590
A. V. Luzanov
which makes sense only for computations of G
QCTB
0
by (2). Here δ is an orbital
splitting parameter by which different orbital for different spins are introduced into
the TB scheme, thus taking into implicit account the π -electron correlation effects.
A further improvement is attained by combining QCTB and RHF models. The
approach is suggested in [21] and termed the extended quasi-correlated (EQC)
method. The preliminary results were given in [19] in terms of the quasi-correlated
long-range interaction (QCLRI) scheme which is identical to EQC from [21]. In this
case we construct the intermediate Fock matrix f [1] (also shifted by the Fermi energy).
This matrix is normally computed by using the TB density matrix (bond-order matrix)
P. Hence, we do not invoke any self-consistency procedure. The obtained intermediate Fockian f [1] is then renormalized [see (25)] and used straightforwardly in
computing G
EQC
0
by (2) with applying a formal Hamiltonian similar to (5):
h
EQC
⇒ [( f [1] )
2
+ δ
2
]/ f [1]
The explicit representation is provided by (26) and (27). The benefit of EQC is
owing to accounting for long-range effects, so that the drawbacks inherent to QCTB
(due to a short-range nature of TB) are removed. In doing so, π -correlation effects are
also presented in EQC via the previous splitting parameter δ. Hence, this approach
is more preferable, especially for nano-sized systems and singular π -structures.
It is also worth mentioning another recently developed model [19] based on the
variatonal treatment of electron detachment/attachment processes within the halfprojected Hartree-Fock (HPHF) method. The appropriate GF will be represented by
G
HPHF
0
. As seen from [19], among the models considered there, G
HPHF
0
is the best
but only for not too large systems because HPHF lacks a size-consistency.
At last, the complete account for all electronic effects is achieved by the π -electron
full configuration interaction (FCI) method [24]. The related approach for GF was
elaborated in [25]. The thus obtained G
FCI
0
can be qualified as a “gold standard“
in the molecular Green’s function theory. Unfortunately, FCI is feasible for small
systems only (e.g., in our examination below we could provide G
FCI
0
for maximum
14-electron π -structures). Therefore, G
FCI
0
serves us here for testing G
X
0 (X= TB,
RHF, EQC and HPHF) on small-size systems. The QCTB results are not included
explicitly in the present paper because they are qualitatively close to those of EQC.
3 Polyene-like Toy Models
As our first concrete problem we consider model polyene-like π -systems in the
same specific setting as in [13]. In the cited work the simple TB model of even
cumulene chains is exploited in order to examine the size dependence of molecular
A. V. Luzanov
which makes sense only for computations of G
QCTB
0
by (2). Here δ is an orbital
splitting parameter by which different orbital for different spins are introduced into
the TB scheme, thus taking into implicit account the π -electron correlation effects.
A further improvement is attained by combining QCTB and RHF models. The
approach is suggested in [21] and termed the extended quasi-correlated (EQC)
method. The preliminary results were given in [19] in terms of the quasi-correlated
long-range interaction (QCLRI) scheme which is identical to EQC from [21]. In this
case we construct the intermediate Fock matrix f [1] (also shifted by the Fermi energy).
This matrix is normally computed by using the TB density matrix (bond-order matrix)
P. Hence, we do not invoke any self-consistency procedure. The obtained intermediate Fockian f [1] is then renormalized [see (25)] and used straightforwardly in
computing G
EQC
0
by (2) with applying a formal Hamiltonian similar to (5):
h
EQC
⇒ [( f [1] )
2
+ δ
2
]/ f [1]
The explicit representation is provided by (26) and (27). The benefit of EQC is
owing to accounting for long-range effects, so that the drawbacks inherent to QCTB
(due to a short-range nature of TB) are removed. In doing so, π -correlation effects are
also presented in EQC via the previous splitting parameter δ. Hence, this approach
is more preferable, especially for nano-sized systems and singular π -structures.
It is also worth mentioning another recently developed model [19] based on the
variatonal treatment of electron detachment/attachment processes within the halfprojected Hartree-Fock (HPHF) method. The appropriate GF will be represented by
G
HPHF
0
. As seen from [19], among the models considered there, G
HPHF
0
is the best
but only for not too large systems because HPHF lacks a size-consistency.
At last, the complete account for all electronic effects is achieved by the π -electron
full configuration interaction (FCI) method [24]. The related approach for GF was
elaborated in [25]. The thus obtained G
FCI
0
can be qualified as a “gold standard“
in the molecular Green’s function theory. Unfortunately, FCI is feasible for small
systems only (e.g., in our examination below we could provide G
FCI
0
for maximum
14-electron π -structures). Therefore, G
FCI
0
serves us here for testing G
X
0 (X= TB,
RHF, EQC and HPHF) on small-size systems. The QCTB results are not included
explicitly in the present paper because they are qualitatively close to those of EQC.
3 Polyene-like Toy Models
As our first concrete problem we consider model polyene-like π -systems in the
same specific setting as in [13]. In the cited work the simple TB model of even
cumulene chains is exploited in order to examine the size dependence of molecular