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Natural Transition Orbitals
Richard L. Martin Los Alamos National Laboratory
Ketimide complexes
• Cp*2An(CH3)2 + 2 R-CN → Cp*2An[N=C(CH3)(R)]2
• Th(IV): f0; absorption assigned to LMCT
• TDDFT suggests the lowest states arise from ligand-based excitation : N (lp) → CN π*
• Collaborative synthetic, spectroscopic and theoretical approach.
UN
N
C
R
R
CR
R
Th(2.26)2.25 (1.26)
1.29(108.9)105.2
(174.0)176.3 (179.4)
178.2
Calcs: A.E. Clark et al., JPC A 2005Synthesis: K. Jantunen et al., OM 2004Spectra: R. daRe et al., JACS (2005).
6000
4000
2000
0
Ext
inct
ion
Co-
effi
cien
t (
M -
1 cm
-1 )
4.0 3.5 3.0 2.5 2.0 1.5
Energy ( eV )
1000
500
0
Ext
inct
ion
Co-
effi
cien
t (
M -1 c
m -
1 )
3.2 3.0 2.8 2.6 2.4 2.2 2.0
Energy ( eV )
Data
Gaussian Fit
Fit ComponentsS2 S1
Interpretation of Excited States using NaturalTransition Orbitals
• Description of excited states as simple particle-hole pairs is difficult due to many contributions.
• Example: Cp*2Th(N=CPh2)2 S1 state
HOMO LUMO 0.382HOMO LUMO+1 -0.263HOMO-1 LUMO 0.213HOMO-1 LUMO+1 -0.309HOMO-2 LUMO 0.200
HOMOHOMO-1 LUMO LUMO+1
Natural transition orbitals (NTOs)
• Form transition density matrix T: the physically relevant quantity.
Tia = < Ψ
ex | c
i+ c
a | Ψ
0>
• Diagonalize T T† and T†T to obtain occupied and virtual NTOs
T T† Ui = λi Ui i = 1, nocc
T†T Vi = λi Vi i = 1, nvirt
• Each occupied orbital is paired with single virtual orbital; the transition density is unchanged; the magnitude of λ shows how important it is to the transition.
R.L. Martin, JCP 118, 4775 (2003).Batista and Martin, Encyclopedia of Computational Chemistry, 2004.
HOTO LUTO
HOTO LUTO λ = 0.92
λ1/2 = 0.96
...
0
00
No
No
Nv-No
...
c22cia N
o
Nv
c11... c12
c21 ......
...
... ......
......
...
......
Natural transition orbitals (NTOs)
For special cases : singles CI: λi = 1
NTO’s = attachment/detachment orbitals (Head-Gordon); both equivalent to the NO’s of the excited state;
excited state generated from first NTO pair maximizes overlap with excited state.
TDDFT: the deviation of λi from unity measures the importance of
the de-excitation operators;
For general cases: CISD, CC-EOM: T is now square;the deviation of λi from unity measures 2-particle character of excitation.
all 1e- properties simple sums over single p-h transitionsr = i {ui, r vi)
R.L. Martin, JCP 118, 4775 (2003).Batista and Martin, Encyclopedia of Computational Chemistry, 2004.
Pt monomer
HOMOHOMO
HOMO-1HOMO-1
HOMO-2HOMO-2
LUMO+2LUMO+2
LUMO+1LUMO+1
LUMOLUMO
Ground state geometryGround state geometry
• Batista and Martin, JPCA, 109, 9856 (2005).
• Symmetric geometry around with two C-C triple bonds
• Delocalized molecular orbitals
Molecular OrbitalsMolecular Orbitals
Pt monomer excitations (GS geometry)
State Energy (eV) type
T1 3.06 3*
T2 3.10 3*
T3 3.76 3LMCT
T4 3.89 3LMCT
S1 3.99 1LMCT
T5 4.03
T6 4.07 3*
S2 4.12 1*
g u
u g
T1
T1
T2
Natural Transition Orbitals (NTOs)Natural Transition Orbitals (NTOs)for the lowest two excitationsfor the lowest two excitations
At the ground state geometry the lowest triplet At the ground state geometry the lowest triplet excitationsexcitations
are delocalized over the whole moleculeare delocalized over the whole molecule
TT11 composed of 2 NTO pairs; composed of 2 NTO pairs; =(0.59, 0.32)=(0.59, 0.32)
Pt monomer (lowest triplet geometry)
L=0.04Å
At the lowest triplet geometry the symmetry is broken withAt the lowest triplet geometry the symmetry is broken withone of the ethynyl longer indicating a change from triple toone of the ethynyl longer indicating a change from triple to
double bond.double bond.
Pt monomer excitations (triplet geometry)
T1
T2
S1
2.17 eV
2.87 eV
3.26 eV
NTOsNTOs EE
• The triplet excitation localizes on one side of the moleculeThe triplet excitation localizes on one side of the molecule
• The singlet one, however, remains delocalized over the whole The singlet one, however, remains delocalized over the whole moleculemolecule
Exciton landscape. Migration barrier
(nm)
(eV) 2.48 2.07 1.773.10
phosphorescence
fluorescence
Experimental photoluminescence spectrum.[Liu et al. JACS 124, 12412 (2002)]
Calculated energy landscape for ground state and
Conclusions and AcknowledgementsNTO approaches very helpful for spectroscopic assignment.
Theory– Ping Yang (PNNL)– Aurora Clark (WSU)– Enrique Batista
Synthesis and spectroscopy– Jackie Kiplinger– Eric Schelter– Dave Morris
Support– Office of Science, Heavy Element Chemistry– Seaborg Institute
NTOs for F-substituted Cp*2 Th[N=C(R1)(R2)]2 complexes
Ph, Ph Me, F-Ph Me, F5-Ph
H
P
Ph, Ph Me, F-Ph Me, F5-Ph
S1 S2
2.56 eV 2.69 eV 3.03 eV 2.61 eV 2.76 eV 3.05 eV
• Fluorine substituted species possess mirror plane.• S1 is odd, S2 is even, and nearly degenerate.
F-substituted Th ketimide complexes
R1, R2 S1,S2 calc
(eV)
S1, S2 expt
(eV)
Ph, Ph 2.56, 2.61 2.48, 2.64
Me, F-Ph 2.69, 2.76 2.62, 2.85
Me, F5-Ph 3.03, 3.05 2.96, 2.97
DFT, spectroscopy and synthesis resultsE. J. Schelter et al., JACS 129, 5139 (2007).
Cp*2Th[N=C(R1)(R2)]2• Good agreement of TDDFT excitation energies (S1,S2)avg with expt.
• S1 follows trend for anion [N=C(R1)(R2)]- series
Lowest triplet state of Cp*2 Th[N=C(Me)(F5-Ph)]2
• The triplet NTOs for T1 and T2 are similar to S1 and S2.
• In T1, phenyl ring distorts to break the symmetry, allowing T1 and T2 to mix (SOJT).
• Preliminary spectroscopic results in agreement with double well. (David E. Morris)