硅桥调控的聚茂钒体系电子结构和输运性质

裴　蕾　张桂玲　尚　岩　孙翠翠　甘　甜

(哈尔滨理工大学化学与环境工程学院，哈尔滨150080)

硅桥调控的聚茂钒体系电子结构和输运性质

裴蕾张桂玲*尚岩孙翠翠甘甜

(哈尔滨理工大学化学与环境工程学院，哈尔滨150080)

利用密度泛函理论和非平衡格林函数的方法对硅桥调控后的聚茂钒体系([V(Cp)2(SiH2)n]m(n=1(a)，n=2(b)，n=3(c)；m=∞；Cp=环戊二烯基))的电子结构和输运性质进行了研究。研究结果表明：随着硅桥的增长，V-V的铁磁性耦合变弱而反铁磁性耦合增强。a和b证实为铁磁性基态，而c更倾向为反铁磁性基态。a和b的铁磁性基态中的每个钒原子的磁距为3.0µB，超过钒-苯络合物或者纯聚茂钒体系的3倍。a－c的输运性质同它们的电子结构相一致，导电性变化规律为c>b>a。对于a和b，自旋向下状态的导电性略强于自旋向上状态。a和c都发生了明显的负微分电阻效应而b却没有，这主要是由于两个二茂钒的排列取向不同：a和c(SiH2为奇数)中二茂钒呈V-型取向排列，进而导致了类似于离子键的量子点耦合，而b(SiH2是偶数)中二茂钒是平行-型取向排列，从而导致了类似于共价键的量子点耦合。此外，由于散射区和两个电极之间的不对称耦合，a－c的导电性对电压施加方向较敏感。

硅桥键；聚茂钒；电子结构；输运性质；理论研究

1　Introduction

Bridge linked polymetallocenes have attracted continuous interest over the past decade due to their unusual electrical,magnetic,and optical properties1－8.Abroad variety of such polymers has been synthesized in laboratory.The bridge moiety can vary fromgroup 13(B,Al,Ga,In)9－12to group 14(Si,Ge,Sn)13－17,group 15(P,As)18－20,and group 16 elements(S,Se)21,22.The metallocene can cover almost the whole first-row transition metal series(Sc-Ni)and some second-and third-row transition metal species(Zr, Hf,Pt)23－27.Much of the interest in these polymers has been focused on the saturated silicon-bridged polymetallocenes;representative examples are the silicon-bridged polyferrocenes28－33.It is confirmed that these copolymers can be utilized as charge dissipation coatings,variable refractive index sensing materials, and magnetic ceramic precursors over a range of length scales34－39.

The silicon linkages possess a remarkable ability to tune the physicochemistry property of the resulting bridged polymetallocenes.The frontier orbitals of a metallocene largely preserve the d character of the transition metal atom;the cyclic π-coordinated carbon ligands confine the d states,making the metal atom an intrinsic molecular quantum dot.The saturated silicon bridges block the adjacent metallocene units spatially and energetically, ensuring the quantum dot behavior of the metal atom40.Quantum dots are of great interest in many research applications such as transistors,solar cells,light emitting diodes(LEDs),and diode lasers because electron transport through quantum dots can be precisely controlled by tailoring the molecular size41,42.The length of the silicon bridge plays a significant role in the interdot coupling.For example,Dement′ev et al.43have shown that the Fe－Fe interaction decreases with increasing of the bridge length in a series of silicon-bridged biferrocenes.Experiments have demonstrated that the conducting behavior of ferrocenylsilane polymers is highly dependent on the length of silicon bridge44. Studying the silicon moiety effect on the electronic and transport properties of the silicon-bridged polymetallocenes is desirable for the generation of functioned molecular devices.

Recently,polymers derived from sandwiched vanadium complexes are of particular hot topics owing to the high density of unpaired spins of V atoms which are expected to exhibit remarkable physical properties with regard to magnetism or conductivity19.So far,much effort has been invested in the synthesis of silicon bridged polymers of vanadium complexes.Pioneering work in this area includes that of Elschenbroich et al.44－49and Braunschweig et al.50－52,who were the first to obtain such silicon bridged polymers by using ring-opening polymerization method of[V(η6-C6H5)2SiMeiPr]and[V(η5-C5H5)(η7-C7H7)SiMeiPr].They demonstrated that these polymers show a pronounced intramolecular electronic and magnetic communication.The silicon bridged vanadium containing polymers[V(Cp)2(SiH2)n]mare expected to be excellent candidates for exploring novel functional materials with fantastic magnetism and conductivity.Similar to the case in ferrocenylsilane polymers41,the silicon bridge length n in [V(Cp)2(SiH2)n]mmay play important role in governing the electronic and transport properties.

In this context,three polyvanadocenes,[V(Cp)2(SiH2)n]m(n= 1,2,3;Cp=cyclopentadienyl),are the major focus of our studies by using density functional method(DFT)and non-equilibrium Green′s function(NEGF)methods(Fig.1).We first investigate the electronic properties of their infinite long systems(n=∞),followed by computing the transport properties of their two-probe devices by curving out one supercell(n=2)sandwiched between two Au electrodes.For the sake of facilitating discussions,we denote infinite long systems of[V(Cp)2(SiH2)]∞,[V(Cp)2(SiH2)2]∞, and[V(Cp)2(SiH2)3]∞as a,b,and c,respectively(Fig.1(a));we also denote two-probe devices of Au/[V(Cp)2(SiH2)]2/Au,Au/ [V(Cp)2(SiH2)2]2/Au,andAu/[V(Cp)2(SiH2)3]2/Au as D-a,D-b,and D-c(Fig.1(b)).We find that the length of the silicon moiety has notable effects on the electronic and transport properties of the silicon bridged polyvanadocenes.

2　Models and computational methods

For computing electronic structures,the infinite long systemsof a,b,and c are modeled via using the periodic condition in the axial direction(Fig.1(a)).Each repeated cell included two vanadocene units.Such supercell could facilitate to consider the magnetic coupling between V atoms.The polymers are separated by~2.4 nm from each other to neglect inter-chain interaction.All the periodic systems are fully optimized until the maximum absolute force is less than 0.2 eV·nm－1.

Table 1　Calculation results of reaction energy(ΔEreaction),supercell length(L),total energy in the FM andAFM states(ETot,FMand ETot,AFM), energy difference between FM andAFM states(ΔEFM-AFM),magnetic moment(S)for a,b,c,D-a,D-b,and D-c

For computing transport properties,the two-probe devices of D-a,D-b,and D-c are adopted(Fig.1(b)).We carved out one supercell,i.e.,[V(Cp)2(SiH2)]2,[V(Cp)2(SiH2)2]2,and[V(Cp)2(SiH2)3]2,as the central scatter region based on the optimized periodic structures to be sandwiched between two Au electrodes. The semi-infinite Au electrodes were modeled by two Au(111)-(3×3)surfaces,and five layers were used for the left and right sides.As the sulfur atom has good affinity with the gold surface, dithiolate derivatives have been used for the construction of metal/ molecule/metal junctions in general53－56.Therefore,in the present work,we also used the sulfur atom as the junction to link the Au electrode and the bivanadocene system.The sulfur atom was set to the hollow site of the electrode as most of the studies had elucidated that the hollow site was more favorable in energy than the top and bridge adsorption sites53－56.In this model,the S－Au distance was set as 0.2341 nm according to the reported literature57,58.Calculations were carried out by changing the applied bias in the step of 0.2 V in the range of－1.0－1.0 V.

All the computations for the infinitely long and two-probe systems are performed using an ab initio code package,Atomistix ToolKit(ATK),which is based on combination of DFT and NEGF methods59－62.Ageneralized gradient approximation(GGA)within the Perdew-Burke-Ernzerhof(PBE)formalism is employed to describe the exchange correlations between electrons.Spin polarization of V atom is considered in all calculations.The on-site correlation effects among 3d electrons of the Vatom are accounted for by using the GGA+U scheme62,where the parameter U－J (Ueff)62is set to be 3.4.A double-ζ basis functional with polarization(DZP)is used for all atoms.A(1×1×100)k-point in string Brillouin zone(x,y,z directions,respectively)is employed. 150 Ry cutoff energy is applied to describe the periodic wave function.

3　Results and discussion

The stability of introducing silicon bridge between vanadocenes is evaluated by the reaction energy ΔE as given following:

Fig.2　Computed projected density of states(PDOS)of polymetallocenes a,b,and c

The calculated ΔEreactionare listed in Table 1.These values of ΔEreactionare all negative indicating exothermic reaction.Hence, inserting silicon bridge between vanadocenes is energetically reasonable.

In this section,we first show results of magnetism and band structures of a－c,followed by transport properties computed based on the two-probe devices of D-a－D-c.

3.1Magnetism

Both the AFM state and FM state of a－c are considered.The calculated energy differences ΔEFM-AFMbetween the FM and AFM states are listed in Table 1.The values of ΔEFM-AFMare－5.88,－0.11,and 0.53 meV for a,b,and c,respectively.This case clearly demonstrates that the length of the silicon bridge plays important role in governing the magnetism.With the lengthening of the silicon bridge,the V-V FM coupling is weakened while the AFM coupling is enhanced.The polymers a and b favor the FM ground state while c prefers the AFM state.The same case is also found for the two-probe devices D-a,D-b,and D-c(Table 1).In fact,the short SiH2unit in a serves as a FM coupling unit for two spin V atoms to be FM coupled.However,in c,the V spin dots are separated far away by the long(SiH2)3segment,direct V-V FM coupling is destroyed.The FM state of a and b shows a magnetic moment S~6.0µBper supercell,i.e.,~3.0µBper V atom(Table 1), three times larger than that of the V-benzene or V-cyclopentadiene multidecker complex63.This value is in agreement with that in vanadocene64.The magnetic behavior of the FM and AFM states is reflected in the projected density of states(PDOS)shown in Fig.2.For the FM state of a and b,the majority spin below the Fermi level(Ef)is greater than the minority spin.The spin polarization is mainly due to the Vatoms.For theAFM state of c,the majority spin and the minority spin are nearly the same near the Efso that their net magnetic moments are nearly zero.These novel magnetic properties of a－c may have potential applications for magnetic nanodevices.

Fig.3　Computed band structures(left panels)of(a,b)polymetallocene a,(c,d)polymetallocene b,and(e,f)polymetallocene c and the Kohn-Sham orbitals(right panels)corresponding to the energy levels(highlighted in color lines)near Efat the Γ point The iso-surface value is 5 e·nm－3.

3.2Band structure

Fig.3 plots the band structures of a－c.It is known that in vanadocene the five d orbitals of V atom split into adz2(a1)orbital and two sets of doubly degeneratedxy,x2－y2(e2)anddxz,yz(e1)orbitals under the Cp ligand field.Here,the a－c supercell contains two V atoms which contribute ten d orbitals to couple with the Cp π orbitals,thereby resulting in ten bands:two a1-like bands,four e2-like bands,and four e1-like bands.In the spin-up state of a and b, the a1-like bands and the e2-likebands are occupied while the e1-likebands are unoccupied.However,in the spin-down state,all the a1-,e2-,and e1-like bands are unoccupied.Therefore,each vanadocene unit in a and b possesses a magnetic moment of S~3.0µB, in line with the computed magnetism.Clearly,the spin-down state has a slightly lower band gap than the spin-up state,suggesting a slightly stronger conductivity in the spin-down state of a and b. In the AFM c,the spin-up state and the spin-down state exhibit a symmetrical band structure.The band gaps are in the order of a> b>c,indicating that the conductivity should follow the sequence of c>b>a.Another feature can be found that the valence and conduction bands in the spin-down state of b display larger dispersion owing to the good coupling between the vanadocene unit and the silicon bridge while those of c show evident flat character due to the block effect of the long silicon bridge.From the PDOS, one can see that the valence band mainly comes from the Vd state, while the conduction band stems from both V d and Si p states. Therefore,the silicon σ orbitals can also participate in conducting by accepting electrons from the V atom.

Fig.4　(a)Total I－V curves of D-a,D-b,and D-c two-probe devices;(b,c,d)Spin polarized I－V curves of D-a,D-b,and D-c two-probe devices,respectively

3.3Transport properties

To confirm the predication of the transport property based on the electronic structures,we have also computed transport properties of two-probe devices D-a,D-b,and D-c by sandwiched finite-sized a,b,and c between two Au electrodes(c.f.Fig.1(b)). The computed current－voltage(I－V)curves based on the twoprobe devices are shown in Fig.4,from which several characteristics attributable to silicon bridge can be found at the bias voltage of－1.0－1.0 V.

First,the silicon bridge could remarkably tune the magnitude of total current(Fig.4(a)).Overall,the two-probe system D-c shows the highest conductivity,followed by D-b,while D-a is the lowest.This is in good agreement with the band structure analysis. Fig.5(a)gives the transmission spectra(TS)at 0.0 V bias voltage. Clearly,near the Ef,D-c shows the largest TS peak,while D-a has the smallest.

Second,D-a and D-b systems show spin polarized transport property,i.e.,the spin-down state gives a higher conductivity than the spin-up state(Fig.4(b,c)).In contrast,for D-c,the spin-up state and the spin-down state exhibit close magnitude of current under a certain bias voltage,suggesting an unpolarized transport property.These results are consistent with electronic structures of their infinitely long systems.Fig.5(a)also indicates that the spindown states of D-a and D-b offer larger TS peaks than the spin-up state near Ef,while the spin-up state and spin-down state in D-c devote similar TS contributions.

Third,D-a and D-c give rise to evident negative differentialresistance(NDR)peaks at the considered bias voltage－1.0－1.0 V,while D-b cannot.In fact,in metallocene polymers,the Cp ligands confine the d states of metal atom,making the metal atom an intrinsic molecular dot.Experiments have demonstrated that the metal-to-metal communication plays an important role in the conducting behavior65－67.Fig.6 plots the calculated electrostatic potential for D-a,D-b,and D-c two-probe devices.Evidently,in D-a and D-c,the saturated silicon bridge blocks the two vanadocene units effectively,leading to an ionic-like interdot coupling. Electronic transport through ionic-like coupled quantum dots are covered by Coulomb blockade theory68,69,which usually results in NDR behavior.In contrast,electron delocalization through silicon bridge becomes easier for the parallel orientation compared to the V-shape.The covalent-like interdot coupling occurs in D-b owing to the high electron delocalization through the silicon bridge.The strong covalent-like interdot coupling in D-b induces a coherent tunneling,and thus cannot give a significant NDR behavior.The above differences may be originated from the orientation of the two V(Cp)2,which is V-shape for a and c(odd-numbered SiH2unit)and parallel for b(even-numbered SiH2unit).The NDR phenomenon of D-a and D-c is of important application in multiple-valued logic devices.For D-a,NDR peaks appear at 0.2 and－0.8 V;and for D-c,NDR peaks locate at 0.6 and－0.8 V.This NDR feature can be further interpreted from the TS distribution exemplified by D-a in Fig.5(b).Clearly,at 0.2 V and near the Ef, the magnitude of the TS of D-a is much larger than that of 0.4 V, resulting in the sharp dropping of the current from 0.2 to 0.4 V.

Fig.5　(a)Transmission spectra(TS)of D-a,D-b,and D-c twoprobe devices at 0.0 V bias voltage;(b)TS of D-a two-probe device at 0.0,0.2,and 0.4 V bias voltages;(c)TS of D-b two-probe device at 1.0 and－1.0 V bias voltages

Last,the conductivity is sensitive to the current direction owing to the asymmetric coupling between the scatter region and the two electrodes.The magnitude of the current under a negative bias voltage is evidently larger than that under a corresponding positive bias voltage.This phenomenon can be reflected from the TS in Fig.5(c).Take D-b as an example,clearly,TS peaks near Efat V=－1.0 V are larger than those at V=1.0 V.

Fig.6　Computed contour plot of potential distribution for D-a,D-b,and D-c

4　Conclusions

Silicon bridge tuned electronic and transport properties of polymetallocenes,[V(Cp)2(SiH2)n]m(n=1(a),n=2(b),n=3(c); m=∞;Cp=cyclopentadienyl),are studied using DFT and NEGF methods.With the lengthening of the silicon bridge,the V-V FM coupling is weakened while the AFM coupling is enhanced.a and b favor the ferromagnetic(FM)state ground state,while c prefers the antiferromagnetic(AFM)ground state.Each V atom in the FMstate of a and b shows a magnetic moment of~3.0µB,three times larger than that in the V-benzene or V-cyclopentadiene multidecker complex.The transport properties of a－c are in good agreement with the electronic structures.The conductivity follows the sequence of c>b>a.For a and b,the spin-down state has a slightly stronger conductivity than the spin-up state.a and c can both give rise to evident negative differential resistance behavior while b cannot.This differences may be originated from the orientation of the two V(Cp)2:V-shape for a and c(odd-numbered SiH2unit) leading to ionic-like interdot coupling while parallel for b(evennumbered SiH2unit)leading to covalent-like interdot coupling.In addition,the conductivity of a－c is sensitive to the current direction owing to the asymmetric coupling between the scatter region and the two electrodes.

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Silicon Bridge-Tuned Electronic Structures and Transport Properties of Polymetallocenes

PEI LeiZHANG Gui-Ling*SHANG YanSUN Cui-CuiGAN Tian
(College of Chemical and Environmental Engineering,Harbin University of Science and Technology,Harbin 150080,P.R.China)

Silicon bridge-tuned electronic structures and transport properties of polymetallocenes, [V(Cp)2(SiH2)n]m(n=1(a),n=2(b),n=3(c);m=∞;Cp=cyclopentadienyl),are studied using the density functional theory(DFT)and non-equilibrium Green′s function(NEGF)methods.As the silicon bridge is lengthened,the V-V ferromagnetic(FM)coupling is weakened,while the antiferromagnetic(AFM)coupling is strengthened.Polymetallocenes a and b favor the FM ground state,while c prefers the AFM ground state.Each V atom in the FM state of a and b has a magnetic moment of~3.0µB,three times larger than that in the V-benzene or V-cyclopentadiene multidecker complex.The transport properties of a－c are in good agreement with their electronic structures.Their conductivities follow the sequence c>b>a.For a and b,the spin-down state has slightly higher conductivity than the spin-up state.Polymetallocenes a and c can both display evident negative differential resistance(NDR)behavior,while b cannot.This difference may originate from the orientation of the two V(Cp)2units,which is V-shaped for a and c(odd number of SiH2units),leading to ioniclike inter-quantum dot coupling,and parallel for b(even number of SiH2units),leading to covalent-like interquantum dot coupling.In addition,the conductivity of a－c is sensitive to the current direction because of the asymmetric coupling between the scattering region and two electrodes.

Silicon bridge;Polymetallocene;Electronic structure;Transport property;Theoretical study

April 5,2016;Revised:June 28,2016;Published online:June 29,2016.

.Email:guiling-002@163.com;Tel:+86-451-86392705.

O641

10.3866/PKU.WHXB201606295

The project was supported by the National Natural Science Foundation of China(51473042).国家自然科学基金(51473042)资助项目©Editorial office ofActa Physico-Chimica Sinica

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