vibrational spectra of [pd(dmit) {2}] dimer (dmit=1,3 ... · transport, magnetic, and optical...

Vibrational Spectra of [Pd(dmit)2] Dimer

(dmit = 1,3-dithiole-2-thione-4,5-dithiolate):

Methodology for Examining Charge, Inter-Molecular Interactions, and Orbital

Takashi YAMAMOTO�, Yakuhiro NAKAZAWA, Masafumi TAMURA

1,Takeo FUKUNAGA1, Reizo KATO

2, and Kyuya YAKUSHI3

Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan1Department of Physics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, Japan

2RIKEN, Wako, Saitama 351-0198, Japan3Institute for Molecular Science, Okazaki, Aichi 444-8581, Japan

(Received March 8, 2011; accepted May 23, 2011; published online July 11, 2011)

We have developed a methodology for analyzing the lattice, charge, and orbital in two-dimensional molecularconductors comprising dimers of [Pd(dimt)2] ([Pd(dimt)2]2) using C¼C stretching vibrational modes. After confirmingvibrational modes for non-dimerized and loosely dimerized materials, we provide assignments for the four C¼Cstretching modes— two IR-active modes and two Raman-active modes— for the tight dimer. Of the four modes, theRaman-active and the lowest frequency mode is attributed to redistribution of the molecular orbital due to tightdimerization. By analyzing the vibrational spectra in the charge-ordered (CO) state of Et2Me2Sb[Pd(dmit)2]2, we havefound that the four modes are reflect in the intra-dimer interaction, the inter-dimer interaction, molecular charges andorbital levels. The results suggest that the vibrational spectroscopy is a powerful method to investigate electroniccorrelations, electron–phonon interactions, etc. in [Pd(dimt)2] salts.

KEYWORDS: molecular conductors, pseudo (effective) half-filled system, vibrational spectroscopy, infrared spectra,

Raman spectra, electronic transitions, dimer orbital, molecular charge, inter-dimer interaction, intra-dimer

interaction

1. Introduction

Molecular conductors consisting of ET [= bis(ethylene-dithio)tetrathiafulvalene] have been studied as modelcompounds for low-dimensional physics. A rich variety oftransport, magnetic, and optical properties is observed forET-containing materials whose crystal structures are quitedifferent.1–3) For example, the superconductivity of dimer-ized ET-salts has been studied from the viewpoint ofmagnetic fluctuation, whereas the charge fluctuation of non-dimerized ET-salts has attracted attention.4–6) Because of thevariation in crystal structure, a comprehensive and general-ized model of the conducting and magnetic properties ofET-salts has not yet been proposed. On the other hand,the structures in the conducting and two-dimensional layersof [Pd(dmit)2] salts (dmit = 1,3-dithiol-2-thione-4,5-dithio-late) are nearly identical.7) As shown in Fig. 1, two[Pd(dmit)2] molecules form the tight dimer, whose Pd–Pddistance is 2.9–3.2 �A. Tight dimers exhibit a columnarstructure, and neighboring columnar structures are arrangedso as to form a two-dimensional and conducting layer.Despite the universality in the two-dimensional structure,there is great diversity in the physical properties; theseinclude charge-ordered (CO), superconducting (SC), anti-ferromagnetic and insulating (AFI), and spin frustration (SF)states as well as a SC state neighboring non-magneticinsulator (NMI) state.8–16) Such diversity is expected to becontrolled by the subtle changes in the two-dimensionallayer, affecting inter-molecular Coulomb interactions, over-lap integrals, on-site Coulomb interactions in dimers,electron–phonon interactions, dimensionality, etc. For ex-ample, highest occupied molecular orbital (HOMO) level and lowest unoccupied molecular orbital (LUMO) level

exhibit crossing because of the tight dimerization,17–22) andsuch an orbital effect could also contribute to the diversity in

(b)

(a)

o

a

c

"Layer A" "Layer B" "Layer A"

ob

a

ob

a

"Layer A" "Layer B"

Fig. 1. (a) Crystal structure of Et2Me2Sb[Pd(dmit)2]2, projected onto

ac-planes, obtained from the data at 300K in ref. 8. (b) Molecular

arrangements of two conducting layers viewed along the long axis of the

[Pd(dmit)2] molecules. Each pair of layers is separated by a counter anion

layer. Pd atoms in a tight dimer form a short distance,�3:1 �A. The arrows in

(b) denote the center of inversion symmetry. Owing to a non-center

symmetric anion, the number of the [Pd(dmit)2] molecules in the unit cell is

doubled, but a repeat unit in two-dimensional layer consists of one tight

dimer. Et2Me2P[Pd(dmit)2]2 also takes the two layer system.

�E-mail: [email protected]

Journal of the Physical Society of Japan 80 (2011) 074717

074717-1

FULL PAPERS

#2011 The Physical Society of Japan

DOI: 10.1143/JPSJ.80.074717

http://dx.doi.org/10.1143/JPSJ.80.074717


physical properties.10) Therefore, molecular crystals consist-ing of [Pd(dmit)2] dimers are one of the key materialstoward the generalized and comprehensive mechanisms ofthe physical properties in molecular solids, and it is ofconsiderable importance clarifying the roles of charge, spin,lattice, and orbital level.

However, there remains a paucity of reliable methodol-ogies for evaluating charge, spin, lattice, and orbital level.As shown in our previous studies on the ET-salts, vibrationalspectroscopy is useful for capturing fluctuations in thecharge and lattice as well as the static charge and staticdistortion in lattice.4,23,24) We expect that the orbital effectcan also be evaluated from the C¼C stretching modes,assuming the C¼C bonds contribute substantially to thefrontier orbital of the dimer. Therefore, detailed analyses ofC¼C stretching modes may open the door to studying thefactors contributing to the physical properties of [Pd(dmit)2]salts.

The vibrational spectra of dmit-complexes have beenreported previously.25–30) However, no reliable assignmentshave been given for the IR and Raman spectra of [Pd(dmit)2]dimer in the frequency region between 1200 and 1400 cm�1,where the C¼C stretching modes are expected to beobserved. As for a monomer, two C¼C bonds in a moleculecontribute to two fundamental vibrational modes; �1 and �2modes. In contrast, at least four vibrational modes areallowed for tight dimer, because there are four C¼C bondsin a dimer. One doublet is observed in the IR spectra andanother in the Raman spectra. Among four modes, two IR-active modes and one Raman-active mode might beunderstood from the magnitudes of the electron–molecularvibrational (e–mv) coupling. Such interpretation is similar tothat of the ET-salts. However, the forth and Raman-activemode cannot be interpreted within a framework of theordinal e–mv coupling. In this article, we give assignmentsof C¼C stretching modes using several experimental data,and present a methodology for analyzing the charge, lattice,and orbital of [Pd(dmit)2] salts. Once the properties of theC¼C stretching modes are established, the vibrationalspectroscopy will be a powerful tool to study phenomenasuch as the NMI–SC transition, charge separation dueto redistribution of the orbital level or inter-molecularCoulomb interaction, and spin frustration among others.These results will be described in subsequent papers.

The rest of the present paper is organized as follows. Theexperimental procedure is described in x2. Before discussingdetails, the outline of our assignments for the tightlydimerized structure is presented in x3. The assignmentsand properties of the standard �1 and �2 modes are describedin x4. In x5, we give the assignments and discuss theproperties of the �1- and �2-related modes. Throughout x4and x5, the observation of at least four C¼C stretchingmodes is recognized. In x6, we give the assignments of theC¼C stretching modes of Et2Me2Sb[Pd(dimt)2]2 in the COstate. According to the electronic transitions in the near-infrared (NIR) region and X-ray structural analysis, this COstate is ascribed to the orbital effect.8,9) We then show thatobservation of C¼C stretching modes in the CO state isa good test condition to establish the methodology foranalyzing the charge, inter-molecular interactions, andorbital levels of [Pd(dimt)2] salts. Finally, in x7, we

summarize the properties of the C¼C stretching modes ofthe dimerized [Pd(dimt)2] molecules.

2. Experiments

Raman spectra were measured by using a RenishawRamascope with a backward scattering configuration. Theincident light was polarized and unpolarized scattered lightwas collected. A single crystal was excited by a He–Ne(633 nm), Ar ion (514 nm), or diode laser (780 nm). Theintensity of the incident laser light was reduced below0.1mW to avoid damage to the crystal. The spectralresolution was 2 cm�1. IR reflectance spectra were measuredusing a Nicolet Magna 760 FT-IR spectrometer equippedwith a Spectratech IR-Plan microscope. A polarizer wasplaced on the microscope. The spectral resolution was4 cm�1. Conductivity spectra were obtained after performingKramers-Kronig transformation of the IR reflectancespectra. Some spectra were observed at low temperatures.In examining the temperature dependence of IR and Ramanspectra, the single crystals were cooled using a helium-flowtype cryostat with the cooling rate kept below 1K/min.

Table I shows the abbreviations of the materials usedin the present study. e2m2P and e2m2Sb exhibit tightdimerization whereas T2 (T1) shows no dimerization (loosedimerization). We first confirmed the �1 and �2 modes usingT2, T1, e2m2P, and e2m2Sb at 300K. Note that e2m2P at300K is not in the anti-ferromagnetic state,14) nor is e2m2Sbat 300K in the CO state.8,9) Next, we gave the assignmentsfor the additional C¼C stretching modes of T1, e2m2P, ande2m2Sb at 300K. Strictly speaking, the additional modescan be classified into either the �1 or �2 mode. However, asdescribed in the following sections, their properties are quitedifferent from those of the original �1 or �2 modes.Hereafter, the additional modes are designated as the non-standard modes. We observed the spectra of some isotopeanalogues to confirm that the non-standard modes belong tothe C¼C stretching mode. As shown in Fig. 2, the carbonatoms in the dmit ligands were partially or fully substitutedby 13C. Both partial and full substitutions were performedfor e2m2P. We hereafter use the notations e2m2P(13-2) ande2m2P(13-6) to refer to the partially and fully substitutedmaterials, respectively. These notations are shown inTable I. For e2m2Sb, the partially substituted analogueand naturally abundant isotope, denoted by e2m2Sb(13-2)and e2m2Sb(13-0), respectively were used for the experi-ment. When it is not necessary to distinguish between thenaturally abundant isotope and its analogues, we use thenotations e2m2P and e2m2Sb. By comparing the spectraamong e2m2P(13-2), e2m2P(13-6), e2m2Sb(13-2), ande2m2Sb(13-0), we can distinguish the C¼C modes from

Table I. Materials used for the present experiments.

Material Abbreviation

(TBA)2[Pd(dmit)2] T2

(TBA)[Pd(dmit)2] T1

Et2Me2P[Pd(dmit)2]2 e2m2P

�e2m2P(13-2)

e2m2P(13-6)

Et2Me2Sb[Pd(dmit)2]2 e2m2Sb

�e2m2Sb(13-0)

e2m2Sb(13-2)

TBA: tetra-n-butylammonium

T. YAMAMOTO et al.J. Phys. Soc. Jpn. 80 (2011) 074717 FULL PAPERS

074717-2 #2011 The Physical Society of Japan

the C¼S modes, combination tones, and overtones. The laststep is to observe and analyze the temperature dependence ofthe C¼C stretching modes for e2m2Sb.

To understand the polarization dependence of the IR-active modes in e2m2P and e2m2Sb, we briefly describe thecrystal structures at 300K. As shown in Fig. 1, the stackingdirection in one conducting layer is different from that inadjacent conducting layers. Because of such structuralproperties, the maximum reflectance in the IR region wasobtained from a-polarized spectra. The minimum reflectancein the conducting layer (= ab-plane) was obtained fromb-polarized spectra. The electron–molecular vibrationalcoupling mode (e–mv mode) also exhibited the samepolarization dependence as the electronic transition in theIR region. In addition, we measured the reflectance spectrausing c-polarized spectra— the incident light polarizedalong the inter-layer direction. In this configuration, theincident light was irradiated onto the edge of the singlecrystal. As the crystal edge is perpendicular to theconducting plane, there is no marked electronic transitionin the IR region. Therefore, the intensity of the e–mv modeis also significantly lower than that obtained from theconducting plane. The absence of electronic transition andthe weak intensity of the e–mv mode are advantageous forobserving the vibrational mode which is free from the e–mvinteraction.23)

As structural data for T2 and T1 were unavailable, weconducted X-ray structural analysis and compared the resultswith the vibrational spectra. No remarkable atomic contactis observed in [Pd(dimt)2] molecules for T2. As for T1,[Pd(dimt)2] molecules form the dimer, but the inter-molecular contacts are weak as compared with those oftight dimers of e2m2Sb and e2m2P.

3. Outlines of the C¼C Stretching Modes

Before discussing the details, we present the outlines ofour assignments for C¼C stretching modes. Figure 3 showsthe vibrational motions of the C¼C stretching modes for amonomer, a loose dimer and a tight dimer, those whichcorrespond to the vibrational modes for T2, T1, and e2m2P(or e2m2Sb at 300K), respectively. Two standard C¼Cstretching modes, the �1 and �2 modes, are observed in thespectra of T2. An additional C¼C stretching mode isobserved in the IR-conductivity spectra of T1 and e2m2P,which is denoted as the �1(IR) and C modes, respectively.These modes are the out-of-phase vibrations composed of �1

modes between neighboring molecules in a dimer. Thisvibration, which is classified into the e–mv mode, has afrequency lower than that of the unperturbed �1 mode. Incontrast, no IR-active vibronic mode belonging to the �1mode is observed in the conductivity spectra of T2. Theabsence of the e–mv mode is supported by the X-raystructural analysis: no short-range contacts between adjacentmolecules. Observation of the D mode in the Raman spectrais characteristic of tight dimerization. The D mode is anout-of-phase vibration composed of �2 modes betweenneighboring molecules in a dimer. A large perturbation ofthe D mode is quite different from the less perturbationin the corresponding mode of T1 which is not shown inFig. 3. The large perturbation of the D mode is ascribedto redistribution of the molecular orbital (MO) of tightdimerization (see x5).

Figure 4 shows the IR-conductivity and Raman spectraof e2m2P(13-2) and e2m2P(13-6) at 300K. One doublet,denoted as A and D [A� and D� for e2m2P(13-6)], is

1ν 1νand -related 2ν 2νand -related

SS

S

S

SSS

SS

SPd

SS

S

SS

SS

SS

SPd

SS

S

S

SSS

SS

SPd

SS

S

SS

SS

SS

SPd

SS

S

S

SSS

SS

SPd

SS

S

SS

SS

SS

SPd

SS

S

S

SSS

SS

SPd

SS

S

SS

SS

SS

SPd

SS

S

S

SSS

SS

SPd

SS

S

SS

SS

SS

SPd

Monomer = T2

Loose dimer = T1

SS

S

S

SSS

SS

SPd

SS

S

SS

SS

SS

SPd

SS

S

S

SSS

SS

SPd

SS

S

S

SSS

SS

SPd

SS

S

S

SSS

SS

SPd

A(R)

C(IR)

D(R)

B(IR)

1ν (R)

(IR)1ν

Tight dimer = e2m2P and e2m2Sb

1ν (R)(IR)2ν

(IR)2ν

Fig. 3. The C¼C stretching mode of a monomer, a loose dimer and a tight

dimer. For each structure, the frequency decreases from top to bottom. ‘‘R’’

and ‘‘IR’’ in the parentheses denote the Raman-active and IR-active modes,

respectively. Raman active mode composed of the �2 modes in neighboring

molecules in a loose dimer, �2(R), is omitted, because this mode is almost

unperturbed and negligibly weak (or absence) in Fig. 5.

Pd

S S

SS

S

S

S

S

S S

Pd

S S

SS

S

S

S

S

S S**

*Pd

S S

SS

S

S

S

S

S S***

*

*

(13-2)

(13-0)

(13-6)

Fig. 2. The naturally abundant isotope of [Pd(dmit)2] and its analogues

used in the experiments. The asterisks denote the positions of 13C.



observed in the Raman spectra. The other doublet, denotedas B and C (B� and C�), is observed in the IR-conductivityspectra. The frequencies of the A–D (A�–D�) modes aresummarized in Table II along with those of the C¼Cstretching modes for T2, T1 and e2m2Sb(13-0). Because theA–D modes exhibit isotope shifts, they all belong to theC¼C stretching mode. This result is also supported from

almost no isotope shift in the A–D modes betweene2m2Sb(13-0) and e2m2Sb(13-2). The details of each modewill be described in x4 and x5.4. Standard �1 and �2 Modes

4.1 Standard �1 modeFigure 5 shows the Raman spectra for T2, T1,

e2m2Sb(13-0), e2m2P(13-2), and e2m2P(13-6) at 300K.The spectra were obtained from a 633 nm laser. The sharpand strong peaks of T2 and T1 are easily assigned to the�1 mode. As for materials containing of a tight dimer,two vibrational modes are observed. The frequencies of

Wavenumber ( cm )-1

) (

S c

m)

σ(

ω

Raman shifts ( cm )-1

) (

arb.

uni

ts)

( ω I

780 nm

c -polarized

Raman

A

IR-conductivity

300 K

1100 1200 1300 1400 15000

100

200

300

400

500

600

700

800

1100 1200 1300 1400 1500

A*

DD*

B

B*

CC*

300 K

b -polarized

a -polarized

e2m2P(13-2)

e2m2P(13-6)

e2m2P(13-2)

e2m2P(13-6)

Fig. 4. Top panel: Raman spectra of e2m2P at 300K. Bottom panel: IR-

conductivity spectra of e2m2P at 300K. Solid and dotted curves are the

spectra for e2m2P(13-2) and e2m2P(13-6), respectively. Asterisks denote

the 13C¼13C stretching mode. The frequencies of the A–D and A�–D�

modes are summarized in Table II.

Table II. Frequencies of the C¼C stretching mode for T2, T1, and tightly-dimerized salts at 300K. Frequencies of e2m2Sb(13-2) are identical to those of

e2m2Sb(13-0). Crosses between two molecules denote the inversion center.

Degree of

dimerization

Non-dimerized Loosely dimerized Tightly dimerized

Charge[Pd(dmit)2]

�2 [Pd(dmit)2]�1 [Pd(dmit)2]2

�1

� ¼ �2 � ¼ �1 � ¼ �0:5

Material T2 T1 e2m2P(13-2) e2m2P(13-6) e2m2Sb(13-0)

�1(R) 1397A(R) 1357 A�(R) 1308 A(R) 1358

Frequency �1(R) 1445�2(IR) 1375

B(IR) 1327 B�(IR) 1275 B(IR) 1329

(cm�1) �2(IR) 1441�1(IR) 1310

C(IR) 1292 C�(IR) 1242 C(IR) 1290

D(R) 1267 D�(R) 1220 D(R) 1266

�Raman active mode consisting of �2 in a loose dimer, �2(R), is omitted because this mode is almost unperturbed and negligibly weak in Fig. 5.


e2m2Sb(13-0)

T2)

(ar

b. u

nits

)(

ωI

1100 1200 1300 1400 1500 1600

1100 1200 1300 1400 1500 1600


1ν

e2m2P(13-2)

e2m2P(13-6)

1ν

1ν

1ν

1ν

1445 cm-1

1397 cm-1

1358 cm-1

1357 cm-1

1308 cm-1

(=A)

(=A)

(=A*)

D

D

D*

T1

Fig. 5. Raman spectra of T2, T1, and tightly dimerized salts at 300K. The

spectra were measured with a 633 nm laser. The frequencies of the �1, A, D,

A�, and D� modes are summarized in Table II. The asterisks denote the

vibrational modes due to the 13C¼13C double bonds.



e2m2P(13-6) are lower than those of e2m2Sb(13-0) ande2m2P(13-2). The isotope shift between e2m2P(13-2) ande2m2P(13-6) is approximately 50 cm�1/1357 cm�1 ¼��3:7%, which closely agrees with the estimate of1� ð12=13Þ1=2 ¼ 3:9%. Hence, both modes are C¼Cstretching modes. The high frequency mode has a narrowerline-width as compared with the low frequency mode.Therefore, the former is assigned to the standard and Raman-active mode, whereas the latter is considered a non-standardmode perturbed by inter-molecular interaction.

As shown in Fig. 5, the frequency of the �1 modedecreases in the order of T2, T1, and e2m2Sb(13-0) [ore2m2P(13-2)]. Because their formal charges of �2, �1, and�0:5 (�0:5), respectively, these shifts indicate that thefrequency of the �1 mode decreases with decreasingfractional charge, which is consistent with the previouswork.28) The relationship between the fractional charge andfrequency from � ¼ �2 to �1 is estimated as �47 cm�1/electron. By extrapolation of the frequency shift of �40

cm�1/electron from � ¼ �1 to �0:5, the relationship from� ¼ �1 to 0 is estimated as �80 cm�1/electron. Bothrelationships shows a discontinuity, indicating that thefrequency of [Pd(dimt)2]2

2� (dimer dianion, � ¼ �1) isnot always identical to that of [Pd(dimt)2]

� (radical anion ata monomer, � ¼ �1). In other words, the electronic densityat C¼C bonds of the tight dimer is a little different from thatof a monomer. Indeed, the molecular structure in a tightdimer is a little different from that of T1 or T2. According toX-ray structural analysis, T1 and T2 show the flat structures.On the other hand, the tight dimer exhibits a boat structureso as to form short-range intra-dimer contacts around thecenter of the molecules. The frontier orbital of the tightdimer is also different from that of the flat molecule,particularly around the C¼C bonds, which will be describedin x5.2. This accounts for the discontinuity in frequency.31)

In this sense, a different notation should be used for theRaman-active �1 mode of the tight dimer. Hereafter, wedenote such a mode as the A mode. Consequently, thetentative relationship between fractional charge and fre-quency of �80 cm�1/electron from � ¼ �1 and 0 is notused for quantitatively evaluation of molecular charges,particularly in the CO state. Nevertheless, qualitativediscussions of the A mode provide fruitful information onthe charge and lattice (x6.2).

4.2 Standard �2 modeFigure 6 shows the IR-conductivity spectra of T2,

c-polarized conductivity spectra of T1, c-polarized con-ductivity spectra of e2m2P, and c-polarized spectra ofe2m2Sb in the non-CO state. The IR-conductivity spectra ofT2 is obtained from the elongated surface of the needle-likecrystal. The only vibrational mode observed in this spectralregion is the �2 mode. In the spectra of T1, two vibrationalmodes are observed. The �1310 cm�1 mode is assigned tonot the �2 mode but one of the �1 mode, which is discussedin Appendix A. The �2 mode is observed at 1375 cm�1. Theassignment of the B (B�) mode for a tight dimer is supportedfrom polarization dependence of the B (B�) mode. In thec-polarized spectra, the intensity of the B (B�) mode ishigher than that of the C (C�) mode. This polarizationdependence satisfies that of the �2 mode because the out-of-

phase vibrations between the two ring C¼C bonds inducethe intra-molecular CT along the molecular long axis.32)

In contrast, in the a- and b-polarized spectra, the B (B�)mode is weaker than the C (C�) mode. This polarizationdependence indicates that the B mode is free from thee–mv interaction. However, the B (B�) mode is observed inthe a- and b-polarized spectra, which is ascribed toinclination of the [Pd(dimt)2] molecule toward the conduct-ing plane (see Fig. 1).

The frequencies of the �2 mode and the B (B�) modedecrease from � ¼ �2 to �0:5. This � dependence alsosupports that the B (B�) mode belongs to the �2 mode. Asshown in Fig. 3, the C¼C bonds between neighboringmolecules vibrate in-phase. Such vibrational motion isexpected to be free from the inter-molecular CT, that is,free from the e–mv interaction. We can expect that thefrequency is sensitive to the molecular charge. In this sense,the �2 mode and B mode of [Pd(dmit)2] is comparable to the�27 mode of ET.23)

The relationship between the fractional charge andfrequency from � ¼ �2 to �1 is estimated as �66 cm�1/electron. By extrapolation of the frequency shift from� ¼ �1 to �0:5, the relationship from � ¼ �1 to 0 isestimated as �92 cm�1/electron. In analogy to the �1 mode,these relationships are discontinuous. The discontinuities inthe �2 and B (�1 and A) modes strongly indicate that short-

1200 1300 1400 15000

100

50

10

0

20

Wavenumber ( cm )-1

σ(

)

(S

cm

)ω

σ( ) (S

cm)

ω

0

100

50

0

100

50

0

100

50

1200 1300 1400 1500

30

Wavenumber ( cm )-1

σ(

)

(S

cm

)ω

σ( ) (S

cm)

ω

σ(

)

(S

cm

)ω

2ν1441 cm-1

1375 cm-1

1329 cm-1

1327 cm-1

1275 cm-1C*

2ν

2ν

2ν

2ν

C

C

1ν (IR)

(= B)

(= B)

(= B*)

+ +

+ +

e2m2Sb(13-0)

T2

e2m2P(13-2)

e2m2P(13-6)

T1

Fig. 6. IR-conductivity spectra of T2, T1, and tightly dimerized salts at

300K. The spectra of T1 is identical to the c-polarized spectra in Fig. A�1.The spectra of e2m2P(13-2) is identical to the c-polarized spectra in Fig. 4.

The frequencies of the �2, B, C, B�, and C� modes are summarized in

Table II. Asterisks denote the 13C¼13C stretching modes. Crosses denote

the CH2-related modes, which are not discussed in the present article.



range intra-dimer contacts due to tight dimerization inducesthe change in the frequency of the C¼C stretching mode. Inthis sense, a different notation, ‘‘the B mode’’, is used for theIR-active �2 mode of the tight dimer. As for a qualitativediscussion, any sample whose molecular charge, �, isconfirmed to be �1 and 0 ([Pd(dmit)2]2

2� and [Pd(dmit)2]20,

respectively) is required. Unfortunately, such sample cannotbe available to our best knowledge. A detailed and exactnormal mode analyses might contribute to the quantitativediscussions, which is a future’s task. Nevertheless, we canexpect that the B mode is sensitive to subtle changes inthe molecular charge, which will be confirmed usingthe temperature dependence of the c-polarized spectra fore2m2Sb (x6.1).5. �1- and �2-Related Modes

Prior to discussing the �1- and �2-related modes of thetight dimer, we give comments on the C¼C stretchingmodes of T1. As described in Appendix A, the IR-active �1mode is observed because of the loose dimerization.Analogous to many ET salts, the observation of this modeis obviously attributed to the e–mv interaction. In contrast,no additional �2 mode, whose frequency is lower than that ofthe unperturbed �2 mode, is observed in both IR and Ramanspectra. This result indicates that almost no perturbation inthe frequency of the �2 mode is occurred owing to the weakinter-molecular interaction in the loose dimer. This behavioris also consistent with the property of the �27 mode of the ETsalts.23) Therefore, the total number of the C¼C stretchingmodes, whose frequencies are different from each other, isthree for the loose dimer. As for T2, on the other hand,no IR-active vibronic mode belonging to the �1 mode isobserved in the conductivity spectra. The absence of thee–mv mode is supported by X-ray structural analysis: noshort-range contacts between adjacent molecules.

5.1 Non-standard �1-related modeFigure 7 shows the Raman and a-polarized conductivity

spectra of e2m2P(13-2). These spectra are the same as thosein Fig. 4. When repeating unit is a tight dimer, the totalnumber of the C¼C stretching mode is four, which issignificantly different from that of T1. Between two kinds ofadditional modes; C and D modes, the IR-active C modeis discussed in this subsection. Assuming that the C is thee–mv mode, two molecules in a dimer vibrate out-of-phaseand CT due to the e–mv interaction is induced along thestacking direction. Indeed, the intensity of the C mode isstrong in the a-polarized spectra; hence, the polarizationdependence of the C mode confirms that the C mode isassigned to the vibronic �1 mode. Like the �1(R) and �1(IR)modes of the T1, the behavior of the A and C modes isqualitatively reproduced from a simple dimer model whereinone electron is accommodated in a dimer. We have usedmethodologies in the previous literatures, and thesemethodologies are also applied to Appendix A.33–36) Thecalculated result is shown in Fig. 8. Here, the transferintegral, td, and the coupling constant in the tight dimer,g, are assumed to be 450meV and 0.1 eV, respectively.Unfortunately, as described in x4.1, the frequencies of theradical anion and neutral molecule (� ¼ �1 and 0) with aboat structure are not settled, so that we have tentatively

used the frequency of the �1 mode of T1 as a frequency at� ¼ �1. The frequency at � ¼ 0 is tentatively obtained fromthe extrapolation using the �1 of T1 (� ¼ �1) and A mode ofe2m2P (� ¼ �0:5). As shown in Fig. 8, the weak perturba-tion of the A mode and the large perturbation of the C modeare qualitatively reproduced. The frequency of the A mode

σ(

)

(S

cm

)ω


(

) (

arb.

uni

ts)

ωI

780 nmRaman

A

IR-conductivity

300

400

500

600

700

800

Wavenumber ( cm-1

1100 1200 1300 1400 15000

1100 1200 1300 1400 1500

D

B

C

a-polarized

e2m2P(13-2)

e2m2P(13-2)

)

Fig. 7. Raman and IR-conductivity spectra of e2m2P(13-2) at 300K. The

set of spectra is prototypical of [Pd(dmit)2] salts in which the repeating unit

is a tight dimer.

Dimer: t intra = 0.45 eVUnperturbed

ν(c

m-1

0.0 0.2 0.4 0.6 0.8 1.01250

1300

1350

1400

1450

C(IR)

A(R)

ρ at left molecule

0-1 0

-1-0.5-0.5

)

Fig. 8. Site-charge dependence of the frequencies of the A and C modes

for the tight dimer with one electron. Dotted lines denote the bare

frequencies of the �1 mode without the e–mv interaction.



at � ¼ �0:5 is exactly identical to that of the �1 at � ¼ 0:5.When � is more ore less smaller (larger) than �0:5, thefrequency of the A mode is almost unchanged. The degree ofperturbation of the C mode corresponds to the difference inthe frequencies between the C mode and �1 at � ¼ �0:5.The degree of perturbation at � ¼ �0:5 (�80 cm�1)estimated from the calculation roughly agrees with theexperimental value of 60–70 cm�1.

The perturbation for the C mode is not as large as thatfor the vibronic �3 mode of �-type ET salts (110–240cm�1).37–40) This difference is attributed to the differencein the inter-dimer transfer integral. For [Pd(dimt)2] saltsconsisting of a tight dimer, the magnitude of the inter-dimertransfer integral, ti ¼ 20{40meV, is significantly smallerthan that of td (400–500meV). Thus the frequency of the Cmode largely depends on the intra-dimer transfer integral. Incontrast, td of �-type ET salts, which is slightly less than300meV, is at most triple the size of ti.

1) For �-type ET salts,both td and ti have a non-negligible contribution to theperturbation of the e–mv mode. Hence, the frequency of theC mode is not so perturbed as compared with the frequencyof the vibronic �3 mode of �-type ET salts.

We also examined the role of the inter-dimer interactionin the frequencies of the C mode, assuming two tight dimersneighbor one another.41) td and ti are assumed to be 450 and30meV, respectively, and the intra-dimer and inter-dimernearest neighbor Coulomb interactions to be Vd ¼ 0:4 andVi ¼ 0:1 eV, respectively. Owing to the inter-dimer interac-tion, the C mode split into two modes, Ca and Cb modes.Nevertheless, the degrees of perturbations of the Ca (and Cb)modes, �70 cm�1 (�90 cm�1) is almost comparable to thatof the C mode in a dimer model, �80 cm�1. This behavior issignificantly different from the large perturbation in thecorresponding modes of the �-type ET salts. We haveevaluated the degrees of perturbation in the �3 mode of ETapplying a similar calculation. The parameters in two dimersare assumed to be td ¼ 300meV, ti ¼ 100meV, Vd ¼0:3 eV, and Vi ¼ 0:1 eV. Indeed, the degrees of perturbationsof the two vibronic �3 modes, �130 and 160 cm�1 aresignificantly larger than that of the Ca and Cb modes. Thisdifference obviously lies in the magnitude of ti. This resultsuggests that the inter-dimer (intra-dimer) interactioncontributes less (more) to the frequency of the C modebecause of small ti (large td).

Applying the above model to the A mode, the A modealso split into two modes, the Aa and Ab. Analogous to the Cmode, the difference in the frequencies between the Aa andAb modes is small (lower than �30 cm�1). Nevertheless,because of the narrow line-width, the Aa and Ab modes areexpected to be independently observed. This property isuseful to examine the inter-dimer interactions, which will bedescribed in x6.2.

5.2 Non-standard �2-related modeAs shown in Fig. 7, an additional Raman-active mode, D,

is observed for the [Pd(dmit)2]2 salts containing a tightdimer. The frequency of the D mode is lowest among thethose of the A–D modes, suggesting that the intra-dimer CTcontributes to its perturbation. To the extent that a repeatingunit in the two-dimensional layer consists of one dimer, theD mode does not belong to the vibronic �1 mode because the

C mode has already been assigned as the perturbed �1 mode.We assume that the D mode belongs to the �2 mode, whosevibrational motion is shown in Fig. 3. Not only the intra-molecular C¼C bonds but also the inter-molecular C¼Cbonds exhibit the out-of-phase vibrations. Such a motioncould contribute to intra-dimer and intra-molecular CT,resulting in the lowest frequency among four vibrationalmodes. The large perturbation of the D mode is supportedfrom the viewpoint of MO, where rigid bonding orbital isformed between the molecules in a dimer, which will bedescribed in Appendix B.

In contrast, the absence of an additional Raman-activemode in T2 is ascribed to no remarkable inter-molecularcontact between [Pd(dmit)2]2 molecules. From the viewpointof the group theory, an additional mode is allowed for T1.Owing to a loose dimer, the frequency is expected to bealmost comparable to that of the �2 mode, �1375 cm�1.However, no remarkable vibrational mode is observedaround 1375 cm�1 in the Raman spectra shown in Fig. 5,or a very weak peak at �1375 cm�1 might be an additionalmode. We consider that the resonance condition is notrealized for T1. As shown in Fig. A�1, the highest transitionenergy of a loose dimer is estimated to be �1:55 eV(800 nm), which is significantly lower than excitation energyof He–Ne laser, 633 nm.

Having confirmed the assignments of the C¼C stretchingmodes for the tight dimer, the detailed properties of the A–Dmodes will be examined in x6.6. C¼C Stretching Modes of Et2Me2Sb[Pd(dimt)2]2

Prior to discussing the vibrational modes in the CO state,we first comment on the C¼C stretching modes in the non-CO state and the resonant effect. Figure 9 shows the IR andRaman spectra at 100K: a temperature higher than the COtransition temperature (�70K). The assignments of the A–Dmodes are identical to those at 300K and the assignments ofe2m2P. Each frequency at 100K is �3 cm�1 higher than thatat 300K. The slightly increase in the frequency is attributedto the thermal contraction. We have examined excitationenergy dependence in the A and D modes using the spectraat 100K, which is described in Appendix B. The excitationenergy dependence is explained from the energy level of theMOs. The resonant effect is also observed in the CO state.The excitation energy dependence is useful to give theassignments of the A and D modes and useful to discuss thedegree of dimerization.

The distribution of site charges in the CO state is alreadyobtained from the X-ray structural analysis, wherein twocharge-rich dimers and two charge-poor dimers are alter-nately arranged along the stacking direction.8) The samestructure is independently obtained from the vibrationalspectroscopy.

6.1 Temperature dependence of the B modeFigure 10 shows the temperature dependence of the

c-polarized conductivity spectra. From 68 to 66K, the Bmode at 1333 cm�1 splits into two peaks denoted as the B1and B2 modes. The temperature of peak-splitting closelyagrees with the transition temperature obtained from thelattice parameter, electrical resistivity, and magnetic sus-ceptibility. It is reasonable to attribute the peak-splitting of



the B mode to the CO transition. The B1 and B2 modes areassigned to the B modes of the charge-rich and charge-poormolecules, respectively. As described in x4.2, we can expectthat the frequency of the B mode has a linear relationshipwith a molecular charge. Interestingly, the averagedfrequencies between B1 and B2 modes, 1336 cm�1, is nearlyidentical to the frequency at � ¼ �0:5, 1333 cm�1. Further-more, the ratio of charge-rich and charge-poor molecules,1 : 1, has been already confirmed from the X-ray structuralanalysis. These facts ensure that the frequency of the Bmode has a liner relationship with a molecular charge: B1and B2 correspond to �0:5��=2 and �0:5��=2,respectively (0 < ��=2 < 0:5). This result means that theratio of charge-rich and charge-poor molecules in the COstate of other [Pd(dmit)2] salts can be estimated from thenumber of the B mode and these frequencies. One maysurmise, on the other hand, that the ratio is also estimatedfrom the relative intensity between B1 and B2. However,this method is not necessary applicable to the B mode. Inanalogy with �27 mode of ET, the B mode induces the intra-molecular charge transfer along the long axis of molecule.Since the transition dipole moment contributes to theintensity, the intensity depends on the molecular charge aswell as the ratio. Therefore, it is not so useful to estimate theratio from the relative intensity.

As described in x4.2, any exact equation between chargeand frequency cannot be obtained from the experimentalresults at this stage. Nevertheless, qualitative discussion ofmolecular charge can be useful for examining the degree oflocalization. Let us examine the difference in the molecular

charges between the charge-rich and charge-poor sites, ��,because this value closely reflects the degree of localization,i.e., the conductive behavior. According to previous studiesof ET salts, the �� values in the CO states of�-(ET)2RbZn(SCN)4 and �00-(ET)4Ni(CN)4H2O are �0:5and �0:4, respectively, whereas the �� of the metallicmaterial is close to 0.5,42) By applying the tentativerelationship between the fractional charge and frequencyfrom � ¼ �1 to 0 (�92 cm�1/electron) to the difference inthe frequencies between the B1 and B2 modes, �37 cm�1,�� is estimated to be �0:4. By extrapolating the relation-ship from � ¼ �2 to �1 (�66 cm�1/electron) to the presentdata, �� is estimated as ��0:56. In both estimates, the ��of e2m2Sb in the CO state is comparable to those of�-(ET)2RbZn(SCN)4 or �00-(ET)4Ni(CN)4H2O rather than�� of metallic materials. This suggests that long-range orderdevelops well in the two-dimensional layer of e2m2Sb in theCO state. As will be described in x6.2–x6.4, the develop-ment of long-range order is supported by factor groupsplitting in the A, C, and D modes.

We briefly comment on the Raman active B mode. In theRaman spectra shown in Fig. 11, very weak peaks denoted

e2m2Sb

c -polarized

10 K

1150 1200 1250 1300 1350 1400 1450 15000

50

100

150

Wavenumber ( cm )-1

σ( ) (S

cm)

ω

σ(

)

(S

cm

)ω 0

0

0

0

0

0

0

0

0

0

50

100

1150 1200 1250 1300 1350 1400 1450 1500

Wavenumber ( cm )-1

100 K

50 K

200 K

300 K

66 K

67 K

68 K

69 K

70 K

72 K

C ( = 0.5)ρ

Charge Rich

Charge Poor

B

B1B2

[Pd(dmit) ]2 2-1

A2'

Fig. 10. Temperature dependence of the c-polarized IR conductivity

spectra for e2m2Sb(13-0). The charge-sensitive mode corresponds to the B

mode in the non-CO state and to the B1 and B2 modes in the CO state.

Wavenumber ( cm )-1

σ(

)

(S

cm

)ω


633 nm

a -polarized

e2m2SbRaman

e2m2SbIR-conductivity

100 K

1200 1250 1300 1350 14000

200

400

600

800

1200 1250 1300 1350 1400(a

rb. u

nits

)

(

)ω

I

A

D

B

C

b -polarized

c -polarized

100 K

Fig. 9. Top panel: Raman spectra of e2m2Sb(13-0) at 100K obtained

from 633 nm laser. Bottom panel: IR-conductivity spectra of e2m2Sb(13-0)

at 100K.



as the B10 and B20 are observed at 1350 and 1320 cm�1.According to the X-ray structural analysis, the repeating unitin the conducting layer consists of two charge-rich dimersand two charge-poor dimers. As shown in Fig. 12, thenumber of vibrational modes assigned to the B mode is four.Then, the vibrational modes due to the two charge-richdimers, B1 and B10, are expressed as [+�][+�] and[+�][�+], respectively, where ‘‘+’’ and ‘‘�’’ are denoted asthe phases of vibration at a monomer and the brackets as adimer. When the direction of the intra-molecular chargetransfer is designated as the arrow, these modes areexpressed as [#"][#"] and [#"]["#], respectively. Thevibrational modes of two charge-poor dimers, B2 and B20,are also express as the same manners. B10 and B20 aresymmetric whereas B1 and B2 remain asymmetric. There-

fore, B10 and B20 are Raman-active, and B1 and B2 are IR-active. Between B1 and B10 (B2 and B20) modes, the degreesof the inter-dimer charge transfer is exactly different fromeach other. Nevertheless, the frequency of the B10 (B20)mode is identical to those of the B1 (B2) mode. Thisbehavior is significantly different from those in the A, C,and D modes, which will be described in x6.2–x6.4. Theconsistency in the frequencies between Raman-active andIR-active modes is attributed to the fact that the B mode isfree from the e–mv interaction, in other words, the B mode isinsensitive to the inter-dimer interaction. This propertyensures that the B mode is the most sensitive to molecularcharges among four C¼C stretching modes.

6.2 A mode in the CO stateFigure 11 shows the IR and Raman spectra of e2m2Sb in

the CO state. The spectral shapes are quite different fromthose in the high-temperature phase (Fig. 9). The number ofvibrational modes exceeds four. The multiple peaks indicatethat a repeat unit is composed of several dimers. The two-dimensional structure, already obtained from X-ray struc-tural analysis,8) can be independently obtained from theanalysis of the multiple peaks. Figure 12 shows a correlationdiagram of the C¼C stretching modes and frequencies ofcorresponding modes in Fig. 11. As shown in Fig. 12, ourexperimental results are explained by assuming two charge-rich and two charge-poor dimers alternately arranged alongthe stacking direction. The multiple peaks in the CO stateshould belong to the A–D modes. Hereafter, a series of A,(B, C, and D) modes in the CO state is denoted as the A- (B-,C-, and D-) group when it is unnecessary to distinguish one

1100 1150 1200 1250 1300 1350 1400

Wavenumber ( cm )-1

σ( ) (S

cm)

ω

σ(

)

(S

cm

)ω

Raman shifts ( cm-1σ

(

) (

S c

m)

ω

Raman

IR-conductivity

514 nm, 30 K

(

) (

arb.

uni

ts)

ωI

0

300

600

900

0

20

40

60

80100

0

200

400

600

800

0

20

40

60

80

1100 1150 1200 1250 1300 1350 1400

514 nm, 30 K

633 nm, 50 K

633 nm, 50 K

780 nm, 50 K

σ( ) (S

cm)

ω

a-polarized

A1

b-polarized

c-polarized

e2m2Sb(13-0)

e2m2Sb(13-2)

A2

A2

T

S

U

B1

Y

B2

Z

XY

1000 1500 20000

500

1000Y a -polarized

at 50 K

T A1'

B2'B1'

A1'A2'

Z

S

)

Fig. 11. Top panel: Raman spectra of e2m2Sb in the CO state. Bottom

panel: IR-conductivity spectra of e2m2Sb in the CO state. Solid and dotted

lines denote the spectra of e2m2Sb(13-0) and e2m2Sb(13-2), respectively.

Broken curves and straight lines are included as visual guides. The

frequencies of each vibrational mode are summarized in Fig. 12.

1νA2(s)

A2'(as)

A1(s)A1'(as)

C2(as)C2'(s)

C1(as)C1'(s)

D2(s)

D2'(as)

D1(s)D1'(as)

monomer

C(as)

A(s)

B(as)

A tight dimer

Four tight dimers

An isolatedCharge

(s)

2ν (as)

B2(as)B2'(s)

B1(as)B1'(s)

D(s)

Charge-rich-poor

(cm )-1

Figure 11

Obs.

13371330

1373

1362

1354

1317

1306

1267

1290

1260

1250

1300

~

A1A1'

S

A2A2'

Z

T,Y

B2'

B1'

XU

B2

B1

Fig. 12. Schematic correlation diagram of the C¼C stretching modes for

the isolated monomer, the tight dimer, and four tight dimers. ‘‘(s)’’ and

‘‘(as)’’ denote the symmetric and asymmetric vibrations, respectively. The

right column is the assignments of the C¼C stretching modes in Fig. 11.



of the A (B, C, and D) modes from another. Assuming thatfour dimers participate in a repeating unit in the two-dimensional layer, the A- (B-, C-, and D-) group consists offour vibrational modes. Four vibrational modes belongingto the A-group—A1, A10, A2, and A20 —are observedbetween 1330 and 1373 cm�1. Interestingly, the frequency ofthe A1 mode, 1373 cm�1, is higher than that of the A modein the non-CO state at 100K (1361 cm�1; this frequencycorresponds to that at � ¼ �0:5). This observation indicatesthat the intra-dimer charge separation is excluded. Byassuming the intra-dimer charge separation, as shown inFig. 8, the A mode is a little perturbed by the e–mvinteraction. When �� is not close to 1, the frequency of theA mode should be nearly identical to that in the non-COstate (�1361 cm�1 at 100K, corresponding to the frequencyat � ¼ �0:5 at 100K). However, the frequency of the A1mode is significantly higher than �1361 cm�1, in otherwords, the A1 is not so perturbed. Therefore, the CO state ofe2m2Sb lacks the intra-dimer charge separation.

It should be noted that the frequency of the A1 (A10)mode, 1373 cm�1 (1362 cm�1) is higher than that of the A2(A20) mode [1337 cm�1 (1330 cm�1)]. This indicates that theA1 and A10 (A2 and A20) modes belong to the charge-rich(poor) molecules and suggests that the inter-molecularinteraction between the charge-rich and charge-poor mole-cules is negligibly small. In other words, a charge-rich dimerand a charge-poor dimer participate in the repeating unit. Wedesignate such a CO state as ‘‘inter-dimer separation’’ todistinguish it from the above-mentioned intra-dimer separa-tion. In inter-dimer separation, the difference in thefrequencies between the A1 and A2 (or A10 and A20) modesis largely attributed to the difference in the molecularcharges between the charge-rich and charge-poor dimers.Indeed, the difference in the frequencies between the A1and A2 (or A10 and A20) modes, �36 cm�1 (�32 cm�1),is comparable to that between the B1 and B2 modes(�37 cm�1). The assignment based on the inter-dimerseparation is consistent with the excitation laser dependence(Appendix B).

The averaged frequency between the A1 and A2 modes,1355 cm�1, is lower than that in the non-CO state,�1361 cm�1 at 100K, which is different from the propertyof the B mode. This inconsistency indicates that the A-groupis perturbed by the inter-dimer interaction and not sosensitive to molecular charges as compared to the B-group.Let us examine the inter-dimer interaction in the A-group.The IR-active A-group is polarized along the stackingdirection. Hence, we consider the inter-dimer interactionalong the stacking direction. The vibrational motion of theA-group is expressed using A modes of four local dimers,RA

I, RAII, P

AI, and PA

II:

A1 ¼ �ðRAI þ RA

IIÞffiffiffi2

p þffiffiffiffiffiffiffiffiffiffiffiffiffi1� �2

pðPA

I þ PAIIÞffiffiffi

2p ; ð1Þ

A10 ¼ �ðRAI � RA

IIÞffiffiffi2

p þffiffiffiffiffiffiffiffiffiffiffiffiffi1� �2

pðPA

I � PAIIÞffiffiffi

2p ; ð2Þ

A2 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffi1� �2

pðRA

I þ RAIIÞffiffiffi

2p � �ðPA

I þ PAIIÞffiffiffi

2p ; ð3Þ

A20 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffi1� �2

pðRA

I � RAIIÞffiffiffi

2p � �ðPA

I � PAIIÞffiffiffi

2p : ð4Þ

RAI and RA

II (PAI and PA

II) are corresponds to the Amodes at isolated and charge-rich (isolated and charge-poor)dimers. The parameters � and � express the degree of inter-dimer interaction; they approach 1=

ffiffiffi2

pwhen the interaction

is significantly large, whereas they are equal to 1 when thecharge is completely localized at a specific dimer. Thedifference in the frequencies between the A2 and A20 modes,�7 cm�1, is small, as is the difference between the A1 andA10 modes (�11 cm�1). The small frequency shifts suggestthat two charge-poor (charge-rich) dimers neighbor oneanother, resulting in less perturbation due to the CTinteraction. Such a distribution agrees with that obtainedfrom X-ray structural analysis.8) These observations suggestthat � and � are close to 1.

A detailed analysis of the A-group is useful for furtherdiscussing the inter-dimer interaction. The difference in thefrequencies between the A2 and A20 modes, �7 cm�1,is smaller than that between the A1 and A10 modes(�11 cm�1). The degree of perturbation depends on themagnitude of the transfer integral and the e–mv couplingconstant. Our observations indicate that the inter-dimertransfer integral between two charge-poor dimers, tPP, issmaller than that between two charge-rich dimers, tRR.Indeed, the inter-dimer distance between charge-poordimers, �5:45 �A, is longer than that between charge-richdimers, �5:11 �A.8) The inter-dimer transfer integral based onthe structural analysis is also consistent with our analysis.Therefore, we can conclude that a group of two charge-richdimers and a group of two charge-poor dimers arealternately arranged along the stacking direction, resultingin alternation of the inter-dimer transfer integral.

The A-group is useful to examining whether the inter-dimer separation or the intra-dimer separation. A subtlechange in the inter-dimer interaction is also examined fromthe A-group. However, the A-group is not necessarysensitive to molecular charges.

6.3 C mode in the CO stateIn x6.3 and x6.4, we discuss the vibrational modes

between 1200 and 1300 cm�1 in Fig. 11, where the C- andD-groups are expected to be observed. Owing to thecomplicated spectral shapes, we tentatively use the notationsZ–S bands. We also use the notations C1, C10, . . . , D20

modes in the correlation diagram of Fig. 12. As shown inFig. 11, a broad band, denoted as the T band, is observed inthe Raman spectra measured with the 514 nm laser. In theb-polarized conductivity spectra, the broad Y band is alsoobserved. Their broad line-widths suggest that the T and Ybands belong to the C-group, which is strongly perturbed bythe intra-dimer e–mv interaction. As shown in the inset ofFig. 11, the intensity of the Y band is largest in thea-polarized conductivity spectra. However, its spectral shapeis more complicated; at least three vibrational modes, the S,X, and Z bands (and possibly the B2 mode), overlap with theY band. The line-width of the Y and T bands, �50 cm�1, issignificantly larger than that of the C mode in the non-COstate (�15 cm�1, in Fig. 9). The broad line-width suggeststhat alternation of the inter- and intra-dimer transfer integralscontributes to the further perturbation. Moreover, each of theT and Y bands is not necessarily a single band. As shown inFig. 12, four modes belonging to the C-group are allowed;



C1–C20. When C1 (C10) overlaps with C2 (C20), the T (Y)band exhibits an extraordinarily broad line-width. Therefore,a detailed assignment cannot be given for the C-group in theCO state because the C-group is extremely sensitive to inter-molecular interactions.

6.4 D mode in the CO stateThe assignments of the D-group are summarized in

Fig. 12. Although the U band in the Raman spectra hassmaller line-widths than the C-group, they have lowerfrequency than the C-group. Because this property isinconsistent with that of the C-group, the U band belongsto the D-group. The Z band observed as a dip in the IRspectra is also belongs to the D-group because of the narrowline width. The frequency of the Z band is not identical tothat of the U band, indicating that the Z band inherentlydiffers from the U band. The line-width of the S band,�7 cm�1, is smaller than that of the T band (�50 cm�1). Thefrequency of the S band is higher than that of the T band.One may surmise that the S band belongs to the C-groupsince the line-width of the e–mv mode becomes narrowerwith increasing frequency. However, the remarkably smallline-width of the S band is inconsistent with the broad line-width of the C-group. It is thus reasonable to conclude thatthe S band belongs to the D-group. In the b-polarized IR-conductivity spectra, a dip denoted as the X band is observedat �1290 cm�1. Since a-polarized spectra exhibit theinflection at �1290 cm�1, we can conclude that the X bandis also observed in the a-polarized spectra. The line-width ofthe X band in the b-polarized spectra is smaller than that ofthe C-group and comparable to that of the S band. Thisproperty leads to the conclusion that the X band belongs tothe D-group. The observation of the S (Z) band in the IR(Raman) spectra indicates that the mutual exclusion rule isnot exactly applied to the IR and Raman spectra, which isdiscussed in x6.5.

Let us discuss the properties of the D-group. Thedifference in the frequencies between the U and S (Z andX) bands, �46 cm�1 (�23 cm�1), is comparable to thatbetween the B1 and B2 modes, �37 cm�1. Therefore, onemay surmise that the D-group is sensitive to the charge at adimer. However, the averaged frequency of the S and U(or Z and X) bands, �1283 cm�1 (�1279 cm�1), is higherthan the frequency of the D mode in the non-CO state(�1269 cm�1 at 100K). This behavior is significantlydifferent from that of the charge sensitive B-group, in whichthe averaged frequency of the B1 and B2 modes is almostidentical to the frequency of the B mode in the non-CO state.In addition to this, the difference in the frequencies of theD-group is different from the fact that the frequenciesbetween B1 and B10 (B2 and B20) modes are identical toeach other. This property means that the D-group is sensitiveto inter-molecular interaction. Therefore, the D-group is notso sensitive to the molecular charge.

The remarkable difference in the frequencies between theU and S (Z and X) bands should be ascribed to anothereffect. As described in x5.2, the frequency largely dependson the degree of CT within a dimer, i.e., the D mode isproduced by the strong intra-dimer interaction. This yieldsthe relation, tintra (charge-rich dimer) < tintra (non-CO) <tintra (charge-poor dimer). Our conjecture is supported by

X-ray structural analysis.8) The intra-dimer distances (dintra)are �3:33, �3:1, and �2:91 �A for the charge-rich, non-COstate, and charge-poor dimers, respectively, and theestimated transfer integrals are �350, �450, and �550meV,respectively.8) It should be noted that the perturbation of theD-group is reduced when the intra-dimer interaction isdecreased. This property is in agreement with the fact thatthe frequency of the S band is remarkably high as comparedwith the other D modes in both CO and non-CO states.Therefore, the frequency of the Raman active D-groupdepends on the degree of dimerization. This conclusion leadsto the views that the U and Z bands belong to the chargepoor dimer and that the S and X bands to the charge richdimer. Our assignments are supported from the excitationenergy dependences (Appendix B). In Appendix B, the largeperturbation of the D mode is also discussed from theviewpoint of the molecular orbital.

The D-group is also sensitive to the inter-dimer interac-tion as well as the intra-dimer interaction. The difference inthe frequency between the S and X bands (= D1 and D10

modes), �16 cm�1, is larger than that between the U and Zbands (D2 and D20 modes), �7 cm�1. This indicates that theinter-dimer transfer integral between the charge-rich dimersis larger than that between the charge-poor dimers.Interestingly, this behavior is consistent with that of theA-group. The consistency between the A- and D-groups isascribed to the fact that both vibrational modes belong to theAg mode in a dimer and the frequency is perturbed by thee–mv interaction between the neighboring dimers. The fourvibrational modes in the D-group are also expressed likethose of the A-group in eqs. (1)–(4) and the parameters arecloser to 1 than to 1=

ffiffiffi2

p. Therefore, the D-group is sensitive

to the inter-dimer interaction as well as the intra-dimerinteraction.43)

6.5 Geometrical pattern in the CO stateWe briefly comment on the two-dimensional structure in

the CO state. The distributions of the site-charge and transferintegrals obtained from the vibrational spectroscopy areconsistent with those obtained from X-ray structural analy-sis.8) However, the mutual exclusion rule can not be exactlyapplied to both IR and Raman spectra. The A10 and D20

(= Z) modes, which are inherently IR-active, are observedin the Raman spectra. Moreover, the D1 (= S) mode, whichis inherently Raman-active, is also observed in the IR-conductivity spectra. These observations strongly indicatethe loss of inversion symmetry, which is different from theresults of structural analysis. Nevertheless, a pseudo-inver-sion center can be located in a repeating unit because somevibrational modes— the A1, A2, and X—almost satisfy themutual exclusion rule. In the present material, two organiclayers are separated by a countercation layer which has noinversion center. Our observations indicate that a weakinteraction between the organic and cation layers induces theslightly asymmetric structure in the organic layer.

7. Summary of the C¼C Stretching Modes

We have confirmed the C¼C stretching modes in a tightdimer. The A and C modes belong to the �1 mode, and the Band D modes belong to the �2 mode. The B mode is sensitiveto the molecular charge because it is free from the e–mv



interaction. The A mode is sensitive to the inter-dimerinteraction, and is somewhat sensitive to the fractionalcharge at a dimer as far as the inter-dimer charge separation,but insensitive when charges within a dimer are differentfrom each other. The degree of perturbation of the C mode isunderstood within a framework of the standard e–mv model.Like the �3 mode of the ET salts, the C mode might be usefulfor investigating subtle changes in inter-molecular interac-tions if the number of molecules in a repeating unit issmaller than that of e2m2Sb in the CO state. The largeperturbation of the D mode is characteristic of tightdimerization. Its frequency is significantly lower than thatof the B mode since the D mode induces the inter-molecularcharge transfer within a dimer. The frequency of the D modelargely depends on the intra-dimer interaction, in otherwords, the degree of dimerization. The inter-dimer interac-tion also contributes to weak but non-negligible perturba-tion. Therefore, both intra- and inter-dimer interactions canbe analyzed from the D-group. The excitation energydependence of the A- and D-groups provides informationon the energy levels of the MO in a dimer. We conclude thatvibrational spectroscopy is a powerful tool for analyzing themolecular charges, intra- and inter-dimer transfer integrals,inter-molecular Coulomb interactions in a dimer, and energylevels of the MO. In the subsequent articles, we will presentthe vibrational spectra of several [Pd(dmit)2] salts whichexhibit different types of CO transitions, superconductingtransitions, and spin frustrations.

Acknowledgement

This research was supported by Grants-in-Aid forScientific Research (No. 05J04172, 16GS0219, 20110003,and 20850024) from the Japan Society for the Promotion ofScience and the Ministry of Education, Culture, Sports,Science and Technology (MEXT). Portions of the calcula-tions were performed using the RIKEN Cluster of Clusters(RICC) facility.

Appendix A: Vibronic C¼C Stretching Modeand Electronic Transitionsof TBA[Pd(dmit)2](TBA = tetra-n-butylammonium)

Let us examine the IR-active �1 mode of T1. Figure A�1shows the conductivity spectra obtained from the polarizedIR and NIR-reflectance spectra. The inset shows the pseudo-two-dimensional layer of [Pd(dimt)2] molecules viewedalong the c-axis. The TBA cations are located between the[Pd(dimt)2] layers but omitted in the figure. The b- andc-polarized spectra were obtained from the bc-plane. Thea-polarized spectra are not shown since the reflectancespectra obtained from the ab- and ac-planes displayedinterference, presumably due to the staircase surface. As forthe a-polarized spectra, both the electronic transitions in theNIR region and vibrational parts due to C¼C stretchingmodes are consistent with those of the b-polarized spectra.

The spectra can be separated into two frequency regions;one reflecting electric transitions in the NIR region, the otherreflecting vibrations in the IR region. In the IR region, theintensity of the vibrational mode at �1310 cm�1 in theb-polarized spectra is the higher than that in the c-polarizedspectra. This polarization dependence suggests that this IR-

active mode is the e–mv mode since sulfur–sulfur contactsextend in the ab-plane. Furthermore, its frequency issignificantly lower than that of the Raman-active �1 modein Fig. 5 (1397 cm�1). This strongly indicates that thevibrational mode at �1310 cm�1 can be assigned to the IR-active �1 mode due to the e–mv interaction in the dimer.Hereafter, the IR- and Raman-active modes are denoted as�1(IR) and �1(R), respectively. The mutual exclusion rule isapplied to both IR and Raman spectra, which is fullyconsistent with the crystal structure; the repeating unit in the[Pd(dimt)2] layer is a dimer on the inversion center and theinter-molecular distances exhibit an alternation.

Let us discuss the degree of perturbation in the �1 mode.The evaluation of the e–mv coupling constant is importantfor considering the e–mv modes. However, whereas thee–mv coupling constant of [Ni(dmit)2] has been reportedpreviously, that of [Pd(dmit)2] has not.28–30) The degree ofperturbation, i.e., the observed difference in the frequenciesbetween �1(R) and �1(IR), depends on both the e–mvcoupling constant and the magnitude of the transfer integral.Interestingly, the degree of perturbation, �1ðRÞ � �1ðIRÞ ¼87 cm�1, is significantly large. However, the small transferintegral for T1 is supported from the fact that theinter-molecular sulfur–sulfur distances are approximately�4 �A—a value larger than the intra-dimer distances fore2m2P and e2m2Sb (�3 �A). Furthermore, whereas e2m2Pand e2m2Sb take face-to-face contact, T1 does not. Thesefacts strongly indicate a loose dimerization with intra-dimertransfer integrals smaller than those of e2m2P and e2m2Sb.Indeed, as shown in the caption of Fig. A�1, overlapintegrals calculated from the result of structural analysis atroom temperature are small. Although the intermoleculardistance exhibits a slight alternation and the e–mv modeis observed, the calculated overlap integrals are almostuniform. Such condition is similar to those of K-TCNQ andRb-TCNQ (tetracyanoquinodimethane) above the transitiontemperatures, where the e–mv mode persists owing to thefluctuation of the dimerization.44) Therefore, the largeperturbation in the �1(IR) mode is neither ascribed to themagnitude of transfer integral nor the alternation in thetransfer integral. It is reasonable to consider that the largeperturbation is attributed to a large e–mv coupling constant.

This hypothesis is examined by model calculations basedon the previous studies.23,33–36,41) We have calculated thefrequency assuming two electrons are accommodated intothe symmetric dimer. The e–mv coupling constant, g, of the�1 mode is assumed to be g ¼ 0:1 and 0.02 eV, those whichare the same as those of the �3 and �2 modes for ET,respectively. The results between g ¼ 0:1 and 0.02 eV arecompared. The frequencies of the �1 modes at � ¼ �2 and�1 (1445 and 1397 cm�1, respectively) are taken fromRaman active �1 of T2 and �1(R) of T1. The frequency at� ¼ 0 (1317 cm�1) is estimated by extrapolation using �1(R)of T1 and A mode of e2M2P (� ¼ �0:5 at a monomer).Figure A�2 shows the degree of perturbation, where themolecular charge is fixed at � ¼ �1 and the transfer integralis varied. In both coupling constants, the frequency of the�1(R) mode is insensitive to inter-molecular interaction. Incontrast to the �1(R) mode, the frequency of the �1(IR) modedepends on the coupling constant. As for g ¼ 0:1 eV, the�1(R) is significantly perturbed despite small t. This result is



in agreement with the experimental result. However, itshould be noted that the frequency is overestimated, that is,an underestimation in the degree of perturbation, becauseany inter-molecular interaction except for the intra-dimerinteraction is neglected. In particular, the overestimation isserious for small t. In order to examine the coupling constantmore precisely, we have compared the frequencies for larget. Based on the extended Huckel method, the overlapintegral, jSj, of charge-rich dimer in the CO state of e2m2Sbis estimated to be �35:5� 10�3. The transfer integral isusually estimated from the relation of t ðmeVÞ ¼ EjSj.There is no consensus on the factor E (eV) for the tightdimer. However, the factor takes within a range of10� 104 � E � 20� 104.9) Then, the perturbed frequencyis estimated to be 1250–1300 cm�1 for g ¼ 0:1 eV, which isin agreement with the frequency of the C-group of e2m2Sb(details of the C-group is discussed in x6.3). These resultssuggest that the e–mv coupling constant of [Pd(dimt)2] isclose to that of the �3 mode of ET, �0:1 eV, rather than thatof the �2 mode of ET, �0:02 eV. It roughly agrees with thatof [Ni(dmit)2].

28–30)

In the rest of this section, we will describe the electronictransitions of T1 because very little work is currentlyavailable on the electronic transition for X[Pd(dimt)2]. Asshown in Fig. A�1, two electric transitions are observed at�5500 and �7000 cm�1. Hereafter, the former is denoted as

the � band, the latter as the � band, respectively. In thelower panel of Fig. A�1, schematic views of the energydiagrams between the loose dimer and the tight dimer areshown. No HOMO–LUMO crossing is occurred for theloose dimerization. As discussed by Tamura et al., thetransition energy of the � band is independent of the inter-molecular interaction because the � band originates fromthe HOMO–LUMO transition of a monomer.9,10) Indeed, thetransition energy of a tight dimer is identical to that of the[Pd(dimt)2]

� solution.18,19) Therefore, � band in our spectraalso originates from the HOMO–LUMO transition of amonomer.

By assuming the inter-molecular interaction is non-negligible, the � band is assigned to the electronic transitionbetween MO(3) and MO(4) levels. However, as describedabove, the overlap integral is remarkably small as comparedwith that of a tight dimer. Therefore, the transition energy ofthe � band is attributed to Coulomb interactions. The � bandinduces the charge transfer (CT) between the neighboringcharged molecules: ðanionÞ�1 þ ðanionÞ�1 ! ðdianionÞ�2 þðneutralÞ0. As far as the uniform lattice, the transition energyof � band is comparable to U � V , where U (V ) denotes theon-site (inter-molecular) Coulomb interaction. From theviewpoint of the band picture, the � band corresponds to thetransition across the lower and upper bands whose energygap is U � V . When molecules form a dimer, the intra-dimerCT and the inter-dimer CT are allowed. The transitionenergy is modified into U � Vd and U � Vi, where Vd (Vi)denotes the intra-dimer (inter-dimer) Coulomb interaction.However, no remarkable additional electronic transition,suggesting the separation of the � band, was observed in ourspectra. This result is in agreement with the small overlapintegral and a slightly alternation in the transfer integralbecause the loose inter-molecular contacts lead to

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.71250

1300

1350

1400

1450

ν(c

m

)-1

Loose-dimer

, g = 0.1 eV

U = 0.7 eVV = 2t / 3 + 0.1 eV

t (eV)

-1

-1

1ν (IR)

1ν (R)

-1-1

, g = 0.02 eV1ν (IR)

Charge-rich and tight-dimer

Fig. A�2. Transfer integral dependence of the frequencies of the �1(R)

and �1(IR) modes. The dimer with two electrons are assumed in the

calculation, and the result of � ¼ �1 is shown. The relation between V and t

is fixed for easier viewing. The e–mv coupling constant, g, is assumed to be

0.1 and 0.02 eV. �1(R) of g ¼ 0:1 eV is almost identical to that of

g ¼ 0:02 eV. �1(IR) of g ¼ 0:1 eV (solid line) is significantly different from

that of that of g ¼ 0:02 eV (broken line). The gray ellipsoids denote the

regions of a loose dimer and a tight dimer.

1000 10000

0

100

200

300

Wavenumber ( cm )-1

σ(

)

(S

cm

)ω

σ( ) (S

cm)

ω

0

100

200

b -polarized

b

c

5000

Δ

Δ

1ν (IR)

ao

c -polarized

e-mv

-1

LooseDimer

TightDimer-2

(Monomer)

HOMO

LUMO

MO(3)

MO(4)

MO(1)

MO(2)

MOT(3)

MOT(4)

MOT(1)

MOT(2)Δ

Δ

Δγ

Γ

Γ

γ

γ

Fig. A�1. Top: IR-conductivity spectra of T1. The inset shows the

arrangements of [Pd(dmit)2] molecules in a two-dimensional layer projected

onto the crystallographic ab-plane. The countercations are omitted for

clarity. Gray ellipses denote the loosely dimerized structures. Bottom:

Schematic energy diagrams of ‘‘monomer’’, ‘‘Loose Dimer’’ and ‘‘Tight

Dimer’’. Closed (open) circle denotes the occupied (unoccupied) state.



U � U � Vd, � U � Vi (small Vd and Vi). This behavior issignificantly different from that of X-TCNQ (X ¼ K and Rb)below the transition temperatures, where two electronictransitions due to U � Vd and U � Vi are observed.45) Thebehavior of T1 is a little different from that of X-TCNQabove the transition temperatures, where the transitionenergy is depend on U � V rather than U owing to thefinite transfer integral. Since Vd and Vi are small for T1, U ofa monomer can be estimated from our spectra, and theestimated value is �0:7 eV (¼ 5500 cm�1).

Appendix B: Excitation Energy Dependenceof A and D Modes and Calculationof Molecular Orbital

The Raman intensity is generally enhanced with increas-ing excitation energy. On the other hand, some vibrationalmodes do not necessary obey the general rule owing to theresonant effect. Figure B�1 shows Raman spectra of e2m2Sbin the non-CO state at 100K. Among the three Ramanspectra, the relative intensity of the D (A) mode, D/A(A/D), obtained with the 780 nm (514 nm) laser is thehighest. This phenomenon is explained from the MO energydiagram. Figure B�2 shows the energy diagrams deducedfrom the NIR-VIS reflectance spectra in the non-CO and COstates.9) The energy levels in the non-CO state correspond to(b). The excitation energy of the 780 nm laser, �1:59 eV is alittle higher than the transition energies of the � transition[¼ MOTð1Þ ! MOTð3Þ and MOTð2Þ ! MOTð4Þ], �1:25eV, which is close to a resonance condition. The excitationenergy of 514 nm laser, �2:41 eV, is also a little higher thanthat of MOTð1Þ ! MOTð4Þ, �2:17 eV. On the other hand,the excitation energy of the 633 nm laser is lower thanMOTð1Þ ! MOTð4Þ and much higher than the transitionenergies of �.

Interestingly, the � transition favor with the D modewhereas MOTð1Þ ! MOTð4Þ with the A mode. We cansurmise that � involves the intra-dimer charge transferbecause the D mode is coupled with the intra-dimer CT. Thisconjecture is supported from the resonant effect in the COstate. The energy diagrams of the charge poor-dimer and

rich-dimer are shown in Figs. B�2(a) and B�2(c), respec-tively. The transition energies of the � and MOTð1Þ !MOTð4Þ in the charge-poor dimer is identical to the energyof the 780 and 514 nm lasers, respectively. As shown inFig. 11, the U and A2 are enhanced with the 780 and 514 nmlasers, respectively. Concerning the charge-rich dimer, theexcitation energy of 633 nm laser is a little lower than thetransition energy of MOTð1Þ ! MOTð4Þ, which means thepre-resonance Raman effect. On the contrary, the transitionenergy of � does not much with three kinds of lasers. Indeed,the A1 mode is observed with 633 nm laser whereas the Sband is not (Fig. 11). Therefore, the D mode is resonant withthe � transition whereas the A mode with MOTð1Þ !MOTð4Þ.

It should be noted that neither A1 mode nor S band isobserved in the spectra obtained with 780 nm laser (Fig. 11).The absence in these modes is explained from the fact thatthe excitation energy of 780 nm laser does not much withany transition energies in a charge rich dimer [Fig. B�2(c)].

633 nm

780 nm

514 nm

e2m2SbRaman100 K

1200 1250 1300 1350 1400

(

) (

arb.

uni

ts)

ωI

A

D


Fig. B�1. Raman spectra of e2m2Sb(13-0) at 100K. The spectra obtained

from 633 nm laser is identical to that in Fig. 9.

MOT(2)

MOT(3)

MOT(1)

MOT(4)

[Pd(dmit) ]2 20 [Pd(dmit) ]2 2

-1 [Pd(dmit) ]2 2-2

1.96 eV (633 nm

)

1.54

eV

2.46

eV

1.25

eV

2.17

eV

1.16

eV

2.08

eV

1.54

eV

1.25

eV HOMO

LUMO2.41 eV (514 nm

)

1.59 eV (780 nm

)

2.41 eV (514 nm

)

1.59 eV (780 nm

)

MOT(2)

MOT(3)

MOT(1)

MOT(4)

(a) (b) (c)

Fig. B�2. Schematic views of the energy levels of the molecular orbital for (a) [Pd(dmit)2]20, (b) [Pd(dmit)2]2

�, and (c) [Pd(dmit)2]22�. The energies of the

� [¼ MOTð1Þ ! MOTð3Þ and MOTð2Þ ! MOTð4Þ] and MOTð1Þ ! MOTð4Þ transitions are compared with the laser energies. The numbers between the

arrows in the left sides of each diagram are the transition energies (unit: eV) obtained from ref. 9. The lengths of the arrows in the right sides of each diagram

denote the excitation laser energies. The solid (open) circle denotes the occupied (unoccupied) state. Molecular orbitals of neutral monomer and neutral tight

dimer are shown in the right and left ends, respectively.



In summary, the intensities of the A and D modesdepend on the laser wavelength. This property is aclue to the assignment of C¼C stretching mode. Theresonance effect is also useful to discussing the intra-dimer transfer integral, because the transition energiesof � and MOTð1Þ ! MOTð4Þ depend on the degree ofdimerization.

The difference in the resonant conditions between the Aand D modes are also understood from the viewpoint of theMO. The MO was obtained using B3LYP/LANL2DZ withthe Gaussian03 program after geometrical optimization. Weassumed a neutral dimer, [Pd(dimt)2]2

0, since the result ofgeometrical optimization is almost consistent with thestructure of the charge-poor dimer of e2m2Sb in the COstate. Although the relativistic effect on Pd atoms isincorporated, the numbers of basis sets at the carbon andsulfur atoms are smaller than with the B3LYP/6-31G��

method. The diffuse function is not incorporated into thesulfur atoms, leading to underestimation of the intra-molecular interaction including that between sulfur andpalladium. However, the inter-molecular interactions be-tween carbon atoms at C¼C bonds are included in thecalculation. In analogy with the previous calculations, ourcalculation reproduces the boat-shaped molecular structurein a dimer and HOMO–LUMO crossing.21,22) The Pd–Pddistance, �2:94 �A, is almost identical to that of the chargepoor dimer of e2m2Sb, �2:93 �A. To our best knowledge,the Pd–Pd distance from our calculation is the bestvalue compared with the previous calculated results. The� transition [¼ MOTð1Þ ! MOTð3Þ and MOTð2Þ !MOTð4Þ] corresponds to the electronic transition from thebonding to the anti-bonding orbitals consisting of HOMOsand LUMOs, respectively. The � transition involves thecharge transfer because an electron resonated in a dimergets localized due to the � transition. On the other hand,the MOTð1Þ ! MOTð4Þ transition consists of HOMO–LUMO transition, which inherently has a nature of localtransition.

As described above, the molecular structure, HOMO–LUMO crossing and the resonance condition have beenunderstood from the standpoint of the MO calculation. Wehave extended our calculation to the degree of perturbationof the D mode using the same computational method.Indeed, the large perturbation, �90 cm�1, was obtainedfrom the difference in the frequencies of the A and D modes.This calculated value is almost consistent with the experi-mental result, !ðUÞ � !ðA2Þ ¼ �77 cm�1. As for thequantitative discussions, however, a more detailed normalmode analysis, including the sulfur–palladium contacts, isrequired. Such calculation might also allow us to betterestimate the molecular charge using the frequency of the Bmode.

We briefly comment on the C¼S stretching mode fromthe viewpoint of the MO. As shown in Fig. B�2, the carbonatoms in the thioketone groups do not contribute to the MO.This indicates that the C¼S stretching modes are insensitiveto the charge and inter-molecular interaction. Indeed,compared to C¼C stretching modes, the asymmetric C¼Sstretching modes are insensitive to the molecular charge,and the symmetric mode has a small e–mv couplingconstant.28,46)

1) The crystal structures of �, �, and �-type ET salts are summarized in

T. Mori: Bull. Chem. Soc. Jpn. 72 (1999) 179.

2) The crystal structures of �, �0, and �00-type ET salts are summarized in


3) The crystal structures of and �0-type ET salts are summarized in


4) Magnetic fluctuation of the SC transition in �-type ET salts is reported

in A. Kawamoto, K. Miyagawa, Y. Nakazawa, and K. Kanoda:

Phys. Rev. Lett. 74 (1995) 3455; A. Kawamoto, K. Miyagawa, Y.

Nakazawa, and K. Kanoda: Phys. Rev. B 52 (1995) 15522; A.

Kawamoto, K. Miyagawa, and K. Kanoda: Phys. Rev. B 55 (1997)

14140.

5) Charge fluctuation of the insulator-SC transition in �00-type ET salts is

reported in T. Yamamoto, H. M. Yamamoto, R. Kato, M. Uruichi, K.

Yakushi, H. Akutsu, A. Sato-Akutsu, A. Kawamoto, S. S. Turner, and

P. Day: Phys. Rev. B 77 (2008) 205120.

6) Charge fluctuation of the metal–SC transition in �00-type ET salts is

reported in N. Drichko, S. Kaiser, Y. Sun, C. Clauss, M. Dressel, H.

Mori, J. Schlueter, E. I. Zhyliaeva, S. A. Torunova, and R. N.

Lyubovskaya: Physica B 404 (2009) 490.

7) R. Kato: Chem. Rev. 104 (2004) 5319.

8) The structural analysis in the CO state was conducted in A. Nakao and

R. Kato: J. Phys. Soc. Jpn. 74 (2005) 2754.

9) The NIR spectra in the CO state were reported in M. Tamura, K.

Takenaka, H. Takagi, S. Sugai, A. Tajima, and R. Kato: Chem. Phys.

Lett. 411 (2005) 133.

10) The electronic structure in the CO state was discussed in M. Tamura

and R. Kato: Chem. Phys. Lett. 387 (2004) 448.

11) The AFI, pressure-induced SC, and pressure-induced metallic state are

summarized in ref. 7.

12) For the SC and metallic states, see for example, R. Kato, Y.

Kashimura, S. Aonuma, N. Hanasaki, and H. Tajima: Solid State

Commun. 105 (1998) 561.

13) For the AFI state, see for example, K. Seya, Y. Kobayashi, T.

Nakamura, T. Takahashi, Y. Osako, H. Kobayashi, R. Kato, A.

Kobayashi, and H. Iguchi: Synth. Met. 70 (1995) 1043.

14) The FS state is reported in M. Tamura and R. Kato: J. Phys.: Condens.

Matter 14 (2002) L729. According to the recent experiment, the

material denoted as ‘‘Et2Me2Sb Salt’’ in Fig. 2 turn out to be the mixed

alloy composed of Et2Me2Sb [Pd(dmit)2]2 and EtMe3Sb[Pd(dmit)2]2.

Note that the former (the latter) exhibits the CO state (the SF state) in

the low temperature.

15) M. Tamura, A. Nakao, and R. Kato: J. Phys. Soc. Jpn. 75 (2006)

093701.

16) Y. Ishii, M. Tamura, and R. Kato: J. Phys. Soc. Jpn. 76 (2007) 033704.

17) E. Canadell, I. E.-I. Rachidi, S. Ravy, J. P. Pouget, L. Brossard, and

J. P. Legnos: J. Phys. (Paris) 50 (1989) 2967.

18) H. Tajima, T. Naito, M. Tamura, A. Kobayashi, H. Kuroda, R. Kato,

H. Kobayashi, R. A. Clark, and A. E. Underhill: Solid State Commun.

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vibrational spectra of [pd(dmit) {2}] dimer (dmit=1,3 ... · transport, magnetic, and optical...

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