2D17
Spin Coupling Effects in Excited States
Fanica Cimpoesu,*a Yuichi Fujimura,a Michael Philpottb and Yoshiyuki Kawazoeba) Graduate School of Science, Tohoku University, Sendai 980-8578, Japanb) Institute For Materials Research, Tohoku University, Sendai 980-8577 JapanThe Spin Coupling concepts offer tools (e.g. the Valence Bond and its modern CASVB
versions in quantum computation or the phenomenological Heisenberg Hamiltonian, routinely
employed in magnetochemistry) and explanatory clues to the problems from a large area of theoreticaland applied chemistry. Heuristically, the chemical bond itself is a matter of effective spin coupling.
Special varieties of chemical bonding, like the resonance and aromaticity also naturally belong to theSpin Coupling paradigm. Phenomena of direct interest for the material science (localization vs.
delocalization bistabilities, conducting polymers, organic magnets) are also properly addressable interms of VB-like phenomenology and as subject of theoretical investigation are, in fact, much akin to
the academic topics like aromaticity vs. antiraomaticity, being driven by general spin coupling effects.
We selected as case study the bonding in the electronic excited states of the CnHn series ofconjugated cyclic polyenes and the related polyhedrane valence isomers of the CnHn (n=4,8,6)hydrocarbons. The antiaromatic molecules with 4k electron count are turning aromatic-like in thetriplet excited states, by reaching a set of 4(k-1)+2 electrons in doubly occupied π orbitals, aside to
the triplet electron pair. The DFT optimized geometries show regular planar polygons with D4h and D8hsymmetry for the n=4,8 members. For polyhedranes, the excitation is in principle related withpossibilities of disconnecting a C-C bond, but the nature of the excited state geometry distortion is
dictated by the symmetry factors of the frontier orbitals. Thus, the triplet state optimized starting fromtetrahedrane is a regular square-planar, the same as starting from the rectangular cyclo-butadiene. The
triplet state of the cubane is an elongated square prism, while hexa-prismane ends in a nonplanar
Dewar-like skeleton.
aTable 1. TD-DFT excited states of cyclobutadiene

B3g
B2u
B3u
B2g
B3u
Au
B1g
B1u
B2g
B2uTriplet
ET(eV)
1 0.544
2 4.107
3 4.849
4 4.915
5 4.995
6 5.219
7 5.777
8 5.990
9 6.169
10 6.243

SingletES(eV)
1 2.620
8 6.249
3 5.039
2 4.950
5 5.503
4 5.269
6 5.864
7 6.092
9 6.380
12 7.228

∆EST
(eV)
2.077
2.142
0.190
0.035
0.508
0.050
0.087
0.102
0.212
0.985

ba

T1

T2

H

H

H

Hb

H

H

H

H

H

H 22.21% H

H

22.21% H

H

25.42%

H

25.42%

HFig 1. C4H4: a) TD-DFT
density flow of first two triplets;b) NRT weights of the first
triplet (excited state aromaticity)

The Spin Coupling and aromatic resonance are properly described in the CASSCF andrelated frames. For the sake of methodological purposes we aimed to check the applicability of DFT
and TD-DFT in this topic. In principle, there are limitations, if consider the single determinant natureof DFT, and single-excitation definition of the TD-DFT excited states. However, for processes*In leave of absence from Institute of Physical Chemistry, Bucharest 77208, Romania

accompanied by a density flow, like the redistribution of the bonding densities, charge transfer
excitations in chromophores, the TD-DFT is appropriate. Moreover, the TD-DFT transitions can becompletely characterized with the help of difference density map (excited vs. groundstate). For
cyclobutadiene (see Fig.1) the first excitations (singlet and triplet) look like a π density flow from
C=C bonds toward the former C-C of thea
rectangular C4H4 frame. The Naturalb1
Resonance Theory (NRT ) offers ananalysis of excited state resonancestructures, the triplet state aromaticity
20.80%
20.80%
consisting in the manifestation of almost
equal weights of the four components
from in Fig.1b. The aromatic benzene
turns antiaromatic in excited state,
2.62%
19.82%
19.82%
showing tendencies of D2h distortion in theFig 2. C6H6: a) TD-DFT density flow in triplet states;b) Corresponding NRT weights
geometry and spin distribution (see Fig.2).
A problem of different nature, treated also in terms of TD-DFT is the modeling of chargetransfer induced spin transition in Prussian-Blue type Fe-Co systems,2 considered here in the minimal
molecular unit [(LiNC)5Fe-CN-Co(NCLi)5]4+ (the Li atoms were added as charge surrogate forneighbor lattice). The closed shell nature of the low spin state (LS), with d6 configurations on Fe andCo makes appropriate the TD-DFT study of singlet and triplet states.
E (eV)

3.5
FeCo

1BIIIIIIII

II

LS: [(NC)5Fe -CN-Co (CN)5]1

A1

HS: [(NC)5Fe -CN-Co (CN)5]

2.5
15A1

Fe

Chare Transfer Transitions

Fe Co → Fe Co
IIIII

IIIIIFig.3
Charge transfer in thebinuclear Fe-Co cyanide
system modeling chargetransfer induced spintransition.

Co1.51EθFeCo

10.5

1E

3E5HSA1LS
1EεR M L (Å)

-0.5
1.9

Left side: density

A1 difference maps

2

associated to 1E and 1B1TD-DFT states,
Right side: HS and LS
ground states and thefirst TD-DFT singlet andtriplet with respect of LS

2.1

The switch of the system between LS (1A1) and HS (5A1) states is spin forbidden. The interaction ofS=0 and S=2 ground states via spin coupling in excited state (singlet and triplet of charge transfer
excitation in FeIICoIII with the corresponding states resulted by exchange coupling in FeIIICoII) points a
new perspective on the intimate mechanism of the spin transition. The density difference map
confirms the charge transfer nature of the first excitations. The light color shows density depletion anddark color density accumulation areas. The first excited states correspond to a Fe to Co electron jump.
Acknowledgements
FC is indebted to COE (Japan) and CNCSIS (Romania). MP and FC acknowledge the support of CMS
supercomputer center of the Tohoku University, Sendai.
1

Glendening ED, Weinhold F, J. Comput. Chem. 1998, 19, 593.

2

N. Shimamoto, Shin-ichi Ohkoshi, O. Sato and K. Hashimoto, Inorg. Chem. 2002, 41, 678-684.