2 Theoretical and Calculation Methods
2.1 Calculation Models
In the construction of PES for proton transfer, we focused on the four proton transfer
models: (a) AmH
+
-Am, (b) ImH
+
-Im as homo-molecular pairs, and (c) ImH
+
-Am,
(d) AmH
+
-Wat as hetero-molecular pairs (Fig. 1). Figure 2 shows also these models
and potential energy coordinates. For homo-molecular pairs, coordinate R denotes
the intermolecular distance and x is the translating proton position that defines as a
displacement from the center of the intermolecular distance. For hetero-molecular
pairs, r is used as the displacement between a proton-bonded atom and the proton.
2.2 Diabatic Potential Functions (V
di
11 , V
di
22 and V
di
12 )
In this study, we constructed a PES for proton transfer by using diabatic picture.
Diabatic potentials can be constructed using a variety of valence bond (VB) configurations [7–11]. Here, we considered a two-state VB electronic wave function as
the diabatic basis corresponding to the reactant and product states, i.e., Equation (1). In particular, the EVB approach can be related to use of molecular
mechanical potential functions describing the molecular vibration, which is rational
for understanding chemical reaction. In most cases, the diagonal matrix elements
(V
di
11 and V
di
22 ) are taken as the harmonic normal-mode or Morse potentials [14, 15,
17, 18, 25, 26]. On the other hand, Chang and Millar [14] suggested the use of a
generalized Gaussian function as the non-diagonal matrix element (V
di
12 ).
Therefore, we selected the Morse function as the V
di
11 and V
di
22 , and Gaussian
function as the V
di
12 to construct PES for proton transfer. For homo-molecular pairs,
V
di
11 , V
di
22 and V
di
12 are explicitly defined as
N
H
H
H
H
N
H
H
H
x
R
(a) AmH
+
-Am
N
N
H
H
N
N
H
R
x
(b) ImH
+
-Im
N
N
H
H
R
N
H
H
H
r
(c) ImH
+
-Am
N H
H
O
H
r
H
H
H
R
(d) AmH
+ -Wat
Fig. 2 Proton transfer model
and potential energy
coordinates for a AmH
+ -Am,
b ImH
+ -Im, c AmH
+ -Wat,
and d ImH
+
-Am
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Y. Hori et al.