Vibrational Averaging of the Isotropic Hyperfine Coupling Constants for the Methyl Radical
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1 Averaging of the Isotropic Hyperfine Coupling Constants for the Methyl Radical surface and Sergei 1 Fachbereich C-Physikalische und theoretische Chemie, Bergische Universitt Wuppertal,D Wuppertal, Germany 2 Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom aadam@uni-wuppertal.de June 19, 2014
2 Overview surface surface Temperature 4 Summary and Conclusions 5 Acknowledgement
3 ESR surface structure of radicals detection of radicals chemical kinetics chemistry, biology, and medicine
4 Simulated spectrum of CH 3 radical with hyperfine coupling constant a surface Figure : Bovet, C.; Barron, A. EPR : An Overview, OpenStax-CNX Web site. http//cnx.org/content/m22370/1.3/, May 23, 2009
5 surface Bond distance CCSD(T)/aVTZ = Å CCSD(T)/aQTZ = Å = Å Figure : from Principles of General Chemistry (v.1.0 M) by Bruce A. Averill
6 surface Method/Basis Set A iso eql,g UB3LYP/ERP-III 28.2 CISD/DZ 25.7 CCSD(T)/Chipman 28.5 B3LYP/Huz-IVu4s 30.1 UB3LYP/EPR-III 28.6 UB2PLYP/EPR-III 30.0 OO-RI-MP2/EPR-III 30.0 OO-SCS-RI-MP2/EPR-III 22.0 CCSD(T)/EPR-III 24.7 Table : 13 C isotropic in CH 3 (Table data from Chen X, Rinkevicius Z, Ruud K, Ågren H., J. Chem. Phys. 2013, 138, See this paper for original references.)
7 surface Method/Basis Set A iso eql,g UB3LYP/ERP-III 28.2 CISD/DZ 25.7 CCSD(T)/Chipman 28.5 B3LYP/Huz-IVu4s 30.1 UB3LYP/EPR-III 28.6 UB2PLYP/EPR-III 30.0 OO-RI-MP2/EPR-III 30.0 OO-SCS-RI-MP2/EPR-III 22.0 CCSD(T)/EPR-III Table : 13 C isotropic in CH 3 (Table data from Chen X, Rinkevicius Z, Ruud K, Ågren H., J. Chem. Phys. 2013, 138, See this paper for original references.)
8 Thermal Averaging surface < P > T = 1 Q Q = i i g i exp( E rv (i) kt ) < P > i =< Φ (i) rv P Φ (i) rv > where.. P = operator T = absolute temperature Q = partition function g i = degeneracy g i exp( E rv (i) kt ) < P > i
9 Thermal Averaging surface < P > T = 1 Q Q = i i g i exp( E rv (i) kt ) < P > i =< Φ (i) rv P Φ (i) rv > where.. P = operator T = absolute temperature Q = partition function g i = degeneracy g i exp( E rv (i) kt ) < P > i E (i) rv Φ (i) rv = eigenvalues = eigenvectors
10 Thermal Averaging more details surface
11 and s surface 2625 unique symmetry points near equilibrium geometry UHF-CCSD(T)/aug-cc-pVTZ for UHF-CCSD(T)/EPR-III for surface Least squares fitting
12 surface Method/Basis Set A iso eql A iso vib A iso vib Temp. (G) (G) (G) (K) B3LYP/Huz-IIIsu (41%) 0 P(CI)/DZ (58%) 96 MCSCF/cc-pVTZus2st (35%) 0 CCSD(T)/EPR-III (48%) 0 CCSD(T)/EPR-III (48%) Table : 13 C isotropic in CH 3 (Table data from Chen X, Rinkevicius Z, Ruud K, Ågren H., J. Chem. Phys. 2013, 138, See this paper for original references.) Our work is in blue color
13 Temperature surface Method/Basis Set A iso eql A iso vib A iso vib Temp. (G) (G) (G) (K) B3LYP/Huz-IIIsu (41%) 0 P(CI)/DZ (58%) 96 MCSCF/cc-pVTZus2st (35%) 0 CCSD(T)/EPR-III (48%) 0 CCSD(T)/EPR-III (48%) CCSD(T)/EPR-III (52%) 300 Table : 13 C isotropic in CH 3 (Table data from Chen X, Rinkevicius Z, Ruud K, Ågren H., J. Chem. Phys. 2013, 138, See this paper for original references.) Our work is in blue color
14 Summary and Conclusions surface effects cannot be ignored in the case of 13 C isotropic for CH 3 Compared to other averaging methods, our averaging included the rotational motion and coupling between vibrational modes With temperature effects, the ro-vibrational contribution will exceed the electronic contribution
15 Acknowledgment surface Thanks to.. Yachmenev (UCL) for many helpful discussions Sergei Yurchenko (UCL) and Per Jensen (BUW) Financial support by DFG - Deutsche Forschungsgemeinschaft
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