The NBO method is particularly well suited to analyze charge transfer mechanisms between two interacting systems through the NBO second order perturbation
analysis between the occupied orbitals of the base and the empty orbitals of the acid
[36]. These ‘‘localized hybrids’’ are obtained as local block eigenvectors of the
one-particle density matrix.
An alternative approach to specifically investigate the charge transfer between
the interacting subunits of a molecular complex is the Charge Displacement
(CD) function, introduced by Belpassi et al. [82] to study the chemical bond
between gold and the noble gases, and later on successfully employed to study the
charge transfer in noncovalent interactions [83–86] and in coordination chemistry
[87–91]. This theoretical scheme permits a quantitative analysis of the actual
electronic charge fluctuation and allows to measure the exact amount of electron
charge that, upon formation of an adduct from two constituting fragments, is
transferred across a plane perpendicular to the bond axis.
In the present study, we used this method to investigate cooperativity between
different non-covalent interactions. For sake of comparison, we also carried out a
parallel analysis using the QTAIM, ELF and NBO approaches. In particular, we
have chosen as suitable benchmark cases complexes stabilized simultaneously by
beryllium bonds, which lead usually to rather strong linkages, and halogen bonds,
which conversely are rather weak non-covalent interactions. As prototypes of
halogen bond, we have considered the complexes that FCl may form with nitrogen
bases in which the hybridization of the basic site changes from sp 3 , ammonia, to
sp 2 , methanimine, to sp, hydrogen cyanide. Then these complexes were allowed to
interact, through the fluorine atom of the FCl subunit, with beryllium difluoride, to
form the corresponding beryllium bond.
Since beryllium bonds have attracted much attention in recent years, the first part
of this study will focus on the information that the CD scheme provides on these
kind of linkages, when the base that interacts with the beryllium derivative presents
as basic sites first or second-row atoms. In particular, we have studied the beryllium
bond between BeH 2 or BeF 2 and H 2 O, SH 2 , NH 3 and PH 3 .
17.2 Computational Details
Geometries and electron densities were calculated at the DFT level with the B3LYP
functional, that combines the Becke’s three-parameter non-local hybrid exchange
functional [92] with non-local correlation function of Lee et al. [93]. DFT calculations have been carried out with Gaussian 09 [94] program using aug-cc-pVTZ basis
set [95] and with ADF suite of programs in combination with TZ2P basis set [96].
The good performance of the B3LYP method to describe the structure of both
beryllium and halogen bonds has been previously assessed in the literature [19, 75].
The QTAIM and the ELF calculations have been carried out by using the
AIMAll [97] and the TopMod [98] program packages, respectively. The NBO
464
K. Mykolayivna Lemishko et al.
analysis between the occupied orbitals of the base and the empty orbitals of the acid
[36]. These ‘‘localized hybrids’’ are obtained as local block eigenvectors of the
one-particle density matrix.
An alternative approach to specifically investigate the charge transfer between
the interacting subunits of a molecular complex is the Charge Displacement
(CD) function, introduced by Belpassi et al. [82] to study the chemical bond
between gold and the noble gases, and later on successfully employed to study the
charge transfer in noncovalent interactions [83–86] and in coordination chemistry
[87–91]. This theoretical scheme permits a quantitative analysis of the actual
electronic charge fluctuation and allows to measure the exact amount of electron
charge that, upon formation of an adduct from two constituting fragments, is
transferred across a plane perpendicular to the bond axis.
In the present study, we used this method to investigate cooperativity between
different non-covalent interactions. For sake of comparison, we also carried out a
parallel analysis using the QTAIM, ELF and NBO approaches. In particular, we
have chosen as suitable benchmark cases complexes stabilized simultaneously by
beryllium bonds, which lead usually to rather strong linkages, and halogen bonds,
which conversely are rather weak non-covalent interactions. As prototypes of
halogen bond, we have considered the complexes that FCl may form with nitrogen
bases in which the hybridization of the basic site changes from sp 3 , ammonia, to
sp 2 , methanimine, to sp, hydrogen cyanide. Then these complexes were allowed to
interact, through the fluorine atom of the FCl subunit, with beryllium difluoride, to
form the corresponding beryllium bond.
Since beryllium bonds have attracted much attention in recent years, the first part
of this study will focus on the information that the CD scheme provides on these
kind of linkages, when the base that interacts with the beryllium derivative presents
as basic sites first or second-row atoms. In particular, we have studied the beryllium
bond between BeH 2 or BeF 2 and H 2 O, SH 2 , NH 3 and PH 3 .
17.2 Computational Details
Geometries and electron densities were calculated at the DFT level with the B3LYP
functional, that combines the Becke’s three-parameter non-local hybrid exchange
functional [92] with non-local correlation function of Lee et al. [93]. DFT calculations have been carried out with Gaussian 09 [94] program using aug-cc-pVTZ basis
set [95] and with ADF suite of programs in combination with TZ2P basis set [96].
The good performance of the B3LYP method to describe the structure of both
beryllium and halogen bonds has been previously assessed in the literature [19, 75].
The QTAIM and the ELF calculations have been carried out by using the
AIMAll [97] and the TopMod [98] program packages, respectively. The NBO
464
K. Mykolayivna Lemishko et al.