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T. Ishimoto and M. Tachikawa
the phase transition, the origin of the isotope effect is not yet completely elucidated.
We should address here that the origin of the isotope effect is among the major subjects in condensed matter physics. The history of research of the isotope effect is
introduced below.
More than sixty years ago, Slater first investigated the mechanism of the phase
transition of KDP using a statistical mechanism [6]. He concluded the order-disorder
type phase transition using the classical double-minimum protonic potential functions, while he did not refer to the isotope effect.
Since the chemical nature of the hydrogen and deuterium atoms is believed to
be the same, the origin of the isotope effect is related to the difference in only their
masses. In order to elucidate the isotope effect, various theoretical approaches were
proposed after his work. Among the various theoretical models, the proton tunneling model [7–10] has been most widely accepted, since it was supported by the light
scattering experiment [11, 12] and high-pressure measurement [13]. In the tunneling model, which occurs in the disordered phase at high temperature, each proton
(deuteron) occupies two equilibrium positions with equal probability in a symmetric double well potential, and proton (deuteron) tunneling between these positions
opposes localization. Within this model, the phase transition is driven by the direct
proton-proton interaction. The isotope effect is explained as the difference of the
splitting of energy levels by the proton (deuteron) tunneling amplitudes.
Some serious doubts, however, have been thrown upon the proton tunneling
model. Ichikawa has pointed out the importance of the isotope effect on geometry and symmetry of the hydrogen bond for inducing the large isotope effect of the
T c [14]. This is called the “geometrical isotope effect” based on the empirical investigation of KDP families at various temperatures and pressures. This indicates that
the large difference of T c might be interpreted without invoking proton tunneling.
Recent developments in experimental techniques have made it possible to give
various novel information. Noda and Kasatani et al. observed the difference in
the electronic population around the proton and deuteron by the X-ray diffraction
study [15–18]. The total number of electrons around the proton and deuteron in the
tripotassium hydrogen disulfate (KHS) and its deuterium compound DKHS are 0.65
and 1.19, respectively. They suggested that the charge difference is important for the
occurrence of the large isotope effect. In addition, there is no evidence of the proton
(deuteron) tunneling phenomena from the Raman spectroscopic analysis by Tominaga [19]. In this sense, the some experimental results such as the origin of isotope
effect on the T c of hydrogen-bonded dielectric materials cannot be fully understood
by only proton tunneling model.
Recently, new models which take into account the quantum effect of nucleus such
as proton and deuteron are proposed [20–22]. In particular, Koval et al. [20] studied
the nuclear quantum effects of KDP (DKDP) based on the density functional theory
(DFT) [23]. The DFT is not fully unveiled the hydrogen-bonded dielectric materials,
even though the DFT based on the local density approximation (LDA) [24] and generalized gradient approximation (GGA) [25] with the plane wave basis expansion
has been employed with great success to theoretically analyze the various materials.
This method is no longer able to predict the difference in the electronic charge distributions around the proton (deuteron) and polarized structures such as hydrogen
T. Ishimoto and M. Tachikawa
the phase transition, the origin of the isotope effect is not yet completely elucidated.
We should address here that the origin of the isotope effect is among the major subjects in condensed matter physics. The history of research of the isotope effect is
introduced below.
More than sixty years ago, Slater first investigated the mechanism of the phase
transition of KDP using a statistical mechanism [6]. He concluded the order-disorder
type phase transition using the classical double-minimum protonic potential functions, while he did not refer to the isotope effect.
Since the chemical nature of the hydrogen and deuterium atoms is believed to
be the same, the origin of the isotope effect is related to the difference in only their
masses. In order to elucidate the isotope effect, various theoretical approaches were
proposed after his work. Among the various theoretical models, the proton tunneling model [7–10] has been most widely accepted, since it was supported by the light
scattering experiment [11, 12] and high-pressure measurement [13]. In the tunneling model, which occurs in the disordered phase at high temperature, each proton
(deuteron) occupies two equilibrium positions with equal probability in a symmetric double well potential, and proton (deuteron) tunneling between these positions
opposes localization. Within this model, the phase transition is driven by the direct
proton-proton interaction. The isotope effect is explained as the difference of the
splitting of energy levels by the proton (deuteron) tunneling amplitudes.
Some serious doubts, however, have been thrown upon the proton tunneling
model. Ichikawa has pointed out the importance of the isotope effect on geometry and symmetry of the hydrogen bond for inducing the large isotope effect of the
T c [14]. This is called the “geometrical isotope effect” based on the empirical investigation of KDP families at various temperatures and pressures. This indicates that
the large difference of T c might be interpreted without invoking proton tunneling.
Recent developments in experimental techniques have made it possible to give
various novel information. Noda and Kasatani et al. observed the difference in
the electronic population around the proton and deuteron by the X-ray diffraction
study [15–18]. The total number of electrons around the proton and deuteron in the
tripotassium hydrogen disulfate (KHS) and its deuterium compound DKHS are 0.65
and 1.19, respectively. They suggested that the charge difference is important for the
occurrence of the large isotope effect. In addition, there is no evidence of the proton
(deuteron) tunneling phenomena from the Raman spectroscopic analysis by Tominaga [19]. In this sense, the some experimental results such as the origin of isotope
effect on the T c of hydrogen-bonded dielectric materials cannot be fully understood
by only proton tunneling model.
Recently, new models which take into account the quantum effect of nucleus such
as proton and deuteron are proposed [20–22]. In particular, Koval et al. [20] studied
the nuclear quantum effects of KDP (DKDP) based on the density functional theory
(DFT) [23]. The DFT is not fully unveiled the hydrogen-bonded dielectric materials,
even though the DFT based on the local density approximation (LDA) [24] and generalized gradient approximation (GGA) [25] with the plane wave basis expansion
has been employed with great success to theoretically analyze the various materials.
This method is no longer able to predict the difference in the electronic charge distributions around the proton (deuteron) and polarized structures such as hydrogen