*trans*-formanilide

^{1}, David M. Leitner

^{1,a)}, Evgeniy M. Myshakin

^{2}and Kenneth D. Jordan

^{3,b)}

### Abstract

A potential energy surface for *trans*-formanilide (TFA)- is calculated and applied to study energy flow in the complex as well as the kinetics of water shuttling between hydrogen bonding sites on TFA. In addition to the previously identified and minima, with the water monomer bound to the and NH groups, respectively, the new surface reveals a second local minimum with the water bound to the group, and which lies energetically above the previously identified global minimum. On this surface, the energy barrier for water shuttling from global minimum to is , consistent with the experimental bounds of 796 and [J. R. Clarkson *et al.*Science307, 1443 (2005)]. The ergodicity threshold of TFA is calculated to be ; for the TFA- complex, the coupling to the water molecule is found to lower the ergodicity threshold to below the isomerization barrier. Energy transfer between the activated complex and the vibrational modes of TFA is calculated to be sufficiently rapid that the Rice-Ramsperger-Kassel-Marcus (RRKM) theory does not overestimate the rate of water shuttling. The possibility that the rate constant for water shuttling is higher than the RRKM theory estimate is discussed in light of the relatively high energy of the ergodicity threshold calculated for TFA.

Support for this work by the National Science Foundation (CHE-0512145 to one of the authors D.M.L. and CHE 0518253 to another author K.D.J.) is gratefully acknowledged. The authors thank Professor T. Zwier for insightful discussions of the experimental work on TFA-.

I. INTRODUCTION

II. COMPUTATIONAL METHODS

A. Quantum energy flow and isomerization kinetics

B. Electronic structure calculations

III. RESULTS AND DISCUSSION

A. Potential energy surface and reaction pathways

B. Energy flow and shuttling kinetics

IV. CONCLUDING REMARKS

### Key Topics

- Energy transfer
- 29.0
- Isomerization
- 16.0
- Hydrogen bonding
- 13.0
- Potential energy surfaces
- 11.0
- Vibrational states
- 9.0

## Figures

Geometries of the stationary points on the potential energy surface of -TFA obtained at the B3LYP/aug-cc-pVDZ level of theory. The numerical values of the imaginary frequencies associated with transition state structures are given in parentheses. For TS I the imaginary frequency corresponds to the in-plane waging motion of the water molecule. For TS II the imaginary frequencies correspond to a rock and a waging motion of the water molecule. For TS III the imaginary frequency corresponds to a motion of the waging water molecule. For the imaginary frequency corresponds to an OH wag motion.

Geometries of the stationary points on the potential energy surface of -TFA obtained at the B3LYP/aug-cc-pVDZ level of theory. The numerical values of the imaginary frequencies associated with transition state structures are given in parentheses. For TS I the imaginary frequency corresponds to the in-plane waging motion of the water molecule. For TS II the imaginary frequencies correspond to a rock and a waging motion of the water molecule. For TS III the imaginary frequency corresponds to a motion of the waging water molecule. For the imaginary frequency corresponds to an OH wag motion.

(a) Potential energy surface of the -TFA complex obtained at the level of theory. (b) Contour plot of (a) with contour lines of . Red lines designate the pathways of water shuttling between the CO (I) and NH sites.

(a) Potential energy surface of the -TFA complex obtained at the level of theory. (b) Contour plot of (a) with contour lines of . Red lines designate the pathways of water shuttling between the CO (I) and NH sites.

(a) The positions of water above TFA corresponding to the calculated PES. (b) Contour plot of (a) with contour lines of .

(a) The positions of water above TFA corresponding to the calculated PES. (b) Contour plot of (a) with contour lines of .

Average cubic matrix elements for . B3LYP/aug-cc-pVDZ results (x), results obtained using the scaling relation given by Eq. (5) with and (open circles). The transition parameter, , obtained with values from the electronic structure calculations (squares) as well as using the scaling relation (circles) is also plotted. The arrows indicate the appropriate axis.

Average cubic matrix elements for . B3LYP/aug-cc-pVDZ results (x), results obtained using the scaling relation given by Eq. (5) with and (open circles). The transition parameter, , obtained with values from the electronic structure calculations (squares) as well as using the scaling relation (circles) is also plotted. The arrows indicate the appropriate axis.

Value of the transition parameter, , defined by Eq. (4), calculated using anharmonicity terms only through third-order (open circles), fourth-order (squares), fifth-order (triangles), and eighth-order (X). The curve obtained allowing for contributions to all orders is given by the filled circles. The arrow indicates the position of the IVR threshold where .

Value of the transition parameter, , defined by Eq. (4), calculated using anharmonicity terms only through third-order (open circles), fourth-order (squares), fifth-order (triangles), and eighth-order (X). The curve obtained allowing for contributions to all orders is given by the filled circles. The arrow indicates the position of the IVR threshold where .

RRKM theory rate calculated assuming a barrier (solid) and a barrier (dashed) for TFA- water shuttling (black) and the reverse reaction (gray). The fastest vibrational energy transfer rates from intermolecular modes to TFA modes are shown for each conformer. These correspond to the mode of TFA- (dotted) and the mode of TFA- (dot dashed). Arrows indicate the appropriate axis.

RRKM theory rate calculated assuming a barrier (solid) and a barrier (dashed) for TFA- water shuttling (black) and the reverse reaction (gray). The fastest vibrational energy transfer rates from intermolecular modes to TFA modes are shown for each conformer. These correspond to the mode of TFA- (dotted) and the mode of TFA- (dot dashed). Arrows indicate the appropriate axis.

## Tables

Potential energy barriers , relative energies , and binding energies for the -TFA complex at and B3LYP/aug-cc-pVDZ levels of theory. Energies corrected for vibrational ZPE are given in parentheses.

Potential energy barriers , relative energies , and binding energies for the -TFA complex at and B3LYP/aug-cc-pVDZ levels of theory. Energies corrected for vibrational ZPE are given in parentheses.

The six “intermolecular modes” and their projections onto the water molecule displacement coordinates are listed for each isomer.

The six “intermolecular modes” and their projections onto the water molecule displacement coordinates are listed for each isomer.

Intrinsic rate from reactive states to product computed at the barrier energy assuming barriers of 750 and .

Intrinsic rate from reactive states to product computed at the barrier energy assuming barriers of 750 and .

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