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<div style="font-size: 16px; font-family: Tahoma; color: rgb(0, 0, 0); font-weight: 400; font-style: normal;">I think I have got the reasons for such results:</div>
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<div style="font-size: 16px; font-family: Tahoma; color: rgb(0, 0, 0); font-weight: 400; font-style: normal;">1- I had to constrain the distribution of electrons over the levels to prevent redistribution of them in the course of iterations,</div>
<div style="font-size: 16px; font-family: Tahoma; color: rgb(0, 0, 0); font-weight: 400; font-style: normal;">2- The redistribution takes more time (# of iterations) for those initial distributions that were further from the distribution over the lowest lying levels.</div>
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<div style="font-size: 16px; font-family: Tahoma; color: rgb(0, 0, 0); font-weight: 400; font-style: normal;">M Payami</div>
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<div style="font-family: Tahoma; color: rgb(0, 0, 0); font-size: 16px; font-weight: 400; font-style: normal;">
<blockquote class="as91pFk8AX8sDPOUp66RUy8IoCRjefxNG8oLk8fg" style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">From: "Mahmoud Payami Shabestari" <mpayami@aeoi.org.ir><br />
To: "users@lists.quantum-espresso.org" <users@lists.quantum-espresso.org><br />
Cc: "mahmoud.payami@gmail.com" <mahmoud.payami@gmail.com><br />
Date: Fri, 19 Feb 2021 22:49:58 +0330<br />
Subject: [QE-users] DFT+U and metastable states<br />
<div style="font-size: 16px; font-family: Tahoma; color: rgb(0, 0, 0); font-weight: 400; font-style: normal;">Dear QE-users/Developers,</div>
<div style="font-size: 16px; font-family: Tahoma; color: rgb(0, 0, 0); font-weight: 400; font-style: normal;"> </div>
<div style="font-size: 16px; font-family: Tahoma; color: rgb(0, 0, 0); font-weight: 400; font-style: normal;">Hi.</div>
<div style="font-size: 16px; font-family: Tahoma; color: rgb(0, 0, 0); font-weight: 400; font-style: normal;">I am trying to do an SCF calculation on a system with AFM order in z-direction with a metallic impurity atom in the unit cell.</div>
<div style="font-size: 16px; font-family: Tahoma; color: rgb(0, 0, 0); font-weight: 400; font-style: normal;">I am employing the simplest version of DFT+U (lda_plus_u_kind=0) and QE-6.7.</div>
<div style="font-size: 16px; font-family: Tahoma; color: rgb(0, 0, 0); font-weight: 400; font-style: normal;">The values of Hubbard_U is set to some non-zero value for the spin-up and spin-down atoms.</div>
<div style="font-size: 16px; font-family: Tahoma; color: rgb(0, 0, 0); font-weight: 400; font-style: normal;">It is seen from the eigenvalues after iteration #1:</div>
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<div style="font-size: 16px; font-family: Tahoma; color: rgb(0, 0, 0); font-weight: 400; font-style: normal;">
<div>
<div>------------------------------------------</div>
<div>atom 1 Tr[ns(na)] (up, down, total) = 0.67656 0.33866 1.01522<br />
spin 1<br />
eigenvalues:<br />
0.057 0.060 0.060 0.111 0.111 0.116 0.162</div>
<div> spin 2<br />
eigenvalues:<br />
0.037 0.037 <strong><u>0.039</u></strong> 0.041 0.041 <strong><u>0.044</u></strong> <strong><u>0.101</u></strong></div>
<div><br />
atom 2 Tr[ns(na)] (up, down, total) = 0.38044 2.32226 2.70270<br />
spin 1<br />
eigenvalues:<br />
0.033 0.033 <u><strong>0.035</strong></u> <u><strong>0.053</strong></u> <strong><u>0.058</u></strong> <u><strong>0.077</strong></u> <u><strong>0.093</strong></u></div>
<div> spin 2<br />
eigenvalues:<br />
0.091 0.121 0.126 0.191 0.372 0.656 0.766</div>
<div>------------------------------------------</div>
<div> </div>
<div>that we should have (?) total number of 3x5=15 metastable states.</div>
<div> </div>
<div>To discover the properties of those states, I used the following 15 different combinations of "starting_ns_eigenvalues":</div>
</div>
<div> </div>
<div>----------------------------</div>
<div>
<div> starting_ns_eigenvalue(3,2,1)=1.0, starting_ns_eigenvalue(3,1,2)=1.0<br />
starting_ns_eigenvalue(3,2,1)=1.0, starting_ns_eigenvalue(4,1,2)=1.0<br />
starting_ns_eigenvalue(3,2,1)=1.0, starting_ns_eigenvalue(5,1,2)=1.0<br />
starting_ns_eigenvalue(3,2,1)=1.0, starting_ns_eigenvalue(6,1,2)=1.0<br />
starting_ns_eigenvalue(3,2,1)=1.0, starting_ns_eigenvalue(7,1,2)=1.0<br />
starting_ns_eigenvalue(6,2,1)=1.0, starting_ns_eigenvalue(3,1,2)=1.0<br />
starting_ns_eigenvalue(6,2,1)=1.0, starting_ns_eigenvalue(4,1,2)=1.0<br />
starting_ns_eigenvalue(6,2,1)=1.0, starting_ns_eigenvalue(5,1,2)=1.0<br />
starting_ns_eigenvalue(6,2,1)=1.0, starting_ns_eigenvalue(6,1,2)=1.0<br />
starting_ns_eigenvalue(6,2,1)=1.0, starting_ns_eigenvalue(7,1,2)=1.0<br />
starting_ns_eigenvalue(7,2,1)=1.0, starting_ns_eigenvalue(3,1,2)=1.0<br />
starting_ns_eigenvalue(7,2,1)=1.0, starting_ns_eigenvalue(4,1,2)=1.0<br />
starting_ns_eigenvalue(7,2,1)=1.0, starting_ns_eigenvalue(5,1,2)=1.0<br />
starting_ns_eigenvalue(7,2,1)=1.0, starting_ns_eigenvalue(6,1,2)=1.0<br />
starting_ns_eigenvalue(7,2,1)=1.0, starting_ns_eigenvalue(7,1,2)=1.0</div>
<div>---------------------------------------</div>
<div>and performed the 15 scf calculations. </div>
<div>Surprisingly, I got the same results for the total energies for all 15 different inputs:</div>
<div> </div>
<div>------------------------------</div>
<div>
<div>! total energy = -879.68389676 Ry<br />
! total energy = -879.68389676 Ry<br />
! total energy = -879.68389676 Ry<br />
! total energy = -879.68389676 Ry<br />
! total energy = -879.68389676 Ry<br />
! total energy = -879.68389676 Ry<br />
! total energy = -879.68389676 Ry<br />
! total energy = -879.68389676 Ry<br />
! total energy = -879.68389676 Ry<br />
! total energy = -879.68389676 Ry<br />
! total energy = -879.68389676 Ry<br />
! total energy = -879.68389676 Ry<br />
! total energy = -879.68389676 Ry<br />
! total energy = -879.68389676 Ry<br />
! total energy = -879.68389676 Ry</div>
<div>-------------------------------------------</div>
<div>On the other hand, the convergency has been achieved with different numbers of iterations:</div>
<div> </div>
<div>-----------------------------</div>
<div> convergence has been achieved in 70 iterations<br />
convergence has been achieved in 58 iterations<br />
convergence has been achieved in 48 iterations<br />
convergence has been achieved in 67 iterations<br />
convergence has been achieved in 57 iterations<br />
convergence has been achieved in 65 iterations<br />
convergence has been achieved in 52 iterations<br />
convergence has been achieved in 72 iterations<br />
convergence has been achieved in 59 iterations<br />
convergence has been achieved in 48 iterations<br />
convergence has been achieved in 54 iterations<br />
convergence has been achieved in 57 iterations<br />
convergence has been achieved in 46 iterations<br />
convergence has been achieved in 70 iterations<br />
convergence has been achieved in 62 iterations<br />
---------------------------------------</div>
<div> </div>
<div>Now question arises:</div>
<div>1- If the total energies are the same, maybe the QE code, irrespective of the starting_ns_eigenvalues, leads the system to global-minimum (or specific state) state ?</div>
<div>2- Why the number of convergency iterations differ?</div>
<div> </div>
<div>Any comments is highly appreciated. </div>
<div> </div>
<div>With kind regards,</div>
<div>Mahmoud Payami</div>
</div>
</div>
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<div style="font-family: Tahoma; color: rgb(0, 0, 0); font-size: 16px; font-weight: 400; font-style: normal;">AEOI, Tehran, Iran</div>
<div style="font-family: Tahoma; color: rgb(0, 0, 0); font-size: 16px; font-weight: 400; font-style: normal;">Email: mpayami@aeoi.org.ir</div>
<div style="font-family: Tahoma; color: rgb(0, 0, 0); font-size: 16px; font-weight: 400; font-style: normal;">Phone: +98 (0)21 82066504</div>
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