Pariser-Parr-Pople (P-P-P) model Hamiltonian has been used extensively over the years to perform calculations of electronic structure and optical properties of $\pi$-conjugated systems successfully. In spite of tremendous successes of \emph{ab initio} theory of electronic structure of large systems, the P-P-P model continues to be a popular one because of a recent resurgence in interest in the physics of $\pi$-conjugated polymers, fullerenes and other carbon based materials. In this paper, we describe a Fortran 90 computer program developed by us, which uses P-P-P model Hamiltonian to not only solve Hartree-Fock (HF) equation for closed- and open-shell systems, but also for performing correlation calculations at the level of single configuration interactions (SCI) for molecular systems. Moreover, the code is capable of computing linear optical absorption spectrum at various levels, such as, tight binding (TB) Hueckel model, HF, SCI, and also of calculating the band structure using the Hueckel model. The code also allows the user to solve the HF equation in the presence of finite external electric field, thus, permitting calculations of quantities such as static polarizabilities and electro-absorption spectra. We demonstrate the capabilities of our code by performing calculations of various properties on conjugated systems such as $trans$-polyacetylene ($t$-PA), poly-\emph{para}-phenylene (PPP), poly-\emph{para}-phenylene-vinylene (PPV), \textit{oligo}-acenes, and graphene nanodisks.
arXiv:0912.4576v1 [physics.comp-ph] 23 Dec 2009
A
general
purp
ose
F
ortran
90
ele troni
stru ture
program
for
onjugated
systems
using
P
ariser-P
arr-P
ople
mo
del
Priy
a
Son
y1
,
Alok
Sh
ukla2
Dep
artment
of
Physi s,
Indian
Institute
of
T
e
hnolo
gy,
Bomb
ay,
Powai,
Mumb
ai
400076,
INDIA
Abstra t
P
ariser-P
arr-P
ople
(P-P-P)
mo
del
Hamiltonian
has
b
een
used
extensiv
ely
o
v
er
the
y
ears
to
p
erform
al ulations
of
ele troni
stru ture
and
opti al
prop
erties
of π
-
onjugated
systems
su essfully
.
In
spite
of
tremendous
su esses
of
ab
initio
theory
of
ele troni
stru ture
of
large
systems,
the
P-P-P
mo
del
on
tin
ues
to
b
e
a
p
opular
one
b
e ause
of
a
re en
t
resurgen e
in
in
terest
in
the
ph
ysi s
of π
- onjugated
p
olymers,
fullerenes
and
other
arb
on
based
materials.
In
this
pap
er,
w
e
des rib
e
a
F
ortran
90
omputer
program
dev
elop
ed
b
y
us,
whi
h
uses
P-P-P
mo
del
Hamiltonian
to
not
only
solv
e
Hartree-F
o
k
(HF)
equation
for
losed-
and
op
en-shell
systems,
but
also
for
p
erforming
orrelation
al ulations
at
the
lev
el
of
single
on guration
in
tera tions
(SCI)
for
mole ular
systems.
Moreo
v
er,
the
o
de
is
apable
of
omputing
linear
opti al
absorption
sp
e trum
at
v
arious
lev
els,
su
h
as,
tigh
t
binding
(TB)
Hü
k
el
mo
del,
HF,
SCI,
and
also
of
al ulating
the
band
stru ture
using
the
Hü
k
el
mo
del.
The
o
de
also
allo
ws
the
user
to
solv
e
the
HF
equation
in
the
presen e
of
nite
external
ele tri
eld,
th
us,
p
ermitting
al ulations
of
quan
tities
su
h
as
stati
p
olarizabilities
and
ele tro-absorption
sp
e tra.
A
dditionally
,
it
an
p
erform
transformation
of
P-P-P
mo
del
Hamiltonian
from
the
atomi
orbital
(A
O)
represen
tation
(also
alled
site
represen
tation)
to
the
mole ular
orbital
(MO)
one,
so
that
the
transformed
matrix
elemen
ts
an
b
e
used
for
high
lev
el
p
ost-HF
al ulations,
su
h
as,
full
CI
(F
CI),
quadruple
CI
(QCI),
and
m
ulti-referen e
singles-doubles
CI
(MRSDCI).
W
e
demonstrate
the
apabilities
of
our
o
de
b
y
p
erforming
al ulations
of
v
arious
prop
erties
on
onjugated
systems
su
h
as trans -p
oly
a et
ylene
(t -P
A),
p
oly-p
ar
a
-phen
ylene
(PPP),
p
oly-p
ar
a
-phen
ylene-vin
ylene
(PPV),
oligo
-a enes,
and
graphene
nano
disks.
Key
wor
ds:
Hartree-F
o
k
metho
d,
self- onsisten
t
eld
approa
h
PPP
mo
del
Hamiltonian,
Mole ular
orbitals
P
A
CS:
31.15.xr,
31.15.Ne,
31.15.bu,
31.15.-p
Preprin
t
submitted
to
Elsevier
O tob
er
23,
2018
1
e-mail:
pson
y ph
y
.iitb.a .in
2
Author
to
whom
all
the
orresp
onden e
should
b
e
addressed.
e-mail:
sh
ukla ph
y
.iitb.a .in
2
Program
Summary
Title
of
pr
o
gr
am:
ppp.x
Catalo
gue
Identi er:
Pr
o
gr
am
summary
URL:
Pr
o
gr
am
obtainable
fr
om:
CPC
Program
Library
,
Queen’s
Univ
ersit
y
of
Belfast,
N.
Ireland
Distribution
format:
tar.gz
Computers
:
PC’s/Lin
ux
Linux
Distribution:
Co
de
w
as
dev
elop
ed
and
tested
on
v
arious
re en
t
v
ersions
of
F
edora
in luding
F
edora
11
(k
ernel
v
ersion
2.6.29.4-167)
Pr
o
gr
amming
language
use
d:
F
ortran
90
Compilers
use
d:
Program
has
b
een
tested
with
In
tel
F
ortran
Compiler
(non-
ommer ial
v
ersion
11.1)
and
gfortran
ompiler
(g
v
ersion
4.4.0)
with
opti-
mization
option
-O.
Libr
aries
ne
e
de
d:
This
program
needs
to
link
with
LAP
A
CK/BLAS
libraries
ompiled
with
the
same
ompiler
as
the
program.
F
or
the
In
tel
F
ortran
Com-
piler
w
e
used
the
A
CML
library
v
ersion
4.3.0,
while
for
gfortran
ompiler
w
e
used
the
libraries
supplied
with
the
F
edora
distribution.
Numb
er
of
bytes
in
distribute
d
pr
o
gr
am,
in luding
test
data,
et .:
size
of
the
tar
le
……
b
ytes
Numb
er
of
lines
in
distribute
d
pr
o
gr
am,
in luding
test
data,
et .:
lines
in
the
tar
le
…….
Car
d
pun hing
o
de:
ASCI
I
Natur
e
of
physi
al
pr
oblem:
The
problem
of
in
terest
at
hand
is
the
ele troni
stru ture
of π
- onjugated
systems.
F
or
su
h
systems,
the
ee tiv
e π
-ele tron
P-P-P
semi-empiri al
mo
del
Hamiltonian
prop
osed
b
y
P
ariser,
P
arr,
and
P
ople
oers
an
attra tiv
e
alternativ
e
as
ompared
to
the
ab
initio
approa
hes.
The
presen
t
program
an
solv
e
the
HF
equations
for
b
oth
op
en-
and
losed-shell
systems
within
the
P-P-P
mo
del.
Moreo
v
er,
it
an
also
in lude
ele tron
or-
relation
ee ts
at
the
singles
CI
lev
el.
Along
with
the
w
a
v
e
fun tions
and
energies,
v
arious
prop
erties
su
h
as
linear
absorption
sp
e tra
an
also
b
e
om-
puted.
Metho
d
of
Solution:
The
single-parti le
HF
orbitals
of
a π
- onjugated
system
are
expressed
as
linear
om
binations
of
the pz
-orbitals
of
individual
atoms
(assuming
that
the
system
is
in
the xy
-plane).
Then
using
the
hopping
and
Coulom
b
parameters
pres rib
ed
for
the
P-P-P
metho
d,
the
HF
in
tegro-dieren
tial
equations
are
transformed
in
to
a
matrix
eigen
v
alue
problem.
Thereb
y
,
its
solu-
tions
are
obtained
in
a
self- onsisten
t
manner,
using
the
iterativ
e
diagonalizing
1
e-mail:
pson
y ph
y
.iitb.a .in
2
Author
to
whom
all
the
orresp
onden e
should
b
e
addressed.
e-mail:
sh
ukla ph
y
.iitb.a .in
3
te
hnique.
T
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