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<TITLE>CuO, LDA+U, Pseudopots, again</TITLE>
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<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">To All:</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Please refer to a previous pw_forum thread "CuO, LDA+U, Pseudopots,</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">etc."</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">I'm continuing to try to achieve a pwscf calculation which will yield a</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">"Hubbard gap" in any compound containing Cu++ and O--. My efforts to</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">date have been unsucessful. My "model" has been a pseudo-rocksalt CuO</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">structure based on "proxy" lattice constants near those of FeO, NiO and</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">MgO.</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">I strongly suspect my problem involves use (or misuse or unavailability)</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">of a proper Cu pseudopotential. The issue of Cu++ bonded to O-- is</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">central to the physics of high temperature superconductivity, and a</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">failure of pwscf to properly resolve this difficulty would be</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">detrimential to the future deployment of quantum-espresso to this very</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">important and critical area of computational materials physics, not</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">just HTSC, but possibly GMR</FONT></SPAN><SPAN LANG="en-us"><FONT FACE="Calibri"> structures</FONT></SPAN><SPAN LANG="en-us"><FONT FACE="Calibri"> as well.</FONT></SPAN><SPAN LANG="en-us"><FONT FACE="Calibri"> Note in what follows</FONT></SPAN><SPAN LANG="en-us"> <FONT FACE="Calibri">is that I changed occ_loc in tabd.f90 from 10 to 9.</FONT></SPAN><SPAN LANG="en-us"></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">I attach below 1) the list of PPs I've tried and their d-level</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">configurations.</FONT></SPAN><SPAN LANG="en-us"> <FONT FACE="Calibri"> </FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">None really contain the generally assumed 3d9 Hund's</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Rule configuration for CuO complexes. Following this is the output 2)</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">of a "hand written grep-er" of the scf.out file for a typical example</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">(one of about 20) combinations of Cu PPs and the "starting_ns_eigenvalue</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">suggestions" to escape the "minimum energy trap." I selected</FONT></SPAN><SPAN LANG="en-us"> <FONT FACE="Calibri">my</FONT></SPAN><SPAN LANG="en-us"><FONT FACE="Calibri"> "best</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">attempt" at this effort. The critical (IMHO) lines are pointed to by a</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">"-->" marker. BTW, I didn't try any Wannier projections since the</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">eigenvalue forcings didn't work, and my lesson from Example 25 is that</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">these have to be done</FONT></SPAN><SPAN LANG="en-us"> <FONT FACE="Calibri">successfully</FONT></SPAN><SPAN LANG="en-us"><FONT FACE="Calibri"> first.</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Any of those in the pwscf community aware of a "better" PP for my</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">problem, please e-mail such to me. In the meantime, I'm experimenting</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">"rolling my own" with the tools available at the Berlin-FHI site,</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">trying 3d9-4s2 as a first attempt--stay tuned.</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Sorry for all my American slang. We didn't invent the language...the</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Brits did</FONT></SPAN><SPAN LANG="en-us"><FONT FACE="Calibri">, and shoved it down our throats</FONT></SPAN><SPAN LANG="en-us"><FONT FACE="Calibri">. We just made English more user friendly.</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">-Paul</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">----------------------------------</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">1)</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Cu.blyp-n-van_ak.UPF</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> nl pn l occ</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 3D 3 2 9.50</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 4S 4 0 1.00</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 4P 4 1 0.50</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Cu.pbe-d-rrkjus.UPF</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> nl pn l occ</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 3D 3 2 10.00</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 3D 3 2 0.00</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 4P 2 1 -1.00</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 4S 1 0 1.00</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Cu.pbe-n-van_ak.UPF</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> nl pn l occ</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 3D 3 2 9.50</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 4S 4 0 1.00</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 4P 4 1 0.50</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Cu.pw91-n-van_ak.UPF</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> nl pn l occ</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 3D 3 2 9.50</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 4S 4 0 1.00</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 4P 4 1 0.50</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Cu.pz-d-rrkjus.UPF</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> nl pn l occ</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 3D 3 2 10.00</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 3D 3 2 0.00</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 4P 2 1 -1.00</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 4S 1 0 1.00</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Cu.pz-n-van_ak.UPF</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> nl pn l occ</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 3D 3 2 9.50</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 4S 4 0 1.00</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> 4P 4 1 0.50</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">---------------------------------------</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">2)</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Today is Wed Jan 9 19:07:17 PST 2008</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Now is Wed Jan 9 19:10:07 PST 2008</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">SCF Run preparatory to post-processing</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Script is ./CuO_3.scf.sh, Output is CuO_3.scf.data</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> kinetic-energy cutoff = 30.0000 Ry</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> charge density cutoff = 240.0000 Ry</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> convergence threshold = 1.0E-06</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> pwscf_exec = /home/pmpgrant/O-sesame/PW/pw.x</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> a_Ang = 4.200</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> a_Bohr = 7.93950</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> nbnd = 20,</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> nelec = ,</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> occupations = 'smearing',</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> smearing = gauss,</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> degauss = 0.01,</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> la2F = .false.,</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> diagonalization = 'david',</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> starting_magnetization(1) = 0.0</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> starting_magnetization(2) = 0.5</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> starting_magnetization(3) = -0.5</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> nspin = 2,</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> lda_plus_u = .true.,</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> Hubbard_U(2) = 5.0</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> Hubbard_U(3) = 5.0</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> U_projection_type = norm-atomic</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> starting_ns_eigenvalue(1,2,2) = 0.0</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> starting_ns_eigenvalue(2,2,2) =</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> starting_ns_eigenvalue(3,2,2) =</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> starting_ns_eigenvalue(4,2,2) =</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> starting_ns_eigenvalue(5,2,2) =</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> starting_ns_eigenvalue(1,1,3) = 0.0</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> starting_ns_eigenvalue(2,1,3) =</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> starting_ns_eigenvalue(3,1,3) =</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> starting_ns_eigenvalue(4,1,3) =</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri"> starting_ns_eigenvalue(5,1,3) =</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> TM_pseudopot = Cu.pz-d-rrkjus.UPF</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> A_pseudopot = O.LDA.US.RRKJ3.UPF</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">Run_Type npk Ef(eV) Total E(Ry) CPU_Time Wall_Time</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">scf 8 11.1457 -239.16751151 1m 8.04s 2m50.40s</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">d-orbital occupations</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">138:eigenvalues: 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Wingdings">è<FONT FACE="Courier New"> </FONT></FONT></SPAN><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"> <FONT FACE="Calibri">152:eigenvalues: 0.8000000 0.8000000 0.8000000 0.8000000 0.8000000</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Wingdings">è<FONT FACE="Courier New"> </FONT></FONT></SPAN><SPAN LANG="en-us"> <FONT FACE="Calibri">167:eigenvalues: 0.8000000 0.8000000 0.8000000 0.8000000 0.8000000</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"><FONT FACE="Calibri">181:eigenvalues: 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">213:eigenvalues: 0.9976937 0.9976937 0.9984132 0.9984132 1.0008045</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">227:eigenvalues: 0.5164626 0.5164626 0.9680621 0.9823458 0.9823458</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">242:eigenvalues: 0.5164626 0.5164626 0.9680621 0.9823458 0.9823458</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">256:eigenvalues: 0.9976937 0.9976937 0.9984132 0.9984132 1.0008045</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">277:eigenvalues: 0.9976937 0.9976937 0.9984132 0.9984132 1.0008045</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> 291:eigenvalues: 0.0000000 0.5164626 0.9680621 0.9823458 0.9823458</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> 306:eigenvalues: 0.0000000 0.5164626 0.9680621 0.9823458 0.9823458</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">320:eigenvalues: 0.9976937 0.9976937 0.9984132 0.9984132 1.0008045</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">353:eigenvalues: 0.9936756 0.9936756 0.9968054 0.9968054 0.9991184</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> 367:eigenvalues: 0.7870114 0.7870114 0.9938818 0.9938818 0.9969944</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> 382:eigenvalues: 0.7867963 0.7867963 0.9938806 0.9938806 0.9969906</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">396:eigenvalues: 0.9936787 0.9936787 0.9968055 0.9968055 0.9991185</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">429:eigenvalues: 0.9914062 0.9914062 0.9971611 0.9971611 0.9994970</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">443:eigenvalues: 0.7968500 0.7968500 0.9944826 0.9944826 0.9975186</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">458:eigenvalues: 0.7971215 0.7971215 0.9944915 0.9944915 0.9975167</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">472:eigenvalues: 0.9914126 0.9914126 0.9971603 0.9971603 0.9994966</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">507:eigenvalues: 0.9667233 0.9667233 0.9969086 0.9969086 0.9992909</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">521:eigenvalues: 0.8723219 0.8723219 0.9959798 0.9959798 0.9984415</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">536:eigenvalues: 0.8713559 0.8713559 0.9959649 0.9959649 0.9984298</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">550:eigenvalues: 0.9663176 0.9663176 0.9968918 0.9968918 0.9992743</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">585:eigenvalues: 0.9525509 0.9525509 0.9963181 0.9963181 0.9986638</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">599:eigenvalues: 0.9127300 0.9127300 0.9961748 0.9961748 0.9985388</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">614:eigenvalues: 0.9146296 0.9146296 0.9962191 0.9962191 0.9985819</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">628:eigenvalues: 0.9537915 0.9537915 0.9963783 0.9963783 0.9987221</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">663:eigenvalues: 0.9458265 0.9458265 0.9962868 0.9962868 0.9986542</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">677:eigenvalues: 0.9104092 0.9104092 0.9959371 0.9959371 0.9983246</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">692:eigenvalues: 0.9047312 0.9047312 0.9957990 0.9957990 0.9982026</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">706:eigenvalues: 0.9417229 0.9417229 0.9961282 0.9961282 0.9984984</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">741:eigenvalues: 0.9354950 0.9354950 0.9960520 0.9960520 0.9984263</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">755:eigenvalues: 0.9174694 0.9174694 0.9958534 0.9958534 0.9982404</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">770:eigenvalues: 0.9179431 0.9179431 0.9958601 0.9958601 0.9982469</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">784:eigenvalues: 0.9358828 0.9358828 0.9960625 0.9960625 0.9984347</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">819:eigenvalues: 0.9341625 0.9341625 0.9960316 0.9960316 0.9984028</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">833:eigenvalues: 0.9222122 0.9222122 0.9959062 0.9959062 0.9982848</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">848:eigenvalues: 0.9216331 0.9216331 0.9958882 0.9958882 0.9982692</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">862:eigenvalues: 0.9336231 0.9336231 0.9960127 0.9960127 0.9983843</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">897:eigenvalues: 0.9327282 0.9327282 0.9960266 0.9960266 0.9983951</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">911:eigenvalues: 0.9284646 0.9284646 0.9959858 0.9959858 0.9983585</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">926:eigenvalues: 0.9283145 0.9283145 0.9959811 0.9959811 0.9983538</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">940:eigenvalues: 0.9325413 0.9325413 0.9960218 0.9960218 0.9983904</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">975:eigenvalues: 0.9318453 0.9318453 0.9960271 0.9960271 0.9983966</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">989:eigenvalues: 0.9297349 0.9297349 0.9960062 0.9960062 0.9983772</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">1004:eigenvalues: 0.9299729 0.9299729 0.9960136 0.9960136 0.9983841</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">1018:eigenvalues: 0.9320457 0.9320457 0.9960350 0.9960350 0.9984044</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">1053:eigenvalues: 0.9311035 0.9311035 0.9960273 0.9960273 0.9983963</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">1067:eigenvalues: 0.9316853 0.9316853 0.9960330 0.9960330 0.9984016</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">1082:eigenvalues: 0.9316968 0.9316968 0.9960336 0.9960336 0.9984023</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">1096:eigenvalues: 0.9310994 0.9310994 0.9960275 0.9960275 0.9983966</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> 1131:eigenvalues: 0.9314650 0.9314650 0.9960338 0.9960338 0.9984027</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> 1145:eigenvalues: 0.9312033 0.9312033 0.9960312 0.9960312 0.9984004</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> 1160:eigenvalues: 0.9311989 0.9311989 0.9960309 0.9960309 0.9984001</FONT></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><FONT FACE="Calibri">--> 1174:eigenvalues: 0.9314517 0.9314517 0.9960337 0.9960337 0.9984026</FONT></SPAN><SPAN LANG="en-us"></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><B><I></I></B></SPAN><SPAN LANG="en-us"><B><I></I></B></SPAN><SPAN LANG="en-us"><B><I></I></B></SPAN><B><I><SPAN LANG="en-us"><FONT SIZE=4 FACE="Comic Sans MS">Paul M. Grant, PhD</FONT></SPAN></I></B><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><B></B></SPAN><SPAN LANG="en-us"><B></B></SPAN><SPAN LANG="en-us"><B></B></SPAN><B><SPAN LANG="en-us"><FONT SIZE=2 FACE="Arial">Principal, W2AGZ Technologies</FONT></SPAN></B><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><B></B></SPAN><SPAN LANG="en-us"><B></B></SPAN><SPAN LANG="en-us"><B></B></SPAN><B><SPAN LANG="en-us"><FONT SIZE=2 FACE="Arial">Visiting Scholar, Applied Physics, Stanford University</FONT></SPAN></B><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"></SPAN></P>
<P DIR=LTR><SPAN LANG="en-us"><B></B></SPAN><SPAN LANG="en-us"><B></B></SPAN><SPAN LANG="en-us"><B></B></SPAN><B><SPAN LANG="en-us"><FONT SIZE=2 FACE="Arial">EPRI Science Fellow (Retired)</FONT></SPAN></B><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"></SPAN><SPAN LANG="en-us"></SPAN></P>
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