interests in electrochemical cell, corrosion, membrane potential and analytical

technique. Their importance has extensively been recognized in recent years, for

example, in the context of energy conversion related to photoelectrochemical cells

based on advanced fabrication technology. To analyze these electrochemical processes,

it is required to clarify electronic structures of a system in electrochemical

environment. Nevertheless, it is computationally demanding to carry out

first-principles calculations of such electronic states. This is simply because

reactant-solvent and reactant-electrode interactions, which are completely absent in

isolated molecular systems, play an important role. Therefore, the electrochemical

processes have so far been studied within various numerical models at different levels

of theory. The problems in the electrochemical processes can be classified into two

parts. The first problem is difficulty in carrying out electronic structure calculations of

the reactant molecule at a constant chemical potential µ, and the other one is how to

appropriately describe the reactant-solvent and the reactant-electrode interactions.

The conventional

structures at a constant number of electrons,

straightforwardly applied to electronic structure calculations at a constant µ, in

which the number of electrons is not a suitable variable. Although several studies have

been devoted to development of the methods calculating electronic structures at a

constant µ, their methods are still substantially based on the constant

calculations. Therefore, it is desirable to develop an alternative method to directly

calculate electronic structures at a constant µ. Finite-temperature density functional

theory (FTDFT) treats a system in a grand canonical ensemble average and thus one

can propose a numerical method based on FTDFT to describe electrochemical

processes.

In addition to the requirement for the electronic structure calculation at a constant

µ, reactant-solvent and reactant-electrode interactions should be considered in

electrochemical processes, as mentioned above. He primarily focuses on developing the FTDFT method of electronic structure calculation of reactant molecules at a constant

µ. Therefore, he approximates the solvent effects in terms of a simple continuum

model and limit electrochemical processes to outer-sphere ones in which the electrode

is treated as a reservoir with µ. It should be noted that the development of the

electronic structure calculation has nothing to do with the treatment of the

reactant-solvent interaction, so that the present FTDFT method can be

straightforwardly improved by employing more sophisticated procedures describing

the solvent effects.

In this thesis, he develops a method of the FTDFT ab initio quantum chemistry

calculations combined with a continuum solvent model and discuss the electronic

properties of molecules in electrochemical environment. The actual calculations are

carried out by solving the finite-temperature Kohn-Sham (KS) equation with the

GAMESS package of quantum chemistry programs in which the present numerical

methodology of FTDFT is implemented. The KS orbitals are expanded in terms of

Dunning's augmented correlation-consistent basis set (aug-cc-pVDZ).

He applies the present method to the electrochemical reaction,NO

Becke three-parameter hybrid exchange functional with the Lee-Yang-Parr correlation

functional (B3LYP) is used as the exchange-correlation potential. He does not

consider the temperature dependence of the exchange-correlation potential although

the potential in the FTDFT approach should depend on temperature in a narrow sense.

The solvent effects are treated at the level of conductor-like polarizable continuum

model (C-PCM), assuming the equilibrium condition between the solute and the

solvent. He gives the size of the cavity in C-PCM as a function of the molecular charge.

The calculation is carried out at the chemical potentials µ -3.40, -5.40, and -7.40 eV.

These values correspond to the electrode potentials

SHE (standard hydrogen electrode), respectively. It has successfully been

demonstrated that the grand potential curve depends on µ, i.e., the electrode

potential. The calculation showed that the charge is a function of the chemical

otential and the internuclear distance of NO. The FTDFT/C-PCM approach has

proved to be a useful computational tool for electronic structure calculations at a

constant µ of a molecule interacting with solvent molecules.

Although the FTDFT/C-PCM method has succeeded in giving the reasonable results,

there are two problems to be addressed: the B3LYP functional is used uncritically and

the nonequilibrium solvation effect is not taken into account. These unsettled

problems might give rise to serious disadvantages in analysis of electrochemical

kinetics. Thus, he improves the FTDFT approach further by employing a different

functional and a different continuum solvent model, as mentioned bellow. This

improved FTDFT method is also applied to the electrochemical reaction

of NO

In the extension of the Hohenberg-Kohn theorem to the system with a fractional

number of electrons

calculated by using DFT should show derivative discontinuity with respect to

However, it is known that the B3LYP functional does not reproduce the derivative

discontinuity condition. He alternatively employs the Becke exchange and

Lee-Yang-Parr correlation functional with a long-range correction (LC-BLYP). The

result obtained by using the LC-BLYP functional depends on the parameter ω that

divides the Coulomb operator into short-range and long-range parts. It has been found

that the B3LYP functional completely fails to describe the grand potential surface

whereas the LC-BLYP functional gives a proper grand potential surface if an

appropriate value of ω is taken. This is because the result of the LC-BLYP functional

with the optimal value of ω satisfies the requirement of the derivative discontinuity

with respect to

To treat the nonequilibrium solvation effect, he uses the extended self-consistent

reaction field (SCRF) model. This model allows considering the nonequilibrium

solvation effect by dividing solvent polarization into long-lived and short-lived

components. The calculated activation free energy, 12 kcal/mol, was in good agreement

with an experimental result, 11 kcal/mol, whereas the result obtained by using the

conventional SCRF model (i.e., not taking account of the nonequilibrium solvation

effect) gave considerably lower value, 3 kcal/mol. He has clearly shown that the

nonequilibrium solvation effect has a great influence on the electrochemical process

and the extended SCRF model significantly improves the calculated activation free

energy.

In summary, he has developed a computational method based on FTDFT combined

with a continuum solvent model to analyze electrochemical processes. The FTDFT

method allows calculating the electronic structures as a function of the chemical

potential. To apply the method to the studies of electrochemical kinetics, use of a

nonequilibrium solvation model and an exchange-correlation potential satisfying the

derivative discontinuity is crucially important. This study provides a powerful and

intuitive approach to analysis of electrochemical reactions.

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