Supporting information on Singlet Diradical Character from Experiment Kenji Kamada,,* Koji Ohta, Akihiro Shimizu, Takashi Kubo,,* Ryohei Kishi, Hideaki Takahashi, Edith Botek, Benoît Champagne,,* and Masayoshi Nakano,* Photonics Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Ikeda, Osaka 563-8577, Japan Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan Laboratoire de Chimie Théorique (LCT), Facultés Universitaires Notre-Dame de la Paix (FUNDP), Rue de Bruxelles, 61, B-5000 Namur (Belgium) * Corresponding authors. E-mail for M.N.: mnaka@cheng.es.osaka-u.ac.jp 1
Contents 1. Derivation of Eq. (1) and electronic states (Figure 1S) as well as its illustration in the case of a twosite model like the stretched H 2 molecule. 2. Calculation formula of diradical character from the occupation numbers of spin-unrestricted Hartree- Fock natural orbitals (UNOs) using the 6-31G** basis set 3. Molecular structure (Figure 2S) and cartesian coordinates (Table 1S) of 1 optimized at the UB3LYP/6-31G** level of approximation and the occupation numbers of frontier UNOs/6-31G** 4. Molecular structure (Figure 3S) and cartesian coordinates (Table 2S) of 2 optimized at the UB3LYP/6-31G** level of approximation and the occupation numbers of frontier UNOs/6-31G** 5. Molecular structure (Figure 4S) and cartesian coordinates (Table 3S) of anthracene optimized at the RB3LYP/6-31G** level of approximation and the occupation numbers of frontier UNOs/6-31G** 6. Molecular structure (Figure 5S) and cartesian coordinates (Table 4S) of naphthalene optimized at the RB3LYP/6-31G** level of approximation and the occupation numbers of frontier UNOs/6-31G** 7. Molecular structure (Figure 6S) and cartesian coordinates (Table 5S) of chrysene optimized at the RB3LYP/6-31G** level of approximation and the occupation numbers of frontier UNOs/6-31G** 8. Molecular structure (Figure 7S) and cartesian coordinates (Table 6S) of fluorene optimized at the RB3LYP/6-31G** level of approximation and the occupation numbers of frontier UNOs/6-31G** 9. Molecular structure (Figure 8S) and cartesian coordinates (Table 7S) of TIPS-pentacene using the geometry, isopropyl groups of which are replaced by H atoms, derived from the crystal structure (Ref. 31) and the occupation numbers of frontier UNOs/6-31G**. 10. All the calculations in 3-9 are carried out by Gaussian 03. The reference is given. 2
1. Derivation of Eq. (1). We briefly provide the derivation of Eq. (1) according to Refs. [21] and [24], which employs a twosite model A B with two electrons in two orbitals as the simplest example of symmetric diradical molecules. The magnetic orbitals can be either symmetry-adapted, g and u, or localized natural orbitals (LNO), a and b, which are related through a(x) 1 2 [ g(x)+ u(x) ], and b(x) 1 [ g(x) u(x) ]. (s1.1) 2 For M S = 0 (singlet and triplet), using LNOs there are two neutral, ab and b a, and two ionic, aa and bb, determinants, where the upper-bar (non-bar) indicates the β (α) spin. The configuration interaction (CI) matrix in the LNO representation { ab, ba, aa, bb } takes the form 0 K ab t ab t ab K ab 0 t ab t ab, (s1.2) t ab t ab U K ab t ab t ab K ab U where the energy of the neutral valence bond (VB) determinants is taken as the energy origin. The U( U aa U ab ) indicates the difference between on-site and inter-site Coulomb integrals, K ab ( ab 1 r 12 ba 0) is a direct exchange integral, and t ab ( a F b ) is a transfer integral, where F is the Fock operator. The diagonalization of this matrix gives the four electronic states: (I) an essentially neutral lowest-energy singlet state of g symmetry S 1g = κ( ab + ba )+ η( aa + bb ) (κ > η > 0), (s1.3) with energy 1 E 1g = K ab + U U 2 2 +16t ab 2, (s1.4) (II) an ionic singlet state with u symmetry S 1u = ( aa bb ) 2 (s1.5) with energy 1 E 1u =U K ab, (s1.6) (III) an essentially ionic higher-energy singlet state of g symmetry S 2g = η( ab + ba )+κ( aa + bb ) (κ > η > 0) (s1.7) with energy 1 E 2g = K ab + U + U 2 2 +16t ab 2, (s1.8) 3
and (IV) a neutral triplet state with u symmetry with energy T 1u ( = ( ab ba ) 2) (s1.9) 3 E 1u = K ab. (s1.10) Here, and κ = 1 2 1+ U U 2 2 +16t ab, (s1.11) η = 2 t ab U + U 2 2 ( +16t ab ) U 2 2 +16t ab. (s1.12) On the other hand, the singlet ground state is also described using the symmetry-adapted MOs, g and u, [see Eq. (s1.1)]: S 1g = ξ gg ζ uu, (s1.13) where we get the following relation from Eqs. (s1.3), (s1.11), (s1.12) and (s1.13): ξ = κ +η = 1 2 1+ U U 2 2 +16t ab + 4 t ab U + U 2 2 ( +16t ab ) U 2 2 +16t ab (s1.14) and ζ = κ η = 1 2 1+ U U 2 2 +16t ab 4 t ab U + U 2 2 ( +16t ab ) U 2 2 +16t ab. (s1.15) Since the diradical character (y) is defined as the twice the weight of double excitation configuration in the ground state (s1.13), y 2ζ 2 =1 4 t ab U 2 2 +16t ab. (s1.16) From Eqs. (s1.4), (s1.6), (s1.8) and (s1.10), we obtain the relations between parameters and observables: t ab = 1 4 ( 1 E 2g 1 E 1g ) 2 ( 1 E 1u 3 E 1u ) 2, (s1.17) 4
and U= 1 E 1u 3 E 1u. (s1.18) Substituting (s1.17) and (s1.18) into (s1.16), we obtain 1 E 1u 3 E 1u y =1 1 1 E 2g 1 E 1g 2 =1 1 E 2 S 1u,S 1g E T1u,S 1g, (s1.19) E S2g,S 1g where E S1u,S 1g, E S2g,S 1g and E T1u,S 1g represent the excitation energies of higher singlet state with g symmetry (two-photon allowed excited state), of lower singlet state with u symmetry (one-photon allowed excited state), and of triplet state with u symmetry, respectively (see Figure S1). S 2g ( 1 E 2g ) S 1u ( 1 E 1u ) E S 2g, S 1g E S1u, S 1g T 1u ( 3 E 1u ) E T1u, S 1g S 1g ( 1 E 1g ) Figure 1S. Four electronic states for a symmetric two-site model with two electrons in two orbitals. We now consider the right-hand side of Eq. (s1.19) for the H 2 molecule (this is also valid for any two-site model). From Fig. 1S and Eq. (s1.18), in the case of small U (corresponding to the H 2 model near its equilibrium geometry), 1 E 1u approaches 3 E 1u, i.e., the parentheses inside the square root become small (<< 1), which leads to y 0. On the contrary, in case of large U (U >> t ab ) (corresponding to a stretched H 2 model), from Eqs. (s1.4), (s1.6), (s1.8) and (s1.10), the relations become: 1 E 2g U + K ab, 1 E 1u U K ab, 1 E 1g K ab and 3 E 1u = K ab, so that we get the relation: 1 E 2g 1 E 1g 1 E 1u 3 E 1u, leading to y 1. More details on the H 2 dissociation model are available in the following reference: Nakano, M.; Kishi, R.; Ohta, S.; Takebe, A.; Takahashi, H.; Furukawa, S.; Kubo, T.; Morita, Y.; Nakasuji, K.; Yamaguchi, K. et al. Origin of the Enhancement of the Second Hyperpolarizability of Singlet Diradical Systems with Intermediate Diradical Character, J. Chem. Phys. 2006, 125, 074113-1-9 5
2. Calculation formula of diradical character from the occupation numbers of spin-unrestricted Hartree-Fock natural orbitals (UNOs) using the 6-31G** basis set The diradical character y i related to HOMO-i and LUMO+i is defined by the weight of the doublyexcited configuration in the multi-configurational (MC)-SCF theory and is formally expressed in the spinprojected UHF (PUHF) theory as [23] y i =1 2T i 1+T i 2, (s2.1) where T i is the orbital overlap between the corresponding orbital pairs [23] ( χ HOMO i and η HOMO i ) and can also be represented using the occupation numbers ( n i ) of UHF natural orbitals (UNOs): T i = n HOMO i n LUMO+i 2, (s2.2) The diradical character y i obtained from the UNO occupation numbers takes a value between 0 and 1, which correspond to the closed-shell and pure diradical systems, respectively. The present calculation scheme using the UNOs is the simplest but it can well reproduce the diradical character calculated by other methods such as the ab initio configuration interaction (CI) method [S1]. It is noted that the present formula employs the UHF NOs and not the UDFT NOs, which would lead to incorrect lower diradical character in the present formula. Reference (S1) D. Herebian, K. E. Wieghardt, F. Neese, J. Am. Chem. Soc. 2003, 125, 10997. 6
3. Molecular structure and cartesian coordinates of 1 Top view Figure 2S. Molecular structure of 1 7
Table 1S: Cartesian coordinates [Å] of 1 optimized at the UB3LYP/6-31G** level of approximation and the occupation numbers of frontier UNOs/6-31G** Atom x y z C1 1.435622 0.000002 0.000000 C2-1.435622-0.000002 0.000000 C3 0.722425 0.000005 1.199863 C4 0.722425-0.000003-1.199864 C5-0.722425 0.000003 1.199863 C6-0.722425-0.000005-1.199864 C7 0.000000 0.000016 4.769413 C8 1.275419 0.000020 5.438931 C9-1.275419 0.000018 5.438931 C10 1.219637 0.000028 6.851277 C11-1.219636 0.000025 6.851277 C12 0.000000 0.000030 7.523277 C13 2.499809 0.000018 4.635546 C14-2.499809 0.000013 4.635546 C15 2.405192 0.000014 3.240630 C16-2.405192 0.000008 3.240630 C17 0.000000 0.000011 3.377615 C18 1.165455 0.000010 2.585729 C19-1.165455 0.000007 2.585729 C20 0.000000-0.000016-4.769413 C21-1.275419-0.000022-5.438931 C22 1.275419-0.000016-5.438931 C23-1.219636-0.000028-6.851276 C24 1.219636-0.000026-6.851276 C25 0.000000-0.000031-7.523276 C26-2.499809-0.000020-4.635546 C27 2.499809-0.000010-4.635546 C28-2.405192-0.000014-3.240630 C29 2.405192-0.000007-3.240630 C30 0.000000-0.000011-3.377615 C31-1.165454-0.000010-2.585729 C32 1.165454-0.000007-2.585729 H33 2.120644 0.000034 7.445796 H34-2.120644 0.000027 7.445796 C35 3.907783 0.000021 5.284756 C36-3.907783 0.000014 5.284756 H37 3.307333 0.000013 2.643460 H38-3.307333 0.000005 2.643460 H39-2.120644-0.000032-7.445796 H40 2.120644-0.000029-7.445796 C41-3.907783-0.000026-5.284756 C42 3.907783-0.000008-5.284756 H43-3.307332-0.000014-2.643459 H44 3.307332-0.000004-2.643459 H45 0.000000 0.000036 8.609488 H46 0.000000-0.000037-8.609488 H47 2.523124 0.000003 0.000000 H48-2.523124-0.000003 0.000000 C49 5.041484 0.000171 4.233041 C50 4.124403-1.282139 6.131788 C51 4.124287 1.282043 6.132027 C52-5.041484 0.000036 4.233041 C53-4.124336 1.282095 6.131924 8
C54-4.124354-1.282087 6.131890 C55-5.041484 0.000009-4.233041 C56-4.124354-1.282137-6.131875 C57-4.124335 1.282045-6.131940 C58 5.041484-0.000254-4.233041 C59 4.124437 1.282201-6.131706 C60 4.124253-1.281981-6.132109 H61 6.005475 0.000159 4.751294 H62 5.014930 0.888593 3.594456 H63 5.015002-0.888130 3.594282 H64 5.126224-1.269909 6.575437 H65 4.050232-2.170165 5.495624 H66 3.403888-1.403106 6.940441 H67 5.126107 1.269820 6.575676 H68 3.403758 1.402794 6.940701 H69 4.050037 2.170181 5.496028 H70-6.005475 0.000034 4.751294 H71-5.014971-0.888317 3.594357 H72-5.014961 0.888406 3.594382 H73-5.126157 1.269870 6.575574 H74-4.050120 2.170185 5.495855 H75-3.403813 1.402939 6.940590 H76-5.126174-1.269860 6.575540 H77-3.403833-1.402961 6.940553 H78-4.050149-2.170161 5.495797 H79-6.005475 0.000001-4.751295 H80-5.014961 0.888387-3.594393 H81-5.014972-0.888336-3.594346 H82-5.126175-1.269915-6.575524 H83-4.050150-2.170204-5.495771 H84-3.403834-1.403022-6.940536 H85-5.126155 1.269815-6.575589 H86-3.403811 1.402878-6.940606 H87-4.050118 2.170143-5.495881 H88 6.005475-0.000230-4.751295 H89 5.014910-0.888719-3.594516 H90 5.015023 0.888004-3.594223 H91 5.126257 1.269974-6.575355 H92 4.050287 2.170188-5.495485 H93 3.403925 1.403238-6.940352 H94 5.126073-1.269756-6.575759 H95 3.403720-1.402662-6.940790 H96 4.049981-2.170158-5.496167 Occupation numbers of UNOs/6-31G** n HOMO = 1.12056 n LUMO = 0.87944 9
4. Molecular structure and cartesian coordinates of 2 Top view Side view Figure 3S. Molecular structure of 2 10
Table 2S: Cartesian coordinates [Å] of 2 optimized at the UB3LYP/6-31G** level of approximation and the occupation numbers of frontier UNOs/6-31G** Atom x y z C1 0.735396 0.000109-0.006421 C2-0.735410 0.000157 0.006417 C3 1.447889-0.000169 1.250195 C4-1.425854 0.000412 1.274213 C5 1.425841 0.000354-1.274219 C6-1.447902-0.000130-1.250196 C7 0.745195-0.000094 2.446400 C8-0.702181 0.000299 2.459080 C9 0.702169 0.000272-2.459084 C10-0.745207-0.000085-2.446403 C11 0.053001 0.000023 6.032703 C12 1.297396-0.000422 6.713032 C13-1.181958 0.000418 6.734401 C14 1.279668-0.000459 8.128175 C15-1.133660 0.000360 8.142431 C16 0.082850-0.000058 8.856836 C17 2.480304-0.000810 5.912831 C18-2.379571 0.000840 5.952432 C19 2.449993-0.000759 4.520543 C20-2.371592 0.000867 4.561029 C21 0.040993 0.000059 4.635089 C22 1.211963-0.000318 3.841131 C23-1.144243 0.000467 3.860242 C24-0.053007-0.000002-6.032706 C25-1.297400-0.000360-6.713038 C26 1.181953 0.000311-6.734401 C27-1.279670-0.000404-8.128181 C28 1.133658 0.000253-8.142432 C29-0.082850-0.000105-8.856839 C30-2.480309-0.000653-5.912840 C31 2.379565 0.000655-5.952430 C32-2.450001-0.000606-4.520552 C33 2.371583 0.000690-4.561027 C34-0.041002 0.000039-4.635092 C35-1.211974-0.000265-3.841136 C36 1.144232 0.000384-3.860245 H37 2.237129-0.000839 8.634765 H38-2.074904 0.000648 8.683640 H39 3.444567-0.001159 6.414903 H40-3.335178 0.001151 6.470661 H41 3.388731-0.001068 3.984447 H42-3.319013 0.001196 4.040453 H43-2.237129-0.000684-8.634773 H44 2.074904 0.000491-8.683638 H45-3.444572-0.000926-6.414914 H46 3.335173 0.000897-6.470656 H47-3.388741-0.000840-3.984460 H48 3.319002 0.000956-4.040448 C49 0.012661-0.000134 10.405977 C50-0.012657-0.000149-10.405980 C51 2.940305-0.000814 1.415403 C52-2.915127 0.001047 1.465827 C53 2.915114 0.000930-1.465833 11
C54-2.940318-0.000761-1.415399 C55 1.397009-0.000211 11.125290 C56-0.762939 1.260076 10.866389 C57-0.763003-1.260365 10.866221 C58-1.397004-0.000596-11.125297 C59 0.762598 1.260283-10.866360 C60 0.763353-1.260158-10.866252 C61 3.634136 1.203556 1.593216 C62 4.989250 1.204521 1.923322 C63 3.632974-1.205830 1.593374 C64 4.988082-1.208071 1.923498 C65 5.670917-0.002094 2.092403 C66-3.605592-1.203340 1.656049 C67-4.954395-1.204341 2.011013 C68-3.604396 1.206056 1.656464 C69-4.953191 1.208288 2.011448 C70-5.632815 0.002280 2.192821 C71 3.605488-1.203451-1.656429 C72 4.954305-1.204444-2.011336 C73 3.604489 1.205946-1.656041 C74 4.953305 1.208186-2.010946 C75 5.632835 0.002182-2.192700 C76-3.634096 1.203576-1.593627 C77-4.989195 1.204487-1.923797 C78-3.633028-1.205808-1.593005 C79-4.988125-1.208104-1.923173 C80-5.670906-0.002156-2.092499 H81 2.254156 0.000897 10.453183 H82 1.503847 0.878886 11.767357 H83 1.504703-0.880489 11.765596 H84-0.237683 2.171473 10.562664 H85-1.772059 1.301025 10.446889 H86-0.855118 1.269051 11.958204 H87-0.237834-2.171747 10.562301 H88-0.855116-1.269527 11.958040 H89-1.772151-1.301157 10.446770 H90-2.254153-0.000754-10.453191 H91-1.504504 0.878995-11.766577 H92-1.504032-0.880380-11.766391 H93 0.237106 2.171529-10.562588 H94 1.771715 1.301479-10.446875 H95 0.854754 1.269327-11.958177 H96 0.238419-2.171692-10.562381 H97 0.855494-1.269252-11.958069 H98 1.772504-1.300702-10.446783 H99 3.102247 2.143908 1.483239 H100 5.510149 2.148288 2.057511 H101 3.100168-2.145681 1.483542 H102 5.508061-2.152324 2.057830 H103 6.724637-0.002584 2.355841 H104-3.075743-2.143628 1.536151 H105-5.472763-2.148110 2.154665 H106-3.073601 2.145856 1.536912 H107-5.470611 2.152524 2.155445 H108-6.681495 0.002752 2.475637 H109 3.075560-2.143736-1.536856 H110 5.472602-2.148207-2.155280 H111 3.073771 2.145751-1.536180 H112 5.470813 2.152428-2.154591 H113 6.681529 0.002662-2.475462 12
H114-3.102172 2.143943-1.483953 H115-5.510050 2.148230-2.058322 H116-3.100259-2.145643-1.482862 H117-5.508136-2.152381-2.057217 H118-6.724615-0.002690-2.355981 * Maximum displacement in the optimization procedure is 0.004430 au, which is slightly over the standard threshold in Gaussian03 (0.00180 au), although other convergence criteria in optimization procedure are all satisfied. Using several nearly optimized geometries, such slight changes in geometries are found to cause negligible changes (less than 0.01) in the diradical character. Occupation numbers of UNOs/6-31G** n HOMO = 1.07092 n LUMO = 0.92908 13
5. Molecular structure and cartesian coordinates of anthracene Figure 4S. Molecular structure of anthracene 14
Table 3S: Cartesian coordinates [Å] of anthracene optimized at the RB3LYP/6-31G** level of approximation and the occupation numbers of frontier UNOs/6-31G** Atom x y z C1 1.403700 0.000000 0.000000 C2-1.403700 0.000000 0.000000 C3 0.722569 0.000000 1.223575 C4 0.722569 0.000000-1.223575 C5-0.722569 0.000000 1.223575 C6-0.722569 0.000000-1.223575 C7 1.406936 0.000000 2.479065 C8 1.406936 0.000000-2.479065 C9-1.406936 0.000000 2.479065 C10-1.406936 0.000000-2.479065 C11 0.712975 0.000000 3.659837 C12 0.712975 0.000000-3.659837 C13-0.712975 0.000000 3.659837 C14-0.712975 0.000000-3.659837 H15 2.491400 0.000000 0.000000 H16-2.491400 0.000000 0.000000 H17 2.493833 0.000000 2.476755 H18 2.493833 0.000000-2.476755 H19-2.493833 0.000000 2.476755 H20-2.493833 0.000000-2.476755 H21 1.246213 0.000000 4.605909 H22 1.246213 0.000000-4.605909 H23-1.246213 0.000000 4.605909 H24-1.246213 0.000000-4.605909 Occupation numbers of UNOs/6-31G** n HOMO = 1.55841 n LUMO = 0.44159 15
6. Molecular structure and cartesian coordinates of naphthalene Figure 5S. Molecular structure of naphthalene 16
Table 4S: Cartesian coordinates [Å] of naphthalene optimized at the RB3LYP/6-31G** level of approximation and the occupation numbers of frontier UNOs/6-31G** Atom x y z C1 0.716900 0.000000 0.000000 C2-0.716900 0.000000 0.000000 C3 1.402435 0.000000 1.244702 C4 1.402435 0.000000-1.244702 C5-1.402435 0.000000 1.244702 C6-1.402435 0.000000-1.244702 C7 0.708302 0.000000 2.433139 C8 0.708302 0.000000-2.433139 C9-0.708302 0.000000 2.433139 C10-0.708302 0.000000-2.433139 H11 2.489431 0.000000 1.242107 H12 2.489431 0.000000-1.242107 H13-2.489431 0.000000 1.242107 H14-2.489431 0.000000-1.242107 H15 1.245153 0.000000 3.377281 H16 1.245153 0.000000-3.377281 H17-1.245153 0.000000 3.377281 H18-1.245153 0.000000-3.377281 Occupation numbers of UNOs/6-31G** n HOMO = 1.72350 n LUMO = 0.27650 17
7. Molecular structure and cartesian coordinates of chrysene Figure 6S. Molecular structure of chrysene 18
Table 5S: Cartesian coordinates [Å] of chrysene optimized at the RB3LYP/6-31G** level of approximation and the occupation numbers of frontier UNOs/6-31G** Atom x y z C1-0.361380 0.000000 0.609988 C2 0.361380 0.000000-0.609988 C3 0.352700 0.000000 1.875298 C4-0.352700 0.000000-1.875298 C5 1.791649 0.000000-0.561237 C6-1.791649 0.000000 0.561237 C7 2.469645 0.000000 0.621864 C8-2.469645 0.000000-0.621864 C9 1.780417 0.000000 1.870924 C10-1.780417 0.000000-1.870924 C11-0.299630 0.000000 3.134566 C12 0.299630 0.000000-3.134566 C13 2.490098 0.000000 3.096360 C14-2.490098 0.000000-3.096360 C15 1.823440 0.000000 4.302709 C16-1.823440 0.000000-4.302709 C17 0.414138 0.000000 4.316808 C18-0.414138 0.000000-4.316808 H19 2.358872 0.000000-1.484048 H20-2.358872 0.000000 1.484048 H21 3.556426 0.000000 0.628311 H22-3.556426 0.000000-0.628311 H23-1.381913 0.000000 3.185916 H24 1.381913 0.000000-3.185916 H25 3.576594 0.000000 3.066730 H26-3.576594 0.000000-3.066730 H27 2.377399 0.000000 5.236684 H28-2.377399 0.000000-5.236684 H29-0.116568 0.000000 5.264303 H30 0.116568 0.000000-5.264303 Occupation numbers of UNOs/6-31G** n HOMO = 1.65435 n LUMO = 0.34565 19
8. Molecular structure and cartesian coordinates of fluorene Figure 7S. Molecular structure of fluorene 20
Table 6S: Cartesian coordinates [Å] of fluorene optimized at the RB3LYP/6-31G** level of approximation and the occupation numbers of frontier UNOs/6-31G** Atom x y z C1 0.000000 0.000000 0.000000 C2-0.945373 0.000000 1.184359 C3-0.945373 0.000000-1.184359 C4-0.659199 0.000000 2.544683 C5-0.659199 0.000000-2.544683 C6-2.282514 0.000000 0.734772 C7-2.282514 0.000000-0.734772 C8-1.716539 0.000000 3.461239 C9-1.716539 0.000000-3.461239 C10-3.336300 0.000000 1.651454 C11-3.336300 0.000000-1.651454 C12-3.042938 0.000000 3.016486 C13-3.042938 0.000000-3.016486 H14 0.369303 0.000000 2.896469 H15 0.369303 0.000000-2.896469 H16-1.506031 0.000000 4.526743 H17-1.506031 0.000000-4.526743 H18-4.368658 0.000000 1.312749 H19-4.368658 0.000000-1.312749 H20-3.852461 0.000000 3.740711 H21-3.852461 0.000000-3.740711 H22 0.658380 0.879089 0.000000 H23 0.658380-0.879089 0.000000 Occupation numbers of UNOs/6-31G** n HOMO = 1.76837 n LUMO = 0.23163 21
9. Molecular structure and cartesian coordinates of TIPS-pentacene Figure 8S. Molecular structure of TIPS-pentacene 22
Table 7S: Cartesian coordinates [Å] of TIPS-pentacene using the geometry, isopropyl groups of which are replaced by H atoms, derived from the crystal structure (Ref. 31) and the occupation numbers of frontier UNOs/6-31G** Atom x y z Si1 3.574600 5.421800 5.324400 C2 4.455600 7.215300 1.319800 C3 3.469800 8.046200 0.736400 C4 2.294400 8.401400 1.419600 C5 1.307000 9.183000 0.847800 C6 0.109600 9.536600 1.542300 C7-0.840400 10.293600 0.952400 C8-0.673300 10.748200-0.383100 C9 0.437100 10.443100-1.081900 C10 1.477600 9.647000-0.505000 C11 2.636400 9.322500-1.186400 C12 3.651200 8.530200-0.615300 C13 4.231100 6.683800 2.634700 C14 4.002900 6.203400 3.716600 Si15 5.710200 9.982500-5.324400 C16 4.829100 8.189000-1.319800 C17 5.814900 7.358100-0.736400 C18 6.990300 7.002900-1.419600 C19 7.977700 6.221300-0.847800 C20 9.175100 5.867700-1.542300 C21 10.125100 5.110700-0.952400 C22 9.958000 4.656100 0.383100 C23 8.847600 4.961200 1.081900 C24 7.807100 5.757400 0.505000 C25 6.648300 6.081800 1.186400 C26 5.633500 6.874100 0.615300 C27 5.053600 8.720500-2.634700 C28 5.281800 9.200900-3.716600 H29 3.782412 3.969329 5.234714 H30 2.166493 5.697206 5.644224 H31 4.431231 5.975623 6.382872 H32 2.172900 8.092700 2.308900 H33-0.021400 9.234000 2.434200 H34-1.625400 10.524800 1.434800 H35-1.353200 11.273500-0.788300 H36 0.530700 10.761100-1.972400 H37 2.751800 9.645100-2.073000 H38 5.502403 11.434974-5.234729 H39 4.853617 9.428686-6.382916 H40 7.118320 9.707075-5.644150 H41 7.111800 7.311600-2.308900 H42 9.306100 6.170300-2.434200 H43 10.910100 4.879500-1.434800 H44 10.637900 4.130800 0.788300 H45 8.754000 4.643200 1.972400 H46 6.532900 5.759200 2.073000 Occupation numbers of UNOs/6-31G** 23
n HOMO = 1.30218 n LUMO = 0.69782 24
10. Full reference of Gaussian 03 program package. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, Gaussian 03, Revision C.02, Gaussian, Inc., Wallingford CT, 2004. 25