Unified Theory of the Role of Vibronic Interactions in Micro- and Mcroscopic Sized Superconductivity August 18, 2010, University of Fribourg

Transcription

1 Unified Theory of the Role of Vibronic Interactions in Micro- and Mcroscopic Sized Superconductivity August 18, 21, University of Fribourg Takashi KATO Institute for Innovative Science and Technology, Graduate School of Engineering, Nagasaki Institute of Applied Science, Japan Part 1: Vibronic interaction analyses and their application to superconductivity Part 2: The mechanism of the occurrence of diamagnetic currents in molecular systems; towards high temperature superconductivity

2 Part 1: Vibronic interaction analyses and their application to superconductivity in modern physics and chemistry Vibronic interactions Electron phonon interactions spectroscopy electrical conductivity superconductivity polyacenes polyphenanthrenes

3 Superconductive transition temperatures T c s T c ln 1. 2 exp * 1.62 ln 1. 2 exp 1.4 1N F l LUMO+1 N F l LUMO+1 * 1.62N F l LUMO+1 molecular vibrations LUMO negatively charged picene theoretically predicted T c - 1 K Jahn Teller onference held in Leuven, Belgium, in 22 8 years later superconductivity K 3 picene; T c = 7 or 18 K Y. Kubozono et al. (Okayama Univ.) Nature (21) K atoms; completely ionized? picene; monoanions (l LUMO =.26 ev, ln,lumo = 11 cm 1 ) or trianions (l LUMO+1 =.179 ev, ln,lumo+1 = 899 cm 1 )?

4 Part 2: The mechanism of the occurrence of diamagnetic currents in molecular systems; towards high temperature superconductivity nondissipative diamagnetic intramolecular ring currents introduced in many textbooks of chemistry and Physics even at 298 K mechanism has not been elucidated not insulator from the point of view of solid state physics? H applied what is electrical conductivity? closed-shell electronic structures in small molecules LUMO occupied level unoccupied level k

5 what is electrical conductivity from the point of view of solid state physics? total + E applied total E = (H = total E = E applied (H = H applied total random moving additional momenta according to the applied spontaneous electric current cannot be expected electric or magnetic field without any applied electric or magnetic field total momentum of electrons is changed Total momentum states of electrons should be changed by applied magnetic or electric fields in order for the electrical current to occur.

6 occupied level unoccupied level monocation k monoanion k first-order perturbation first-order perturbation k k hole doping electron doping Total momentum states of electrons can be changed by applied magnetic or electric fields hole doping electron doping effective ways for materials to become metallic for a long time

7 occupied level bulk systems nondissipative diamagnetic intramolecular ring currents unoccupied level k continuous neutral small materials k discrete second-order perturbation occupied level unoccupied level k k closed-shell electronic structures with small valence conduction band gap Total momentum states of electrons can be changed by applied magnetic or electric fields closed-shell electronic structures with large LUMO gap H applied graphite Total momentum states of electrons can not be changed by applied magnetic or electric fields not insulator from the point of view of solid state physics? semimetallic bulk (solid state) system (~1 8 Å)

8 nondissipative diamagnetic intramolecular ring currents H k neutral small materials H = k j, s intraatomic H applied S k j,s k H,induced k H,induced k j,s occupied level unoccupied level k electron pairing k j,s total,neutral N [N]annulene k j, s k H,induced l ground state = k j, s k H,induced electron pairing total,neutral N j neutral N an V oulomb [N]annulene Total momentum states of electrons can not be changed by applied magnetic or electric fields closed-shell electronic structures with large LUMO gap U Q If two electrons with opposite momenta and spins occupying the same orbital form electron pair, nondissipative diamagnetic ring current can occur. k 1 k1 (A) (B) g electronic state g neutral occupied g i i g i i an nondissipative diamagnetic intramolecular ring currents be explained? Strengths of electron phonon interactions are zero in the closed-shell electronic structures in -conjugated hydrocarbons. Electron phonon interactions cannot play a role in electrical conducting. Another mechanism should be investigated.

9 H = V oulomb,n,j k j, s electron pairing k j,s orbital,n,j V kin,n, j V oulomb,n, j orbital energy kinetic energy oulomb energy +2 total,intra N V oulomb,n,j orbital,n,j V kin,n,j orbital,n, j negative or very very large positive small positive (frontier orbitals) oulomb energy (ev) oulomb interactions play an essential role in attractive electron electron interactions V oulomb,n,j very large negative Orbital energy level (ev)

10 nondissipative diamagnetic currents are destroyed energy difference between the ground and excited states normal metallic state one electron excited state LUMO E LUMO, 6 an kcal / mol ~1 4 K LUMO localized Kekulé structure nondissipative localized diamagnetic currents RE 6 () neutral an RE 36. kcal / mol 18 K LUMO ground state delocalized structure nondissipative delocalized diamagnetic currents

11 T c (K) supercurrent transition temperature neutral T N an c,re neutral T N an c, LUMO electron phonon interactions T c,bs microscopic sizes (intramolecular) macroscopic sizes (bulk) N closed shell material size microscopic sizes (intramolecular): we must consider each energy level in a discrete manner natural electron pair easily formed not easily destroyed neutral N an T c E higher than room temperature LUMO discrete macroscopic sizes (bulk): we must consider the summation of electron phonon interactions between various vibrations and various electronic states in a thin-shell around the Fermi level continuously. artificial electron phonon interactions electron pair not easily formed easily destroyed T c,bs 2 e 1/ usually very low 2 F continuous

12 (a) normal metallic ground states (not realistic at any temperature) electron pairs are formed by nature V NM,e p,ground T V NM,total,ground T V NM,ground T V NM,e p,ground T V NM,ground T (b) normal metallic excited states (T > T c,vibronic ) F electron pairs formed by nature are destroyed by electron phonon interactions 2 V NM,e p,excited T V NM,total,excited T V NM,ground T V NM,e p,excited T V S,total,ground T V NM,eff,e p,excited T V PD,total,ground T V NM,eff,e p,excited T (c) ground states in the conventional superconductivity or the Peierls distorted states (T < T c,vibronic ) stable electronic states in which electron pairs can be formed are realized by the forming of the energy gap as a consequence of electron phonon interactions V S,e p,ground T V PD,e p,ground T V S,total,ground T V S,ground T V S,e p,ground T V S,ground T V PD,total,ground T V PD,ground T V PD,e p,ground T V PD,ground T F () vibronic

13 (a) conventional superconductivity (b) diamagnetic current states in annulenes and diamonds LUMO 2 F electron pair formed by nature continuous: energy gap between the and LUMO is very small vibronic interactions V NM,e p,excited T T >> 298 K discrete: energy gap between the and LUMO is very large LUMO 2 V NM,e p,excited T () BS F T << 298 K electron pair destroyed by vibronic interactions vibronic interactions electron pair reformed by vibronic interactions V S,e p,ground T V S,e p,ground T Bose Einstein condensation room temperature is very high temperature for the macroscopic sized materials not easily formed easily destroyed electron pair formed by nature room temperature is very low temperature for the microscopic sized materials rigid and not easily destroyed by vibronic interactions

14 BS theory; electron phonon interactions play an essential role in attractive electron electron interactions Our theory; electron phonon interactions do not play an essential role in attractive electron electron interactions but play an essential role in the forming of energy gap by which electron pairs formed by oulomb interactions in the conventional superconductiving states become more stable than those in the normal metallic states at low temperatures

15 tornado-like diamagnetic intramolecular ring supercurrents in one bulk system (T<T c ) hurricane-like perfect diamagnetic conventional superconductivity in one bulk system (T<T c ) H diamagnetic H diamagnetic H diamagnetic H diamagnetic H diamagnetic H diamagnetic H diamagnetic Hdiamagnetic H diamagnetic H applied H diamagnetic H diamagnetic H applied H perfect diamagnetic microscopic sized high temperature superconductivity macroscopic sized low temperature superconductivity macroscopic sized high temperature superconductivity perfect diamonds: room temperature superconductivity???

16 T c (K) sp 3 -type alkanes and diamonds supercurrent transition temperature 1 4 ~ NM NDD T c, LUMO 2 H 6 (2alka) 3 H 8 (3alka) 4 H 1 (4alka) 5 H 12 (5alka) 5 H 12 (5dia) 14 H 24 (14dia) microscopic sizes (intramolecular) macroscopic sizes (bulk) material size N closed shell macroscopic sized perfect diamonds alkanes room temperature macroscopic sized superconductivity??? (T c ~1 5 K >> 298 K)

17 oncluding remarks (Part 2) 1. It has been believed for a long time that electron phonon interactions play an essential role in attractive electron electron interactions. However, according to our recent theoretical studies, electron phonon interactions do not play an essential role in attractive electron electron interactions but play an essential role in the forming of energy gap by which electron pairs formed by oulomb interactions in the conventional superconductiving states become more stable than those in the normal metallic states at low temperatures. 2. Room temperatures are very high temperatures for macroscopic sized materials, on the other hand, room temperatures are very low temperatures for microscopic sized materials. 3. By analogy with the nondissipative diamagnetic currents in the closed-shell electronic structures with large valence conduction band gaps in microscopic sized materials, there is a possibility that perfect diamonds exhibit room temperature macroscopic sized superconductivity.

18 Acknowledgments Prof. Yoshihiro Kubozono (Okayama Univ., Japan) Prof. Takashi Kambe (Okayama Univ., Japan) Prof. Michiya Fujiki (NAIST, Japan) Prof. Tokio Yamabe (NIAS, Japan) Prof. Katsumi Yoshino (NIAS, Japan) Prof. Kazunari Yoshizawa (Kyushu Univ., Japan) Prof. Susumu Sato (NIAS, Japan) Dr. Heinz Barentzen (MPI, Stuttgart, Germany) Prof. Ole Andersen (MPI, Stuttgart, Germany) Prof. Shyamal Bose (Brock Univ., anada) Dr. Ove Jepsen (MPI, Stuttgart, Germany) Dr. Siegmar Roth (MPI, Stuttgart, Germany)

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20 intramolecular diamagnetic currents intraatomic diamagnetic currents 298 K 298 K H applied H diamagnetic H diamagnetic H applied organic molecules polyacenes annulenes atomic systems with closed-shell electronic structures He atoms Ne atoms H 2 electron pair easily formed not easily destroyed electron pair easily formed not easily destroyed

21 (a) negatively charged electronic state an electron injection LUMO (b 1g ) electron doping (a u ) A g B 1g neutral monoanion (b) positively charged electronic state LUMO (b 1g ) hole doping (a u ) A g LUMO (b 1g ) photoinduced h A u an electron removal neutral monocation (c) excited electronic state polyacenes (a u ) A g neutral B 1u excited

22 vibronic interactions and electron phonon interactions A g m Q Ag m 161 cm 1 Q Ag m E electronic states QAg m A g m 1 2 K 2 A g mq Ag m m Q Ag m m b 3u LUMO h A g m b Q 3u LUMO Ag m vibronic coupling constant g b 3u LUMO m 1 h m h Ag m b 3u LUMO b q 3u LUMO Ag m m = 1,2,...,12 q Ag m 2 m / hq A g m h Ag m m Q Ag m

23 vibronic interactions and electron phonon interactions A g m 161 cm 1 Q Ag m vibronic coupling constant g b 3u LUMO m 1 h m h Ag m b 3u LUMO b 3u q LUMO m = 1,2,...,12 Ag m t = t 1 t = t t = t

24 t = t 1 t = t t = t vibronic interactions and electron phonon interactions 1 2 attractive interactions between electrons 1 and 2 electron pairing (Bose particle) is formed stabilization in energy Bose Einstein condensation superconductivity (Bardeen-ooper-Schrieffer (BS) theory)

25 LUMO+2 LUMO+1 LUMO monoanion electron doping LUMO+2 LUMO+1 LUMO ± ± ± LUMO LUMO LUMO t LUMO LUMO LUMO t 2 ± ± ± LUMO LUMO LUMO

26 (a) neutral ground state One electron approximation occupied E electronic state i i E neutral i i U m A g m neutral ground A g neutral E neutral Q i i Q Q Ag m 2 1 Q 2 2 Q 2 1 Q 2 Q occupied g electronic state g i i g neutral g i i 2 g 1 2g 2 2g 1 2g (b) monocation occupied E monocation i i U m A u m monocation A g neutral E monocation Q 2 1 Q 2 2 occupied i i Q Q 2 1 Q Q Q Ag m occupied g monocation g i i 2 g 1 2g 2 2g 1 g

27 A g occupied g electronic state g i i g neutral neutral One electron approximation g i i 2 g 1 2g 2 2g 1 2g neutral ground state U m A g m neutral ground Q A g m (a) negatively charged electronic state an electron injection U m B 1g m monoanion LUMO (b 1g ) electron doping (a u ) Q A g m g monoanion m A g neutral 2g 1 m 2g 2 m B1g monoanion 2g m g LUMO m g LUMO m (b) positively charged electronic state LUMO (b 1g ) hole doping g monoanion m U m g LUMO m A u m monocation (a u ) g monocation m A g neutral 2g 1 m 2 g 1 m 2g 2 m 2g 2 m A u an electron removal monocation g m 2g m g m Q A g m g m g monocation m g m

28 One electron approximation occupied g electronic state g i i neutral ground state U m A g m neutral ground A g neutral g neutral g i i 2 g 1 2g 2 2g 1 2g Q Ag m (c) excited electronic state LUMO (b 1g ) photoinduced h U m B 1u m excited (a u ) A g neutral B1u excited Q Ag m g excited m 2g 1 m 2g 2 m g m g LUMO m 2 g 1 m 2g 2 m 2g m g m g LUMO m g m g LUMO m g excited m g m g LUMO m

29 anthracene LUMO LUMO b 3u b 2g b 3u b 3u A g 1 anthracene D 2h vibronic interactions between A g vibrational mode and b 3u LUMO g b 3u LUMO m 1 b h 3u LUMO h A g m b m q 3u LUMO Ag m m = 1,2,...,12 q A g m 2 m / hq A g m h Ag m m Q Ag m Energy sheet of the LUMO of anthracene A g m Q Ag m D 2h D 2h QAg m A g m 1 2 K 2 A g mq Ag m m Q Ag m m b 3u LUMO h A g m b 3u LUMO Q Ag m

30 Molecular crystals H applied H perfect diamagnetic

31 dimensionless electron phonon coupling constants in molecular crystals molecular crystal formed by the monoanions We assume that the conduction band of the monoanion crystals consists mainly of the LUMOs of each molecule. 1 1 LUMO LUMO 1 1 LUMO LUMO 1 LUMO 1 LUMO 1 LUMO 1 LUMO monoanion l LUMO m m 2 g LUMO monoanion,m monoanion,m nl LUMO m m h m molecular crystal formed by the monocations We assume that the conduction band of the monocation crystals consists mainly of the s of each molecule monocation l m monocation,m m monocation,m nl m 2 g m h m

32 monocation monocation,m monocation,m n l m m molecular crystal formed by the monocations We assume that the conduction bandof the monocation crystals consists mainly of the sof each molecule. +1 electronic state electronic state,m m electronic state,m n l electronic state m +1 l dimensionless electron phonon coupling constants in molecular crystals m 2 g m h m intermolecular intramolecular n : density of states at the Fermi level closely related to the number of electron pairs intermolecular characteristics l electronic state m : electron phonon coupling constant for vibrational mode m 2 l electronic state m g electronic state m h m intramolecular characteristics

33 Superconductive transition temperatures T c s T c ln 1. 2 exp *1.62 ln * : logarithmically averaged phonon frequencies : oulomb pseudopotential n : dimensionless electron phonon coupling constants : density of states at the Fermi level m m n m l e2u LUMO m T c ln 1. 2 exp *1.62 ln 1. 2 exp n n l LUMO m m l LUMO m * 1. 62l LUMO m m m

34 Optimized structures a 1a 3a 1a 1b 3b 1b 1c 2b 1d e 1g benzene naphthalene a u anthracene b 2g tetracene pentacene hexacene

35 A 1g and E 2g vibrational modes of benzene and A g vibrational modes of acenes benzene naphthalene 121 cm cm 1 A 1g 1656 cm cm 1 E 2g 521 cm cm cm 1 A g anthracene tetracene 399 cm cm cm 1 pentacene A g 318 cm cm cm 1 A g hexacene 264 cm cm cm 1 A g 225 cm cm cm 1 A g

36 -1 b 1g LUMO -2 b 1g LUMO -3-4 olumn 2 b 1g LUMO cm 1 A g m m b 1g LUMO h A g m Q Ag m b 1g LUMO D 2h D 2h A g m QAg m 1 2 K 2 A g mq Ag m m Q Ag m Q Ag m g b1g LUMO m 1 h m h Ag m b 1g LUMO q Ag m 2 l b1g LUMO m g b1g LUMO m b 1g LUMO m

37 Electron phonon coupling in naphthalene 2a oupling constant (mev) H 8 b 1g LUMO b 1g LUMO 3a 3b 1a 1b 2b b 1g LUMO 1417 cm 1 b 1g LUMO Frequency (cm 1 ) olumn cm cm

38 Total electron phonon coupling constants.4 Electron phonon coupling constant benzene naphthalene anthracene tetracene pentacene hexacene LUMO l (ev) Number of atoms benzene naphthalene anthracene tetracene.322 ev.254 ev pentacene.186 ev.154 ev hexacene.127 ev.16 ev The total electron phonon coupling constant decreases with an increase in molecular size. The total electron phonon coupling constant becomes smaller with a decrease in the carrier density per carbon atom.

39 Electron phonon interactions in polyacenes and polyphenanthrenes anthracene ( 14 H 1 ) phenanthrene ( 14 H 1 ) tetracene ( 18 H 12 ) chrysene ( 18 H 12 ) pentacene ( 22 H 14 ) picene ( 22 H 14 )

40 Electron phonon coupling constants (l LUMO ( m )) anthracene ( 14 H 1 ) tetracene ( 18 H 12 ) pentacene ( 22 H 14 ) coupling constant (mev) coupling constant (mev) coupling constant (mev) coupling constant (mev) frequency (cm 1 ) 14 phenanthrene ( 14 H 1 ) frequency (cm 1 ) coupling constant (mev) frequency (cm 1 ) frequency (cm 1 ) chrysene ( 18 H 12 ) coupling constant (mev) 14 picene ( 22 H 14 ) frequency (cm 1 ) frequency (cm 1 )

41 .4 Total electron phonon coupling constants l LUMO (ev) of polyacenes and polyphenanthrenes electron phonon coupling constant benzene naphthalene phenanthrene anthracene chrysene tetracene pentacene LUMO l (ev) picene number of carbon atoms.186 ev.154 ev.127 ev The molecular structures as well as the molecular sizes have relevance to the strengths of electron phonon coupling. phenanthrene.3 ev chrysene.194 ev picene.179 ev

42 Electron phonon coupling constants (l LUMO ( m )) coupling constant (mev) anthracene ( 14 H 1 ) coupling constant (mev) phenanthrene ( 14 H 1 ) frequency (cm 1 ) 1a 3a 2a 4a frequency (cm 1 ) b 2b 3b 4b b 3u LUMO a 2 LUMO 399 cm cm cm cm cm cm 1

43 Excited electronic state LUMO (b 1g ) photoinduced U m B 1u m excited h (a u ) A g neutral B1u excited Q Ag m g excited m g m g LUMO m (i) : destabilized LUMO: stabilized (ii) : stabilized LUMO: destabilized (iii) : stabilized LUMO: stabilized (iv) : destabilized LUMO: destabilized LUMO (b 1g ) LUMO (b 1g ) LUMO (b 1g ) LUMO (b 1g ) (a u ) (a u ) (a B B u ) (a u ) 1u B 1u B1u 1u B 1u B B 1u 1u excited excited excited excited B excited 1u excited excited excited g excited m g m g LUMO m g excited m g m g LUMO m

44 Electron phonon coupling constants oupling constant (mev) cm cm 1 LUMO oupling constant (mev) cm cm 1 oupling constant (mev) excited Frequency (cm 1 ) Frequency (cm 1 ) Frequency (cm 1 ) out of phase LUMO LUMO 1417 cm 1 LUMO in phase 1417 cm 1 g excited m g m g LUMO m 163 cm 1

45 Perspective monoanion (electron doping) LUMO l LUMO =.254 ev T c = K for n() = 2 and * =.1.2 monocation (hole doping) LUMO l =.173 ev T c = K for n() = 2 and * =.1.2 theoretically predicted excited (photoinduction) LUMO l -LUMO =.795 ev T c = K for n() = 2 and * =.1.2 excited electronic states: unstable It would be very difficult for the excited electronic states to exhibit superconductivity. Superconductivity: very unstable and appears only at very low temperatures Bardeen-ooper-Schrieffer (BS) theory: can not predict what kind of materials can exhibit superconductivity well. New theory which enables us to predict what kind of materials can exhibit superconductivity very well is awaited.

46 trianion LUMO+2 LUMO+1 LUMO electron doping LUMO+2 LUMO+1 LUMO LUMO+1 LUMO+1 LUMO+1 LUMO LUMO LUMO t LUMO+1 LUMO+1 LUMO+1 LUMO LUMO LUMO t LUMO+1 LUMO+1 LUMO+1 LUMO LUMO LUMO

47 Optimized structures of the dianions of polyphenanthrenes a 2 LUMO b g LUMO a 2 LUMO

48 Electron phonon coupling constants in the trianions of polyphenanthrenes ph 3 18ph 3 22ph coupling constant (ev b 1 LUMO+1 b g LUMO+1 b 1 LUMO ) coupling constant (ev ) coupling constant (ev ) frequency (cm 1 ) frequency (cm 1 ) frequency (cm 1 ) 1241 cm cm cm cm cm cm cm cm cm 1

49 Total electron phonon coupling constants in the trianions of polyphenanthrenes total electron phonon coupling constant (ev).4 phenanthrene.3 chrysene.2 picene number of carbon atoms Total electron phonon coupling constants on the basis of the one-electron approximation; phenanthrene trianion:.336 ev chrysene trianion:.275 ev picene trianion:.26 ev Total electron phonon coupling constants originating from the higher-order as well as the first-order electron phonon interactions; phenanthrene trianion:.372 ev chrysene trianion:.29 ev picene trianion:.225 ev

50 Superconductive transition temperatures T c s T c ln 1. 2 exp * 1.62 ln 1.2 exp 1.4 1N F l LUMO+1 N F l LUMO+1 * 1.62N F l LUMO+1 N F ; density of states at the Fermi level (states ev 1 per picene per spin) l ev, ln,lumo+1 11 cm 1 2 K; N F 1.362, *.1; N F 1.628, *.15; N F 1.92, * K; N F , *.1; N F , *.15; N F , *.2 8 K; N F 1.18, *.1; N F , *.15; N F 1.64, * K; N F 1. 83, *.1; N F , *.15; N F , * K; N F 1.77, *.1; N F , *.15; N F , *.2

51 Superconductive transition temperatures T c s T c ln 1. 2 exp * 1.62 ln 1.2 exp 1.4 1N F l LUMO+1 N F l LUMO+1 * 1.62N F l LUMO K; N F 2.3, * K; N F 2.75, * K; N F 3.25, *.2 2.3, * K; N F K; N F 2.75, * K; N F 3.25, *.2

52 H F substitutions H H F F H H F F H H H F substitutions F F oupling constant (mev) H H b 1g LUMO Frequency (cm 1 ) oupling constant (mev) F F b 1g LUMO Frequency (cm 1 )

53 oupling constant (mev) Frequency (cm 1 ) 25 1 H 8 1 F 8 oupling constant (mev) Frequency (cm 1 ) b 1g LUMO 1417 cm 1 b 1g LUMO 142 cm F 6 1 F 8 stretching modes 1 H 8 ; displacements of H atoms large Total coupling constant (ev) H 6 1 H 8 14 F 1 18 F F14 14 H 1 18 H H 14 1 F 8 ; displacements of atoms large The LUMO is localized on carbon atoms both in 1 H 8 and 1 F Number of carbon atoms

54 oupling constant (mev) Frequency (cm 1 ) oupling constant (mev) 25 1 H 8 1 F Frequency (cm 1 ) b 1g LUMO Logarithmically averaged phonon frequency 1417 cm H H 8 6 F H 1 F F 118 F H 22 F H Molecular weight M w ln(cm 1 b 1g LUMO ) 142 cm 1

55 Superconductive transition temperatures T c s T c ln 1. 2 exp * 1.62 ln 1. 2 exp 1.4 1N F l LUMO+1 N F l LUMO+1 * 1.62N F l LUMO+1 the normal isotope effect; the T c value decreases because the ln value becomes smaller by heavier atoms substitutions. Electron phonon interactions become much larger if the atoms in a frontier orbital, the electron density of which is very low, are substituted by heavier atoms and the phase patterns of the frontier orbital are not significantly changed. H H H H H F substitution F F F F H H H H F F F F H H H H H H F F F F F F l LUMO+1 =.225 ev T c = 2 K l LUMO+1 =.435 ev T c = 15 K

56 oncluding remarks (Part 1) 1. The total electron phonon coupling constant becomes smaller with an increase in molecular size in both polyacenes and polyphenanthrenes becuase the carrier density per carbon atom becomes lower with an increase in molecular size. 2. The total electron phonon coupling constants for polyphenanthrenes are larger than those for polyacenes. Therefore, the molecular structures as well as the molecular sizes are closely related to the strengths of the electron phonon interactions. 3. Electron phonon interactions become much larger if the atoms in a frontier orbital, the electron density of which is very low, are substituted by heavier atoms and the phase patterns of the frontier orbital are not significantly changed.