Multinuclear âStaircaseâ - ACS Publications

Subscriber access provided by UNIV OF DURHAM

Article 2

2

4

4

6

6

6

Multinuclear “Staircase” Oligomers Based on (EtCBH)Fe(#-CH)Sandwich Unit: Quantitative Tailorable and Redox Switchable Nonlinear Optics Hongqiang Wang, Li Wang, Yangyang Xia, Jin-Ting Ye, Hongyan Zhao, and Yongqing Qiu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b03834 • Publication Date (Web): 12 Jul 2017 Downloaded from http://pubs.acs.org on July 18, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 45

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

The Journal of Physical Chemistry

Multinuclear “Staircase” Oligomers Based on (Et2C2B4H4)Fe(η6-C6H6) Sandwich Unit: Quantitative Tailorable and Redox Switchable Nonlinear Optics

Hong-Qiang Wang,† Li Wang,† Yang-Yang Xia,‡ Jin-Ting Ye,† Hong-Yan Zhao*‡ and Yong-Qing Qiu*†

†

Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal University,

Changchun 130024, People’s Republic of China ‡

State Environmental Protection Key Laboratory of Wetland Ecology and Vegetation Restoration,

Northeast Normal University, Changchun 130024, People’s Republic of China

1

ACS Paragon Plus Environment


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 To provide a new approach for enhancing second order nonlinear optical (NLO) response, a series of multinuclear “staircase” oligomers composed of Fe(Et2C2B4H4) ferracarborane clusters and benzene rings have been systematically designed and investigated. The calculations of geometric and electronic structures, electronic absorption spectra, first hyperpolarizabilities and first hyperpolarizability densities were carried out by density functional theory and time-dependent density functional theory. It is found that the NLO properties have obvious multiple relationship with the numbers of sandwich unit. Moreover, all of the possibility for one-, two-, and three-electron oxide complexes have also been considered. The results firstly revealed some remarkable changes upon charge transfer pattern which is from the unexpected “interrupted” to desired “continuous” forms in the two-electron oxidation reactions, accompanied by significant differences in the relevant second-order NLO properties. The considerable “ON/OFF” switching ratios for the hyperpolarizability values declare that these multinuclear sandwich complexes can be deemed as high-efficiency redox-triggered NLO switches. Hence, we hoped that the conception and performance in our work will strongly provide a fundamental guideline and reference for further research for novel NLO materials.

2


Page 2 of 45

Page 3 of 45

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


1. INTRODUCTION Since the first scientific publication dealing with the production of second harmonic generation presented by Franken et al.,1-3 complexes with excellent second-order nonlinear optical (NLO) properties have received continuous attention for their potential applications in optical computing, optical data processing and storage, as well as electro-optical devices.4-6 During past several decades, it has been witnessed the progress that a surge of novel NLO materials have been designed theoretically and synthesized experimentally.7-12 Compared to inorganic counterparts, organic materials have lots of advantages such as faster response times, lower dielectric constants, and structural flexibility.13-16 Among them, organometallic complexes can provide metal-to-ligand or ligand-to-metal charge transfers (CT) because of the presence of redox-active metal center. This could be exploited in materials with switchable responses, which have been regarded as especially promising candidates.17-21 Nearly almost half a century, interests in the chemistry of carboranes and metallacarboranes have been extended to the electrical, magnetic and NLO properties since their first discovered and characterized in 1960s.22-26 However, compared to the most well-known and extensively studied example of closo-carborane like icosahedral ortho-, meta-, and para-C2B10H12, systematic studies of nido-carborane (nest-like) such as [C2B4H6]2– or [C2B9H11]2– and arachno-carborane (cobweb-like) such as [C2B3H5]4– are remain exceedingly rare up to now.27, 28 In the preceding publications, Russell N. Grimes and coworkers have described the synthesis of several families of 3



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

metallacarborane sandwich complexes like cobaltacarboranes and ferracarboranes, which covalently bound aryl- and alkynyl-linked polynuclear metallacarboranes that incorporate MC2B4 clusters (Scheme 1).29-35 Meanwhile, in these metallacarborane complexes, it has been demonstrate that the pyramidal Et2C2B4H42- carborane ligand has strong electron-donating properties. Hence, within individual sandwich unit (Et2C2B4H4)Fe(η6-C6H6), the electron density would flow from the ferracarborane cluster to the ferrocenyl moiety. Many studies have revealed that molecules containing donor-acceptor (D-A) framework as potential building blocks are usually able to form advanced NLO materials, which is mainly ascribed to the fact that the large charge transfer can cause a large difference between the ground-state and excited-state dipole moments and low energy charge transfer transition.36-38 In light of the above reports and appealing features, this kind of sandwich complexes are very promising to be utilized for designing novel smart NLO materials, which attracted our attention and stimulated our further research. Scheme 1. Representative reactions of the general procedure for the synthesis of ferracarborane sandwich complex

4


Page 4 of 45

Page 5 of 45

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


Unlike the rudimentary methods (i.e., increasing the donor/acceptor strength,39, 40 extending the length of the π-conjugated linker,41 introducing metal atom,38, 42 etc.) for enhancing NLO properties, in this work, we explore a novel design strategy which repeating the small individual sandwich unit 1 (Et2C2B4H4)Fe(η6-C6H6) through “series connection” mode for forming the “staircase” oligomers (two units as in D-A-D-A configuration, 2; three units as in D-A-D-A-D-A configuration, 3) (Figure 1). On the other hand, specially, it has been reported that this category of multinuclear metallacarborane complexes are sufficiently robust that they undergo multiple changes in metal oxidation state without structural disintegration.30, 32 Therefore, their oxide states 21+, 22+, 122+, 322+, 23+, 132+, 332+, 233+ and 433+ (for example: in complex 1 2+

3 , 1 means the spin multiplicity, 2+ means the valence.) were also prepared as a

counterpart to examine the possibility of redox switching of NLO response and attempt to cast light on some unexplained features of earlier studies. In this spotlight on applications, we performed density functional theory (DFT) to calculate the geometric

and

electronic

structures,

electronic

absorption

spectra,

first

hyperpolarizabilities and first hyperpolarizability densities of the complexes. We aimed at: (1) describing the variations of electronic structure with increasing the chain length; (2) discussing the feasibility of substantial expected CT pattern as D→A→D→A→D→A along with “staircase” during the electron transformation; (3) determining the dependence of first hyperpolarizability values on the numbers of sandwich structural unit; (4) exploring the effect of the electronic structure and NLO 5



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 6 of 45

properties in redox reaction. We hope that the present work is helpful for introducing a new gateway for further exploration of other excellent switchable NLO materials containing metallacarborane.

Figure 1. (a) Calculation models of the “staircase” complexes. (b) Optimized geometrical structure of complex 1 (Hydrogen atoms are omitted for clarity. Ct1 is the centroid of the C2B3 ring, while Ct2 is the centroid of the benzene ring).

2. COMPUTATIONAL DETAILS The geometry optimizations of all the complexes were performed by the Becke three-parameter exchange with Lee-Yang-Parr correction functional (B3LYP).43,

44

Equilibrium structures were confirmed to be global minima of the potential energy surface by evaluating harmonic vibrational frequencies. The calculated values of 6


Page 7 of 45

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


for the square of total spin were quite close to their eigenvalue (Table S1 in the Supporting Information), which suggests that the spin contamination is minor in an acceptable range. The 6-31G(d) basis set was adopted for C, B and H atoms and Stuttgart/Dresden double-ζ (SDD)45 basis set for Fe atom. In order to obtain more accurate geometry, the solvent effect has been taken into account and modeled using the integral equation formalism variant of the polarized continuum model (IEFPCM).46-48 Dichloromethane solvent was selected for reproduce the experimental results. Natural bond orbital (NBO) calculation was then calculated at the abovementioned level to obtain the natural population analysis (NPA) charge of the studied complexes. When it comes to the calculation of the hyperpolarizability, choosing a proper method is of great importance. The coupled cluster method such as CCSD(T)49 are known to be extremely accurate for calculating hyperpolarizabilities. However, the expense of its computational effort can be feasible for only some small- and medium-sized systems. It is commonly believed that DFT can be alleviated this deficiency owing to its desired compromise between computational efficiency and accuracy. But, the calculated β values of the DFT results are functional-dependent, which is due to their different exchange-correlation potentials.50-52 Hence, in the present discussion, the conventional hybrid functionals containing different HF exchange weighting B3LYP (20%), PBE1PBE (25%),53,

54

BHandHLYP (50%),55

M062X (54%)56 and the range-separated (RSE) exchange functionals CAM-B3LYP and ωB97XD were employed with the 6-31+G(d,p)/SDD basis set to check the 7



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 8 of 45

consistency of our calculations. The CAM-B3LYP functional, which adds a long-range correction using the Coulomb-attenuating method and includes 19% and 65% of short- and long-range HF exchange.57 The ωB97XD functional is the latest functional from Head-Gordon and Chai, which includes 100% long-range exact exchange, a small fraction (about 22%) of short-range exact exchange.58 In the present work, the first hyperpolarizabilities of all complexes were evaluated by the analytical coupled

perturbed

Hartree-Fock

(CPHF)

method

and

its

DFT

analogue

(coupled-perturbed Kohn-Sham, CPKS) due to its accuracy and economical efficiency.59-61 According to Kleinman’s symmetry conditions,62 the 27 components of the 3×3×3 matrix for β can be reduced to 10 components. All reported hyperpolarizabilities are given within the T convention63 as defined in ref. 63 expressed by Willetts et al. The total static first hyperpolarizablity βtot was calculated using the following equation:

β tot = (β x2 + β y2 + β z2 )

12

(1)

where individual static component β i was defined as:

βi = βiii +

1 ∑[(βijj + β jij + β jji )] 3 i≠ j

i , j = x, y , z

(2)

To obtain more insight on the description of the electronic structure and further probe the second-order NLO properties of the studied complexes, time-dependent density functional theory (TD-DFT) method was performed to describe their electronic spectra. In recent years, the TD-DFT method has emerged as a powerful

8


Page 9 of 45

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


tool for understanding and predicting the behavior of electronic transition properties in quantum chemistry owing to its efficiency and accuracy.64-66 The PBE1PBE functional has been shown to improve the accuracy of excitation energies and CT bands for both gas phase and solution calculations.67, 68 Hence, the vertical electronic transition energies between the ground and excited states were calculated using TD-PBE1PBE. All the DFT and TD-DFT calculations were carried out using Gaussian 09W computational chemistry program package.69

3. RESULTS AND DISCUSSION 3.1. Geometric and Electronic Structures. The optimized structures in the ground states of all complexes were obtained at (U)B3LYP/6-31G(d)/SDD level. We compared the optimized geometry of complex 1 with its X-ray crystallographic data70 and semi-empirical PM3 calculated results33 in the Russell N. Grimes’s work, while the equilibrium structure and more relevant geometric parameters were proposed in Figure 1 and Table S2 (shown in Supporting Information). The absolute deviation of primary bond lengths, distances (d1, d2 and d3), as well as the bond angle Ct1-Fe-Ct2 (Ct1: the centroid of the C2B3 ring, Ct2: the centroid of the benzene ring.) between the calculated and experimental data is 0.001-0.035 Å, 0.028-0.042 Å, and 0.8°, respectively. The values are also in favorable agreement with the available analysis obtained by PM3 semi-empirical methods but much more accurate than them, which are 0.017-0.057 Å, 0.011-0.138 Å, and 2.7°, respectively. These results clearly demonstrate that the geometrical calculations are 9



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

reliable for the current systems. NBO analysis has been performed on the optimized complexes to get insight into the concentration or depletion of atomic charge on different atom centers (Table 1). For complex 1, the carborane (1Cb) and Fe (1Fe) fragments are negatively charged, whereas the net charge on benzene (1Ph) fragment is positive. It indicates that the carborane and Fe fragments display the electron donor character, and benzene fragment displays the electron acceptor character, which is paralleling with earlier electrochemical publication.71 When comes to complex 2, notably, the NPA charges have a very trivial difference in comparison to complex 1 except for the 1Ph and 2Cb fragments. The values of 1Ph fragment and 2Cb fragment sharply decreased and increased, respectively. It suggests that there is a strong interunit interaction in the link area and obviously electron-delocalization behavior between the sandwich units. This phenomenon can also be found in complex 3 (between the 1Ph and 2Cb, 2Ph and 3Cb parts). From another perspective, turning our attention to the values of different sandwich units, the region of more negative charge is found on unit I for complexes 2 and 3 (-0.327 and -0.333 e). In contrast, the net positive charge is mostly located on the unit II (0.327 e for complex 2) and unit III (0.331 e for complex 3). It reveals that increasing the sandwich units can obviously enlarge the amplitude of charge distribution.

10


Page 10 of 45

Page 11 of 45

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


Table 1. The NPA charges (e) of complexes 1-3 at the B3LYP/6-31G(d)/SDD level in dichloromethane solution complex

1 2 3 a

unit I a

unit II

1Cb 1Fe 1Ph -0.251 -0.361 0.612 -0.302 -0.319 0.294 (-0.327)b -0.309 -0.315 0.291 (-0.333)

2Cb

2Fe

unit III 2Ph

-0.337 0.631 (0.327) -0.018 -0.291 0.311 (0.002)

3Cb

3Fe

3Ph

0.033

0.030 -0.334 0.636 (0.331)

Cb, Fe, and Ph are the carborane, Fe atom, and benzene fragment,respectively. 1, 2, and 3 mean the number of

different units. b

The NPA charges for each unit are given in the parentheses.

The quantitative analysis of electrostatic potential (ESP) used in Bader charge model72 on the van der Waals (vdW) surface has also been performed in order to gain a more intuitive insight into the nature of charge distribution. As depicted in Figure 2, the primary area with more negative charge is mainly on carborane moieties, whereas the net positive charge is largely found on the last benzene moieties. As we all know, the dipole moment (µ) is primarily associated with the electric quantity of positive/negative charge center (q) and distance (l) between them. Hence, the large and long-range charge distribution will produce the huge dipole moment values. Complexes 2 and 3 present a very huge µtot values as large as 18.96 and 30.03 Debye, which is 2.2 and 3.6 times with respect to complex 1 (8.41 Debye) (Table S3). This tremendous quantity can offer a great possibility of large long-range intramolecular charge transfer during electronic excitation. Hence, the dipole moment is more directly related to the NLO properties and can be a valid indicator for the first

11



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

hyperpolarizabilitiy.

Figure 2. ESP distributions and corresponding dipole moments of complexes 1-3 (Red regions represent negative charge, while blue regions represent positive charge).

3.2. Analysis of Density States. For the purpose of more detailed study of the relationship between the electronic properties and geometric structures, the total density of states (TDOS) and projected partial density of states (PDOS) calculations have been carried out. As described in Figure 3, for the three complexes, the carborane and Fe moieties play a significant role in the formation of the highest occupied molecular orbital (HOMO). However, for the lowest unoccupied molecular orbital (LUMO), the Fe and benzene moieties are the mainly contribution. The phenomenon elucidates that the electron density is 12


Page 12 of 45

Page 13 of 45

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


flow from the ferracarborane cluster to the ferrocenyl moiety. From another point of view, for complex 2, the PDOS of unit I possesses a huge proportion in the HOMO, whereas unit II gives the major formation of LUMO. A similar situation can be also found in complex 3. The proportion of PDOS for different units in HOMO and LUMO are in the order of I > II > III and III > II > I, respectively, which is in close agreement with the Mulliken populations of their frontier molecular orbitals (Figure S1 in Supporting Information). The tremendous different distribution between HOMO and LUMO can result in a long-range intramolecular charge transfer transition from unit I to unit II or III along with the “staircase” molecular structure. It is our expected that this pronounced charge transfer may produce a significant enhancement for the first hyperpolarizability. Furthermore, it is generally believed that the energy gap (Egap) between the HOMO and LUMO can affect the NLO properties. The Egap results for complexes 1-3 decreased in the following order: Egap(1) > Egap(2) > Egap(3) (Figure 3). It suggests that the Egap can be significantly narrowed by adding the number of sandwich unit, further predicting that the relevant βtot values may gradually increased from complex 1 to 3.

13



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

Figure 3. Total density of states, partial density of states and the frontier molecular orbital energy levels for complexes 1-3.

3.3. Absorption Spectrum. For the purpose of obtaining a more comprehensive description of the electronic absorption spectra and the origin of second order NLO properties, a detailed study has been carried out about the crucial transitions in dichloromethane solution with TD-PBE1PBE/6-31G (d, p)/SDD method. For all the studied complexes, the origin of the Cartesian coordinate system is located at the center of benzene ring of unit I. And the xy-plane is placed in the benzene ring with the longitudinal y axis points to C-H or C-B bond (Figure 1). The simulated UV− vis absorption spectra of complexes 1-3 along with charge density difference (CDD) maps corresponding to the crucial 14


Page 14 of 45

Page 15 of 45

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


electronic transitions are depicted schematically in Figure 4. In single-electron

Figure 4. Absorption spectra of complexes 1-3 along with CDD maps corresponding to the crucial excited states. (Yellow color represents negative value, while blue color represents positive value.)

excitation process, hole distribution denotes the region where an electron leaves, whereas electron distribution means where it goes to. The CDD between excited state ele hole ele and ground state is evaluated as: ∆ρ (r ) = ρ (r ) − ρ (r ) , where ρ (r ) and

ρ hole(r ) represent the density of hole and electron distribution respectively. Hence, negative value (yellow colors) and positive value (blue colors) suggest the depletion and accumulation of electron density, respectively. Moreover, excited state transition

15



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

energies ( ∆E ge ), simulated wavelengths (λ), oscillator strengths ( f os ), variation of dipole moment between ground and excited state ( ∆µ ge ) and major molecular orbital contributions calculated for the crucial singlet excited states have been summarized in Table 2.

Table 2. Excited state transition energies ( ∆E ge , eV), simulated wavelengths (λ, nm), oscillator strengths ( f os ), variation of dipole moment between ground and excited state ( ∆µ ge , a.u.), and major molecular orbital contributions of the studied complexes calculated by TD-PBE1PBE method in dichloromethane solution complex

state

∆E ge

λ

f os

∆µ ge

1

S13

4.82

257.1

0.1649

2.92

S22

5.40

229.8

0.1377

3.44

H-1→L+2 (25%), H-3→L (17%), H→L (12%), H-2→L+1 (10%), H→L+3 (11%) H-3→L+3 (60%), H-5→L (14%)

S22

4.18

296.7

0.0791

7.94

H→L+1 (56%), H-1→L (8%)

S34

4.84

256.4

0.2068

5.62

H-3→L (32%), H-1→L+3 (8%), H-1→L+6 (8%)

S30

4.10

302.2

0.2744

3.70

H-8→L (12%), H-5→L (12%), H-2→L (10%)

S45

4.60

269.7

0.3411

3.79

H-1→L+3 (12%), H-4→L (8%), H-10→L+3 (8%), H-1→L+6 (7%)

2

3

a

major contributiona

Assignment: H = HOMO, L = LUMO, H-1 = HOMO−1, L+1 = LUMO+1, etc.

As depicted in the Figure 4, the simulated absorption spectra of complex 1 contains one high energy electronic transition absorbing at 229.8 nm along with a low-energy absorption band with maximal oscillator strength located at 257.1 nm. The transition state of S13 (257.1 nm) is composed of HOMO-1→LUMO+2, 16


Page 16 of 45

Page 17 of 45

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


HOMO-3→LUMO,

HOMO→LUMO,

HOMO→LUMO+3

and

HOMO-2→LUMO+1 excitations, respectively. The HOMO-1 is delocalized on dx2-y2 orbital of metal Fe, whereas the LUMO+2 is dxy character at Fe atom and antibonding combinations π* orbital of the benzene ligand (Figure S2 in Supporting Information). Hence, this excitation can be designated as d-d transitions and metal to ligand charge transfer (MLCT) from Fe atom to benzene ring. The other HOMOs in this state are mainly located at the carborane fragment with slightly dxy orbital at the metal Fe, whereas the LUMOs are located on benzene fragment with slightly dxz orbital of Fe, reflecting obviously ligand (carborane) to ligand (benzene) charge transfer (LLCT) combined with slightly d-d transitions. The electronic transition state (S22) absorbing at 229.8 nm is assigned to HOMO-3→LUMO+3 and HOMO-5→LUMO. The HOMO-3 and HOMO-5 exhibit the delocalization on carborane and Fe (dxy orbital character), whereas the LUMO+3 and LUMO are largely delocalized on benzene ring and Fe (dxz orbital character). Hence, this transition state can be also mainly described as LLCT and d-d transition. According to the CDD, both of the low-energy and high-energy electronic transitions can be viewed as intramolecular CT transition from ferracarborane cluster to the ferrocenyl moiety along the z axis, which is in line with the discussion implied above. The unidirectional CT pattern means that, for complex

1, the βz value would be relatively large and as the principal component with respect to rest tensorial components (will be elaborated later). Coming to complex 2, the absorption spectrum exhibits one strong absorption peak along with a weak shoulder peak. The CDD map of the low-energy electronic 17



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 18 of 45

transition located at 296.7 nm shows that there is a substantial flow of electron density from unit I to unit II. The same results can be also found in the molecular orbital configurations (Figure S3). The other major electronic transition with maximal oscillator strength absorbing at 256.4 nm is associated with HOMO-3→LUMO, HOMO-1→LUMO+3, and HOMO-1→LUMO+6 excitations, respectively. Taking into account of the shape of HOMOs and LUMOs, the HOMO-1 is mainly located on dx2-y2 orbital of metal Fe, while the LUMO+3 and LUMO+6 are largely delocalized on benzene ring as antibonding combinations π* orbital, accounting for the MLCT. However, when comes to HOMO-3→LUMO excited transition, the CT pattern is mainly from the ferracarborane fragment of unit I and II to the link area (C-B bond). It indicates that there is an unexpected electronic transition pattern along the negative direction of y axis which breaks the “CT continuity” along with “staircase” construction.

This

opposite

CT

direction

also

clearly

reflects

the

electron-delocalization behavior between the two sandwich units presented in the NPA charge distribution on 1Ph and 2Cb moieties. With regard to complex 3, the simulated absorption spectrum is quite similar to complex 2, containing one strong absorption peak with maximal oscillator strength as well as a weak shoulder peak. From the CDD maps, both of the two crucial excited states show that the intramolecular CT from carborane and Fe fragment to benzene ring. However, it is not sufficient to determine whether the electronic transitions occurred within the two adjacent units or between the conjoint benzene and carborane moieties. The low-energy, less intense electronic transition at 302.2 nm arises mainly 18


Page 19 of 45

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


from HOMO-8→LUMO, HOMO-5→LUMO and HOMO-2→LUMO, respectively. According to the relevant shape of the MOs (Figure S4), the electronic transitions could be assigned as a CT pattern from ferracarborane moieties for unit I and II to the conjoint area between unit II and III along with slightly opposite CT from Fe atom on unit III to the area. For the most intense absorption peak at 269.7 nm, HOMO-1→LUMO+3 and HOMO-10→LUMO+3 can be assigned as LLCT from ferracarborane to the ferrocenyl moiety. Additionally, the HOMO-4→LUMO and HOMO-1→LUMO+6 electronic transitions exhibit a similarly opposite MLCT and LLCT between the related two adjacent units along the negative direction of y axis, which can also be confirmed by NPA charge discussion in the 3.1 section. From what has been discussed above, the electronic transitions for the three complexes are generally assigned as mixed charge transfer for LLCT, MLCT and d-d excited transition type, in which the ferracarborane moieties displays the electron donor character and the ferrocenyl moieties act as electron acceptor. With increasing chain length, there is a much more obvious CT transition, which indicates that the first hyperpolarizability values will be enhanced effectively. However, for the “staircase” oligomers (complexes 2 and 3), the electron transformation is largely as the D→A←D→A←D→A model of a “interrupted” form which is conflict with the early idea of us for D→A→D→A→D→A unidirectional and sequential CT form along with “staircase” construction. This interesting phenomenon inspired us to further investigate the first hyperploarizabilites of these di- and trinuclear sandwich complexes. 19



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 20 of 45

3.4. First Hyperpolarizability of Neutral Complexes. As the aforementioned speculation, multinuclear “staircase” oligomers have much more obvious charge transfer character in comparison to the original individual sandwich unit, which is associated with remarkably large first hyperpolarizabilities. The second-order NLO properties for the neutral states of these complexes were discussed in this section. In order to accumulate experience on the performance of different approaches in influencing the first hyperpolarizability, the computed values using B3LYP, PBE1PBE, BHandHLYP, M06-2X, CAM-B3LYP and ωB97XD functionals with the same basis set have been summarized in Table S4. At first glance, in the case of βtot values, M06-2X method provides broadly consistent trend and the largest results with respect to other functionals (Figure 5, noteworthy is that 1 a.u. = 8.639 × 10-30 esu for β value). Additionally, the results calculated by the RSE functionals (CAM-B3LYP and ωB97XD) are smaller as compared with the global hybrid functionals (B3LYP, PBE1PBE, BHandHLYP and M06-2X). It is due to that there is an overestimation when predict the amplitude of hyperpolarizability by traditional DFT functionals. This overestimated influence can be removed by the long-range corrected functionals effectively.73, CAM-B3LYP

and

ωB97XD

are

better

74

Hence, RSE functionals such as

choices

to

calculate

the

first

hyperpolarizabilities and produce reasonable βtot values in our case. Moreover, it is worthy of note that different functionals have almost no significant influence on the hyperpolarizabilities. The increased tendency of βtot values agree well with each other. To discuss these results in more detail, in the present paper, the following relevant 20


Page 21 of 45

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


computations and illustrations of the first hyperpolarizabilities for the studied complexes are completely based on the reliable CAM-B3LYP functional.

Figure 5. Comparison of the total static first hyperpolarizabilities (βtot) of complexes 1-3 computed at various levels of theory.

Turning our attention to the magnitude of the hyperpolarizability results (Table 3), as expected, the βtot values of complexes 1-3 increase as the order of βtot (1) < βtot (2) < βtot (3), in keeping with the previous conjecture from density states and absorption spectrum characteristic analysis. Among them, complexes 2 and 3 present the βtot values as 18.3 × 10-30 esu and 28.5 × 10-30 esu, which is almost 2.1 and 3.3 times compared to complex 1 (8.6 × 10-30 esu). This fact demonstrates that the βtot values can be adjusted regularly by controlling the numbers of sandwich unit, which increased as approximate 10 × 10-30 esu for each unit. For deep understanding the origin of the second-order NLO responses, perspective was taken from the tensorial 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

components. The diagonal tensorial components βyyy (for complex 2 and 3) and βzzz are the dominant ones (Table S4), leading inevitably to the large βy and βz total components. For complex 1, the βtot is determined by only one component βz, because of the intramolecular charge transfer can be almost seen as unidirectional along the z axis. When come to complexes 2 and 3, we can seen that βz possess the largest values and βy as the second largest gains, suggesting that the intramolecular charge transfer degree occurring along the z axis is more obvious than the y direction. From another point of view, the sign of βy and βz total components are positive, elucidating that during a polarization process electronic transition is parallel to the z- and y- direction identical to the corresponding CDD maps. In addition, the tendencies of both βy and βz values are in close agreement with that of βtot. And, the magnitudes of the βz are nearly equal to the βtot values which is further verified the βz total components dominate the NLO response in such materials. Another interesting phenomenon bearing mention is that the variations for βy and βz show obvious connection with the numbers of sandwich unit. The βz values for two and three units are almost 2 and 3 times as large as that of one unit. And the βy value for three units is about 2 times larger as compared to the two units. Summarized the content of the above discussion, the first hyperpolarizabilities of the multinuclear sandwich complexes can be significantly modified by connecting the small sandwich unit via the “series connection” mode.

22


Page 22 of 45

Page 23 of 45

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


Table 3. Components of first hyperpolarizabilities (10-30 esu) and total first hyperpolarizabilities (10-30 esu) of the studied complexes computed at the CAM-B3LYP/6-31+G(d,p) (SDD for Fe atom) level in dichloromethane solution complex 1 2 + 1 2 2 + 2

βy

βz

βtot

ra

0.5 0.2 0.4 -0.4

2.5 3.9 7.5 25.9

8.2 2.8 16.7 1.9

8.6 4.8 18.3 26.0

1 2+

178.3

2215.1

-1399.3

2626.1

143.9

3 2+

2 3 2 + 3

-1.3 0.9 7.6

-0.2 17.2 56.7

16.6 22.7 -6.1

16.7 28.5 57.5

0.9

1 2+

-144.7

20647.3

-15997.4

26119.9

916.6

3 2+

3

2.6

25.7

17.4

31.2

1.1

2 3+

3

-3.8

19.4

-7.4

21.1

0.7

4 3+

8.1

23.1

-18.8

30.9

1.1

2

3

3

a

βx

0.6 1.4

2.0

The ratio r is defined as βtot(oxide state)/βtot(neutral state).

3.5. Second Order NLO Switch Induced by Redox Stimuli. As mentioned above, these multinuclear sandwich complexes are very promising candidates for NLO switches, because they can provide unique reversible redox properties. This inspired us to further investigate the first hyperpolarizabilities for their oxide complexes. The total electronic energies containing zero-point correction of the studied complexes have summed in Table S5. (It is worthy of note that conversion relations for energy is 1 a.u.= 627.51 kcal/mol). The differences of the energies under the same valence and various spin multiplicity are almost 1.18, 25.96 and 17.79 kcal/mol, respectively, indicating the statistical distribution of two possible

23



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 24 of 45

spin states. Hence, we have considered all of the possibility and listed the βx, βy, βz and βtot values of complexes 21+, 22+, 122+, 322+, 23+, 132+, 332+, 233+ and 433+ (Table 3). Inspection of the βtot results, all of the oxide complexes have little changes except for complexes 122+ and 132+, which produced very huge βtot values as 2626.1 × 10-30 esu and 26119.9 × 10-30 esu. Hence, we mainly focused on the detailed electrochemical studies of relative properties for the two singlet states in the following discussions. It can be found that unlike their neutral species, the βyyy, βyzz, βzzz, and βyyz are the primary tensorial components (Table S6), leading to the large βy and βz values. The absolute values for βy are lager than that of βz, suggesting the contributions of charge transfer along the y axis are dominant ones. In addition, a further observation of interest is that the sign of total components βz have become negative compared with the positive values of neutral species, which predicts the significantly

changes

happened

on

charge

transfer

direction

in

the

two-electron-oxidized forms. Furthermore, it is worth noting that the β-ratio defined as βtot(oxide state)/βtot(neutral state) are as huge as 143.9 and 916.9 for complexes 122+ and 132+. Therefore, the neutral state forms are regarded as the nonlinearity “OFF”, and the two-electron-oxidized state complexes are related to the nonlinearity “ON”, which a combination of remarkable NLO switchable behaviors. Taken together, we can judge that this kind of multinuclear “staircase” complexes can be the novel excellent molecular switches of NLO responses and potential building blocks for advanced electronic materials, especially for 3/132+. To elucidate the original variation of NLO response, we also considered the 24


Page 25 of 45

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


difference of CT transition between the neutral and oxide species associated with the crucial excited states. Relative parameters of TD-DFT calculation are summarized in Table S7. Clearly, for both of the two-electron-oxidized forms, the HOMOs are mainly located at the ferracarborane moieties of the last unit (II or III) acted as the electron donor (Figure 6). The electron densities of LUMOs delocalize over the ferracarborane moieties of the front unit (unit I for complexes 122+, whereas unit I and II for complexes 132+) as the electron acceptor character, and the benzene ring display as conduits for electron delocalization between units. Consistent results can also be found in CDD maps. In order to strengthen the comparability, we also proposed the CDD maps of the crucial electronic transitions of triplet complexes 322+ and 332+ in Figure S5. It is a conspicuous different CT pattern compared to the neutral and triplet species. Notably, in this process, the CT pattern is a unidirectional and sequential model along with “staircase” construction (Figure 7). The exact “continuous” long-range charge transfer will significantly enhance their first hyperpolarizabilities. This interesting observation indicates that the CT continuity dependence on the NLO response would be a significant topic worthy of inquiry.

25



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

Figure 6. The MOs (a) along with relative CDD maps (b) of the crucial electronic transitions of complexes 122+ and 132+.

Figure 7. Comparison of CT patterns between the neutral states (2/3) and two-electron-oxidized species (122+/132+ and 322+/332+). (Yellow arrows represent the CT along the z-axis, while blue arrows represent the CT along the y-axis.)

26


Page 26 of 45

Page 27 of 45

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


There is another approach to evaluate the first hyperpolarizability that originates from perturbation theory approaches. Oudar and Chemla have proposed a simple link between the β and CT transition through the well-known two-level expression,75, 76 which has been often used by experimentalists to presage the first hyperpolarizability amplitudes. According to the approximately two-level model, the β value is mainly dependent on three important factors: the oscillator strength ( f os ), the variation of dipole moment between ground and excited state ( ∆µ ge ) and excited state transition energies ( ∆E ge ).

β ∝ ∆µ ge

f os 3 ∆E ge

(3)

It is well known that oscillator strength is proportional to the transition energy and

(

)

2 transition dipole moment f os = 8πme 3e 2 h ∆E ge µ ge , which is the key factor in

decision of β values.21 Therefore, the electronic transition with the maximal oscillator strength was considered to be the main electronic transition with major contribution to NLO responses. To shed light on the molecular structure-NLO property relationship in our case, relevant parameters can be obtained from Table 2 and S7. As expected, to some extent, all the f os ∆µ ge ∆E ge3 values qualitatively reproduce a large part of βtot results of the studied complexes. The monotonic dependence of the first hyperpolarizabilities on the f os ∆µ ge ∆E ge3 values visualized in Figure 8, further supporting that the intense absorption states noted by us make major contributions to the NLO response.

27



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 28 of 45

Figure 8 Relationship between the βtot values (blue square) and the corresponding f os ∆µ ge ∆E ge3 values (purple pentacle) for the five complexes.

3.6. First Hyperpolarizability Density Analysis. To further address the spatial contributions of electrons to the first hyperpolarizabilities, the first hyperpolarizability density analysis was performed in this section. The β density, ρyy and ρzz, are defined according to equation (3):77-79 ρ yy (r ) = ( 2)

∂ 2 ρ (r ) 2 ∂Fy

F =0

ρ zz ( 2) (r ) =

∂ 2 ρ (r ) 2 ∂Fz

F =0

(3)

And the β values are given by equation (4): 1 2 1 β yyz = − ∫ − ρ（yy2）(r )zdr 2

β yyy = − ∫ − ρ（yy2）(r ) ydr

1 2 1 = − ∫ − ρ（zz2）(r )ydr 2

β zzz = − ∫ − ρ（zz2）(r )zdr β yzz

28


(4)

Page 29 of 45

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


Figure 9. Plots of the − yρ yy( 2 ) (a) and − zρ zz( 2) (b) for the neutral complexes 1-3. (Orange color represents positive value, while cyan color represents negative value.)

In order to offer more intuitive insight about contribution to the primary tensorial components, the plots of − yρ yy( 2 ) , − zρ zz( 2) , − yρ zz( 2 ) , and − zρ yy( 2 ) together with corresponding β values for the neutral complexes 1-3 and the singlet states of two-electron-oxidized complexes

1 2+ 1 2+

2 /3

are proposed in Figure 9 and 10,

respectively. The local contribution can be decomposed as a pair of positive (orange region) and negative (cyan region) parts. In the case of the neutral complexes (Figure 9), the positive contribution of − yρ yy( 2 ) function is principally located on the unit II and III parts. The positive contribution of − zρ zz( 2) function is mainly distributed in the ferracarborane moieties of unit I and the benzene rings of unit II and III. Notably, the − yρ yy( 2 ) function of complex 1 shows significantly smaller amplitudes of the

29



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

positive and negative contribution. The two contributions are almost canceled by each other, and hence present the smallest positive βyyy value (only 1.3 × 10-30 esu). Moreover, the specific localization of positive contribution prevailing over negative parts. Thus, the primary components βyyy and βzzz are positive values. On the other hand, with increasing the sandwich units, the area of positive contribution amplitude going much larger. It is not surprising that the β values would be enhanced subsequently. For the two-electron-oxidized complexes 122+/132+ (Figure 10), the large positive contributions of − yρ yy( 2 ) and − yρ zz( 2 ) function enveloping the left side of unit I and unit III moieties, which is larger with respect to the negative parts. In contrast, the region of negative contributions dominate the − zρ zz( 2) and − zρ yy( 2 ) function. This interpretation undoubtedly presents the large positive βyyy, βyzz and negative βzzz, βyyz values. Therefore, the difference between the positive/negative β density distributions can be an efficient approach to exemplify the relative amplitudes of the β values.

30


Page 30 of 45

Page 31 of 45

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


Figure 10. Plots of the − yρ yy( 2 ) , − zρ zz( 2) , − yρ zz( 2 ) , and − zρ yy( 2 ) for complexes 1 2+

2 (a) and 132+ (b). (Orange color represents positive contribution, while cyan color represents negative contribution.)

4. CONCLUSIONS In this work, a series of novel “staircase” oligomers incorporating mono-, di- and tri-nuclear Fe(Et2C2B4H4) ferracarborane clusters connected by benzene ring have been systematically designed and investigated by quantum chemical calculations. We proposed a new strategy by means of repeating sandwich unit via “series connection” mode to effectively manipulated and modified the electronic and NLO properties. Correlating electrochemical calculations demonstrated that increasing sandwich units can obviously enlarge the amplitude of charge distribution and narrow the energy gap between HOMO and LUMO. More interestingly, the first hyperpolarizabilities are significantly dependent on the numbers of sandwich unit as a multiple relationship,

31



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

that is, the βtot values grown by 10 × 10-30 esu for each unit. It is indicating that for this class of multinuclear complexes having three or more units, linked-sandwich oligomers or polymers, the NLO properties can be effectively optimized by controlling their relative sandwich units. On the other hand, some important electronic properties changes during reversible redox process which are accompanied by drastically variation in the relevant second-order NLO responses. It has been established that the variation is due to the change in their charge transfer pattern from the unexpected “interrupted” to desired “continuous” forms. The “ON/OFF” switching ratio are as large as 143.9 and 916.9 for complexes 2/122+ and 3/132+. Considering these predictions and results, these multinuclear sandwich complexes would be well suited as potential building blocks for excellent switchable NLO materials. In perspective, to obtain more efficient and stable switching behaviors, introducing groups or other approaches for achieve the much more stable singlet state of such kind of two-electron-oxidized complexes is extremely interesting and will be researched in a forthcoming work.

ASSOCIATED CONTENT Supporting Information. Calculated square of total spin. Geometric parameters of calculated and experimental values for complex 1. Dipole moments, first hyperpolarizability tensor components and total first hyperpolarizabilities at various levels of theory. Total electronic energies containing zero-point correction. TD-DFT calculated results of complexes 122+, 322+, 132+ and 332+. Optimized geometrical structure of complex 1. Frontier molecular orbital diagram. Molecular orbitals and

32


Page 32 of 45

Page 33 of 45

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


charge density difference maps involved in the electronic transitions.

AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] (Y. Q. Qiu) Telephone: +86 0431 85099291 [email protected] (H. Y. Zhao)

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS The authors gratefully acknowledge the National Natural Science Foundation of China (No.41471165), the Education Department of Jilin Province (No. 2016506) and the “12th Five-Year” Science and Technology Research Project of the Education Department of Jilin Province ( [2016] 494).

REFERENCES (1) Franken, P. A.; Hill, A. E.; Peters, C. W.; Weinreich, G. Generation of Optical Harmonics. Phys. Rev. Lett. 1961, 7, 118-119. (2) Bass, M.; Franken, P. A.; Ward, J. F.; Weinreich, G. Optical Rectification. Phys. Rev. Lett. 1962, 9, 446-448. (3) Franken, P. A.; Ward, J. F. Optical Harmonics and Nonlinear Phenomena. Rev. Mod. Phys. 1963, 35, 23-39.

33



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

(4) Bloembergen, N. Organic Technology. Science 1994, 264, 448. (5) Marder, S. R. Organic Nonlinear Optical Materials: Where We Have Been and Where We Are Going. Chem. Commun. 2006, 131-134. (6) Zyss, J.; Ledoux, I. Nonlinear Optics in Multipolar Media: Theory and Experiments. Chem. Rev. 1994, 94, 77-105. (7) Eaton, D. F. Nonlinear Optical Materials. Science 1991, 253, 281-287. (8) Laidlaw, W. M.; Denning, R. G.; Verbiest, T.; Chauchard, E.; Persoons, A. Large Second-Order Optical Polarizabilities in Mixed-Valency Metal Complexes. Nature

1993, 363, 58-60. (9) Coe, B. J. Switchable Nonlinear Optical Metallochromophores with Pyridinium Electron Acceptor Groups. Acc. Chem. Res. 2006, 39, 383-393. (10) Chen, W.; Li, Z. R.; Wu, D.; Li, Y.; Sun, C. C.; Gu, F. L. The Structure and the Large Nonlinear Optical Properties of Li@Calix[4]pyrrole. J. Am. Chem. Soc. 2005, 127, 10977-10981. (11) 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, 1094-1098. (12) Wang, W. Y.; Kan, Y. H.; Wang, L.; Sun, S. L.; Qiu, Y. Q. Large Nonlinear Optical Responses of Dimers Bearing a Donor and Acceptor: Long, Intradimer Multicenter Bonding. J. Phys. Chem. C 2014, 118, 28746-28756. 34


Page 34 of 45

Page 35 of 45

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


(13) Dalton, L. R.; Sullivan, P. A.; Bale, D. H. Electric Field Poled Organic Electro-optic Materials: State of the Art and Future Prospects. Chem. Rev. 2010, 110, 25-55. (14) Kuzyk, M. G. Using Fundamental Principles to Understand and Optimize Nonlinear-Optical Materials. J. Mater. Chem. 2009, 19, 7444-7465. (15) Gieseking, R. L.; Mukhopadhyay, S.; Risko, C.; Marder, S. R.; Brédas, J. L. 25th Anniversary Article: Design of Polymethine Dyes for All-Optical Switching Applications: Guidance from Theoretical and Computational Studies. Adv. Mater.

2014, 26, 68-84. (16) Wang, L.; Ye, J. T.; Chen, H.; Chen, Z. Z.; Qiu, Y. Q.; Xie, H. M. A Structure-Property Interplay Between the Width and Height of Cages and the Static Third Order Nonlinear Optical Responses for Fullerenes: Applying Gamma Density Analysis. Phys. Chem. Chem. Phys. 2017, 19, 2322-2331. (17) Di Bella, S. Second-Order Nonlinear Optical Properties of Transition Metal Complexes. Chem. Soc. Rev. 2001, 30, 355-366. (18) Coe, B. J.; Foxon, S. P.; Helliwell, M.; Rusanova, D.; Brunschwig, B. S.; Clays, K.; Depotter, G.; Nyk, M.; Samoc, M.; Wawrzynczyk, D., et al. Heptametallic, Octupolar Nonlinear Optical Chromophores with Six Ferrocenyl Substituents. Chem. - Eur. J. 2013, 19, 6613-6629. (19) Wang, W. Y.; Ma, N. N.; Sun, S. L.; Qiu, Y. Q. Impact of Redox Stimuli on Ferrocene-Buckybowl Complexes: Switchable Optoelectronic and Nonlinear Optical Properties. Organometallics 2014, 33, 3341-3352. 35



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 36 of 45

(20) Muhammad, S.; Xu, H. L.; Janjua, M. R.; Su, Z. M.; Nadeem, M. Quantum Chemical Study of Benzimidazole Derivatives to Tune the Second-Order Nonlinear Optical Molecular Switching by Proton Abstraction. Phys. Chem. Chem. Phys. 2010, 12, 4791-4799. (21) Muhammad, S.; Janjua, M. R.; Su, Z. M. Investigation of Dibenzoboroles Having π-Electrons: Toward a New Type of Two-Dimensional NLO Molecular Switch? J. Phys. Chem. C 2009, 113, 12551-12557 (22) Wee, K. R.; Han, W. S.; Cho, D. W.; Kwon, S.; Pac, C.; Kang, S. O. Carborane Photochemistry Triggered by Aryl Substitution: Carborane-Based Dyads with Phenyl Carbazoles. Angew. Chem., Int. Ed. 2012, 51, 2677-2680. (23) Zhang, J.; Xie, Z. W. Synthesis, Structure, and Reactivity of 13- and 14-Vertex Carboranes. Acc. Chem. Res. 2014, 47, 1623-1633. (24) Wang, H. Q.; Wang, L.; Li, R. R.; Ye, J. T.; Chen, Z. Z.; Chen, H.; Qiu, Y. Q.; Xie, H. M. Second-Order Nonlinear Optical Properties of Carboranylated Square-Planar Pt(II) Zwitterionic Complexes: One-/Two-Dimensional Difference and Substituent Effect. J. Phys. Chem. A 2016, 120, 9330-9340. (25) Ma, N. N.; Li, S. J.; Yan, L. K.; Qiu, Y. Q.; Su, Z. M. Switchable NLO response induced

by

rotation

of

metallacarboranes

[NiIII/IV(C2B9H11)2]-/0

and

C-,B-functionalized derivatives. Dalton Trans. 2014, 43, 5069-5075. (26) Mukherjee, S.; Thilagar, P. Boron Clusters in Luminescent Materials. Chem. Commun. 2016, 52, 1070-1093.

36


Page 37 of 45

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


(27) Muhammad, S.; Xu, H. L.; Su, Z. M.; Fukuda, K.; Kishi, R.; Shigeta, Y.; Nakano, M. A New Type of Organic-Inorganic Hybrid NLO-phore with Large Off-Diagonal First Hyperpolarizability Tensors: A Two-Dimensional Approach. Dalton Trans 2013, 42, 15053-15062. (28) Muhammad, S.; Minami, T.; Fukui, H.; Yoneda, K.; Kishi, R.; Shigeta, Y.; Nakano, M. Halide Ion Complexes of Decaborane (B10H14) and Their Derivatives: Noncovalent Charge Transfer Effect on Second-Order Nonlinear Optical Properties. J. Phys. Chem. A 2012, 116, 1417-1424 (29) Yao, H.; Sabat, M.; Grimes, R. N.; Fabrizi de Biani, F.; Zanello, P. Metallacarborane-Based Nanostructures: A Carbon-Wired Planar Octagon. Angew. Chem., Int. Ed. 2003, 42, 1002-1005. (30) Fabrizi de Biani, F.; Corsini, M.; Zanello, P.; Yao, H.; Bluhm, M. E.; Grimes, R. N.

Electronic

Properties

of

Mononuclear,

Dinuclear,

and

Polynuclear

Cobaltacarboranes: Electrochemical and Spectroelectrochemical Studies. J. Am. Chem. Soc. 2004, 126, 11360-11369. (31) Malaba, D.; Sabat, M.; Grimes, Russell N. Alkynyl Substitution and Linkage in Cobaltacarborane Sandwich Complexes. Eur. J. Inorg. Chem. 2001, 2001, 2557-2562. (32) Grimes, R. N. Boron-Carbon Ring Ligands in Organometallic Synthesis. Chem. Rev. 1992, 92, 251-268. (33) Fabrizi de Biani, F.; Fontani, M.; Ruiz, E.; Zanello, P.; Russell, J. M.; Grimes, R. N. Electronic Interactions in (η6-Arene) Ferracarboranes1. Organometallics 2002, 21, 4129-4137. 37



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 38 of 45

(34) Bluhm, M.; Pritzkow, H.; Siebert, W.; Grimes, R. N. Benzene-Centered Tri- and Tetrametallacarborane Sandwich Complexes. Angew. Chem. 2000, 112, 4736-4738. (35) Stockman, K. E.; Boring, E. A.; Sabat, M.; Finn, M. G.; Grimes, R. N. Small Carborane Ligands as Tailorable Cp Surrogates. Halogenation, Alkylation, and Arylation at Metal and Cage Positions on CpX2M(Et2C2B4H4) Complexes (M = Ta, Nb)1. Organometallics 2000, 19, 2200-2207. (36) Xu, H. L.; Li, Z. R.; Wu, D.; Wang, B. Q.; Li, Y.; Gu, F. L.; Aoki, Y. Structures and Large NLO Responses of New Electrides: Li-Doped Fluorocarbon Chain. J. Am. Chem. Soc. 2007, 129, 2967-2970. (37) Wang, L.; Wang, W. Y.; Qiu, Y. Q.; Lu, H. Z. Second-Order Nonlinear Optical Response of Electron Donor-Acceptor Hybrids Formed between Corannulene and Metallofullerenes. J. Phys. Chem. C 2015, 119, 24965-24975. (38) Muhammad, S.; Xu, H. L.; Liao, Y.; Kan, Y. H.; Su, Z. M. Quantum Mechanical Design and Structure of the Li@B10H14 Basket with a Remarkably Enhanced Electro-Optical Response. J. Am. Chem. Soc. 2009, 131, 11833-11840. (39) Senge, M. O.; Fazekas, M.; Notaras, E. G. A.; Blau, W. J.; Zawadzka, M.; Locos, O. B.; Ni Mhuircheartaigh, E. M. Nonlinear Optical Properties of Porphyrins. Adv. Mater. 2007, 19, 2737-2774. (40) Wang, H. Q.; Wang, W. Y.; Fang, X. Y.; Wang, L.; Zhu, C. L.; Chen, Z. Z.; Chen,

H.;

Qiu,

Y.

Q.

Second-Order

Nonlinear

Optical

Responses

of

Carboranyl-Substituted Indole/Indoline Derivatives: Impact of Different Substituents. J. Mol. Graphics Modell. 2016, 67, 111-118. 38


Page 39 of 45

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


(41) Coe, B. J.; Foxon, S. P.; Pilkington, R. A.; Sánchez, S.; Whittaker, D.; Clays, K.; Van Steerteghem, N.; Brunschwig, B. S. Rhenium(I) Tricarbonyl Complexes with Peripheral N-Coordination Sites: A Foundation for Heterotrimetallic Nonlinear Optical Chromophores. Organometallics 2016, 35, 3014-3024. (42) Ye, J. T.; Wang, L.; Wang, H. Q.; Chen, Z. Z.; Qiu, Y. Q.; Xie, H. M. Spirooxazine Molecular Switches with Nonlinear Optical Responses as Selective Cation Sensors. RSC Adv. 2017, 7, 642-650. (43) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648-5652. (44) Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A 1988, 38, 3098-3100. (45) Dolg, M.; Wedig, U.; Stoll, H.; Preuss, H. Energy-Adjusted ab Initio Pseudopotentials for the First Row Transition Elements. J. Chem. Phys. 1987, 86, 866-872. (46) Miertuš, S.; Scrocco, E.; Tomasi, J. Electrostatic Interaction of a Solute with a Continuum. A Direct Utilizaion of AB Initio Molecular Potentials for the Prevision of Solvent Effects. Chem. Phys. 1981, 55, 117-129. (47) Pascual-ahuir, J. L.; Silla, E.; Tuñon, I. GEPOL: An Improved Description of Molecular Surfaces.

III.

A New Algorithm for the Computation

of a

Solvent-Excluding Surface. J. Comput. Chem. 1994, 15, 1127-1138. (48) Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. Energies, Structures, and Electronic Properties of Molecules in Solution with the C-PCM Solvation Model. J. 39



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 40 of 45

Comput. Chem. 2003, 24, 669-681. (49) Bartlett, R. J.; Purvis, G. D. Many-Body Perturbation Theory, Coupled-Pair Many-Electron Theory, and the Importance of Quadruple Excitations for the Correlation Problem. Int. J. Quantum Chem. 1978, 14, 561-581. (50) Champagne, B.; Perpète, E. A.; Jacquemin, D.; van Gisbergen, S. J. A.; Baerends, E.-J.; Soubra-Ghaoui, C.; Robins, K. A.; Kirtman, B. Assessment of Conventional Density

Functional

Schemes

for

Computing

the

Dipole

Moment

and

(Hyper)polarizabilities of Push-Pull π-Conjugated Systems. J. Phys. Chem. A 2000, 104, 4755-4763. (51) Champagne, B. t.; Perpète, E. A.; Gisbergen, S. J. A. v.; Baerends, E. J.; Snijders, J. G.; Soubra-Ghaoui, C.; Robins, K. A.; Kirtman, B. Assessment of Conventional Density

Functional

Schemes

for

Computing

the

Polarizabilities

and

Hyperpolarizabilities of Conjugated Oligomers: An ab Initio Investigation of Polyacetylene Chains. J. Chem. Phys. 1998, 109, 10489-10498. (52) van Gisbergen, S. J. A.; Schipper, P. R. T.; Gritsenko, O. V.; Baerends, E. J.; Snijders, J. G.; Champagne, B.; Kirtman, B. Electric Field Dependence of the Exchange-Correlation Potential in Molecular Chains. Phys. Rev. Lett. 1999, 83, 694-697. (53) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868. (54) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]. Phys. Rev. Lett. 1997, 78, 40


Page 41 of 45

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


1396-1396. (55) Becke, A. D. A New Mixing of Hartree-Fock and Local Density-Functional Theories. J. Chem. Phys. 1993, 98, 1372-1377. (56) Zhao, Y.; Truhlar, D. G. Comparative DFT Study of van der Waals Complexes: Rare-Gas Dimers, Alkaline-Earth Dimers, Zinc Dimer, and Zinc-Rare-Gas Dimers. J. Phys. Chem. A 2006, 110, 5121-5129. (57) Yanai, T.; Tew, D. P.; Handy, N. C. A New Hybrid Exchange-Correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP). Chem. Phys. Lett. 2004, 393, 51-57. (58) Chai, J. D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615-6620. (59) Caves, T. C.; Karplus, M. Perturbed Hartree-Fock Theory. I. Diagrammatic Double-Perturbation Analysis. J. Chem. Phys. 1969, 50, 3649-3661. (60) Langhoff, P. W.; Karplus, M.; Hurst, R. P. Approximations to Hartree-Fock Perturbation Theory. J. Chem. Phys. 1966, 44, 505-514. (61) Gerratt, J.; Mills, I. M. Force Constants and Dipole-Moment Derivatives of Molecules from Perturbed Hartree-Fock Calculations. I. J. Chem. Phys. 1968, 49, 1719-1729. (62) Kleinman, D. A. Nonlinear Dielectric Polarization in Optical Media. Phys. Rev.

1962, 126, 1977-1979. (63) Willetts, A.; Rice, J. E.; Burland, D. M.; Shelton, D. P. Problems in the 41



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 42 of 45

Comparison of Theoretical and Experimental Hyperpolarizabilities. J. Chem. Phys.

1992, 97, 7590-7599. (64) Pescitelli, G.; Sreerama, N.; Salvadori, P.; Nakanishi, K.; Berova, N.; Woody, R. W. Inherent Chirality Dominates the Visible/Near-Ultraviolet CD Spectrum of Rhodopsin. J. Am. Chem. Soc. 2008, 130, 6170-6181. (65) Vlček, A.; Záliš, S. Comments on “Theoretical Studies of Ground and Excited Electronic States in a Series of Halide Rhenium(I) Bipyridine Complexes”. J. Phys. Chem. A 2005, 109, 2991-2992. (66) van Faassen, M.; Burke, K. Time-Dependent Density Functional Theory of High Excitations: to Infinity, and Beyond. Phys. Chem. Chem. Phys. 2009, 11, 4437-4450. (67) Barone, V.; Polimeno, A. Integrated Computational Strategies for UV/vis Spectra of Large Molecules in Solution. Chem. Soc. Rev. 2007, 36, 1724-1731. (68) Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 model. J. Chem. Phys. 1999, 110, 6158-6170. (69) 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 D.01; Gaussian, Inc.: Wallingford, C., 2009. (70)

Swisher,

R.

G.;

Sinn,

E.;

Grimes,

R.

N.

Organotransition-Metal

Metallacarboranes. 2. Synthesis and Structures of (η6-Arene)Fe[(C2H5)2C2B4H4] Complexes. Organometallics 1983, 2, 506-514. (71) Merkert, J. W.; Geiger, W. E.; Attwood, M. D.; Grimes, R. N. Electrochemical Properties of (η6-Arene)MII(η5-Et2C2B4H4) Complexes: Formation of Persistent d5 (M 42


Page 43 of 45

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


= Fe, Ru) and d7 (M = Fe) Redox Products. Organometallics 1991, 10, 3545-3549. (72) Bader, R. F. W.; Carroll, M. T.; Cheeseman, J. R.; Chang, C. Properties of Atoms in Molecules: Atomic Volumes. J. Am. Chem. Soc. 1987, 109, 7968-7979. (73) Suponitsky, K. Y.; Liao, Y.; Masunov, A. E. Electronic Hyperpolarizabilities for Donor-Acceptor Molecules with Long Conjugated Bridges: Calculations versus Experiment. J. Phys. Chem. A 2009, 113, 10994-11001. (74) Torrent-Sucarrat, M.; Anglada, J. M.; Luis, J. M. Evaluation of the Nonlinear Optical Properties for Annulenes with Hückel and Möbius Topologies. J. Chem. Theory Comput. 2011, 7, 3935-3943. (75) Oudar, J. L.; Chemla, D. S. Hyperpolarizabilities of the Nitroanilines and Their Relations to the Excited State Dipole Moment. J. Chem. Phys. 1977, 66, 2664-2668. (76) Oudar, J. L. Optical Nonlinearities of Conjugated Molecules. Stilbene Derivatives and Highly Polar Aromatic Compounds. J. Chem. Phys. 1977, 67, 446-457. (77) Nakano, M.; Yamada, S.; Yamaguchi, K. Second Hyperpolarizability Density Analyses for Trithiapentalene and Dioxathiapentalene: Visualization of Unique π-Electron Contributions. Chem. Phys. Lett. 1999, 306, 187-196. (78) Nakano, M.; Kishi, R.; Nitta, T.; Champagne, B.; Botek, E.; Yamaguchi, K. Hyperpolarizability

Density

Analysis

of

the

Enhancement

of

Second

Hyperpolarizability of π-Conjugated Oligomers by Intermolecular Interaction. Int. J. Quantum Chem. 2005, 102, 702-710. (79) Nakano, M.; Shigemoto, I.; Yamada, S.; Yamaguchi, K. Size-Consistent 43



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

Approach and Density Analysis of Hyperpolarizability: Second Hyperpolarizabilities of Polymeric Systems with and without Defects. J. Chem. Phys. 1995, 103, 4175-4191.

44


Page 44 of 45

Page 45 of 45

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


TOC Graphic

45


Multinuclear âStaircaseâ - ACS Publications

Recommend Documents

Multinuclear âStaircaseâ - ACS Publications