR>
</FONT><FONT color=#444444>> >
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> I great appreciate your help.
<BR>
</FONT><FONT color=#444444>> >
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> Sincerely, -----------------------------------------------
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> Loc Duong Dinh
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> Ms-Ph.D Student
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> Sungkyunkwan Advanced Institute of Nanotechnology,
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> Sungkyunkwan University,
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> Suwon, 440-746, Korea
<BR>
</FONT><FONT color=#444444>> </FONT><FONT color=#444444>> Email: <A href=mailto:mambom1902@yahoo.com>mambom1902@yahoo.com</A>, <A href=mailto:ddloc@skku.edu>ddloc@skku.edu</A>
<BR>
</FONT><FONT color=#444444>> >
<BR>
</FONT><FONT color=#444444>> >
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</FONT><FONT color=#444444>> >
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</FONT><FONT color=#444444>>
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</FONT><FONT color=#444444>> --
<BR>
</FONT><FONT color=#444444>> --------------------------------------------------
<BR>
</FONT><FONT color=#444444>> Duy Le
<BR>
</FONT><FONT color=#444444>> PhD Student
<BR>
</FONT><FONT color=#444444>> Department of Physics
<BR>
</FONT><FONT color=#444444>> University of Central Florida.
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------
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======================================================================
<BR>
L.F.Huang(黄良锋) ph.D candidate
<BR>
======================================================================
<BR>
Add: Research Laboratory for Computational Materials Sciences,
<BR>
Instutue of Solid State Physics,the Chinese Academy of Sciences,
<BR>
P.O.Box 1129, Hefei 230031, P.R.China
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Tel: 86-551-5591464-328(office)
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Fax: 86-551-5591434
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Web: <A href=http://theory.issp.ac.cn target=_blank>http://theory.issp.ac.cn</A</FONT><FONT color=#444444>> (website of our theory group)
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