3D-Printed Potential and Free Energy Surfaces

This page contains examples of the potential and free energy surfaces we fabricated using 3D printing technology. We use these surfaces in undergraduate and graduate courses to illustrate such concepts as transition state, minimum energy reaction path, reaction trajectory, harmonic frequency and anharmonicity. More details can be found in the following publication:

D.S. Kaliakin, R.R. Zaari, S.A. Varganov, 3D Printed Potential and Free Energy Surfaces for Teaching Fundamental Concepts in Physical Chemistry,  J. Chem. Ed. 92, 2106-2112 (2015) 

Hydrogen Exchange Reaction

H3

 

 

Two valleys on this potential energy surface represent two reaction channels in which one of the terminal hydrogen atoms dissociates from the transition state complex. Reaction coordinates defined as the interatomic distances r1 and r2. The dissociation of terminal hydrogen atoms are indistinguishable from one another.

 

 


Rotations of Methyl Groups in 1‑Fluoro‑2‑Methylpropene

C4H7F

 

 

 

 

On this potential energy surface the rotation of two methyl groups is described by the dihedral angles φ1 and φ2. The difference in steric interactions of two methyl groups with H1 and F atoms results in the different activation energies for the transitional states TS1 and TS2. The structure with both methyl groups rotated into “high-energy” conformations corresponds to the second-order saddle point (SP) on the potential energy surface. 

 

 

 

 

 


Funnel Surface of Protein Folding

Funnel

 

The 3D funnel surface demonstrates multiple conformations a protein can achieve as a result of folding. This free energy surface is based on the analytical function that represents the general form of a funnel surface. To generate this model surface we modified the Mathematica notebook obtained from Prof. T. G. Oas’s group (http://www.oaslab.com/Drawing_funnels.html).

 

 


Triatomic Molecule ABC

ABC

 

This potential energy surface has one minimum corresponding to the equilibrium structure of the linear molecule ABC, two reaction paths with transition states TS1 and TS2 leading to dissociation products AB + C and A + BC, and a barrierless reaction path corresponding to A + B + C atomization.

 

 

 


Adsorption on a Surface

Adsorption

 

Multiple minima on this surface correspond to energetically favorable adsorption sites, while maxima (also second-order saddle points) correspond to energetically unfavorable sites. Dashed lines indicate the minimum energy reaction paths for surface diffusion of adsorbed molecules or atoms.

 

 


Double Minimum Surface

Double

 

The x- and y-axis of this model surface represent two general reaction coordinates, while the z-axis designates the potential energy of the system. The shallow well represents the local minimum (Min 2) of the system, while the deep well  corresponds to the global minimum (Min 1). This model allows for simple demonstrations of a chemical reaction proceeding from reactants to products through a transition state (TS).

 

 


Quadruple Minimum Surface

Quadruple

 

 

All four minima on this model surface have different depths, with the global minimum labeled as Min 1. The surface also has four non-equivalent transitional states and one second-order saddle point.