Origin of the Enhancement of the Second Hyperpolarizabilities of

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Origin of the Enhancement of the Second Hyperpolarizabilities of Metal–Carbon Bonds Shota Takamuku, Yasutaka Kitagawa, Takanori Nagami, Junya Fujiyoshi, Benoît Champagne, and Masayoshi Nakano J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b05711 • Publication Date (Web): 03 Aug 2016 Downloaded from http://pubs.acs.org on August 7, 2016

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The Journal of Physical Chemistry

Origin of the Enhancement of the Second Hyperpolarizabilities of Metal–Carbon Bonds Shota Takamuku, † Yasutaka Kitagawa, † Takanori Nagami, † Jun-ya Fujiyoshi, † Benoît Champagne, ¶ and Masayoshi Nakano*, † †

Department of Materials Engineering Science, Graduate School of Engineering Science,

Osaka University, Toyonaka, Osaka 560-8531, Japan ¶

Laboratoire de Chimie Théorique, University of Namur, rue de Bruxelles, 61, B-5000

Namur, Belgium

ABSTRACT

Spin-unrestricted coupled-cluster method was employed to investigate the origin of the second hyperpolarizabilities (γ) in model systems involving metal–carbon bonds with various bond lengths as a function of their diradical character (y) and charge transfer (CT). These systems exhibit unique features: (i) σ electrons give the dominant contribution to γ, (ii) the π electrons contribution to γ is negative, (iii) when increasing the bond length γ exhibits two positive extrema, which are associated with the CT nature and the intermediate diradical character, respectively, (iv) and one negative extremum corresponding to intermediate CT and diradical character, and (v) in the bond stretching process, the maximum γ amplitude per

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σ bond is about 7 times larger than that per π bond. These features are significantly different from those observed in pure organic systems.

1. Introduction Nonlinear optical (NLO) materials are fundamental materials for the future photonics and optoelectronics.

1-4

Organometallic systems have attracted considerable attention

large second-order NLO properties in ferrocene derivatives were reported.

7

5, 6

since

From previous

theoretical analyses, the charge transfer (CT) nature between the metal atoms and the organic ligands control the amplitude of the second-order NLO properties.

8, 9

Furthermore, the

electronic structure of these compounds can be triggered by light irradiation, changing the pH or the redox potential, by applying a static electric or magnetic field, and also by ion complexation 5, 6 Consequently, switching the second-order NLO properties can be achieved by changing the oxidation state,

10-14

and the magnetic interaction.15-16

compounds with large third-order NLO properties have also been reported.

Organometallic 17-20

Some of

them show switching of the third-order NLO responses together with electrochromism, photochromism and halochromism. 21,22 Furthermore, they can exhibit very large third-order NLO properties as compared to organic systems.

23,24

Although in such compounds the CT

nature was speculated to be an important factor for controlling the second hyperpolarizability γ, it has not been investigated in detail. On the other hand, open-shell singlet molecules have attracted much attention from theoretical and experimental researchers due to their unique electronic structures outstanding physicochemical properties including remarkable NLO properties.

29-32

25-28

and

A large

number of investigations of the third-order NLO properties of open-shell molecular systems have revealed that the intermediate diradical characters cause significant enhancements of γ.


2

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29-32

Moreover, recent theoretical studies have predicted that asymmetricity combined with

intermediate diradical character exhibit further enhancement of γ amplitudes with positive or negative sign.

32

Unfortunately, until now, only a few compounds with such properties have

been found, for example, transition-metal heterodinuclear systems,

33

donor/acceptor-

substituted diphenalenyl diradicaloids, 34 and azulene-like asymmetric acene. 35 Because they display both large CT (between the metal and organic moieties) and open-shell character, open-shell organometallic systems are expected to have a potential for exhibiting extremely large, positive or negative, γ values. To clarify the effects of the CT and open-shell character on the γ values in organometallic systems, we theoretically investigate the variation in diradical character, CT, and γ value for simple metal(M)–carbon(C) bond models as a first step towards investigating more realistic open-shell organometallic systems. Indeed, the M– C single/double/triple bonds are observed in real organometallic NLO systems involving different transition metals.

10–24

For example, Humphrey and coworkers have reported on a

protonation-triggered switching of NLO properties for structure changes between vinylidene (double bond) and alkynyl (single bond) ruthenium complexes.

22

Namely, the M–C bonds

are considered critical for generating large NLO responses in realistic organometallic systems (Scheme 1) because these bonds are at the origin of the CT and open-shell characters. Nevertheless, only a few studies have been devoted to the M–C bonds and they have been limited to the electronic excitation properties 36, 37 or to the analysis of the bond contributions to γ.

38

In contrast, the present study provides a detailed insight into the relationships

between the bond nature, the open-shell character, the CT, and the γ values for M–C bonds.


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Scheme 1. Schematic diagram of organometallic systems.

2. Theoretical Calculations Figure 1 shows the selected structures with M–C bonds m1–m3 and C–C bonds c1–c3. These bonds are single (m1, c1), double (m2, c2), or triple (m3, c3). Although in real organometallic systems, transition metals tend to have various spin states due to ligand field effects, the purpose of this study is to reveal the relationship between the metal–carbon bond and the second hyperpolarizabilities.

Therefore, we fix Mn(I) in its highest spin

configuration 3d54s1, which has half-filled 3d and 4s atomic orbitals and which is the most stable electronic structure.

This determines the spin state of the M–C systems as follows:

sextet (m1), quintet (m2), and quartet (m3) states.

Although these are just models of

organometallic NLO systems, they are sufficient for revealing the essence of the interaction between the transition metal and the organic moiety on the third-order NLO properties because the latter are governed by the M–C bond. Then, since the results are interpreted as a function of the diradical character and CT nature, the relationships between these factors and γ are expected to be observed in more complex organometallic compounds involving single, double and triple M–C bonds.

19-24

On the other hand, organic systems c1–c3 are ground

state singlets. M–C and C–C bonds are oriented along the z-axis. Geometry optimizations were performed using the spin-unrestricted coupled-cluster with singles and doubles (UCCSD) method. The effective core potential (ECP) of the Stuttgart group was employed


4

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with the corresponding valence basis set (SDD) for Mn and aug-cc-pVTZ basis set for the C and H atoms.

The same level of approximation and basis set were employed in all

calculations, except when explicitly indicated. The optimized structures correspond to local minima, as evidenced by the Hessian analysis. The successive diradical characters yi were defined as the occupation numbers of the lowest unoccupied natural orbitals (LUNO)+i (i = 0, 1, …) 39

yi = nLUNO+i .

(1)

Both y(σ) and y(π) are defined, for the LUNO+i having these orbital symmetries. For the non-metallic atoms, the aug-cc-pVDZ basis set was used (see Figure S1 in the Supporting Information for basis set dependence). The natural population analysis (NPA) was also performed to clarify the charge transfer (CT) nature of these systems. calculated by the finite-field approach

40

γ values were

using both the UCCSD and UCCSD including

perturbative triples (UCCSD(T)) methods and the aug-cc-pVDZ basis set (for C and H). The choice of extended basis sets with diffuse functions is necessary for calculating γ values with semiquantitative accuracy. To analyze the γ contribution of electrons in orbitals of different symmetries, the γ density analysis was employed.

41

It consists in the third-order

differentiation of the electron density ρ with respect to the external electric field F:

∂3 ρ ρiii ( r ) = ∂Fi∂Fi∂Fi (3)

.

(2)

F=0

From this density, the γiiii values are calculated according to

γ iiii = −

1 3 ri ρiii( ) ( r ) dr , ∫ 3!

(3)

where ri denotes the i component of the electron coordinate. Then, the electronic density of the mth NO, ρm, is defined as follows: 2

ρ m ( r ) = nm φ m ( r ) ,

(4)


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which enables the evaluation of the contribution of the mth NO to γiiii and its partitioning into σ and π electron contributions. Gaussian 09 43 was used for performing all calculations.

m γ iiii =−

1 1 ∂3ρ m m( 3) r ρ r dr = − r ∫ i iii ( ) ∫ i ∂F∂F∂F 3! 3! i i i

R

dr ,

(5)

F=0

R

R

R

R

R

Figure 1. Structures of Mn(I)–C (m1–m3) and C–C (c1–c3) bond models. Definition of each bond length R [Å] is also shown.

3. Results and Discussion 3.1. Geometric and Electronic Structures. In the m1–m3 organometallic systems, the optimized bond lengths (Ropt) decrease with increasing bond order (Table 1), like in the corresponding organic systems c1–c3.

Although at equilibrium y(σ) values in the

organometallic systems are close to 0, that is, almost closed-shell for the σ orbitals, the y(π) values lie around 0.5. This implies that the π orbital shows an intermediate diradical nature at equilibrium. This is attributed to the small overlap between the metal and carbon π


6

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orbitals. On the other hand, in the corresponding organic compounds, both y(σ) and y(π) are close to 0. For a given bond order, the differences between the Ropt values of the organic and organometallic systems amount to 0.5 – 0.6 Å. This originates from the respective size of the valence orbitals, 3d and 4s in Mn(I) versus 2p orbital in C, as well as from the differences between the d-p and p-p interactions. m1 presents the largest γ value among all the systems and it mostly originates from the σ valence electrons of the M–C bond (Table 1). Dominant σ-electron contributions are also observed for all M-C bonds while the π-electron contributions are smaller and negative. So, although m2 shows the largest γ(σ) value among the M-C systems, m2 does not present the largest γ value because of the significant negative γ(π). m3 shows significantly smaller γ(σ) and γ(π) amplitudes, which is caused by the smaller CT in m3 than in m1 and m1. The details of their origins are discussed in Sec. 3.3. On the other hand, in organic systems both y(σ) and y(π) are much smaller and both are positive. The relative π-electron contribution increases from c2 (44%) to c3 (70%). Note that π electron contributions are known to get larger and larger in extended π-conjugated organic systems 44. The γ values of m1 and m2 systems are about 10 times as large as those of the corresponding organic systems c1 and c2, respectively. We will discuss the origin of such differences in the subsequent sections.

Table 1. Optimized bond lengths (Ropt [Å]), diradical characters of the σ and π orbitals (y(σ), y(π)), γ [a.u.] values and their σ and π contributions (γ(σ), γ(π) [a.u.]) for m1–c3 at UCCSD level of approximation. Ropt [Å]

y(σ)

y(π)

γ [a.u.]

γ(σ) [a.u.]

γ(π) [a.u.]

m1 Mn(I)CH3

2.043

0.080

–

8220

5800

–

m2 Mn(I)CH2

1.936

0.066

0.595

6700

9120

-2910


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m3 Mn(I)CH

1.809

0.048

0.503

792

1540

-681

c1 C2H6

1.527

0.027

–

859

846

–

c2 C2H4

1.332

0.024

0.066

658

299

287

c3 C2H2

1.204

0.027

0.058

465

10.7

326

3.2. Open-Shell and Charge Transfer Character. Figure 2 shows the R dependences of y(σ) and y(π). No matter what is the nature of the systems, they increase with R, as expected in a bond dissociation process because the diradical character is an index of instability of an effective chemical bond. 44,45 The y(σ) values in m1–m3 are almost the same when R < 2.5 Å, while for R > 2.7 Å they increase in the order, m1 < m2 < m3 (Figure 2(a)). The same tendency is observed in the organic systems (Figure 2(c)) when R > 1.7 Å, which originates from the difference in the hybridization of s and p orbital on the C atoms. Indeed, the bond strength of hybrid orbitals increases with the fraction of s orbital (sp: 50 %, sp2: 33 % and sp3: 25 %). Therefore, for a given R, single bond systems m1 (or c1) with sp3 hybrid orbital have smaller diradical character than the double m2 (or c2) and triple m3 (or c3) bond systems. On the other hand, the y(π) values of m2 and m3 show almost the same values in the whole region (Figure 2(b)); this is also same behavior with organic systems (Figure 2(d)).


8

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(a)

(b)

(c)

(d)

Figure 2. Variations of the diradical characters y(σ) and y(π) of M–C bond systems (m1, m2, m3) as shown in (a) and (b) and of organic systems (c1, c2, c3) as shown in (c) and (d) as a function of R [Å] at UCCSD level of approximation. The Ropt of each system is indicated by a dashed line.

In order to probe the CT character in m1–m3, the NPA charges on the Mn(I) atoms (Q(Mn)) were calculated as a function of R (Figure 3). Each system presents a maximum of the CT. The maximum Q(Mn) values (Qmax) and corresponding R values (RQmax) increase with the bond order (RQmax = 1.8 Å in m1, RQmax = 1.9 Å in m2, and RQmax = 2.1 Å in m3). In the R < RQmax region, the electronic repulsion is so strong that the CT is reduced, that is, Q(Mn) decreases with decreasing the R value. On the other hand, in the R > RQmax region, the


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CT character goes down due to a reduction in the orbital interactions. Qmax and RQmax are correlated with the balance between the CT and the orbital interaction. m1 with sp3 hybrid orbital shows the smallest Qmax and RQmax due to the highest orbital energy and smallest orbital size along the bond direction of sp3 hybrid orbital. In the same way, m3 with sp hybrid orbital displays the largest Qmax and RQmax due to its lowest orbital energy and largest orbital.

In summary, the CT amplitude and RQmax are correlated with the degree of s

character of the hybrid orbital.


10

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Figure 3. Variations of the NPA charge on the Mn(I) atoms (Q(Mn) [a.u.]) in the M–C bond systems as a function of bond length (R). The Ropt of each system is indicated by a dashed vertical line.

To get a more detailed picture, the Q(Mn) value of m2 and m3 are decomposed into their σ and π counterparts (q(σ) and q(π)) (Figure 4). q(σ) is defined as the difference between their formal electron number (2) and the natural atomic orbital occupancies of the 4s and 3dz2 orbitals of the Mn atom: q(σ) = 2 − (natural atomic orbital occupancies of 4s and 3d z2 ) .

(7)

Similarly, in m2, q(π) is defined by using the natural atomic orbital occupancies of 3dxz and the formal electron number (1) of 3dxz of the Mn atom: q(π) = 1 − (natural atomic orbital occupancies of and 3d xz ) ,

(8)

while in m3, q(π) is related to the real and formal occupancies of 3dxz and 3dyz atomic orbitals of the Mn atom: q(π) = 2 − (natural atomic orbital occupancies of 3d xz and 3d yz ) .

(9)

It should be noted that charges (Q) do not correspond to the sum of the contribution to charge from each orbital symmetry (q(σ) and q(π)) because of the +1 charge form Mn(I). Considering this point, the sum of q(σ) and q(π) reproduces the behavior of NPA charge (Q) (see Figure S2). Figure 4 shows a π-electron transfer from C to Mn (negative q(π)) together with a σ-electron transfer from Mn to C (positive q(σ)) in both systems. In addition, m3 exhibits larger charge transfers (larger |q(σ)| and |q(π)|) than m2.


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(a)

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(b)

Figure 4. Evolution of the σ and π electron charges of Mn atom (q(σ) and q(π) [a.u.]) in Mn(I)CH2 m2 (a) and Mn(I)CH m3 (b) as a function of the bond length (R). The Ropt and RQmax are indicated by dashed vertical lines.

3.3. Origin of γ values. To unravel the origin of the γ values in terms of the CT and openshell natures, Figure 5 shows the R dependences of γ values and of its σ and π contributions in Figure 5. Note that in the triple bond systems (m3 and c3) there are two π bonds, so that the γ(π) values per bond are represented instead of the total γ(π). UCCSD(T) calculations on m1–m3 were also performed to substantiate the UCCSD results. Figure 5(a)–(c) show that the UCCSD method well reproduces the γ variation obtained from UCCSD(T) calculations except at R = 2.3 Å for m3. The errors of γ values are within 90% except in the regions with very small γ value. Therefore, we discuss the γ values and the σ/π orbital contributions to γ at UCCSD level of theory except at R = 2.3 Å in m3. In the case of the reference organic systems, the single bond system c1 presents a maximum at R = 2.9 Å (see Figure 5(d)), the double bond system c2 has a maximum at R = 2.7 Å together with shoulder around R = 2.0 Å (see Figure 5(e)), and the triple bond system c3 has a maximum at R = 2.6 Å with a stronger


12

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shoulder around R = 1.9 Å (see Figure 5(f)). The main contribution to these shoulders comes from the π electrons, while the maximum γ is attributed to the σ electrons. In the organic systems γmax(σ) and γmax(π) have the same order of magnitude and they correspond to the intermediate diradical character regions of the σ and π bonds, respectively (Table 2). Although the ratio of γmax(σ) to γmax(π) per bond are similar in c2 [γmax(σ)/γmax(π) = 1.55] and c3 [γmax(σ)/(γmax(π)/2) = 1.65], γmax(σ) value of c2 is three times larger than that of c3. This difference can be understood by employing the 2-electron 2-site model expression:

γ=

4 R BA f (y, rK ) , U3

(10)

where RBA is the effective length between the diradical sites, U is the effective Coulomb repulsion between the two sites, rK is the ratio between the direct exchange integral (K) and effective Coulomb repulsion, rK = K/U. f(y,rK) presents a maximum in the intermediate y region. Indeed, i) the size effect contributes to a factor of 1.2 ~ (R(c2)/R(c3))4 = (2.7/2.6)4 = 1.2, ii) the effective Coulomb repulsion of c3 is predicted to be larger than that of c2 since c3 has 6 electrons between the Mn and C while there are only 4 in c2, and iii) the f (y, rK ) terms are expected to be similar owing to small differences between their diradical characters, i.e., y(σ) = 0.492 in c2 and y(σ) = 0.607 in c3.


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(a)

(b)

(c)

(d)

(e)

(f)

Figure 5. Evolution of γ [x103 a.u,] and its σ and π orbital contributions as a function of bond length R [Å]. Values obtained at the UCCSD and UCCSD(T) levels for m1–m3 ((a)(c)) and with the UCCSD method for c1–c3 ((d)-(f)). The Ropt and RQmax are indicated by dashed vertical lines.

For the organometallic systems γ presents two maxima located around R = 2.0 Å [γmax1 and Rmax1] and R = 3.2 - 4.0 Å [γmax2 and Rmax2]. All three compounds have a minimum close to R = 2.6 Å [γmin2 and Rmin2] while m2 and m3 displays another one around R = 1.8 Å in m2 and R = 2.1 Å in m3 [γmin1 and Rmin1] [Figure 5(a)-(c)]. Again, the largest contribution originates from σ electrons. Moreover, γmin1 is attributed to the negative contribution of π electrons.


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Table 2. Maximum γ(σ) and γ(π) values (γmax(σ) and γmax(π) [x103 a.u.]) as well as their corresponding R (Rmax(σ) and Rmax(π) [Å]) and y(σ) and y(π) values. γmax(σ)

Rmax(σ)

y(σ)

γmax(π)

Rmax(π)

y(π)

m1 Mn(I)CH3

31.6

4.0

0.843

–

–

–

m2 Mn(I)CH2

11.7

3.2

0.652

1.74

2.5

0.853

m3 Mn(I)CH

20.0

3.2

0.694

5.68

2.6

0.837

c1 C2H6

15.5

2.9

0.491

–

–

–

c2 C2H4

6.21

2.7

0.492

4.00

1.9

0.352

c3 C2H2

2.15

2.6

0.607

2.60

1.9

0.480

The organometallic systems show large variations of γ values as a function of the M–C bond distance. Based on our theoretical prediction, this behavior is explained by the CT and diradical characters. 32 The origin of these γ maxima in the R = 1.9–2.3 Å range is attributed to the charge transfer. Indeed, the variations in Rmax1 value among m1–m3 follows those of RQmax (Table 3) and a similar dependence is observed between γmax1 and Qmax. The second maximum (γmax2), around R = 3.2–4.0 Å, is dominated by the σ electron contribution and the corresponding intermediate y(σ) values. Then, γmin1 comes from the contribution of the π electrons, while γmin2 from the σ electrons. For m1-m3, in the Rmin2 region the CT nature and y(σ) decreases and increases, respectively, as a function of R. Therefore, such two natures exist simultaneously in this region. In a previous study, the coexistence of these two effects was predicted to cause negative γ values with large amplitudes. 32 Therefore, the M-C bond systems display such negative γ region as the result of the synergetic effect between the intermediate diradical character and CT nature. This is indirectly confirmed by the fact that the organic systems with no CT nature do not exhibit such negative peak. Finally, the Rmin1 region is associated with π-electron CT and intermediate y(π). Since the region of Rmin2 is


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Page 16 of 34

also shown to have the CT nature and the intermediate diradical character of σ electrons, we can conclude that the γmin2 comes from the coexistence of the CT nature and the intermediate diradical character of the σ electron.

Table 3. Maximum γ values in R = 1.9 – 2.3 Å (γmax1 [x103 a.u.]) calculated using the UCCSD(T) method and corresponding Rmax1 [Å] in comparison to the maximum Q(Mn) value (Qmax [a.u.]) calculated using the UCCSD method and RQmax [Å]. γmax1

Rmax1

Qmax

RQmax

m1 Mn(I)CH3

14.1

1.9

1.368

1.9

m2 Mn(I)CH2

14.8

2.1

1.379

2.0

m3 Mn(I)CH

17.2

2.3

1.463

2.2

The γ extrema amplitudes are related to the CT, the size of the molecule, and the balance between the contributions of σ and π electrons. To disentangle the effects of bond length, 46 (eq 10 ) we compare the γmax1/R4max1. γmax1/R4max1(m1)/γmax1/R4max1(m2) = 1.4 whereas it attains 1.8 for γmax1/R4max1(m1)/γmax1/R4max1(m3), demonstrating a decrease of γmax1/R4max1 as a function of the bond order because of the negative π electron contributions.

The γ(π)

amplitude per bond of m3 at Rmax1 (-4620 a.u.) is about 2.8 times larger than that of m2 (1680 a.u.) due to the larger CT in m3 than in m2. In spite of the larger CT nature of the σ electrons and larger γ(σ) amplitude in m3 at Rmax1 than those in m2 at Rmax1, the ratio γmax1/R4max1 of m2 to m3 shows a small value (14.8x103/2.14)/(17.2x103/2.34) = 1.2 due to the increase in the negative π electron contributions. The balance between γ(σ) and γ(π) can explain the tendency in γ in the optimized structures discussed in Sec 3.1 as follows. It is found that i) m1 exhibits large γ values since the Ropt values are close to Rmax1 and it lacks the


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π contribution, that ii) m2 exhibits large γ values since the Ropt values are close to Rmax1 and the π contribution is smaller than the σ contribution, and that iii) m3 has a much smaller γ value for the optimized structure than m1 and m2 because of the large difference between the Ropt (1.809 Å) and RCTmax (2.3 Å), associated with small CT. In the case of γmax2, the γmax(σ) amplitudes decrease in the order: m1 > m3 > m2. The largest value for m1 comes from the large (Rmax(σ)/Rmax(σ))4 = (4.0/3.2)4 ratio of 2.4. At the same time, y(σ) of m1 is very large (0.843), which has a detrimental contribution to γmax(σ). Therefore, other effects, like CT or small effective Coulomb repulsions between the valence electrons,32 might contribute to enhancing the γmax(σ) of m1. m2 and m3 systems show almost the same diradical character and size (see Table 2). The region around Rmax(π) corresponds to intermediate y(π) but it is slightly larger than that of the σ bond. The γmax(σ) amplitudes are shown to be about 7 times larger than the γmax(π) amplitudes per bond in m2 and m3 systems. This feature is in sharp contrast to organic systems, in which the γmax(σ) amplitudes are about 1.6 times larger than γmax(π) per bond in c2 and c3. One of the possible reasons for such a difference between organometallic and organic systems is the size because the larger overlap of σ electrons than π electrons leads to the larger R values in the intermediate diradical region.

The

(Rmax(σ)/Rmax(π))4 quantities confirm the size effect: (3.2/2.5)4 = 2.7 in m2, (3.2/2.6)4 = 2.3 in m3, (2.7/1.9)4 =4.1 in c2 and (2.6/1.9)4 = 3.5 in c3. These features do not reproduce the difference between the γmax(σ) and γmax(π) amplitudes per bond. The other possibilities are the CT nature and the diradical character in the Rmax region. In c1-c3, there is no CT nature between the carbons, while in the organometallic systems, there is CT between the metal and carbon atoms due to the difference of their ionization potentials. In the organometallic systems, the CT nature of π electrons is different from that of σ electrons, resulting in the difference between γmax(σ) and γmax(π) per bond.

32

The diradical characters in the Rmax(π)


17


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region (y(π) = 0.8–0.9) are larger than those in the Rmax(σ) region (y(σ) = 0.6 - 0.7), which leads to the small γ(π) values due to the localization of π electrons. 29,30 Table 4 shows the σ and π electron contributions to γmin(σ) and γmin(π) and the corresponding R (Rmin(σ) and Rmin(π) [Å]). The γmin1 values originate from the π electrons. Therefore, we compare the γmin(π) and Rmin(π) in order to clarify the origin of the difference of γmin(π) between m2 and m3. It turns out that the ratio of γmin(π), ( -4620/-3040 = ) 1.52, almost corresponds to the size effect, ( (2.2/2.0)4 = ) 1.46. This implies that the difference of γmin(π) comes form the size effect. The origin of γmin2 values is σ electrons (Figure 5 (a)-(c)). The γmin(σ) and Rmin(σ) increase in the order: m1 < m2 < m3: this indicates that the order of γmin(σ) is correlated with the size effect. Indeed, the ratios related to γmin(σ) and Rmin(σ)4 between the systems are ( -21000/-15100 = 1.40 ) and ( (2.6/2.5)4 = ) 1.17, in m1 and m2, and ( -35500/-21000 = ) 1.69 and ( (2.7/2.6)4 = ) 1.16, in m2 and m3, respectively. The ratios between γmin(σ) and γmin(π) amount to about 7.0 in m2 and m3, respectively, while the ratios between Rmin(σ)4 and Rmin(π)4 are about 2.7 in m2 and m3, respectively: this implies that not only the size effect but also the other effects related to the difference of bond nature between σ and π bonds, like the CT or small effective Coulomb repulsions between the valence electrons, make the difference between γmin(σ) and γmin(π).

Table 4. Mimimum γ(σ) and γ(π) values (γmin(σ) and γmin(π) [x103 a.u.]), R giving the γmin(σ) and γmin(π) (Rmin(σ) and Rmin(π) [Å]). γmin(σ)

Rmin(σ)

γmin(π)

Rmin(π)

m1 Mn(I)CH3

-15.1

2.5

–

–

m2 Mn(I)CH2

-21.0

2.6

-3.04

2.0

m3 Mn(I)CH

-35.5

2.7

-4.62

2.2


18

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4. Conclusions Using the UCCSD or UCCSD(T) methods, we have investigated the geometric and electronic structures, the bond length dependences of diradical character and second hyperpolarizability γ for Mn(I)-C bond systems and their organic analogues. From the comparison between the Mn(I)-C bond systems and organic systems, we have revealed the characteristic behavior of the γ values in Mn(I)-C bond systems: (i) π electrons provide a negative contribution to γ, (ii) σ electrons primarily contribute to γ, (iii) the γ values have two maxima that originates from the CT nature and the intermediate diradical character, respectively, (iv) the maximum γ(σ) is about 7 times larger than the maximum γ(π), (v) the γ values have minima in the region with CT nature and intermediate diradical character. These features are found to be different from those observed in the corresponding organic systems, in which the π electrons give the main contribution, the maximum γ(σ) values are about 1.6 times larger than the maximum γ(π), and there is no negative γ region. By considering the two factors, diradical character and CT nature, we have revealed the singular behavior of γ as a function of the M–C bond distance and have presented design guidelines for highly efficient organometallic NLO materials. On this basis, large negative γ values could be achieved by tuning the diradical character and CT nature through modifying the bond distance and metal species. Furthermore, as seen from Figure 5a, singly-bonded systems such as Mn(I)CH3 with large M–C bond distance (presenting an intermediate diradical character) are predicted to exhibit much larger γ amplitudes than similar size traditional M–C bonded NLO systems with only large CT nature. Furthermore, real organometallic systems could exhibit a broader variety in the nature of the metal atom, the oxidation state, the spin state, the M-C bonding character, etc. The results obtained in this study will provide useful information to analyze such structure-


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property relationships and to construct design guidelines for highly efficient NLO materials composed of open-shell organometallic systems.

ASSOCIATED CONTENT Supporting Information Available: The comparison of the charge on Mn and the σ and π electron distributions in Mn. AUTHOR INFORMATION Corresponding Author *Email: [email protected] Telephone number: +81-6-6850-6265 Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT This work is supported by JSPS KAKENHI Grant Number JP25248007 in Scientific Research (A), Grant Number JP24109002 in Scientific Research on Innovative Areas “Stimuli-Responsive Chemical Species”, Grant Number JP15H00999 in Scientific Research on Innovative Areas “π-System Figuration”, and Grant Number JP26107004 in Scientific Research on Innovative Areas “Photosynergetics”.

This work is also supported by the

Interactive Materials Science Cadet program, Japan, by the Belgian Government (IUAP No P7/5 “Functional Supramolecular Systems”), and the Francqui Foundation.


Theoretical

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calculations

are

partly

performed

using

Research

Center

for

Computational

Science, Okazaki, Japan.

REFERENCES (1) Kawata, S.; Sun, H.-B.; Tanaka, T.; Takada, K. Finer Features for Functional Microdevices. Nature 2001, 412, 697-698. (2) Kawata, S.; Kawata, Y. Three-Dimensional Optical Data Storage Using Photochromic Materials. Chem. Rev. 2000, 100, 1777-1788. (3) Day, D.; Gu, M.; Smallridge, A. Rewritable 3D Bit Optical Data Storage in a PMMABased Photorefractive Polymer. Adv. Mater. 2001, 13, 1005-1007. (4) Soljačić, M.; Joannopoulos, J. D. Enhancement of Nonlinear Effects Using Photonic Crystals. Nat. Mater. 2004, 3, 211-219. (5) Long, N. J. Organometallic Compounds for Nonlinear Optics-The Search for En-lightenment! Angew. Chem. Int. Ed. 1995, 34, 21-38. (6) Bella, S. D. Second-order Nonlinear Optical Properties of Transition Metal Complexes. Chem. Soc. Rev. 2001, 30, 355-366. (7) Green, M. L. H.; Marder, S. R.; Thompsom, M. E.; Bandy. J. A.; Bloor, D.; Kolinsky, P. V.; Jones. R. J. Synthesis and Structure of (cis)-[1-ferrocenyl-2-(4-nitrophenyl)ethylene], an Organotransition Metal Compound with a Large Second-order Nonlinearity. Nature. 1987, 330, 360-362.


21


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

Page 22 of 34

(8) Kanis, D. R.; Ratner, M. R; Marks, T. J. Description of Quadratic Optical Nonlinearities for Transition-Metal Organometallic Chromophores Using an SCF-LCAO MECI Fromalism. J. Am. Chem. Soc. 1990, 112, 8203-8204. (9) Kanis, D. R.; Lacroix, P. G.; Ratner, M. R; Marks, T. J. Electronic Structure and Quadratic Hyperpolarizabilities in Organotransition-Metal Chromophores Having Weekly Coupled π-Networks. Unusual Mechanism for Second-Order Response. J. Am. Chem. Soc. 1994, 116, 10089-10102. (10) Coe, B. J.; Houbrechts, S.; Asselberghs, I.; Persoons. A. Efficient, Reversible RedoxSwitching of Molecular First Hyperpolarizabilities in Ruthenium(II) Complexes Possessing Large Quadratic Optical Nonlinearrities. Angew. Chem. Int. Ed. 1999, 38, 366-369. (11) Coe, B. J. Switchable Nonlinear Optical Metallochromophores with Pyridinium Electron Acceptor Groups. Acc. Chem. Res. 2006, 39, 383-393. (12) Malaun, M.; Reeves, Z. R.; Paul, R. L.; Jeffery. J. C.; McCleverty, J. A.; Ward. M. D.; Asselberghts,

I.;

Clays,

K.;

Persoons,

A.

Reversible

Switching

of

the

First

Hyperpolarizability of an NLO-active Donor-Acceptor Molecule Based on Redox Interconversion of the Octamethylgerrocene Donor Unit. Chem. Commun. 2001, 49-50. (13) Paul, P.; Costuas, K.; Ledoux, I.; Deveau, S.; Zyss, J.; Halet, J-H.; Lapinte, C. RedoxSwitchable Second-Order Molecular Polarizabilities with Electron-Rich Iron σ-Aryl Acetylides. Organometallics. 2002, 21, 5229-5235. (14) Zhang, Y.; Castet, F.; Champagne, B. Theoretical Investigation of the First Hyperpolarizability Redox-Switching in a Ruthenium Complex, Chem. Phys. Lett. 2013, 574, 42-46.


22

Page 23 of 34

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


(15) Averseng, F.; Lepetit, C.; Lacroix, P. G.; Tuchagues, J. P. Theoretical Investigation of the Effect of a spin Transition on the Second-Order Molecular Hyperpolarizability of a Bis(saliculaldiminato)FeII Schiff Base Complex. Chem. Matt. 2000, 12, 2225-2229. (16) Coe, B. J. Molecular Materials Possessing Switchable Quadratic Nonlinear Optical Properties. Chem. Eur. J. 1999, 5, 2464-2471. (17) McDonagh, A. M.; Humphrey, M. G.; Samoc, M.; Luther-Davies, B.; Houbrechts, S.; Wada, T.; Sasabe, H.; Persoons, A. Organometallic Complexes for Nonliner Optics. 16. Second and Third Order Optical Nonlinearities of Octopolar Allunulruthenium Complexes. J. Am. Chem. Soc. 1999, 121, 1405-1406. (18) Li, G.; Hou, H.; Li, L.; Fan, Y.; Zhu, Y.; Meng, X.; Mi, L. Synthesis, Crystal Structures, and Third-Order Nonlinear Optical Properties of a Series of Ferrocenyl Organometallics. Inorg. Chem. 2003, 42, 913-920. (19) Fillaut, J-L.; Perruchon, J.; Bianchard, P.; Roncali, J.; Golhen, S.; Allain, M.; Migalsaka-Zalas, A.; Kityk, I. V.; Sajraoui, B. Design and Synthesis of Ruthenium Oligothienylacetylide Complexes. New Materials for Acoustically Induced Nonlinear Optics. Organometallics. 2005, 24, 687-695. (20) Samoc, M.; Morrall, J. P.; Dalton, G. T.; Cifuentes, M. P.; Humphrey, M. G. TwoPhoton and Three-Photon Absorption In an Organometallic Dendrimer. Angew. Chem. 2007, 119, 745-747. (21) Powell, C. E.; Humphrey, M. G.; Cifuentes, M. P.; Morrall, J. P.; Samoc, M.; LutherDavies, B. Organometallic Complexes for Nonlinear Optics. 33. Electrochemical Switching of the Third-Order Nonlinearity Observed by Simultaneous Femtosecond Degenerate FourWave Mixing and Pump-Probe Mesurements. J. Phys. Chem. A. 2003, 107, 11264-11266.


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(22) Green, K. A.; Cifuentes, M. P.; Corkery, T. C.; Samoc, M.; Humphrey, M. G. Switching the Cubic Nonlinear Optical Properties of an Electro-, Halo- and Photochromic Ruthenium Alkynyl Complex Across Six States. Angew. Chem. Int. Ed. 2009, 48, 7867-7870. (23) Roberts, R. L.; Schwich, T.; Corkery, T. C.; Cifuentes, M.; Green, K. A.; Farmer. J. D.; Low, P. J.; Marder, T. B.; Samoc, M.; Humphrey, M. G. Organometallic Complexes for Nonlinear Optics. 45. Dispersion of the Third-Order Nonlinear Optical Properties of Triphenylamine-Cored Alkynylruthenium Dendrimers. Adv. Mater. 2009, 21, 2318-2322. (24) Schwich, T.; Cifuentes, M.; Gugger, P. A.; Samoc, M.; Humphrey, M. G. Electronic, Morecular Weight, Molecular Volume, and Financial Cost-Scaling and Comparison of TwoPhoton Absorption Efficiency in Disparate Molecules (Organometallic Compexes for Nonlinear Optics. 48.) – A Response to “Comment on ‘Organometallic Complexes for Nonlinear Optics. 45. Dispersion of the Third-Order Nonlinear Optical Properties of Triphenylamine-Cored Alkynylruthenium Dendrimers.’ Increasing the Nonlinear Response by Two Orders of Magnitude.” Adv. Mater. 2011, 23, 1433-1435. (25) Lambert, C. Towards Polycyclic Aromatic Hydrocarbons with a Singlet Open-Shell Ground State. Angew. Chem. Int. Ed. 2011, 50, 1757-1758. (26) Sun, Z.; Ye, Q.; Chi. C.; Wu, J. Low Band Gap Polycyclic Hydrocarbons: from Closed-Shell near Infrared Dyes and Semiconductors to Open-Shell Radicals. 2012, 41, 7857-7889. (27) Abe, M. Diradicals. Chem. Rev. 2013, 113, 7011-7088. (28) Kubo, T. Recent Progress in Quinoidal Singlet Biradical Molecules. Chem. Lett. 2015, 44, 111-122.


24

Page 25 of 34

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


(29) Nakano, M.; Kishi, R.; Ohta, S.; Takahashi, H.; Kubo, T.; Kamada, K.; Ohta, K.; Botek, E.; Champagne, B. Relationship between Third-Order Nonlinear Optical Properties and Magnetic Interactions in Open-Shell Systems: A New Paradigm for Nonlinear Optics. Phys. Rev. Lett. 2007, 99, 033001. (30) Nakano, M.; Champagne, B. Theoretical Design of Open-Shell Singlet Molecular Systems for Nonlinear Optics. J. Phys. Chem. Lett. 2015, 6, 3236-3256. (31) Nakano, M.; Champagne, B. Nonlinear Optical Properties in Open-Shell Molecular Systems. WIREs Comput. Mol. Sci., 2016, 6, 198–210. (32) Nakano, M.; Champagne, B. Diradical Character Dependences of the First and Second Hyperpolarizabilities of Asymmetric Open-Shell Singlet Systems. J. Chem. Phys. 2013, 138, 244306. (33) Yamada, T.; Inoue, Y.; Champagne, B.; Nakano, M. Theoretical Study on the Diradical Characters and Third-Order Nonlinear Optical Properties of Transition-Metal Heterodinuclear Systems. Chem. Phys. Lett. 2013, 579, 73-77. (34) Nakano, M.; Minami, T.; Yoneda, K.; Muhammad, S.; Kishi, R.; Shigeta, Y.; Kubo, T.; Rougier, L.; Champagne, B.; Kamada, K. et al. Giant Enhancement of the Second Hyperpolarizabilities of Open-Shell Singlet Polyaromatic Diphenalenyl Diradicaloids by an External Electric Field and Donor-Acceptor Substitution. J. Phys. Chem. Lett. 2011, 2, 10941098. (35) Nakano, M.; Fukuda, K.; Champagne, B. Third-Order Nonlinear Optical Properties of Asymmetric Non-Alternant Open-Shell Condensed-Ring Hydrocarbons: Effects of Diradical Character, Asymmetricity, and Exchange Interaction. J. Phys. Chem. C. 2016, 120, 11931207.


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(36) Villaume, S.; Daniel, C.; Strich, A.; Perera. S. A.; Bartlett, R. J. Quantum Chemical Study of the Electronic Structures of NiCH2+ in its Ground State and Low-Lying Excited States. J. Chem. Phys. 2005, 122, 044313. (37) Villaume, S.; Strich, A.; Ndoye, C. A.; Daniel, C.; Perera. S. A.; Bartlett, R. J. Quantum Chemical Study of the Electronic Structures of NiCH2+ in its Ground State and Low-Lying Excited States. J. Chem. Phys. 2007, 126, 154318. (38) Shigemoto, I.; Nakano, M.; Yamada, S.; Kiribayashi, S.; Yamanaka, S.; Yamaguch, K. Theoretical Studies on Nonlinear Optical Properties of Organometallic Conjugated Systems III: Second Hyperpolarizabilities of Mn(I)-Carbene Systems. Syn. Met. 1997, 86, 2241-2242. (39) Yamaguchi, K. Theory and Applications. In Self-Consistent Field; Carbo, R., Klobukowski, M., Eds.; Elsevier: Amsterdam, 1990; pp 727. (40) Cohen, H. D.; Roothaan, C. C. J. Electric Dipole Polarizability of Atoms by the Hartree—Fock Method. I. Theory for Closed‐Shell Systems. J. Chem. Phys. 1965, 43, S34S39. (41) Nakano, M.; Shigemoto, I.; Yamada, S.; Yamaguchi, K. Sizeconsistent Approach and Density Analysis of Hyperpolarizability: Second Hyperpolarizabilities of Polymeric Systems with and without Defects. J. Chem. Phys. 1995, 103, 4175-4191. (42) Nakano, M.; Fukui, H.; Minami, T.; Yoneda, K.; Shigeta, Y.; Kishi, R.; Champagne, B.; Botek, E.; Kubo, T.; Ohta, K. et al. (Hyper)polarizability Density Analysis for Open-Shell Molecular Systems Based on Natural Orbitals and Occupation Numbers. Theo. Chem. Acc. 2011, 130, 711-724; Erratum. Theo. Chem. Acc. 2011, 130, 725-726.


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(43) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision B.01; Gaussian, Inc.: Wallingford CT, 2010. (44) Sautret, C.; Hermann, J.-P.; Frey, R.; Pradére, F.; Ducuing, J.; Baughman, R. B.; Chance, R. R. Oprical Nonlinearities in One-Dimentional-Conjugated Polymer Crystals. Phys. Rev. Lett. 1976, 36, 956-959. (45) Hayes, E. F.; Siu, A. K. Q. Electronic Structure of the Open Forms of ThreeMembered Rings. J. Am. Chem. Soc. 1971, 93, 2090-2091. (46) Yamaguchi, K. The Electronic Structures of Biradicals in the Unrestricted HartreeFock Approximation. Chem. Phys. Lett. 1975, 33, 330-335. (47) Nakano, M.; Yamaguchi, K. A Proposal of New Organic Third-Order Nonlinear Optical Compounds. Centrosymmetric Systems with Large Negative Third-Order Hyperpolarizabilities. Chem. Phys. Lett. 1993, 206, 285-292.

TOC graphic

Second Hyperpolarizability (γ) of Metal− Carbon Bond H Mn(I)

C

H H

H

Mn(I)

Mn(I)

C

C

H

H

σ Electrons Govern γ


27


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M

C

Organic moieties

Ligand


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R

R

R

R

R


R


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

(a)

(b)

(c)

(d)


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Page 31 of 34


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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

(a)

(b)


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(a)

(b)

(c)

(d)

(e)

(f)



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Second Hyperpolarizability (γ) of Metal−Carbon Bond H Mn(I)

C

H H

H

Mn(I)

Mn(I)

C

C

H

σ Electrons Govern γ


H

Origin of the Enhancement of the Second Hyperpolarizabilities of

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