Unusual Manipulative Effects of Spin Multiplicity and Excess Electron

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Unusual Manipulative Effects of Spin Multiplicity and Excess Electron Number on the Structure and Nonlinear Optical Response in New Linear and Cyclic Electride Molecules with Multi-Excess Electrons Hui-Min He, Zhi-Ru Li, Ying Li, Wei-Ming Sun, Jia-Jun Wang, Jia-Yuan Liu, and Di Wu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp503566x • Publication Date (Web): 23 Sep 2014 Downloaded from http://pubs.acs.org on September 26, 2014

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The Journal of Physical Chemistry

Unusual Manipulative Effects of Spin Multiplicity and Excess Electron Number on the Structure and Nonlinear Optical Response in New Linear and Cyclic Electride Molecules with Multi-Excess Electrons Hui-Min He, Zhi-Ru Li,* Ying Li, Wei-Ming Sun, Jia-Jun Wang, Jia-yuan Liu, Di Wu* State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, 130023, P.R.China. E-mail: [email protected]; [email protected].

ABSTRACT: Using the M06-2X density functional theory, unusual manipulative effects of spin multiplicity and excess electron number on structure and static first hyperpolarizability (β0) are revealed for new electride molecules with multi-excess electrons. (1) For the spin effect on molecular structure, the low spin multiplicity brings bent structures (1L2 and 2L3) for linear isomers. (2) For the dramatic effect of spin multiplicity on β0, the considerable β0 of 22.7 ×104 au for low spin structure 2L3 is larger by 21 times than that of 1.1×104 au for high spin structure 4L3 due to one excess electron spin reversal. The low spin structure with double and single occupied frontier orbitals is relevant to the low transition energy and complex distribution of electron density, which dramatically enhances β0. (3) For the effect of excess electron number on β0, the β0 value increases acceleratedly with increasing excess electron number. A long chain-shaped electride molecule (for instance 2L3) with multi-excess electrons in low spin state may bring considerable static first hyperpolarizability, which is a novel manipulation strategy of enhancing molecular NLO response.

KEYWORDS: Nonlinear Optics, Spin Multiplicity, Excess Electron, Electride

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1. INTRODUCTION A revolution in electronics is in view along with the contemporary evolution of the two novel disciplines of spintronics and molecular electronics. Molecular spintronics as a fundamental link between these two fields can be established using single-molecular magnets.1 As a result of exciting evolution in optics, molecular optics may be established on the basis of the development and application of (non) linear optical material of molecular level, especially nonlinear optical (NLO) molecule. NLO molecule may not only form macroscopical NLO materials with potential applications in photonic and electro-optic devices,2-6 but also serve as available material of molecular optics. In recent years, a new research field on NLO molecule with excess electron has been established. Especially, electride7-13 molecule including the excess electron anion has attracted great attention since it is discovered that introducing the excess electron in molecule is a new approach to remarkably enhance static first hyperpolarizability (β0).14,15 Doping alkali metal into organic complexant is an efficient method introducing the excess electron and forming electride molecule. Champagne et al.16 investigated the effect of doping alkali metal atoms on the second hyperpolarizability of polyacetylene chains. It has been shown that doping dramatically enhances the static electronic and vibrational hyperpolarizabilities.17 The electrides11,12,18-21 and alkalides with alkali anion22-24 are typical compounds with excess electrons caused by a doping effect: the lone pair of complexant pushing out the valence electron of doped alkali metal atom. These typical compounds have large first hyperpolarizability due to the contained excess electron. Our previous works have reported that the alkali metal atom-doped systems with cup-like, cage-like and chain-like complexants exhibit large first hyperpolarizability, in which the excess electron is generated by the push/pull-electron effect of the complexant. Typical such systems include the cup-like Li@calix[4]pyrrole,18 and the cage-like M+(e@C20F20)¯

2


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and

(M3O)+(e@C20F20)¯19

H–(CF2–CH2)3–H20

as

with

well

as

electride

a

Li-doped

character;

fluorocarbon organic

chain

alkalides

Li+(calix[4]pyrrole)K¯21 and (M+@n6adz)M0¯ (M, M0 = Li, Na and K; n = 2, 3).22 The basket-like Li@B10H14 electride23 has also been reported, in which the valence electron of the doped Li atom is pulled into the cavity of the electron-deficient B10H14 complexant forming the excess electron. Besides, nano-systems have also been considered as complexants to generate excess electron and bring forth large first hyperpolarizability. For example, NH2-GNR-NO225 and BNNT.26 It indicates that the diffuse excess electron dramatically enhances the β0 value. Some influencing factors of β0 including complexant scale,22,27-30 complexant flexibility31-33 and alkali metal atomic number,34-36 have been found for the electride systems.18-20,33,37 Notably, the effect of the excess electron number has not been reported and the spin nature of the excess electron has not been paid sufficient attention in molecular nonlinear optics. Therefore, constructing electride molecules with the multi-excess electrons (n ≥ 2) and revealing the effects of excess electron number and related spin multiplicity on structure and static first hyperpolarizability (β0) are fascinating projects. Nakano and coworkers have reported the interesting spin multiplicity effect on the second hyperpolarizability for a series of phenalenyl radical systems.3,38-43 Naturally,

spin

multiplicity

and

relevant

property

effects

on

the

first

hyperpolarizability should be interesting as well. How does the spin affect the molecular structure and characteristics of the electride molecules? How does the β0 value change with the spin multiplicity and the excess electron number? The answers of these questions are expected. In present work, we theoretically designed seven electride molecules with different excess electron number (n = 1, 2 and 3) and systematically investigated the spin multiplicity and excess electron number effects on manipulating molecular shape and NLO response for electride molecules from the viewpoint of molecular optics. This work will also enlighten new electronic perspective on new NLO molecular investigation including the manipulations of spin multiplicity and excess electron

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number for electride molecules.

2. COMPUTATIONAL DETAILS A great deal of researches of seeking appropriate computational method for different types of nonlinear optical molecules have been reported.44-48 For the calculation on the static first hyperpolarizability, systematic ab initio and density functional theory (DFT) studies have been reported,47,49-51 which include the comparisons between DFT methods and ab initio methods for some molecular systems. Particularly, the studies of basis set effect52-57 show the importance of embedding

diffuse

basis

functions in

accurately

calculating

the

first

hyperpolarizabilities for small and larger molecules. The second-order Møller–Plesset perturbation (MP2) method is more acceptable than DFT in such calculations for not large systems,18,23 but it is very costly for the larger systems. In recent years, a new density functional theory (DFT), namely, the novel hybrid meta exchange correlation functional M06-2X, as proposed by Zhao and co-workers,58,59 has been successfully employed to evaluate the structures and static first hyperpolarizabilities for the larger electride molecules with excess electron.26,60-63 Our studied species bear a general resemblance to the reported systems, so the M06-2X functional should be a suitable choice in the present calculations. In order to confirm this, we calculated the static polarizabilities and first hyperpolarizabilities of two selected molecules using several long-range DFT methods. The results are listed in Table 1, and clearly show that M06-2X method is reliable to reveal physical rules in the electrical properties. As a result, in this work, the optimum geometric structures of the seven electride molecules with all real frequencies are obtained at the M06-2X/6-31G(d) level. To explore the effects of the spin multiplicity and the excess electron number as well as the molecular shape on the β0, similarly, we use the M06-2X/6-31++G(d) method to calculate the polarizability (α0), first hyperpolarizability and vertical ionization potential (VIP) due to the importance of diffuse basis functions in such calculations.52-57 For electronic transition properties, the transition energy ∆E, 4


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oscillator strength f0, and the difference of dipole moment ∆µ between the ground and the crucial excited state are estimated by TD-M06-2X theory with the 6-31G(d) basis set. The static polarizability (α0), first hyperpolarizability (β0) and vertical ionization potential (VIP) are noted as:

α0 =

1 (α xx + α yy + α zz ) 3

(1)

β 0 = (β x2 + β y2 + β z2 )1 / 2 (2) where

3 5

β x = (β xxx + β xyy + β xzz ) 3 5

β y = ( β yyy + β yxx + β yzz )

3 5

β z = (β zzz + β zxx + β zyy ) VIP = E[M+ at the neutral geometry] - E[M]

(3)

The values of spin eigenvalue show that spin contamination is negligible in the current calculations. All the calculations were carried out by using the GAUSSIAN 09 program package.64 The molecular orbital plots were generated with the GaussView program.65

3. RESULTS AND DISCUSSION 3.1

Equilibrium

geometries.

[Cs+(15C5)(18C6)·e¯]6·(18C6),66 we

Based

on

theoretically

the

synthesized

designed

several

electride electride

molecules with different excess electron numbers (n = 1, 2 and 3), in which the modest-sized 9C3 crown ether units are connected by bridge unit (C2H4) forming a push electron complexant (n > 1) and alkali metal Na atoms act as the source of the excess electrons. The seven optimized structures with all real frequencies are exhibited in Figure 1.

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These molecular structures have different shapes and excess electron numbers (or Na atom numbers) as well as spin multiplicities. From Figure 1, the linear and cyclic structures are named as L and C, respectively. Meanwhile, the subscript represents the excess electron number, and the superscript denotes the spin multiplicity. The selected geometric parameters and the relative energies (Ers) of different spin states are listed in Table 2. From Table 2, the Ers show that the low spin states (1L2, 2C3, 2L3 and 2L1) are ground states because each possesses the lower energy. The Na···O distance relates to the local interaction between the Na and O atom of the 9C3 unit in these molecular structures. As shown in Table 2, the Na···O distances are 2.325-2.501 Å, which are slightly longer than that of 2.254 Å in the Na(H2O)n+ system67, and similar to those of 2.39-2.63Å in the Na4UO5 compound68. The Na···Na distance is relevant to the interaction between two Na@9C3 units, which may influence the molecular shape and the spin multiplicity. The important minimal Na···Na distance (Na···Namin) of each electride molecule (n ≥ 2) is taken into account. From Table 2, for the linear structures of low spin, the Na···Namin distances of short 3.103 Å (1L2) and 3.208 Å (2L3) are close to those of 3.169-3.205 Å for Na doped H4C4N232 and larger than that of 2.73 Å for Na doped carbon nanotubes.69 For corresponding high spin structures, the Na···Namin distances are as long as 7.359 Å (3L2) and 8.823 Å (4L3). Obviously, the linear structure of low spin has much shorter Na···Namin distance than corresponding high spin isomer. The short Na···Namin distance favors the formation of Na-Na bond and excess electron pair which ensures low spin multiplicity of the molecule. Meanwhile, the dependence of Na-Namin distance on the excess electron number has also been exhibited as 3.103 Å (1L2 with 2 electrons) < 3.208 Å (2L3 with 3 electrons) for low spin structures, and 7.359 Å (3L2) < 8.823 Å (4L3) for high spin structures. Apparently, the Na···Namin distance increases with the increasing excess electron number. We turn next to the issue of spin effect on chain span (l) of linear molecules. From Figure 1, the low spin produces a short Na···Namin distance which pulls two Na@9C3 units near to each other and leads to a bended molecular chain, so low spin 6


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linear structures have shorter chain spans l. As a result, the l values shown in Table 2 are 11.127 Å (1L2) < 11.668 Å (3L2) for the two Na@9C3 unit molecules and 15.598 Å (2L3) < 18.832 Å (4L3) for the three Na@9C3 unit molecules. As for the cyclic structures, the 4C3 isomer of high spin has larger Na···Namin distance than 2C3 of low spin, i.e., 9.489 Å (4C3) > 4.261 Å (2C3). As the cyclic structure of 4C3 is strongly twisted, the Na···Na distance is elongated, which favors the high spin multiplicity (see Figure 1). 3.2 Electride characteristic. Figure 2 illustrates the occupied frontier molecular orbitals. These orbital lobes of s or p type near Na atom(s) exhibiting molecular orbital (MO) character of excess electron. The Merz−Kollmann charges of Na atoms are shown in Table 2. From Table 2, we can see that all the Na atoms are positively charged with 0.220−0.478|e| charges, which indicates that the O atoms in the complexant pushed the valence electrons of Na atoms away to form excess electrons. Therefore, these species are electride molecules with excess electron anion(s). In Figure 2, we exhibit all the molecular orbitals occupied by excess electron(s) for structures of high spin and low spin states. It is known that both the linear structures of 2L3 and 4L3 have 3 excess electrons, thereinto, two opposite spin excess electrons of the low spin 2L3 occupy one s-type orbital (HOMO-1) with large orbital lobe covering two Na atoms, whereas the other excess electron occupies the HOMO with a small s-type lobe covering the other Na atom. However, three excess electrons of the high spin 4L3 occupy three different s-type orbitals (HOMO-2, HOMO-1 and HOMO), in which each small s-lobe covers one Na atom. The feature of these excess electrons will affect the vertical ionization potential (VIP) and first hyperpolarizability (β0) of the electride molecule. Considering the multi-excess electrons character of such electride molecules, we obtained the first several VIPs of these species. These VIP values at the M06-2X/6-31++G(d) level are given in Table 2. For the low spin electride molecules, the VIP(I) value decreases with increasing excess electron number in the order of 3.34 (2L1 for n = 1) > 3.26 (1L2 for n = 2) > 3.12 (2L3 for n = 3) > 2.36 eV (2C3 for n = 3). 7



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For the high spin structures, the similar variation of VIP(I) is found to be 3.45 (3L2) > 3.42 (4L3) > 2.59 eV (4C3). These two tendencies clearly indicate the effect of excess electron number on VIP(I), that is, the more the former, the smaller the latter. According to Koopmans’ theorem,70 the first ionization energy of a molecular system is equal to the negative of the HOMO orbital energy. From Table 2, we can see that the VIP(I) value of high spin structure is slightly larger than that of corresponding low spin isomer. This accords well with the negative HOMO orbital energy shown in Figure 2, though the Koopmans’ values are smaller by 0.86-0.50 eV than corresponding those in Table 2. Note that our VIP(I) values (2.36-3.45 eV) are smaller than 3.9-5.4 eV of alkali-metal atoms with loose binding electron,71 and close to those of 2.81-3.65 eV for superalkali clusters and relative systems.72-74 Notably, these VIP values of above systems (except alkali-metal atoms) are not only small but also close to each other. Why? All these systems have excess electrons and hence possess the small VIP of about 3 eV. In addition, for two low spin structures in this work, 1L2 has larger VIP (II) of 8.18 eV and 2C3 has larger VIP(III) of 11.59 eV, which may be understood by the fact that the ionizing electron is a rest electron of doubly-occupied orbital and the orbital level has been greatly lowered due to the leaving of ionized electron firstly. In these Na doped crown ether systems with multi-excess electrons, whether the Na-Na bond occurred? Comparing Na···Na distances at M06-2X/6-31G(d) level is meaningful. The single bond formed in Na2 molecule has the bond length of 2.947 Å, which is close to the short Na···Namin distances of 3.103 Å for 1L2 and 3.208 Å for 2L3. Besides, the natural atomic orbital (NAO) bond order of 0.77 for Na2 is also close to those of 0.76 (1L2) and 0.75 (2L3). It is obvious that Na-Na single bond formed between two doped Na atoms in the low spin electride structures. Interestingly, Na-Na single bond is a bond between two doped Na atoms. Especially, the bonding electron pair is the excess electron pair pushed by complexant and the corresponding electron cloud is deviated from the Na-Na axis (see HOMO orbital for 1L2 and HOMO-1orbital for 2L3 in Figure 2) under the push of complexant. Therefore the special Na-Na bond is 8


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a bent σ single bond including the bent bridge of excess electron pair and two bridgehead Na cations. Here the electronic structure of Na-Na can be interestingly described as Na+- (e2)2- -Na+ for the first time. 3.3 Static first hyperpolarizabilities. The polarizabilities (α0) and static first hyperpolarizabilities (β0) of these proposed multi-excess electrons electride molecules at the M06-2X/6-31++G(d) level are exhibited in Table 3. From Table 3, Spin multiplicity effect on α0 is complex. For short linear structures and cyclic structures, high spin isomer exhibits a larger α0 value, namely, 471 (1L2) < 546 au (3L2) and 798 (2C3) < 913 au (4C3). Whereas, the order is reversed as far as the long linear structures are concerned, i.e., 1808 au (2L3) > 851 (4L3). From Table 3, the order of α0 is obvious: 269 (2L1) for 1 excess electron system < 471 (1L2) and 546 (3L2) for 2 excess electron systems < 798 (2C3), 851 (4L3), 913 (4C3) and 1808 au (2L3) for 3 excess electron systems, which shows the excess electron number effect on polarizability. This effect is that the α0 increases reasonably with increasing excess electron number, based on the system dependence of the linear polarizability on essentially number of atoms of the molecule. Now we focus on the effects of the spin multiplicity and the molecular shape as well as the excess electron number on the hyperpolarizability. The calculated static first hyperpolarizabilities for multi-excess electrons electride molecules are exhibited in Table 3 and Figure 3. The order of the β0 values from Table 3 is 0.7×104 (3L2), 1.0×104 (1L2), 1.1×104 (2L1), 1.1×104 (4L3) < 5.7×104 (4C3) < 10.3×104 (2C3) < 22.7×104 au (2L3). Considering the relationship between β0 value and spin multiplicity, the two largest β0 values of 22.7×104 and 10.3×104 au belong to the low spin structures 2L3 and 2C3, respectively, while the smallest β0 value of 0.7×104 au belongs to the high spin structure (3L2). Clearly, it is shown that the low spin multiplicity brings large β0 value. The considerable β0 of 22.7×104 au (2L3 with the low spin multiplicity of 2) is about 21 times larger than that of 1.1×104 au (4L3 with the high spin multiplicity of 4) for the linear electride structures with 3 excess electrons. Figure 4 shows the 9



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interesting effect of spin multiplicity. With spin reversal of an excess electron, 2S+1 lowers from 4 to 2, which leads to the shortening of Na···Namin distance and bend of molecular chain as well as a dramatic 21 times increase of β0. For relevant works, in the research of the pyrrole radical,75 low spin ground state has a larger β0, which agrees with above spin multiplicity effect. However, a different case occurs for the second hyperpolarizability, which are quite reduced in the singlet state for the systems with intermediate diradical character.42 The molecular shape effect on β0 value is also examined. From Table 3, the β0 values are 10.3×104 (cyclic 2C3) < 22.7×104 au (linear 2L3), indicating that the circular structure reduces β0 value for the low spin structures. In contrast, the β0 order of 1.1×104 (4L3) < 5.7×104 au (4C3) suggests that the circular structure is beneficial for enhancing the β0 value (about 5 times) for the high spin structures. Whether the dramatic spin effect on the β0 value includes the fraction of effect of geometry for this type of electride molecules? This is an interesting question. The β0 values of the one spin state at the equilibrium geometry of the other spin state are calculated and listed in Table 4. Table 4 includes symbol “state/geom”, where 2L3/4L3 represents the electric state 2L3 at the equilibrium geometry of the 4L3 spin state. For low spin 2L3 state, geometric change from bent 2L3 to extended 4L3, β0 value greatly increases from 22.7×104au (2L3/2L3) to considerable 7184×104 au (2L3/4L3), which shows that the extending of molecular chain greatly increases β0 value in the low spin state. For high spin 4L3 states, geometric change from bent 2L3 to extended 4L3, β0 value greatly decreases from considerable 4749×104 (4L3/2L3) to 1.1×104 au (4L3/4L3), which show that the bending of molecular chain greatly increases β0 value in the high spin state. For cycle structures, the influence of structure on β0 value in different spin states is not great due to small length difference of cycle structures. In short, not only spin multiplicity but also geometry, influence β0 value. For hypothetical β0 values of the one spin state at the equilibrium geometry of the other spin state, 7184×104 au (2L3/4L3) > 4749×104 (4L3/2L3) still exhibits the rule of low spin > high spin. So the dramatic spin effect on β0 of this type of electrides includes the fraction of an effect of

10


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geometry. Considering the excess electron number effect on β0, the two largest β0 values of 22.7×104 and 10.3×104 au belong to the structures with the maximum 3 excess electrons (2L3 and 2C3) but small β0 values of about 1.0×104 au belong to the electride structures with only 1 and 2 excess electrons. Furthermore, excess electron number effect on β0 of low spin and high spin states are exhibited respectively. The β0 of 2L3 is obviously larger than that of 4L3 (from 22.7×104 to 1.1×104 au) for molecules with 3 excess electrons, while the β0 of 1L2 is just slightly larger than that of 3L2 (from 1.0×104 to 0.7×104 au) for molecules with 2 excess electrons. In a word, the β0 increases acceleratedly with increasing excess electron number, as shown in Figure 5. Obviously, more excess electrons can bring considerable β0 value. Inevitably, these interesting effects relate to the electronic structure and electronic transition properties. Let us consider the two-level model76,77 which derives from the sum-over-states method:

β0 ∝

∆µ ⋅ f 0 ∆E 3

where ∆E, f0, and ∆µ are the transition energy, oscillator strength, and the difference of the dipole moment between the ground state and the crucial excited state, respectively. In the two-level expression, the third power of the ∆E is inversely proportional to the β0 value, ∆µ and f0 are proportional to the β0 value. These physical quantities describing electron transition properties are important to understand the relationships between β0 value and the spin multiplicity as well as excess electron number. Therefore, for a noncentrosymmetric molecule, the low transition energy is the decisive factor for the large β0. In this work, the TD-M06-2X calculations are carried out to estimate the crucial excited states of the seven electride molecules. The transitions energies (∆Ε) and the oscillator strengths (f0) of the crucial transitions for the seven electrides are also listed in Table 3. Figure 3 shows the relationship between the first hyperpolarizability and the crucial transition energy (∆E). Table 3 also provides the crucial transitions for 11



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these multi-excess electrons electride molecules. From Table 3, the ∆Ε order is 1.741 (1L2) > 1.740 (3L2) > 1.634 (4L3) > 1.625 (2L1) > 1.538 (4C3) > 0.814 (2C3) > 0.493 eV (2L3). Obviously, the decreasing order of ∆Ε is consistent with the increasing order of β0, as illustrated in Figure 3. As a result, ∆Ε is a control factor of β0 in these proposed electride molecules. Clearly, the above-mentioned effects of the spin multiplicity and the excess electron number on β0 value can be understood through the ∆Ε values. On the other hand, the electron density that connects β0 value and MO localizations of excess electrons is another intriguing electronic property contributing to understand the new effects noted above. According to finite field theory, electron density distribution ρ(r) can also be expanded in a Taylor series in the electric field78,79 ρ(r)=ρ(r)0+Aj(r)Fj+Bjk(r)FjFk+... The βijk is also obtained easily from the second-order polarization density coefficient Bjk(r) βijk = ∫ ri B jk ( r ) dr 2 This formula shows the correlation between the molecular electron density distribution (electron cloud) and β0 value through βijk. In the molecular electron cloud, the excess electron cloud may be the most important due to the dispersion of excess electron, so the excess electron cloud should be relevant to the β0 value. Considering the two largest β0, 10.3×104 (2C3) and 22.7 ×104 au (2L3) exhibiting the remarkable effects of low spin multiplicity and multi-excess electrons in this work, the structures (2C3 and 2L3) have the orbitals with large lobe of over two Na atoms and the orbitals with small lobe of over one Na atom(see Figure 2). Corresponding electron density distribution (electron cloud) is complex and may associate with large second-order polarization density coefficient. So the special excess electron orbital with large lobe of over two Na atoms is molecular orbital base of the effects of low spin multiplicity and more excess electrons.

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The comparison between our β0 values with previously reported results is meaningful. The electrides and alkalide with organic push-electron complexant have large β0 values of about 104-105 au, for example, Li@calix[4]pyrrole (7326 au),18 Li2-H-(CF2-CH2)3-H (7.70×104 au),20 and (K+@n6adz)K− (3.2×105 au).22 The electride molecules with cagelike pull-electron complexant have large β0 value of about 104-106 au, including 10000 au for (M3O)+(e@C20F20)-,19 7.1×105 au for electride salt of multi-cage

K+[e@3C8(O)]−,27

and

considerable

9.5×106

au

for

e−@C20F19−(CH2)4−NH2...Na+.36 Using Nano-complexant, medium β0 value of about 103-104 au has been obtained: 1.35×103 au for Li@B-BNNT,26 10018 au for [email protected] A new inorganic electride compound M@r6-Al12N12 has a β0 value of 8.89×105 au.80 It is noted that our β0 value of 22.7×104 au for 2L3 with low spin multiplicity and 3-excess electrons is comparable to those very large β0 values of electride molecules. Therefore, a longer linear electride molecule with low spin multiplicity and multi-excess electrons may possess further enhanced NLO response.

4. CONCLUSION In present work, using the density functional with medium-range electron correlation M06-2X method, we obtain seven new linear/cyclic structures of electride molecules with different excess electron numbers (n = 1, 2 and 3). The novel effects of the spin multiplicity and the excess electron number on structure and static first hyperpolarizability (β0) are revealed for new electride molecules with multi-excess electrons. (1) For the spin effect on molecular structure, the low spin multiplicity (ground state) of linear structures (1L2 and 2L3) brings a short Na···Na distance indicating the formation of extraordinary Na-Na bond, which bends the linear molecular structure. Notably, extraordinary Na-Na single bond between two doped Na atoms is a special Na-Na bent σ single bond including the bent bridge of excess electron pair and two bridgehead Na+ cations for the first time. Here the electronic structure of the Na-Na unit can be interestingly described as Na+- (e2)2-Na+. (2) For nonlinear optical (NLO) response, the low spin multiplicity brings very 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

large β0 value, for instance, the considerable β0 of 22.7×104 au for 2L3 with the low spin multiplicity is larger by about 21 times than that of 1.1×104 au for 4L3 with the high spin multiplicity due to the spin reversal of only one excess electron. It shows that the spin multiplicity effect on first hyperpolarizability is remarkable. The low spin structure with double and single occupied frontier orbitals is relevant to the low transition energy and complex distribution of electron density, which dramatically enhances the first hyperpolarizability. (3) For the effect of excess electron number, it is shown that the β0 value increases acceleratedly with increasing excess electron number. (4) For the molecular shape effect on β0, the circular structure dramatically reduces β0 value for the low spin states but obviously enhances β0 value for the high spin states. Based on effects of the spin multiplicity and the excess electron number as well as the molecular shape on static first hyperpolarizability, a novel molecular manipulation strategy of enhancing NLO response is found. That is, a long chain-shaped electride molecule (for instance, 2L3) with multi-excess electrons in low spin state may bring considerable static first hyperpolarizability. Besides traditional structural influencing factors, this work will also enlighten new electronic perspective on new NLO molecule investigation including the manipulations of spin multiplicity and excess electron number for electride molecules.

SUPPORTING INFORMATION The detailed information for references 33, 42, and 65 is included in the supporting information. This material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGEMENTS This work was financially supported by the National Natural Science 14


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Foundation of China (Nos. 21173098, 21173095, 21103065, and 21043003).

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22


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Tables Table 1. A Comparison of Different Method Results with 6-31++G(d) for β0 and α0 Values of 2

L3 and 4L3 (see Section 3.1).

β0 (104au)

η(α0)

LC-wPBE

BHandHLYP

CAM-B3LYP

M06-2X

2

L3

8.27

9.46

16.9

17.6

22.7

4

L3

0.4

0.3

1.2

0.58

1.1

21

32

14

30

21

η(β0)

α0 (au)

LC-BLYP

2

L3

2108

2267

1804

1890

1808

4

L3

961

1040

1048

994

851

2

2

2

2

2

η(β0) and η(α0) are the ratio of 2L3 to 4L3 for β0 and α0 values, respectively.

23



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Page 24 of 33

Table 2. Selected Geometric Parameters (in Å) for the Multi-excess Electrons Electride Molecules at the M06-2X/6-31G(d) Level. The Relative Energy Er (kcal/mol), Vertical Ionization Potential VIP (eV) and Merz−Kollmann Charges qNa on the Na Atoms as well as NAO Bond Order of Na-Na bond at the M06-2X/6-31++G(d) Level. 2

L1

Na···O

2.491

1

L2

3

L2

2

L3

4

L3

2

C3

4

C3

2.383 2.412

2.325 2.399

2.397 2.416 2.477

2.477 2.482 2.494

2.419 2.472 2.501

2.387 2.412 2.443

3.103

7.359

3.208 7.741

8.823 9.549

3.235 3.687 4.261

4.985 6.976 9.489

0

11.127 0

11.668 11.2

15.598 0

18.832 2.0

0

22.7

3.34

3.26

3.45

3.12

3.42

2.36

2.59

8.18

5.66

0.286 0.293

0.351 0.466

4.26 6.77 0.238 0.343 0.392 0.750

4.66 6.80 0.372 0.377 0.393

6.74 11.59 0.220 0.240 0.252

5.32 7.92 0.400 0.433 0.478

Na···Na Na···Namin

Er VIP VIP (I) VIP (II) VIP (III)

qNa

NAO bond order

0.371

0.760

24


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Table 3. The First Hyperpolarizability β0 (104 au), Polarizability α0 (au) at the M06-2X/6-31++G(d) Level; the Transition Energy ∆E (eV), the Oscillator Strength f0, and the Difference in the Dipole Moment between the Ground and the crucial Excited State ∆µ (D) from the TD-M06-2X Theory.

β0

α0

ƒ0

∆E

∆µ

Transitiona

3

L2

0.7

546

0.2235

1.740

3.87

0.75(H-1→L+2)

1

L2

1.0

471

0.3619

1.741

1.43

0.71(H→L)

2

L1

1.1

269

0.1892

1.625

1.83

1.00(H→L+1)

4

L3

1.1

851

0.0502

1.634

11.19

0.45(H-2→L+4)

4

C3

5.7

913

0.2768

1.538

4.48

0.65(H→L+4)

2

10.3

798

0.0388

0.814

7.41

0.85(H→L+3)

22.7

1808

0.2281

0.493

30.30

0.51(H-1→L+7)

C3

2

L3

a

H is HOMO, L is LUMO.

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Table 4. The β0 and α0 Values for the Spin States at the Equilibrium Geometries of the Different Spin States at M06-2X/6-31++ G(d) Level. State/geom

2

L3/2L3a

β0 (104 au)

22.7

7184

4749

1.1

α0 (au)

1808

1119

8601

851

2

L3/4L3

4

L3/2L3

4

L3/4L3b

2

C3/2C3c

2

4

4

10.3

9.97

5.1

5.7

798

966

919

913

a2

L3/2L3 = 2L3; b 4L3/4L3 = 4L3; c 2C3/2C3= 2C3; d 4C3/4C3= 4C3

Figure Captions:

26


C3/4C3

C3/2C3

C3/4C3d

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Figure 1. The structures of multi-excess electrons electride molecules with the subunit of Na doped 9C3 crown ether.

Figure 2. The occupied orbitals of excess electrons in the multi-excess electrons electride molecules.

Figure 3. The relationship between the first hyperpolarizability and the crucial transition energy (∆E).

Figure 4. Spin multiplicity effect. One excess electron spin reversal, 2S+1 lowering from 4 to 2 leads to the shortening of Na···Namin distance and bending of molecular chain as well as dramatic 21 times increase of β0.

Figure 5. The relationship between the first hyperpolarizability and the excess electron number: the β0 value increases acceleratedly with the increasing of excess electron number.

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Figure 1. The structures of multi-excess electron electride molecules with the subunit of Na doped 9C3 crown ether.

28


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Figure 2. The occupied orbitals of excess electrons in the multi-excess electron electride molecules.

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Figure 3. The relationship between the first hyperpolarizability and the crucial transition energy (∆E).

30


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Figure 4. Spin multiplicity effect. One excess electron spin reversal, 2S+1 lowering from 4 to 2 leads to the shortening of Na···Namin distance and bending of molecular chain as well as dramatic 21 times increase of β0.

31



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Figure 5. The relationship between the first hyperpolarizability and the number of excess electron: the β0 value increases acceleratedly with increasing excess electron number.

32


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Table of Contents

33


Unusual Manipulative Effects of Spin Multiplicity and Excess Electron

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