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

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

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

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

5. b
b
a
0
Typical PES

6. Use of PES in spectroscopy

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

8. Be=h/(8pmRec)
D=ℏ2/(2m2Re
2k)
h Plank constant k Force constant
m Reduced mass
c Light speed
u=1/2p*(k/m)1/2
u Vibrational frequency
Re Distance between nucleus
cewe=we
2/4De
we
Parameters in spectral calculation

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

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

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

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

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

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

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

16. Use of PES in reaction dynamics

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

18. AB+CA+BC
RBC
R
AB
Re1
R
e2
AB
BC
C
A
Trajectory
For example:
Br + HCl(v) → HBr + Cl
Na + HF(v’,J’) → H + NaF(v’’,J’’)
v =0,1,2.. J=0, 1, 2…

19. Different shaped contour plot

20. Reaction progress

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

22. 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
References

23. Thank you !