Chalcogenide Letters Vol. 11, No. 7, July 2014, p THE QUANTUM MECHANICAL STUDY OF CADMIUM SULFUR NANOPARTICLES IN BASIS OF STO s

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1 Chalcgende Letters Vl. 11, N. 7, July 014, p THE QUNTUM MECHNICL STUDY OF CDMIUM SULFUR NNOPRTICLES IN BSIS OF STO s M.. RMZNOV *, F. G. PSHEV,. G. GSNOV,. MHRRMOV,. T. MHMOOD Baku State Unversty, zerbajan, The electrnc structure f the cadmum sulfur nanpartcles were nvestgated by sememprcal Wlfsberg Helmhlz methd. Ths s a varant f the mlecular rbtals methd. Mlecular rbtals are represented as a lnear cmbnatn f valence atmc rbtals f the atms f the nanpartcle. s the atmc rbtals used 5s-, 5p x -, 5p y - and 5p z - Slater type atmc rbtals(sto s) f cadmum atms and 3s-, 3p x -, 3p y - and 3p z - rbtals f sulfur atms. The expnental parameters f STO s were calculated and defned the analytc expressn f the bass functns. The numercal values f the unknwn ceffcents f the lnear cmbnatn are fund by slutn f euatns f mlecular rbtals methd. Calculatns were carred ut wth ts wn cmputer prgram. The rbtal energes, ptental nzatn, the ttal electrnc energy and effectve charge f atms f cadmum sulfur nanpartcles were calculated. The results ndcate that the cadmum sulfur nanpartcle are sft, electrphle and sem-cnductve stable materal. (Receved June 31, 014; ccepted July 5, 014) Keywrds: Quantum mechancal calculatns, nantechnlgy, cmputer mdelng. 1. Intrductn The cadmum sulfur nanpartcles have a wde range f applcatns due t ther nvel prpertes. Cadmum sulfur s bradly used as a p-type semcnductr n electrncs. They are valuable materals n preparng phtelements, sun batteres, pht and lght dds. Fr ths reasn, they have attracted the attentn f great number f expermental and theretcal grups. [1,, 3]. The prpertes f nanpartcles depend n ther sze and number f atms. In the presented wrk cnsdered the determnatn f number f atms n the dependence f sze f dfferently structured nanpartcles. In rder t defne the number f atms n nanpartcles, whch s cmpsed wth the same type f atms, n [4], s gven the fllwng frmula. N 3 D N (1) 6M N - number f atms, - dencty f materal, N -vgadr number, M - mlar mass, D - s dametr f sphere that nanpartcle s settled. There are sme ther euatns fr determnatn the number f atms and sze f nanpartcles. But these euatns nclude mre cmplcated parts and t s dffcult t calculate them. The presented wrk s devted t calculatn f number f atms n nanpartcles wth gven sze, but cmpsed by dfferent atms. It s suppsed that nanpartcle has the spherdal shape. Let s cnsder the determnatn f n n cmpund the sze f ts radus s r h rcd rs (Pc.1.). Where cd ( CdS) n nanpartcle. Fr spherdal CdS r and r s - are cvalent radus f Cd and S atms. The number f atms n nanpartcle wth R radus (Pc..) can be calculated ( R - the gven radus): * Crrespndng authr: mamed_r50@mal.ru

2 360 Where 3 r h R rh, nternal radus f nanpartcle (pc..), h r R 0, 5nm then n= fr ( CdS) n. The number f atms s eual R r n () r - radus f CdS (pc. 1.). When Pc 1. Pc. Pc 3. Cadmum sulfur (CdS) nanpartcle In ths wrk the electrnc structure f the (CdS) nanpartcles were nvestgated by sem-emprcal Wlfsberg Helmhlz (WH) methd. It s knwn that the WH methd s a smple sem- emprcal varant f the mlecular rbtal (MO) methd [5- ]. In MO the state f the electrn s descrbed wth ne electrn wave functn s-called mlecular rbtal. Mlecular rbtals U are multcenter functns. Thus, the dstances frm electrn t varus nucleus f atms are nclude nt ther expressn. There are varus ways t cnstruct mlecular rbtals. One f them s MO LCO apprxmatn. In ths apprxmatn the mlecular rbtals are represented as a lnear cmbnatns f valence atmc rbtals f atms f the nanpartcles. U where, C- the unknwn ceffcents, - atm rbtals gven as bass functns. In ths wrk the real Slater type atmc rbtals (STO s) were used as bass functns. It s well-knwn that the calculatn f multcenter matrx elements ver expnental type rbtals (ETO s) s the great mprtance fr accurate evaluatn f prblems n uantum chemstry and physcs. mng the ETO s cmmnly used are the Gaussan type rbtals (GTO s) and STO s. The STO s represent the real stuatn fr the electrn densty n valence regn, but are nt s gd nearer t the nucleus. Many calculatn ver the years have been carred ut wth STO s[10-]. The real STO s are determned as nlm 1 n ( ) (, r) r (n)! n1 m 1 e r C S lm (, ) (3). (4)

3 S (, ) - are real sphercal harmncs and n,, m are the prncpal, rbtal and magnetc lm uantum numbers, s expnental parameter wth determned by frmulas gven n [17]. Usually n uantum mechancs calculatns f electrnc structure mlecules satsfed wth nly cnsderng the atmc rbtals f valence electrns. Fr the creatn f mlecular rbtals f (CdS) nanpartcles are used 5s-, 5p x -, 5p y -, 5p z - STO s frm each Cd atms and 3s-, 3p x -, 3p y -, 3p z - STO s frm each S atms. Thus, 7 STO s were used. The analytc expressns f atmc rbtals are cnsdered as fllw : 361 3s 3 p x 3 p y 3 pz 5 s 5 px 5 py 5 pz 1, , ( Cd ) (,088, r) r e 311 4, Cd (,088, r) r e 311 4, Cd (,088, r) r e 310 1, S (, , r) r e 500 1, S (,18183, r) r e 511 1, S (,18183, r ) r e 511 1, S (,18183, r) r e 510 1,8765r Cd (1,8765, r) r e,088r sn cs,088r sn sn,088r cs, r,18183r,18183r,18183r sn cs sn sn cs (5) (6) (7) (8) () (10) (11) (1) In the expressns f (5) (1) r,, are sphercal crdnates f electrn. Based n the frmula () 7 mlecular rbtal had been establshed. The nanpartcle (CdS) has * *6 7 valence electrns. They fll 36 lw energetc levels. The unknwn ceffcents C are fund by slvng the fllwng system f euatns[8]: There the fllwng defntns are ntrduced: H ( H S ) C 0 (13) * H p ef S * dv p dv S - are the verlap ntegrals between atmc rbtals p and peratr fr the ne electrn. (14) (15) 1 H ( r ef U ). H ef s effectve Hamltn The uantty H are matrx elements f effectve Hamltnan (), fr ne electrn mvng n a mlecule n sme effectve feld ndependent frm ther electrns. Thus, fr slutn f system f euatns(13),.e. fr determnatn f the rbtals energes and crrespndng ()

4 36 sets f ceffcents C, ne must knw numercal H and S values. Hwever, H values can nt be calculated exactly, because the explct expressns fr the peratr s unknwn. S need t estmate them by varus ways, ne f whch based uantum chemcal sem-emprcal methd VH. ccdng methd VH each dagnal matrx elements H are guessed eual t ptental f nzatn accrdng valence state f the gven atms. The nn-dagnal elements are defned by a rat[6, 7]. H.5 K S ( H H ) (17) 0 pp where the meanng f cefcent K can be calculated theretcal due t the cndtn f mnmum f energy r cmparsn wth expermental data. s seen frm (13) and (17) expressn fr the mplementatn uantum mechancal calculatng by VH methd t s mprtant t knw the value f verlap ntegrals n mlecular crdnatn system. In ths wrk the expressns frm [18-1]. were used n rder t calculate f verlap ntegrals n bass f STO s. On the bass f these expressns fr the calculatng verlap ntegrals shuld be ncluded the n,, m uantum number, - expnental parameters f atmc rbtals and the cartesan crdnates f atms. In rder t calculate f H matrx elements, we use the fllwng value f ptental nzatn f valence state f Cd and S atms: By knwng the value f ( 5s Cd 5s) ( 5p Cd 5p) ( 3s S 3s) ( 3p S 3p) (13) we can defne the value f rbtal energes, a.u a.u a.u a.u. H and S matrx elements and slvng the system euatns E ttal electrnc energy, Ip ptental nzatn and C ceffcents n the VH apprach. The numercal values f ceffcents C allw ne t determne the effectve charge a (n a.u.) f an atm n the nanpartcles accrdng t the MO LCO methd by the frmula []. n n C (18) where n s the pstve charge f the nuclear cre f atm (fr the Cd atms n =, fr the s atms n =6), n s the number f electrns n the -th mlecular rbtals. Summatn fr s perfrmed ver the ccuped mlecular rbtals. We desgned sftware fr cmputatns and determned the numercal values f C, rbtal energes ttal energy E, ptental nzatn Ip and effectve charge f atms n VH apprach.. The cmputer calculatns fr (CdS) nanpartcles by the Wlfsberg-Helmhlz methd Ttal electrnc energy E = a.u. Ptental nzatn I p =.8580 ev

5 363 Orbtal energes (a.u.) EFFECTIVE CHRGES OF TOMS ND COORDINTES N0 Z tm Charge Crdnates (a.u.) x y z Interpretatn f results fr (CdS) nanpartcles Startng frm the lwest energy level the 7 valence electrns f (CdS) nanpartcles are placed n levels tw by tw. The energy f the hghest level whch ccuped by electrns, eual t the value f ptental nzatn wth negatve sgn. I p = ev. The value f band gap can be calculated as the dfference the energy f the lwest unccuped mlecular rbtal = ev and the energy f the hghest ccuped mlecular rbtal LUMO 37. HUMO 36 LUMO HUMO eV. Ths ndcates that (CdS) nanpartcles are sem-cnductrs. Strength can be calculated as 1 LUMO HUMO = ev. Thus, 1eV and (CdS) nanpartcles are cnsdered sft materal. The energy f the lwest unccuped mlecular rbtal s negatve sgn (CdS) and ths ndcates that nanpartcles are electrphlcs. The stablty f (CdS) nanpartcles can be expressed by the frmula. E CdS ) ). Here, E CdS ) ) s the parameter whch dentfed the (( E CdS E ( ) CdS ((

6 364 stablty f (CdS) nanpartcles. If the E ((CdS) ) 0 materal s nt stable, but f E ((CdS) ) 0 materal s cnsdered stable. E - s ttal energy f (CdS) nanpartcles, E CdS - s ttal energy f CdS mlecules. Due t a.u. and (( CdS ) ) nanpartcles are stable. (CdS) E = a.u., E CdS = -- (CdS) E a.u. (( CdS ) ) 0 E then (CdS) 4. Results The electrnc structure f the cadmum sulfur nanpartcles were nvestgated by sememprcal VH methd n bass STO s. The cmputer calculatns were carred ut by scentsts f Department f Chemcal Physcs f Nanmaterals f Baku State Unversty wth ts wn cmputer prgram thrugh a Wndws OS prepared Delph Stud. The rbtal energes, ptental nzatn, the ttal electrnc energy and effectve charge f atms f cadmum sulfur nanpartcles were calculated. The results f calculatns shw that, cadmum sulfur nanpartcles are sft, electrphle and sem-cnductve stable materal. Reference [1] P.P. Faver, etc. Brazlan Jurnal f Physcs. 36(3B), 103(006). [].M. Magerramv M..Ramazanv, F.V. Gadjyeva Optelectrn. dv. Mater. Rapd Cmmun (11), 743(008). [3] Xuewu Ge, Ynghng N, Zhcheng Zhang, Radatn Physcs and Chemstry, 64, 3(00) [4] X. Lu, M. twater, J. Wang, Q. Hu Cllds and Surfaces B: Bnterfaces, 58(1), 3 (007). [5] M. Wlfsberg, L.J. Helmhlz, J.Chem.Phyc., 0, 837, (15). [6] G.. Shembelv, etc. Quantum chemcal methds f calculatn f mlecules, M., Chemstry, 180. [7] А.S. Fedrv, P.B. Srkn and etc. Mdelng f the prpertes f the electrnc structure f sme carbn and nn-carbn nanclusters and ther nteractn wth lght elements. Nvsbrsk, 006. [8]. Stretweser, Mlecular rbtal thery fr rganc chemst, New Yrk, Wley, 161. [] R. leva, F.G. Pashaev,.G. Gasanv, K.T. Mahmudv Russn J. f Cr. Chemstry, 35, 41, (00). [10] L. Berlu, H. Safuh J. Ther. Cmp. Chem., 4, 787, (005). [11] H. Safuh Int. J. Quantum Chem., 100, 17, (004). [1] L. Berlu, H. Safuh, P. Haggan Int. J. Quantum Chem.,, 11, (004). [13] J.F. Rc, etc. J. Cmput. Chem. 5, 187(004) [14] I.I. Gusenv, J. Ml. Str., (Thechem) 757, 5, (005). [15] I.I. Gusenv, J. Chem. Phys., 180, 454, (004). [] I.I. Gusenv, J. Ml. Mdel.,, 10, (00).. [17] N Bess, G. Bess J. Chem, Phys., 47(6), 38, (181). [18] I.I. Gusenv, F.G. Pashaev and etc. J. Str. Chem., 30, 183, (18). [1] I.I. Gusenv, Int. J. Quantum Chem., 1, 6, (003). [0] I.I. Gusenv and etc., Int. J. Quantum Chem., 61, 1, (18). [1] F.G. Pashaev, J. Math. Chem., 45, 884 (00). [] I.S. Dmtrev, Electrn by eyes f chemsts, L., Chem., 186.