_{3}]

^{2+}in aqueous solution

^{1,a)}

### Abstract

A simple model electronic Hamiltonian to describe the potential energy surfaces of several low-lying d−d states of the [Fe(bpy)_{3}]^{2+} complex is developed for use in molecular dynamics (MD) simulation studies. On the basis of a method proposed previously for first-row transition metal ions in aqueous solution, the model Hamiltonian is constructed using density functional theory calculations for the lowest singlet and quintet states. MD simulations are then carried out for the two spin states in aqueous solution in order to examine the performance of the model Hamiltonian. The simulation results indicate that the present model electronic Hamiltonian reasonably describes the potential energy surfaces of the two spin states of the aqueous [Fe(bpy)_{3}]^{2+} system, while retaining sufficient simplicity for application in simulation studies on excited statedynamics.

The author thanks Professors Nobuaki Koga and Takeshi Yamamoto for valuable comments and discussions. The computations were partly carried out on the Information Technology Center, Nagoya University.

I. INTRODUCTION

II. MODEL ELECTRONIC HAMILTONIAN

A. Basic strategy

B. Interaction matrix elements

1. Basis functions

2. Isolated system terms

3. Electrostatic terms

4. Exchange terms

5. Charge transfer terms

6. Auxiliary potential energy functions

C. Evaluations of electronic energies and gradients

III. POTENTIAL ENERGY CURVES AND PARAMETER FITTINGS

A. Reference potential energy curves

B. Parameter fitting

C. Fitting results

IV. MOLECULAR DYNAMICS SIMULATIONS OF AQUEOUS SOLUTION

A. MD conditions

B. Simulation results and discussions

V. CONCLUSIONS

### Key Topics

- Molecular dynamics
- 31.0
- Excited states
- 18.0
- Density functional theory
- 17.0
- Ab initio calculations
- 14.0
- Potential energy surfaces
- 7.0

## Figures

Definitions of local frame , atom symbols, and partial charges for the bipyridine ligand.

Definitions of local frame , atom symbols, and partial charges for the bipyridine ligand.

Potential energy curves along the linearly interpolated path between the LS and HS geometries obtained by DFT calculations. The horizontal axis displays Fe−N distance; the linearly interpolated path includes other geometric changes of the complex, such as bond lengths and angles. Results from the model Hamiltonian and DFT calculations are shown by lines and circles, respectively.

Potential energy curves along the linearly interpolated path between the LS and HS geometries obtained by DFT calculations. The horizontal axis displays Fe−N distance; the linearly interpolated path includes other geometric changes of the complex, such as bond lengths and angles. Results from the model Hamiltonian and DFT calculations are shown by lines and circles, respectively.

(a) Comparisons between normal-mode frequencies of DFT and model Hamiltonian. (b) Inner product of normal-mode vectors, , with respect to normal-mode frequencies of the model Hamiltonian. In both figures, low frequencies up to 1000 cm^{−1} are shown for clarity.

(a) Comparisons between normal-mode frequencies of DFT and model Hamiltonian. (b) Inner product of normal-mode vectors, , with respect to normal-mode frequencies of the model Hamiltonian. In both figures, low frequencies up to 1000 cm^{−1} are shown for clarity.

Potential energy curves of several d−d states along the same linearly interpolated path as shown in Fig. 2. Assignment of electronic states is given by irreducible representation of the *D* _{3} (*O* _{ h }) point group. Solid, dashed, and dashed-dotted lines denote singlet, triplet, and quintet states, respectively. Energy origin is set to the minimum energy point of the LS (^{1} *A* _{1}) state.

Potential energy curves of several d−d states along the same linearly interpolated path as shown in Fig. 2. Assignment of electronic states is given by irreducible representation of the *D* _{3} (*O* _{ h }) point group. Solid, dashed, and dashed-dotted lines denote singlet, triplet, and quintet states, respectively. Energy origin is set to the minimum energy point of the LS (^{1} *A* _{1}) state.

Distributions of (a) Fe−N bond length, (b) C_{2}− bond length, (c) N−Fe−N^{′} angle, and (d) N−C_{2}−−N^{′} dihedral angle of the [Fe(bpy)_{3}]^{2+} complex in aqueous solution. Solid and dashed lines denote singlet (LS) and quintet (HS) results, respectively.

Distributions of (a) Fe−N bond length, (b) C_{2}− bond length, (c) N−Fe−N^{′} angle, and (d) N−C_{2}−−N^{′} dihedral angle of the [Fe(bpy)_{3}]^{2+} complex in aqueous solution. Solid and dashed lines denote singlet (LS) and quintet (HS) results, respectively.

Radial distribution functions of (a) Fe−O and (b) Fe−H for singlet (LS) state (solid), quintet (HS) state (dashed), and the pseudoatom (dashed-dotted).

Radial distribution functions of (a) Fe−O and (b) Fe−H for singlet (LS) state (solid), quintet (HS) state (dashed), and the pseudoatom (dashed-dotted).

Ratio of hydrogen and oxygen coordination numbers, *N* _{H}/*N* _{O}, with respect to the distance from the Fe^{2+} ion for the singlet (LS) state (solid), quintet (HS) state (dashed), and the pseudoatom (dashed-dotted).

Ratio of hydrogen and oxygen coordination numbers, *N* _{H}/*N* _{O}, with respect to the distance from the Fe^{2+} ion for the singlet (LS) state (solid), quintet (HS) state (dashed), and the pseudoatom (dashed-dotted).

A representative first solvation structure within 6.3 Å from Fe^{2+} (green) sampled from a trajectory for the HS state. Red, white, cyan, and blue balls represent oxygen, hydrogen, carbon, and nitrogen atoms, respectively. The figure was created using the VMD program.^{56}

A representative first solvation structure within 6.3 Å from Fe^{2+} (green) sampled from a trajectory for the HS state. Red, white, cyan, and blue balls represent oxygen, hydrogen, carbon, and nitrogen atoms, respectively. The figure was created using the VMD program.^{56}

## Tables

Properties of optimized [Fe(bpy)_{3}]^{2+} geometries.

Properties of optimized [Fe(bpy)_{3}]^{2+} geometries.

Parameters in the model electronic Hamiltonian.

Parameters in the model electronic Hamiltonian.

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