66
M. Senami and A. Fukushima
and the result in inner region (< about 1 [bohr]) should be neglected. Analytical
solution for Hf 4+ is not known, and we judge the accuracy by comparing with results
of the largest basis set group. Fortunately, all results are consistent with each other,
and basis set dependence is negligible for Hf 4+ . The response to electric field is
small in spite of large electron density, since four valence electrons are removed
and rest electrons are significantly stabilized. As a result, it is concluded that the
choice of basis sets is not important for cation, Hf 4+ .
On the other hand, valence electrons are destabilized significantly in anion.
Hence, larger basis sets are required for accurate description of local polarizability.
However, unfortunately, we cannot confirm this in a numerical method using a
single nucleus system, since the highest occupied molecular orbital (HOMO) of O 2−
has positive energy, and isolated O 2− cannot be calculated correctly. Nevertheless,
computations of isolated O 2− were studied in Ref. [28] for the purpose of the
numerical confirmation of strong dependence on the choice of basis sets. It was
shown in Ref. [28] that results with larger basis sets have larger polarizability, and
diffuse functions are important. This is plausible, since HOMO is not bounded.
As a result, we can summarize the basis set dependence as follows. From the
hydrogen result, it is conjectured that triple- or quadruple-zeta basis sets are accurate
enough to describe local polarizability density for neutral atoms. For cations, the
basis set dependence is small, while a larger basis set is required for anions.
3.3.2 Local Dielectric Property of Molecules XH n (X = C, N,
O, F, Si, P, S, Cl, Ge, As, Se, and Br)
In this subsection, we explain results of local dielectric response properties of
simple molecules, XH n (X = C, N, O, F, Si, P, S, Cl, Ge, As, Se, and Br), by wave
packets based on quantum mechanics computations. These molecules are chosen
to be typical examples of covalent molecules, and these X atoms are elements of
group IV–VII in the second to fourth period. Most results in this section are based
on Ref. [27]. Results of these simple molecules are used for systematic analysis of
local dielectric properties in a molecule. In this subsection, the order of eigenvalues
is the descending order of real part.
Wave packets used in this section were computed by ordinary electronic structure
computations carried out by GAMESS program package [42]. The cc-pVQZ basis
set [34, 43, 44] was chosen, and geometrical optimization computations were
performed by Hartree-Fock (HF) method. Singlet spin multiplicity was chosen for
all molecules. Configuration interaction single and double (CISD) was adopted for
electronic structure computations. This choice is better than the usage of density
functional theory (DFT), since the problem of overestimate of dielectric constant is
known for DFT [45–49]. Excitation of all electrons in occupied orbitals is taken
into account in this CISD computation. Local polarizability was computed by
QEDynamics program package [50–55].
M. Senami and A. Fukushima
and the result in inner region (< about 1 [bohr]) should be neglected. Analytical
solution for Hf 4+ is not known, and we judge the accuracy by comparing with results
of the largest basis set group. Fortunately, all results are consistent with each other,
and basis set dependence is negligible for Hf 4+ . The response to electric field is
small in spite of large electron density, since four valence electrons are removed
and rest electrons are significantly stabilized. As a result, it is concluded that the
choice of basis sets is not important for cation, Hf 4+ .
On the other hand, valence electrons are destabilized significantly in anion.
Hence, larger basis sets are required for accurate description of local polarizability.
However, unfortunately, we cannot confirm this in a numerical method using a
single nucleus system, since the highest occupied molecular orbital (HOMO) of O 2−
has positive energy, and isolated O 2− cannot be calculated correctly. Nevertheless,
computations of isolated O 2− were studied in Ref. [28] for the purpose of the
numerical confirmation of strong dependence on the choice of basis sets. It was
shown in Ref. [28] that results with larger basis sets have larger polarizability, and
diffuse functions are important. This is plausible, since HOMO is not bounded.
As a result, we can summarize the basis set dependence as follows. From the
hydrogen result, it is conjectured that triple- or quadruple-zeta basis sets are accurate
enough to describe local polarizability density for neutral atoms. For cations, the
basis set dependence is small, while a larger basis set is required for anions.
3.3.2 Local Dielectric Property of Molecules XH n (X = C, N,
O, F, Si, P, S, Cl, Ge, As, Se, and Br)
In this subsection, we explain results of local dielectric response properties of
simple molecules, XH n (X = C, N, O, F, Si, P, S, Cl, Ge, As, Se, and Br), by wave
packets based on quantum mechanics computations. These molecules are chosen
to be typical examples of covalent molecules, and these X atoms are elements of
group IV–VII in the second to fourth period. Most results in this section are based
on Ref. [27]. Results of these simple molecules are used for systematic analysis of
local dielectric properties in a molecule. In this subsection, the order of eigenvalues
is the descending order of real part.
Wave packets used in this section were computed by ordinary electronic structure
computations carried out by GAMESS program package [42]. The cc-pVQZ basis
set [34, 43, 44] was chosen, and geometrical optimization computations were
performed by Hartree-Fock (HF) method. Singlet spin multiplicity was chosen for
all molecules. Configuration interaction single and double (CISD) was adopted for
electronic structure computations. This choice is better than the usage of density
functional theory (DFT), since the problem of overestimate of dielectric constant is
known for DFT [45–49]. Excitation of all electrons in occupied orbitals is taken
into account in this CISD computation. Local polarizability was computed by
QEDynamics program package [50–55].