Introduction to DFTB+
Martin Persson
Accelrys, Cambridge
•
DFTB
–
Why DFTB?
–
Basic theory DFTB
–
Performance
•
DFTB+ in Materials Studio
–
Energy, Geometry, Dynamics, Parameterization
–
Parameterization
•
Basic theory
•
Setting up a parameterization
Outline
Why DFTB+
•
DFT codes are good for small systems
•
Nano
structures and bio molecules are often too large
for DFT but their electronic properties are still of interest
–
hence quantum mechanical description is needed.
•
Classical force field based codes can handle large
systems but are missing the QM part
•
Empirical TB has been applied to systems up to a few
million atoms
–
No charge self consistency
–
Limited transferability
–
Using simplified energetic expressions
QM vs. CM
•
DFTB merges the reliability of DFT with the
computational efficiency of TB
–
Parameters are based on an atomic basis
–
The parameters can be made transferable
–
Charge self consistent
–
Describes both electronic as well as energetic
properties
–
Can handle thousands of atoms
This is where DFTB+ comes in
Examples of what can be done with DFTB+
Diamond nucleation
Novel
SiCN
ceramics
Si cluster growth
Magnetic Fe clusters
WS2
nanotubes
Basic DFTB Theory
•
DFTB
–
Pseudo atomic orbital basis
–
Non SCC Hamiltonian elements are parameterized
–
2
nd
order charge self consistent theory
–
Charges are treated as
Mulliken
charges
–
Short range potential is used to correct the
energetics
–
Hamiltonian matrix is sparse and can partly be
treated with O(N) methods
DFTB theory in short
•
Minimal basis set
•
Pseudo atomic
orbitals
–
Slater
orbitals
–
Spherical harmonics
DFTB basis set
v
v
v
v
v
m
l
n
m
l
r
n
l
n
v
r
r
e
r
a
r
,
,
,
Pseudo atomic
orbitals
S
P
1
P
2
P
3
D
5
D
4
D
3
D
2
D
1
Silicon sp
3
d
5
orbitals
For Silicon the d

orbitals
are un

occupied but needed to
properly model the conduction band.
Hamiltonian elements
otherwise
if
if
0
atom
free
0
B
A
V
V
T
H
B
B
A
A
•
Diagonal elements use
free
atom energies
•
Two centre integrals
•
Tabulated values
1.
Expand the Kohn

Sham total energy expression of DFT to 2
nd
order in
terms of electron and magnetization density fluctuations
2.
Represent the Hamiltonian elements in a minimal basis of pseudo

atomic
orbitals
3.
Express the charge density in terms of
Mulliken
charges
4.
Expand the magnetization density in terms of non

overlapping
spherically symmetric functions
5.
Replace the remaining terms with a short range repulsive energy
DFT
DFTB
N
xc
occ
i
i
i
i
tot
R
R
Z
Z
n
E
r
r
r
d
r
n
v
n
E
2
1
,
)
(
2
1
2
,
3
2
1.
Expand the Kohn

Sham total energy expression of DFT to 2
nd
order in
terms of electron and magnetization density fluctuations
2.
Represent the Hamiltonian elements in a minimal basis of pseudo

atomic
orbitals
3.
Express the charge density in terms of
Mulliken
charges
4.
Expand the magnetization density in terms of non

overlapping
spherically symmetric functions
5.
Replace the remaining terms with a short range repulsive energy
DFT
DFTB
r
rd
d
r
r
n
n
r
d
n
n
V
R
R
Z
Z
n
E
r
rd
d
E
r
rd
d
n
n
n
n
E
r
r
n
V
r
r
r
d
n
v
n
E
xc
N
xc
n
xc
n
xc
occ
i
i
xc
i
i
tot
3
3
0
0
3
0
0
0
3
3
0
,
2
3
3
0
,
2
,
0
3
2
2
1
0
,
2
1
0
,

2
1

1
2
1
0
,
2
1
2
0
0
n
n
n
0
0
1.
Expand the Kohn

Sham total energy expression of DFT to 2
nd
order in
terms of electron and magnetization density fluctuations
2.
Represent the Hamiltonian elements in a minimal basis of pseudo

atomic
orbitals
3.
Express the charge density in terms of
Mulliken
charges
4.
Expand the magnetization density in terms of non

overlapping
spherically symmetric functions
5.
Replace the remaining terms with a short range repulsive energy
DFT
DFTB
r
rd
d
r
r
n
n
r
d
n
n
V
R
R
Z
Z
n
E
W
p
p
q
q
H
c
c
n
E
xc
N
xc
N
l
l
l
l
l
l
occ
i
i
i
i
tot
3
3
0
0
3
0
0
0
,
0
2
1
0
,
2
1
0
,
2
1
2
1
1.
Expand the Kohn

Sham total energy expression of DFT to 2
nd
order in
terms of electron and magnetization density fluctuations
2.
Represent the Hamiltonian elements in a minimal basis of pseudo

atomic
orbitals
3.
Express the charge density in terms of
Mulliken
charges
4.
Expand the magnetization density in terms of non

overlapping
spherically symmetric functions
5.
Replace the remaining terms with a short range repulsive energy
DFT
DFTB
rep
N
l
l
l
l
l
l
occ
i
i
i
i
tot
E
W
p
p
q
q
H
c
c
n
E
2
1
2
1
,
0
DFTB+ Performance
Performance figures
N
2.9
N
1.5
•
10x10 CNT
•
32 atoms/
unitcell
•
Run on single core
•
Intel(R) Xeon(TM) CPU 3.00GHz
•
Small systems (<300 atoms) O(N) processes dominate
•
Large systems (>300) O(n)
eigenvalue
solver dominates
•
Around 100 times faster then normal DFT
DFTB+ in Materials Studio 6.0
•
First official release that includes the DFTB+
module
•
Supported tasks
–
Energy
–
Geometry optimization
–
Dynamics
–
Parameterization
•
Also support
–
Dispersion correction
–
Spin unrestricted calculations
DFTB+ in Materials Studio 6.0
•
Slater

Koster
libraries
instead of DFT
Functionals
–
CH, CHNO and
SiGeH
•
What if I don’t have the
needed library?
–
Download academic
libraries at
www.dftb.org
•
mio
, C

H

N

O

S

P
•
pbc
, Si

F

O

N

HFe
•
matsci
, various parameters
–
Make your own
Starting a DFTB+ job
•
Need to register to get access.
•
The downloaded parameters will
contain many different Slater
Koster
files
Downloading parameters
•
To be used in MS

DFTB+ the parameters need to be packed up in a .
skflib
format.
•
The .
skflib
file is just a tagged concatenation of the different files
•
[Begin section] [End section], surrounds list of all files
•
[Begin file <filename>] [End file <filename>], surrounds content of file.
•
Will prevent accidental mixing of files between libraries and makes handling
easier
•
Band structure
•
Density of states
•
Electron density
•
Fermi surface
•
Orbitals
•
Slater

Koster
parameters
•
Dynamics analysis is done
using the
Forcite
analysis
tools
DFTB+ Analysis
Materials Studio 6.0 Parameterization tool
•
DFTB+ depends on parameters
–
Hamiltonian and overlap integrals
–
Hubbard terms (orbital resolved)
–
Spin constants
–
Wave function coefficients
–
Short range repulsive potential
The DFTB+ Parameterization Tool
The DFTB+ parameterization tool enables you
to make your own parameterizations.
It calculates all of the needed parameters.
The result is packed up in a single file (.
skflib
)
Repulsive fitting
rep
N
l
l
l
l
l
l
occ
i
i
i
i
tot
E
W
p
p
q
q
H
c
c
n
E
2
1
2
1
,
0
pairs
j
i
ij
ij
type
tot
bare
DFTB
tot
DFT
rep
r
U
E
E
E
)
(
)
(
,
The remaining terms,
E
rep
, will be
described using fitted repulsive pair
potentials.
The pair potentials are fitted against a
basis of
cutoff
polynomials
otherwise
r
r
if
0
)
(
)
(
cutoff
n
cutoff
n
r
r
r
f
Pair potentials
•
Short range pair potentials are fitted against small molecules or
solids
•
Path generators
–
Stretch, Perturb, Scale, Trajectory
•
Fitting against Energy and optionally forces
•
Use of spin unrestricted calculations
•
Steps, weights and width are set under Details...
Systems
Bond order fitting
Use weight distributions to combine several
bond orders into a single potential fit
•
C

H.txt

Job summary
•
Best fit (C

H.skflib
)
returned in the base folder
•
Fits for alternative
cutoff
factors are returned in the
Alternatives folder
Parameterization job results
Evaluating the result
benzene

DMol3 C3

C2 = 1.39838 C3

H9 = 1.09097
DFTB+ C3

C2 = 1.41171 C3

H9 = 1.10386
Diff C3

C2 = 0.01333 C3

H9 = 0.01289
DMol3 C2

C7

C6 = 120.00000 H12

C7

C6 = 120.00000
DFTB+ C2

C7

C6 = 119.99783 H12

C7

C6 = 120.00930
Diff C2

C7

C6 =

0.00217 H12

C7

C6 = 0.00930
Atomization Diff =

111.42032
==============================================
ethene

DMol3 C2

C1 = 1.33543 C2

H5 = 1.09169
DFTB+ C2

C1 = 1.33114 C2

H5 = 1.09898
Diff C2

C1 =

0.00429 C2

H5 = 0.00729
DMol3 C1

C2

H6 = 121.65149 H4

C1

H3 = 116.69702
DFTB+ C1

C2

H6 = 121.55765 H4

C1

H3 = 116.88453
Diff C1

C2

H6 =

0.09384 H4

C1

H3 = 0.18751
Atomization Diff =

48.44673
==============================================
Bond Error Statistics:
C

C = 8.81072e

03
C

H = 1.00915e

02
=================
Total Average = 9.45112e

03
Angle Error Statistics:
HCH = 1.87511e

01
CCC = 2.16738e

03
HCC = 5.15662e

02
=================
Total Average = 7.32028e

02
1.
Initial evaluation against small set of
structures
2.
Final evaluation against larger set of
structures
3.
Validation against larger structures
Materials Studio supplies a MS Perl
script which compares geometry and
atomization energy for structures.
•
sp3d5 basis
•
LDA(PWC)
•
Fitted against
–
Si,
Ge
and
SiGe
solids
–
Si
2
H
6
, Si
2
H
4
–
Ge
2
H
6
, Ge
2
H
4
–
SiGeH
6
, SiGeH
4
–
SiH
4
, GeH
4
and H
2
•
Tested against:
–
Solids
–
Nanowires
–
Nanoclusters
–
Si vacancy
SiGeH
N
N
f
E
N
N
E
E
1
1
Si vacancy Formation energy
E
f
(
eV
)
DFTB+
2.6
DMol3
2.7
•
sp3 basis
•
GGA(PBE)
•
Tested against a large set
(~60) of organic molecules
•
Also, validated against a
smaller set of larger
molecules
•
Good diamond cell
parameter, 3.590 (3.544) Å
CHNO
Bond type
Average difference (Å)
C

C
0.0108
C

N
0.0131
C

O
0.0105
C

H
0.0081
N

N
0.0070
N

O
0.0123
N

H
0.0087
Average bond difference: 0.0096
Å
Average angle difference: 1.16
degrees
Accuracy is comparative to that of the
Mio library.
•
Successfully tested
for:
–
CNT
–
C
60
–
Caffeine
–
Glucose
–
Porphine
–
N

Acetylneuraminic
acid
CHNO: Larger molecules
Bond
Diff (
Å
)
C

C
0.0095
C

N
0.0075
C

O
0.0078
C

H
0.0028
Bond
Diff (
Å
)
C

C
0.005
Bond
Diff (
Å
)
C

C
0.0148
C

N
0.0118
C

O
0.0100
C

H
0.0114
N

H
0.0127
O

H
0.0019
CNT

6x6
Caffeine
N

AA
Thanks for your attention
Other contributors:
Paddy Bennett (Cambridge, Accelrys)
Bálint Aradi (Bremen, CCMS)
Zoltan
Bodrog
(Bremen, CCMS)
•
The Kohn

Sham equation is solved for a single
atom.
•
Using an added extra confining potential to
better model molecules and solids
Generating the orbitals
)
(
)
(
)
(
ˆ
2
0
r
r
r
r
r
V
T
at
eff
1.
Expand the Kohn

Sham total energy expression of DFT to 2
nd
order in
terms of electron and magnetization density fluctuations
2.
Represent the Hamiltonian elements in a minimal basis of pseudo

atomic
orbitals
3.
Express the charge density in terms of
Mulliken
charges
4.
Expand the magnetization density in terms of non

overlapping
spherically symmetric functions
5.
Replace the remaining terms with a short range repulsive energy
DFT
DFTB
N
xc
occ
i
i
i
i
tot
R
R
Z
Z
n
E
r
r
r
d
r
n
v
n
E
2
1
,
)
(
2
1
2
,
3
2
1.
Expand the Kohn

Sham total energy expression of DFT to 2
nd
order in
terms of electron and magnetization density fluctuations
2.
Represent the Hamiltonian elements in a minimal basis of pseudo

atomic
orbitals
3.
Express the charge density in terms of
Mulliken
charges
4.
Expand the magnetization density in terms of non

overlapping
spherically symmetric functions
5.
Replace the remaining terms with a short range repulsive energy
DFT
DFTB
r
rd
d
r
r
n
n
r
d
n
n
V
R
R
Z
Z
n
E
r
rd
d
E
r
rd
d
n
n
n
n
E
r
r
n
V
r
r
r
d
n
v
n
E
xc
N
xc
n
xc
n
xc
occ
i
i
xc
i
i
tot
3
3
0
0
3
0
0
0
3
3
0
,
2
3
3
0
,
2
,
0
3
2
2
1
0
,
2
1
0
,

2
1

1
2
1
0
,
2
1
2
0
0
n
n
n
0
0
r
rd
d
r
r
n
n
r
d
n
n
V
R
R
Z
Z
n
E
r
rd
d
E
r
rd
d
n
n
n
n
E
r
r
H
c
c
n
E
xc
N
xc
n
xc
n
xc
occ
i
i
i
i
tot
3
3
0
0
3
0
0
0
3
3
0
,
2
3
3
0
,
2
,
0
*
2
1
0
,
2
1
0
,

2
1

1
2
1
0
0
1.
Expand the Kohn

Sham total energy expression of DFT to 2
nd
order in
terms of electron and magnetization density fluctuations
2.
Represent the Hamiltonian elements in a minimal basis of pseudo

atomic
orbitals
3.
Express the charge density in terms of
Mulliken
charges
4.
Expand the magnetization density in terms of non

overlapping
spherically symmetric functions
5.
Replace the remaining terms with a short range repulsive energy
DFT
DFTB
i
i
H
H
0
0
ˆ
i
i
c
1.
Expand the Kohn

Sham total energy expression of DFT to 2
nd
order in
terms of electron and magnetization density fluctuations
2.
Represent the Hamiltonian elements in a minimal basis of pseudo

atomic
orbitals
3.
Express the charge density in terms of
Mulliken
charges
4.
Expand the magnetization density in terms of non

overlapping
spherically symmetric functions
5.
Replace the remaining terms with a short range repulsive energy
DFT
DFTB
r
r
r
r
n
n
r
n
n
V
R
R
Z
Z
n
E
r
r
E
q
q
H
c
c
n
E
xc
N
xc
n
xc
occ
i
i
i
i
tot
3
3
0
0
3
0
0
0
3
3
0
,
2
,
0
2
1
0
,
2
1
0
,

2
1
2
1
0
β
α
β
α
interacion
Coulomb
U
Hubbard
a
n
n
0
q
q
q
1.
Expand the Kohn

Sham total energy expression of DFT to 2
nd
order in
terms of electron and magnetization density fluctuations
2.
Represent the Hamiltonian elements in a minimal basis of pseudo

atomic
orbitals
3.
Express the charge density in terms of
Mulliken
charges
4.
Expand the magnetization density in terms of non

overlapping
spherically symmetric functions
5.
Replace the remaining terms with a short range repulsive energy
DFT
DFTB
r
rd
d
r
r
n
n
r
d
n
n
V
R
R
Z
Z
n
E
W
p
p
q
q
H
c
c
n
E
xc
N
xc
N
l
l
l
l
l
l
occ
i
i
i
i
tot
3
3
0
0
3
0
0
0
,
0
2
1
0
,
2
1
0
,
2
1
2
1
l
l
al
p
p
p
n
interactio
spin
l
l
W
1.
Expand the Kohn

Sham total energy expression of DFT to 2
nd
order in
terms of electron and magnetization density fluctuations
2.
Represent the Hamiltonian elements in a minimal basis of pseudo

atomic
orbitals
3.
Express the charge density in terms of
Mulliken
charges
4.
Expand the magnetization density in terms of non

overlapping
spherically symmetric functions
5.
Replace the remaining terms with a short range repulsive energy
DFT
DFTB
rep
N
l
l
l
l
l
l
occ
i
i
i
i
tot
E
W
p
p
q
q
H
c
c
n
E
2
1
2
1
,
0
•
Most of DFTB+ is running with O(N) routines
•
Two exceptions
–
DFTB+ SCC
•
Ewald

summation, O(N
2
)
–
DFTB+
eigenvalue
solvers
•
LAPACK solvers, O(N
3
)
•
Small systems (<300 atoms), the O(N) processes
dominate
•
Large systems (>300), the
eigenvalue
solver
dominates
Calculation time vs. structure size
Performance figures
N
2.9
N
1.5
•
10x10 CNT
•
32 atoms/
unitcell
•
Run on single core
•
Intel(R) Xeon(TM) CPU 3.00GHz
•
Small systems (<300 atoms) O(N) processes dominate
•
Large systems (>300)
eigenvalue
solver dominates
#
cpu
Speedup Efficiency
1
1.0
2
0.87
3
0.80
4
0.72
OpenMP
•
DFTB+ is significantly faster than a normal DFT code
•
Depending on what DFT code we compare to its a factor 10
2

10
3
faster
•
DFTB+ compared to DMol3 is a factor of 30

80 faster
DMol3 vs. DFTB+
Atoms
Time
DFTB
+
(s)
Time
DMol3
(s)
Time
DMol3
/
Time
DFTB
+
32
4
233
58
64
8
632
79
96
17
872
51
128
26
1092
42
160
46
1501
33
Starting a DFTB+ job: Setup
•
Available t
asks
•
Energy
•
Geometry optimization
•
Dynamics
•
Parameterization
•
Dispersion
correction
•
Spin
unrestricted
The parameterization dialogs are
accessed through the
More...
Button.
•
Select Slater

Koster
library
–
CH, CHNO and
SiGeH
–
Use Browse... to access local
library
•
What if I don’t have the
needed library?
–
Download academic libraries
at
www.dftb.org
•
mio
, C

H

N

O

S

P
•
pbc
, Si

F

O

N

HFe
•
matsci
, various parameters
–
Make your own
Starting a DFTB+ job: Electronic
•
Select any properties that
should be calculated
–
Band structure
–
DOS
–
Electron density
–
Orbitals
–
Population analysis
•
Properties will be calculated
at the end of the job
Starting a DFTB+ job: Properties
•
Select server or run on
local machine
•
DFTB+ support
OpenMP
but not MPI
•
On a cluster it will run
on the cores available to
it on the first node
•
Parameterization is
always run as a serial job
Starting a DFTB+ job: Job Control
•
The DFTB+ calculations are run by Materials
Studio as an energy server
•
Geometry optimization and Dynamics jobs are
controlled by the same code that is used during
a
Forcite
job
During a DFTB+ job
•
<>.
xsd
–
Final structure
•
<>.
xtd
(dynamics)
–
Dynamics trajectory
•
<>.txt
–
Compilation of the results
•
<>.
dftb
–
The last output from DFTB+
•
<>.
skflib
(parameterization)
–
Slater

Koster
library
DFTB+ Result files
•
*.tag
–
Final
output data
•
*.cube
–
Density and orbital
data
•
*.bands
–
Band structure data
Visible files
Hidden files
Zn compounds using DFTB+
•
Zn

X (X = H, C, N, O, S, Zn)
•
Can be downloaded at
www.DFTB.org
(znorg

0

1)
•
Reference systems during fitting
–
ZnH
2
, Zn(CH
3
)
2
, Zn(NH
3
)
2
, Zn(SH)
2
–
fcc

Zn,
zb

ZnO
•
Applied to:
–
Zinc solids, Zn,
ZnO
,
ZnS
–
Surfaces,
ZnO
–
Nanowires
and
Nanoribbons
,
ZnO
–
Small species interaction with
ZnO
surface (H, CO
2
and NH
3
)
–
Zn in biological systems
Working with Zn containing compounds
N. H.
Moreira
, J. Chem. Theory
Comput
.
2009
, 5 , 605
Zn Solids
Method
E
coh
a(
Å
)
b(
Å
)
B
0
(
GPa
)
w

ZnO
DFTB+
9.77
3.28
5.25
161
PBE
8.08
3.30
5.34
124
EXP
7.52
3.25
5.20
208
zb

ZnS
DFTB+
7.93
5.43

44.2
LDA
7.22
5.35

82
EXP
6.33
5.40

76.9
W

ZnO
DFTB+
W

ZnO
PBE
•
Reasonable solid state properties
N. H.
Moreira
, J. Chem. Theory
Comput
.
2009
, 5 , 605
ZnO
Surface stability
F.
Claeyssens
J. Mat. Chem.
2005
, 15 139
N. H.
Moreira
, J. Chem. Theory
Comput
.
2009
, 5 , 605
•
Predicts correct order and magnitude for the
cleavage energy
•
Bond and angle deviation ~1

2%
DFTB+
DFT
ZnO
nanowires
•
Good geometries and electronic structure
•
Excellent agreement with DFT results
•
Surface Zn atoms move inwards
N. H.
Moreira
, J. Chem. Theory
Comput
.
2009
, 5 , 605
CO
2
•
Bond difference 1

2%
•
Binding too strong
~0.5
eV
/CO
2
•
Turn over point for
monolayer well
described
NH
3
•
Overall good
agreement with
experiments and
DFT calculations
Small molecule surface interaction
ZnO
(10
1
0)

CO
2
ZnO
(10
1
0)

NH
3
2
/
)
(
0
1
10
n
E
E
E
ZnO
T
abs
N. H.
Moreira
, J. Chem. Theory
Comput
.
2009
, 5 , 605
•
Choose functional (LDA(PWC) or GGA(PBE))
•
The electronic fitting can be done in two modes
–
Potential mode, confinement potential for wave function
–
Density mode, confinement potentials for wave function and
electron density
•
Each element will have its own settings
–
What basis to use
–
Electron configuration
–
Confinement potential(s)
Electronic settings
•
Each fitting is done
using different
polynomial orders
•
Fittings are done
for a set of
cutoff
radius scale factors
Polynomial fitting setup
otherwise
r
r
if
0
)
(
)
(
cutoff
n
cutoff
n
r
r
r
f
Possible future extensions to DFTB+
•
Optical Properties
–
LR

TD

DFTB
•
Electronic transport
–
NEG

DFTB
•
QM/MM
•
Vibrational
modes
DFTB+ features outside of Material Studio
Please let us know what extensions and enhancements you
would like to see for DFTB+ in the future.
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