Eq. (2), V
di
12 contributes to the stability of the adiabatic potential V
ad and the
A ̸ V
di
11 x = 0 or r = r c
ð
Þis assumed to be determined the rate of contribution to the
possibility of proton transfer. For both homo-molecular pairs, the value of A ̸ V
di
11
decreased as R increased and was approximately 50 to 80% at various intermolecular distance. Thus, the proton can easily transfer at the location formed
hydrogen bond for homo-molecular pairs. On the other hand, for both
hetero-molecular pairs, the value of A ̸ V
di
11 was constantly about 20% over wide
range intermolecular distance, which was lower than homo-molecular pairs for all
intermolecular distance. It indicates that the proton for homo-molecular pairs can
easily transfer than for hetero-molecular pairs. From the above discussion, we find
that the obtained potentials give the qualitative information about proton transfer
even if a simple two-state diabatic model is used.
4 Conclusion
Potential energy surface (PES) is an important theoretical approach for understanding chemical reactions. Diabatic potentials are used to understand proton
transfer reactions. Especially, EVB approach based on the diabatic picture is used to
the molecular mechanical function to construct PES and applied to many applications including molecular dynamics simulation. In this paper, we constructed the
PES based on diabatic model for proton transfer models: (a) AmH
+
-Am, (b) ImH
+
-
Im, (c) ImH
+
-Am and (d) AmH
+ -Wat. We confirmed that Morse potentials as the
diagonal matrix element (V
di
11 and V
di
22 ) and Gaussian function as the non-diagonal
matrix element (V
di
12 ), which are important to apply widely to understanding the
chemical reaction including the classical or quantum dynamics simulations,
described the proper PES for proton transfer. In addition, we proposed a simple
method to uniquely construct the diabatic potentials using these analytical functions. The diabatic potentials at various intermolecular distance were obtained using
fewer reference points than the adiabatic potentials to describe an entire proton
transfer system. Therefore, our construction method is useful and can be applied to
the large molecular systems such as proteins.
From the values of estimated the potential parameters, V
di
12 was broadly distributed and the proton-bonded mixture between the reactant and product states
occurred over a wide range of reaction coordinates, and not only at the TS. Furthermore according to the relation between diagonal and non-diagonal matrix elements, it is found that the proton for homo-molecular pairs can transfer easily than
for hetero-molecular pairs.
Acknowledgements This work was supported by a Grant-in-Aid for Scientific Research
(23310063, 26286002) from the Ministry of Education, Science and Technology, Government of
Japan.
Construction of a Potential Energy Surface …
191
di
12 contributes to the stability of the adiabatic potential V
ad and the
A ̸ V
di
11 x = 0 or r = r c
ð
Þis assumed to be determined the rate of contribution to the
possibility of proton transfer. For both homo-molecular pairs, the value of A ̸ V
di
11
decreased as R increased and was approximately 50 to 80% at various intermolecular distance. Thus, the proton can easily transfer at the location formed
hydrogen bond for homo-molecular pairs. On the other hand, for both
hetero-molecular pairs, the value of A ̸ V
di
11 was constantly about 20% over wide
range intermolecular distance, which was lower than homo-molecular pairs for all
intermolecular distance. It indicates that the proton for homo-molecular pairs can
easily transfer than for hetero-molecular pairs. From the above discussion, we find
that the obtained potentials give the qualitative information about proton transfer
even if a simple two-state diabatic model is used.
4 Conclusion
Potential energy surface (PES) is an important theoretical approach for understanding chemical reactions. Diabatic potentials are used to understand proton
transfer reactions. Especially, EVB approach based on the diabatic picture is used to
the molecular mechanical function to construct PES and applied to many applications including molecular dynamics simulation. In this paper, we constructed the
PES based on diabatic model for proton transfer models: (a) AmH
+
-Am, (b) ImH
+
-
Im, (c) ImH
+
-Am and (d) AmH
+ -Wat. We confirmed that Morse potentials as the
diagonal matrix element (V
di
11 and V
di
22 ) and Gaussian function as the non-diagonal
matrix element (V
di
12 ), which are important to apply widely to understanding the
chemical reaction including the classical or quantum dynamics simulations,
described the proper PES for proton transfer. In addition, we proposed a simple
method to uniquely construct the diabatic potentials using these analytical functions. The diabatic potentials at various intermolecular distance were obtained using
fewer reference points than the adiabatic potentials to describe an entire proton
transfer system. Therefore, our construction method is useful and can be applied to
the large molecular systems such as proteins.
From the values of estimated the potential parameters, V
di
12 was broadly distributed and the proton-bonded mixture between the reactant and product states
occurred over a wide range of reaction coordinates, and not only at the TS. Furthermore according to the relation between diagonal and non-diagonal matrix elements, it is found that the proton for homo-molecular pairs can transfer easily than
for hetero-molecular pairs.
Acknowledgements This work was supported by a Grant-in-Aid for Scientific Research
(23310063, 26286002) from the Ministry of Education, Science and Technology, Government of
Japan.
Construction of a Potential Energy Surface …
191