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Multiscale, multiphysics computational chemistry methods based on artificial intelligence integrated ultra-accelerated quantum molecular dynamics for the application to automotive emission control.

ABSTRACT

On the basis of extensive experimental works about heterogeneous catalysts, we developed various software for the design of automotive catalysts such as Ultra-Accelerated Quantum Chemical Molecular Dynamics (UA-QCMD), which is 10 million times faster than the conventional first principles molecular dynamics, mesoscopic modeling software for supported catalysts (POCO2), and mesoscopic sintering simulator (SINTA) to calculate sintering behavior of both precious metals (e.g., Pt, Pd, Rh) and supports (e.g., [Al.sub.2][O.sub.3], Zr[O.sub.2], Ce[O.sub.2], or Ce[O.sub.2]-Zr[O.sub.2]). We integrated the previous programs in a multiscale, multiphysics approach for the design of automotive catalysts. The method was efficient for a variety of important catalytic reactions in the scope of the automotive emission control. We demonstrated the efficiency of our approach by comparing our data with experimental results including both simple laboratory experiments and chassis dynamometer exhaust gas emission control experiments. We also demonstrated that the UA-QCMD method is an efficient tool for the estimation of mesoscopic sintering activation energies for both precious metals and supports. On the basis of our successful applications of the UA-QCMD to various important chemical processes of exhaust emission controls and sintering predictions of both precious metals and support of automotive catalysts, we employed in the present study artificial intelligence to determine fundamental parameters from all electron density functional methods and thermodynamic results. This new technique was proven highly efficient for optimizing parameters necessary in our simulations.

CITATION: Miyamoto, A., Inaba, K., Ishizawa, Y., Sato, M. et al., "Multiscale, Multiphysics Computational Chemistry Methods Based on Artificial Intelligence Integrated Ultra-Accelerated Quantum Molecular Dynamics for the Application to Automotive Emission Control," SAE Int. J. Engines 9(4):2016.

INTRODUCTION

Catalytic converters are widely used in the automotive industry to limit/control emissions of harmful species (carbon monoxide (CO), hydrocarbons, mono-nitrogen oxides (N[O.sub.x]), particulate matter (PM)) contained in exhaust gases. However, performances of such devices are highly affected because of materials aging in high temperature conditions, reducing the lifetime of vehicle catalyst in maintaining low exhaust gas emissions. In that case, aging is characterized by a loss of active surface area in metal components as a result of sintering, causing a decrease in the catalytic activity. This is a longstanding problem that affects many other applications using highly dispersed metal nanoparticles (or nanoclusters). Experimentally, mid-life catalyst durability performances are examined through engine dyno evaluations. In such experiments, various kinds of catalyst prototypes are employed in continuous tests, implying the use of a large amount of fuel.

Usually, exhaust catalysts are made of a honeycomb structure where ceramic materials support clusters of precious metals used for the catalytic reaction (Fig. 1). Supported precious metals, like platinum (Pt), rhodium (Rh), and palladium (Pd), are commonly employed to facilitate catalytic processes in the industry. In particular, Pt is found at the core of catalysts for three-way (CO and hydrocarbon oxidation/N[O.sub.x] reduction) conversions within car exhausts.

The most widely used ceramic materials as a support in Three-Way Catalysts (TWC) for the control of harmful emissions are alumina ([Al.sub.2][O.sub.3]), ceria (Ce[O.sub.2]), and zirconia (Zr[O.sub.2]). [Al.sub.2][O.sub.3] has a high hardness and wear resistance. Among different phases, [gamma]-[Al.sub.2][O.sub.3] exhibits large surface area and a good thermal stability, making it widely used as a support material [1]. Ceria acts as an oxygen storage/release component by changing its stoichiometry between Ce[O.sub.2] and Ce[O.sub.2-x] x being a function of temperature and oxygen partial pressure, under reaction conditions due to high availability of surface oxygen. This allows the storage and the release of oxygen easily. However, for pure ceria, oxygen storage/release capacity (OSC) and durability remain inadequate for practical use in TWC. ZrO2 has a lower surface area with respect to other compounds, but adding it to other ceramic materials increases their fracture toughness. In particular, addition of Zr[O.sub.2] into the Ce[O.sub.2] lattice (i.e., a Ce-Zr mixed oxide) has been found to be strongly effective in preventing ceria from sintering and promotes the OSC [2,3].

To design automotive catalysts with sustainable performances, the development of more efficient and durable TWC necessitates investigating and clarifying more the relationship between supported precious metal and support material. For such work, some of us previously employed a multiscale, multiphysics computational approach [4,5,6], which was proven useful and highly effective for various industrial systems and is well suited for analyzing automobile catalytic reactions. This bottom-up approach relied on quantum chemical calculations at the smallest scale (atomic-scale; microscopic) and was used in combination with the ceramic grain-scale (mesoscopic simulations). The approach was applied to Pt/[gamma]-[Al.sub.2][O.sub.3], Pt/Zr[O.sub.2], and Pt/Ce[O.sub.2] systems at a temperature condition (1073 K) where durability of materials is important.

From microscopic simulations (Fig. 1), authors [4] found that adsorption energies of [Pt.sup.37] on supports decreased as follows; Pt/Ce[O.sub.2] (445.37 kJ/mol), Pt/Zr[O.sub.2] (363.83 kJ/mol), and Pt/[gamma]-[Al.sub.2][O.sub.3] (296.55 kJ/mol). They also found that the magnitude of the binding energy of Pt atoms with oxygen atoms of the substrate play a role on the diffusion of Pt nanoclusters. Indeed, while Pt diffuse easily on [gamma]-[Al.sub.2][O.sub.3] substrates, diffusion of Pt nanoclusters is reduced with respect to [gamma]-[Al.sub.2][O.sub.3] substrates. This is due to the stronger binding energy for Pt-O bonds observed in Pt/Zr[O.sub.2] systems. For Pt/Ce[O.sub.2] systems, authors observed almost no diffusion in the course of the simulation, because Pt clusters are strongly anchored on the Ce[O.sub.2] substrate through Pt-O-Ce bonds. Binding energies for the three systems follow the same order as the one for adsorption energies; Pt-O(-Al) < Pt-O(-Zr) < Pt-O(-Ce). It also revealed that Pt becomes gradually cationic.

From mesoscopic simulations, authors first built catalyst models that exhibit specific surface area consistent with experimental values [7] obtained using the BET (Brunauer-Emmett-Teller) method. Initial Pt nanoclusters had a size of ~1.0 nm and represent 2.0 wt. % of the model, considering the mass density of each phase, 7.132 g/[cm.sup.3] for Ce[O.sub.2], 5.68 g/[cm.sup.3] for Zr[O.sub.2], and 3.9 g/[cm.sup.3] for [gamma]-[Al.sub.2][O.sub.3]. After simulating sintering at constant temperature (1073 K) and for 5 hours with the Kinetic Monte Carlo method (Fig. 2), authors found that the size of ceramic grains for the [gamma]-[Al.sub.2][O.sub.3] model remained small (1-5 nm) rendering the porous structure thermally stable. Thus, Pt nanoclusters at the surface of ceramic grains stay in a fine porous structure environment and their average size was found to be ~2.27 nm using the cluster size distribution. However, when agglomeration occurs, clusters can reach sizes up to 23 nm, which is in the range given by Ref [7,8]. For the Pt/Zr[O.sub.2] system, the cluster size of Pt atoms after aging was in the range 11-18 nm with an average ~ 14.83 nm, which is in good agreement with the experimental value (~ 15 nm) obtained using the CO pulse method [7]. For the Pt/Ce[O.sub.2] system, clusters of Pt atoms remained highly dispersed on the Ce[O.sub.2] support and their average size was ~ 1.24 nm, which agrees well with experiments showing that Pt in the Ce[O.sub.2] catalyst did not sinter at all [8].

To go beyond the previously mentioned preliminary theoretical work, we refined our multiscale, multiphysics computational approach by adding a third level of simulation, i.e., the reactor-scale (macroscopic chemical kinetics simulations), we provided results directly comparable with chassis dynamometer and engine dynamometer experiments (i.e., macroscopic results). Furthermore, the use of a human-based approach for the derivation of fundamental parameters for microscopic simulations is tedious, time consuming limiting simulations to a few cases, and subject to errors. Here, we employed artificial intelligence (AI) to overcome these problems. With these two improvements to our original approach we were able to simulate the exhaust catalyst in a more realistic way. In the remainder of this technical article, we first present methods employed to simulate our systems. Then, we showed results obtained with our macroscopic simulator, microscopic simulation of various catalytic supports for the prediction of sintering parameters at higher scales, and first outcomes and validations of AI-aided derivation of fundamental parameters for microscopic simulations.

METHODS

Ultra-Accelerated Quantum Chemical Molecular Dynamics

To estimate mesoscopic sintering activation energies for both precious metals and supports, we used Ultra-Accelerated Quantum Chemical Molecular Dynamics (UA-QCMD). This technique is based on a Tight-Binding Quantum Chemical (TB-QC) approach to compute electronic structures of materials, which is implemented in our in-house computer code COLORS that can calculate energies, charges, and bond populations for large-scale systems [4,5,9,10]. COLORS is used to periodically evaluate pair potential energy functions in the course of classical molecular dynamics (MD) simulations performed with our code NEW-RYUDO. The period between each update of pair potentials is chosen so that considerable changes in the atomic structure occur, which also modify strongly the electronic structure of the system. Using this scheme, the simulation time is accelerated by about [10.sup.7] times with respect to conventional molecular dynamics density functional theory (DFT) computations. The basic idea of this approach is summarized in Fig. 3 and details of the scheme are given below.

In COLORS, the electronic structure was obtained through the resolution of the Schrodinger equation ([H.sup.e]C = [epsilon]SC; where [H.sup.e], C, [epsilon], and S refer to the electronic Hamiltonian matrix, eigenvectors, eigenvalues, and the overlap integral matrix, respectively) with the diagonalization condition ([C.sup.T]SC = I ; I being the identity matrix). To determine [H.sup.e] and S, we needed exponents of Slater-type atomic orbital (AO), noted [[zeta].sub.r], and valence state ionization potentials (VSIPs) for the considered atomic species in this work, i.e., the 1s AO of hydrogen atoms as well as the 2s and 2p AOs of carbon atoms. The relationship between diagonal elements [[H.sup.e].sub.rr] and VSIP of the [r.sup.th] AO of the [i.sup.th] atom ([[I.sup.i].sub.r]) was: [H.sub.rr] = -[[I.sup.i].sub.r]. In our approach, [[zeta].sub.r] and [H.sub.rr] were finally approximated using polynomial functions of atomic charges:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where [Z.sub.i] is the charge of the atom i, and [a.sub.0], [a.sub.k], [b.sub.0], and [b.sub.k] are polynomial coefficients. The previous a and b parameters were determined using DFT calculations as provided by D[Mol.sup.3] [11] and CASTEP [12] codes. DFT energies were computed in the frame of the generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. Since parameters are obtained using DFT calculations, they implicitly include exchange and correlation effects. They are tuned to reproduce ground state energies, but not band gaps. Parameters are summarized in Ref [13]. The determination of off-diagonal elements ([H.sup.e.sub.rs]) in the Hamiltonian matrix (H) was obtained using the corrected distance-dependent Wolfsberg-Helmholz formula [14]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where r and s are matrix indices and K is a parameter related to the Wolfsberg-Helmholtz constant (~ 1.75) in the extended Huckel molecular orbital theory.

On the basis of previous electronic structure calculations and in the frame of the Born-Oppenheimer approximation, the total energy of the system is computed as follow:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

where first, second, and third terms on the right-hand side are the molecular orbital (MO) energy, the Coulomb energy, and the exchange-repulsion energy, respectively. The MO energy on the right-hand side of Eq. (4) can be written as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

where the first and second terms on the right-hand side are the mono-atomic and the diatomic contributions to the binding energy, respectively ([n.sub.k] is the number of electrons occupied in the [k.sup.th] MO). We computed the covalent binding energy by summing the exchange-repulsion energy (Eq. (4)) and the diatomic contribution to the binding energy (Eq. (5)). Considering a pair of atoms A and B, we used the covalent binding energy between these atoms as the potential well-depth, [D.sub.AB], in the Morse-type pair potential function:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

where [E.sub.AB], [D.sub.AB], [[beta].sub.AB], [R.sub.AB], and [R*.sub.AB] are the pair potential energy between atoms A and B, the binding energy (potential well-depth), a form factor (width of the potential), the interatomic distance, and the equilibrium distance, respectively. The previously determined potentials were used for intramolecular interactions. Intermolecular interactions were performed using Lennard-Jones type pair potentials with parameters taken from the cvff force field [15]. We performed classical molecular dynamics (MD) simulations using NEWRYUDO. In this code, integration of equations of motion is performed through the use of the Verlet algorithm and we used a temperature scaling method similar to the Woodcock thermostat [16] to regulate the temperature. To integrate equations of motion we used a time step of [delta]t = 0.1 fs. We used the Ewald summation technique [17] to account for the long-range component of the electrostatic interactions with a number of k-vectors in each direction of reciprocal space of [k.sub.max] = 6, and [C.sub.Ew, 1] = 4, and [C.sub.Ew, 2] = 0.00027 [pm-.sup.1] defining the width of the Gaussian charge distribution surrounding each partial charges ([alpha] [L.sub.min] = [C.sub.Ew, 1] + [C.sub.Ew, 2] [L.sub.min]).

Kinetic Monte Carlo Method

Kinetic Monte Carlo (KMC) [18] was used for sintering simulations, allowing the diffusion of supported particles (precious metal nanoclusters) as well as support particles (ceramic grains). During the simulation, a diffusion direction is randomly generated and the diffusion length of the KMC step (l) is calculated as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (7)

where D(r) and [DELTA]t are the diffusion coefficient given as a function of particle size and the real-scale diffusion time per KMC step, respectively. At the mesoscale, the thermal diffusion behavior of supported precious metals like Pt is strongly related to its adsorption energy on the substrate. This aforementioned property is well described at the atomic scale and, in fact, can be computed directly by using the Tight-Binding based quantum chemistry calculation program, COLORS. We estimated the activation energy for sintering of the supported metal diffusion ([E.sub.M]) from calculated adsorption energy of Pt on supports (Fig. 4).

It is reflected in the sintering simulator by describing thermal diffusions as expressed in Eq. (8), which is dependent on Pt nanoparticle size, [r.sub.M].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

where T, R, and n denote the absolute temperature, the ideal gas constant, and the particle size dependent coefficient of diffusion of supported metals. [D.sub.M0] stands for the surface diffusion coefficient of supported metals. In the course of the simulation, sintering can also occur between ceramic grains constituting the support. This has been taken into account by an equation similar to Eq. (8) but applied to support particles.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

Here, [E.sub.S] is the activation energy for sintering of ceramic grains (or particles) from the support, [r.sub.S] is the size of ceramic grains, and [D.sub.S0] denotes thermal diffusion coefficient of the support. KMC simulation proceeds by repeating a sintering event for a determined number of particles in the supports and supported precious metals for a determined number of steps. Output coordinates of the system are then used to characterize sintering processes of supported precious metals, enabling one to compare it with experiments.

RESULTS AND DISCUSSION

Macroscopic Catalytic Performances for Honeycomb Reactor

Simulations at the macroscopic scale are very useful, since we can compare directly output data with experiments like chassis dynamometer automotive catalytic performance. Our macroscopic simulator is based on the three following fundamental equations:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

where [C.sub.k], v, [k.sub.j] [[theta].sub.j], [N.sub.surf] and V, are respectively, the concentration of the k species (in ppm or vol%), the flow velocity (m/s), the reaction rate constant, the coverage of reaction sites, the number of sites at the support surface, and the volume. [n.sub.i], [n.sub.c], and [n.sub.[theta]] are coefficients. In combination with these equations, we implemented in the macroscopic simulator various elementary chemical reactions encountered in the honeycomb structure of the exhaust catalyst for mononitrogen oxides (N[O.sub.x]), hydrocarbons (HC), and carbon monoxide (CO). Results are shown and compared with experiments of chassis dynamometer automotive catalytic performance in Fig. 5.

Overall, we observed a good agreement between results produced by our simulator and experimental data. Using the same approach, we also simulated cumulative tailpipe emission experiments as shown in Fig. 6. Again, simulation results exhibit a very good agreement with experiments for CO and NOx, validating our approach for these compounds at the macroscale. For HC, simulation results depart from experiments and the approach need to be further improved.

Theoretical Prediction of Sintering Parameters for Multiscale Simulation

Mesoscale simulations necessitate the knowledge of activation energies corresponding to the system under study, i.e., a combination of support materials (ceramics) and supported nanoclusters (precious metals). We previously mentioned that those activation energies correlate with microscopic quantities like the adsorption energy for [E.sub.M] and the metal-oxygen binding energy for [E.sub.S]. Here, we considered two precious metals, Pt and Ir, and various support materials to refine correlations and improve our predictions of activation energies for mesoscale simulations. Note that while adsorption energies and metal-oxide binding energies are computed with our code COLORS, activation energies are taken from the literature. We reported our data in Fig. 7. We found for both microscopic quantities, i.e., the adsorption energy and the metal-oxygen binding energy, a very good correlation with activation energies.

Artificial Intelligence-based Derivation of Fundamental Parameters for UA-QCMD

Because the use of a human-based approach for the derivation of fundamental parameters for microscopic simulations is tedious, time consuming limiting simulations to a few cases, and subject to errors, we employed artificial intelligence to overcome these problems. The method is based on the Adaptative-Objective-Selection-Base (AOSB) Global Optimization method. It operates with MATLAB[R] and it uses an objective function that could be either non-differentiable or discontinuous and which is defined as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

where [E.sub.target] and [L.sub.target] stand for target values, [E.sub.current] and [L.sub.current] stand for actual values, and [Tol.sub.energy] and [Tol.sub.electron] stand for normalization factors of the binding energy and the electron configuration, respectively. Here, we can see that we optimized at the same time both the binding energy and the electronic structure by minimizing the objective function.

Using the previous technique in combination with our code COLORS we developed a hybrid software called COLAUTO. It employs a simulated annealing (SA) technique to find the global optimum of a given function. The direction of change is decided randomly in the phase space that could be multidimensional. Such combination is set to avoid convergence of the function in a local minimum. We applied this technique to the determination of fundamental parameters for UA-QCMD and we reported our data on binding energy computed with COLORS as well as data from DFT and thermodynamics in Tables 1 and 2.

We found an overall good agreement between our data and DFT and thermodynamics data. Furthermore, to assess the benefit of introducing AI in our approach, we compared in Fig. 8 our new set of binding energy ratios ([E.sub.DFT]/[E.sub.Colors] or [E.sub.Thermo]/[E.sub.Colors]) with previous one obtained with a human-based approach (handmade). We found a clear improvement of the accuracy on binding energies, i.e., there is a narrower distribution around 100%.

To assess further the improvement obtain by including AI in our approach, we used microscopic data computed with our new sets of parameters and we introduced them in our macroscopic simulator. Then, we computed the concentration of [O.sub.2] and the coverage as a function of temperature. We compared our new data with previous simulation and experimental data [19,20] in Fig. 9 and we found a good qualitative agreement.

SUMMARY

In summary, we employed a multiscale, multiphysics computational approach to investigate aging properties of exhaust catalysts at temperature conditions where the durability of materials is important. We refined our computational approach by adding a third level of simulation, i.e., the reactor-scale (macroscopic chemical kinetics simulations), we provided results directly comparable with chassis dynamometer and engine dynamometer experiments (i.e., macroscopic results). Since the use of a human-based approach for the derivation of fundamental parameters for microscopic simulations is tedious, time consuming limiting simulations to a few cases, and subject to errors, we employed artificial intelligence (AI) to overcome these problems. With these two improvements to our original approach, we were able to simulate the exhaust catalyst in a more realistic way and we achieved better accuracy of our microscopic data with the use of artificial intelligence.

REFERENCES

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[4.] Suzuki, A., Sato, R., Nakamura, K., Okushi, K. et al., "Multiscale Theoretical Study of Sintering Dynamics of Pt for Automotive Catalyst," SAE Int. J. Fuels Lubr. 2(2):337-345, 2010, doi:10.4271/2009-01-2821.

[5.] Suzuki A., Nakamura K., Sato R., Okushi K., Koyama M., Tsuboi H., Hatakeyama N., Endou A., Takaba H., Del Carpio C.A., Kubo M., and Miyamoto A., "Development and Application of Sintering Dynamics Simulation for Automotive Catalyst," Topics in Catalysis 52, 1852, 2009.

[6.] Suzuki, A., Sato, R., Nakamura, K., Okushi, K. et al., "Multiscale Theoretical Study of Sintering Dynamics of Pt for Automotive Catalyst," SAE Int. J. Fuels Lubr. 2(2):337-345, 2010, doi:10.4271/2009-01-2821.

[7.] Nagai Y., Hirabayashi T., Dohmae K., Takagi N., Minami T., Shinjoh H., Matsumoto S., "Sintering inhibition mechanism of platinum supported on ceria based oxide and Pt-oxide-support interaction", J. Cat., 242, 103-109, 2006.

[8.] Suzuki A., Selvam P., Kusagaya T., Takami S., Kubo M., Imamura A., Miyamoto A., "Chemical Reaction Dynamics of PeCB and TCDD Decomposition: A -Binding Quantum Chemical Molecular Dynamics Study with First-Principles Parameterization", Int. J. Quantum Chem. 102-3, 318-327, 2005.

[9.] Suzuki A., Nakamura K., Sato R., Okushi K., Tsuboi H., Hatakeyama N., Endou A., Takaba H., Kubo M., Williams M.C., and Miyamoto A., "Multi-Scale Theoretical Study of Support Effect on Sintering Dynamics of Pt," Surface Science 603, 3049, 2009.

[10.] Ahmed F., Alam M.K., Suzuki A., Koyama M., Tsuboi H., Hatakeyama N., Endou A., Takaba H., Del Carpio C.A., Kubo M., and Miyamoto A., "Dynamics of Hydrogen Spillover on Pt/g-[Al.sub.2][O.sub.3] Catalyst Surface: A Quantum Chemical Molecular Dynamics Study," Journal of Physical Chemistry C 113 (35), 15676-15683, 2009.

[11.] Delley B., "An all-electron numerical method for solving the local density functional for polyatomic molecules,"Journal of Chemical Physics, 92, 508-517, 1990; Delley B., "From Molecules to Solids with the DMol3 Approach," Journal of Chemical Physics, 113, 7756-7764, 2000.

[12.] Clark S.J., Segall M.D., Pickard C.J., Hasnip P.J., Probert M.I.J., Refson K., and Payne M.C., "First principles methods using CASTEP," Zeitschrift fur Kristallographie, 220 (5-6). Computational Crystallography, 567-570, 2005.

[13.] Alam Md.K., Ahmed F., Nakamura K., Suzuki A., Sahnoun R., Tsuboi H., Koyama M., Hatakeyama N., Endou A., Takaba H., Del Carpio C.A., Kubo M., and Miyamoto A., "Study of Carbon Monoxide Oxidation on Ce[O.sub.2] (111) Using Ultra Accelerated Quantum Chemical Molecular Dynamics," J. Phys. Chem. C, 113, 7723-7727, 2009.

[14.] Calzaferri G., Forss L., and Kamber I., "Molecular geometris by the extended Huckel molecular orbital method," J. Phys. Chem., 93, 5366, 1989.

[15.] Dauber-Osguthorpe P., Roberts V.A., Osguthorpe D.J., Wolff J., Genest M., and Hagler A. T., "Structure and energetics of ligand binding to proteins: E. coli dihydrofolate reductasetrimethoprim, a drug-receptor system," Proteins: Structure, Function, and Bioinformatics, 4 (1), 31-47, 1988.

[16.] Woodcock L.V., "Isothermal molecular dynamics calculations for liquid salts," Chem. Phys. Lett. 1971, 10 (3), 257-261.

[17.] Frenkel D. and Smit B., Understanding Molecular Simulation: From Algorithms to Applications, 2nd Ed., Academic Press, London, 2002.

[18.] Chatterjee A., Vlachos D.G., "An overview of spatial microscopic and accelerated kinetic Monte Carlo methods", J. Computer-Aided Mater. Des. 14, 253-308, 2007.

[19.] Olsson L., Persson H., Fridell E., Skoglundh M., and Andersson B., "A Kinetic Study of NO Oxidation and N[O.sub.x] Storage on Pt/[Al.sub.2][O.sub.3] and Pt/BaO/[Al.sub.2][O.sub.3]", J. Phys. Chem. B, 105, 6895, 2001.

[20.] Olsson L., Fridell E., Skoglundh M., and Andersson B., "Mean Field Modelling of N[O.sub.x] Storage on Pt/BaO/Al2O3", Catalysis Today, 73, 263, 2002.

CONTACT INFORMATION

Prof. A. Miyamoto

New Industry Creation Hatchery Center (NICHe), Tohoku University 403 NICHe II, 6-6-10, Aoba, Aramaki, Aoba, Sendai 980-8579 Japan

Phone: (+81) 022-795-7235

miyamoto@aki.niche.tohoku.ac.jp

Akira Miyamoto, Kenji Inaba, Yukie Ishizawa, Manami Sato, Rei Komuro, Masashi Sato, Ryo Sato, Patrick Bonnaud, Ryuji Miura, Ai Suzuki, Naoto Miyamoto, Nozomu Hatakeyama, and Masanori Hariyama

Tohoku Univ.

Table 1. Binding energies from Tight-binding simulations (COLORS),
Density Functional Theory (DFT), and thermodynamics data for various
compounds.

                               Colors        DFT       Thermo
                             [kcal/mol]  [kcal/mol]  [kcal/mol]

Mg                             1706.12     1706.79     1687.53
Si[O.sub.2]                  101435.00   103393.46    99528.78
[Mn.sub.2][O.sub.3]            8441.73     8450.29     8672.83
[alpha]_[Al.sub.2][O.sub.3]   52529.20    51542.51    53057.43
Li                             5072.21     5031.54     4873.31
[Nd.sub.2][O.sub.3]           24527.81       --       24555.43
NiO                           22938.00    22821.00       --
C[O.sub.2]                      437.65      433.78      384.46
[Pr.sub.2][O.sub.3]           24191.77       --       24996.72
Ge[O.sub.2]                   37246.10    35854.68    37437.72
[Li.sub.2]O                   30739.92    30961.65    30089.05
S[O.sub.2]                      264.86      283.50      256.30
Zr[O.sub.2]                   17527.90    17216.32    16885.25
P                              9835.11     9609.01     9682.37
Ga                             2125.40     2093.64     2080.26
Ta                            45307.50    46538.03    46724.50
[Ga.sub.2][O.sub.3]           14033.96    13578.02    13655.70
Ge                             5408.82     5006.20     5690.11
Si                            25069.50    27144.99    23230.80
Sb                             4366.18     4144.92     4513.66
Sc                             5917.12     6298.89     5778.82
MgO                            7894.65     8574.56     7632.00

                             DFT/Colors  Thermo/Colors
                                 [%]          [%]

Mg                             100.04         98.91
Si[O.sub.2]                    101.93         98.12
[Mn.sub.2][O.sub.3]            100.10        102.74
[alpha]_[Al.sub.2][O.sub.3]     98.12        101.01
Li                              99.20         96.08
[Nd.sub.2][O.sub.3]             --           100.11
NiO                             99.49         --
C[O.sub.2]                      99.12         --
[Pr.sub.2][O.sub.3]             --           103.33
Ge[O.sub.2]                     96.26        100.51
[Li.sub.2]O                    100.72         97.88
S[O.sub.2]                     107.04         96.77
Zr[O.sub.2]                     98.22         96.33
P                               97.70         98.45
Ga                              98.51         97.88
Ta                             102.72        103.13
[Ga.sub.2][O.sub.3]             96.75         97.30
Ge                              92.56        105.20
Si                             108.28         92.67
Sb                              94.93        103.38
Sc                             106.45         97.66
MgO                            108.61         96.67

Table 2. Binding energies from Tight-binding simulations (COLORS),
Density Functional Theory (DFT), and thermodynamics data for various
compounds.

                       Colors        DFT       Thermo
                     [kcal/mol]  [kcal/mol]  [kcal/mol]

PtO                   -7359.32    -7353.16    -7351.20
V                     -6436.53    -6446.72    -6636.27
Nb                    -9096.23    -8808.12    -9368.47
Si                    -6672.01    -6463.41    -6883.20
Ti[O.sub.2]           -7795.05    -7432.59    -8236.20
Fe                   -12164.75   -11612.62   -12729.54
Cu                    -2470.95    -2360.64    -2580.48
Ft                   -32502.73   -30474.09   -34587.32
HCN                    -314.57     -325.05     -304.08
[Si.sub.3][N.sub.4]   -1972.98    -2049.13    -1904.50
HN[O.sub.2]            -325.31     -347.99     -303.06
[H.sub.2]S             -147.83     -157.51     -138.17
Amine                  -941.43     -941.13       --
Ethoxylate            -2489.07    -2489.29       --
Amine

                     DFT/Colors  Thermo/Colors
                         [%]          [%]

PtO                     99.92        99.89
V                      100.16       103.10
Nb                      96.83       102.99
Si                      96.87       103.17
Ti[O.sub.2]             95.35       105.66
Fe                      95.46       104.64
Cu                      95.54       104.43
Ft                      93.76       106 41
HCN                    103.33        96.67
[Si.sub.3][N.sub.4]    103.86        96.53
HN[O.sub.2]            106.97        93.16
[H.sub.2]S             106.54        93.46
Amine                   99.97        --
Ethoxylate             100.01        --
Amine
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Author:Miyamoto, Akira; Inaba, Kenji; Ishizawa, Yukie; Sato, Manami; Komuro, Rei; Sato, Masashi; Sato, Ryo;
Publication:SAE International Journal of Engines
Article Type:Report
Date:Dec 1, 2016
Words:5028
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