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Theoretical Investigation on Structures and Nonlinear Optical Properties of the Alkalis and Low Coordination Acenes Salt.

Byline: Wenmin XIAO and Dongmei LUO

Summary:

The alkalis and low coordination acenes salts a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) were designed to investigate the effect of the increasing atomic number of alkali metals and the number n of conjugated benzenoid rings on the nonlinear optical responses. Alkalis Li, Na and K were selected herein, and both DFT (M05-2X, M06-2X and PBE0) and MP2 methods and 6- 311+G(D) basis set are employed to optimize geometrical structures and to calculate the polarizability (a0) and first hyperpolarizability (AYvec) of the a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3). Results show that the a0 values of a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) increase with increasing number of n conjugated benzenoid rings and the atomic number of alkali metals and AYvec values of a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) are opposite.

The AYvec values of a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) are inceasing remarkably (397.6 au. for a-Li@ benzene less than 1196.5 au. for a-Na@benzene less than 1608.6 au. for a-K@benzene and tending to decease with increasing number of n by M06-2X method. Our present research may be favorable to the development of excellent nonlinear optical (NLO) materials.

Keywords: a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3); Nonlinear optical properties; First hyperpolarizability; Theoretical Investigation; Polarizability; Interaction energy.

Introduction

Materials with nonlinear optical (NLO) characteristic [1] have been developed rapidly owing to their widespread applications research and development and optical communications improvement. Different types of unexceptionable NLO materials have been widely reported [2] and theoretical investigation plays a significant role in finding approaches to improve nonlinear optical response.[3] Under the influence of these effective ways the strength of donors and receptors were enhanced, p-electron systems were twisted , push- pull effects were increased, bond lengths were alternated (BLA), metals were doped into organic compounds, and the length of p conjugations were widened.[4] Some organic compounds which have extended p-delocalized systems have been paid close attention because of their low cost, feasibility of fabrication and so on. of improvement extremely recently.[5-8]

In 2000, the lithiation effects of the conjugated benzenoid rings on the second hyperpolarizability were investigated first by Papadopoulos et al.[6] The results show that lithiation of the conjugated benzenoid rings with small planar p conjugation leads to a tremendous enhancement of the second hyperpolarizability. Further, the lithiation effects on the first hyperpolarizability of tubiform [5] cyclacenes with tubular p conjugation were investigated by Li's group [7] in 2009. Obviously, the first hyperpolarizability was significantly increased about 1200 times from [5]cyclacenes to Li5-[5]cyclacenes ascribed to the lithiation effect. Thus, the lithiation effect can remarkably increase the nonlinear optical response of p-conjugated systems. In 2011 the relationship between the first hyperpolarizability and the of the conjugated benzenoid rings number of Li@n- Acenes Salt (n =1, 2, 3, and 4) was studied by Cui- Cui Zhang.[9]

The results revealed that the tot values for a-Li@n-acenes are slowly decreasing with increasing number n of conjugated benzenoid rings.

Since there are interesting effects of Li to the conjugated benzenoid rings we had like to know what will Na and K ions do in the similar systems, and what regulations can be found for such potential nonlinear optical materials. Inspired by the information above, the a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) were designed to research the nonlinear optical responses to acquire different alkali metals doped NLO molecules. The a- M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) were formed by a Li(or Na and K) atom substituting a-H. We are interested in the changing polarizability and first hyperpolarizability on changing the element of alkali metals and increasing the number n of conjugated benzenoid rings. Some useful regulations have been found in the paper herein.

Computational Details

The geometrical structures of the a-M@n- acenes (M = Li, Na and K) salts (n = 1, 2 and 3) were optimized by using the B3LYP/6-311+g(d) level.[10] The level is sufficient to optimize the structures of the a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3), and the geometric parameters are listed in Table-1. Li@benzene was taken as an example to test the basis set, and the results were reliable. We use ab together with FF to analyze their nonlinear optical characteristics. However, the MP2[11] method is a dependable method compared with B3LYP, but it is resources and time consuming. It was lucky that the results of the DFT methods M05-2X, M06-2X and PBE0 together with FF are similar to those of the MP2 results. M05-2X is a new kind of density functional which is proposed by Zhao and Truhlar and can be used well to describe medium-range correlations and is satisfactory for some organic compounds research.[12]

Zhao and Truhlar have recently developed the M06 family of local hybrid (M06, M06-2X)that how promising performance for studying main group elements themochemistry, kinetics ,noncovalent interactions, excited states, and transition elements.[13] Meanwhile, PBE0 is the 1996 gradient-corrected correlation functional of Perdew, Burke and Ernzerh.[14] Most calculations using the MP2, M05-2X and PBE0 were carried out with the Gaussian 09 program package,[15] whereas the NBO (natural bond orbit) analysis was performed by the Gaussian 03 program package.[16] The dipole moment (0) and polarizability (a0) are expressed as follows.

Equations

Table-1: Symmetry (PG), Energy (HF), Geometrical parameters (bond length and bond angle) and NBO charge distribution of a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3)

System###PG###HF(eV)###Bond###Bond angle###NBO(C)###NBO(M)

###length(A )###(deg)###Q(X)/e

###-

###1a-Li###C2v###-6507.6###1.9581,1.9582,1.9583###122.91,122.92,122.93###Q(C

###-0.649)/e###0.897

###1a-Na###C2v###-10719.1###2.2971###122.41###-0.574###0.886

###1###1

###1a-K###C2v###-22626.8###2.715###122.9###-0.562###0.921

###1###1

###2a-Li###Cs###-10688.7###1.975###121.0###-0.597###0.894

###1###1

###2a-Na###Cs###-14900.1###2.309###122.6###-0.524###0.888

###1###1

###2a-K###Cs###-26807.9###2.719###119.0###-0.511###0.922

###1###1

###3a-Li###Cs###-14869.5###1.974###120.6###-0.590###0.897

###1###1

###3a-Na###Cs###-19084.1###2.314###121.7###-0.518###0.890

###1###1

###3a-K###Cs###-30992.8###2.663###116.4###-0.906###0.924

where E0 is the energy of the molecule in the absence of an electric field, i is its permanent dipole moment, aij is the dipole polarizability, and AYijk and ijkl are the first and second hyperpolar-izablities, respectively. As implied by this, the polarizabilities can be computed by employing derivatives of the energy or dipole moment with respect to the incident electric field. Tocomputethe polarizability and hyperpolarizability, one option is to take the derivates either analytically or numerically. In the present work, we have investigated the difference between analytical derivative methods and FF Method in order to get better results of systems selected.

The static first hyperpolarizability AYvec was calculated by M06-2X Method combined with FF(finite field method), which is more efficient and less expensive than other methods compared with, where AYvec represent the hyperpolarizability along the molecular dipole moment defined as follows:

Equations

Results and Discussion

Geometrical Parameters

The optimized structures of a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) are named as 1a-Li, 2a-Li and 3a-Li in a-Li@n-acences system, and 2a-Li, 2a-Na and 2a-K belong to a-Na@n- acences and a-K@n-acences systems, (as shown in Fig. 1) The parameters of structures of the a-M@n- acenes (M = Li, Na and K) salts (n = 1, 2 and 3) are listed in Table-1. From Table-1, noticeably, the C-Li bond lengths of a-Li@n-acenes are from 1.958 A to 1.975 A , and the changes of C-Li bond lengths are more slightly than those of a-Na@n-acences and a- K@n-acences (C-Na: from 2.297 A to 2.309 A , C-K: from 2.715 A to 2.719 A ) in which the number n of conjugated benzenoid rings is from 1 to 3, and bond lengths of C-M (M=Li, Na and K) become larger same alkali metal atom.

We can see that bond lengths of C-M (M=Li, Na and K) become larger and larger from Li to K when n is equal in different system, which is consistent with atom radiuses of Li, Na and K. Interestingly, the C-Li bond lengths of a-Li@n- acenes salts all increa se with increasing number n, and the adding of the conjugated effect obviously increases the C-Li bond lengths than others.

From Fig. 2, the bond angles which are formed by the Li(K)-C-C atoms are expressed as . On the contrary we can see from the C-Li bond lengths that the values decrease with increasing number n, while the values of bond angle which are formed by the Na-C-C atoms increases with increasing number n. Also, the values, 122.9 degree formed by the Li (K)-C-C atoms which is somewhat larger than that formed by the Na-C-C atoms 122.4 degree when the number n is equal to 1, but the opposite result appears when n is equal to 2.

The natural bond orbit (NBO) charges of C- combined with alkali metal atom, Li+, Na+, K+ are acquired by the B3LYP method. NBO charge of a- M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) alkalis ions are larger on Li+ to K+ than that on Na+, and the values of NBO charge exceeds +0.886 on all alkalis ions, which indicates that a-M@n-acenes (M=Li, Na and K) are new type alkalis salts, especially on K+ ion where the NBO charge value is over +0.920. The variation ranges of the C-Na bond properties and the NBO charge are very small, while which of C-K (Li) are varying in relatively obvious ranges.

Optical Characteristic

Linear Optical Characteristic Dipole Moment( 0) The 0 values of a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) were computed with B3LYP method, which are in detail listed in Table-2. From Table-2 in a-Li@n-acences system 0 values are 0.86, 1.05 and 1.11 a.u., respectively. The same changing tend can be found in a-Na@n-acenes salts which 0 values are and 0.86, 0.93 and 1.24 a.u., and in a-K@n-acenes salts with 0 values 1.05, 1.58 and 1.81 a.u., respectively.

The 0 values increase with increasing number n in a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) system, and interestingly the same regulation can be found in them when the number n is equal according to the different alkali metal atoms from Li to K. Properties of a-M@n- acenes (M = Li, Na and K) salts (n = 1, 2 and 3) are together affected by adding the conjugated benzenoid rings and different alkali metal atoms with different losing electron feasibility and atomic radius, which also obviously increases 0 values when losing electron feasibility and atomic radius of alkali metals increase 0 values are increase correspondingly.

Linear Optical Characteristic Polarizability (a0)

The polarizability (a0) of a-Li@n-acenes was calculated by using MP2, PBE0, M06-2X and M05-2X methods and the results were listed in Table-2. a0 values of a-Li@n-acenes are uniformly uptrended. The a0 values acquired by the three methods above are enhancive with the increasing number n. The M05-2X a0 values are highest and the PBE0 a0 values are lowest while the MP2 a0 values are middle among these a0 values, and the a0 values by M06-2X method are close to those by MP2 method. After all the three methods were compared for a0 values, we found that M06-2X and PBE0 a0 values are in good consistent regularity with MP2 does. Yet, the a0 values acquired by M06-2X methods are very consistent with that obtained by the MP2 and the method M06-2X are better computing time and resources saving than MP2 does, therefore we choose the two methods to perform all calculations for a0.

Furthermore, taking M06-2X as an example to compare the a0 values of a-Li@n- acenes, a0 values (81.8 a.u. to 188.2 a.u.) increase when the number n increases, and in a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) system a0 values (81.8 a.u. to 97.4 a.u.) increase when the number n is equal to 1 similar regularity when the number n is equal to 2 with a0 values from 119.2 a.u. to 134.1 a.u. in a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) when atoms are from Li to K. We can see from Table-2 that a0 values increase when n increases as far as the same alkalis ion is concerned.

Nonlinear Optical Characteristic First Hyperpolarizability (AYvec) in Static State

First hyperpolarizability (AYvec) values in static state of a-Li@n-acenes acquired from different methods are listed in detail in Table-2. Interestingly, Table-2 reveals that the AYvec values of a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) are not changed dramaticlly with increasing number n, and the AYvec values are the largest ones when n is equal to 2, while AYvec values increase obviously when the number n is equal and when atoms are from Li to K. From Table-2, the AYvec values acquired by the PBE0 method are the largest ones compared with the other two methods. The PBE0 method sometimes overestimates the AYvec values, and the method of M06- 2X exhibits similar AYvec values and it reproduces the MP2 results for the a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3). As a comparison, M05-2X method is also performed to get a kind of AYvec values, but the results from which are not regular as PBE0 and not close to those from MP2.

Therefore, the MP2, M06-2X methods are in good compromise situation for their quality and efficiency in calculations of polarizability and hyperpolarizability, but M06-2X method is better computing time and resources saving than MP2 does, therefore we choose the M06-2X and PBE0 methods to perform all calculations for AYvec because the results from PBE0 method reveals the same regularity and changing tend with M06-2X method. We can see from Table-2 that the AYvec values of a-Li@n-acenes reduce slowly from 397.6 a.u. for a-Li@benzene to 407.8 a.u. when the number n is changed from 1 to 2 at the same time, and which is decreases to 331.2 a.u. when n is equal to 3, which is consistent with geometrical parameters such as bond length and bond angle, and it might be the warping induced by large anthrecene molecule with the M06- 2X method.

On the contrary, from Table-2 the AYvec values of a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) are significantly enhanced when atoms are from Li to K at different methods from 397.6 a.u. to 1608.6 a.u., and the AYvec values are more and more larger contrasted to a-Li@n-acenes because the feasibility of losing electron increases from Li to K.

The orders of the AYvec values in the a-Na@n-acenes and those of the AYvec values of a-K@n-acenes are concordant. As is shown in the above discussion, the AYvec values of a-Li@n-acenes salt have been overestimated by the PBE0 method. The M06-2X method acquired the extremely close AYvec values compared with the MP2 result, whereas the AYvec values acquired by the M06-2X method are smaller than those of the other methods. Comparing these AYvec values from different methods shows amazing variation trends as is shown in Table-2. Thus, the AYvec values of a-Li@n-acenes (by the reliable M06-2X method) are reducing and the AYvec values of a- Na(K)@n-acenes are increasing with the increasing number n. The data from Table-2 reveals that the a0 values and AYvec values show remarkable specialties of the a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3). Thus, all the a0 values and AYvec values are likely about to the structure of a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3).

On the basis of the two-level formula, [19] the first hyperpolarizability is mainly affected by the transition energy, and it can interpret the relationship between components and composing structures with nonlinear optical property.[9] To further understand the first hyperpolarizability, the transition energies of a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) were computed by the TD-PBE0 method and the results of which are listed in Table-3.

Equations

where , which means the difference value of dipole moments between the basic state and the excited state, Eeg refers to the transition energy, and feg refers to the oscillator strength. From Formula (4) we can see AYvec values are in proportion to the oscillator strength feg and in inverse proportion to the cube of.

Theoretical research indicates that PBE0 method can obtain much reliable prediction of the transition energy.[20]

Table-2: Dipole moment ( 0), polarizability (a0)and Static First Hyperpolarizability (AYvec) at Different Levels of a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3)

###System###0(a.u.)###0(a.u.)###vec(a.u.)

###1a-Li###0.86###79.6a###83.3b###81.8c###82.4d###379.0a###450.4b###397.6c1###381.4c2###399.5d

###1a-Na###0.93###95.6a###102.0 b

###94.0c###1291.9a###1633.5b###1196.5c

###1a-K###1.24###97.3a###109.8b###97.4c###2103.1a###3637.9b###1608.6c

###2a-Li###1.05###129.3a###131.6b###119.2c###287.6a###332.8b###407.8c

###2a-Na###1.13###141.8a###149.2b###141.0c###1093.5a###1508.6b###1001.7c888

###2a-K###1.58###145.4a###155.8 b

###134.1###1699.1a###2765.4b###1606.4c

###3a-Li###1.11###187.0a###193.0b###188.2c###329.8a###389.1b###331.2c

###3a-Na###1.22###198.6a###198.5b###197.8c###1151.5a###1148.6b###1035.9c

###188.5cccc

###3a-K###1.81###200.7a###215.3 b

###cc###1241.7a###2638.0b###1445.9c

Table-3: Transition energy and oscillator strength and correspongding dominant molecular orbital(MO) tran sitions of a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3)

###System###Eeg###eg###main assignments (coefficient)

###HOMO-2LUMO+8(44%)

###1a-Li###6.88###0.3311

###HOMO-3LUMO+7(30%)

###HOMO-2LUMO+9(36%)

###1a-Na###6.80###0.4940###HOMO-1LUMO+7(20%)

###HOMOLUMO+14(19%)

###HOMO-2LUMO+9(43%)

###1a-K###6.74###0.5222

###HOMO-1LUMO+8(19%)

###HOMOLUMO+11(23%)

###2a-Li###5.87###0.5096

###HOMO-2LUMO+1(13%)

###HOMO-2LUMO+1(24%)

###2a-Na###5.75###0.6309

###HOMOLUMO+6(17%)

###HOMOLUMO+16(23%)

###2a-K###5.71###0.4156###HOMOLUMO+15(22%)

###HOMO-2LUMO+14(17%)

###HOMOLUMO+9(27%)

###3a-Li###5.10###0.9210

###HOMO-2LUMO+1 (17%)

###HOMO-2LUMO+1(24%)

###3a-Na###5.12###1.23

###HOMOLUMO+4(22%)

###HOMO-2LUMO+1(31%)

###3a-K###5.02###1.383

###HOMOLUMO+6(24%)

The Eeg values show an decreasing trend for a-Li@n-acenes (6.88 eV greater than 5.87 eV greater than 5.10 eV) with the increasing number n and a decreasing trend of Eeg values for a-M@n-acenes (M = Li, Na and K) salts (n = 1) (6.88greater than 6.80greater than 6.74 eV) when the number n is equal with the metal atoms are changed from Li to K from Table-3. Thus, the Eeg values of a-M@n- acenes (M = Li, Na and K) salts (n = 1, 2 and 3) are decreasing with the increasing number n, which is inconsistent with the increasing alkali metal atomic number from Li to K. From corresponding AYvec values of a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) we can see the results are coincident with Formula (4), which can interpret well why in a- M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) system AYvec values decrease with the increasing number n and in a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) system AYvec values increase with the increasing alkali metal atomic number from Li to K.

Therefore, systems selected her ein, a-H on benzenoid rings substituted by alkali metals with more feasibility of losing electron atoms which can gain more stronger nonlinear optical response in a- M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) system.

Electronic Transition

It is well-known that the frontier molecular orbits (FMOs) and HOMO-LUMO gaps (Eg) are heavily related to the optical and electronic properties. An electronic excitation results electron density redistribution that affects the molecular geometry.[21] To gain insight into the influence of the optical and electronic properties, the distributions of the FMOs in a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) are investigated, and their sketches are plotted in Fig. 3. The FMOs transition energies from EHOMO to ELUMO, , and HOMOs and LUMOs contributions of individual fragments (in %) to the FMOs of a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) using the TD-PBE0/6-311+G(D) method are given in Table-3.

The major assignment of the lowest electronic transitions for a-M@n- acenes (M = Li, Na and K) salts (n = 1, 2 and 3) are basically HOMO (0,-2) LUMO and HOMO LUMO (+1 to +16), while the corresponding lowest electronic transitions for a-Li @n-acenes sa lts are mainly HOMOs (-2, 0) LUMOs (+8 to +11). The lowest electronic transitions for a-M@n-acenes (M = Li, Na and K) salts (n = 1, 2 and 3) correspond to a s-p excited singlet state as visualized in Fig. 3. In a-Li @1-acene salt, in HOMO-2,electronic cloud concentrates on benzenoid ring, while in LUMO+8 electronic cloud concentrates on benzenoid ring and a-Li, which indicates charge has been transferred from benzenoid ring to a-Li.

For a-Li@2-acenes salt the HOMO is mainly composed of contributions of benzenoid rings at HOMO fragments, with major contributions to the whole molecule in LUMO+11, but the electronic cloud is more on conjugated benzenoid rings than that on a-Li. As to a-Li@3- acenes salt, in HOMO, electronic cloud distributes on conjugated benzenoid rings equally, while LUMO+11, electronic cloud distributes on the whole molecule unequally, and it is minor on the benzenoid ring combined with a-Li. In compare of the three systems, we can see that the largest transiting distance is in a-Li @1-acene salt, which might be the right reason for its maximum first hyperpolarizability AYvec value. In a-Na(K)@n-acenes salt systems , when n is equal to 1 in HOMO-2 orbit, the electronic cloud concentrates on benzenoid rings, while in LUMO+8 orbit the electronic cloud decentralizes on a-Li and benzenoid rings which reveals that there is charge transfer from benzenoid rings to a-Li.

In a-Na@1- acenes salt system in HOMO-2 orbit, the electronic cloud totally concentrates on benzenoid ring in average from the right side to the left side by a line via a-Na atom, while in LUMO-9 orbit the electronic cloud averages on the whole benzenoid ring shared by every carbon atom. The same electron transition phenomenon appears in a-K@1-acenes salt, and the maximum electronic cloud concentrates on C-K bond, therefore the obvious charge transition occurs there. Comparison of the three systems, we can see the transferring distance in a-K@1-acenes salt is longer than the other two, which maybe the fundamental reason for its larger first hyperpolarizability AYvec values.

In a-Na(K)@n-acenes salt systems , when n is equal to 2 in a-Li@2-acene salt the electronic density totally concentrates on conjugated benzenoid rings in HOMO orbit, while the electronic density decentralizes on the whole system in LUMO+11 orbit which is somewhat more on the conjugated benzenoid rings than that of other parts of the complex, which indicates that charge has been transferred from conjugated benzenoid rings to a-Li. As to a-Na@2-acenes salt system in HOMO-2 orbit the electronic density totally concentrates on conjugated benzenoid rings in three parts equally and vertically, while in LUMO+1 orbit the electronic cloud decentralizes on the conjugated benzenoid rings in average, which reveals that there is no obvious charge transition.

From the electron transiting Fig we can see that in HOMO orbit the electron density concentrates on a-K and its combining conjugated benzenoid ring in a-K@2- acenes salt, while in LUMO+16 orbit, the electronic cloud are almost concentrated on a-K, but there is very little of which on the conjugated benzenoid rings. Comparison of the three systems, we can see the transferring distance in a-K@2-acenes salt is longer than the other two, which maybe the fundamental reason for its larger first hyperpolarizability AYvec values. In a-Na@3-acenes salt system in HOMO-2 orbit the electronic density totally concentrates on conjugated benzenoid rings in three parts equally and vertically, while in LUMO+1 orbit the electronic cloud decentralizes on the conjugated benzenoid rings in average, which reveals that there is no obvious charge transition.

It is interesting that the distribution of electronic cloud in a-K@3-acenes salt system is similar to that of a- Na@3-acenes salt system, and the percentage of orbits is nearly the same, too. From Fig. 3 we can see that with the increasing atomic number of alkali metal atom, the radius of which increases and the feasibility of losing electron increases also, therefore, the electronic cloud is easy to be polarized, which maybe the right reason for its increasing first hyperpolarizability AYvec values.

Conclusion

Three computational methods CAM-B3LYP, M05-2X, M06-2X and PBE0 have been used to calculate the nonlinear optical property of a-M@n- acenes (M = Li, Na and K) salts (n = 1, 2 and 3) alkali metal salts, among which we get the relationship between their structures and the first hyperpolarizability AYvec values as follows: With the increasing of the number n, the AYvec values of a- Li@n-acence reveal the tend of decreasing. But when the n is equal, with the increasing of the atomic number of alkali metal atoms which substitutes the a- H and the increasing feasibility of losing electron, the values of the first hyperpolarizability AYvec are increasing dramatically in a-Na(K)@n-acenes alkali metal salts, therefore the change regulation of the values of the first hyperpolarizability AYvec are opposite in a-Li@n-acence and in a-Na(K)@n-acenes alkali metal salts.

The values of the first hyperpolarizability AYvec and their corresponding transition energy Eeg in a-Li@n-acence salts are not coincid ent with the simple two-level energy formula, while in a- Na(K)@n-acenes alkali metal salts the values of the first hyperpolarizability AYvec are in good relationship of inverse proportion to the cube of Eeg , which indicates that a-Na(K)@n-acenes alkali metal salts have higher nonlinear response than those of a- Li@n-acence alkali metal salts. From the figure of electron transition we can see, if a system has longer distance of electron transition, it maybe has larger first hyperpolarizability AYvec value among a-M@n- acenes (M = Li, Na and K) salts (n = 1, 2 and 3) alkali metal salts herein.

Acknowledgments

The authors gratefully acknowledge the financial support from the Natural Science Foundation of Inner Mongolia, P.R. China (No. 2014MS0214) and Inner Mongolia Key Laboratory of Photoelectric Functional Materials and Youth Science Foundation of Heilongjiang Province, P.R. China (QC2010121).

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