Transcript Document

Holding Computations of Conical Intersections
to a Gold Standard
The Laser Spectroscopy Facility
Department of Chemistry
Conical Intersections in Chemistry
M. A. Robb and co-workers.
CONICAL INTERSECTIONS
The Electronic Hamiltonian Near the Conical
Intersection in (φ1, φ2) Basis
1 0
 cos  sin  
H Q  H Q 
  R Q  

0 1
 sin   cos  
with
H Q   1
H 11  H 22  ; H  Q   1 H 11  H 22 

2
2
R  Q    H  H
2

2 12
12
  Q   cos 1  H R   sin 1 H 12 R 
General Eigenpairs
E Q  H  R
   cos  2  1  sin  2  2
    sin  2  1  cos  2  2
The Jahn-Teller Conical Intersection
H 11  Q   H 22  Q   e H e  Q  e
H 12  Q   H
*
21
Q  
e H e  Q  e  e H e  Q  e
*
where
e  ea  i eb , Q  Qa  iQb
with ea and eb real, electronic eigenfunctions calculable
by standard quantum chemistry programs
For the Jahn-Teller casea,
E  Q   e H e  Q  e  e H e  Q  e
and   Q    2
a U.
Höper, P. Botschwina, H. Köppel, J. Chem. Phys. 112, 4132 (2000).
Power Series Expansions of matrix elements over p linear
Jahn-Teller modes, and s quadratic Jahn-Teller active modes
p
e H e e  

i 1

1
i Qi ,r
2
r  , 
3 N 62 p
2
1

i Qi ,r  e H h e
2

i 1
p
e H e e


i 1
r  , 
s

i 1
s

i 1
p

i 1
2
ki Qi ,r

r  , 
2
1
gii  Qi ,r 
2
s
 
j 1

r  , 
r  , 
1
gij  Qi ,r Q j ,r 
2
3 N 6 2 p

j 1
1
bij  Qi ,r Q j 
2
 e H l  H q  H CQ  H B e
Relation to PES Derivatives
 Vˆ 
ki  E 
E
 Q 
 i ,  0
  2Vˆ
Bij  E 
 Q Q
j ,
 i
  2Vˆ 
i  E 
 E
 Qi , Qi , 0
  2Vˆ 
gij  E 
E
 Q Q 
 i ,  j ,  0

 E

0
Typical Spectroscopic Hamiltonian
H  H h Hl H q
where  HCQ  H B  has been neglected and spin-orbit coupling,H SO ,
added as necessary
Connecting the Jahn-Teller Parameters and the PES
 e ,i 
Di 
Ki 
1 2

i
2 c
1
k i2
2
i 3 2
g ii

a e
Linear J-T coupling constant of mode i
Quadratic J-T coupling constant of mode i
i
Spin-orbit coupling parameter (cm-1)
with
 i  D i   e ,i
J-T stabilization energy due to mode i
1
2
 total    i   iB
i
Equilibrium vibrational frequency (cm-1) of mode i
 iB  2 Di e,i K i
Total J-T stabilization energy
Barrier to pseudorotation
Vibronic Eigenvalues and Eigenfunction
Solution of
 e H e  T  E e H e   n 

  
0
e H e  T  E   n 
 e H e
Vibronic Eigenvalues and Eigenfunction
Solution of
 e H e  T  E e H e   n 

  
0
e H e  T  E   n 
 e H e
If H SO is neglected and T is set to zero, then one achieves
the usual Jahn-Teller PES, U  , where
M r
M
1 2
1
2
2

U    i Q i  i i  [ki i  gii i cos(ni )]
i  M  r 1 2
i 1 2
Cross-Sections of Potential Surface
H
h
H
h
+H
+H
l
+H l+H
SO
+H
+H
SO
+H
q
l
+H
q
+H
SO
l
Quantities Calculated on the
Potential Energy Surface
E0, X0
xd
εtotal
E0, X0
Emin, Xmin
xd
Qi, etc.
εtotal, εB
Emin, Xmin
εB
energy and geometry at the symmetric point
energy and geometry at the distorted minimum
distortion vector
normal coordinates and first derivatives at X0
Jahn-Teller stabilization energy and barrier to pseudorotation
Computational methods
Value
Method
e,i, i
Qi
X0, E0, xd (I)
Generalized Restricted Hartree-Fock
(GRHF) calculation at the
symmetric point
Xmin,Emin, xd(II),
total (I)
total (II)
CASSCF conical intersection
calculation at the symmetric point
CASSCF calculation at the distorted
minimum
E0 - Emin
   f [x
i
i
i
i
d
( II ), e,i ]
Jahn-Teller Active Molecules
•Linear Jahn – Teller coupling - h(ωe)+ l (D)
•Quadratic Jahn – Teller coupling - q (K)
•Spin-orbit coupling - SO (aξe)
•Quantizing the nuclear moton - T
•Multi-mode effects – Di, Ki, ωei
Jahn-Teller Active Radicals
Methoxy Family
Metal Monomethyl Family
CX3Y
X = H or F
Y = O or S
~
X 2E (C3V)
M-CH3
M = Mg, Ca, Zn, Cd
Cyclopentadienyl Radicals
Benzene Cations
C5X5
C6X3Y3+
X = H or D
X = H or F, Cl, Br
Y = H or F, Cl, Br
~
X ~2E1g (D6h) or
X 2E" (D3h)
~
X 2E"1 (D5h)
~
A 2E (C3V)
PES, REMPI, ZEKE SPECTROSCOPY
ZEKE
PES
h2
h
h
REMPI
h1
(T ~ 300 K)
(T ~ 10 K)
(a)
(b)
Experimentally Characterizing the Jahn-Teller,
Spin-Vibronic Structure
2
3
1
5
1
3
~
A 2A1
1
6
0
0
~
~
-
615 1
+
61
-
51
61
+
61
-
~2
X E
61
+
00
-
00
j = 1/2
j = 3/2
Brief History of Studies of Jahn-Teller
Effect in Cyclopentadienyl
Experimental Spectroscopy
Ab Initio Theory
(stabilization energy in cm-1)
Thrush, 1956
Liehr, 1956 (560)
Liebling & McConnell, 1965
Snyder, 1960 (728)
Carrington, et al., 1965
Hobey & McLachlan, 1960 (495)
Porter & Ward, 1968
Borden & Davidson, 1979 (2484)
Englman & Ramsey, 1970
Meyer, et al., 1979 (5072)
Purins & Feeley, 1973
Bearpark, Robb, & Yamamoto, 1999 (2147)
Engelking & Lineberger, 1977
Cunha & Canuto, 1999 (1614)
Nelson, et al., 1983
Kiefer, et al., 2001 (1655)
Yu, et al., 1988, 1993
Zilberg & Hass, 2002 (2554)
Bernstein, et al., 1995, 1999
Molecular Orbitals involved in
Jahn-Teller Distortion of C5H5
C2v
Diene
Allyl
Distortion
Distortion
D5h
C2v
Pseudorotation around the C5H5
PES
E
Ra
Rb
Ra
E
Rb
C5H5
E2' Vibrational Mode
12 (815)
11 (1058)
10 (1411)
9 (3030)
C5H5
A1 Vibrational Mode
1 (3060)
2 (1098)
Experimentally Characterizing the Jahn-Teller,
Spin-Vibronic Structure
2
3
1
5
1
3
~
A 2A1
1
6
0
0
~
~
-
615 1
+
61
-
51
61
+
61
-
~2
X E
61
+
00
-
00
j = 1/2
j = 3/2
Cyclopentadienyl Excitation Spectrum
C5H5
C5D5
C5H5 Emission from 111
Experimental
21
Ab initio fundamentals
and overtones
Fit fundamentals
and overtones
j=1/2
nj 1
j=3/2
nj 1
82
71
2
2
3
4
5
3
22
6
7
4
8
5
9
6
10
7
11 12
8 9 10 11
Ab initio
Jahn-Teller
Fit Jahn-Teller
Simulation
Experimental
0
500
1000
1500
-1
E (cm )
2000
2500
C5H5 Emission from Origin
Experimental
82
Ab initio fundamentals
and overtones
131141
142
21
3 1 42
3
4
132
22
Fit fundamentals
and overtones
j=1/2
nj 1
2
5
6
7
8
9
10
11 12
Ab initio Jahn-Teller
Fit Jahn-Teller
Simulation
Experimental
0
500
1000
1500
-1
E (cm )
2000
2500
C5H5 Emission from 121
Experimental
Ab initio fundamentals
and overtones
132
82
142
21
Fit fundamentals and overtones
j=1/2
nj 1
j=3/2
nj 1
2
3
2
4
5
3
6
7
4
8
5
9
6
10
7
11 12
8 9 10 11
Ab initio
Jahn-Teller
Fit Jahn-Teller
Simulation
Experimental
0
500
1000
1500
-1
E (cm )
2000
2500
C5D5 Emission From Origin
Experimental
Ab initio fundamentals
and overtones
82
2142
42
142
21
44
132
2 18 2
84
22
Fit fundamentals
and overtones
j=1/2
nj 1
2
3
4
5
6
Ab initio Jahn-Teller
Fit Jahn-Teller
Simulation
Experimental
0
500
1000
1500
-1
E (cm )
2000
2500
Jahn-Teller Parameters
C5H5
calculated
experimental
GRHF
CASSCF (minimum)
CASSCF (intersection)
mode
ωi
Di
ρimin
εi
ωi
Di
ρimin
εi
Di
ρimin
εi
9
-
-
-
-
3030
<0.01
<0.01
<1
<0.01
<0.01
<1
10
1320
0.36
0.14
477
1411
0.68
0.18
959
0.98
0.26
1387
11
1041
0.57
0.19
594
1058
0.34
0.15
360
0.48
0.18
509
12
872
0.19
0.12
166
815
0.19
0.13
155
0.30
0.16
245
εtotal
1237
1474
2147
C5D5
experimental
calculated
GRHF
CASSCF (minimum)
CASSCF (intersection)
mode
ωi
Di
ρimin
εi
ωi
Di
ρimin
εi
Di
ρimin
εi
9
-
-
-
-
2237
<0.01
<0.01
<1
<0.01
<0.01
<1
10
1353
0.63
0.18
852
1378
0.87
0.21
1199
1.24
0.25
1719
11
861
0.39
0.17
336
836
0.36
0.17
301
0.51
0.20
431
12
-
-
-
-
716
<0.01
<0.01
<1
<0.01
<0.01
4
εtotal
1188
1500
2147
Cyclopentadienyl Geometric
Distortion
k=
0
-1
1
-2
S
k
 S
0
2
 4k

 
 5

 S cos
ΔS
(Å/rad.)
Symmetry
coordinate
C5H5
exp
C5D5
C5(H/D)5
calc
C-C-C bend
0.012
0.0093
0.0080
C-C stretch
0.059
0.059
0.066
C-C-H bend
0.022
0.013
0.020
C-H stretch
<0.001
~
~
<0.001
~
<0.001
Benzene Cation Experimental Results
C6F6+, C6H3F3+ LIF jet-cooled excitation and emission spectra T. A. Miller and
V. E. Bondybey, in Molecular Ions: Spectroscopy, Structure, and Chemistry (North-Holland,
1983), The Jahn-Teller Effect in Benzenoid Cations: Theory and Experiment, pp. 201-229.
ZEKE and MATI Spectroscopy
C. H. Kwon and M. S. Kim, J. Chem. Phys. 120, 11578 (2004).
C6H6+, C6D6+
ZEKE and MATI Spectroscopy
R. Linder, K. Müller-Dethlefs, E. Wedum, K. Haber, and E. R. Grant, Science 271, 1698 (1996).
R. Linder, Dissertation, TU Müchen, 1996.
C. H. Kwon, H. L. Kim and M. S. Kim, J. Chem. Phys. 119, 4305 (2003).
A. B. Burrill, Y. K. Chung, H. A. Mann, and P. M. Johnson, J. Chem. Phys. 120, 8587 (2004).
IR Spectroscopy of Ar·C6(H/D)6+
R. G. Satink, H. Piest, G. von Helden, and G. Meijer, J. Chem. Phys. 111, 10750 (1999); J.
Bakker, R. G. Satink, G. von Helden, and G. Miejer, Phys. Chem. Chem. Phys. 4, 24
(2002); J. Bakker, L. Mac Aleese, R. G. Satink, G. von Helden, and G. Meijer,
unpublished results.
Computation
J. Eiding, R. Schneider, W. Domcke, H. Koppel, and W. von Neissen, Chem. Phys. Lett. 177,
345 (1991).
B. E. Applegate and T. A. Miller, J. Chem. Phys. 117, 10654 (2002).
A. Avoird and V. F. Lotrich, J. Chem. Phys. 120, 10069 (2004).
BENZENE CATION PES
Benzene Cation Pseudorotation
1
1
1
1
1
1
Benzene Cation e2g Vibrational Modes
18 573
16 1571
17 1152
15 3017
C6H6+ ZEKE Spectrum
00
Ab initio fundamentals
and overtones
81
21
41
61
71
82
Fit fundamentals
and overtones
Ab initio quadratic
Jahn-Teller
201
(e1g, e1u, e2u)
111
191
202
Fit and split
quadratic
Jahn-Teller
nj 1
j=1/2
2
nj
1 2
j=3/2
3
4
3
Ab initio linear JahnTeller (e2g)
4
5 6
5
6
7
7
8
x30
x30
Fit linear Jahn-Teller
Simulation
Experimental
0
500
cm-1
1000
1500
9
C6D6+ ZEKE Spectrum
00
Ab initio fundamentals
81
and overtones
41
71
82
101
21
61
4181
Fit fundamentals
and overtones
Ab initio quadratic
Jahn-Teller
201
(e1g, e1u, e2u)
202
191
111
Fit and split
quadratic
Jahn-Teller
nj 1
j=1/2
nj
1
j=3/2
2
2
3
Ab initio linear JahnTeller (e2g)
3
4
4
5
6 7
5
6
8
7 8
9
9 10
10
11 12
x4
x4
Fit linear Jahn-Teller
Simulation
Experimental
0
500
cm-1
1000
1500
400
600
800
1000
cm-1
1400
1200
1400
191+|1/2, 2>
1200
141+|1/2, 2>
41 81
1600
3
1600
82141
6171
2141
131
81141
91
41+|3/2, 3>
41+|3/2, 4>
81191
141+|3/2, 1>
141+|3/2, 2>
201+|3/2, 2>*
201+|3/2, 1>*
2
21191
21101
2
41+|3/2, 3>
41+|3/2, 4>
1000
101
141
191*
|1/2, 2>*
41 *
1
6171
1
41+|1/2, 3>
800
141+|3/2, 1>
141+|3/2, 2>
Ar-C6D6+
191*
418 1*
101*
600
141
400
201+|3/2, 1>*, 81201
201+|3/2, 2>*, 81201
41 *
Benzene
Cation
IR
Spectra
81201
Ar-C6H6+
3
4
1800
4
1800
Benzene Cation Jahn-Teller Energy
Stabilization and Geometric Distortion
S
Exp
εT
εB
Minimum
Intersection
εT
εB
εT
εB
726
1
757
-9
1542
62
+
821
3
1019
5
2094
86
1237
0
1474
0
2147
0
C5H5
0
 2k
 3
 S cos




ΔS (Å/rad)
Exp
Calc
C6H6+
C6D6+
C6(H/D)6+
C-C-C bend
0.032
0.033
0.029
C-C stretch
0.038
0.036
0.037
C-C-H bend
0.022
0.014
0.011
C-H stretch
0.0005
0.008
0.0009
Calc
C6H6+
C6F6
 S
Symmetry
coordinate
Stabilization Energy (cm-1)
in e2g modes
Molecule
k
Jahn-Teller Parameters
C6H6+
C6D6+
Constant
Ab initio calc.
Exp. fit
Ab initio calc.
Exp. fit
ωe,18
573
584
546
555
D18
0.42
0.51
0.38
0.46
K18
0.013
0.022
0.015
0.032
ε18π/3
240
293
206
245
ε180
246
306
213
262
ωe,17
1152
1161
844
856
D17
0.12
0.12
0.11
0.13
K17
-0.020
-0.008
-0.018
-0.008
ε17π/3
144
138
94
116
ε170
138
136
91
114
ωe,16
1571
1543
1518
1486
D16
0.23
0.18
0.29
0.24
K16
-0.012
-0.018
-0.013
-0.022
ε16 π/3
373
275
453
366
ε160
364
265
442
350
εT
757
707
753
727
εB
-9
1
-7
-1
PES Scans
State Averaged CAS(5,6)/aug-cc-pVDZ
200
Linear Stabilization (cm-1)
16
17
18
ε18
ε17
ε16
εT
State Averaged
299
162
440
901
CAS Analytical
246
138
364
757
Experimental
306
136
265
707
ε18B
ε17B
ε16B
εBa
State Averaged
17
-1
-6
10
CAS Analytical
6
-6
-9
-9
Experimental
13
-2
-10
1
-1
E(cm )
0
-200
a
-400
-0.4
B2g
B3g
0
/3
-0.2
0.0
o
(amu1/2 A)
0.2
0.4
Net barrier to B3g(Φ=π/3) geometry
with respect to B2g(Φ=0) geometry
CH3O
A1 Vibrational Modes
3(1040)
2 (1422)
1(2822)
CH3O
E Vibrational Mode
6 (1082)
5 (1434)
4 (2891)
Methoxy Dispersed Fluorescence
~
SPIN-VIBRONIC CONSTANTS OF THE X2E STATES OF THE METHOXY
FAMILY OF RADICALS
Parameter
CH3O
CD3O
CH3S
CF3O
CF3S
Totally symmetric modes
e,1
-
-
2776
1215
1142
e,2
1350
005
1313
088
865
e,3
1050.5
1036
727
527
449
Degenerate modes
aFixed
bFor
e,4
2835
2100
-
-
-
D4
0.02
0.03
0
0
0
K4
0
0
0
0
0
e,5
1417
1070
-
600
536
D5
0.075
0.17
0
0.04
<0.01
K5
-0.032
-0.03
0
0
0
e,6
1065
825
913a
465b
320
D6
0.24
0.20
0.045
0.45
0.24
K6
-0.14
-0.16
0
0.05
0
ae
-145
-145
-340
-140
-360
total
419
410
41
233
77
SOtotal
370
367
0
203
0
at ab initio value
CF3O an anharmonicity in 6 was observed, exe=8cm-1
6(TH)=221
5(TH)=33
4(TH)=2
6=256
5=106
4=57
6(SO)=251
5(SO)=94
4(SO)=34
(TH)total=i i(TH)=256
total=i i=419
 (SO) total=i i(SO)=379
All values in cm-1
6(TH)=217
5(TH)=0
4(TH)=0
6=77
5=0
4=0
6(SO)=0
5(SO)=0
4(SO)=0
(TH)total=i i(TH)=217
total=i i=77
(SO)total=i i(SO)=0
All values in cm-1
Spin-Orbit Splitting in Methoxy Family Radicals
O atom
Observed
Splitting
(v=0)
-159
a
Observed
Splitting
(v=0)
a
-159
S atom
-396
-396
OH
-139
-139
SH
-377
-377
CH30
-61
-145
CH3S
-256
-340
CD3O
-56
-145
CF3O
-41
-140
CF3S
-350
-360
FO
-196
-196
FS
-398
-398
Conclusions
•Jahn-Teller active molecules serve as excellent tests of our
understanding of conical intersections
•The spectra of Jahn-Teller active organic radicals can be
reproduced using analytical PESs, but require the inclusion of
other than traditional Jahn-Teller terms
•Modern computational chemistry codes can be utilized to
provide excellent initial estimates for Jahn-Teller parameters
• Best parameter estimates result from computations at the
global minimum rather than the conical intersection
ACKNOWLEDGEMENTS
Tim Barckholtz - Exxon-Mobil
Brian Applegate - UNC
Chris Carter – Johns Hopkins
Ilias Sioutis - OSU
György Tarczay – Eötvös U
National Science Foundation
Photochemical Processes with Conical Intersections
2+2 cycloadditions
Paterno-Buchi reaction
Acrolein photophysics
1,2-dioxetanes
Annulene
Azulene S1 decay
Ring opening of
cyclobutenes
Carbene formation from
diazirine and diazomethane
Photodegradation of
polysilanes
Sigmatropic Rearrangement Photorearrangement of
Fulvene S1 decay
of But-1-ene
acylcyclopropenes to furans
Cycloaddition of Dewar
Benzene
Styrene photoisomerization
Cis-trans Isomerisation of
polyenes
Photochemical
Photochemistry of hexatransformation of ergosterol 1,5-dienes
1,3-diazabicyclo
[2.2.1]hept-2 ene
Singlet and triplet
photofragmentation of
ketene
Oxadi-p-methane and [1,3]acyl sigmatropic
rearrangements of
beta,gamma-enones
M. A. Robb and co-workers
Cyclohexadiene/hexatriene
photochemical
interconversion
Origins of Life
1. Genesis
Can’t be understood by chemistry or
physics
2. Panspermia Life arrived on earth from outer space
Arrhenius, Crick
3. Biopoiesis
Abiogenic synthesis of organic
compounds from prebiotic materials
Miller and Urey, 1953
NH3 + CH4 + H2O + H2 + lightning, UV light
 amino acids, sugars, nucleobases
1% solution of amino acids in ancient oceans:
prebiotic soup
Sagan
DNA, RNA: Biology's Natural Sunscreens
Nucleotides transform electronic energy into heat in < 1 ps
Rapid conversion made possible by conical intersection
between S1 and S0
Subpicosecond nonradiative decay is responsible for high
intrinsic photostability
 same functionality as sunscreens, photostabilizers
J. M. Pecourt, J. Peon, and B. Kohler, J. Am. Chem. Soc.
122, 9348 (2000) and New Scientist 167 12 (2000).
JAHN-TELLER POTENTIAL ENERGY
SURFACE (PES)
Comparison of ab initio Calculations
C 6H 6+
C 6D 6+
This work
Eiding et al.
This work
Eiding et al.
ωe,15
3017
3168
2241
2340
D15
<0.01
<0.01
<0.01
<0.01
ε15
<1
<1
<1
<1
ωe,16
1571
1610
1518
1560
D16
0.23
0.35
0.29
0.43
ε16
373
564
453
671
ωe,17
1152
1178
844
863
D17
0.12
0.15
0.11
0.14
ε17
144
177
94
121
ωe,18
573
607
546
579
D18
0.42
0.58
0.38
0.52
ε18
240
352
206
301
εT
757
1092
754
1093
Methoxy Spectrum and Simulation
(a) Experimentally determined spectrum
61 (j = 3/2)
(b) Simulated spectrum using ab initio parameters
62 (j = 3/2)
-3000
-2500
61 (j = 1/2)
62 (j = 1/2)
-2000
-1500
-1000
-1
Energy (cm )
-500
0
Experimental ZEKE Apparatus
MCP/ Electromultiplier
Excimer
Photolysis
TOF Tube
Zn(C2H5)2
Skimmer
Repeller Plate
10-7 Torr
Nozzle
10-3 Torr
= two dye lasers
Lowest Vibronic Levels and Eigenfunctions
h(ωe)
h(ωe)+ l(D)+ q(K)
h(ωe)+ l (D)
h(ωe)+ q(K)
h(ωe)+ l (D)
h(ωe)+ q(K)