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Journal ArticleDOI

Work function anisotropy and surface stability of half-metallic CrO(2)

04 Apr 2008-Physical Review B (AMER PHYSICAL SOC)-Vol. 77, Iss: 16, pp 165109-165109

AbstractInsight in the interplay between work function and stability is important for many areas of physics. In this paper, we calculate the anisotropy in the work function and the surface stability of $\mathrm{Cr}{\mathrm{O}}_{2}$, a prototype half-metal, and find an anisotropy of $3.8\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. An earlier model for the relation between work function and surface stability is generalized to include the transition-metal oxides. We find that the lowest work function is obtained for surfaces with the most electropositive element, whereas the stable surfaces are those containing the element with the lowest valency. Most $\mathrm{Cr}{\mathrm{O}}_{2}$ surfaces considered remain half-metallic, thus the anisotropy in the work function can be used to realize low resistance, half-metallic interfaces.

Summary (2 min read)

Introduction

  • The authors calculate the anisotropy in the work function and the surface stability of CrO2, a prototype halfmetal, and find an anisotropy of 3.8 eV.
  • The authors find that the lowest work function is obtained for surfaces with the most electropositive element, whereas the stable surfaces are those containing the element with the lowest valency.
  • Electron injection is also important for spin injection, i.e., spintronics.

II. COMPUTATIONAL METHOD

  • The calculations were carried out using density functional theory with the PW91 generalized gradient approximation functional.
  • 12,13 We employed projector augmented plane waves14,15 as implemented in the Vienna ab initio simulation package VASP .16–18the authors.the authors.
  • The kinetic energy cutoff was set to 400 eV.
  • The work functions and surface stabilities were calculated using a supercell approach.
  • The surfaces at both sides of the slab were taken identical; therefore, some slabs are nonstoichiometric.

III. BULK CrO2

  • The half-metallic character of CrO2 and several CrO2 surfaces 100 and 110 has been shown using spin-resolved photoemission,20,21 x-ray absorption,22,23 optical spectroscopy,24 and point contact Andreev reflection.
  • The half-metallic property of CrO2 is mainly caused by its chemical composition, i.e., the chromium valency, rather than the crystal structure.
  • 27,28 Special attention has been given to the importance of correlation effects.
  • 29,30 Because the authors are interested in structural optimizations and work functions, i.e., electrostatics, local density approximation LDA is adequate.
  • As the chromium atoms have an octahedral coordination, its d band splits into a threefold degenerate t2g band and a doubly degenerate eg band.

IV. SURFACES OF CrO2

  • For NiMnSb, the first discovered and, consequently, the most extensively studied half-metal, surfaces and interfaces are generally not half-metallic.31.
  • This symmetry is destroyed at the interface and, therefore, the halfmetallic character is lost; only with careful engineering can half-metallic interfaces be constructed.
  • Indeed, earlier calculations for the 001 surface showed that the half-metallic character was maintained.
  • The authors will first describe in detail the calculated surfaces, both before and after structural relaxation, and they will compare with the literature where available.
  • At the end of the section, general conclusions will be presented.

A. (100) surfaces

  • Three different 100 surfaces can be constructed:.
  • One surface containing a chromium atom 100 Cr , one surface terminating with a single oxygen layer 100 O , and one surface terminating with two oxygen layers 100 OO see Fig. 4 .
  • It has only three oxygen neighbors and, after relaxation, the nearest neighbor distance is 1.80 Å on average.
  • The relaxed structure agrees with the calculations reported by Hong and Che33 Upon relaxation of the 100 O surface, chromium atoms in the second layer shift −0.10 Å along 010 .

C. (110) surfaces

  • In the 110 direction, there are again three different terminations.
  • The oxygen atoms in the first layer move 0.51 Å outward.
  • In the 011 OO surface, the first layer oxygens have only one chromium neighbor.

F. Conclusions

  • The relaxations described in the previous sections have been summarized in Table I, and the authors can draw the following conclusions.
  • The variation in work function is very large 3.8 eV for the relaxed surfaces .
  • Both the chromium and the double oxygen surfaces are very unstable initially and are significantly stabilized by relaxation.
  • The surface energies for the 100 surfaces depicted in Fig. 12 show quite a different situation.
  • With the same reasoning, the single oxygen terminated surfaces are more stable than the double oxygen terminated surfaces.

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University of Groningen
Work function anisotropy and surface stability of half-metallic CrO(2)
Attema, J. J.; Uijttewaal, M. A.; de Wijs, G. A.; de Groot, R. A.
Published in:
Physical Review. B: Condensed Matter and Materials Physics
DOI:
10.1103/PhysRevB.77.165109
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Publication date:
2008
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
Attema, J. J., Uijttewaal, M. A., de Wijs, G. A., & de Groot, R. A. (2008). Work function anisotropy and
surface stability of half-metallic CrO(2).
Physical Review. B: Condensed Matter and Materials Physics
,
77
(16), [165109]. https://doi.org/10.1103/PhysRevB.77.165109
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Work function anisotropy and surface stability of half-metallic CrO
2
J. J. Attema,
1
M. A. Uijttewaal,
1,
*
G. A. de Wijs,
1
and R. A. de Groot
1,2,
1
ESM, IMM, Radboud University, Toernooiveld 1, 6525ED Nijmegen, The Netherlands
2
Zernike Institute for Advanced Materials, Nijenborgh 6, 9747AG Groningen, The Netherlands
Received 8 October 2007; revised manuscript received 20 February 2008; published 4 April 2008
Insight in the interplay between work function and stability is important for many areas of physics. In this
paper, we calculate the anisotropy in the work function and the surface stability of CrO
2
, a prototype half-
metal, and find an anisotropy of 3.8 eV. An earlier model for the relation between work function and surface
stability is generalized to include the transition-metal oxides. We find that the lowest work function is obtained
for surfaces with the most electropositive element, whereas the stable surfaces are those containing the element
with the lowest valency. Most CrO
2
surfaces considered remain half-metallic, thus the anisotropy in the work
function can be used to realize low resistance, half-metallic interfaces.
DOI: 10.1103/PhysRevB.77.165109 PACS numbers: 73.30.y, 75.30.Gw, 72.25.Mk, 73.20.At
I. INTRODUCTION
Electron-emitting materials are applied in many estab-
lished areas of technology, for example, vacuum electronic
devices such as cathode-ray tubes, microwave devices, and
free electron lasers. They are also of interest in emerging
technologies such as organic light emitting diodes and spin-
tronics, which can benefit from an understanding of the work
function.
An important aspect of the electron-emitting properties of
the cathode material is the work function. The lifetime of the
device is related to the surface stability and the applied volt-
age. This often implies that cathodes need to have both a low
work function and a high surface stability. At first, these
requirements appear to be incompatible: A low work func-
tion means loosely bound electrons, implying a less stable
surface. This reasoning holds for the elements. For instance,
cesium has a low work function 2.14 eV but it is highly
reactive, whereas gold is stable but has a high work function
5.1 eV.
1
Experimental results for alloys suggest the alloy
effect: The work function and surface stability interpolate
between those of the constituting elements.
2
However, recent
theoretical work has shown a different picture for intermetal-
lic compounds. If a compound allows the formation of a
surface of nonstoichiometric composition and charge transfer
occurs, surfaces with a resulting surface dipole are possible.
This surface dipole, depending on its orientation, raises or
lowers the work function. The work function may be lowered
to even below the work functions of the constituting ele-
ments. This was first demonstrated in a computational study
for BaAl
4
.
3
The barium terminated 001 surface has a work
function of 1.95 eV, which is lower than that of elemental
barium 2.32 eV. It is even lower than that of any element,
which is clearly in contradiction with the alloy effect. It is
important to notice that the work function for polar com-
pounds, i.e., compounds containing atoms with different
electronegativities, is expected to show a large anisotropy, as
the surface dipole depends on surface orientation. For BaAl
4
and similar compounds, the surface with the lowest work
function was calculated to be the most stable as well. This
was explained by the lower electronegativity of barium.
4,5
The following model was formulated: For an intermetallic
compound with polar surfaces, the difference in electronega-
tivity determines the work function, and the most stable sur-
face has the lowest work function.
Electron injection is also important for spin injection, i.e.,
spintronics. Spintronics aims to integrate the control of spin
degrees of freedom with the conventional charge based elec-
tronics. For spin injection, a source of spin polarized elec-
trons is needed. Materials considered for spin injection are
half-metals, as they intrinsically have 100% spin polariza-
tion. Work on spin injection further focuses on obtaining a
spin polarization as high as possible at surfaces and
interfaces.
6,7
Recently, the importance of electrical band en-
gineering for spin injection has become apparent.
8,9
Ideally,
the states carrying the current on either side of the interface
are aligned. However, in practice, there is a difference in
chemical potential see Fig. 1. This difference in potential
causes a barrier at the interface and reduces the electrical
efficiency of the spin injection. Although an interface is more
complex than two surfaces, some properties of the two indi-
vidual surfaces carry over to the interface. In a first approxi-
mation, the height of the interface barrier is related to the
work function of the two separate surfaces.
10
For a given
half-metal/semiconductor interface, the anisotropy in work
FIG. 1. A schematic drawing of the energy levels of an electron
injector/semiconductor interface. Filled and empty states are shaded
dark and light gray, respectively. The work function of the injector
is the difference between the chemical potential in the bulk and
the vacuum potential. A mismatch in the chemical potential of the
injector and conduction band of the semiconductor results in a po-
tential barrier at the interface V.
PHYSICAL REVIEW B 77, 165109 2008
1098-0121/2008/7716/1651099 ©2008 The American Physical Society165109-1

function can be used to minimize the potential barrier.
We will extend the applicability of the model and include
materials that are of interest for spintronic applications:
transition-metal oxides. In this paper, we investigate the an-
isotropy in the work function and the surface stability of
ferromagnetic CrO
2
. CrO
2
is widely studied; it is a half-
metal in calculations and it has experimentally shown a very
high spin polarization.
11
The main difference between inter-
metallics and transition-metal oxides is in the combination of
electronegativity and valency. For intermetallic compounds,
the most electropositive atom also has the lowest valency,
resulting in stable, low work function surfaces. For
transition-metal oxides, the situation is reversed: The lowest
valency occurs almost always for the most electronegative
atom, in this case oxygen. Another difference between
transition-metal oxides and the previously studied com-
pounds is the occurrence of magnetism. They will provide a
challenging test for the model.
This paper is organized as follows. First, we describe the
computational method. Then results on bulk CrO
2
are briefly
discussed. Results on the structural relaxation are presented,
followed by the work functions and surface stabilities, and
an outlook.
II. COMPUTATIONAL METHOD
The calculations were carried out using density functional
theory with the PW91 generalized gradient approximation
functional.
12,13
We employed projector augmented plane
waves
14,15
as implemented in the Vienna ab initio simulation
package VASP.
1618
The kinetic energy cutoff was set to
400 eV. The Brillouin zone was sampled with a Monkhorst–
Pack mesh with a 668 grid for bulk CrO
2
,168 for
the 100 surfaces, 148 for the 110 surfaces, and 7
71 for the 001 and 011 surfaces. The work functions
and surface stabilities were calculated using a supercell ap-
proach. The supercell contained slabs with thicknesses of six
bulk unit cells for 001, 100, and 011, and eight bulk unit
cells for 110, and at least 10 Å of vacuum. We used a
minimal unit cell in the directions parallel to the surface.
Surface reconstructions involving more than one unit cell or
the formation of a Cr
2
O
3
surface was not considered. The
surfaces at both sides of the slab were taken identical; there-
fore, some slabs are nonstoichiometric. During relaxation,
the central region of the slab was held fixed to obtain faster
convergence.
III. BULK CrO
2
Experimentally, CrO
2
is a ferromagnet with a Curie tem-
perature of 386 K.
19
The half-metallic character of CrO
2
and
several CrO
2
surfaces 100 and 110 has been shown using
spin-resolved photoemission,
20,21
x-ray absorption,
22,23
opti-
cal spectroscopy,
24
and point contact Andreev reflection.
25
Earlier photoemission measurements found a small intensity
near E
F
only, but this was probably due to surface disorder or
the formation of Cr
2
O
3
at the surface.
20
Basically, CrO
2
is an ionic compound containing Cr
4+
and
O
2−
. It has a magnetic moment of 2
B
/ f.u., located almost
entirely on the chromium atoms. The half-metallic property
of CrO
2
is mainly caused by its chemical composition, i.e.,
the chromium valency, rather than the crystal structure. CrO
2
is a strong magnet, the chromium magnetic moment does not
depend on the size of the exchange splitting, as can be seen
from the density of states in Fig. 3.
The crystal structure of CrO
2
is depicted in Fig. 2.It
crystallizes in the rutile structure, space group P4
2
/ mnm
No. 136, with experimental lattice parameters a
=4.4218 Å and c =2.9182 Å. The chromium is at position
2a, oxygen is at position 4f with parameter x =0.301.
26
The
chromium atoms are almost perfectly octahedrally sur-
rounded by oxygen atoms, with Cr-O distances of 1.90 and
1.89 Å; each oxygen atom has three chromium neighbors.
The calculated electronic structure of bulk CrO
2
has been
extensively studied before.
27,28
Special attention has been
given to the importance of correlation effects.
29,30
Because
we are interested in structural optimizations and work func-
tions, i.e., electrostatics, local density approximation LDA
is adequate. In view of the comparison between LDA and
LDA+U and the experiment made in Ref. 29,wedonot
expect that the latter performs better for our purposes. After
relaxation of the lattice parameters and the positional param-
eter of the oxygen atoms, we found a =4.405 Å, c
=2.905 Å with the oxygen at position 4f, and x =0.303. The
calculated parameters agree with the experimental values
FIG. 2. Color online A CrO
2
unit cell. Oxygen atoms are large
blue, while chromium atoms are small white.
-4
-2
0
2
4
-6 -4 -2 0 2
states / unit cell eV
E-E
F
(eV)
FIG. 3. Calculated density of states for CrO
2
.
ATTEMA et al. PHYSICAL REVIEW B 77, 165109 2008
165109-2

within 0.5% and they will be used in this paper. For con-
venience, we show the calculated density of states in Fig. 3.
It shows the crystal field splitting of the chromium 4d band.
As the chromium atoms have an octahedral coordination, its
d band splits into a threefold degenerate t
2g
band and a dou-
bly degenerate e
g
band. The t
2g
band shows additional struc-
ture due to the deviation from perfect octahedral symmetry.
In the minority spin direction, the exchange interaction shifts
the chromium 4d band completely above the Fermi level and
opens a band gap.
IV. SURFACES OF CrO
2
Although bulk CrO
2
is a half-metal, it is not a priori clear
that surfaces of CrO
2
should be half-metallic. For NiMnSb,
the first discovered and, consequently, the most extensively
studied half-metal, surfaces and interfaces are generally not
half-metallic.
31
The half-metallic character of NiMnSb is a
consequence of the specific symmetry in the bulk. This sym-
metry is destroyed at the interface and, therefore, the half-
metallic character is lost; only with careful engineering can
half-metallic interfaces be constructed.
7
However, for CrO
2
,
surfaces will be half-metallic as long as the chromium va-
lency is conserved. Indeed, earlier calculations for the 001
surface showed that the half-metallic character was
maintained.
32,33
In this section, we will first describe in detail the calcu-
lated surfaces, both before and after structural relaxation, and
we will compare with the literature where available. At the
end of the section, general conclusions will be presented.
A. (100) surfaces
Three different 100 surfaces can be constructed: One
surface containing a chromium atom 100 Cr, one surface
terminating with a single oxygen layer 100 O, and one
surface terminating with two oxygen layers 100 OO兲共see
Fig. 4.
For the 100 Cr surface, the chromium in the first layer
shifts 0.11 Å inward. It has only three oxygen neighbors and,
after relaxation, the nearest neighbor distance is 1.80 Å on
average. The oxygen atoms move 0.28 and 0.15 Å along
010, and 0.61 and 0.24 Å outward for the second and fifth
layers. The third layer moves 0.13 Å outward. The relaxed
structure agrees with the calculations reported by Hong and
Che
33
Upon relaxation of the 100 O surface, chromium atoms
in the second layer shift −0.10 Å along 010. The second
and fifth layers also shift 0.10 Å outward. The oxygen atoms
shift 0.24 and 0.16 Å along 010, and 0.20 and 0.28 Å out-
ward for the first and third layers, respectively. Compared to
that of Hong and Che, the relaxation parallel to the surface is
similar, but our shift perpendicular to the surface is larger.
For the 100 OO surface, the first oxygen moves 0.18 Å
outward and the oxygens in the fourth layer move 0.14 Å
outward. The chromium atoms in the third layer move
0.41 Å outward and 0.15 Å along 010, while the chromium
atoms in the sixth layer move 0.14 Å outward. The oxygen
atom in the top layer has only one chromium neighbor and,
as a result, the Cr-O distance after relaxation is reduced to
1.59 Å.
B. (001) surface
In the 001 direction, only one termination is possible
see Fig. 5. The surface is stoichiometric, containing one Cr
and two O atoms. The oxygen atoms in the top layer have
(100 Cr) (100 O) (100 OO)
FIG. 4. Color online A view along 001 of the relaxed 100 surfaces. The top of the figure is the surface facing the vacuum, while the
bottom is toward the bulk. Oxygen atoms are large blue, while chromium atoms are small white.
(001)
FIG. 5. Color online A view along 100 of the relaxed 001
surface. The top of the figure is the surface facing the vacuum,
while the bottom is toward the bulk. Oxygen atoms are large blue,
while chromium atoms are small white.
WORK FUNCTION ANISOTROPY AND SURFACE PHYSICAL REVIEW B 77, 165109 2008
165109-3

lost one chromium neighbor, while the chromium has four
oxygen neighbors. After relaxation, the chromium atoms
move 0.15 Å inward and 0.23 Å outward for the first and
second layers, respectively. The oxygen atoms in the first
layer move 0.31 Å outward and 0.23 Å along 110 toward
the nearest chromium atom. The Cr-O distance for the sur-
face oxygens is 1.72 Å.
C. (110) surfaces
In the 110 direction, there are again three different ter-
minations. One containing two oxygen and two chromium
atoms 110 CrO, and two surfaces containing one oxygen
the 110 O and 110 OO surfaces兴共see Fig. 6.
After relaxation of the 110 CrO surface, the fivefold
surrounded chromium atom in the top layer moves 0.16 Å
outward, while the fourfold surrounded chromium atom
moves 0.05 Å inward. The oxygen atoms in the first layer
move 0.51 Å outward. The second and third oxygen layers
move 0.10 Å and 0.21 Å outward.
Adding another oxygen layer gives the 110 O surface.
Upon relaxation, the oxygen in the first layer moves 0.10 Å
outward. The oxygens in the second layer move 0.24 Å out-
ward. The second layer also contains two chromium atoms,
one with five oxygen neighbors and one with six neighbors.
The sixfold surrounded chromium moves 0.27 Å outward,
while the fivefold surrounded chromium moves slightly in-
ward. The third layer oxygen moves 0.13 Å outward.
Finally, the 110 OO surface is obtained by adding an-
other oxygen layer. All chromium atoms have a bulklike six-
fold coordination, but the first two oxygen layers have miss-
ing neighbors. The first layer oxygen atom has only one
neighboring chromium, while the second layer oxygen atoms
has two. The oxygens in the first layer relax 0.11 Å outward.
In the third layer, one chromium moves 0.41 Å outward,
reducing the distance with the first layer oxygen to 1.59 Å;
the other chromium moves 0.15 Å outward.
D. (011) surfaces
In the 011 direction see Fig. 7, CrO
2
consists of planes
containing either two oxygen or two chromium atoms. There
are three possible terminations: a chromium terminated sur-
face 011 Cr, one with a single oxygen layer 011 O, and
one with a double oxygen layer 011 OO.
For the 011 O, the relaxation has only a small effect.
The chromium atoms in the second layer only have five near-
est oxygen atoms; they relax slightly outward and move
0.16 Å along 100. The oxygens in the first layer are also
missing a neighbor; they move a little inward and 0.08 Å
along 100. The final Cr-O distance at the surface is 1.81 Å.
In the 011 OO surface, the first layer oxygens have only
one chromium neighbor. They move 0.23 Å along 011 and
0.07 Å inward, reducing the Cr-O distance to 1.59 Å. The
(110 CrO) (110 O) (110 OO)
FIG. 6. Color online A view along 001 of the relaxed 110 surfaces. The top of the figure is the surface facing the vacuum, while the
bottom is toward the bulk. Oxygen atoms are large blue, while chromium atoms are small white.
(011 Cr) (011 O) (011 OO)
FIG. 7. Color online A view along 100 of the relaxed 011 surfaces. The top of the figure is the surface facing the vacuum, while the
bottom is toward the bulk. Oxygen atoms are large blue, while chromium atoms are small white.
ATTEMA et al. PHYSICAL REVIEW B 77, 165109 2008
165109-4

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Journal ArticleDOI
TL;DR: An efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set is presented and the application of Pulay's DIIS method to the iterative diagonalization of large matrices will be discussed.
Abstract: We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order ${\mathit{N}}_{\mathrm{atoms}}^{3}$ operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special ``metric'' and a special ``preconditioning'' optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order ${\mathit{N}}_{\mathrm{atoms}}^{2}$ scaling is found for systems containing up to 1000 electrons. If we take into account that the number of k points can be decreased linearly with the system size, the overall scaling can approach ${\mathit{N}}_{\mathrm{atoms}}$. We have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable. \textcopyright{} 1996 The American Physical Society.

64,484 citations


Journal ArticleDOI
Peter E. Blöchl1
TL;DR: An approach for electronic structure calculations is described that generalizes both the pseudopotential method and the linear augmented-plane-wave (LAPW) method in a natural way and can be used to treat first-row and transition-metal elements with affordable effort and provides access to the full wave function.
Abstract: An approach for electronic structure calculations is described that generalizes both the pseudopotential method and the linear augmented-plane-wave (LAPW) method in a natural way. The method allows high-quality first-principles molecular-dynamics calculations to be performed using the original fictitious Lagrangian approach of Car and Parrinello. Like the LAPW method it can be used to treat first-row and transition-metal elements with affordable effort and provides access to the full wave function. The augmentation procedure is generalized in that partial-wave expansions are not determined by the value and the derivative of the envelope function at some muffin-tin radius, but rather by the overlap with localized projector functions. The pseudopotential approach based on generalized separable pseudopotentials can be regained by a simple approximation.

48,474 citations


Journal ArticleDOI
Abstract: The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Bl\"ochl's projector augmented wave (PAW) method is derived. It is shown that the total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addition, critical tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed core all electron methods. These tests include small molecules $({\mathrm{H}}_{2}{,\mathrm{}\mathrm{H}}_{2}{\mathrm{O},\mathrm{}\mathrm{Li}}_{2}{,\mathrm{}\mathrm{N}}_{2}{,\mathrm{}\mathrm{F}}_{2}{,\mathrm{}\mathrm{BF}}_{3}{,\mathrm{}\mathrm{SiF}}_{4})$ and several bulk systems (diamond, Si, V, Li, Ca, ${\mathrm{CaF}}_{2},$ Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.

46,297 citations


Journal ArticleDOI
Abstract: We present a detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set. We will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temperature density-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order Natoms2 scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge density including a new special ‘preconditioning’ optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. We have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio molecular-dynamics package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.

40,008 citations


Journal ArticleDOI
Abstract: We present ab initio quantum-mechanical molecular-dynamics calculations based on the calculation of the electronic ground state and of the Hellmann-Feynman forces in the local-density approximation at each molecular-dynamics step. This is possible using conjugate-gradient techniques for energy minimization, and predicting the wave functions for new ionic positions using subspace alignment. This approach avoids the instabilities inherent in quantum-mechanical molecular-dynamics calculations for metals based on the use of a fictitious Newtonian dynamics for the electronic degrees of freedom. This method gives perfect control of the adiabaticity and allows us to perform simulations over several picoseconds.

27,360 citations


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In this paper, the work function is defined as the difference between the Fermi level and the potential in the vacuum far from the surface.