Efficient External Electric Field Manipulated Nonlinear Optical Switches of All-Metal Electride Molecules with Infrared Transparency: Nonbonding Electron Transfer Forms an Excess Electron Lone Pair

Focusing on the interesting new concept of all-metal electride, centrosymmetric molecules e–+M2+(Ni@Pb12)2–M2++e– (M = Be, Mg, and Ca) with two anionic excess electrons located at the opposite ends of the molecule are obtained theoretically. These novel molecular all-metal electrides can act as infrared (IR) nonlinear optical (NLO) switches. Whereas the external electric field (F) hardly changes the molecular structure of the all-metal electrides, it seriously deforms their excess electron orbitals and average static first hyperpolarizabilities (β0e(F)). For e–+Ca2+(Ni@Pb12)2–Ca2++e–, a small external electric field F = 8 × 10–4 au (0.04 V/A) drives a long-range excess electron transfer from one end of the molecule through the middle all-metal anion cage (Ni@Pb12)2– to the other end. This long-range electron transfer is shown by a prominent change of excess electron orbital from double lobes to single lobe, which forms an excess electron lone pair and electronic structure Ca2+(Ni@Pb12)2–Ca2++2e–. Therefor...


INTRODUCTION
Exploring new chemical species is an eternal theme in chemistry, physics, materials science, pharmacology and so on, due to the new species are the basis and source of unique properties. Electrides are a kind of special ionic solids in which excess electrons serve as anions. 1 In the positively charged crystalline lattice, anionic electrons in electrides are confined within a interstitial space or cavity. [2][3][4][5][6][7][8][9] Recently, a new research area of nonlinear optical (NLO) molecules with excess electrons has a rapid development because it has been known that introducing excess electron(s) into a molecule can dramatically increase its static electric first hyperpolarizability (β0). 10-12 Especially, many researchers pay attention to the molecular electrides 2,4,6-8,13-19 containing excess electron anions. Subsequently, a variety of new strategies including the regulation of the push-pull effect, size, shape, and coordination site number of complexants, 12 as well as spin state of excess electrons and excess electron number, 20 have been proposed to enhance the NLO response and electronic stability of electride molecules. In previous research works, [16][17][18][19] many electride molecules were constructed by doping alkali atoms into various non-metallic complexants. These electride molecules have large first hyperpolarizabilities (β0) and the working waveband in the visible light range. Last year, a new approach to unambiguously characterize molecular electrides based on the analysis of their electron density was reported. 21

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On the other hand, the effect of an external electric field on a substance is a wide research area, and has attractive prospects in spintronics, [51][52][53] superconductivity, 54,55 nano material, 56,57 NLO properties, 58,59 and so on. For NLO switches, electric-field-driven switching has been noticed by researchers. Nakano and colleagues have shown that switching on an external electric field generates a considerable increase of the second hyperpolarizability in a polyaromatic diradicaloid. 60 For centrosymmetric aromatic benzene molecule, we have also shown that a large external electric field generate a high contrast in static first hyperpolarizability (from β 0 (0)= 0 to β 0 ( ) = 3.9×10 5 au) due to the breaking of the centrosymmetry of its electron density. 61 For the heterobicycles bisboronate, 62 the electric field induced molecular NLO switch have also been researched. Very recently, an organic molecular electride e -···K(1) + ···calix[4]pyrrole···K(2) + ···ehaving two excess electrons with singlet diradical characteristic has been reported as an electric field manipulated molecular NLO switch. 63 The above-mentioned NLO switches involve organic molecules, organometallic complexes and organic electride molecules. However, all-metal electride molecule with IR-transparent characteristic as new NLO switch has not been reported. As all-metal molecular electride not only possesses easily driven excess electrons by external electric field, but also show high IR NLO contrast, all-metal molecular electride may be regarded as potential IR NLO switch. Therefore, we have designed and investigated by means of the computational chemistry three all-metal electride 6 / 38 molecules M(Ni@Pb12)M (M = Be, Mg and Ca) as novel external electric field driven NLO switches.

COMPUTUTIONAL METHODS
The exact-exchange-incorporated PBE0 is the one of most appropriate functionals in the study of the electronic structure of molecules containing transition metals. [64][65][66][67][68][69][70] For molecular structure and property calculations, the choice of a suitable basis sets is another significant concern. For systems with heavy metals, Los Alamos pseudopotential and double-zeta type basis set, LANL2DZ, 71-73 for the transition metals and Pople-type basis sets for the other atoms have been shown to be competent basis set combination. 74 In this article, optimized geometric structures with all real frequencies under various external electric field strengths from 0 to 40 × 10 −4 au were obtained for all-metal electride molecules M(Ni@Pb12)M (M = Be, Mg and Ca) at the PBE0 level with the LANL2DZ pseudopotential and basis sets for Ni and Pb and the 6-311++G(2d) basis set for Be, Mg and Ca. The vertical ionization potentials (VIP) of these molecules under the external electric fields were obtained at the same level. The VIP is defined as follows: 18 Where, the energies E[M + ] and E[M] are calculated at the optimum geometry of the neutral molecule. We used unrestricted orbitals for the ionic molecule and restricted orbitals for the neutral molecule.
For accurately calculating the static electronic first hyperpolarizabilities, the research of the optimum basis set [76][77][78][79][80][81] show the crucial significance of introducing diffuse basis functions. Furthermore, the basis sets effects have been discussed in detail for electrides, 82 and singlet diradical systems. 83 The electronic and vibrational contributions to the first hyperpolarizabilities of these all-metal molecular electride within an external electric fields were calculated by the finite field approach based on the calculations using second-order Møller−Plesset (MP2) method 84,85 in conjunction with the LANL2DZ pseudopotential and basis set for Ni and Pb and the 6-311+G(3df) basis set for Be, Mg and Ca. The average static first hyperpolarizability (β0) is noted as follows: The electronic contributions to first hyperpolarizabilities were evaluated numerically based on the differentiation of the analytic dipole moment (µ e ) and electronic polarizability (α e ) respect to the electric field. The comparison between the β e values obtained from the differentiation of µ e and α e allows us to check that the numerical errors of the β e values were negligible.
The vibrational contributions to the first hyperpolarizability was computed using the Bishop-Hasan-Kirtman approach. 86 According to Bishop and coworkers, if we denote the equilibrium molecular geometry with an external electric field F present by RF and without the field present, by R0, then we may define: and (∆µ ) The electronic contribution to the (hyper)polarizabilities can be derived from the contributions to the (hyper)polarizabilities. 87 The same approach is used in this paper to compute the ( ) and ( ) contributions of a molecule within a permanent static electric field. In order to check the reliability of the numerical values of ( ), we compared the results obtained using at least two different sets of two field values in the second derivative finite-field difference formula. The optimal applied electric field strengths were between ±0.0010 au and ±0.0015 au for Be(Ni@Pb12)Be; between ±0.0001 au and ±0.0003 au for Mg(Ni@Pb12)Mg; and between ±0.0002 au and ±0.0006 au for Ca(Ni@Pb12)Ca..
All of the calculations were performed by using the Gaussian09 program package. 88 Molecular orbitals were generated with the GaussView program. 89

Equilibrium Geometries
We sandwiched the all-metal cage Ni@Pb12 with two alkaline-earth metal M atoms to  Figure 1.
Besides, the geometry-optimized minimum structures of these molecules are also achieved under different external electric fields.  Table 1). The sum of two distances, the M1-M2 distance, also slightly increases (< 1%) when the strength of the electric field increases. As the influence of external electric field on molecular structures is small, used external electric fields hardly change the molecular structures. The external electric fields also do not alter the valence and chemical bond nature in the molecular structure due to the dependencies between the geometrical structure and chemical bond nature.

Molecular Stabilities
For these all-metal electride molecules, the electronic stability is important in view of the existence of loosely-bound excess electrons. The electronic stability of a molecule may be characterized by its first vertical ionization potential (VIP) value.
From Table 2, it can be seen that field-free VIP values of M(Ni@Pb12)M (M = Be, Mg and Ca) increase in the order Ca < Be < Mg. The VIP values of these molecules are slightly larger than the reported values of inorganic and organic electride molecules, 16,91,92 but smaller than the large value (7.78 eV) of the electride molecule with the excess electron protected inside the C36F36 cage. 93 Hence, these all-metal electride molecules exhibit moderate electronic stability among investigated electride molecules. Note that the VIP values of these all-metal electride molecules only slightly vary with increasing external electric field (see Table 2), indicating that the influence of external electric field on electronic stability is small.
It is well-known that the gap between HOMO (the highest occupied molecular orbital) and LUMO (the lowest unoccupied molecular orbital) is another useful quantity for examining the molecular chemical stability. A large gap value reflects a high chemical stability. Table 2  ion. 96 Therefore, these studied all-metal electride molecules have the chemical stabilities close to those of some organic electrides and all-metal clusters.

Changes of Excess Electron Orbitals Caused by Increasing External Electric
As far as we know, molecular orbital (MO) changes caused by an external electric fields are rarely reported, 61,63 let alone field-induced evolution of excess electron   97 However, the singlet diradical characteristic of an all-metal electrides molecule has not been discussed yet. Figure 3 shows the HOMO of two isolated electride molecules e -···Ca + F···FCa + ···eand the HOMO of an organic electride molecule e -···Li + NH2PhNH2Li + ···ewith two separated isolated excess electrons.
Its high diradical character is y0 = 0.99, obtained from natural orbital populations of

The Role of All-Metal Electride Molecules as NLO Switches
As mentioned before, some organic molecules, 60,62 organometallic complexes 32 have non-centrosymmetry and switchable first hyperpolarizability, so they may serve as NLO switch molecules. Recently, we have found that the organic electride molecule e − ···K(1) + ···calix[4]pyrrole···K(2) + ···e − , which has two isolated excess electrons, may also serve as external electric field driven NLO switch molecule. 63 However, an NLO switch of novel all-metal electrides molecule has not been reported although it be expected.

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The all-metal electride molecules M(Ni@Pb12)M (M = Be, Mg and Ca) with centrosymmetry have loosely-bound excess electrons, which are easily polarized and cause a strong shift in the electron density. Naturally, a small stimulus of an external electric field may alter the electron density of the molecule, which will bring high   When external electric field is applied, the partial excess electrons gradually transfer from one side M1 through the middle (Ni@Pb12) 2to the other side M2. In

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consequence, its centrosymmetric electronic structure will be broken, and then a high 0 ( ) contrast may occur.

Figure 4
Evolutions of 0 ( ) and excess electron orbital (HOMO) of Be(Ni@Pb12)Be with increasing electric field strength (See Table S4).
For Be(Ni@Pb12)Be, for all the range of studied electric field strengths, its electronic 0 ( ) value increases when electric field increases. Hence, the function 0 ( ) could be approximated to a monotonically increasing curve as it is shown in  Table S4).
The dependence of Ca(Ni@Pb12)Ca 0 ( ) (10 3 au) respect to external electric field strength F (10 -4 au) can also be presented by a monopeak curve，as shown in  Table S4).
Above all, our all-metal electrides switch is based on an electronic structure isomerization due to only an excess electron transfer process. Therefore, these new type of switches are associated with a novel nonbonding electronic mechanism, instead of a chemical bonding mechanism to alter the molecular geometrical structure.
Then the valence and chemical bond nature of the electrides are unchanged in the switching process. This is different from reported cases (forming new valence/bond in altered molecular structure) of chemical change in redox reaction NLO switches and light irradiation NLO switches and so on. Considering the special mechanism of merely altering electronic structure, this switch may be named as electronic structure isomerization switch, while the others are chemical change switches. So such switching should be more sensitive, faster and reversible due to the implementation of a distinctive nonbonding evolution in the electride molecules.
In this work, the field-induced NLO response for an all-metal molecule cannot be explained with the aid of simple two-level model 98,99 involving electron transitionproperties (see Tables S1, S2 and S3 in the Supporting Information).
Nevertheless, some correlations between the maximum β 0 ( ) and corresponding transition energy (∆E) and the oscillator strength f0 are exhibited for these all-metal electride molecules. In Table 4 it is shown that the increasing maximum β 0 ( ) order is consistent with the decreasing order of ∆E and increasing order of f0. Table 4 Working electric field strength (Fw/10 -4 au), the field-dependent electronic contribution to the average static first hyperpolarizability (β 0 ( )/10 3 au), and the corresponding transition energy (ΔE), oscillator strength (f0), and electronic (β ( )/10 3 ) and vibrational (β ( )/10 3 ) contributions to the z diagonal β component (the z axis is defined as the axis that connects the two alkali metals). ηnr/e is the ratio between β ( ) and β ( ).

∆E (eV) f0
transition a Fw β 0 ( ) β ( ) β ( ) ηnr/e  Based on the results obtained for the other two all-metal electride one can assume that also for Be(Ni@Pb12)Be there will be a correspondence between the maximum value of β 0 ( ) and a single lobe or quasi-single lobe shape of the HOMO.
Luis and coworkers have determined and analyzed the vibrational, as compared to the electronic, NLO properties for a representative set of electrides. 82 The effect of vibrations on the hyperpolarizability can be quite important and may even be much larger than the electronic counterpart. 100 In Table 4  For the NLO molecules, the transparent region of electronic absorption spectrum is selected as its working waveband. The region of the working waveband has great importance in the design of NLO devices. Figure 7 show that the three all-metal electride molecules have infrared (IR) transparent region from 1.5 to 10µm (their infrared region to vibrational excitations is > 25μm). Thus, these three all-metal electride molecules could be used as new IR NLO materials.

Figure 7
The electronic absorption spectra of the three all-metal electride molecules.

Notes
The authors declare no competing financial interest.  In the all-metal electride NLO switch molecules, an excess electron is driven by an external electric field from one end of the molecule to the other end, which brings dramatic β0 contrast from 0 (off form) to 10 6 au (on form).