electronic structure of solids: quantum espressoazufre.quimica.uniovi.es/zcam/th1b.pdf ·...

Electronic structure of solids: quantum espresso

Víctor Luaña (†) & Alberto Otero-de-la-Roza (‡) & DanielMenéndez-Crespo (†)

(†) Departamento de Química Física y Analítica, Universidad de Oviedo(‡) National Institute of NanoTechnology, Edmonton, Alberta, Canada

European school on Theoretical Solid State ChemistryZCAM, Zaragoza, May 12–16, 2014

VLC & AOR & DMC () Electronic structure of solids: quantum espresso ZCAM, Zaragoza 2014 1 / 104

Electronic structure Crystal

Part I

crystallography and electronic structure calculations(th-1b)



Hartree-Fock and Kohn-Sham equations

Hartree-Fock (closed shell)Orbital approximation to solve the non-relativistic electronic stationary states:

HeΨ({xi}; {Rα}) = EΨ ⇒ Fψλ = ελψλ (1){−

12∇2

r +

N∑α

Zαriα

+

∫R3

ρ(r′dr′)|r− r′|

+VX

}ψλ(x; {Rα}) = ελ({Rα})ψλ(x; {Rα}) (2)

where

VXψλ = −occ.∑

i

∫R3

ψ∗i (r′)ψλ(r′)|r− r′|

dr′ψi(r) (3)

is the Hartree (exact) exchange acting over orbital ψλ.

SCF: both, HF and KS equations must be solved iteratively until convergence (self-consistency).

Kohn-ShamOrbital ansatz to solve the density functional non-relativistic electronic ground state:

HeΨ0({xi}; {Rα}) = EΨ0 ⇒ Fψλ = ελψλ (4){−

12∇2

r +

N∑α

Zαriα

+

∫R3

ρ(r′)dr′

|r− r′|+Vxc

}ψλ(x; {Rα}) = ελ({Rα})ψλ (5)

where Vxc is the unknown exchange and correlation functional.



Quantum Chemistry vs Solid State formalisms I

The Quantum Chemistry approach

Objective: wavefunctions and total energies of any stationary state.Born-Oppenheimer: separate nuclear and electronic motions to simplify.Nonrelativistic: use classical kinetic energy, separate spin and orbital parts, ...Orbitals: way to produce antisymmetric many electron wavefunctions, via Slater determi-nants. HF orbitals fulfill Koopmans and Brillouin theorems.HF closed or open shell (main method to produce orbitals): minimize the energy of anelectronic configuration under orthonormality of the spinorbitals.Other methods to produce orbitals: UHF (unrestricted HF), GVB (generalized ValenceBond), MCSCF (Multiconfigurational SCF), ...Basis sets (molecular systems): primitive gaussians (GTO), usually combined to form con-tracted GTOs. Pople family: STO-3G, 3-21G, 6-311++G**, ... Dunning family: cc-PVDZ,cc-PVTZ, cc-PVQZ, aug-cc-PVDZ, ... CBS: Complete Basis Set (extrapolation).techniques: HF assumes an average interaction between electrons. The difference to theexact solution is the correlation problem. Correlation techniques: Möller-Plesset (Many BodyPerturbation Theory: MP2, MP3, ...), Configuration Interaction (CIS, CISD, CISDT, ...), Cou-pled Cluster (CCSD, CCSDT, ...), ... Full CI.

lim→CBS,→FCI

calculation = exact



Size scaling (N: spinorbitals, electrons)

method lin.† HF, KS HF, KS‡ KS∗ MP2 MP3 CCSD CCSD(T)Q FCIO N N3 N4 N5 N6 N7 N10 N!

† Special linear versions of HF and KS methods; ‡ KS with LDA, LSDA, or GGA xcfunctionals; ∗ KS with hybrid functionals.

Solid State (Density Functional)Objective: electron density and total energy of the ground state.

Born-Oppenheimer:Nonrelativistic formalism: most solid state codes include relativistic corrections.

Different types of basis set formalisms: (1) planewaves and pseudopotentials(pw+ps); (2) GTO’s; (3) local orbitals and ps.; (4) FPLAPW (Full Potential LinearAugmented PlaneWaves); ...

xc functionals: Metaphorical classification (Jacob’s Ladder): (1) LDA/LSDA [Ex:VWN91]; (2) GGA [Ex: PBE, PW91]; (3) meta-GGA [Ex: TPSS]; (4) hybrid [Ex:B3LYP]; (5) double hybrid [Ex: XYG3]; (¿?) the unknown exact functional.



Electronic structure solid state codes

code basis webpage price sourceabinit pw+ps www.abinit.org GNU yesCPMD pw+ps www.cpmd.org 0 yescrystal09 CGTO www.crystal.unito.it 1000 Eur. noelk FPLAPW elk.sourceforge.org GNU yesgpaw! PAW wiki.fysik.dtu.dk/gpaw GNU yesQE (pwscf) pw+ps www.quantum-espresso.org GNU yessiesta Loc+ps www.icmab.es/siesta 0 yesvasp pw+ps cms.mpi.univie.ac.at/marsweb yes yeswien2k FPLAPW www.wien2k.at yes yes

Others: adf, castep (free for UK academics), dacapo (free), fhi98md (free), fleur (free),g09, octopus (free), ...Visualizing codes: xcrysden (free), mercury, ...


www.abinit.org

www.cpmd.org

www.crystal.unito.it

elk.sourceforge.org

wiki.fysik.dtu.dk/gpaw

www.quantum-espresso.org

www.icmab.es/siesta

cms.mpi.univie.ac.at/marsweb

www.wien2k.at


KS equations on a crystal (quantum espresso version)

{−∇2

r +∑α

Vαsf + VH(r) + Vxc(r)}ψnk(r) = εn(k)ψnk(r) (6)

−∇2r : kinetic energy, Rydberg units are used throught.

Vαsf : non-local pseudopotential. Either norm-conserving, ultrasoft, or PAW (pro-jected augmented wave) pseudopotentials can be used.

VH(r) =∂EH[ρ]

∂ρ=

∫R3

ρ(r′dr′

|r− r′| : Coulomb potential or Hartree term.

Vxc(r) =∂Exc[ρ]

∂ρ: exchange and correlation potential.

Bloch states: ψnk(r) = eikrunk(r), where ψnk(r) is periodical over reciprocal spaceand unk(r) is periodical over real space.

ρ(r) =∑

nk

fnk |ψnk|2 =∑

nk

fnk |unk|2 , with fi ∈ {0, 1} (a typical insulator) or fi =

1/(1 + e−εi/kT) (Mermin functional, used on metals).k ∈ BZ1. Running special points and directions in iBZ1 (irreducible first Brillouinzone) is the basis for band diagrams. Total properties (energy, DOS, etc) requiresintegration of BZ1.



KS calculations on a basis

Let φ~q+~G(~r) be a basis function φ~q(~r) at the reciprocal cell ~G. The basis is used to buildthe KS orbitals:

ψn~q(~r) =∑

n~q

cn~q(~G)φ~q+~G(~r). (7)

By minimizing the energy with cn~q(~G) as the variational parameters the KS equationstransform into

∀~G∑~G′

(H~q+~G,~q+~G′ − εn~qS~q+~G,~q+~G′

)cn~q(~G) = ~0, (8)

that must be solved for every ~q ∈ BZ1. In the above equation:

H~q+~G,~q+~G′ =

⟨φ~q+~G(~r)

∣∣∣∣−12∇2 + V

∣∣∣∣φ~q+~G′(~r)⟩ , S~q+~G,~q+~G′ =⟨φ~q+~G

∣∣∣φ~q+~G′ ⟩ , (9)

and the KS equation takes the form of a generalized eigen equation HC = SCE thatmust besolved for every ~q.By sampling ~q-points along special directions on the BZ1 we get the band diagrams:εn~q.The total energy (E), Density of States (DOS, g(E)), and the Fermi surface in the caseof a metal (εF(~q)), are produced by integration for all ~q ∈ BZ1. Monkhorst-Pack specialpoints methods is popular for doing this integration.



Planewaves (3D) and the movement of a free electron I

The hamiltonian is h = p2/2m, ~p = −i~~∇, and the solutions are planewaves (PW)again:

|~k〉 = ψ~k(~r ) = V−1/2ei~k·~r, ε~k =~2k2

2m, ~r,~k ∈ R3. (10)

with V being the volume of the normalization box. Some properties

The PWs are eigenfunctions of the momentum operator: ~p |~k〉 = ~~k |~k〉.The particle velocity is proportional to ~k, the wavevector : ~v = ~~k/m.The |~k〉 and |−~k〉 PWs are degenerated.The wavelength of a PW is λ = 2π/k.

To enforce periodic boundary conditions in a general way we define the parallelepipediccell a

˜and an arbitrary primitive translation~t = a

˜n, n ∈ Z3. For any~r ∈ R3:

ψ~k(~r +~t ) = ψ~k(~r ) =⇒ ei~k·~t = 1. (11)

If ~k is a vector in the reciprocal cell, ~k = a˜

?k = 2πa˜

?h, the periodicity condition is

1 = ei~k·~t = ei2π(hTn) =⇒ h1nx + h2ny + h3nz ∈ Z for all n ∈ Z3. (12)



Planewaves (3D) and the movement of a free electron II

The wavevector of the periodic PWs is then

~k = 2π(h1~a ? + h2~b ? + h3~c ?) = 2πa˜

?h = a˜

?k, (h1, h2, h3) ∈ Z3. (13)

This discrete mesh of allowed ~k-points is distributed uniformly in the reciprocal space.Each ~k point can be associated with a small parallelepiped of volumev~k = (2π)3V? = (2π)3/V, where V is the volume of the main cell. It is implicitelyassumed that a primitive cell is used to describe the reciprocal space.The periodic PWs form an orthonormal set

〈~k|~k ′〉 =1V

∫V

ei(~k−~k ′)~rd~r = δ~k,~k ′ , (14)

where the integral is done on a unit cell. The set is also complete, which means thatany 3D function can be expanded as

f (~r ) =∑~k

f~kei~k·~r ⇐⇒ f~k =

∫V

f (~r )e−i~k·~rd~r. (15)



Brillouin zones I

The first Brillouin zone (BZ-1) is the common name for the Wigner-Seitz primitivecell of the reciprocal or ~k-space lattice. Whereas primitive and centered cells are bothused for the direct lattice, centering is avoiding in the manipulation of the ~k lattice.An alternative definition for BZ-1 is the set of points in ~k space that can be reachedfrom the origin (~k = ~0) without crossing any Bragg plane. A Bragg plane for any twopoints in the lattice being the plane which is perpendicular to the line between the twopoints and passes through the bisector of that line.The concept of BZ-1 can be generalized. The second BZ (BZ-2) is the set of points thatcan be reached from the first zone by crossing only one Bragg plane. BZ-(n+1) isformed is the set of points not in {BZ-1, BZ-2, ... BZ-(n−1)} that can be reached fromBZ-n by crossing only one Bragg plane. Alternatively, the n Brillouin zone can bereached from the origin by crossing n−1 Bragg planes, but not fewer.The construction of the BZ is illustrated in the next slides for a simple square lattice. Animportant point to check is that every Brillouin zone has the same volume, namely thevolume of a primitive reciprocal lattice. In addition, any BZ can be mapped back to thefirst zone by using just primitive translations, i.e. all the BZ’s are equivalent bytranslation symetry.



nn

2nd nn

3rd nn

4th nn



Al BZs are equivalent due to the translational part of the crystal space group.Furthermore, the rotational symmetry determines the equivalence between differentpositions within a Brillouin zone. The special symmetry points receive particularnames. Although there are different naming conventions, Γ is typically used todesignate the origin of the reciprocal cell (~k = ~0).Let’s examine the BZ for the cubic P, I and F Bravais lattices, directly from the KVECplots of the excellent Bilbao Crystallographic Server. The plot and the list of special ~kpositions is available for all the space groups.

Fm3m

L

zk z

Γ

k x

ky

W

VΣS 1

3X

Λ

∆

KM

Q

1X

U

XS

Im3m

k

k

x

y

zk z

HGNΣΓ ∆

DΛF

P

F1

RN1

3H

F2

Pm3m

zk z

Γ

Λ

k y∆

Z

k x

X

M

Σ

R

T

S

3X


http://www.cryst.ehu.es

http://www.cryst.ehu.es/cgi-bin/cryst/programs/nph-kv-list?gnum=225




Band diagrams and electronic density of states

InN: a direct gap semiconductor



Crystal geometry

a

c

bα

γβ

Cell parameters: (a, b, c, α, β, γ).

Cell vectors matrix: h = (a, b, c)T .

Cell volume: V = a · (b× c) = b · (c× a) = c · (a× b).

Crystallographic coordinates: ri = hT xi = xia + yib + zic.

{x, y, x} ∈ [0, 1) (main cell).

Metric tensor: G = hT h.

Scalar product: ~x ·~y = xT Gy.



CaF2, fluorite type structure (C1)

Cubic, Fm3m (225), a = 5.4626 Å,Z = 4.

Ca 4a (0, 0, 0)F 8c (1/4, 1/4, 1/4)

From the International Tables ofCrystalography:

Wyckoff Sim. Equiv. positions4a m3m (0, 0, 0)8c 43m (1/4, 1/4, 1/4), (1/4, 1/4, 3/4)

Centering vectors(0, 0, 0), (1/2, 1/2, 0), (1/2, 0, 1/2), (0, 1/2, 1/2)

Simple tasks: Cell volume? Density?Neighbor distances? Atoms in the maincell? Cell plot?



Some simple crystal structures IGrouped by structure symbols.(More structures in http://som.web.cmu.edu/StructuresAppendix2.pdf)

A1 Cu, Cubic, a = 3.609 Å, Fm3m, Z = 4.fcc Cu (4a) (0, 0, 0).A2 Li, Cubic, a = 3.46 Å, Im3m, Z = 2.bcc Li (2a) (0, 0, 0).A3 Be, Hexag., a = 2.2860, c = 3.5843 Å, (hcp ideal: c/a =

√8/3 ≈ 1.63) P63/mmc, Z = 2.

Be (2c) (1/3, 2/3, 1/4).A4 C (diamond), Cubic, a = 3.5667 Å, Fd3m, Z = 8.

C (8a) (1/8, 1/8, 1/8).A9 C (graphite), Hexag., a = 2.456, c = 6.696 Å, P63/mmc, Z = 4.

C (2b) (0, 0, 1/4); C (2c) (1/3, 2/3, 1/4).

A1: Cu A2: Li A3: Be A4: diamond A9: graphiteVLC & AOR & DMC () Electronic structure of solids: quantum espresso ZCAM, Zaragoza 2014 20 / 104

http://dwb.unl.edu/Teacher/NSF/C06/C06Links/cst-www.nrl.navy.mil/lattice/index.html

http://som.web.cmu.edu/StructuresAppendix2.pdf

http://www.cryst.ehu.es/cgi-bin/cryst/programs/nph-wp-list?gnum=225



http://www.cryst.ehu.es/cgi-bin/cryst/programs/nph-wp-list?gnum=227&gor=2



Some simple crystal structures II

B1 NaCl, Cubic, a = 5.6402 Å, Fm3m, Z = 4.Na (4a) (0, 0, 0); Cl (4b) (1/2, 1/2, 1/2).

B2 CsCl, Cubic, a = 4.123 Å, Fm3m, Z = 1.Cs (1a) (0, 0, 0); Cl (1b) (1/2, 1/2, 1/2).

B3 β-ZnS (blend), Cubic, a = 5.4060 Å, F43m, Z = 4.Zn (4a) (0, 0, 0); S (4c) (1/4, 1/4, 1/4).

B4 ZnO (zincite, wurtzite), Hexag., a = 3.2495, c = 5.2069 Å, P63mc, Z = 1.Zn (2b) (1/3, 2/3, z ≈ 0); O (2b) (1/3, 2/3, z ≈ 0.345).

B1: NaCl B2: CsCl B3: ZnS (blend) B4: ZnO (wurtzite)

Plots made with tessel (http://azufre.quimica.uniovi.es/software.html)and POVRay (http://www.povray.org).






http://azufre.quimica.uniovi.es/software.html

http://azufre.quimica.uniovi.es/software.html

http://www.povray.org

http://www.povray.org


Crystal geometry

Molecular crystals are usuallyrepresented including all themolecules that have at least oneatom in the main cell and showingthe crystal cell.

urea



The crystallographic information file (cif)

# Crystallography Open Database (COD),# http://www.crystallography.net/#data_1011280_chemical_name_systematic ’Calcium chloride’_chemical_name_mineral ’Hydrophilite’_chemical_compound_source ’synthetic’_chemical_formula_structural ’Ca Cl2’_chemical_formula_sum ’Ca Cl2’_publ_section_title;Die Kristallstruktur von Calciumchlorid, Ca Cl2;loop__publ_author_name’van Bever, A K’’Nieuwenkamp, W’

_journal_name_full;Zeitschrift fuer Kristallographie, Kristallgeometrie,Kristallphysik, Kristallchemie (-144,1977);_journal_coden_ASTM ZEKGAX_journal_volume 90_journal_year 1935_journal_page_first 374_journal_page_last 376_cell_length_a 6.24_cell_length_b 6.43_cell_length_c 4.2_cell_angle_alpha 90_cell_angle_beta 90_cell_angle_gamma 90_cell_volume 168.5

_cell_formula_units_Z 2_exptl_crystal_density_meas 2.22_symmetry_space_group_name_H-M ’P n n m’_symmetry_Int_Tables_number 58_symmetry_cell_setting orthorhombicloop__symmetry_equiv_pos_as_xyz’x,y,z’’-x,-y,z’’1/2+x,1/2-y,1/2-z’’1/2-x,1/2+y,1/2-z’’-x,-y,-z’’x,y,-z’’1/2-x,1/2+y,1/2+z’’1/2+x,1/2-y,1/2+z’

loop__atom_type_symbol_atom_type_oxidation_numberCa2+ 2.000Cl1- -1.000

loop__atom_site_label_atom_site_type_symbol_atom_site_symmetry_multiplicity_atom_site_Wyckoff_symbol_atom_site_fract_x_atom_site_fract_y_atom_site_fract_z_atom_site_occupancy_atom_site_attached_hydrogens_atom_site_calc_flagCa1 Ca2+ 2 a 0. 0. 0. 1. 0 dCl1 Cl1- 4 g 0.275(8) 0.325(8) 0. 1. 0 d

_cod_database_code 1011280



The protein databank file (PDB)

HEADER DE NOVO PROTEIN 19-AUG-03 1Q7OTITLE DETERMINATION OF F-MLF-OH PEPTIDE STRUCTURETITLE 2WITH SOLID- STATE MAGIC-ANGLE SPINNING NMRTITLE 3SPECTROSCOPY...DBREF 1Q7O A 1 3 PDB 1Q7O 1Q7O 1 3SEQRES 1 A 3 FME LEU MTY...CRYST1 1.000 1.000 1.000 90.00 90.00 90.00 P 1 1ORIGX1 1.000000 0.000000 0.000000 0.00000ORIGX2 0.000000 1.000000 0.000000 0.00000ORIGX3 0.000000 0.000000 1.000000 0.00000SCALE1 1.000000 0.000000 0.000000 0.00000SCALE2 0.000000 1.000000 0.000000 0.00000SCALE3 0.000000 0.000000 1.000000 0.00000MODEL 1HETATM 1 N FME A 1 -2.621 -3.439 0.640 1.00 0.00 NHETATM 2 CN FME A 1 -2.629 -4.738 0.349 1.00 0.00 CHETATM 3 O1 FME A 1 -1.977 -5.224 -0.578 1.00 0.00 O...HETATM 19 HE3 FME A 1 -3.705 -0.383 -4.831 1.00 0.00 HATOM 20 N LEU A 2 -0.242 -0.725 0.342 1.00 0.00 NATOM 21 CA LEU A 2 0.288 0.451 0.987 1.00 0.00 CATOM 22 C LEU A 2 -0.272 1.663 0.264 1.00 0.00 C...ATOM 38 HD23 LEU A 2 1.007 -1.229 3.026 1.00 0.00 HHETATM 39 N MTY A 3 -0.268 1.582 -1.067 1.00 0.00 NHETATM 40 CA MTY A 3 -0.778 2.668 -1.896 1.00 0.00 C...HETATM 58 HZ MTY A 3 5.192 2.389 -3.177 1.00 0.00 HTER 59 MTY A 3ENDMDL...CONECT 1 2 4 11CONECT 2 1 3CONECT 3 2...END



Crystal Data Bases I

Cambridge Structural Database (CSD) (http://www.ccdc.cam.ac.uk/products/csd/): The mainsource of crystal structures for organic and organometallic compounds. Commercial, access by subscription.596810 structures as of 2012-01-01.Inorganic Crystal Structure Database (ICSD) (http://www.fiz-karlsruhe.de/icsd.html?&L=0):

Natural and synthetic inorganic compounds. Commercial, access by subscription. 142179 entries (nov 2011).See a fully functional subset at http://icsd.ill.fr/icsd/ (3592 samples).CRYSTMET (http://www.tothcanada.com/databases.htm): Metals, including alloys, intermetallics

and minerals. Commercial, access by subscription. 139058 entries (Dec 1, 2010).American Mineralogist Crystal Structure Database (AMCSD)

(http://rruff.geo.arizona.edu/AMS/amcsd.php): Minerals. Free access (financed by NSF). 3156different minerals (many more entries, as a mineral may appear at different pressures and temperatures).Reciprocal Net (http://www.reciprocalnet.org/): Small but well choosen set of quite common

molecules and materials. Data from CSD and other sources. Free access (financed by NSF).Protein Data Bank (PDB) (http://www.rcsb.org/pdb/): Structures of large biological molecules,

including proteins and nucleic acids. Free access (international support). 78992 structures (Jan 31, 2012).Indispensable portal for anyone working on biomolecules.Crystallography Open Database (COD) (http://www.crystallography.net/): Voluntary effort to

provide an open alternative to CSD and ICSD. Absolutely free access. 158240 entries (feb 2, 2012) and growingfast. A sister PCOD database specializes on theoretically predicted structures (>1000000 in Nov 2009).Structural Classification of Proteins (SCOP) (http://scop.mrc-lmb.cam.ac.uk/scop/): Further

analysis of the proteins contained in PDB: folds, superfamilies, evolutionary relationship, etc. Free access.


http://www.ccdc.cam.ac.uk/products/csd/

http://www.ccdc.cam.ac.uk/products/csd/

http://www.fiz-karlsruhe.de/icsd.html?&L=0

http://www.fiz-karlsruhe.de/icsd.html?&L=0

http://icsd.ill.fr/icsd/

http://www.tothcanada.com/databases.htm

http://www.tothcanada.com/databases.htm

http://rruff.geo.arizona.edu/AMS/amcsd.php

http://rruff.geo.arizona.edu/AMS/amcsd.php

http://www.reciprocalnet.org/

http://www.reciprocalnet.org/

http://www.rcsb.org/pdb/

http://www.rcsb.org/pdb/

http://www.crystallography.net/

http://www.crystallography.net/

http://scop.mrc-lmb.cam.ac.uk/scop/

http://scop.mrc-lmb.cam.ac.uk/scop/


Crystal Data Bases II

Nucleic Acids Data Bank (NADB) (http://ndbserver.rutgers.edu/): Similar to PDB, but specializedon oligonucleotides. Free access (international support). 3745 structures (2008-01-17).Mineralogy Database (http://webmineral.com/): Good database on minerals and gems maintained by

commercial dealers. Free access.Crystal Lattice Structures (http://cst-www.nrl.navy.mil/lattice/): Very good description of the

common crystal lattice structures of the elements and simple compounds. Free access.Powder diffraction file (PDF) (http://www.icdd.com/): Largest DB on single phase powder diffraction

pattern. Widely used to identify compounds based on their fingerprint spectra. Commercial.Database of Macromolecular Movements (http://molmovdb.mbb.yale.edu/molmovdb/): Analysis

and prediction of the dynamical behaviour of macromolecules. Movies, morphings, etc. Free access.Do you know any other good structures database? Please, e-mail me the address and details(mailto:[email protected])


http://ndbserver.rutgers.edu/

http://ndbserver.rutgers.edu/

http://webmineral.com/

http://webmineral.com/

http://cst-www.nrl.navy.mil/lattice/

http://cst-www.nrl.navy.mil/lattice/

http://www.icdd.com/

http://www.icdd.com/

http://molmovdb.mbb.yale.edu/molmovdb/

http://molmovdb.mbb.yale.edu/molmovdb/

mailto:[email protected]

mailto:[email protected]

Part II

Examples of Quantum Espresso calculations (2014)


Quantum Espresso: pw+ps GNU code

opEn Source Package for Research in Electronic Structure, Simulation, andOptimization

PWSCF, CP, PHONON, FPMD, Wannier, ...Suite of codes for DFT electronic structure calculations and materials modeling. Basedon the use of plane waves and pseudopotentials (both, norm-conserving and ultrasoft).

http://www.quantum-espresso.org/

Installation from source is simple:

1 cd2 mkdir -p src/qe/3 cd src/qe/4 wget http://qe-forge.org/frs/download.php/211/espresso-5.0.tar.gz5 cd espresso-5.06 ./configure # f i n d s compi lers , l i b r a r i e s , and creates "make . sys "7 ./make all # creates executables i n ~/ src / qe / espresso−5.0/ b in /8 cat << EOF >> ~/.bashrc9 export QE_HOME=~/pkgs/qe/espresso-5.0/

10 export PATH=${PATH}:${QE_HOME}bin:11 EOF12 source ~/.bashrc



Using QE in zcam2014:

1 . /home/apps/zcam2014/environ.zcam2014 # Create the environment2 pw < input_file > output # Run quantum espresso

See in /.bashrc how the environ.zcam2014 is automatically run and the pw is really analias to the real executable code.

QE webpage (Documentation, pseudopotentials, ....)http://www.quantum-espresso.org/

In the VCL directory you will see a set of input and output examples. For instance:

1 $ cd2 $ ls VLC3 $ mkdir mydir4 $ cp -r VLC/* mydir5 $ cd mydir/si



pwSCF: Input scheme (pw.x < input > output) I

Input structured into mandatory and optional "&NAMELISTS" and "INPUT_CARDS".Each namelist contains a number of control variables, most of them with appropriatedefault values, but a few are essential and must always be specified. Full description:"INPUT_PW.txt"

&CONTROL: declare addresses and names for pseudopotentials, and other datafiles,select the amount of I/O (input/output), etc. Important variables: calculation (task to be performed: ’scf’, ’nscf’, ’bands’, ’relax’, ’md’, ’vc-relax’,’vc-md’).

&SYSTEM: describe the system to be calculated. Enforced variables: ibrav (0–14,Bravais-lattice index). celldm (cell parameters required by the crystalline system);nat (number of atoms in the unit cell); ntyp (number of atomic types); ecutwfc(kinetic energy cutoff).

&ELECTRONS: control the SCF process and the algorithm to be used. The most im-portant variable is diagonalization, the main options being Davidson iterative(’david’) and conjugate gradient like (’cg’).

&IONS: needed when atoms move (structural relaxation and molecular dynamicsruns) and ignored otherwise.


pwSCF: Input scheme (pw.x < input > output) II

&CELL: needed when the cell moves (structural relaxation and variable sell MDruns) and ignored otherwise.

&PHONON: prepare input for a PHONON task.


Each input card, on the other hand, corresponds to some vector or matrix.

ATOMIC_SPECIES:<atom> <mass> <pseudopotential> for every different atomic species.

ATOMIC_POSITIONS:<atom> <x> <y> <z> for every different atomic position.

K_POINTS:<number-of-k-points><x> <y> <z> <multiplicity>The k-points can correspond to the integration of iBZ1 or to special points used fordepicting band structure.

CELL_PARAMETERS:

OCCUPATIONS:

CLIMBING_IMAGES: special data for the NEB (nudge elastic band) algorithm.

CONSTRAINTS:


pwSCF: Control of the input structure

There are several methods to introduce the crystal structure in pwscf. They are controlled byibrav, celldm, nat, and the CELL_PARAMETERS input card.

ibrav 0 1 2 3 4 5cell free cP (sc) cF (fcc) cI (bcc) hP hR(1)celldm (1) a (1) a (1) a (1) a (1) a (1) a

(3) c/a (4) C = cosαv1 a(1, 0, 0) a(−1, 0, 1)/2 a(1, 1, 1)/2 a(1, 0, 0) a(tx,−ty, tz)v2 a(0, 1, 0) a(0, 1, 1)/2 a(−1, 1, 1)/2 a(−1/2,

√3/2, 0) a(0, 2ty, tz)

v3 a(0, 0, 1) a(−1, 1, 0)/2 a(−1,−1, 1)/2 a(0, 0, c/a) a(−tx,−ty, tz)

• Cell: shows the crystalline system ([c]ubic, [t]etragonal, [o]rthorhombic, [h]exagonal orrhombohedric with hexagonal axes, [m]onoclinic, or [a]=triclininc) and the (P,I,F,A,B,C,R)centering.• hR: the threefold axis is either (1) c, or (2) the < 111 > direction.• hR: tx =

√(1− C)/2; ty =

√(1− C)/6; tz =

√(1 + 2C)/3; u = tz− 2

√2ty; v = tz +

√2ty.

The v1..v3 vectors, except for the a scale, form the R matrix that can be declared in theCELL_PARAMETERS input card.


ibrav -5 6 7 8 9 10cell hR(2) tP (st) tI (bct) oP (so) oC (bco) oF (fco)celldm (1) a (1) a (1) a (1) a (1) a (1) a

(4) C = cosα (3) c/a (3) c/a (2) b/a (2) b/a (2) b/a(3) c/a (3) c/a (3) c/a

v1 a(u, v, v)/√

3 (a, 0, 0) a(1,−1, c/a)/2 (a, 0, 0) (a, b, 0)/2 (a, 0, c)/2v2 a(v, u, v)/

√3 (0, a, 0) a(1, 1, c/a)/2 (0, b, 0) (−a, b, 0)/2 (a, b, 0)/2

v3 a(v, v, u)/√

3 (0, 0, c) a(−1,−1, c/a)/2 (0, 0, c) (0, 0, c) (0, b, c)/2

ibrav 11 12 -12 13 14cell oI (bco) mP(c) (sm-c) mP(b) (sm-b) mC aP (tric)celldm (1) a (1) a (1) a (1) a (1) a

(2) b/a (2) b/a (2) b/a (2) b/a (2) b/a(3) c/a (3) c/a (3) c/a (3) c/a (3) c/a

(4) cos γ (5) cosβ (4) cos γ (4) cosα(5) cosβ(6) cos γ

v1 (a, b, c)/2 (a, 0, 0) (a, 0, 0) (a, 0,−c)/2 (a, 0, 0)v2 (−a, b, c)/2 (b cos γ, b sin γ, 0) (0, b, 0) b(cos γ, sin γ, 0) b(cos γ, sin γ, 0)v3 (−a,−b, c)/2 (0, 0, c) (a sinβ, 0, c cosβ) (a, 0, c)/2 c(cosβ,H1,H2)

H1 = (cosα− cosβ cos γ)/ sin γ;H2 = (1 + 2 cosα cosβ cos γ − cos2 α− cos2 β − cos2 γ)1/2/ sin γ.VLC & AOR & DMC () Electronic structure of solids: quantum espresso ZCAM, Zaragoza 2014 34 / 104

Finding information in the Quantum Espresso output

The QE output is huge, like it happens with most computational science codes growthin long periods of time. Using tools like grep or scripting tools (awk, perl, python,...) is imprescindible. In this table you will find a most useful information for it:

keyword pos variable unitlattice parameter 5 a bohr! 5 E Rydbergunit-cell volume 4 a bohr3


Electronic structure textbooks Bib

Part V

Electronic structure textbooks



Electronic structure textbooks

R. M. Martin, "Electronic Structure: Basic theory and practical meth-ods" (Cambridge, 2004).L. N. Kantorovich, "Quantum Theory of the Solid State: An Introduc-tion" (Kluwer, 2004).E. Kaxiras, "Atomic and Electronic Structure of Solids" (Cambridge,2003).M. Marder, "Condensed Matter Physics" (Wiley-Interscience, 2000).



References I

[1] A. D. Becke, E. R. Johnson, Exchange-hole dipole moment and the dispersion interaction, J. Chem. Phys122 (2005) 154104.

[2] A. Otero-de-la Roza, E. R. Johnson, van der waals ineractions in solids using the exchange-hole dipolemoment, J. Chem. Phys 136 (2012) 174109.

[3] A. Otero-de-la Roza, E. R. Johnson, A benchmark for non-covalent interactions in solids, J. Chem. Phys137 (2012) 054103.

[4] A. Otero-de-la Roza, E. R. Johnson, V. Luaña, Critic2: a program for real-space analysis of quantum chem-ical interactions in solids, Comput. Phys. Commun. 182 (2013) 2232–2248.

[5] A. Otero-de-la Roza, V. Luaña, GIBBS2: A new version of the quasi-harmonic model code. I. Robust treat-ment of the static data, Comput. Phys. Commun. 182 (2011) 1708–1720, source code distributed by theCPC program library: URL:http://cpc.cs.qub.ac.uk/summaries/AEIY_v1_0.html.

[6] M. A. Hopcroft, W. D. Nix, T. W. Kenny, What is the young’s modulus of silicon?, IEEE J. Microelectrome-chanical Systems 19 (2010) 229–238.

[7] S. Bhagavantam, Crystal symmetry and physical properties, Academic, New York, 1966.

[8] J. F. Nye, Physical Properties of Crystals, Oxford UP, Oxford, UK, 1985, republication of the 1957 classic.

[9] M. Catti, Calculation of elastic constants by the method of crystal static deformation, Acta Cryst. A 41 (1985)494–500.

[10] M. Catti, Crystal elasticity and inner strain: A computational model, Acta Cryst. A 45 (1989) 20–25.


URL:http://cpc.cs.qub.ac.uk/summaries/AEIY_v1_0.html

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