1. Natural Transition Orbitals Richard L
Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory

2. 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. S2 S1 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 2005
Synthesis: K. Jantunen et al., OM 2004
Spectra: R. daRe et al., JACS (2005).

3. Interpretation of Excited States using Natural Transition 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
HOMO  LUMO
HOMO-1  LUMO
HOMO-1  LUMO
HOMO-2  LUMO
HOMO-1
HOMO
LUMO
LUMO+1

4. Natural transition orbitals (NTOs)Nv
Form transition density matrix T:
the physically relevant quantity.
Tia = < Ψ ex | ci+ ca | 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.
c11
c12
...
...
...
...
c21
c22
...
... No
...
cia
...
...
...
...
...
... l1 l2
lNo
... No
Nv-No
HOTO
LUTO
HOTO  LUTO λ = λ1/2 = 0.96
R.L. Martin, JCP 118, 4775 (2003).
Batista and Martin, Encyclopedia of Computational Chemistry, 2004.

5. Natural transition orbitals (NTOs)
For special cases :
singles CI:
Sλi = 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 Sλi from unity measures the importance of the
de-excitation operators;
For general cases:
CISD, CC-EOM: T is now square;
the deviation of Sλi from unity measures 2-particle character of excitation.
all 1e- properties simple sums over single p-h transitions
r = S li {ui, r vi)
R.L. Martin, JCP 118, 4775 (2003).
Batista and Martin, Encyclopedia of Computational Chemistry, 2004.

6. Pt monomer Ground state geometry Molecular Orbitals HOMO LUMO+2 HOMO-1
Batista and Martin, JPCA, 109, 9856 (2005).
Symmetric geometry around with two C-C triple bonds
Delocalized molecular orbitals
HOMO-2
LUMO

7. Pt monomer excitations (GS geometry)
State
Energy (eV)
type T1
3.06
3pp* T2
3.10 T3
3.76
3LMCT T4
3.89 S1
3.99
1LMCT T5
4.03 T6
4.07 S2
4.12
1pp* T1 g u T2 T1 u g
Natural Transition Orbitals (NTOs) for the lowest two excitations
At the ground state geometry the lowest triplet excitations are delocalized over the whole molecule
T1 composed of 2 NTO pairs; l =(0.59, 0.32)

8. Pt monomer (lowest triplet geometry)
DL=0.04Å
At the lowest triplet geometry the symmetry is broken with one of the ethynyl longer indicating a change from triple to double bond.

9. Pt monomer excitations (triplet geometry)
NTOs DE T1
2.17 eV T2
2.87 eV S1
3.26 eV
The triplet excitation localizes on one side of the molecule
The singlet one, however, remains delocalized over the whole molecule

10. Exciton landscape. Migration barrier
phosphorescence
fluorescence
(nm)
(eV)
3.10
2.48
2.07
1.77
Experimental photoluminescence spectrum.
[Liu et al. JACS 124, (2002)]
Calculated energy landscape for ground state and

11. Conclusions and Acknowledgements
NTO 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

12. NTOs for F-substituted Cp*2 Th[N=C(R1)(R2)]2 complexes
Ph, Ph
Me, F-Ph
Me, F5-Ph
Ph, Ph
Me, F-Ph
Me, F5-Ph
2.56 eV
2.69 eV
3.03 eV
2.61 eV
2.76 eV
3.05 eV P H S1 S2
Fluorine substituted species possess mirror plane.
S1 is odd, S2 is even, and nearly degenerate.

13. F-substituted Th ketimide complexes
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
R1, R2
S1,S2 calc
(eV)
S1, S2 expt
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 results
E. J. Schelter et al., JACS 129, 5139 (2007).

14. 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)