Transcript WG14.pptx
Theoretical Study of the Ethyl Radical Daniel Tabor Sibert Group June 19, 2013 Background 1 Small barrier in planar configuration Looking down the C-C bond 4 3 5 2 Background Dominant torsion-inversion coupling term is where for CCSD(T)/6-311++G(d,p) Coupling involving large-amplitude degrees of freedom R.S Bhatta, A. Gao, D. S. Perry, THEOCHEM 941, 22-29 (2010). Background Raston et al. J. Chem. Phys. 138, 194303 (2013). S. Davis, D. Uy, D.J. Nesbitt J. Chem. Phys. 112, 1823 (2000). He droplet spectra Outline of Calculation Construct a Hamiltonian Classify terms in the Hamiltonian by their torsional dependence Use Van Vleck Perturbation Theory to Reduce the Coupling Diagonalize K11 K12 K13 K14 E1 0 03 0 K21 K22 K23 K24 0 E2 03 0 K31 K32 K33 K34 0 0 E3 0 K41 K42 K43 K44 0 0 0 E4 Generating a Hamiltonian • Several Strategies for PE – Analytic Derivatives – Finite Difference Calculations – Polynomial Fit to a functional form • Kinetic Energy – Expand the G-matrix as a Taylor Series in each coordinate Symmetry Coordinates Equivalent Geometries Symmetry and the Potential CCSD(T)-F12/cc-pVTZ Torsional Dependence of Higher-Order Terms Van Vleck Perturbation theory is a simple way to transform H to a desired form. If we write T as 1 T e T HT e i S i S , He then T is unitary if S is Hermitian. i S e i [ S , ] H K One solves for S by expanding H and K in powers of . e in [ S ( n ) , ] e i2 [ S ( 2 ) , ] i [ S (1) , ] e H K VV Perturbation Theory 1 T HT K H11 H12 H13 H14 K11 K12 K13 K14 H21 H22 H23 H24 K21 K22 K23 K24 H31 H32 H33 H34 K31 K32 K33 K34 H41 H42 H43 H44 K41 K42 K43 K44 Convenient Third-order Calculation With MP2/cc-pVTZ potential Torsional Dependence of Dipole Operator Future Work • Obtain a full quartic potential at the CCSD(T)F12/cc-pVTZ level, plus higher level one- and two-body terms. • Analyze the coupling of the other degrees of freedom to the torsion-inversion coupling Summary • The ethyl radical is a good model system for studying the effects of internal rotors on systems • Molecule has high symmetry, allowing for a fairly robust calculation with only moderate cost Acknowledgements • Sibert Group – Ned – Amber Jain – Britta Johnson • Gary Douberly