68
M. Senami and A. Fukushima
one molecule is taken as an example, and common features explained below are
also seen for other XH n molecules. Other results are dropped since those are a little
lengthy, and all results of other molecules can be seen in Ref. [27]. The upper, middle, and bottom panels are the first, second, and third eigenvalues and eigenvectors,
respectively. Short lines show directions of corresponding eigenvectors. Eigenvalues
are complex in regions enclosed by solid lines. In the result of the largest eigenvalue,
the first eigenvalue, large polarizability region exists between O and H atoms, which
are enclosed by bold dashed line, and the direction of eigenvectors in the region
is that of covalent bond of O and H. This directionality shows salient contrast
compared to that of HfO 2 discussed in the next chapter, whose bonding is ionic. This
directional response is considered to arise from covalent bond. Negative or complex
eigenvalues are seen around the oxygen nucleus. In negative eigenvalue regions,
the direction of polarization response is opposite to ordinary response. In complex
eigenvalue regions, polarization responds to electric field rotationally [18]. This
response is not familiar in macroscopic phenomena and originates in combination of
electric fields from nuclei and external field. These regions are more outstanding for
upper period elements in the periodic table, and similar distribution patterns appear
in a same group [27]. These properties explained above arise from the size of a
molecule, which correlates with the radius of X atom and the internuclear length
between X and H nuclei.
Eigenvalues of local polarizability tensor are shown along internuclear axis of X
and H bonding for XH n (X = C, N, O, F, Si, P, S, Cl, Ge, As, Se, and Br) molecules
in Fig. 3.8 (CH 4 , NH 3 , H 2 O, HF), Fig. 3.9 (SiH 4 , PH 3 , H 2 S, HCl), and Fig. 3.10
(GeH 4 , AsH 3 , H 2 Se, HBr). In these figures, top left panels show results of XH 4 , top
right ones show those of XH 3 , bottom left ones show those of H 2 X, and bottom right
ones show those of HX. In addition to three eigenvalues, the average of eigenvalues
is also shown in this figure. Bold dashed line means α i = 1/(4π) ∼ 0.08.
When α i = 1/(4π), the eigenvalue of dielectric constant tensor corresponding
to α i is divergent. For α i > 1/(4π), the corresponding dielectric constant has
negative sign. From these figures, large local polarizability density is seen in a
region between X and H atoms as seen in Fig. 3.7. This is due to the charge transfer
from a region around a nucleus to bonding region. In contrast, local polarizability
density is smaller around nuclei for all atoms than bonding region. Electrons around
nuclei are bounded strongly by electric field of nuclei, while electrons in bonding
region are not strongly trapped by electric field. From the comparison among a
same period, the average of local polarizability density is larger for smaller atomic
number. The difference of average comes from the difference of the second and
third eigenvalues. This is speculated to originate in the X-H internuclear length and
other X-H bonding. The peak at a X nucleus is formed by 1s core electrons of the
X atom. In Figs. 3.9 and 3.10, multiple peak structure around X nucleus is seen for
elements in the third and fourth period. This structure is formed by shell structure
of atoms. Inner electrons respond to electric field weakly by strong electric field
of a nucleus. Complex eigenvalues around transition region between bonding and
X nucleus regions for elements in V and VI groups. The arguments of complex
M. Senami and A. Fukushima
one molecule is taken as an example, and common features explained below are
also seen for other XH n molecules. Other results are dropped since those are a little
lengthy, and all results of other molecules can be seen in Ref. [27]. The upper, middle, and bottom panels are the first, second, and third eigenvalues and eigenvectors,
respectively. Short lines show directions of corresponding eigenvectors. Eigenvalues
are complex in regions enclosed by solid lines. In the result of the largest eigenvalue,
the first eigenvalue, large polarizability region exists between O and H atoms, which
are enclosed by bold dashed line, and the direction of eigenvectors in the region
is that of covalent bond of O and H. This directionality shows salient contrast
compared to that of HfO 2 discussed in the next chapter, whose bonding is ionic. This
directional response is considered to arise from covalent bond. Negative or complex
eigenvalues are seen around the oxygen nucleus. In negative eigenvalue regions,
the direction of polarization response is opposite to ordinary response. In complex
eigenvalue regions, polarization responds to electric field rotationally [18]. This
response is not familiar in macroscopic phenomena and originates in combination of
electric fields from nuclei and external field. These regions are more outstanding for
upper period elements in the periodic table, and similar distribution patterns appear
in a same group [27]. These properties explained above arise from the size of a
molecule, which correlates with the radius of X atom and the internuclear length
between X and H nuclei.
Eigenvalues of local polarizability tensor are shown along internuclear axis of X
and H bonding for XH n (X = C, N, O, F, Si, P, S, Cl, Ge, As, Se, and Br) molecules
in Fig. 3.8 (CH 4 , NH 3 , H 2 O, HF), Fig. 3.9 (SiH 4 , PH 3 , H 2 S, HCl), and Fig. 3.10
(GeH 4 , AsH 3 , H 2 Se, HBr). In these figures, top left panels show results of XH 4 , top
right ones show those of XH 3 , bottom left ones show those of H 2 X, and bottom right
ones show those of HX. In addition to three eigenvalues, the average of eigenvalues
is also shown in this figure. Bold dashed line means α i = 1/(4π) ∼ 0.08.
When α i = 1/(4π), the eigenvalue of dielectric constant tensor corresponding
to α i is divergent. For α i > 1/(4π), the corresponding dielectric constant has
negative sign. From these figures, large local polarizability density is seen in a
region between X and H atoms as seen in Fig. 3.7. This is due to the charge transfer
from a region around a nucleus to bonding region. In contrast, local polarizability
density is smaller around nuclei for all atoms than bonding region. Electrons around
nuclei are bounded strongly by electric field of nuclei, while electrons in bonding
region are not strongly trapped by electric field. From the comparison among a
same period, the average of local polarizability density is larger for smaller atomic
number. The difference of average comes from the difference of the second and
third eigenvalues. This is speculated to originate in the X-H internuclear length and
other X-H bonding. The peak at a X nucleus is formed by 1s core electrons of the
X atom. In Figs. 3.9 and 3.10, multiple peak structure around X nucleus is seen for
elements in the third and fourth period. This structure is formed by shell structure
of atoms. Inner electrons respond to electric field weakly by strong electric field
of a nucleus. Complex eigenvalues around transition region between bonding and
X nucleus regions for elements in V and VI groups. The arguments of complex