The LDA-1/2 method in exciting
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1 The LDA-1/2 method in exciting Ronaldo Rodrigues Pelá Humboldt Universität zu Berlin Instituto Tecnológico de Aeronáutica
2 Outline DFT-1/2 Exchange-correlation functionals Exact exchange calculations Hybrid-functional calculations Van-der-Waals corrections
3 DFT-1/2 Accuracy: comparable to hybrid functionals Computational cost: semilocal functionals Basic idea: introduce a half-hole Approximate QP corrections: band edges
4 DFT-1/2 Band gaps: binary compounds AIP Advances 1, (2011)
5 DFT-1/2 Band gaps: alloys AlGaN InGaN APL 98, (2011) J. Phys. Cond. Matt. 27, (2015)
6 DFT-1/2 Defects and impurities EF(Si-insterst.) Exp = ev LDA = ev LDA-1/2 = ev Phys. Rev. B 90, (2014) Phys. Rev. B 88, (2013)
7 DFT-1/2 Magnetic semiconductors APL 100, (2012) APL 101, (2012) Band offsets PRB 79, R (2009) JAP 114, (2013)
8 DFT-1/2 Janak's theorem Assuming linearity Slater's half occupation scheme 0 1/2 1
9 DFT-1/2 0 1/2 1 A calculation for N electrons and with a KS potential given by will work as desired
10 DFT-1/2 It is easy to calculate Vs for atoms For more complex systems, it is more difficult Approximation: Vs for a complex system can be obtained from atomic calculations
11 DFT-1/2 Recalling: Atomic calculations
12 DFT-1/2 Trimming function determined by means of a variational process PRB 78, (2008)
13 Exciting DFT-1/2 <species speciesfile="si.xml" rmt="2.1"> <atom coord=" "></atom> <atom coord=" "></atom> <dfthalfparam exponent="8" cut="3.90" ampl="1"> <shell number="0" ionization="0.25" /> </dfthalfparam> </species>
14 Exciting DFT-1/2 <species speciesfile="si.xml" rmt="2.1"> <atom coord=" "></atom> <atom coord=" "></atom> <dfthalfparam exponent="8" cut="3.90" ampl="1"> <shell number="0" ionization="0.25" /> </dfthalfparam> </species>
15 Exciting DFT-1/2 <species speciesfile="si.xml" rmt="2.1"> <atom coord=" "></atom> <atom coord=" "></atom> <dfthalfparam exponent="8" cut="3.90" ampl="1"> <shell number="0" ionization="0.25" /> </dfthalfparam> </species>
16 Exciting DFT-1/2 <species speciesfile="si.xml" rmt="2.1"> <atom coord=" "></atom> <atom coord=" "></atom> <dfthalfparam exponent="8" cut="3.90" ampl="1"> <shell number="0" ionization="0.25" /> </dfthalfparam> </species>
17 Exciting DFT-1/2 <species speciesfile="si.xml" rmt="2.1"> <atom coord=" "></atom> <atom coord=" "></atom> <dfthalfparam exponent="8" cut="3.90" ampl="1"> <shell number="0" ionization="0.25" /> </dfthalfparam> </species> Which atomic shell needs to be ionized (the order is the same as in the species file)
18 Exciting DFT-1/2 <species speciesfile="si.xml" rmt="2.1"> <atom coord=" "></atom> <atom coord=" "></atom> <dfthalfparam exponent="8" cut="3.90" ampl="1"> <shell number="0" ionization="0.25" /> </dfthalfparam> </species> How much charge should be removed from the atomic shell to obtain Vs
19 DFT-1/2 Exciting <groundstate ngridk="8 8 8" xctype="gga_pbe"> <dfthalf printvsfile="false"/> </groundstate> Very important: this triggers a DFT-1/2 calculation
20 DFT-1/2 Tutorial 1) Obtain the gap of Si (given the rcut of 3.9 Bohr) 2) Obtain the rcut of Si Egap = 1.2 ev (exp: 1.17 ev) 3) Obtain the rcut of GaN Egap = 3.4 ev (exp: 3.3 ev)
21 DFT-1/2 Tutorial E.g.: Si Refining, to find the maximum
22 Exchange-correlation functionals KS equation:
23 Exchange-correlation functionals LDA: GGA: meta-gga: EXX: Hybrids:
24 Exchange-correlation functionals exciting input <groundstate ngridk="8 8 8" xctype="gga_pbe"> </groundstate> Specification of the XC functional class_name
25 Exchange-correlation functionals XC Perdew-Zunger/Ceperley-Alder Perdew-Wang/Ceperley-Alder X-alpha von Barth-Hedin Perdew-Burke-Ernzerhof (PBE) Revised PBE PBE for solids (PBEsol) Wu-Cohen exchange (WC06) with PBE correlation Armiento-Mattsson (AM05) asymptotically corrected PBE (acpbe) PBE0 OEP-EXX Input name LDA_PZ LDA_PW LDA_XALPHA LDA_vBH GGA_PBE GGA_PBE_R GGA_PBE_SOL GGA_WC GGA_AM05 GGA_AC_PBE HYB_PBE0 EXX
26 Exchange-correlation functionals The LIBXC library php/libxc [By Miguel A. L. Marques] Library of XC functionals Interfaces to various programs LIBXC
27 Exchange-correlation functionals The LIBXC library <groundstate ngridk="8 8 8"> <libxc xc = "XC_GGA_XC_LYP" /> </groundstate>
28 Exchange-correlation functionals The LIBXC library <groundstate ngridk="8 8 8"> <libxc correlation = "XC_GGA_C_PBE" exchange = "XC_GGA_X_PBE" /> </groundstate> Combination of different X and C functionals possible (use with care!) Available in exciting: L(S)DAs and GGAs
29 Exchange-correlation functionals Tutorial: Si
30 Exact exchange calculations Exchange energy KS potential needed EXX energy is not an explicit functional of the density. How to get the derivative?
31 Exact exchange calculations The chain rule Nonlocal matrix elements PRB 53, 7024 (1996).
32 Exact exchange calculations The chain rule Density response function PRB 53, 7024 (1996).
33 Exact exchange calculations Iterative convergence PRB 68, (2003) For details and spin polarized generalization see: PRL 98, (2007)
34 Exact exchange calculations Input parameters tauoep maxitoep ngridk nempty PRB 68, (2003) For details and spin polarized generalization see: PRL 98, (2007)
35 Exact exchange calculations Input <groundstate ngridk="3 3 3" xctype="exx" nempty="30" > <OEP maxitoep = "XC_GGA_C_PBE" tauoep = " " /> </groundstate> Initial value Values for subsequent iterations
36 Exact exchange calculations Tutorial: C
37 Hybrid functional calculations Input <groundstate ngridk="3 3 3" xctype="hyb_pbe0" nempty="50" > <Hybrid exchangetype = "HF" excoeff = "0.25" /> </groundstate>
38 Hybrid functional calculations Tutorial: C
39 Hybrid functional calculations Tutorial: C. 8x8x8 k-grid, 100 empty states
40 Van-der-Waals corrections Input <groundstate ngridk=" " gmaxvr="20" rgkmax="6.5" xctype="gga_pbe" vdwcorrection="dftd2"> </groundstate> Specification of the VdW correction none DFTD2 : J. Comput. Chem. 27, 1787 (2006). TSvdW : PRL 102, (2009)
41 Van-der-Waals corrections The van-der-waals correction is added to total energy after the last SCF iteration If forces are calculated, an appropriate dispersion correction is applied Parameters corresponding to each method can be specified using the subelements DFTD2parameters and TSvdWparameters inside the element groundstate It is also possible to decouple these van-der-waals corrections from a complete ground-state calculation, using the subelements DFTD2 and TSvdW inside the element properties
42 Van-der-Waals corrections Tutorial: Graphite
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