►
From YouTube: VASP Workshop at NERSC: Beyond DFT (GW and ACFDT)
Description
Presented by Martijn Marsman, University of Vienna
Published on December 18, 2016
Slides are available here http://www.nersc.gov/assets/Uploads/VASP-lecture-RPA.pdf
Presented at the 3-day VASP workshop at NERSC, November 9-11, 2016
A
Okay,
so
this
will
be
the
last
bus.
Well,
let's
say
the
last
bus
feature
related
talk,
I
think
afterwards,
we'll
do
something
about
a
short
little
presentation
or
a
summary
about
parallelization
strategies
in
in
the
program
which
will
help
you
to
decide
how
to
how
to
efficiently
use
the
heart,
and
here
at
misc
I
think
you
will
present
something
as
well
right,
Sanji
in
this
respect,
after
the
after
the
as
a
second
talk
right,
yeah,
okay,
so
I
hope,
I'll
stay
in
time.
So
10:30,
you
said
right:
okay,.
B
A
So
today,
we'll
discuss
one
of
the
more
advanced
features
of
the
code
beyond
TFT
technique,
which
in
general,
we
call
the
random
face
approximation
we
were
heard
about
yesterday.
This
was
one
of
these
approximations
in
the
description
of
dielectric
properties
and
when
we
discuss
dielectric
properties.
A
I
already
mentioned
that
these
dielectric,
the
microscopic
dielectric
properties,
are
input
to
some
methods
that
go
beyond
density,
functional
theory
in
the
description
of
electronic
correlation
and
those
two
methods
are
GW
and
and
ACF
DT,
so
GW
for
electronic
structure
and
a
CFD
T
for
total
energies
within
the
random
phase
approximation
to
the
dielectric
screening.
So
yes,
past
is
TFT.
The
possible
DFT
is
still
very
much
the
workhorse
of
many
projects
in
in
the
present
as
well.
A
A
So
the
very
near
future
we'll
see
something
very
similar
for
the
description
of
electronic
properties
in
random,
face
approximation
as
well.
So
there's
well
there's
many
codes.
Now
that
can
can
do
can
do
total
energies
and
electronic
structure
in
the
random
face.
Approximation
and
efficient
algorithms
are
emerging
and
computers
are
getting
more
stronger.
A
All
the
time,
so
I
think
that
that
what
is
true
for
hybrid
functionals
now
will
be
sort
of
true
for
the
random
face
approximation
tomorrow,
which
is
a
good
thing,
because
there
is
a
need
to
go
beyond
density,
functional
theory
and
hybrid
functional
theory.
I
already
saw
many
of
these
things
yesterday
or
at
least
on
the
slides
of
yesterday,
so
in
terms
of
total
energy
differences
and
atomization
information,
energies,
reaction
barriers
and
things
like
this-
we're
definitely
still
not
there.
A
A
Yes,
so
this
is.
This
is,
for
instance,
one
of
those
one
of
those
cases.
I've
just
put
it
there,
as
as
as
a
sort
of
a
case
study
where
we
see
the
effect
of
where
will
I'll
show
the
effect
of
offer,
including
van
der
Waals
interactions.
So
this
is
a
reaction
side
of
a
zeolite
cage.
So
this
is
one
of
those
things
that
people
study
in
oil
industry.
A
So
there's
all
kinds
of
barriers
in
the
and
difference
between
a
drawn
line
and
the
dashed
line
is
that
in
for
the
dashed
line
there
were
attempts
made
to
include
from
the
last
interactions
in
these
calculations,
so
there
definitely
have
a
large
effect
and
they're
they're,
mostly
not
captured
by
by
density,
functional
theory
and
an
hybrid
functional
theory
at
the
moment.
So,
having
said
that,
there
are
still
a
very
active
development
of
density,
functional
theory
which
is
good
and
there's
promising
functionals
in
merging.
These
are
definitely
not
the
newest
ones.
A
So,
there's
a
newer,
very
promising
density
functionals
around
this
respect,
I
really
like
to
mention
just
the
scan
functional
that
has
been
implemented
in
the
code
as
well
and
will
be
definitely
in
the
in
the
next
update
and
the
scan
function
was
one
of
the
density
functionals.
It's
a
meta
GGA,
one
of
the
density
functionals
that
is
able
to
capture
fire
partly
captured
in
front
of
us
interaction.
So
a
new
meta
GGA
is
a
functional.
A
A
These
vander,
waals
density,
spawned
a
whole
host
of
new
functionals
and,
and
some
of
them
worked
quite
well
in
some
situations,
but
there's
definitely
no
universal
fund.
The
vast
density
functional
at
the
moment.
Okay,
so
this
we
saw
yesterday,
that
is
with
respect
to
a
hybrid
functional
theory.
I
made
the
point
that
that
hybrid
functions
are
definitely
not
general
functionals
at
the
moment.
Have
we
combined
a
molecular
system
with
the
metallic
surface?
A
We
see
that
in
DFT
we
have
problems
describing
these
systems,
which
is
to
see
how
adsorption
on
the
metal
surfaces,
we
have
problems
describing
these
systems,
because
DFT
fails
to
correctly
describe
the
co
electronic
structure
and
if
we
turn
to
hybrid
functionals,
we'll
do
better
for
the
molecule
but
worse
for
the
surface,
and
overall
agreement
with
the
experiment
is
not
good
and
why
do
I
show
this
again,
because
I
will
show
what
kind
of
description
we'll
get
into
a
random
face.
Approximation
as
I'll
come
back
to
this
later.
A
A
So
we
had
a
non-local
potential
here
in
hybrid
functional
theory,
and
now
we
see
that
this
is
not
only
non-local
but
also
energy
dependent,
and
this
object
that
we'll
look
at
in
the
random
face
approximation
fantasies
are
the
GW
passing
quasi
particle
equations
and
it's
object
that
we
introduce
here
is
called
the
self
energy,
and
so
this
is
a
level
of
complexity.
More
so
not
only
no
local
but
also,
and
she
dependent
and
this
energy
is,
of
course,
this
classy
particle
energy.
That
is
partly
a
solution
to
our
equation.
A
A
So
let's
have
a
look
at
what
greens
functions
actually
are,
so
the
greens
function
by
different
definition.
It's
the
inverse
of
the
Hamiltonian
that
is
written
here,
and
the
nice
thing
is
that
for
for
a
Cohen
charm
system
for
our
non
interacting
Hamiltonian,
we
can
write
the
green
greens
function
in
terms
of
quantities
that
we
are
that
we
can
access
right.
So
we
have
here.
Our
greens
function
is
a
sum
over
one
electron,
orbitals
that
we
get
out
of
solving
our
con
charm
equations
and
these
one
electron
eigenenergies.
So
that's
nice!
A
A
So
what
does
the
greens
function
physically
mean?
So
basically
the
greens
function
and
I've
written
it
here
explicitly
in
terms
of
time
out.
You
will
see
terms
of
arguments
of
time
and
arguments
of
frequency
will
frequently
change
within
the
formulas.
That
is
simply
a
transformation
from
time
domain
to
frequency
domain.
So
basically
plays
the
same
role,
so
our
greens
function
depending
on
R
and
R
Prime,
and
on
T
and
T
prime
describes
the
propagation
of
a
particle
so
say:
I
have
a
particle,
an
electron
in
this
case,
for
instance
at
Point
R
at
time
T.
A
So
what
is
the
chance
of
finding
this
particle
at
point,
R,
Prime
at
time,
T,
Prime
so
and
terms
of
time.
This
depends
only
on
the
difference
between
these
times.
So
that
is.
That
is
what
the
greens
function
physically
means,
and
it's
often
called
for
that.
For
that
reason
it's
often
called
a
propagator
because
it
tells
us
how
our
particle,
if
it
that
is
at
some
point
at
a
certain
time,
have
propagates
what
the
chances
of
finding
it
that
it
has
propagated
to
another
point
at
another
time
so
well.
A
This
is
this
is
a
little
shorthand
for
this
L
1
and
2
means
R,
1
and
and
finally
2
and
R
2
and
T
1,
and
if
T
2
is
larger
than
than
T
1.
We
call
this
a
particle
propagator
and
it
describes
an
electron
and
we
often
write
it
in
terms
of
diagrams
and
I.
Will
I
will
sort
of
throw
a
few
diagrams
at
you
and
hopefully
make
a
case
for
the
fact
that
they
that
they
do
elucidate
these
kind
of
theories
and
do
not
necessarily
only
up
obfuscate
things?
A
So
we
have
a
point
1
and
a
point:
2
R,
1,
T,
1
and
the
propagation
from
one
point
to
the
other
in
space-time,
so
this
particular
function.
We
can
write
it
like
this.
Well,
it
depends
on
frequency,
and
here
it
is
explicitly
written
in
terms
of
in
the
in
the
time
domain
right.
So
that's
a
particle
propagator
if
T
2
is
larger
than
T
1
for
the
reverse,
so
I
know
it's
the
reverse
direction.
A
If
time
were
to
be
along
this
axis
for
the
reverse
direction,
it
describes
a
propagation
of
a
whole
from
point
R,
2,
T,
2
to
R,
1,
T,
1
right
so
and
there's
a
there's
a
corresponding
function
again
in
terms
of
of
our
of
our
cone.
Shell
were
battles
and
cone
sham
and
energies
related
to
this.
So
these
lines
that
you
will
see
in
these
diagrams
are
propagators
of
particles
of
electrons
and
holes.
So
the
self
energy
in
terms
in
perturbation
theory,
the
self
energy-
is
a
function
of
these
greens
function.
A
We
can
write
it
as
a
function
of
these
greens
functions
so
and
what
we
see
here,
we
can
draw
all
these
nice
little
diagrams
and
I
will
sort
of
give
some
give
some
indication
of
what
they
mean
a
little.
A
little
thing
like
this.
A
little
ball
like
this
is
just
the
density
at
a
certain
point,
and
this
little
wiggly
line
is
a
Coulomb
interaction.
So
this
is
a
particle
traveling
in
my
system,
interacting
with
the
density
through
a
Coulomb
interaction.
A
So
this
is
a
simple
Hartree
interaction
written
like
this
here,
and
this
is-
and
so
this
is
called
I,
don't
this
is
called
the
density
bubble.
I
think
what
you
see
here
is
called
in
environment.
Diagrams
in
terms
of
final
diagrams
is
called
an
open,
Oster
diagram,
and
this
diagram
represents
exchange
interaction.
A
Well,
I'll
show
you
how
you
can
derive
formulas
even
from
this,
from
this
particles
free
from
these
diagrams,
for
these
elementary
interactions,
but
I
won't
do
that
too
much
I
just
want
to
go
to
to
these
classes
of
diagrams,
because
they
are
very
important
because
they
constitute
a
random
phase
approximation
and
they
say
they
tell
me.
I
have
a
particle
here
that
interacts
with
its
environment
through
the
Coulomb
interaction
and
what
happens
here.
It
creates
an
electron-hole
attractive
to
our
system,
and
this
kind
of
thing
is:
is
we
call
a
polarization
bubble?
A
So
what
does
it?
Do
it
travels
through
the
medium?
It
interacts
with
its
surroundings
and
polarizes
to
me
here.
That
is
actually
this
little
wiggle
and
such
a
polarization
bubble,
so
it
polarizes
the
medium
it.
So
it
induces
a
change
in
the
depth
in
the
density
and
that
works
back
on
our
particle
through
the
Coulomb
interaction.
But
we
could
envision
higher
order
processes
in
information
theory.
So
we
have
our
electron
as
it
travels
happily
through
the
medium
interacts
with
its
surroundings.
A
Polarizes
it
that
polarization
that
changed
in
the
density
works
on
the
surroundings
through
the
Coulomb
interaction,
induces
a
further
change
in
the
density
that
then
works
back
through
the
Coulomb
interaction
on
our
particle
and
so
on,
and
so
on,
and
so
on,
so
that
we
can
can
sort
of
add.
We
can
add
these
polarization
bubbles
at
infinitum
here
so
and
this
whole
class
of
interactions
in
its
together
up
to
in
summed
up
to
infinity,
constitute
the
random
phase
approximation.
So
there's
many
many
many
other
possible
interactions.
A
Right
exchange
will
take
into
account,
but
there's
higher-order
exchange
processes
possible
as
well.
So
you
can
Dragan
draw
all
kinds
of
complicated
diagrams
well
in
the
random
phase
approximation.
The
only
interactions
that
will
include
in
the
in
the
description
of
our
particle
as
it
interacts
with
its
surroundings
are
those
guys,
those
what
we
call
polarization
bubbles,
and
why
do
we
do
this?
So,
let's,
let's
first
okay.
Maybe
this
is
a
little
side
issue.
I
said
to
you
that
this
is
a
density
or
actually
this
shows
you
how
to
construct
power
in
such
a
diagram.
A
How
you
can
construct
a
formula
that
is
sort
of
human-readable
out
of
it,
so
I,
don't
I,
don't
want
to
go
into
this
too
much.
You
can
have
a
look
at
it
if,
if
it's
of
interest
to
you
later-
but
this
shows
you
that
this
yes,
this
indeed
isn't-
is
a
Hartree
interaction
with
the
density
and
yes,
indeed,
such
a
diagram
constitutes
an
exchange
interaction
anyway.
So
why?
Why
make
this
point
of
explaining
these
polarization
bubbles
in
such
detail?
A
Actually
because,
including
other
ones
is
computationally
very,
very
demanding
right,
but
this
we
can
do
more
conveniently
and
than
including
the
elements
so
there's
one
of
the
the
things
which
makes
the
random
phase
of
observation
at
the
moment
popular
not
only
because
it's
it's
I'll
show
you
that
it's
a
fairly
good
approximation
for
the
physics
in
many
cases,
but
it's
also
a
tractable
one
right.
So
we
can
do
it.
C
C
D
A
Yes,
so
this
is,
this
is
actually
yes.
This
is
so
I
refrained
from
saying
that
this
is
the
direction
of
time,
because
in
these
diagrams
I
violated
that
that
that
definition
in
the
exchange
like
once
but
but
for
these
ones,
you
could
say
yeah.
This
is
time
so
I
have
a
particle
coming
in
interacting
with
the
medium,
creating
an
electron
hole
pair
that
travel
through
the
medium
recombine
work
with
recombine,
through
an
interaction
with
the
environment,
create
a
further
electron
hole
pair
that
travel
through.
A
So
so,
yes-
and
in
this
sense
really
one
direction
is
a
propagation
of
an
electron.
The
other
direction
and
arrow
drawn
in
the
other
direction
is
the
propagation
of
a
hole.
So
yes,
in
that
sense,
it
is
there's
a
time
in
their
time
and
and
in
place
and
all
kinds
of
integrations
right.
Sorry,
yes,
if
you
want
to
do
still
formulas
out
of
it,
so
so
what
is
the
nice
thing
about
this
random
phase?
A
A
This
would
be
a
bare
Coulomb
interaction
times,
an
independent
particle
propagating
propagation,
sorry,
an
independent
particle
polarizability
times
a
Coulomb
interaction,
and
this
one
is
V
times
Chi
naught
times
V
times,
V
naught
times
V,
and
this
is
what
we
saw
yesterday
right.
So
this
is
this.
This
thing
that
we
can
express
as
a
geometrical
series
and
that
in
fact
adds
up
to
being
our
our
dielectric
screening
all
right.
So
in
the
end,
this
is
truly
a
screened,
Coulomb
interaction.
A
So
that's
how
we
end
up
from
a
description
of
our
of
our
of
our
from
a
perturbative
description
of
our
self
energy.
We
end
up
with
well
W
the
screened
Coulomb
interaction
times,
propagator
G,
and
that
is
why
what
is
method
is
called
Chi
W,
because
we
have
now
caused
ourself
energy
that
the
thing
that
we
need
for
our
class
of
particle
equations
in
terms
of
a
propagator
in
terms
of
a
greens,
function
uh-huh
and
the
product
with
with
a
screen,
Coulomb
interaction
right
so
that
we
have
seen.
A
So
what
goes
in
that
we
have
seen
yesterday
right.
This
is
our
independent
particle
polarizability,
which
is
in
essence
the
change
in
the
induced
charge
density
due
to
a
change
in
the
sorry,
a
change
in
the
charge
density
due
to
a
change
in
the
effective
potential
in
our
column
system,
and
we
can,
as
we
saw
yesterday,
where
this
formula
looks
a
bit
different.
What
we
saw
a
very
similar
formula
yesterday,
this
is
just
written
in
another
way
and
we
can
compute
this
in
terms
of
our
of
our
block,
orbitals
of
Arkansas,
more
bottles
and
Arkansas.
A
A
One
is
okay,
one
is
the
some
open
occupied
orbitals
and
we
have
these
empty
States
coming
in
as
I
told
you
yesterday,
but
the
nice
thing
is
and
that
I'll
show
you
later
on
that
we
can
actually
write
this
independent
particle
polarizability
in
terms
of
greens
functions
as
well
and
end
up
with
an
algorithm
that
scales
cubically,
so
in
essence,
scales
as
badly
or
or
as
well
as
our
DFT,
with
a
very
different
pre
factor
the
whole.
But
yes,
so
this
is
in
its
canonical
form.
A
It
scales
as
n
to
the
power
4,
but
if
we
cast
it
in
greens,
functions
if
we
end
up
with
with
a
better
scaling
algorithm,
that's
a
point
that
that
we'll
come
to
later.
So
we
see
this
is
essentially
what
I
am.
What
I
showed
you
yesterday
right,
so
that
we
can
write
this
sum
as
the
product
of
of
our
Coulomb
operator
and
geometrical
series
that
represents
the
inverse
of
our
dielectric
matrix?
Yes,
so
yeah,
then
in
essence,
we
are
set
to
to
do
G
W.
A
We
have
an
expression
for
for
our
self
energy,
the
product
of
a
greens
function
and
a
screen,
column
or
Coulomb
interaction.
Well,
it's
written
bit
more
explicitly
here
and
so
screen.
Coulomb
interaction
is
essentially
this
thing
where
we
have
dielectric
screening
and
one
over
R
minus
R
Prime.
In
essence-
and
this
is
this
greens
function
that
I
already
showed
you
yesterday
so
compared
to
folk
exchange.
A
Actually
you
see
that
this
is
a
in
essence,
a
screened
exchange,
interaction
in
GW
right,
if
you,
if
you
make
the
comparison
here,
we
have
two
orbitals
and
at
R
and
R
Prime,
and
this
is
very,
very
much
like
the
focal
potential.
Only
now
the
Coulomb
operator
in
in
this
in
this
potential
has
been
screened
with
the
dielectric
properties
of
our
material,
and
that
is
a
connection
that
you
could
make.
A
For
instance,
two
hybrid
functional
theory
right
because
in
hybrid
functional
theory
we
say
we
use
a
quarter
of
this
yeah,
so
this
would
be
like
using
a
fixed
screening.
So
I'm
saying
we
screen
this
at
every
point:
R
and
R,
prime
and
every
frequency
with
the
same
amount
with
one
quarter,
and
here
we
are,
of
course
we
have
an
object
that
is
material
dependent
right
because
we
compute
this
for
every
system.
So
it's
not
a
fixed
screening,
but
yeah.
B
D
E
A
Now,
I
really
don't
know
it.
It's
used
everywhere
and
I
think
there's
even
a
lot
of
papers
where
they
say
we
don't
know
where
it
comes
and
I
don't
know
either
I
have
the
feeling
it
comes
out
of
high-energy
physics,
an
approximation
that
was
used
in
high
energy
physics,
but
I
couldn't
I
couldn't
say
where
and
I
I
it's
it's
a
feeling.
I
have
that
it
comes
out
of
high
energy
physics,
probably
something
that
somebody
sometime
at
some
point
mentioned
to
me,
but
I
know
I,
really,
don't
know
why
it's
called
random
face
approximation
yeah.
E
A
Yes,
so
you
would
have
to
in
inc
so
but
welcome
I'll
come
to
this
later,
but
this
F,
for
instance,
in
index.
As
far
as
the
exchanges
concert,
ins
there's
only
the
naked
exchange,
the
spoke
exchange,
so
second
order
processes
in
exchange
are
immediately
neglected
already.
So
that's
one
thing
that
that
that
is,
that
has
serious
consequences
and
these
guys
and
there's
a
whole
bunch
of
them
that
have
little
more
wiggly
lines
here.
A
A
E
E
C
A
A
Well,
yeah:
the
screening
is
in
there
right,
so
so
yeah,
but
you
wouldn't
want
to
tinker
with
it
because
I
mean
I
saw.
The
interaction
is
screened,
but
you
wouldn't
want
to
want
to
violate
this
anymore.
Then
you
already
have
because
you
computed
in
a
certain
approximation
but
but
yeah,
so
the
interaction
is
screened,
but
with
the
true
dielectric
properties
of
the
of
the
well,
not
the
true
dielectric
properties,
but
the
property,
the
random
phase,
approximation
to
the
dielectric
properties
of
the
material
yeah.
A
A
We
see
that
the
screening
in
this
area
is
so
this
red
line,
and
this
is
an
important
area
in
terms
of
reciprocal
space,
of
the
dialectic
screening.
We
see
that
this
fairly
well
matches
with
with
what
the
hybrid
does
for
you.
So
this
is
an
HTC
hybrid.
So
it's
not
exactly
one-quarter
right,
because
we
have
this.
We
have
this
error
function,
which
of
course
means
that
every
Fourier
transform
this.
It's
not
simply
one-quarter,
but
we
have
a
little
variation.
D
A
No
sorry
Jesus
reciprocal
space,
vector
yeah,
yes
right
so
as
we
go
to
larger
reciprocal
space
vectors
we're
dealing
with
faster
fluctuations
in
the
response
right.
So
so
we
see
that
that
this
1/4
is
actually
a
fair
compromise
for
for
systems
that
that
have
a
small
small
gaps.
So
this
is
the
reason
why
this
what
is
fairly,
why
this
works
so
well,
these
hybrid
functionals,
so
this
1/4
doesn't
exactly
fall
from
the
sky.
In
that
sense
right,
it
has
some
basis.
A
A
Sorry,
you
compute
the
spectral
function,
and
then
you
from
this
you
get
the
imaginary
part
and
for
Makram
is
chronic
transformation
or
in
this
case
a
Hilbert
kind
of
transformation.
You
get
the
real
part
of
the
of
to
function
as
well
anyway.
This
is
just
I
won't
want
to
put
too
much
emphasis
on
this,
because
actually
we
have
a
better
algorithm
now
to
do
this
and
that
will
be
released
pretty
soon.
A
Okay,
let's
go
to
to
actually
do
it,
GW,
because
we
already
said
that
this
cell
or
I
already
said
that
the
self
energy
depends
on
on
this
particular
energy.
Right
in
this
on
this
classy
particle
energy
Souders,
it
is
there's
a
possibility
to
do
an
additional
level
of
self-consistency
here.
These
classic
particle
energies
are
given
by
this
particular
expectation
value,
and
now
we
could
solve
this
by
iteration
of
unity
right.
A
So
in
essence,
you
calculate
the
DFT
orbitals
get
these
koncham
orbitals
enteragam
energies
simply
plug
them
in
as
how
compute
the
greens
functions,
belonging
to
this
computer
screening
properties
belonging
from
these
orbitals
and
eigenenergies
and
compute
your
scheme,
Coulomb
interaction
and
your
self
energy
and
solve
these
equations.
One
time
ever
here,
the
self
energy
depends
on
the
I
can
energies
on
our
cone,
Sean
again
images,
so
that
is
single-shot
GW
and
where
we
have
linearized
this
equation.
A
So
we
take
variations
of
the
self
energy
around
our
current
cone,
some
eigenenergies
into
account
in
a
linear
fashion.
That
is
what
is
what
is
mentioned
here,
so
that
a
single
shot,
GW
one
step
beyond
this,
would
be
what
what
is
called
G
W
naught,
because
these
eigen
energies
that
we
put
into
our
selves
energy
they
go
into
the
greens
function
right
under
the
into
the
let's:
do
I
have
to
see
it?
Yes,
yeah
so
into
the
greens
function
at
this
point.
A
A
Do
we
want
to
put
them
into
our
new
greens
function,
or
do
we
also
want
to
put
them
into
our
description
of
the
screening
right
so
and
the
most
commonly
used
approximation
beyond
single-shot
TW
is
actually
G
W
naught
where
we
do
not
update
the
the
eigenenergies
with
which
we
have
computed
the
screening
properties.
We
only
update
them
in
our
greens
function
and
the
orbitals
remain.
The
same.
A
They're
still
comes
from
orbitals
and
the
quasi
particles
that
we
get
from
single-shot
GW
are
now
used
to
compute
a
new
greens
function,
and
that
is
what
we
call
G
W
naught
and
that
you
can
repeat
a
few
few
times
I.
So
you
can
again
make
a
loop
over
this
a
few
times
or
three
four
times
and
then
mostly
the
quasi
particles
you
get
out
of
these
G
W
naught
calculations
have
converts,
and
why
do
I
mention
this
this
so
explicitly,
because
this
is
actually
within
the
random
face
approximation.
A
This
is
almost
the
only
thing
that
you
could
do
on
top
of
G
naught
W
naught.
That
makes
any
sense
all
the
other
things.
I
will
show
you
some
examples
or
the
other
things
might
be
helpful
in
some
cases,
but
in
most
cases
won't
work
very
well,
and
that
is
because
actually
and
I'll
show
you
the
examples
of
this,
and
it's
actually
because
there's
there's
a
cancellation
of
errors
involved
in
in
using
the
random
face
approximation
and
using
eigenenergies
and
eigenstates
from
DFT.
So
you
do
get.
A
Actually,
you
do
get
a
very
nice
description
of
your
dielectric
screening
in
the
random
face
approximation
as
long
as
you
use
eigenenergies
and
eigen
functions
from
DFT.
If
you
start
to
update
this,
your
description
of
screening
properties
will
not
improve
in
the
in
most
cases.
So
there's
limits
right,
because
you
know
that
we
do
not
have
the
true
dielectric
screening.
We
have
an
approximation
to
this
and
and
that
approximation
actually
works
quite
well
as
long
as
you
stick
to
two
density-
functional,
let's
say:
PvE
eigenenergies
and
eigenfunctions.
Yes,
I.
D
D
B
A
So
this
is
from
a
practical
point
of
view:
single-shot
GW,
&
GW,
not
where,
as
you
say,
you
actually
only
update
the
quasiparticle
energies
and
not
orbitals.
Those
are
the
things
that,
within
the
random
phase,
approximation
makes
sense,
if
not
you
will
have
to
so.
If
you
want
to
go
beyond
this,
you
will
have
also
to
go
beyond
the
random
phase
approximation
in
your
description
of
dielectric
screening,
which
will
be
possibly
much
more
costly,
then
yeah
right.
D
D
A
A
Okay,
so
yes,
so
what
does
this
yield
right?
So
here
we
have.
Unfortunately,
I
really
should
update
this
graph
to
include
the
hybrid
functions
as
well,
but
here
we
have
DFT
and
the
blue
dots.
As
we
saw
before
strongly
under
estimating
a
band
gaps
for
all
materials,
then
we
have
G
naught
W
naught
using
these
PvE
states.
A
Those
are
the
white
triangles
so
moves
nicely
in
the
right
direction,
but
we
see
still
still
substantial
deviations
and
with
respect
to
and
then
GW
not
only
updating
the
eigenenergies
inside
of
the
greens
function
moves
us
quite
a
bit
closer
to
experiment.
We
see
here
that
there
are
still
cases
that
are
problematic.
I
think
this
is
well
zinc.
A
So
updating
the
orbitals
so
there's
the
possibility
to
update
the
orbitals-
and
this
is
the
self
consistent,
quasiparticle,
GW
and
they're
said
well.
This
is
a
description
of
how
this
is
done.
This
is
approximately
done.
I
won't
go
into
into
the
technicalities
of
this
only
mentioned
that
it
is
possible
to
do
it
and
there's
a
little
flowchart
how
to
do
it.
A
Of
the
comparison
with
with
respect
to
experiment
so-
and
this
is
still
as
you
see-
this
is
still
using
the
screening
from
DFT,
so
we
have
still
not
updated
anything
in
in
in
the
dielectric
properties
of
our
system.
That
is
still
remain
still
firmly
at
the
level
of
DFT
right.
So
what
do
we
do
here?
We
update
now
the
greens
function
in
its
entirety,
right,
so
not
only
the
eigenenergies
but
also
the
orbitals,
and
we
see
that
in
most
cases,
there's
actually.
E
A
No,
no,
that
is,
and
that
that
goes
back
to
exactly
the
same
point
made
before
that
this
combination
is
Brandon,
face
approximation
and
DFT
input
match,
as
well.
Only
when
you're,
when
you're,
when
your
system
at
the
DFT
level
is
really
really
horribly
described,
it
pays
off
to
do
something
like
an
Hz
and
hybrid
functional
calculation
and
G,
naught
W,
naught
so
don't
update
anything
there.
Then
you
can
do
a
single
shot,
the
GW
calculation
on
top
of
it.
A
A
A
Okay,
so
there
are
cases
where
updating
updating
the
orbitals
in
the
greens
function
pays
off
or
is
even
necessary.
So
there's
two
examples
here:
on
the
Left
we
see
barium
titanite
and
that
is
a
G
W
naught
versus
self-consistent
classic
particle
G
W
naught.
We
see,
there's
hardly
any
difference
between
let's
well
mainly
looking
at
the
onset
of
the
blue
and
the
red
lines.
We
see
there
is
hardly
any
difference,
but
if
we
call
two
lanthanum
illuminate,
we
see
that
that
including
updating
the
orbitals
in
the
greens
function
actually
makes
an
appreciable
difference.
A
So
there's
no
real
way
actually
to
say
beforehand
whether
that
should
whether
that
is
the
case,
whether
updating
the
quasi
particles
in
the
greens
function
will
will
change
a
lot,
but
the
cases
where
it
is,
in
fact
so
are
very
seldom
yeah.
So
this
is
this
is
an
example
of
it,
but
there's
not
so
many
as
far
as
I
know.
A
A
But
if
you
go
to
full
self-consistency,
you
see
the
limitations
of
this
random
face
approximation
right.
So
what
is
what
is
one
of
the
things?
What
is
missing
so
one
of
the
one
of
the
most
important
things
that
is,
that
is,
what
is
missing,
is
excitonic
effects.
I
showed
you
these
these.
What
what
is
commonly
called
letter
diagram
so
there's
ways
to
include
it
at
this
level
so
to
go
beyond
the
random
phase
approximation
and
to
a
more
a
more
fancy
description
of
the
dielectric
screening
and
then
actually
at
full
self-consistency.
A
You
move
back
to
words,
experiment,
and
so
this
is
the
random
phase
approximation
where
we
and
when
we
create
electron
and
hole
pairs.
Then,
when
we,
when
these
bubbles
arise,
they
do
not
interact.
This
electron
hole
pairs
s,
they
themselves
travel
through
the
system
so
there.
In
that
sense,
there
is
no
electron
hole,
interaction
as
its
labeled
here,
there's
no
excitonic
effects.
We
can
include
them
mu.
This
is
by
means
of
the
Nano
contour
kernel
and
its
work
by
Leticia.
A
Raining
can
include
them
in
the
screening
and
then
we
move
back
from
these
white
triangles
back
to
experiment,
but
these
unfortunately
scales
like
something
like
n
to
the
power
5
and
to
the
power
6.
So
it
is
possible,
but
it's
not
really
tractable
right,
so
it
doesn't
pay
off
to
go
to
do
anything
self
consistent
within
the
description
of
your
dielectric
properties.
Not
if
you
want
to
remain
within
the
random
face
proximation,
so
that
point
is
made
here
in
terms
of
of
dielectric
constants
I
in
clamped
dielectric
constants
I.
A
So
in
the
rpi
description
of
our
self
energy,
the
electron
interacts
with
itself,
which
should
not
be
obviously
and
and
this
particle
whole
letter
particle
hole
diagrams
or
letter
diagrams.
They
capture
electrostatic
interaction
between
these
electrons
and
holes
that
that
are
created,
and
those
are
these
excitonic
effects
and
another
buzzword
that
you
will
often
her
here
of
is
they
are
the
so-called
vertex
Corrections
in
in
W.
A
Well,
what
they
do
is
they
remove
self
screening
so
as
far
as
there's
an
energetic
contribution
in
the
self
interaction
and
our
electron
that
travels
through
the
system
in
our
PA
also
screens
itself,
which
is
not
correct.
So
those
are
the
things
that
are
that
are
neglected
in
the
RPI
and
that
works
well
in
connection
with
density,
functional
Theory,
konchem,
orbitals
and
eigenenergies,
but
not
so
well.
A
If
we
go
beyond
so,
the
best
approach
is
that
you
could
do
now
is
G
no
W,
not
oranjee
W,
not
possibly
self-consistent
quasiparticle
TW,
not
on
top
of
density
function,
Theory,
orbitals
and
eigenenergies,
or
if
PB,
e
or
density
functional
theory
is
completely
unreasonable
for
your
system.
You
might
do
G,
not
W,
not
on
top
of
a
hybrid
functional,
and
those
are
the
two
things
that
that
that
make
sense
to
do
within
the
random
phase
approximation.
A
So
we
spoke
about
this
yesterday.
The
potentials
that
one
should
use
in
connection
with
these
with
these
calculations
are
the
so-called.
Are
these
G
W
potential
sorry
underscore
GW
Patkar
files
because
they
are
constructed
in
such
a
manner
that
we
represent
scattering
properties
up
to
energies
high
up
in
into
the
excited
state
of
the
of
the
atomic
system,
and
that
is
necessary
to
get
high-quality
virtual
states
that
we
need
in
for
these
methods
that
some
of
our
virtual
states
so
are
any
questions.
A
The
dotted
lines,
okay,
the
drawn
lines
are
the
scattering
properties
and,
and
the
measure
of
the
step
is
scattering
properties.
Is
this
logarithmic
derivative
and
those
are
plotted
here?
The
dotted
lines
are
further
for
the
Trudeau
anthem
and
the
drawn
lines
are
for
the
for
the
for
the
own
election
problem.
So
if
they
match,
we
have
constructed
a
pseudo
potential.
That
truly
represents
the
scattering
properties
of
the
whole
electron
problem,
and
they
do
match
here
close
to
within
the
valence
regime
that
they
match
nicely.
A
D
A
In
fact,
always
use
them,
but
they're
slightly
more
expensive
because
the
so
yeah
we
talked
about
this
via
W
formalism,
where
we
have
these
these
local
functions,
these
need
more
local
functions,
so
the
cost
is
actually
it's
not
not
so
much
higher.
So
the
cost
of
doing
a
ground
state
calculation
with
these-
and
these
will
yield
more
very,
very
similar
results
and-
and
it
will
be
approximately
s,
costly
and
slightly
more
costly
here-
some
of
them
might
be
a
bit
harder
that
could
be.
A
It
could
be
that
in
that,
but
that
would
definitely
not
be
the
case
per
se,
but
it
could
be
that
for
some
examples
and
to
get
to
get
them
to
match
up
to
higher
energies,
the
core
had
to
be
decreased
or
something
creating.
These
potentials
is
sort
of
playing
with
with
many
many
parameters
and
until
you
end
up
with
something
that
is
that
that
looks
nice
in
this
sense
and
still
reason
is
reasonable
in
terms
of
the
number
of
plane
waves
that
you
would
need
to
use
to
the
valence
electrons.
A
So
it
might
be
that
cutoff
energies
are
slightly
different
yeah.
So,
in
that
sense,
one
of
them
might
be
more
expensive
than
the
other
one,
but
it
should
be
very,
very
similar.
So
if
you
use
a
project
where
you
normally,
you
would
say
you
wouldn't
switch
potentials
inside
one
project
right.
So,
if
you're
planning
to
do
GW
and
you're
planning
to
use
these,
you
would
probably
use
the
same
same
potentials
for
your
other
calculations
with
which
you
want
to
compare,
and
so
that
total,
so
that
the
energies
are
directly
comparable.
Yeah.
D
A
Transition
metal
oxide-
it's
mentioned
actually
here
and
it,
and
it's
it's
one
of
these
one
of
these
things
that
so
strongly
localized
states
are
still
a
problem
for
for
GW
as
well,
and
so
there
definitely
is
a
very
big
problem
in
DFT,
as
we
know
so,
d3d
States
or
4f
states
they're
there.
We
know
that
they
are
not
where
they
should
be
in
in
in
DFT,
but
that
is
definitely
still
a
problem
within
GW
as
well.
E
A
E
E
A
D
D
A
A
C
A
A
Okay,
okay,
so
so
what
we
have
seen
before
right,
we
have.
We
have
looked
at
electronic
structure,
so
we
have
looked
at
this
one,
one
electron
energies
and
quasi
particle
energies.
Things
like
this
and
in
kinetic.
Well
all
of
these
all
of
these
equations
that
we
that
we
have
seen
so-called
charm
equations
hold
on
equations
classic
quasi
particle
equations.
So
for
the
confirmed,
equations
and
evolved
on
equations.
There
there's
a
variation
of
a
total
energy
expression
with
respect
to
these
one
electron
orbitals
right.
A
So
now
we
could
ask
ourselves:
are
these
quasi
particle
equations
related
to
some
total
energy
expression
in
the
same
sense,
and
and
actually
they
are
so?
There
is
something
like
an
RPA
total
energy
and
before
we
have
seen
RP
a
band
structure
which
was
our
W
naught
and
these
RPI
total
energies
they
are
computed
in
what
is
what
is
called
a
CF
DT
or
you
can
derive
them
in
in
what
is
called
a
CFD
T
adiabatic
connection
fluctuation
dissipation,
theorem
I
won't
go
through
through
any
of
these
of
these
theorems
or
the
proof.
A
I'll
just
give
you
the
result
and
the
resulting
expression
by
its
it's
a
kinetic
energy
that
is
RPI,
total
energy,
the
kinetic
energy
that
we
simply
compute
from
our
orbitals.
As
we
have
seen
before
a
heart
tree
energy,
depending
on
the
density
completely
common,
then
we
have
an
a
for
exchange,
energy
computed
with
the
density,
functional,
Theory,
orbitals,
and
so
in
that
sense,
it's
different
from
a
hybrid
functional
and
where
you
have
hybrid
functional
orbitals.
A
Approximation
right
and
yeah,
okay,
now
easily
evaluating
this
or
in
a
canonical
form
using
this
Adler.
These
are
formula
these
scales
as
as
n
to
the
power
4,
not
because
evaluating
this
particular
expression.
Scales
like
that,
but
because
computing,
the
independent
particle
polarizability
has
this:
has
this
unfortunate
scaling
behavior
with
respect
to
system
size,
so
in
terms
of
diagrams
we
well,
this
is
sort
of
trying
to
show
you
what
what
this
kind
of
expression
why
this
kind
of
expression
is
related
to
what
we
have
seen
in
GW
before
right.
So
this
is
our.
A
This
is
actually
resonance.
This
is
actually,
if
you
would
sorry
if
you
would
think
to
remove
this
particular
line.
Sorry,
it
is
one
that
is
one
that
that
goes
up.
If
you
would
remove
that
propagator
and
think
of
of
that
one
is
a
straight
line
here,
as
we
saw
before
then
then,
what
you
see
there's
actually
GW.
That
is
again
then
one
of
these
propagators
times
a
screened,
a
Coulomb
interaction.
If
we
look
at
what
this
logarithm
does,
and
so
we
expand
this,
this
logarithm,
it's
a
Taylor
expansion
of
it.
A
A
With
respect
to
the
greens,
function,
taking
the
derivative
with
respect
to
a
greens
function
in
one
of
these
bubbles
means
removing
one
of
these
lines
and
if
you
then
play
this
through,
and
so,
if
you
take
this,
this
expression
in
in
diagrams
that
we
saw
before
for
these
RPI
total
energies
and
you
remove
one
line
everywhere
in
these
diagrams.
You
end
up
with
exactly
the
same
thing
that
we
saw
before
so
there
is
this
connection
between
the
total
energy
and
the
random
phase.
A
Between
electronic
structure
from
your
column,
equations
and
your
and
your
density,
functional
Theory,
total
energy
right,
so,
okay,
so
how
well
does
this
work?
It
works
quite
well.
These
are
all
slides
that
that
try
to
make
this
point
that
compare
random
face,
South
implications
for
lattice
constants
in
the
random
face
approximation
with
other
methods,
PVE
and
p2.
Actually,
for
things
like
this
I
don't
want
to
go
into
into
all
these
details.
A
Yes,
so
if
we
then
go
to
okay,
that
is
sort
of
making
this
point
again
yeah.
Another
thing
is
that
the
behavior
of
the
total
energy
with
respect
to
the
interlayer
distance
in
graphite
has
the
right
character.
So
it
should.
It
should
behave
as
one
offered
the
inter
layer
distance
to
the
power
four
that
we
do
get
out
of
our
random
phase
approximation
calculations
for
the
total
energy.
A
Well,
going
one
step
beyond
this,
you
could
look
at
noble
gas,
solid,
so
they're
they're
actually
only
bound
by
von
der
Waals
interactions
or
primarily
bound
by
Vander
Waals
interactions
and
compute
C
six
coefficients
for
these
compounds,
and
we
do
see
that
we
get
really
quite
nice
results
compared
to
experiment.
So
now
we
have
finally
a
functional
that
captures.
One
of
our
interactions
as
well.
A
Well
does
quite
well
for
heats
of
formation.
The
bad
news
is
that
they're
looking
at
this,
that
if
one
looks
closely
to
the
numbers
one
system
will
receive,
we
have
quite
nice
heats
of
formation,
but
chemical
accuracy
is
not
reached
for
this
particular
functional
all
right.
So
so
we
do
quite
well
for
many
aspects,
but
it's
still
it's
definitely
not
the
end
of
the
line.
Yeah
I've
put
this
on
the
slide.
A
The
other
thing
that
that
I
already
said
that
I
would
come
back
to
this
point.
Is
this
Co
adsorption
on
on
the
metallic
surfaces,
and
so
this
was
the
one
of
those
things
that
were
hard
to
get
a
right,
that
we
didn't
get
right
in
in
DFT
that
we
didn't
get
right
in
using
high-risk
functionals,
and
so
one
of
the
another
way
of
looking
at
these
problems
is
depicted
in
this
graph.
A
So
intuitively
you
wouldn't
expect
this,
because
the
two
small
surface
energy
means
that
the
surface
is
actually
a
bit
too
happy
to
be
a
surface,
and
then
it
should
not
be
so
keen
on
binding
anything.
So
this
is
our
the
sort
of
two
things
that
you
wouldn't
necessarily
expect
to
occur
at
the
same
time,
and
not
only
this
but
going
from
one
functional
to
another.
We
see
a
sort
of
a
trade-off
between
between
those
two
effects
and
we
move
along
these
lines
that
doesn't
get
closer
to
to
experiment.
A
Actually,
if
we
do
this
in
the
random
face
approximation,
we
move
away
from
these
lines
and
break
with
this
and
again
for
some
stuff
get
actually
quite
close
to
experiment
and
the
fact
that
for
platinum,
we're
still
ways
off
with
respect
to
the
experiment
in
terms
of
the
surface
energy.
But
we
partly
blame
the
experiment
for
this.
So
so
we
would
like
to
play
in
the
experiment
for
this:
it's
not
so
easy
to
to
to
get
to
do
good
experiments
on
to
get
really
reliable,
experimental
data
on
these
surface
energies.
A
So
there's
there's
possibly
room
for
improvement
at
the
experimental
side
as
well
anyway,
going
so
recapping
connecting
to
what
what
what
we
compared
to
before
for
this
kind
of
systems.
We
have
looked
at
side,
preference
and
absorption
energies,
and
now
we
see
that
not
only
do
we
get
good
structural
properties,
so
we
get
written
very
reasonable
service
energies.
We
get
good
structural
description
of
the
system,
but
we
also
get
good
absorption
energies
now
and
we
get
the
right
side,
preference
and
that
is
sort
of
collected
in
this
graph.
A
A
At
the
same
time,
and
now
we
can
can
really
fully
describe
this
problem
before
we
saw
that
we
do
either
well
for
homology
with
a
hybrid
functional
but
screw-up
the
description
of
our
metallic
system,
or
vice
versa.
We
have
a
good
description
of
a
metallic
system
in
density,
functional
theory,
but
not
of
our
molecular
States,
and
this
is
reached
here.
So
this
is
sort
of
unified
here
and
works
quite
long,
so
that
point
is
made
actually
here.
So
what
do
we
see
in
density,
functional
theory?
A
We
see
that
our
molecular
states
are
homo
lumo
gap
is
too
small,
so
this
is
where
experiment
claims
it
should
be
or
where
it
should
be.
Experimentally,
overweight,
often
especially
this
a
LUMO-
is
much
too
close
to
the
metallic
States.
If
we
go
to
the
to
the
hybrid
functional-
and
we
do
very
well
actually
for
for
these
molecular
states
very
close
to
where
experiment
would
like
them
to
be,
but
the
D
metal
bandwidth
has
become
too
large,
and
especially
in
this
area,
the
back
bonding
is
is
still
too
strong.
A
A
So
for
the
hands-on
section,
there's
a
script
that
takes
care
of
this
and
and
have
a
look
at
all
these
scripts
because
they
simply
mostly
they
copy
Inc.
Our
files
to
Inc
our
files
to
an
inker
file
that
pertains
to
a
particular
step
is
copied
to
in
current
and
fastest
run.
So
and
then,
if
you
look
into
this
incre
fast
you'll
see
all
these
tags
and,
and
hopefully
the
manual
be
explained
it.
If
enough
to
to
give
you
an
inkling
of
what
is
so?
What
do
you
need
to
test
in
these
cases?
A
Well,
this
is
something
that
will
weaken,
probably
discuss
better
at
the
during
the
hands-on
sessions.
So
what
we
do
have
is
a
well
balanced,
total
energy
expression
that
captures
all
types
of
bonding.
What
he
unfortunately
do
not
have
is
a
total
energy
expression
that
is
accurate
enough
to
reach
the
final
goal,
which
is
this
chemical
accuracy.
A
So
I
would
like
to
mention
this
because
I've
alluded
to
it
a
few
times
and
mentioned
the
fact
that
the
way
that
we
compute
the
independent
particle
polarizability
scales
so
horribly
with
the
fourth
power
of
system
size.
Well,
there's
now
we
have
been
working
on
on
an
algorithm
that
scales
cubic
Li,
and
we
sounded
that
that
removes
this
limitation.
It's
work
of
mayors
of
Caltech,
finishing
klemish
and
and
Gail
christen,
my
boss.
A
Well,
this
is
again
this
what
we
have
seen
our
greens
function.
Now,
it's
it's
written
in
imaginary
time
and
in
terms
of
a
greens
function
in
imaginary
time
we
can
compute
the
polarizability
as
a
product
of
two
greens
functions,
and
this
is
a
well
a
point-by-point
product,
so
a
over
R
and
R
prime.
So
what
is
the
nice
thing
about
this?
A
point-by-point
product
offer
two
quantities
that
scale
with
system
size
scales
as
the
the
square
of
the
system
size
and
not
n
to
the
power
4.
So
getting
the
independent
particle
polarizability.
A
This
way
is
much
much
cheaper,
yeah.
Well,
you
have
to
do
some
clever
stuff
to
to
have
a
transfer,
a
cosine
transform
of
this
guy
to
imaginary
frequency,
and
then
you
can
simply
use
it
in
this
equation.
That
now
is
the
worst
scaling
step,
because
there's
a
diagonals
ation
involved
of
a
matrix
and
that
scales
cubed.
So
you
end
up
with
an
algorithm
that
is
not
scaling
as
n
to
the
power
of
4
but
and
n
to
the
power
3,
as
in
fact
yes,
I.
E
E
E
C
A
B
A
E
A
E
B
A
A
So
we
do
need
only
very
few
points
for
these
transformations
and
that
is
more
or
less
constant,
so
that
doesn't
scale
with
that.
Doesn't
change
with
the
system
size
and
yes.
So
what
can
we
do
this
way?
So
prefactors
are
much
larger
than
in
DFT
is
mentioned
here,
but
we
can
do
these
calculations.
Two
systems
like
a
few
hundreds
of
atoms
within,
while
in
this
case
on
on
128
course,
in
something
like
three
hundred
seconds,
so
that
is,
it's
really
quite
powerful.
A
C
A
E
E
A
E
A
Well,
we
have
spoken
very
spoken
about
this
I
think
I
know
why
you
asked
right
so
if
you
would
want
to,
if
you
would
want
to
excite
your
system
and
follow,
follow
its
state
explicitly
in
time,
you
couldn't
use
this
obviously
right.
But
if
you
then
want
from
this
response
want
to
get
something
like
a
frequency
dependent
response
function,
then
you
could
do
this,
but
if
you
would
want
to
follow
your
state
as
it
decays
in.
B
B
F
F
F
A
F
C
A
So
what
is
the
difference?
The
difference
is
that
one
was
constructed
explicitly
to
reproduce
scattering
properties
at
higher
energies
as
well.
The
other
one
was
not
so
for
the
ground
state
that
shouldn't
actually
be
a
huge
difference,
and
it
shouldn't
really
be
an
advantage
of
using
one
or
the
other
for
ground
size
calculation.