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From YouTube: VASP Workshop at NERSC: Hybrid Functionals
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-Hybrids.pdf
Presented at the 3-day VASP workshop at NERSC, November 9-11, 2016
A
Salva
this
we
did
to
some
degree
yesterday
and
I've
told
you
that
that
one
of
the
one
of
the
key
things
that
we
do
is
is
map
our
whole
electron
problem
onto
onto
a
one
electron
description,
and
yesterday
we
talked
about
DFT
well,
another
one,
electron
theory
would
be
hartree-fock
theory,
so
we
can.
We
can
write
our
many-body
wave
function
as
a
Slater
determinant.
That
involves
is
one
electron
functions
that
we
saw
yesterday
right.
So
this
has.
A
This
has
a
few
interesting
properties,
and
one
of
the
properties
is
that
it
includes
the
Pauli
exclusion
principle
in
a
natural
manner.
Right
so
now,
two
electrons
of
the
same
spin
can
occupy
the
same
orbital,
and
that
is
expressed,
for
instance,
here
right.
So
if
these,
if
you
have,
if
you
put
two
electrons
in
with
the
same
spin
in
the
same
orbital,
this
will
be
essentially
zero.
A
A
That
has
some
consequences
for
the
way
we
solve
for
these
equations
and
obviously
a
sum
over
over
states
here.
Inside
of
this
potential
has
some
computational
consequences
as
well
as
it's
quite
a
bit
more
expensive
to
evaluate
the
action
of
such
a
potential
on
another
orbital
than
the
action
of
the
exchange
correlation
potential
in
density,
functional
Theory
on
orbital,
which
is
a
simple
point
by
point
multiplication
here
we
have
something.
A
So
what
you
see
here
about
I'll
discuss
how
this
is
how
this
is
done
in
a
plane
wave
code,
but
this
is
very
similar
to
to
what
we
do
for
the
heart,
free
energy,
so
so
solving
computing.
The
action
of
this
potential
on
the
orbitals
involves
FFTs
and
and
the
way
in
which
it
involves
f50s
I'll,
discuss
later
so
well.
That
is
hard
to
theory.
So,
but
what
I
will
speak
mostly
about
is
about
a
hartree-fock
DFT,
hybrid
theory.
A
So
is
there
because
we
could
use
hartree-fock,
but
that
is
for
for
our
purposes
of
limited
use,
because
we
actually,
for
instance-
and
let's
have
a
quick
look
at
what
what
the
density
of
states
and
hartree-fock
for
the
homogeneous
electron
gas
would
be.
And
let's
assume
that
this
is
indicated
of
what,
for
instance,
would
happen.
If
you
would
apply
this
theory
to
a
metallic
system,
then
we
see
that
in
Hartlepool
theory
at
the
Fermi
level,
in
home,
electric
gas
there's
a
cusp.
A
So
there's
no,
the
density
of
states
at
the
Fermi
level,
hartree-fock
theory
for
the
homogeneous
electric
gas
goes
to
zero
essentially
means
there.
There
are
no
metals
in
in
hartree-fock
right
so
and
that's
one
of
the
things
that
that's
already
a
good
indication
that
that
this
is
not
going
to
be
the
approximation
that
we
want
to
use.
So
what
we
are
going
to
use
actually
is
a
mixture
of
partly
for
candy
50
we're
going
to
be
adding
some
some
DFT
correlation
to
our
hartree-fock
expressions.
A
So
that
is
so
another
sort
of
hand
waving
argument
why
it
is
nice
to
to
use
mixtures
of
hartree-fock
and
DFT
as
a
functional
White's
would
be
a
good
idea
to
use
these
hybrid
functionals
is
sort
of
made
here.
So
we
see
here
for
a
number
of
materials,
we
see
the
bandgap
to
theoretical
and
computational
bandgap
versus
the
experimental
one,
so
this
line
would
indicate
perfect
agreement.
We
see
that
in
DFT
we
typically
underestimate
the
band
gaps,
so
this
is
essentially
always
the
case
and
in
heart
we
strongly
overestimate
them.
A
So
a
simple
mind
that
approximation
would
be
so.
Why
not
mix
the
two
together
and
end
up
on
this
line
right
so,
and
that
is
one
of
the
things
that
that
we
hope
to
achieve
by
using
these
hybrid
functionals
other
other
arguments
to
go
beyond
DFT
are
typically
well
band
gaps
is
one
that
this
point
is
made
here.
The
other
thing
is
that
that
art
in
DFT,
our
description
of
total
energies
and
total
energy
differences
saw
the
energetics
of
of
chemical
reactions,
for
instance,
is
by
no
means
very
accurately
described.
A
So
DFT
is
very
good
at
predicting
structures
and
the
like,
but
the
total
energy
differences
of
reaction
barriers,
reaction,
enthalpies
and
things
like
this-
are
definitely
not
at
of
comparison
to
experiment
that
we
would
like
yes
and
one
of
the
other
things
that's
missing
in
DFT,
but
that
will
unfortunately
still
not
be
addressed
by
I.
Would
functional
theory
is
the
fact
that
in
DFT
von
der
Waals
interactions
are
missing,
so
those
are
a
few
arguments
why
there's
a
definite
need
to
go
beyond
DFT
and
well.
A
Hybrid
functionals
are
our
first
step
beyond
DFT
in
that
sense,
so
per
definition,
these
exchange
correlation
functionals.
That
makes
a
certain
amount
of
folk
exchange
to
a
part
of
a
local
or
semi
local
density
functional.
So
we're
going
to
be
using
well
the
folk
exchange
in
combination
with
well
description
of
electronic
correlation
based
on
the
density,
functional
and
the
typical
ones
that
that
are
well.
Those
are,
they
have
become
very
popular
in
in
solid-state
physics,
are
called
p,
b0
and
h,
SE
and
PB
0.
So
the
recipe
is
very
simple.
A
So
it's
normal
in
the
sense
that
that
this
admixture
of
a
quarter
of
of
folk
exchange
is
based
on
on
a
theoretical
work.
So
it's
not
simply
fit
to
to
do
experiment
or
something
like
this.
Another
very
popular
functional
is
very
much
alike
pb0.
It's
called
Hz
or
H
SEC
or
3
or
HTC's.
There
are
six
there's
a
few
varieties
of
it
days.
Those
are
essentially
a
quarter
of
the
short
range
component
of
folk
exchanged,
3/4
of
the
short
range
component
of
PVE
exchange,
the
complete
long
range
component
of
PvE
exchange
and
PVE
correlation.
A
So
in
what
sends
short
range
and
long
range
dwell
in
in
this
work.
For
these
functionals,
the
one
over
R,
which
is
the
essential
operator
in
exchange,
one
over
r,
has
been
decomposed
in
short-range
part
and
a
long-range
part
by
min
children
of
an
error
function
and,
and
the
range
at
which
this
separation
is
done,
is
controlled
by
a
parameter
and
that
parameter
is
a
semi
empirical
one.
So
that
has
been
theirs.
A
It's
an
optimal
choice
and
has
been
fitted
to
to
accommodation
energies
for
for
a
test
set
of
molecules
right.
So
the
thought
behind
this
test
the
well
that
the
first
thought
behind
it
was
that
this
was
implemented
in
a
Gaussian
basis
code
and
if
I
do
X,
if
I
do
exchange,
which
is
computationally
intensive,
but
I'm
able
to
to
limit
the
range
of
of
my
interaction,
there's
less
integrals
that
I
would
have
to
have
to
compute.
So
this
was
conceived
as
being
a
cheaper
variety
of
pb0
actually,
but
it
has
some
qualities
of
its
own.
A
Actually
so
these
days
it
is,
it
is
cheaper
to
use
this
than
to
use
pv0
and
a
show
I'll
show
you
why
also
in
plain
life
counts,
but
in
fact
this
has
some.
Some
nice
properties
in
its
description
of
physics
as
well,
that
are
different
from
PV
is
0.
So
it's
a
bit
more
than
just
a
cheaper
variety
of
PVD
0,
but
it's
semi
empirical
in
that
sense,
so
the
one
that
that
that
that
comes
from
quantum
chemistry
average
functional
that
you
can
use
in
vast
as
well.
It's
b3
lib,
it's
the
semi,
empirical
functional.
A
A
Just
are
all
these
different
contributions,
just
to
say
that
this
functionalism
very
limited
use
in
solid-state
physics,
because
the
lyp
correlation
violates
a
certain
certain
limits
or
there's
a
way
that
that
correlation
functional
should
behave
for
the
homogeneous,
electron
gas
there.
We
can
sort
of
know
exactly
what
they
should
do
and
lyp
doesn't
do
it
and
that
hurts
quite
a
bit
in
even
in
solid
state.
A
So
this
is
a
very
popular
functional
from
quantum
chemistry
it
works
well
for
for
for
whole
bunches
of
molecules,
but
in
solid
states
it's
not
so
good,
ok,
so
coming
to
the
computational
aspect.
So
this
is
the
thing
that
we
that
we
would
like
to
evaluate
right.
So
Sol
is
written
it
down
before
you
saw
the
potential
which
was
orbital
dependent,
so
we
have
two
sums
of
Alfred
Alfred
orbitals
had
to
compute
our
folk
exchange
energy
and
we
have
a
1
over
R
minus
R
prime
kernel
or
this.
A
This
energy
is
this
range
separated
kernel.
This
short
ranged
one
right.
So
how
do?
How
do
we
typically
go
about
evaluating
such
a
thing?
So
the
first
thing
that
you
would
do
is
how
you
add,
two
orbitals
at
different
K
points
right
and
two
different
bands.
So
this
sum
is
over
two
x
over
all
K
points
and
two
x
over
all
occupied
bands.
So
this
is
quite
quite
more
and
it's
quite
a
bit
more
expensive
than
DFT
would
be
so
for
each
of
these.
What
we
call
overlap
densities
for
each
of
these
combinations.
A
We
do
an
FFT
and
get
this.
What
is
called
this
overlap
density
into
a
reciprocal
space,
and
then
you
can
easily
evaluate
the
potential
that
this
outlet
density
costs
right,
because
in
reciprocal
space,
one
over
R
minus
R
prime
times.
This
density
is
simply
given
by
the
by
the
by
the
Fourier
component
of
the
density
at
a
certain
g
vector,
divided
by
this,
the
length
of
this
vector
to
the
power
of
two.
So
you
get
this
potential.
A
That
is
the
x
change
potential
that
this
cost
by
this
overlap
density,
and
that
is
then
FFT
it
again.
So
there's
two
FFT
is
already
involved
back
to
real
space
and
there
you
can
then
evaluate
the
action
of
that
particular
potential
on
an
orbital
so
essentially
for
all
combinations
of
K
and
Q,
which
run
out
for
the
over
our
set
of
K
points
and
anime
and
an
M
which
are
our
bands
for
all
these
combinations.
A
So
how
does
it
scale?
Well?
Essentially,
it
scales,
essentially
it
scales
as
an
to
the
powers.
Let
me
see
so
you
have
the
number
of
balance
which
scales
as
the
as
the
size
of
our
system
and
the
number
of
K
points.
So
number
of
bands-
and
this
is
this-
is
essentially
scales
as
the
system
size
right,
so
the
size
of
FFT
grid
scales
as
the
system
size
and
in
the
limit
of
a
large
system
where
we
have
no
K
points.
A
We
end
up
here,
number
of
bands
system,
sized
system
size
and
this
essentially
system
size
as
well.
So
these
scales
cubically
with
respect
to
the
system
size
as
essentially
our
implementations
of
density,
functional
theory,
do
as
well
right
because
we
do
orthogonalization
of
the
wave
functions
with
respect
to
each
other,
and
this
involves
a
matrix,
diagonalization
and
matrix
diagonalization.
The
way
we
do
it
scales
cubic
ly.
You
don't
see
this
behavior
normally
for
DFT,
because
other
contributions
that
scale
better
have
much
larger
pre-factors.
A
B
A
A
You
ignore
the
local
part.
It
would
go
to
n
to
the
power
4
right,
but
in
all
practical
implementations
of
it
in
local
basis
sets
you
can
get
the
scaling
down
below
cubic
scaling,
because
you
can
exploit
the
fact
that
your
basis
functions
well
overlap
only
with
ones
that
are
close
by
right,
yeah
right,
so
I
would
like
to
introduce
this
concept
well.
This
is
this
is
a
few
slides
that
that
will
sort
of
show
you
why
it
is
cheaper
to
use
this
HSE
functional
than
pb0.
A
And
well,
this
dysfunction
was
was
was
first
implemented
for
and
for
code
that
uses
gaussian
basis
and
they
said
well.
We
limit
the
range
of
our
interaction.
That
is
why
we
will
have
less
integrals
to
evaluate,
because
this
orbital
doesn't
interact
anymore
with
an
orbital.
That's
that's
farther
away
if
I
limit
my
interaction,
a
similar
thing,
similar
saving
in
cost
in
computational
cost
we
have
for
HTC
as
well.
If
we
use
plane
waves
and
I
will
I
will
show
you
why
so
there's
two
things
to
remember
here.
So
we
have.
A
We
have
two
sums
over
over
K
points.
One
is
over
Q
and
one
is
over
K.
Well,
let's
assume
that
this
sum
over
Q
is
essentially
is
what
we
call
is
the
the
the
sampling
of
reciprocal
space
for
our
folk
potential
right.
So,
let's,
let's
sign
that
one
defector
Q
and
then
we
can
ask
ourselves:
can
we
can
we
limit
the
the
sampling
for
one
of
these
sums,
namely
the
one
we
used
to
represent
the
folk
exchange?
This
is
one
of
these
sums
over
over
K
points.
A
Can
we
limit
that
to
a
coarser
set,
and
that
is
shown
here?
What
what
the
effect
would
be
so
I
do
here,
a
calculation
for
I
think
this
is
aluminum.
Yes,
FCC
aluminum,
and
it's
done
at
well,
for
instance,
here
at
a
very
dense
grid
at
24
times
24
times,
24
K
points
and
then
I
start
to
coarse
grain.
One
of
these
sums
and
I
see
an
effect
in
the
energy
right,
so
deviation
from
from
the
result,
by
limiting
the
representation
of
folk
exchange,
only
a
folk
exchange.
A
A
So,
there's
a
connection
between
the
number
of
K
points
that
saw
the
K
point
density
sampling,
there's
a
connection
between
that
and
and
the
range
of
the
interactions
that
you
are
are
representing.
So
that
notice,
it's
a
general
general
connection
and
to
to
sort
of
explain
this
point
to
you
and
it's
going
to
be
a
hand
waving
explanation.
I
first
need
to
introduce
the
following
situation:
I'm,
not
sure
if
everybody
is
aware
of
this,
but
I
think
so
anyway.
A
So
if
we
use
a
if
we
use
a
small
cell,
let's
say
this
is
our
unit
cell
and
we
use
two
K
points
right.
So
the
first
K
point,
for
instance,
is
the
gamma
point
and
we
see
that
a
wave
function
in
this
particular
cell
is
simply
repeated
from
one
cell
to
the
next
yeah.
So
if
you
then
go
to
this
situation,
which
is
at
another
K
point,
so
this
would
be,
for
instance,
an
X
point.
We
see
that
the
sign
of
the
wave
function
from
one's
periodic
repeated
image
to
the
next
changes
right.
A
So
we
have
one
band
and
two
K
points,
and
these
are
the
functions
that
we
have.
If
I
now
double
the
size
of
my
cell
I
can
limit,
I
can
have
the
density,
the
sampling
density
of
of
K
space
and
end
up
with
mathematically
exactly
the
same
situation.
Right
because
now
I
have,
in
my
in
my
doubled
cell
I
will
have
a
wave
function
and
it
has
two
peaks
of
the
same
sign
and
I
will
have
another
option.
That
is
still
self
periodic,
where
we
have
the
sign
change
inside
of
my
super
cell
right.
A
So
now,
I
have
two
different
bands
in
my
in
my
in
my
larger
unit
cell
and
I
have
only
one
K
point,
and
this
is
mathematically
exactly
the
same
situation,
so
that
is
sort
of
put
in
in
a
general
fashion
here
so
unit
cells
versus
K
points
is
inversely
proportional
if
I,
if
I
have
n
K
points
along
a
certain
direction.
In
my
unit
cell
and
I
multiply
this
unit
cell
with
and
I
can
limit.
My
cap
on
sampling
by
a
factor
of
n
I
can
divide
it
by
a
factor
of
n
okay.
A
A
Then,
if
I
take
a
super
cell
of
the
this
unit
cell-
and
that
is
twice
this
interaction
range,
then
my
complete
interaction
will
be
contained
within
this
particular
cell
yeah,
and
that
means
that
actually,
that
I
can
use
this
particular
cell,
with
only
one
K
point
to
capture
all
aspects
of
this
particular
interaction
right
so
equivalently.
That
would
mean
that
I
could
that
I
could
go
back
to
a
single
unit
cell
and
sample
my
first
Brillouin
zone
at
two
endpoints
and
capture
all
aspects
of
this
particular
interaction.
A
So
there's
a
direct
connection
between
interaction
range
and
sampling
density
in
the
first
Brillouin
zone
right,
and
that
is
what
the
thing
that
helps
us
when
we
go
to
this
to
this,
to
this
folk
exchange
and
limit
its
its
range
of
interaction.
That
means
that,
as
we
limit
it,
we
need
only
that
that
we
need
a
less
dense
grid
of
of
points
in
reciprocal
space
to
represent
its
potential
in
a
satisfactory
manner.
So
we
can
coarse-grain
a
representation
of
this
interaction
because
of
the
fact
that
it's
that
this
interaction
range
has
been
limited.
A
A
A
So
this
is
this
is
one
of
the
things
that
I
spoke
about
yesterday.
So
what
we
see
here,
the
green
we
saw
the
blue
and
the
green
line.
Yesterday,
it's
a
comparison
off
of
the
atomization
energies
for
test
set
of
molecules
and
in
this
case
for
again
for
PvE
and
PvP
zero
compared
to
a
Gaussian
to
Gaussian
calculation.
So
the
comparison
between
the
two
codes
is
almost
perfect,
so
there
is
there's.
A
Hardly
any
difference
is
much
larger
than
one
kcal
per
mole,
but
we
see
that
with
respect
to
experiment,
there
are
still
quite
big
differences,
they're
smaller
for
for
the
hybrid
functional
than
for
PvE,
so
the
hybrid
functional
is
the
red
line
and
PV
is
the
black
line.
But
we
see
that
our
that
our
accuracy
is
still
far
away
from
chemical
chemical
accuracy.
A
A
Okay,
so
there's
a
whole
bunch
of
slides
that
I
did
I.
Think
I
will
I
will
know
this.
One
I
will
skip
so
itemization
energies
we
have
seen
this
is
I
will
skip
yes,
so
this
is
one
because
the
other
ones
they
they
are
just
sort
of
there
to
show
you
that
structures
we
get
from
hybrid
functional
theory
are
pretty
good
as
good
as
the
ones
from
DFT,
atomization
energies,
so
much
better
in
some
cases
somewhat
worse.
In
other
cases,
it's
not
a
real
big
step
forward.
A
So
the
real
positive
news
about
about
hybrid
functional
theory
is
actually
in
a
description
of
bandgaps,
and
that
is
what
we
see
here.
I
will
remember
the
first
picture
that
we
saw
we
had
all
these
blue
points
are.
Our
DFT
points
on
with
the
pv
functional
has
strong
underestimation
of
the
experimental
gap,
and
we
had
hartree-fock
sort
of
out
here
right
strongly
overestimating
it,
and
now
we
see
here
the
hybrid
functional
theory,
so
PV
is
0
and
HTC
zero,
3
and
they're
pretty
close
to
two
experiments.
A
So
it's
it's
a
nice
step,
nice
step
forward,
especially
if
you're,
if
you're
working
with
with
small
to
medium
sized
gaps
as
I,
hear
in
semiconductor
physics,
then
hybrid
functionals
will
present
a
real
nice
step
forward
for
you
and
there
we
see
as
well.
What
we
see
here
is
that,
and
the
advantage
of
using
this
of
using
this
H
is
a
functional
alpha.
P
V
is
zero.
I
said
that
one
is
cheaper
than
the
other,
but
that's
not
the
only
thing
it
has
some
nice
characteristics
of
its
own.
A
We
get
slightly
better
band
gaps
from
from
this
range
separated,
hybrid
functional
than
from
PvE
0,
and
in
the
talk
about
GW
there's,
a
small
picture
that
sort
of
explains
white
white
is
there's
some
physics
behind
it.
Why
we
do
actually
get
a
better
description,
especially
for
small
gap
systems
with
HSC
than
with
PvE
zero.
So
this
is
a
very
nice.
B
A
A
Well-Well
pbft
always
underestimates
the
band
gabs
and
there's
a
there's,
a
a
world
of
literature
explaining
why
this
is
so.
It's
not
something
that
I
thought
I
could
regurgitate
here,
unfortunately,
for
the
other
matter
is
I
mean
we
saw
that
that
hartree-fock
strongly
all
four
estimates.
Band
caps,
there's
explanations
for
that
as
well,
and
what
we
see
here
is
the
effect
of
the
of
the
admixture.
And
yes,
there
is
reasons
why
band
gaps
come
especially
in
this
particular
part
of
the
of
the
gap.
A
Size
come
out
very
well
with
HSC,
and
that
will
be
can
sort
that
can
be
explained.
I
will
I
will
show
you
this
later
on
when
we
start
looking
at
a
dielectric
screening
in
somewhat
more
detail,
because
the
thing
is
that
what
we,
what
we
would
like
to
use,
we
could
have.
We
would
like
to
use
here.
We
at
mix
one
quarter
of
folk
exchange
over
the
whole
range
right
and
we
simply
add
mix
one
quarter,
and
this
this
mixture
factor
should
actually
be
different
as
we
move
to
to
larger
gap
sized
systems.
A
So
because
here
you
see
that
the
hybrid
functional
still
strongly
underestimate
the
band
gaps
for
large
gap
systems,
one
could
repaired
is
by
simply
adding
more
folk
exchange.
You
would
move
closer
to
this
to
this
gap,
and
that
is
something
that
you
can
and
that
you
can
argue
from
from
the
dielectric
property.
So
if
you
would,
if
you
would
use
a
correctly
screened
exchange
interaction
screened
by
by
the
true
dielectric
properties
of
the
system,
then
you
would
have
this
well.
A
You
would
have
a
variable
variable,
admixture
of
folk
exchange
over
the
whole
range,
and
then
you
would
be
sort
of
as
close
to
experiment
everywhere
so,
and
that
is
a
lettuce
that
is
exactly
the
thing.
So
it
is
this
variable
at
mixture
determined
by
the
by
the
true
dielectric
properties,
or
a
description
of
the
dialect,
dielectric
properties
of
the
system.
That
is
the
essence
of
what
GW
does.
So
what
we'll
come
back
to
this
later?
Okay,
yeah
sure
sure.
C
A
No,
so
very
good,
a
very
good
boy!
Well,
let's
look
here
at
gallium,
arsenide
right
so,
for
instance,
so
quite
a
bit
of
a
left
and
here
sink
or
sink.
What
is
it
sink?
Solenoid,
zinc
oxide
should
be
still
pretty
zinc,
oxide
right,
yeah
sink
oxide,
so
no,
no,
unfortunately
not,
but
it
it's
prone
to
do
it's
prone
to
do
quite
well
for
small
and
medium
sized
lab
systems.
Yes,.
A
So
that
is
something
that
that
so
we
don't
have
particular
tudo
potentials
generated
to
be
used
with
hybrid
functionals.
We
do
have,
as
we
spoke
about
yesterday.
We
do
have
sets
of
pseudo
potentials
that
are
that
are
thought
to
be
used
with
in
connection
with
GW,
but
for
hybrid
functionals,
you
see
mostly,
you
would
simply
use
the
PBE
potentials.
With
these
functionals
I
mean
to
a
very,
very
large
degree.
These
functionals
are
still
being
eaten
right,
so
there
there's,
like
3/4
of
them
or
more,
is
still
PvE.
D
A
Unfortunately,
and
that
and
I'll
go
to
that
the
particular
case
later
d,
if
the
DFT
description
of
metallic
systems
is
better
than
the
hybrid
functional
description
of
metallic
systems,
so
these
are
not
original.
Czar
are
nice
for
a
whole
bunch
of
systems,
but
they
are
not
universal
so,
and
that
is
one
of
the
one
of
the
points
that
so
yes,
that
I
would
like
to
make
here
on
these
slides.
So
this
is
a
long.
This
was
a
long-standing
long-standing
problem.
A
I
should
say-
and
this
is
an
archetypical
archetypical
system-
that
people
have
been
looking
at
quite
intensively,
so
see
how
it's
option
on
on
D
metallic
services
and
in
DFT
we
had
incorrect
predictions
that
CEO
prefers
the
whole
outside
and
and
the
the
absorption
energies
were
off
by
quite
a
bit,
so
there
were
large
errors
in
the
absorption,
energies
and
I
think
this.
What
do
we
see
here?
So
this
is
see.
A
So
there
was
lots
of
hope
when
we
started
out
with
this
hybrid
functional,
so
it
was
a
big
hope
that
that
they
would
get
that
right,
because
people
said
okay.
Why
do
why
does
this
come
out
wrong
in
DFT?
Why
do
we?
Why
do
we
have
an
incorrect
description
of
the
site?
Preference,
for
instance,
and
people
blame
the
fact
that
DFT
doesn't
give
you
a
good
description
of
the
molecule
right?
So
we
have
we
have
in
the
CL
molecule.
A
So
blame
it
blame
it
on
the
DFT
description
of
the
co
molecule
and
hybrid
functionals
do
quite
well
for
the
electronic
structure
of
these
small
molecules
right,
so
they
would
sort
of
fit
to
this,
and-
and-
and
we
have
seen
this-
that
their
atomization
energies
of
such
small
molecules
come
out
much
better.
So
there
was
high
hopes
that
this
is
such
a
particular
setup
where
we're
in
essence,
we
have.
A
We
have
two
extremes
right,
so
we
have
completely
delocalized
metallic
States
and
we
combine
this
with
sort
of
strongly
localized
molecular
type
states,
and
the
hope
was
that
hybrid
functionals
would
do
well
because
of
the
fact
that
they
do
much
better.
They
give
a
much
better
description
of
the
molecular
States.
Well,
this
hope
was
was
unfortunately
idle.
So
we
do
see
that
for
some
for
some
some
of
these
surfaces,
sosial
on
copper,
these
hybrid
functionals
PV
is
zero
and
HTC
0-3
do
quite
well.
So
we
get
the
right
side
preference.
A
We
get
a
reduction
in
the
absorption
energy
get
much
closer
to
experiment.
However,
when
we
then
go
to
something
sort
of
the
same
for
rhodium,
although
here
the
size
of
the
absorption
energy
moves
in
the
wrong
direction
is
even
stronger
over
estimation,
but
at
least
the
side
preference
is
correct.
If
you
don't
go
to
palladium,
we
see
that
not
even
the
side
preference
comes
out
right
so
unfortunately,
and
that
is
that
is
sort
of
telling
you
already
so
did
this.
A
So
we
have
two
things:
we
have
an
overestimation
of
the
metallic
the
metallic
D
bandwidth
in
in
these
hybrid
functionals
and
a
down
down
shift
of
the
D
band
Center
in
copper,
sort
of
counters
it.
So
there
we
see
it
there.
We
have
a
nice
description,
but
in
the
other
cases
this
overestimation
of
metallic
bandwidth
will
sort
of
restore
this
offer
estimation
of
the
back
bonding
again
and
the
description
is
not
good.
So,
yes,
that
was
sort
of
a
blow,
but
that
is
that
is
what
what
we
are
at.
A
So
this
is
nice
if
you
are
in,
for
instance,
in
semiconductor
physics,
this
is
very
nice.
If
you
things
like
you
studied
defects,
where
you
would
like
electrons
to
localize
at
D.
If
T
is
bad
at
locking
localizing
electrons
at
at
defects,
DFT
for
first
delocalized
state
in
in
a
in
a
general
way
of
speaking,
if
you
would
use
hybrid
functionals
there,
you
would
tend
to
do
much
better,
because
this
hartree-fock
part
of
the
description
likes
to
localize
electrons.
A
A
This
is
a
sort
of
a
computational
point
now,
because
the
way
we
do
band
structure
normally
is
we
would
for
a
DFT.
We
would
generate
a
self-consistent
charge
density,
so
we
take
some.
Some
k
point
grid
a
sufficiently
dense
one,
but
a
regular
one
and
do
a
do
a
ground
state
calculation.
Then
we
take
the
charge
density.
A
The
self-consistent
charge
density
that
results
from
this
calculation
read
it
in
at
the
second
calculation,
keep
it
fixed
throughout
and
in
this
second
calculation
we
compute
the
eigen
value
spectrum,
add
a
whole
bunch
of
K
points
along
these
high
symmetry
lines
right.
Why
do
we
do
it
like
this?
We
do
it
like
this,
because
you
couldn't
you
couldn't
really
compute.
A
You
couldn't
do
a
do:
a
reliable
ground
state
calculation
using
the
K
point
sampling
corresponding
to
these
high
symmetry
lines
right,
because
you
would
have
a
few
K
points
along
a
line
and
then
it
would
move
along
another
direction,
but
you
don't
happen.
A
truly
nice
homogeneous
sampling
of
your
breiman
zone,
then
so
the
charge
density
associated
with
with
that
particular
sampling
along
high
symmetry
lines
is
bogus.
So
you
shouldn't
use
it
right,
so
we
use
the
charge
density
from
from
a
previous
calculation
to
do
this.
A
Well,
that
is
now,
unfortunately,
for
these
hybrid
functionals
no
longer
possible,
because
our
our
potential,
so
part
of
our
Hamiltonian
doesn't
only
depend
on
the
density,
so
it
could
read
in
the
density,
but
we
have
a
potential
that
that
depends
on
the
orbitals.
As
well
right,
so
so
there's
a
way
around
this.
So
this
is
the
standard
procedure
right.
So
what
doesn't
spoke
about
first
computer
density,
then
in
a
second
run,
you
fix
the
density
with
this.
A
Our
charge
is
11
and
you
use
a
bunch
of
K
points
in
this
case,
along
a
line
from
from
G
to
X,
for
instance,
and
you
could
plot
it
and
what
we
do
to
compute
band
structure
for
hybrid
functionals
is
the
following.
We
do
a
standard
standard,
DFT
calculation
using
a
conventional,
uniform
k,
point
mesh
and
then
there's
a
file.
That's
called
a
bed
set
k
PT
that
contains
the
summary
symmetry
reduced
k,
points
that
were
used
in
the
standard
calculation,
which
was
a
DFT
calculation.
A
So
those
are
these
points
and
also
the
weights
associated
with
them
right,
because
this
is
the
irreducible
part
of
the
Brillouin
zone
and
also
the
symmetry
we
choose
points
and
also
that
the
weights
associated
with
the
symmetry
reduction
and
then
what
we
do
is
we
add
a
whole
bunch
of
points
to
this
file
and
those
correspond
to
points
along
the
high
symmetry
lines
where
we
are
interested
in
item
values.
Eigen
value
the
dispersion
of
the
bends
along
this
line,
and
we
add
them,
but
we
add
them
with
zero
weight.
A
So
we
will
get
solutions
at
these
K
points.
So
look
at
band
energies
at
these
guy
points,
but
they
will
not
contribute
to
the
density
and
they
won't
contribute
to
the
for
potential.
So
that's
sort
of
a
trick.
So
these
bands
that
go
sorry.
These
K
points
that
correspond
to
a
regular
grid.
They
will
build
up
to
potential
they
will.
E
A
D
D
A
There's
one
thing
that
you
can't
do,
and
that
is
that
is
one
thing
to
remember
what
you
cannot
do.
You
cannot
do,
oh,
that
this.
That
is
wrong
on
this
slide
very
nice.
So
what
you
actually
cannot
do
you
can't
do
start
with
a
step
with
a
hybrid
functional
calculation
here,
so
you
cannot
do
a
regular,
hybrid,
functional
calculation
and
then
restart
and
add
these
other
K
points.
A
A
It
will
see,
there's
no
gradient
on
the
wave
function
anymore
because
you're
in
the
ground
state
and
it
will
not
optimize
the
states
at
these
points
that
are
along
for
the
ride,
because
there
is
no
right
so
now,
because
these
guys
here
are
the
solutions
at
the
sky
points
that
do
not
contribute
to
the
total
energy
they're
not
captured
by
by
the
convergence
criterion,
so
that
can
be
of
any
quality
that
can
be
phone
numbers
and
it
wouldn't
show
up
in
the
total
energy
so
from
one
step
to
the
other.
It
won't.
A
A
That
is
it
in
a
way
expensive
right,
because
if
you
would
start
from
pre
converged
BBE
functional
functions,
white
functions-
you
are
already
quite
a
way
along
along
right,
so
so,
but
you
couldn't
start
from
as
it
is
written
here.
I'm
very
sorry,
you
can't
start
from
from
a
hybrid
functional
calculation
from
a
regular,
hybrid,
functional,
right
yeah.
F
A
F
F
A
B
A
So
for
this
block
of
this
block,
that
represents
the
your
irreducible
wedge
that
you
that
you
copy,
can't
you
simply
copy
it
from
you
copy
this
file.
This
is
that
this
is
this
irreducible
part
of
the
blue
and
so
on.
You
copy
it
to
K
points
to
your
K
points,
file,
rename
it
and
then
add
the
points
that
you're
interested
in
and
adjust
the
number
of
points
accordingly.
B
A
Well,
it
would
it
would
so.
Symmetry
comes
in
at
the
point
where,
for
instance,
the
density
density
is
computed
right,
so
there
these
guys
are
ignored
because
of
the
fact
that
their
weight
is
zero.
So
you
could
do
all
kinds
of
symmetry
operations
on
them,
but
it
doesn't
end
up
in
a
result
because
they're
weighted
with
zero
weight.
So
so
the
fact
that
this
does
not
reflect
the
symmetry
in
any
way
doesn't
show
up.
A
C
A
C
A
Is
a
plan
to
support
3.0
yeah
III
met
average,
most
ophea's
at
some
point
in
the
past
few
months
ago,
and
he
sat
yard
he
he
knew
that
that
we
had
trouble
supporting
2.0
and
he
said
well
hold
off
on
trying
that
now
I
said
yeah.
I
should
really
do
this
and
he
said
hold
off
because
we're
going
to
release
3.0
and
there's
again
a
slight
slight
change
in
the
API.
So
sorry
I
will
I,
will
support
3.0
and
and
we'll
skip
2.0,
yes,
yeah,
actually
that
that
is
the
next
slide.
C
A
C
G
A
So
so
the
Polly
exclusive
exclusion
principle
is
in
hartree-fock,
so
it's
not
a
correlation
effect.
Yes
and
there's
probably
people
that
will
disagree
with
this
definition,
but
I
think
it's
a
very
nice
definition.
It's
a
very
clean
definition
of
correlation
and
as
I
understood
as
I
understand.
Let's
say
that
is
the
history
of
the
field.
It
makes
some
sense
to
be
fine.
It
like
this
because
of
the
fact
when
hartree-fock
was
conceived
of
yeah
everything
else
is
correlation,
so
what
is
still
missing
is
coronation.
A
So
yes,
what
so?
What
so
did
the
part?
So
the
computation
of
the
of
the
action
of
the
potential
on
the
orbitals
has,
in
its
entire,
has
almost
entirely
been
ported
to
GPU
and
people
do
actually
report
nice
speed.
Ups
I
I'm
not
really
willing
to
put
my
hand
into
the
fire
and
called
numbers,
but
you
do
get
I
think
you
do
get
nice
speed.
Ups
with
with
the
current
implementation
for
this
part,
because
it's
so
cool,
it's
quite
compute
heavy
right.
A
A
It
always
I
guess
it
always
depends
on
the
size
of
your
system.
I
have
not
been
able
to
find
one
small
system
where
GPU
gives
you
a
real
speed-up,
so
there's
a
matter
of
overhead
involved
always
but
for
large
systems.
You
should
really
get
decent
speed.
Ups
for
these
compute
heavy
heavy
parts
of
the
code,
mm-hmm.
G
A
C
A
Actually
III
I
would,
you
would
have
to
do
both
I
would
say,
and
you
would
do
MP
2
on
top
of
hartree-fock
I,
don't
know
how
you
would
use
MP
2
to
compute
the
exchange
energy,
but
might
be
that
I.
That
I
misunderstand
the
question,
but
you
would
add,
you
would
add
MP
2
on
top
of
hartree-fock
2,
because
it
gives
you
part
of
the
correlation
energy.
A
Okay,
good,
so,
let's,
let's,
let's
continue
with
a
bit
about
this,
so
how
long
one
and
a
half
hours
right,
so
okay,
good
I'm,
losing
track
again
as
well.
So
yes,
so
another
option
to
do
band
structure
is
through
through
the
interface
to
vast
to
one
year
990
and
to
construct
maximally
localized
one
year
functions
out
of
your
block
orbitals
and
then
use
the
functionality
of
of
one
year.
92
block
band
structures.
So
you
can
you
construct
localized
functions
out
of
your
block
orbitals
and
then
use
them
to
construct
block
functions
at
arbitrary
K
points.
A
A
So
the
underlying
data
that
you
offer
is
still
the
eigen
values
at
the
K
points
of
your
regular
grid,
and
then
this
is
a
clever
way
of
Fourier
interpolating
between
the
data
points
that
you
have
now,
because,
normally,
if
you,
if
you
would
do
band
structure,
I
mean
interpolation,
is
easy.
If
you
know
which
points
to
connect,
you
can
always
throw
a
function
through
it.
A
The
trouble
is
always
that
from
one
K
point
to
the
other,
you
don't
know
how
which
bands
to
connect
to
which,
right
you
don't
know
how
didhow
the
order
of
bands
with
similar
character
might
change
from
one
K
point
to
the
other,
so
how
to
connect
them
same
thing.
Actually,
if
you
do
a
band
structure
with
with
one
of
the
other
methods
that
I
described
right,
so
I
can
take
a
bunch
of
K
points
at
some
point.
A
There
might
be
a
few
close
together
and
you
don't
know
whether
you
should
let
them
cross
or
whether
you
would
have
been
avoided
crossing
from
one
from
okay
point
to
the
other.
This
gives
you
away
this.
This
is
sort
of
a
way
of
food,
ei
interpolation
connected
with
state
following
so
you
would
know
to
which
point
connects
to
which,
and
then
you
fully
I
interpolate
interpolate,
between
the
points
that
you
have.
That's
the
essence
of
this
of
this
particular
way
of
doing
band
structure.
A
A
Equations
I
made
the
point
that
we
could
do
this
by
computing,
the
gradient
and
directly
optimize
the
wave
functions
in
a
direction
that
minimizes
the
total
energy,
or
that
we
can
could
use
this
self-consistency
cycle
and
that
actually
it
was
preferable
to
use
this
self-consistency
cycle.
That
is
unfortunately,
now
no
longer
strictly
true,
and
we
have
here
for
these
hybrid
functionals,
we
return
to
to
the
use
of
direct
optimization,
and
that
is
because
what
we
had
in
the
self-consistency
cycle.
A
So
density
mixing
will
work
in
many
cases
so
and
so
the
usual
algorithms
that
you
would
use
like
Davidson
or
RM,
we'll
work
in
many
cases
for
for
hybrid
functions
as
well,
especially
to
Davidson,
but
it's
not
guaranteed
to
work,
and
actually
it
turns
out
that
there's
a
way
to
do
this
in
indirect
optimization
that
at
least
for
hybrid
functionals
is
even
faster
than
than
doing
the
Davidson
optimization
right.
So
the
problem.
We
said
why,
and
that
was
why
we
went
to
this
self-consistency
cycle
in
combination
with
density.
A
We
need
for
it
for
this
part
of
the
gradient.
We
need
to
find
a
search,
Direction
unitary
transformation
between
the
orbitals
between
our
current
orbitals,
between
the
orbitals
of
our
current
subspace
and
the
search
Direction
is
given
in
through
perturbation
theory.
You
can
write
it
like
this
right,
and
this
is
exactly
the
time
that
the
term
that
is
prone
to
to
charge
washing
and
now
we
will
use
a
will
use
a
density
mixing
scheme
to
only
determine
this
part.
A
A
So
we
have
a
bunch
of
orbitals
that
give
us
an
Hamiltonian
with
a
kinetic
energy
and
a
local
potential
and
an
Evoque
potential
right,
depending
not
on
the
density,
but
on
the
orbitals
and
will
determine
a
subspace
rotation
matrix
that
diagonalizes
this
Hamiltonian
recompute
occupancies
and
things
like
this
transform.
The
orbitals
partial
cupen
sees
rely
on
on
on
density,
so
that
gives
us
a
density,
rely
on
density,
mixing
and
iterate
until
we
find,
and
until
we
find
a
stable
point
right,
but
we'll
keep
this
term
will
keep
fixed.
A
So
we
do
density
mixing
only
with
respect
to
this
part
of
the
Hamiltonian
all
right
and
it's
the
electrostatic
part
that
is
prone
to
charge
washing.
So
we
don't,
we
don't
really
valuate
the
four
potential
all
the
time.
That
would
be
very
expensive,
we'll
use
density,
mixing
to
find
to
only
search
for
an
optimal
subspace
rotation
that
gives
us
a
stable
density
and
we'll
use
that
one
in
in
the
expression
for
our
gradient
for
our
gradient
in
the
direct
optimization.
A
A
Well,
use
we'll
use
the
gradient
so
that
in
each
step,
there's
only
one
evaluation
of
the
four
potential.
This
is.
This
is
a
nice
advantage
with
respect
to
kilo
of
space
methods.
So
to
these
methods
like
Davidson,
where
we
have
to
apply
within
one
iterative
refinement
of
the
wave
function,
we
have
to
apply
the
Hamiltonian
very
often
to
the
orbitals
that
we
have
and
applying
the
Hamiltonian
to
the
orbitals
means
computing,
the
action
of
the
fuc
potential
and
orbital.
So
it's
very
expensive
right
in
its
direct
optimization
methods,
you
compute
a
gradient
which
means
computing.
A
The
action
of
the
potential
new
orbitals
only
once
and
then
follow
the
gradient.
It's
cheaper
in
that
sense,
but
we
do
add
this.
This
additional
loop
inside,
where
we
search
and
we
use
density,
mixing
to
search
for
for
an
optimal
subspace
rotational
matrix
the
density
mixing
to
get
around
to
charge
washing.
So
that's
the
full
mixed
scheme
and
construct
a
Hamiltonian
from
the
current
orbitals.
A
We
have
an
inner
loop
that
that
keeps
the
four
potential
fixed
and
where
we
only
search
for
an
optimal
subspace
rotation
using
density
mixing,
and
then
we
minimize
along
the
search
Direction
defined
by
well.
This
is
the
part
of
the
gradient
outside
of
a
subspace
and
it's
optimal,
rotational
matrix
inside
our
subspace,
and
we
do
well
we'll
repeat
this
and
this
inner
loop
and
and
a
loop
around
it
until
we
reach
convergence
right
so,
and
that
is
shown
here
is
a
very
similar
picture
that
we
saw
before
right.
A
So
we
have
here-
and
these
were
these
elongated
elongated,
FCC
ayran
cells
and
where
we
had
big
trouble
converging
the
electronic
system
using
direct
optimization.
Actually,
this
is
now
the
mixed
scheme.
So
this
is
direct
optimisation,
but
it
uses.
This
is
the
second
loop,
the
second
trick
to
to
get
around
charge
sloshing
in
the
Subspace
rotational
part
that
depends
on
on
density
mixing,
and
we
see
that
that
that
really
really
converges
quite
nicely.
A
F
A
A
So
if
you
go,
if
you
would
do
b3
lip
for
for
a
simple
metal
where
you
have
a
density
that
it's
very
homogeneous
yeah,
the
fact
that
that
your
correlation
functional
doesn't
adhere
to
this
to
the
to
the
homogeneous
electron
gas
limit
and
this
lyp
correlation
doesn't
adhere
to
this
particular
limit.
Hurts
you
a
lot
if
you
go
to
the
molecular
world
where
this
came
from,
their
systems
are
not
so
so
homogeneous
electron
gas
like
so
they
don't
see
this.
E
A
It
works
well
for
their
systems,
I
guess!
Oh
yes,
yes,
I
mean
you
shouldn't
forget
I
mean
something
like
the
three
lip
has
been
has
so
there's
this
mixture
of
a
bunch
of
functional
components
that
has
been
optimized
against
a
test
set
against
properties
of
a
whole
bunch
of
molecules.
So
so,
at
least
for
any
anything
that
is
very
much
like
this
test
said
well,
it's
I
could
envision
it
to
be
superior.
C
C
A
Have
to
set
else
abroad-
yes,
sorry
yeah,
because
that
switch
is
on
this.
This
second
loop,
all
right!
This
is
not
on
this
slide.
Okay!
Yes,
yes,
it's
a
very
important
tag,
because
that
is
exactly
the
one
that
switches
it
switches
it
on.
It's
probably
not
on
this
slide
because
it
used
to
be
the
default,
so
you
could
only
switch
it
off,
but
these
days
you
have
to
switch
it
on.
A
Yes,
because
there's
many
systems
there's
still
many
systems,
especially
if
you
have
a
decent-sized
gap
where
charge
sloshing
is
not
such
a
problem
or
if
you
have,
if
you
don't
have
a
cell,
that
is
very
long
in
in
a
particular
direction.
You
wouldn't
run
into
this
problem
episode
so
often,
yes,
so
the
default
used
to
be
that
it
was
switched
on.
But
now
it's
switched
off
per
default.
You
can
switch
it
on
with
this
else.
Ipod
touch
yeah.
B
A
B
A
I
think
for
SP,
this
problem
is
a
base,
is
much
smaller
yeah.
Yes,
so
it's
these
states
that
that
the
hybrid
from
functional
tends
to
localize
very
strongly
like
like
these
states,
much
more
strongly
than
then
DFT
does
where
DFT
mostly
underestimates
localization,
that
are,
that
are
strongly
affected
by
defect
that
you
use
a
hybrid
functional.
A
C
A
So
in
K
points
it
scales,
quadratically,
with
respect
to
the
number
of
K
points
that
you
use
so
for
the
number
of
atoms
we
saw
that
the
underlying
scaling
was
cubic
right.
So
if
you,
if
you
end
up
in
the
limit
of
large
systems,
then
und
you
see
the
fundamental
scaling
which
is
cubic.
It's
the
number
of
states
times
the
number
of
states,
times
n
log
n
for
the
f50s,
with
with
some
horrible
pre-factor
and
this
n
log
n
is
something
like
n.
A
C
A
Yes,
so
I
did
this
one
I
always
I'd,
always
ask
myself
why
I
have
is
right,
so
I
immediately
got
here.
Yes,
that
is
these
transition,
metal,
monoxides,
they're,
quite
interesting
systems
in
this
respect,
because
so
what
have
people
been
using
so
DFT
is
unsatisfactory
for
these
systems,
so
you
have
magnetic
moments
that
are
that
are
too
small
and
lattice
constants
that
are
too
small
and
and
people
have
been
using
DFT
plus
you
on
these
systems.
So
how
about
you,
onside
onside?
How
about
you
and
and
actually
so
what?
A
What
do
you
do
so
on
with
DFT
plus
you
you
you
on
side
well
within
the
PW
sphere,
for
instance,
you
do
something
that
is
hartree-fock
like
yes,
so
so
you
would
expect
it
with
hybrid
functionals.
You
would
get
an
effect
is
very
similar
without
without
having
to
choose
a
you
or
a
fit
fit,
some
parameter
to
experimental,
to
experimental,
experimental
ii,
known
properties
of
your
system,
and
that
is-
and
that
is
in
fact
the
case,
and
that
is
what
what
is
shown
here
and
so
in
LD
a
we
have,
for
instance,
for
manganese
oxide.
A
We
have
a
lattice
constant.
That
is
much
too
small.
We
have
a
magnetic
moment
is
much
too
small
and
we
have
hardly
any
bandgap
should
be
quite
a
is
quite
a
sizable
gap
in
experiment
and-
and
it
doesn't
have
this
in
in
LD
a
or
in
any
other
a
TFT
functional
right.
So
I
might
change
this
a
bit,
but
not
by
much,
and
if
you
look
at
and
what
you
get
so
you
could
repair
this
with
with
own
side.
A
C
C
A
So
well,
possibly,
but
but
there's,
but
then
of
course,
that
would
that
we
had
changing
this.
This
changing
is
the
screening
length
doesn't
only
affect
affect
the
cost
of
the
functional.
It
will
also
yield
other
results
right.
So
you
will
not
get
the
same
results
at
a
reduced
cost.
You
will
get
other
results
at
a
possibly
reduced
cost,
so
it
might
be
that
you
get
you
get
quicker
to
a
wrong
answer.
Then
I'm
impossible
to
say
so
this
the
screening
length.
Actually
it's
what
it's
it's
a
variable.
A
You
could
set
it,
but
it
has
for
HCC.
It
has
a
particular
value
right.
This
value
has
been
fitted
to
a
whole
bunch
of
test
systems,
so
so
they
did
bandgaps
for
a
whole
bunch
of
test
systems
and
then
and
then
fitted
band
caps
or
a
lattice
constants
I
can't
remember
anyway,
it
has
been
fitted
to
two
experimental
data
and-
and
so
it's
part
of
the
definition,
so
of
course
you
can
can
take
another
value
for
it,
but
you
won't
be
using
HSE
anymore.
Then.
A
Yes,
I
would
I
would
expect
it
to
to
act
much
like
it
does
now.
So,
for
instance,
here
if
this
is
one
of
the
problems
that
you
have,
if
one
of
the
problems
that
you
have
is
that
your
states
are
not
localized
enough,
you're
still
adding
parts
of
folk
exchange,
so
so
your
function
will
tend
to
be
more
yeah
will
tend
to
localize
elections
more,
but
but
I
I
think
it's
yeah.
It's
there's!
No
guarantee
that
that
that
it
will
that
it
will
give
you
a
good
result.
You
would
have
to.
A
You
have
to
look
at
experiment,
then
again
right,
which
is
which
all
all
semi-empirical
things
would
would
would
sort
of
the
same
need
you
have
with
all
semi
empirical
methods,
so
you
can
do
DF,
t,
plus,
u
and
and
then
there's
always
the
question.
So
what
on-site
energy
should
I
use?
What
on
site
you
should
I
use
and
yeah,
and
you
play
with
this
and
you
look
at.
Do
I
reproduce
my
magnetic
moments?
A
A
B
B
A
So
in
this
so
for
this
transition,
metal
monoxides
it
it
localized
system
more
strongly.
Yes,
that's
a
good
question.
You
caught
me
there,
but
it
does
tend
to
localize
them
and
it
does
increase
depending
on
existence.
But
yes,
no,
you
got
me
there.
I,
don't
have
a
quick
answer
for
you,
because
it's
true
right,
yes
yeah,
you
would
say:
ok
if
I
reduce
them,
I
would
reduce
hybridization
and
in
that
way,
reduce
this
person.
But
that
is
not
the
case.
B
A
D
A
My
experience
are
very
similar,
I
mean
that
that
is
so.
What
you
see
here,
for
instance,
in
this
table
which
which
these
are
like
this-
these
typical
systems,
where
you
would
use
L
di
plus?
U
right
so
I
think
without
the
I
plus
you
you
get
and
it's
an
oversight
that
it's
not
on
this
on
this
particular
table.
But
this
I
think
this
is
the
kind
of
agreement
that
you
can
reach
for
all
these
aspects,
so
I'm
sure
that
you
could
that
you
could
get
a
better
band
gap
with
with
another.
You.
D
D
D
C
A
C
A
B
A
C
A
So
there's
especially
for
magnetic
calculations
that
there's
a
few
things
that
are
very
important.
One
thing
is
that
you
would
have
to
always
initialize
your
your
magnetic
subsystem.
Alright,
so
I,
don't
know
you
shouldn't
rely
on
any
default.
I
think
that
per
default
the
code
will
simply
put
one
new
bar
on
each
atom
in
a
sort
of
a
ferromagnetic
way,
so
which
not
necessarily
has
anything
to
do
with
the
magnetic
structure
of
your
system,
so
initializing
it
in
in
a
you
know,
in
a
good
way.
A
So
if
you
have
some
knowledge
of
what
what
the
magnetic
order
should
be,
that
is
very
important
so
and
that
would
drastically
affect
convergence.
On
the
other
hand,
there's
it.
It
is
also
a
problem
that,
especially
if
you,
if
you
use
density,
mixing
I,
don't
so
I,
don't
know
what
kind
of
electronic
optimizer
there
they
are
using,
but
as
soon
as
you
as
soon
as
you
use
something
that
that
relies
essentially
on
density,
mixing,
the
magnetic
degrees
of
freedom
are
often
overlooked
by
the
mixer.
So
what
does
this
mean?
A
So
the
mixer
learns
something
about
a
response
of
your
system
that
starts
with
this
modal
function
and
that
it
improves,
with
every
step
that
it
makes
mixing.
It
learns
something
about
the
dielectric
properties
of
your
system.
It
will
do
such
a
thing
for
for
the
Magnetic
degrees
of
freedom
as
well,
that
the
magnetization
density
is
also
pushed
through
the
mixer
and
and
gets
looked
at,
but
the
dominant,
the
dominant
properties
that
are
learned
are
electrostatic
properties,
and
so
it
learns
more
strongly.
A
G
A
Point
I
think
it's
in
one
part
of
the
manual.
It
is
it's
advisable
to
to
go
away
from
the
Broyden
mixer
completely
and
then
use
straight
linear
mixing,
because
then
the
magnetic
subsystem
gets
pulled
yeah.
It
gets
pulled
on
the
same
level
as
the
SDS,
the
total
charge,
and-
and
it
might
be
that
then
convergence
is
more
rapid.
A
Yes,
it
is
it's
not
something
that
I've
done
I
strongly
advise
that
one
does
because,
of
course,
you
sort
of
enter
and
you
enter
into
the
semi-empirical
domain
again.
So
it's
not
it's
not
the
nicest
thing
to
do,
but
but
there
is
some
justification
for
doing
it
as
well,
and
we'll
see
this
later
on
that
there
is
a
connection
between
the
fraction
of
of
exchange
that
we
use.
So
this
one
quarter.
A
For
instance,
why
is
this
one-quarter
good
for
a
whole
group
of
of
materials,
and
that
is
because,
because
of
the
screening
properties
of
these
materials
and
we'll
see
this
in
connection
with
with
GW,
that
this
1/4
is
sort
of
in
the
range
where
we're
when
important
contributions
in
GW
and
GW
is
essentially
a
screened
exchange.
Interaction
where
we're
in
that
area,
GW
is
sort
of
behaving
like
this
one
1/4,
so
the
dielectric
properties
in
this
one
quarter
of
exchange
they
they
provide
a
reasonable
match
if
you
didn't
go
to
larger
band.
A
A
Yes
I,
so
it's
hard
now
to
quickly
describe
what
DF,
T
plus
U
is
I
mean
I.
Don't
have
any
slides
here
to
support
that,
so
I
would
suggest
that
it's
not
not
so
hard
to
find
out.
But
what
is
the
cost
of
it?
The
cost
is
essentially
the
same
as
doing
DFT
calculations,
so
that
is
of
course,
a
very
attractive,
and
if
this
is
if
this
is
a
an
approximation,
that
works
well
for
your
class
of
systems
and
and
for
that,
I
would
say
would
have
to
look
in
the
literature.
A
So
it's
the
physics
that
are
that
are
going
on
in
your
system,
anything
that
are
sort
of
captured
by
by
something
like
DFT
plus
by
a
DFT
plus
new
approximation.
And
do
you
get
good
results
with
the
DFT
plus
you
then
then
I
I
could
imagine
using
that
instead
of
a
hybrid
functional,
because
it's
so
much
more
expensive
to
use
a
hybrid
functional.
A
A
So
that
would
remove
the
fact
that
that
you
were
so,
then
you
would
no
longer
be
using
a
semi
empirical
method.
It
would
put
it
on
an
opinion
Co
basis
or
at
least
on
a
DFT
basis,
but
sometimes
those
use
are
not
to
use
that
yield.
The
best
agreement
with
experiment
and
people
decide
not
to
use
them,
then
yeah
and
prefer
to
stay
with
the
with
the
semi
empirical
nature.
A
I
would
say
that
I
mean
in
LDI,
plus
you
it.
It
would
strongly
depend
on
you
right
I
mean
you
could
probably
open
up
more
or
less
open
up
a
bandgap
in
any
system.
If
you,
if
you
yeah,
because
this
what
this,
what
does
this
you
sort
of?
Do
it
sort
of
sucks
in
electrons
on
on
the
side
right,
so
it's
and
I
said
contracts
our
states
and
sucks
them
into
the
spheres
very
hand
waving
these
speaking,
so
you
could
sort
of
it.
This
way
open
up
a
gap
in
in
many
systems.
A
If
you
make
this
interaction,
strong
enough
right
so
I
mean
that
that
is
yeah.
So
you
can,
you
can
sort
of
yeah.
You
can
sort
of
do
do
a
lot
of
injustice
to
to
the
physics
of
your
system
with
with
these
methods
and
a
hybrid
functional
doesn't
give
you.
This
is
leeway
right,
so
it
might,
it
might
maybe
wrongly
predict
a
system
to
be
insulating
where
it
should
be
a
metal
could
be.
Why
not?
But
it's
not
simply
it's
not
something
that
you
that
you
tune
right.
So
yeah.
C
A
Yes,
I
I
would
yes,
the
problem
is
that
we
are
sort
of
in
between.
We
are
filling
the
wiki
and
so
there's
stuff.
That's
in
a
manual,
that's
not
in
the
wiki
and
there's
stuff
in
the
wiki.
That's
not
yet
in
the
manual.
So
I
would
advise
people
to
use
the
wiki
where
possible,
but
with
the
caveat
that
some
stuff
is
unfortunately
not
yet
incorporated,
the
wiki
is
definitely
more
up
to
date
with
some
respects,
but
not
it's
not
it's,
not
not.
Everything
that
is
in
the
manual
has
been
carried
over
into
the
wiki.