N 3 inversion: Potential energy surfaces and transition states C342L March 28, 2016 Last week, we used the IR spectrum of ammonia to determine the splitting of energy levels due to inversion of the umbrella bend (Figure 1). This week we re going to explore the potential energy surface. Working through these Gaussian calculations we ll characterize the reactant (and product) basins, find the transition state, determine a reaction coordinate, and understand these as minima and maxima on a potential energy surface at the end of lab. We will use our understanding of the potential energy of umbrella inversion to inform quantum mechanical models for the splitting of energy levels. All electronic structure calculations should be done using DFT with the B3LYP method and an accurate 6-311+G(2d,p) basis. We ll run calculations on WebMO to use its built-in queuing protocol, but because of the special nature of these calculations, we ll need to modify our input files to get WebMO to do what we want. N N Figure 1. The inversion reaction for ammonia. It s like an umbrella flipping inside out. See. Calculation 1: Optimization of a basin Step 1: Optimized geometry Follow along on the big screen to set up a new job on an ammonia molecule. Run a Geometry Optimization Gaussian calculation, but edit your input file to look like the following (see ReacOpt.com on the lab page):
N 3 inversion: Potential energy surfaces and transition states C342L 2 This should only take about 10 seconds. Open up the completed job and complete the following table of geometries: Coordinate Value Sketch B1 A1 D1 Step 2: Normal modes Click New Job Using This Geometry, and run a Vibrational Frequencies calculation. Complete the following tables: Vibrational Modes Mode freq (cm -1 ) Reduced Mass (amu) Sketch Umbrella Bend N Bends (x2) Symmetric Stretch Asymmetric Stretches (x2)
N 3 inversion: Potential energy surfaces and transition states C342L 3 To find the reduced mass of each mode, you ll need to look at the raw output following on the big screen. Rotational Constants Label freq (cm -1 ) a b c Step 3: Orbitals Go back to your optimized geometry, and click New Job Using This Geometry, and run a Natural Bond Orbitals calculation. Complete the following table for the Natural Bond Orbitals that are occupied: Natural Bond Orbital Energy Occupancy Sketch sp 3 N sp 3 N 1s 1s N We ll pause here and talk as a class. Calculation 2: Locating a transition state Part 1: Transition state optimization: We ll use an algorithm implemented in Gaussian to find the transition state. The QST3 algorithm uses a configruation in the reactants, a configuration in the products, and a good guess at a configuration at the transition state to accurately find the saddle point between the reactants and products. Prepare a new Gaussian job on N3 using Transition State Optimization. Replace the text of your control file with (see qst3.com on the lab page):
N 3 inversion: Potential energy surfaces and transition states C342L 4 Make sure to replace the values for B1, A1, and D1 in your reactant and product states with the values you determined in step 1 of calculation 1. Complete the following table with data contained near the end of the raw output:
N 3 inversion: Potential energy surfaces and transition states C342L 5 Coordinate TS Reactant Product B1 A1 D1 Part 2: Transition state normal modes: As you did with the optimized structure in the reactant basin, perform a frequency calculation on the transition state. Complete the following table: Vibrational Modes Mode freq (cm -1 ) Reduced Mass (amu) Sketch Reaction Coordinate N Bends (x2) Symmetric Stretch Asymmetric Stretches (x2) Rotational Constants Label freq (cm -1 ) a b c
N 3 inversion: Potential energy surfaces and transition states C342L 6 Part 3: Transition State Natural Bond Orbitals: As in Calculation 1, part 3, determine the natural bond orbitals of the transition state. Natural Bond Orbital Energy Occupancy Sketch 2p z,n sp 2 N 1s 1s N Calculation 3: Intrinsic Reaction Coordinate Set up a calculation using the IRC Calculation (see ). Edit the input file to be (see irc.com on the lab page): This runs an IRC calculation with a limited number of steps. For a calculation with better sampling along the reaction coordinate import the Gaussian output file irc.log into WebMO and look at those results. Characterize the shape of the barrier. What is the height? ow wide is it? ow far apart are the basins? To what degree does the motion along the reaction coordinate incorporate movement of the atoms? Of the dihedral?
N 3 inversion: Potential energy surfaces and transition states C342L 7 Calculation 4: Coordinate Scanned PES Set up a coordinate scan calculation with an input file that looks like the one below. You ll need to edit the fixed value for the bond lengths and the scanned angles of the dihedral (see BDscan.com on the lab page): Summarizing your calculations On the contour plot in figure 2, 1) draw a point at the minimum at each basin and at the transition state, 2) draw a line for the symmetric stretches and bends at the minima and at the transitions state, 3) draw a line tracing the intrinsic reaction coordinate, and 4) draw a line tracing your coordinate scan from the fourth calculation.
N 3 inversion: Potential energy surfaces and transition states C342L 8 1.05 1.00 0.95 0.90 0.85 z x1 x z1 y -0.50-0.40-0.30-0.20-0.10 0.00 0.10 0.20 0.30 0.40 0.50 z1, A x 1, A Figure 2. The potential energy surface for symmetric motion in the ammonia molecule. The axes are the cartesian coordinates of the hydrogen in the xz-plane with the nitrogen atom at the origin.