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Use of P otential E nergy S urfaces (PES) in Spectroscopy and Reaction Dynamics

This article explores the use of Potential Energy Surfaces (PES) in the fields of molecular spectroscopy and reaction dynamics. It discusses the connection between PES and theory/experiment, as well as the applications of PES in spectroscopy and reaction dynamics. The article also covers topics such as vibrational and rotational calculations, statistical mechanics, and theories of molecular collisions. The text includes a flow chart outlining the process of determining PES, and provides examples of different types of PES. It concludes with a discussion on the use of PES in reaction dynamics and the calculation of reaction rates.

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Use of P otential E nergy S urfaces (PES) in Spectroscopy and Reaction Dynamics

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  1. Molecular spectroscopy and reaction dynamics EFN010F Use of Potential Energy Surfaces (PES) in Spectroscopy and Reaction Dynamics Jingming Long Department of chemistry University of Iceland December 03, 2010

  2. Nucleus, electrons. Schrodinger equation Spectroscopy, Reaction dynamics Potential Energy Surfaces Cross sections Molecular beams Chemical kinetics Thermophysical properties Macroscopic (“bulk”) Coefficients Overview Connection between PES and theory, experiment Vib-rotational calculations Transition state minima Born-Oppenheimer approximation Theories of molecular collision Statistical mechanics

  3. Molecular structure and variable RAB RAB RAB q2 RBC q1 q RBC RCD RAC RAB RAB RAC q RCD RBC RBC

  4. Variable(s) in PES 3N-6 (Nonlinear molecules) Freedom degree = 3N-5 (Linear molecules) N=2, potential energycurve N≧3, potential energy hypersurface Potential energy surfaces U(q1) U(q1, q2) q1, q2, …∈ {Rn, qn} or {xn, yn, zn} U(q1, q2, q3) U(q1, q2, q3, … …qn)

  5. b b a 0 Typical PES

  6. Use of PES in spectroscopy

  7. AB A + B PES for AB Energy, E Dissociation limitation : : Dissociation energy De 3 Vibrational levels 2 Rotational levels 1 0 0 Re Bond length, R k=(ⅾ2U(r)/dr2) |Re

  8. Parameters in spectral calculation we Be=h/(8pmRec) u=1/2p*(k/m)1/2 D=ℏ2/(2m2Re2k) cewe=we2/4De h Plank constant kForce constant mReduced mass uVibrational frequency c Light speed ReDistance between nucleus

  9. EEle ERot EVib Energy level and spectrum E(V, J)= u0+we(V+1/2)-cewe(V+1/2)2+BJ(J+1)-DJ2(J+1)2 V =0,1,2.. J=0, 1, 2… Rotational spectrum DE=E(J’,V)- E(J’’,V) Vib-rotational spectrum DE=E(J’,V’)- E(J’’,V’’)

  10. Flow chart to determinate PES Initial Guess at parameters of potential surface Experimental spectrum ab initio calculation Compare and adjust parameters Calculate potential surface Calculate spectrum Calculate energy levels and wavefunctions

  11. General PES for diatomic molecule Lennard-Jones U(R)=4e {(s/R)12-(s/R)6} , Re=2 1/6s Morse U(R)=De{1-exp[-b(R-Re)]}2 Rydberg U(R)=-De{1+b(R-Re)]}exp[-g(R-Re)] Murrell U(R)=-De{1+a1(R-Re)+a2(R-Re)2+a3(R-Re)3]}exp[-g(R-Re)] … … a1, a2, a3, g, b are adjustable parameters in spectral calculation

  12. Calculated program PES ab initio calculation program Gaussion98, 03www.gaussian.com ABINIT www.abinit.org DMol3 people.web.psi.ch/delley/dmol3.html CPMDwww.cpmd.org VASPcms.mpi.univie.ac.at/vasp MOLPROwww.molpro.net Agust Kvaran’s group www.hi.is/~agust REMPICalc.pxp HCl-DCl rof.pxp HCl_DCl 1.pxp FCF.pxp HClexp.pxp UV-rof 1.pxp … …

  13. PES simulation (a) Different PESs for HCl (b) Wavefunctions

  14. Calculated spectrum (b) (a) F1D2(v’=0)←←X1S+(v’’=0)

  15. Calculated spectrum (2+n) REMPI-TOF spectrum and calculation for HF

  16. Use of PES in reaction dynamics

  17. Intermediate Ts Ts Energy R I P Global minimum Reactants Reaction coordination Transition state Products Reaction dynamics Local minimum For a minimum Stationary point ∂2U/∂q2 > 0 ∂U/∂q = 0 For a transition state ∂2U/∂q2 > 0 ∂U/∂q = 0 ∂2U/∂q2 < 0 Saddle point

  18. RAB Re2 RBC Re1 AB+CA+BC C A AB For example: Br + HCl(v) → HBr + Cl Na + HF(v’,J’) → H + NaF(v’’,J’’) v =0,1,2.. J=0, 1, 2… BC Trajectory

  19. Different shaped contour plot

  20. Reaction progress

  21. Energy Reactants Ea Products DH Reaction coordination Calculation in Reaction dynamics K=Ae-Ea/RT K rate constant A frequency factor T temperature Ea activation energy R gas constant

  22. References Jaime Fernandez Rico, Alfred0 Aguado, Miguel Paniagua .Searching critical points of fitted potential energy surfaces [J] Journal of Molecular Structure (Theochem). 371(1996) 85-90. P.M.Morse, Phys. Rev.,34, 57(1929) Ágúst Kvaran,Huasheng Wang, Kristján Matthiasson, Andras Bodi, Erlendur JónssonandTHE Journal Of Chemical Physics 129, 164313 (2008) Eryin Feng et al, Chem. Phys. Lett.,454 (2008) 7–11 Ralph Jaquet, Interpolation and fitting of potential energy surfaces: Concepts, recipes and applications, March 17, 2002

  23. Thank you !

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