_{4})

_{4}from first-principles calculations: Detecting metastable paths and identifying the minimum free energy path

^{1,a)}

### Abstract

A critical drawback with first-principles thermodynamic calculations is the absence of the vibrational and entropic contributions to the prediction of reaction mechanisms, which could conclusively show that the predicted reaction mechanism might be not the most stable reaction path. This study focused on providing an answer to this problem by examining possible metastable paths for five reactant mixtures whose reaction mechanisms were previously predicted using first-principles thermodynamic calculations. The aim of this study was to find a minimum free energy path among all the possible paths of each reactant mixture. This effort provided the clear conclusion that the original reaction paths predicted from first-principles thermodynamic calculations were the most stable reaction paths at an appropriate H_{2} pressure range for all cases. An additional examination associated with density functional theory uncertainty suggests how the ambiguity of reaction mechanisms predicted based on thermodynamic calculations should be understood and dealt with.

I. INTRODUCTION

II. THEORY

A. Linear programming based thermodynamic calculations

B. Thermodynamic calculations for detecting metastable reaction paths

III. COMPUTATIONAL METHOD

IV. RESULTS AND DISCUSSION

V. CONCLUSIONS

### Key Topics

- Hydrogen reactions
- 74.0
- Reaction mechanisms
- 41.0
- Decomposition reactions
- 34.0
- Reaction enthalphies
- 32.0
- Density functional theory
- 30.0

##### C01B3/00

## Figures

The optimized structure of NaSc(BH_{4})_{4}.

The optimized structure of NaSc(BH_{4})_{4}.

(a) The van't Hoff plots of all possible reaction paths for the reactant NaSc(BH_{4})_{4} in Table III. (b) The deviation of the reaction free energy changes of the metastable path from the original reaction at the same temperature.

(a) The van't Hoff plots of all possible reaction paths for the reactant NaSc(BH_{4})_{4} in Table III. (b) The deviation of the reaction free energy changes of the metastable path from the original reaction at the same temperature.

(a) The van't Hoff plots of all possible reaction paths for the reactant mixture of LiSc(BH_{4})_{4}/NaSc(BH_{4})_{4} in Table II. (b) The deviations of the reaction free energy changes of the metastable paths from the original reaction at the same temperature.

(a) The van't Hoff plots of all possible reaction paths for the reactant mixture of LiSc(BH_{4})_{4}/NaSc(BH_{4})_{4} in Table II. (b) The deviations of the reaction free energy changes of the metastable paths from the original reaction at the same temperature.

(a) The van't Hoff plots of all possible reaction paths for the reactant mixture of Mg(BH_{4})_{2}/NaSc(BH_{4})_{4} in Table IV. (b) The deviations of the reaction free energy changes of the metastable paths from the original reaction at the same temperature.

(a) The van't Hoff plots of all possible reaction paths for the reactant mixture of Mg(BH_{4})_{2}/NaSc(BH_{4})_{4} in Table IV. (b) The deviations of the reaction free energy changes of the metastable paths from the original reaction at the same temperature.

(a) The van't Hoff plots of all possible reaction paths for the reactant mixture of BN/NaSc(BH_{4})_{4} in Table V. (b) The deviations of the reaction free energy changes of the metastable paths from the original reaction at the same temperature.

(a) The van't Hoff plots of all possible reaction paths for the reactant mixture of BN/NaSc(BH_{4})_{4} in Table V. (b) The deviations of the reaction free energy changes of the metastable paths from the original reaction at the same temperature.

## Tables

Original reaction thermodynamics associated with NaSc(BH_{4})_{4} predicted from the DFT based thermodynamic calculations in the previous study.^{16} Δ*U* _{0} is the reaction enthalpy at 0 K. Δ*S* _{conf} is the change of the configurational entropy for a reaction. *T* of *T*Δ*S* _{conf} is the reaction temperature corresponding to the change of the equilibrium state composition of compounds at the linear programming based thermodynamic calculations.

Original reaction thermodynamics associated with NaSc(BH_{4})_{4} predicted from the DFT based thermodynamic calculations in the previous study.^{16} Δ*U* _{0} is the reaction enthalpy at 0 K. Δ*S* _{conf} is the change of the configurational entropy for a reaction. *T* of *T*Δ*S* _{conf} is the reaction temperature corresponding to the change of the equilibrium state composition of compounds at the linear programming based thermodynamic calculations.

Metastable paths for the reactant NaSc(BH_{4})_{4}. Δ*U* _{0} is the reaction enthalpy at 0 K. Δ*S* _{conf} is the change of the configurational entropy for a reaction. *T* of *T*Δ*S* _{conf} is the reaction temperature corresponding to the change of the equilibrium state composition of compounds at the linear programming based thermodynamic calculations.

Metastable paths for the reactant NaSc(BH_{4})_{4}. Δ*U* _{0} is the reaction enthalpy at 0 K. Δ*S* _{conf} is the change of the configurational entropy for a reaction. *T* of *T*Δ*S* _{conf} is the reaction temperature corresponding to the change of the equilibrium state composition of compounds at the linear programming based thermodynamic calculations.

Metastable paths for the reactant mixture of LiSc(BH_{4})_{4}/NaSc(BH_{4})_{4}. Δ*U* _{0} is the reaction enthalpy at 0 K. Δ*S* _{conf} is the change of the configurational entropy for a reaction. *T* of *T*Δ*S* _{conf} is the reaction temperature corresponding to the change of the equilibrium state composition of compounds at the linear programming based thermodynamic calculations.

Metastable paths for the reactant mixture of LiSc(BH_{4})_{4}/NaSc(BH_{4})_{4}. Δ*U* _{0} is the reaction enthalpy at 0 K. Δ*S* _{conf} is the change of the configurational entropy for a reaction. *T* of *T*Δ*S* _{conf} is the reaction temperature corresponding to the change of the equilibrium state composition of compounds at the linear programming based thermodynamic calculations.

Metastable paths for the reactant mixture of Mg(BH_{4})_{2}/NaSc(BH_{4})_{4}. Δ*U* _{0} is the reaction enthalpy at 0 K. Δ*S* _{conf} is the change of the configurational entropy for a reaction. *T* of *T*Δ*S* _{conf} is the reaction temperature corresponding to the change of the equilibrium state composition of compounds at the linear programming based thermodynamic calculations.

Metastable paths for the reactant mixture of Mg(BH_{4})_{2}/NaSc(BH_{4})_{4}. Δ*U* _{0} is the reaction enthalpy at 0 K. Δ*S* _{conf} is the change of the configurational entropy for a reaction. *T* of *T*Δ*S* _{conf} is the reaction temperature corresponding to the change of the equilibrium state composition of compounds at the linear programming based thermodynamic calculations.

Metastable paths for the reactant mixture of BN/NaSc(BH_{4})_{4}. Δ*U* _{0} is the reaction enthalpy at 0 K. Δ*S* _{conf} is the change of the configurational entropy for a reaction. *T* of *T*Δ*S* _{conf} is the reaction temperature corresponding to the change of the equilibrium state composition of compounds at the linear programming based thermodynamic calculations.

Metastable paths for the reactant mixture of BN/NaSc(BH_{4})_{4}. Δ*U* _{0} is the reaction enthalpy at 0 K. Δ*S* _{conf} is the change of the configurational entropy for a reaction. *T* of *T*Δ*S* _{conf} is the reaction temperature corresponding to the change of the equilibrium state composition of compounds at the linear programming based thermodynamic calculations.

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