http://swrc.ontoware.org/ontology#Thesis
Finite-temperature density functional approach to electrochemical reaction
en
白鳥 和矢
シラトリ カズヤ
SHIRATORI Kazuya
総研大甲第1117号
Electrochemical processes have historically been investigated in a wide range of<br> interests in electrochemical cell, corrosion, membrane potential and analytical<br> technique. Their importance has extensively been recognized in recent years, for<br> example, in the context of energy conversion related to photoelectrochemical cells<br />based on advanced fabrication technology. To analyze these electrochemical processes,<br />it is required to clarify electronic structures of a system in electrochemical<br> environment. Nevertheless, it is computationally demanding to carry out<br />first-principles calculations of such electronic states. This is simply because<br />reactant-solvent and reactant-electrode interactions, which are completely absent in<br />isolated molecular systems, play an important role. Therefore, the electrochemical<br> processes have so far been studied within various numerical models at different levels<br />of theory. The problems in the electrochemical processes can be classified into two<br />parts. The first problem is difficulty in carrying out electronic structure calculations of<br />the reactant molecule at a constant chemical potential µ, and the other one is how to<br />appropriately describe the reactant-solvent and the reactant-electrode interactions. <br /> The conventional <i>ab initio</i> calculations are directed toward obtaining electronic<br />structures at a constant number of electrons, <i>N</i> . Such <i>ab initio</i> calculations cannot be<br />straightforwardly applied to electronic structure calculations at a constant µ, in <br />which the number of electrons is not a suitable variable. Although several studies have<br />been devoted to development of the methods calculating electronic structures at a<br />constant µ, their methods are still substantially based on the constant <i>N</i><br />calculations. Therefore, it is desirable to develop an alternative method to directly<br />calculate electronic structures at a constant µ. Finite-temperature density functional<br />theory (FTDFT) treats a system in a grand canonical ensemble average and thus one<br />can propose a numerical method based on FTDFT to describe electrochemical<br />processes. <br /> In addition to the requirement for the electronic structure calculation at a constant<br />µ, reactant-solvent and reactant-electrode interactions should be considered in <br />electrochemical processes, as mentioned above. He primarily focuses on developing the FTDFT method of electronic structure calculation of reactant molecules at a constant<br />µ. Therefore, he approximates the solvent effects in terms of a simple continuum<br />model and limit electrochemical processes to outer-sphere ones in which the electrode<br />is treated as a reservoir with µ. It should be noted that the development of the<br />electronic structure calculation has nothing to do with the treatment of the<br />reactant-solvent interaction, so that the present FTDFT method can be<br />straightforwardly improved by employing more sophisticated procedures describing<br />the solvent effects. <br /> In this thesis, he develops a method of the FTDFT ab initio quantum chemistry<br />calculations combined with a continuum solvent model and discuss the electronic<br />properties of molecules in electrochemical environment. The actual calculations are<br />carried out by solving the finite-temperature Kohn-Sham (KS) equation with the<br />GAMESS package of quantum chemistry programs in which the present numerical<br />methodology of FTDFT is implemented. The KS orbitals are expanded in terms of<br />Dunning's augmented correlation-consistent basis set (aug-cc-pVDZ). <br /> He applies the present method to the electrochemical reaction,NO<sup>+</sup>+e<sup>-</sup>↔ NO . The <br />Becke three-parameter hybrid exchange functional with the Lee-Yang-Parr correlation <br />functional (B3LYP) is used as the exchange-correlation potential. He does not<br />consider the temperature dependence of the exchange-correlation potential although<br />the potential in the FTDFT approach should depend on temperature in a narrow sense.<br />The solvent effects are treated at the level of conductor-like polarizable continuum<br />model (C-PCM), assuming the equilibrium condition between the solute and the<br />solvent. He gives the size of the cavity in C-PCM as a function of the molecular charge.<br />The calculation is carried out at the chemical potentials µ -3.40, -5.40, and -7.40 eV.<br />These values correspond to the electrode potentials <i>v</i> = -0.84, 1.16, and 3.16 V vs<br />SHE (standard hydrogen electrode), respectively. It has successfully been<br />demonstrated that the grand potential curve depends on µ, i.e., the electrode <br />potential. The calculation showed that the charge is a function of the chemical <br />otential and the internuclear distance of NO. The FTDFT/C-PCM approach has<br />proved to be a useful computational tool for electronic structure calculations at a<br />constant µ of a molecule interacting with solvent molecules.<br /> Although the FTDFT/C-PCM method has succeeded in giving the reasonable results,<br />there are two problems to be addressed: the B3LYP functional is used uncritically and<br />the nonequilibrium solvation effect is not taken into account. These unsettled <br />problems might give rise to serious disadvantages in analysis of electrochemical<br />kinetics. Thus, he improves the FTDFT approach further by employing a different<br />functional and a different continuum solvent model, as mentioned bellow. This <br />improved FTDFT method is also applied to the electrochemical reaction<br />of NO<sup>+</sup>+e<sup>-</sup>↔NO. <br /> In the extension of the Hohenberg-Kohn theorem to the system with a fractional<br />number of electrons <i>N</i> by Perdew <i>et al</i>., they demonstrated that the energy<br />calculated by using DFT should show derivative discontinuity with respect to <i>N</i> .<br />However, it is known that the B3LYP functional does not reproduce the derivative<br />discontinuity condition. He alternatively employs the Becke exchange and<br />Lee-Yang-Parr correlation functional with a long-range correction (LC-BLYP). The<br />result obtained by using the LC-BLYP functional depends on the parameter ω that<br />divides the Coulomb operator into short-range and long-range parts. It has been found<br />that the B3LYP functional completely fails to describe the grand potential surface<br />whereas the LC-BLYP functional gives a proper grand potential surface if an<br />appropriate value of ω is taken. This is because the result of the LC-BLYP functional<br />with the optimal value of ω satisfies the requirement of the derivative discontinuity<br />with respect to <i>N</i>. <br /> To treat the nonequilibrium solvation effect, he uses the extended self-consistent<br />reaction field (SCRF) model. This model allows considering the nonequilibrium<br />solvation effect by dividing solvent polarization into long-lived and short-lived<br />components. The calculated activation free energy, 12 kcal/mol, was in good agreement<br />with an experimental result, 11 kcal/mol, whereas the result obtained by using the<br />conventional SCRF model (i.e., not taking account of the nonequilibrium solvation<br />effect) gave considerably lower value, 3 kcal/mol. He has clearly shown that the<br />nonequilibrium solvation effect has a great influence on the electrochemical process<br />and the extended SCRF model significantly improves the calculated activation free<br />energy.<br /> In summary, he has developed a computational method based on FTDFT combined<br />with a continuum solvent model to analyze electrochemical processes. The FTDFT<br />method allows calculating the electronic structures as a function of the chemical <br />potential. To apply the method to the studies of electrochemical kinetics, use of a<br />nonequilibrium solvation model and an exchange-correlation potential satisfying the <br />derivative discontinuity is crucially important. This study provides a powerful and <br />intuitive approach to analysis of electrochemical reactions.<br />