17 Theoretical Analysis of Phase-Transition Temperature
327
bonded dielectric materials, it is essential to elucidate the quantum effect of proton
and deuteron from the microscopic view.
In computational details, the importance of the quantum effect of proton and
deuteron with not only the T c , but also the structures and electronic charge difference
in the hydrogen-bonded dielectric materials was dealt using the adequate cluster
model and multi-component molecular orbital (MC_MO) method which takes into
account the quantum effect, such as, an anharmonicity due to the zero-point energy
of the proton/deuteron directly.
In Sect. 17.3.1, the isotope effect of K 3 H(SO 4 ) 2 (KHS) and K 3 D(SO 4 ) 2 (DKHS)
was discussed in order to verify the importance of the quantum effect of proton/deuteron and the efficiency of the MC_MO method. The difference between
the KHS and DKHS was clearly demonstrated, namely: (1) the shape of potential
energy surface, (2) the geometrical parameter including the hydrogen-bond (Ubbelohde effect), and (3) the electronic charge density. These results are universally
explained the independent various theories. In conclusion, the origin of the isotope
effect of KHS and DKHS is concluded that the difference of the reflection to the
geometrical parameters because of the difference in the proton and deuteron wave
distributions.
In Sect. 17.3.2, the mechanism of the phase transition of H 2 C 4 O 4 (H 2 SQ) was
discussed. The main driving force of phase transition in H 2 SQ crystal was found
to be the Jahn-Teller effect of the constituent molecular unit. The phase transition
causes the distortion of the crystal system because the geometrical change of the unit
propagates throughout the entire system via the hydrogen-bonded network. In addition, the T c difference was shown, as well as, the theoretical geometrical difference
using the MC_MO method. The H 2 SQ and D 2 SQ crystals are different in the way
which propagates the alternation of the unit induced by the shrinkage distribution of
the deuteron as opposed to the proton.
In Sect. 17.3.3, the difference of the T c , geometry, and electronic charge density
of K 3 H 1−x D x (SO 4 ) 2 and (H 1−x D x ) 2 SQ crystals were examined with increasing
deuterium concentration. Calculated T c s of K 3 H 1−x D x (SO 4 ) 2 and (H 1−x D x ) 2 SQ
reproduced the experimental results, since the variation of light nuclear quantum
effect (i.e. exponent value) has influenced the T c , geometry, and electronic charge
density. Furthermore, the T c values of tritiated TKHS and T 2 SQ are predicted to be
equal to 190 and 680 K, respectively. Owing to the localization of charge distribution of triton, hydrogen-bond structure and electronic charge density are longer and
larger than in the case of DKHS and D 2 SQ.
The major aim of manuscript is to explain the difference of T c in hydrogenbonded dielectric materials induced by the H/D isotope effect. The importance of the
quantum effect (i.e. anharmonicity) of proton/deuteron for the KHS (DKHS), H 2 SQ
(D 2 SQ), their mixed K 3 H 1−x D x (SO 4 ) 2 and (H 1−x D x ) 2 SQ, and tritiated TKHS and
T 2 SQ which have special features such as hydrogen-bonded networks and T c were
confirmed. Taking into account the quantum effect of proton/deuteron using the
MC_MO method directly, the difference of T c , as well as, the geometry and electronic charge difference is universally elucidate without a tunneling model. In conclusion, the origin of the isotope effect of hydrogen-bonded dielectric materials is
the anharmonicity due to the difference of the proton/deuteron wave distribution.
327
bonded dielectric materials, it is essential to elucidate the quantum effect of proton
and deuteron from the microscopic view.
In computational details, the importance of the quantum effect of proton and
deuteron with not only the T c , but also the structures and electronic charge difference
in the hydrogen-bonded dielectric materials was dealt using the adequate cluster
model and multi-component molecular orbital (MC_MO) method which takes into
account the quantum effect, such as, an anharmonicity due to the zero-point energy
of the proton/deuteron directly.
In Sect. 17.3.1, the isotope effect of K 3 H(SO 4 ) 2 (KHS) and K 3 D(SO 4 ) 2 (DKHS)
was discussed in order to verify the importance of the quantum effect of proton/deuteron and the efficiency of the MC_MO method. The difference between
the KHS and DKHS was clearly demonstrated, namely: (1) the shape of potential
energy surface, (2) the geometrical parameter including the hydrogen-bond (Ubbelohde effect), and (3) the electronic charge density. These results are universally
explained the independent various theories. In conclusion, the origin of the isotope
effect of KHS and DKHS is concluded that the difference of the reflection to the
geometrical parameters because of the difference in the proton and deuteron wave
distributions.
In Sect. 17.3.2, the mechanism of the phase transition of H 2 C 4 O 4 (H 2 SQ) was
discussed. The main driving force of phase transition in H 2 SQ crystal was found
to be the Jahn-Teller effect of the constituent molecular unit. The phase transition
causes the distortion of the crystal system because the geometrical change of the unit
propagates throughout the entire system via the hydrogen-bonded network. In addition, the T c difference was shown, as well as, the theoretical geometrical difference
using the MC_MO method. The H 2 SQ and D 2 SQ crystals are different in the way
which propagates the alternation of the unit induced by the shrinkage distribution of
the deuteron as opposed to the proton.
In Sect. 17.3.3, the difference of the T c , geometry, and electronic charge density
of K 3 H 1−x D x (SO 4 ) 2 and (H 1−x D x ) 2 SQ crystals were examined with increasing
deuterium concentration. Calculated T c s of K 3 H 1−x D x (SO 4 ) 2 and (H 1−x D x ) 2 SQ
reproduced the experimental results, since the variation of light nuclear quantum
effect (i.e. exponent value) has influenced the T c , geometry, and electronic charge
density. Furthermore, the T c values of tritiated TKHS and T 2 SQ are predicted to be
equal to 190 and 680 K, respectively. Owing to the localization of charge distribution of triton, hydrogen-bond structure and electronic charge density are longer and
larger than in the case of DKHS and D 2 SQ.
The major aim of manuscript is to explain the difference of T c in hydrogenbonded dielectric materials induced by the H/D isotope effect. The importance of the
quantum effect (i.e. anharmonicity) of proton/deuteron for the KHS (DKHS), H 2 SQ
(D 2 SQ), their mixed K 3 H 1−x D x (SO 4 ) 2 and (H 1−x D x ) 2 SQ, and tritiated TKHS and
T 2 SQ which have special features such as hydrogen-bonded networks and T c were
confirmed. Taking into account the quantum effect of proton/deuteron using the
MC_MO method directly, the difference of T c , as well as, the geometry and electronic charge difference is universally elucidate without a tunneling model. In conclusion, the origin of the isotope effect of hydrogen-bonded dielectric materials is
the anharmonicity due to the difference of the proton/deuteron wave distribution.