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HSE functional calculation

已有 11001 次阅读 2014-2-6 01:19 |个人分类:科学札记|系统分类:科研笔记| VASP, hse

HSE hybrid functional：Hartree-Fock (HF) type and hybrid functional calculations

Available only in VASP.5.X.

http://cms.mpi.univie.ac.at/vasp/vasp/Hartree_Fock_HF_type_hybrid_functional_calculations.html

INCAR FOR HSE

# output options

LWAVE = .FALSE. # write or don't write WAVECAR

LCHARG = .FALSE. # write or don't write CHG and CHGCAR

LELF = .FALSE. # write ELF

# ionic relaxation

NSW = 100 # number of ionic steps

IBRION = 1 # 2=conjucate gradient, 1=Newton like

ISIF = 3 # 3=relax everything, 2=relax ions only, 4=keep volume fixed

# precision parameters

EDIFF = 1E-7 # 1E-3 very low precision for pre-relaxation, use 1E-5 next

EDIFFG = -1E-3 # usually: 10 * EDIFF

PREC = high # precision low, med, high, accurate

# electronic relaxation

ISMEAR = 0 # -5 = tetraedon, 1..N = Methfessel

SIGMA = 0.1

ENCUT = 600 # cutoff energy

PSTRESS = 0

#ISYM=0

# Choose DFT functional - HSE06

ISTART = 1

LHFCALC = .TRUE. ; HFSCREEN = 0.2

NBANDS = 16

ALGO = All ; TIME = 0.4

PRECFOCK = Fast ! used PRECFOCK = Normal for high quality calculations

#NKRED = 2 ! omit flag for high quality calculations

HSE hybrid functional：Hartree-Fock (HF) type and hybrid functional calculations

Available only in VASP.5.X.

http://cms.mpi.univie.ac.at/vasp/vasp/Hartree_Fock_HF_type_hybrid_functional_calculations.html

Subsections

(1) Typical hybrid functional and Hartree-Fock calculations

It is strongly recommended to perform standard DFT calculations first, and to start Hartree-Fock type calculations from a preconverged WAVECAR file.

(a) A typical INCAR file for a Hartree-Fock or hybrid HF/DFT calculation for an insulator or semiconductor has the following input lines:

ISTART = 1

LHFCALC = .TRUE. ;

HFSCREEN = 0.2

NBANDS = number of occupied bands

ALGO = All ;

TIME = 0.4

PRECFOCK = Fast #! used PRECFOCK = Normal for high quality calculations

NKRED = 2 #! omit flag for high quality calculationsFor

(b) For metals and small gap semiconductors it is recommended to use.

ISTART = 1

LHFCALC = .TRUE. ;

HFSCREEN = 0.2

ALGO = Damped ;

TIME = 0.4

PRECFOCK = Fast ! used PRECFOCK = Normal for high quality calculations

NKRED = 2 ! omit flag for high quality calculations

These input files select the HSE06 functional, which tends to yield very similar thermochemistry as the PBE0 functional, but converges more rapidly with respect to the number of k-points [99]. We thus recommend to apply and use this functional instead of the more demanding PBE0 functional.

The NKRED flag is applicable, if and only if the number of k-points is dividable by NKRED (see Sec. 6.71.9).

PRECFOCK= fast selects a smaller FFT grid for the fast-Fourier-transforms (see Sec. 6.71.5).

For high accuracy NKRED and in particular PRECFOCK= fast should be ommited, but we recommend to do this only after preconverging the orbitals and atomic positions with the flags specified above.

Mind, that the parameter TIME defaults to 0.4, and for the present algorithm this hardly ever needs to be changed.

If divergence is observed, simply decrease TIME until the damped or conjugate gradient algorithm become stable (see Sec. 6.47 and 6.51).

Standard Hartree-Fock type calculations require one to set the flag AEXX = 1.0 to switch on full non-local exchange (local exchange and correlation are automatically switched off):

ISTART = 1 LHFCALC = .TRUE. ; AEXX = 1.0 ; NBANDS = number of occupied bands ALGO = All ; TIME = 0.4 PRECFOCK = Fast ! used PRECFOCK = Normal for high quality calculations NKRED = 2 ! omit flag for high quality calculations

Concerning NKRED and PRECFOCK the same considerations as above apply. Matter of fact, it is also possible to try to converge using the ``metallic'' setup given above.

(2)Notes

（1）LHFCALC-tag

LHFCALC= .TRUE. | .FALSE.

Default: LHFCALC=.FALSE.

The flag specifies, whether Hartree-Fock type calculations are performed.

At the moment, it is recommended to select an all bands simultaneous algorithm, i.e. ALGO=Damped (IALGO=53) or ALGO=All (IALGO=58) in the INCAR file (see Sec. 6.46 6.47).

The blocked Davidson algorithm ALGO=Normal is, with certain caveat, also supported, whereas calculations for the other algorithms (ALGO=Fast) are not currently supported (note: no warning is printed).

The blocked Davidson algorithm ALGO=Normal is generally rather slow, and in many cases the Pulay mixer will be unable to determine the proper ground-state.

We hence recommend to select the blocked Davidson algorithm only in combination with straight mixing or a Kerker like mixing. The following combination have been successfully applied for small and medium sized systems

LHFCALC = .TRUE. ; ALGO = Normal ; IMIX = 1 ; AMIX = aDecrease the parameter a until convergence is reached.

In most cases, however, it is recommended to use the damped algorithm with suitably chosen timestep. The following setup for the electronic optimization works reliably in most cases:

LHFCALC = .TRUE. ; ALGO = Damped ; TIME = 0.4If convergence is not obtained, it is recommended to reduce the timestep TIME.

（2）HFSCREEN

HFSCREEN determines the range separation parameter in range separated hybrid functionals. In combination with PBE potentials, attributing a value to HFSCREEN will switch from the PBE0 functional (in case LHFCALC=.TRUE.) to the closely related HSE03 or HSE06 functional [93,94,95].

Note: A comprehensive study of the performance of the HSE03/HSE06 functional compared to the PBE and PBE0 functionals can be found in Ref. [99]. The B3LYP functional was investigated in Ref. [100]. Further applications of hybrid functionals to selected materials can be found in the following references: Ceria (Ref. [101]), lead chalcogenides (Ref. [102]), CO adsorption on metals (Refs. [103,104]), defects in ZnO (Ref. [105]), excitonic properties (Ref. [106]), SrTiO and BaTiO (Ref. [107]).

LTHOMAS= .TRUE. | .FALSE.

Default: LTHOMAS=.FALSE.

If the flag LTHOMAS is set, a similar decomposition of the exchange functional into a long range and a short range part is used. This time, it is more convenient to write the decomposition in reciprocal space:

$.displaystyle .frac{4 .pi e^2}{.vert{.bf G}.vert^2}=S_{.mu}(.vert{.bf G}.vert)+... ...{.vert{.bf G}.vert^2} -.frac{4 .pi e^2}{.vert{.bf G}.vert^2 +k_{TF}^2} .right),$

(6.69)

where $k_{TF}$ is the Thomas-Fermi screening length. HFSCREEN is used to specify the parameter $k_{TF}$ . For typical semi-conductors, the Thomas-Fermi screening length is about 1.8 Å $^{-1}$ , and setting HFSCREEN to this value yields reasonable band gaps for most materials.

In principle, however, the Thomas-Fermi screening length depends on the valence electron density; VASP determines this parameter from the number of valence electrons (POTCAR) and the volume and writes the corresponding value to the OUTCAR file:

Thomas-Fermi vector in A = 2.00000Since, VASP counts the semi-core states and -states as valence electrons, although these states do not contribute to the screening, the values reported by VASP are, however, often incorrect. Details can be found in literature [96,97,98]. Another important detail concerns that implementation of the density functional part in the screened exchange case. Literature suggests that a global enhancement factor (see Equ. (3.15) in Ref. [98]) should be used, whereas VASP implements a local density dependent enhancement factor $z= k_{TF}/.bar k$ , where is the Fermi wave vector corresponding to the local density (and not the average density as suggested in Ref. [98]). The VASP implementation is in the spirit of the local density approximation.

（3） ALGO

Default
ALGO	=	Normal

The ALGO tag is a convenient option to specify the electronic minimisation algorithm in VASP.4.5 and later versions. Except for ``None'' and ``Nothing'', ``Exact'' and ``Diag'' (which must be spelled out), the first letter determines the applied algorithm. Conjugate, Subrot, Eigenval, Exact, None and Nothing are only supported by VASP.5.2.12 and newer versions.

ALGO = Normal selects IALGO = 38 (blocked Davidson iteration scheme), whereas ALGO = Very_Fast selects IALGO = 48 (RMM-DIIS). A faily robust mixture of both algorithm is selected for ALGO = Fast. In this case, Davidson (IALGO = 38) is used for the initial phase, and then VASP switches to RMM-DIIS (IALGO = 48). Subsequencly, for each ionic update, one IALGO = 38 sweep is performed for each ionic step (except the first one).

The ``all band simultaneous update of orbitals'' can be selected using ALGO = Conjugate or ALGO = All (IALGO = 58, in both cases the same conjugate gradient algorithm is used). A damped velocity friction algorithm is selected using ALGO = Damped (IALGO = 53). ALGO = Subrot selects subspace rotation or diagonalization in the sub-space spanned by the calculated NBANDS orbitals (IALGO = 4). ALGO = Exact or ALGO = Diag performs an exact diagonalization (IALGO = 90), and we recommend to use this if more than 30-50 % of the states are calculated (e.g. for or RPA calculations). ALGO = Eigenval allows to recalculate one electron energies, density of state and perform selected postprocessing using the current orbitals (IALGO = 3) e.g. read from WAVECAR. ALGO = None or ALGO = Nothing allows to recalculate the density of states (eigenvalues from WAVECAR, e.g. using different smearing or tetrahedron method) or perform other selected postprocessing using the current orbitals and one electron energies (IALGO = 2) e.g. read from WAVECAR.

（4）PRECFOCK

PRECFOCK: FFT grid in the Hartree-Fock and GW related routines

PRECFOCK= Low | Medium | Fast | Normal | Accurate

Default: PRECFOCK=Normal

The PRECFOCK parameter controls the FFT grid for the exact exchange (Hartree-Fock) routines, i.e. it is possible to chose a different grid for the exact exchange part, and for the local Hartree and DFT potentials. In fact, the exchange is rather insensitive to the FFT grids, and in many cases a rather coarse grid can be used to calculate the overlap density and the potentials. Since the exact exchange requires the evaluation of an overlap density (compare 6.59)

$.displaystyle .phi_{{.bf k}n}^{*}({.bf r}).phi_{{.bf q}m}^{*}({.bf r})$

errors in the convolution (aliasing errors) are only avoided, if the FFT grid contains all Fourier components up to twice the plane wave with the largest wave vector ( $2 .vert G_{.rm cut}.vert$ ).

For Low and Fast, however, the smallest possible FFT grid, which just encloses the cutoff sphere ( $.vert G_{.rm cut}.vert$ ) determined by the plane wave cutoff (ENCUT), is used. This accelerates the calculations by roughly a factor two to three, but causes slight changes in the total energies and some noise in the calculated forces. The corresponding FFT grid that is used in the Hartree Fock routines is written to the OUTCAR file after the lines

FFT grid for exact exchange (Hartree Fock)For PRECFOCK=Normal, the FFT grid for the exact exchange is identical to the FFT grid used for the orbitals for PREC=Normal in the DFT part. For PRECFOCK=Accurate, the FFT grid for the exact exchange is identical to the FFT grid used for the orbitals for PREC=Accurate in the DFT part (any combination of PREC and PRECFOCK is allowed).

For PRECFOCK=Fast, Normal and Accurate, the augmentation charges--which are required to restore the norm and dipoles of the overlap density on the plane wave grid --are made soft, such that an accurate presentation on the plane wave grid is possible even for relatively coarse FFT grids. The sphere size is printed out after

Radii for the augmentation spheres in the non-local exchangeThe following table summarises the possible setting:

PRECFOCK	FFT grid	augmentation charge	advantage/disatvantage
VASP.5.2.2 compatible, not recommended
Low	$G_{.rm cut}^a$	identical to standard DFT	large noise in forces/energy errors
Medium	identical to std. FFT	identical to standard DFT	some noise in forces/good energy
VASP.5.2.4 and newer, recommended
Fast	$G_{.rm cut}^a$	very soft augmentation charge	some noise in forces/good energy
Normal	3/2 $G_{.rm cut}^a$	soft augmentation charge	accurate forces and energy
Accurate	2 $G_{.rm cut}^a$	soft augmentation charge	very accurate forces and energy

$^a .quad .frac{ .hbar^2}{2 m_e} .vert G_{.rm cut}.vert^2 = {.tt ENCUT}$

soft augmentation charge: radius for augmentation sphere is increased by factor 1.25 compared to default

very soft augmentation charge: radius is increased by factor 1.35 compared to default except for

like charge, for the

channel the radius of the augmentation sphere is increased by a factor 1.25

Even PRECFOCK=Fast yields fairly low noise in the forces and virtually no egg-box effects (aliasing errors). In the forces, the noise is usually below 0.01 eV/Å. For PRECFOCK=N and PRECFOCK=A, noise is usually not an issue, and the accuracy is sufficient even for phonon calculations in large supercells.

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