Open-Shell Character Dependences of Second Hyperpolarizability in

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Open-Shell Character Dependences of Second Hyperpolarizability in Two-Dimensional Tetraradicaloids Hiroshi Matsui, Soichi Ito, and Masayoshi Nakano J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b12456 • Publication Date (Web): 21 Mar 2018 Downloaded from http://pubs.acs.org on March 22, 2018

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The Journal of Physical Chemistry

Open-Shell Character Dependences of Second Hyperpolarizability in Two-Dimensional Tetraradicaloids Hiroshi Matsui†, Soichi Ito§,¶, Masayoshi Nakano*,†, ‡ †

Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan. §

Institute for Molecular Science and Research Center for Computational Science, 38 NishigoNaka, Myodaiji, Okazaki 444-8585, Japan ¶

Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto University Katsura, Kyoto, Kyoto 615-8520, Japan

‡

Center for Spintronics Research Network (CSRN), Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan

ACS Paragon Plus Environment

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT

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The open-shell character dependences of second hyperpolarizability γ is

investigated for rectangular-shaped tetraradicaloid models such as diradical dimers, using numerically exact solutions of the extended Hubbard model. The newly-defined local diradical characters for intra- and inter-molecular interactions (referred to as yintra and yinter, respectively) are compared to conventional global ones (y0 and y1) and provide comprehensive understanding of the electronic structure of the system. The system shows two kinds of enhancements of γ components, γintra and γinter (caused, respectively, by intra- and inter-molecular diradical interactions): (i) the system with large yintra (yinter) (> ~0.4) exhibits enhancement of a single component of γ, γinter (γintra), at the intermediate yinter (yintra) region (~ 0.3 – 0.4), and (ii) in contrast to conventional diradical systems, the system exhibits further enhancement of both components of γ (γintra and γinter) at the region where yintra ~ yinter with small values (≤ ~0.3). The obtained relationships are verified by using ab initio quantum chemical calculations of realistic tertraradical models, 4,4’-bis(1,2,3,5-dithiazdiazolyl) (BDTDA) dimer and disilene dimer. The present results are expected to pioneer an alternative class of two-dimensional multiradical NLO systems, which potentially cause further enhancement of γ as compared to conventional intermediate diradical NLO systems.

1. INTRODUCTION For the last several decades, the third-order nonlinear optical (NLO) properties – the second hyperpolarizabilities γ at the molecular level – of organic compounds have been theoretically and experimentally studied with great interest due to their versatile future applications in photonics and optoelectronics.1–6 To enhance and control γ for these future applications, several molecular


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design principles have been proposed, for example, extension of π-conjugation,7–10 appropriate electron donor and/or acceptor substitution,11–13 tuning charge state,14–16 and using chrage transfer Mott insulators.17 Regardless of these previous investigations of a novel class of NLO systems, there still remains a large gap between γ of conventional systems and its theoretical upper limit,18,19 which implies that further explorations are necessary for comprehending the structure – NLO property relationships. In the meanwhile, we have proposed an alternative design principle for efficient NLO open-shell molecular systems20–25 based on diradical character y (0 ≤ y ≤ 1),26,27 which represents the instability of effective chemical bond: the system with intermediate y exhibits a significantly larger γ than closed-shell (y = 0) and pure open-shell systems (y = 1) of similar size.20–22 On the basis of this design principle, it has been theoretically and experimentally found that a variety of open-shell singlet compounds with intermediate y exhibit significantly large γ values and third-order NLO properties.22–25 Furthermore, as an extension of this principle, open-shell singlet multiradical systems with one-dimensional antiferromagnetic interaction have been theoretically investigated,28–30 but detailed structure– property relationships and design principles for such multiradical systems have not been revealed in spite of their promising potential for exhibiting further enhancement and controllability of γ. Indeed, revealing the structure–property relationships for two-dimensional multiradical systems has faced the following difficulties in calculation and analysis of their electronic states though there are a lot of real prospective candidates such as molecular aggregates composed of diradical monomers31–37 and tetraradical fused-ring molecular systems.38 First, multiconfiguration nature of multiradical systems causes difficulty of describing their electronic structures even qualitatively. Second, the fact that y is a global index defined for the whole system causes difficulty in clarifying the contribution of local open-shell character in such two-dimensional


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multiradical systems. In previously studied one-dimensional one-dimensional multiradicaloid systems, such as multimers composed of monoradical monomers like phenalenyl radcial 29,39 and cyclic thiazyl radical

40

c’d’]diphenalene (IDPL),

and of slip-stacked diradicaloids like s-indaceno[1,2,3-cd;5,6,734,41

only one longitudinal component of γ is found to enhance

depending on the open-shell character. In two-dimensional multiradical systems, in contrast, direction of bonding interaction is expected to have much effect on γ because the enhanced component of γ tends to be along the bond-breaking direction. 21, revealing relationships between global/local open-shell character and γ in multiradical systems are challenging and important themes in both NLO material design and computational chemistry. In this study, we investigate the relationships between open-shell character and second hyperpolarizability γ (two orthogonal components) of a rectangular-shaped singlet tetraradical model as the simplest model of two-dimensional multiradical systems, for example, a dimer composed of diradical molecules. Using the full configuration interaction method with this simple model, we reveal the relationships between the local open-shell characters and diradical/tetraradical character, as well as between the global/local open-shell characters and the γ values. The obtained relationships are also verified by using ab initio quantum chemical calculations of two realistic tertraradical models, 4,4’-bis(1,2,3,5-dithiazdiazolyl) (BDTDA) dimer and disilene dimer.

2. METHODOLOGY Let us consider four radical sites located at each corner of a rectangular-shaped tetraradical system with D2 symmetry. For this model, there are four canonical orbitals with a, b1, b2, and b3 symmetry, that is, a , b1 , b2 and b3 , respectively (Figure 1). Note here that although the


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system can possess D2h symmetry, two kinds of possible orbital symmetries exist, that is,

{a

g

, b1g , b2g , b3g

} for σ-orbitals, and { a

u

, b1u , b2u , b3u

} for π-orbitals.

The energies of

these orbitals can be obtained under the mean field approximation such as the spin-unrestricted Hartree-Fock method, where a and b1 have the lowest and highest energies, respectively, among those four orbitals. Here, localized natural orbitals (LNOs) { 1 , 2 , 3 , 4

} are adopted

as the basis sets, which tend to be primarily localized at each site with small tails on the neighboring sites since they satisfy the orthogonal condition i j = 0 (i ≠ j). The LNOs can be expressed by linear combination of the canonical orbitals as follows:

Figure 1. Schematic diagrams of a two-dimensional tetraradical model (with site number) and four canonical orbitals. White and black circles indicate the orbitals with positive and negative phase at each radical site, respectively. The definition of site locations is also shown.

1 ≡

1  a + b1 + b2 + b3  , 2


5


2 ≡

1  a − b1 + b2 − b3  , 2

3 ≡

1  a − b1 − b2 + b3  , 2

and 4 ≡

1  a + b1 − b2 − b3  . 2

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(1)

Using these LNOs, all Slater determinants with spin magnetic quantum number MS = 0 are constructed. The extended Hubbard model is employed in this study to investigate electronic structures ranging from weak to strong open-shell nature. There are 36 determinants with two up spins and two down spins, and they satisfy orthonormal condition because the LNOs are orthonormal. We consider a rectangular-shaped tetraradical system possessing four identical radical sites, where on-site Coulomb repulsion is assumed to be identical among all the radical sites (Figure 2a) together with two realistic tetraradical dimer models, BDTDA dimer (Figure 2b) and disilene dimer (Figure 2c). With nearest-neighboring approximation, it has also two types of inter-site relationships, such as intra- and inter-molecular interactions in diradical dimers. Thus, each inter-site interaction, that is, inter-site Coulomb repulsion and transfer integral, possesses two types of interactions. Then, the matrix representation of the Hamiltonian is expressed by the sum of the matrix representation of the following operators.


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Figure 2. Structure of the Hamiltonian for rectangular-shaped tetraradical model (a), and two realistic teraradical models, BDTDA dimer (b) and disilene dimer (c).

By the definition of Coulomb repulsion U, it is expressed as

U = ∑ ∑ p U q n pσ nqσ ' ,

(2)

p≥q σ ,σ '

{

}

where σ and σ’ denote up or down spin ↑, ↓ , and p and q denote the radical site number {1, 2, 3, 4}. With the nearest neighbor approximation, p U q is expressed as follows:

 UOS   U p U q =  intra  U inter  0 

p=q

( p, q) = ( 2,1) , ( 4, 3) ( p, q) = (3,1), (4, 2)

.

(3)

otherwise

Hereafter, subscripts “OS”, “intra”, and “inter” are used to represent on-site, intra-molecule adjacent and inter-molecule adjacent interactions, respectively. Then, the representation of U can be simplified as

U = ∑UOSni↑ni↓ + ∑ U intra ( n2σ n1σ ' + n4σ n3σ ' ) +U inter ( n3σ n1σ ' + n4σ n2σ ' ). i

(4)

σ ,σ '

Since transfer integral t is a one-electron operator, it can be expressed as


7


(

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)

t = ∑ ∑ p σ t qσ a †pσ aqσ = ∑ ∑ p σ t qσ a†pσ aqσ + aq†σ a pσ . p, q σ

p>q σ

(5)

With the nearest neighbor approximation, p σ t qσ is defined as follows:

 t  intra p σ t qσ ≡  tinter  0 

( p, q) = ( 2,1) , ( 4, 3) ( p, q) = ( 3,1) , ( 4, 2)

.

(6)

otherwise

Then, t is expressed in the present model as

t = ∑∑ p σ t qσ ( a†pσ aqσ + aq†σ a pσ ) p>q σ

= ∑tintra ( a2†σ a1σ + a1†σ a2σ + a4†σ a3σ + a3†σ a4σ ) + tinter ( a3†σ a1σ + a1†σ a3σ + a4†σ a2σ + a2†σ a4σ )

. (7)

σ

In summary, the whole of the extended Hubbard model Hamiltonian for Ms = 0 of the rectangular-shaped tetraradical system is expressed as

H = ∑UOSni↑ni↓ + ∑ U intra ( n2σ n1σ ' + n4σ n3σ ' ) +U inter ( n3σ n1σ ' + n4σ n2σ ' ) + i

σ ,σ '

+∑tintra ( a2†σ a1σ + a1†σ a2σ + a4†σ a3σ + a3†σ a4σ ) + tinter ( a3†σ a1σ + a1†σ a3σ + a4†σ a2σ + a2†σ a4σ ) σ

(8) ,

where i denotes the radical site number {1, 2, 3, 4}. Interactions between diagonal radical sites, (2, 3) and (1, 4), are ignored in this model since these are smaller than the others. All exchange


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integrals are also ignored here since it is usually much smaller than UOS in usual non-magnetic organic molecules. To describe local open-shell nature, we define intra- and inter-molecular diradical characters (referred to as yintra and yinter, respectively) based on the analytical expression of diradical character in the two-site diradical model21 as follows:

yintra ≡ 1−

4tintra UOS 1+16 ( tintra UOS )

2

, and yinter ≡ 1−

4tinter UOS 1+16 ( tinter UOS )

2

.

(9)

These represent the diradical characters (bond weakness) by intra- and inter-molecular interactions, respectively.

In realistic systems, for example, yintra can be varied by tuning

monomer electronic structures by appropriate chemical modifications, while yinter can be done by tuning intermolecular distance. Although previous description of electron-correlated systems using diradical/tetraradical characters (y0, y1) in the orbital picture has worked well for designing realistic one-dimensional open-shell molecular systems, ab initio calculation such as density functional theory (DFT) for realistic two-dimensional tetraradical molecular systems faces difficulty to distinguish yintra and yinter. To overcome this difficulty, we need to clarify the relationship between conventional global diradical/tetraradical characters (y0, y1) and the present local ones (yintra, yinter). The y0 and y1 of the system are defined as the occupation number of the lowest unoccupied natural orbital (LUNO) and LUNO+1, respectively.42 Excitation energies, transition moments, y0 and y1 are calculated by diagonalization of the full CI matrix using eq 8. The eigenstates are expressed as linear combination of the Slater determinants with MS = 0, and their spin states are determined by diagonalizing S 2 matrix. Because in the present model all


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the exchange integrals are ignored, the ground state should be singlet in the entire region of the considered parameters. According to the perturbation theory, the diagonal component along a-axis of static electronic second hyperpolarizability γ for symmetric systems is expressed as43

γ aaaa = −4 ∑ m≠0 n≠0

(µ ) (µ ) 2 a 0m

a 2 0n

( E0 m ) 2 E0n

+4

a a µ0am µmn µnna ' µn'0

∑ m,n,n'≠0 m≠n,n≠n '

E0 m E0n E0n '

,

(10)

where m and n denote eigenstates of the system, and 0 denotes the ground state. Note that γ is expressed in B-convention. The transition moment operator can be expressed by

µ = ∑ ∑ pσ µ qσ a †pσ aqσ .

(11)

p, q σ

Under the Mulliken approximation for calculation of transition moments, transition moments are expressed as

1 p q  p µ p + q µ q  2 1 = − p q  p ( rp′ + rp ) p + q (rq′ + rq ) q  , 2 1 = − p q (rp + rq ), 2

pµq ≈

(12)


10

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where rp and r’p denote position vector of the site p and vector from the site p to the electron in that site. Since each LNO is orthonormal p q = δ pq , matrix element of transition moment is approximately expressed by position vector of each site rp:

p σ µ qσ ≈ −δ pq rp ,

(13)

where all position vectors have the same origin of coordinate, so that these quantities depend on the choice of the origin. We here consider two types of transition moments, that is, intra- and inter-molecular transition moments. In order to define dimensionless transition moments, we introduce the vector connecting intramolecular radical sites dintra and that connecting intermolecular radical sites dinter, which are independent on the choice of the origin. Under the approximation in eq 13, we consider the transition moment parallel to dintra and that parallel to dinter expressed, respectively, by

µintra = 1 + 2 µ 1 − 2 = 3 + 4 µ 3 − 4 = r2 − r1 = r4 − r3 = d intra , and

µinter = 1 + 3 µ 1 − 3 = 2 + 4 µ 2 − 4 = r3 − r1 = r4 − r2 = d inter . (14)

For nondimensionalization, both sides of eq 8 are divided by UOS, and transition moments along dintra and dinter are divided by dintra and dinter under the assumption d intra ⊥ d inter , respectively. This implies that UOS and ( dintra , dinter ) are chosen as the unit of energy and of transition


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moment amplitudes (lengths) along dintra and dinter, respectively. In this study, we focus only on intramolecular (dintra) direction component of γ (referred to as γintra, hereafter) and intermolecular (dinter) direction component of γ (referred to as γinter, hereafter). Note that these dimensionless 4 3 4 3 γintra and γinter correspond to real γintra and γinter divided by dintra and dinter , respectively, U OS UOS

under the above approximations.

3. RESULTS AND DISCUSSION 3.1 Model study. We firstly assume Uintra = Uinter = 0 for the simplest case, and later discuss the effect of existence of such intra/inter-site Coulomb repulsions. Generally, decrease of HOMO–LUMO energy gap tends to increase y value.21,22 Thus, it is predicted that y0 becomes 1 in yintra = yinter region due to degeneracy between orbital energies of b2 and b3 and that y1 increases with increasing yintra and yinter since increase of both yintra and yinter reduces energy splitting between a and b1 . Figure 3a and b show the relationship between (yintra, yinter) and yi (i = 0, 1) for Uintra = Uinter = 0, the features of which are in conformity with the prediction. These results show that unlike yintra and yinter, y0 and y1 are not directly related to the intra- and intermolecular radical interactions.


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Figure. 3. Relationship between (yintra, yinter) and yi (i = 0 (a) and 1 (b)), the values of which are represented by the color-scale. Uintra = Uinter = 0 is assumed.

Figure 4a and b show the variations in γintra and γinter, respectively, on the yintra–yinter plane in the case of Uintra = Uinter = 0. The system with yintra ≤ ~0.3 indicates the enhancement of both γintra and γinter around yintra ~ yinter region (y0 ~ 1 region). On the other hand, the system with yintra > ~0.4 exhibits monotonous decrease of its γintra with decrease of yinter, while it shows enhancement of γinter at intermediate yinter (~ 0.3–0.4) region. From comparison between these results and Figure 3, we can deduce novel design guidelines for efficient NLO tetraradical systems: (i) a monomer with large y0 (> ~0.4) exhibits enhancement of γinter at intermediate yinter (~ 0.3–0.4) region by dimerization though it does not exhibit further enhancement of γintra, and (ii) a monomer with small y0 (≤ ~0.3) exhibits enhancement of both γintra and γinter by dimerization, where y0 of dimer is nearly equal to 1.


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Figure. 4. Variations in γintra (a) and γinter (b) on yintra–yinter plane. Uintra = Uinter = 0 is assumed.

Existence of neighboring Coulomb repulsion, Uintra or Uinter, is found to hardly change the yintra/inter–γintra/inter correlation features. However, the amplitudes of γintra and γinter are found to depend on the neighboring Coulomb repulsion (Figure 5a and b). As Uintra/UOS increases, which leads to decrease of effective Coulomb repulsion (UOS – Uintra), γintra is found to increase. This feature can be understood by the fact that the increase of (UOS – Uintra) causes the increase in ease of intramolecular electron transfer in the case of constant intramolecular transfer integral. Since this model is symmetric in swapping the subscripts “intra” and “inter”, increase of Uinter/UOS is found to cause increase of γinter.


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Figure 5. Variations in γintra on yintra–yinter plane, where Uinter = 0: Uintra/ UOS = 0.2 (a) and Uintra/UOS = 0.4 (b).

3.2. Ab initio calculation in a realistic molecular system. To evaluate the reliability of the present model, we performed the ab initio quantum chemical calculations for realistic molecular systems. Let us consider 4,4’-bis(1,2,3,5-dithiazdiazolyl) (BDTDA, Figure 2b) and disilene (H2Si=SiH2) dimer (Figure 2c). The former is a realistic diradical dimer model with an equilibrium intermolecular distance d ~ 3.1 Å in solid phase. 32 The latter is expected to possess small yintra originating from Si=Si double bonds44, 45 and to be regarded as a prototypical partial structure of various π-conjugated systems with Si=Si double bonds such as 1,2-disilabenzene.46,47 The geometrical optimization for the BDTDA monomer was conducted by the UMP2/6-311+G* method under D2h symmetry constraint, and that for the disilene monomer was conducted by the UB3LYP/6-311+G* method under C2h symmetry constraint. The dimer structures are composed of parallel π-stack monomer with intermolecular distance d, and the re-optimizations are not carried out. The y0, y1 and γ values are obtained using the LC-UBLYP (µ = 0.33) method for the


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BDTDA dimer and the UCCSD method for the disilene dimer because the long-range corrected exchange functional or highly correlated wave function method is necessary to obtain reliable NLO properties.48,49 The spin square expectation values are also calculated for the BDTDA dimer at LC-UBLYP level of approximation.

The 6-31+G* basis set is adopted

because addition of diffuse functions is known to have remarkable influence on the calculated (nonlinear) optical properties.50–52 The γ values were calculated by the finite field (FF) approach with Romberg procedure,53 and these values are defined by the B-convention.

Those

calculations were performed using the Gaussian 09 program package.51

Table 1. Intermolecular Distance (d) Dependences of y0, y1, and Second Hyperpolarizabilities γintra and γinter of BDTDA Dimer Calculated Using the LC-UBLYP (µ = 0.33) Method with the 6-31+G* Basis Set γintra/104 a.u.

γinter/104 a.u.

0.426

1.64

7.98

0.426

1.533

2.03

13.0

0.619

0.502

1.698

2.12

14.0

3.6

0.845

0.704

1.992

2.33

8.97

4.0

0.955

0.808

2.068

2.45

4.65

d/Å

y0

y1

2.8

0.119

0.093

3.1

0.529

3.2

S2

Apparently, increasing d corresponds to increasing yinter in the rectangular-shaped tetraradical model. The y0 value of BDTDA monomer, which is regarded as yintra in the BDTDA dimer at yinter = 1.0, is found to be a large value (~0.9). Table 1 shows the d dependences of y0, y1, , γintra and γinter of the BDTDA dimer. It is found that both y0 and y1 for the BDTDA dimer increase with increasing d. Indeed, as seen from Figure 3a and b, in the rectangular-


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shaped tetraradical model, y0 and y1 increase with increasing yinter for yintra ~ 0.9. On the other hand, it is found for the BDTDA dimer that the γintra value increases with increasing d, while the γinter value exhibits a peak around d ~ 3.1–3.2Å. Indeed, as seen from Figure 4a and b, in the rectangular-shaped tetraradical model with yintra ~ 0.9, γintra exhibits monotonous increase with increasing yinter (for example, γintra = 1.8 × 10−3 at yinter = 0.463 vs. γintra = 2.1 × 10−2 at yinter = 1), while γinter takes a maximal peak in the intermediate yinter region.

From these results, the

behaviors of (y0, y1) and (γintra, γinter) in the BDTDA dimer for increase of d are found to be well reproduced by the rectangular-shaped tetraradical model. On the other hand, disilene monomer exhibits a small y0 value of 0.095. Table 2 shows the d dependences of y0, y1, γintra and γinter of the disilene dimer. The dimer with d = 5.0Å, which is expected to correspond to approximately non-interactive two monomers, indicates degenerate small y0 and y1 (= 0.098). When d is shortened to 3.0Å, the dimer exhibits much larger y0 (= 0.881) than that of the dimer d = 5.0Å, the feature of which is predicted in Figure 3a. Moreover, the dimer with d = 3.0Å exhibits larger γintra and γinter than those of the dimer with d = 5.0Å. Since shortening d of the disilene dimer corresponds to decreasing yinter in small yintra region, these tendencies are found to accord with the prediction by the present teraradical model (Figure 4a and b). The previous study predicted that there are gaps approximately 40 times between theoretical upper limit and the measured γ values for molecules typically known to to have “large” γ. 18 According to the results by the present model, it is found that the dimer composed of diradicaloids with small yintra is a prospective candidate. Indeed, for (Uintra, Uinter) ~ 0, the model system with appropriate open-shell nature (small yintra ~ yinter) indicates ~400 times larger γintra (γintra = 0.434 at (yintra, yinter) = (0.263, 0.312) than that of completely dissociated two closed-


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shell molecules (γintra = 0.0013 at (yintra, yinter) = (0.030, 1.000)). Moreover, the system in such region of yintra ~ yinter is expected to exhibit enhancement of γinter. In addition, this novel design principle will be capable of using together with conventional ones, and combination with conventional design principles may cause further enhancement and decrease the gap to the theoretical upper limit. For example, our recent study predicts about 40 times enhancement of γ by one-dimensional open-shell molecular stacking, 40 and therefore a larger number of stacked diradicaloids with small yintra may cause further enhancement of γ.

Table 2. Intermolecular Distance (d) Dependences of y0, y1, Second Hyperpolarizabilities γintra and γinter of Disilene Dimer Calculated Using the UCCSD Method with the 6-31+G* Basis Set d/Å

y0

y1

γintra/104 a.u.

γinter/104 a.u.

3.0

0.881

0.070

1.80

7.57

5.0

0.098

0.098

1.15

2.87

4. CONCLUSION We have investigated the relationships between open-shell characters and second hyperpolarizabilities of rectangular-shaped tetraradical systems by using the full-CI extended Hubbard model.

It is found, (i) that the system with large yintra (yinter) (> ~0.4) exhibits

enhancement of a single component of γ, γinter (γintra), at the intermediate yinter (yintra) region (~ 0.3 – 0.4), and (ii) that in contrast to conventional diradical systems, the system exhibits further enhancement of both components of γ (γintra and γinter) at the region where yintra ~ yinter with small


18

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values (≤ ~0.3). These results enable to deduce novel design guidelines for diradical dimer systems as an example of tetraradical systems: (i) a monomer with large y0 (> ~0.4) exhibits enhancement of γinter at intermediate yinter region (~ 0.3 – 0.4) by dimerization though it does not exhibit further enhancement of γintra, and (ii) a monomer with small y0 (≤ ~0.3) exhibits enhancement of both γintra and γinter by dimerization, where y0 of dimer is nearly equal to 1. This prediction is consistent with the results obtained using the ab initio calculations for the BDTDA dimer and disilene dimer. Those results are predicted to be also applicable not only to diradical dimer systems but also to two-dimensional tetraradicaloid molecules with two kinds of interactions between the radical sites. Thus, the present design guidelines are expected to pioneer an alternative class of two-dimensional multiradical NLO systems, which potentially cause further enhancement of γ as compared to conventional intermediate diradical NLO systems.


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ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website at DOI:?????. Effect of existence of Uintra on γinter; Optimized structures of BDTDA and disilene monomers.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interests. ACKNOWLEDGMENTS This work supported by JSPS Research Fellowship for Young Scientists (JP15J05489), JSPS KAKENHI (No. JP25248007) in Scientific Research (A), a Grant-in-Aid for Scientific Research on Innovative Areas “Stimuli-responsive Chemical Species” (JP24109002), “π-System Figuration” (JP17H05157), and “Photosynergetics” (JP26107004) from JSPS, Japan. This is also partly supported by King Khalid University through a grant RCAMS/KKU/001-16 under the Research Center for Advanced Materials Science at King Khalid University, Kingdom of Saudi Arabia. Theoretical calculations are partly performed using Research Center for Computational Science, Okazaki, Japan.


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