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

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Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory

Transcript of Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory.

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

Natural Transition Orbitals

Richard L. Martin Los Alamos National Laboratory

Page 2: 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

Page 3: Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory.

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

Page 4: Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory.

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 ......

...

... ......

......

...

......

Page 5: Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory.

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.

Page 6: Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory.

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

Page 7: Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory.

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)

Page 8: Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory.

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.

Page 9: Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory.

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

Page 10: Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory.

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

Page 11: Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory.

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

Page 12: Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory.

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.

Page 13: Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory.

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

Page 14: Natural Transition Orbitals Richard L. Martin Los Alamos National Laboratory.

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)