Chemical Reactivity Dynamics and Quantum Chaos in Highly Excited Hydrogen Atoms in an External Field: A Quantum Potential Approach

Transcription

1 In. J. Mol. Sci., 3, Inenionl Jounl of Molecul Sciences ISSN y MDPI Chemicl Reciviy Dynmics nd Qunum Chos in Highly Excied Hydogen Aoms in n Exenl Field: A Qunum Poenil Appoch P. K. Chj * nd B. Mii Depmen of Chemisy, Indin Insiue of Technology, Khgpu, 713, Indi E-mil: pkc@chem.iikgp.ene.in * Coesponding uho. Received: 13 Augus 1 / Acceped: 7 Jnuy / Pulished: 5 Apil Asc: Dynmicl ehvio of chemicl eciviy indices like eleconegiviy, hdness, poliiliy, elecophiliciy nd nucleophiliciy indices is sudied wihin qunum fluid densiy funcionl fmewok fo he inecions of hydogen om in is gound eleconic se (n = 1) nd n excied eleconic se (n = ) wih monochomic nd ichomic lse pulses. Time dependen nlogues of vious eleconic sucue pinciples like he pinciples of eleconegiviy equliion, mximum hdness, minimum poliiliy nd mximum enopy hve een found o e opeive. Insighs ino he viion of inensiies of he geneed highe ode hmonics on he colo of he exenl lse field e oined. The qunum signue of chos in hydogen om hs een sudied using qunum heoy of moion nd qunum fluid dynmics. A hydogen om in he eleconic gound se (n = 1) nd in n excied eleconic se ( n = ) ehves diffeenly when plced in exenl oscilling monochomic nd ichomic elecic fields. Tempol evoluions of Shnnon enopy, qunum Lypunov exponen nd Kolmogoov Sini enopy defined in ems of he disnce eween wo iniilly close Bohmin jecoies fo hese wo cses show mked diffeences. I ppes h lge unceiny poduc nd smlle hdness vlue signl choic ehvio. Keywods: Chemicl eciviy, Eleconegiviy, Hdness, Hydogen om, Qunum heoy of moion(qtm), Qunum chos, Qunum fluid dynmics(qfd), Choic dynmics.

2 In. J. Mol. Sci., I. Inoducion The choic ioniion of hydogen oms [1-3] in highly excied ses y micowve fields hs ecome n impon e of esech fo oh expeimenliss [1-7] nd heoeicins [4]. In 1974 Byfield nd Koch [8] fis sudied he choic ioniion of hydogen oms which hs een consideed o e vey impon in omic heoy [1,,4,5,9-8]. Sndes nd Jensen [4] hve sudied he choic ioniion of hydogen nd helium using clssicl mechnics [4]. When he hydogen om is pomoed o highly excied se i ges ionied in cse he field inensiy is ove some heshold vlue nd he ioniion poiliy depends on he field inensiy [4,6,7]. Sndd dignosics used fo he pesen sudy include eleconegiviy ( χ ), hdness (η ), poliiliy (α ), phse volume (V ps ), elecophiliciy index (W), nucleophiliciy index (1/W), Shnnon enopy (S), qunum Lypunov exponen (Λ) nd Kolmogoov Sini enopy (H) defined in ems of he disnce eween wo iniilly close Bohmin jecoies. In his ppe we hve geneed he highe ode hmonics [3,9,3]. The esponse of he om when i inecs wih he exenl field vis á vis he viion of is eciviy is n impon e of esech. Eleconegiviy ( χ )[31] nd hdness (η ) [3] e wo cdinl indices of chemicl eciviy. Puling [33] inoduced he concep of eleconegiviy s he powe of n om in molecule o c elecons o iself. The concep of hdness ws given y Peson [34] in his hd sof cid se (HSAB) pinciple which ses h, hd likes hd nd sof likes sof. These popul quliive chemicl eciviy conceps hve een qunified in densiy funcionl heoy (DFT) [35]. Anohe impon hdness eled pinciple is he mximum hdness pinciple (MHP) [36,37], which ses h, hee seems o e ule of nue h molecules nge hemselves so s o e s hd s possile. The quniive definiions fo eleconegiviy [38] nd hdness [39] fo n N elecon sysem wih ol enegy E cn especively e given s nd In eqs. (1) nd () µ nd E χ = µ = (1) N v( ) 1 E 1 µ η = N =. () N v( ) v( ) v( ) e chemicl poenil ( Lgnge muliplie ssocied wih he nomliion consin of DFT [34,36] ) nd exenl poenil especively. An equivlen expession [4,41] fo hdness is 1 v v v v v v η = f dd N η(, ) ( ) ρ( ) (3) v v v whee f ( ) is he Fukui funcion [4] nd η (, ) is he hdness kenel given y [4] v v 1 δ F[ ρ] η (, ) = v v (4) δρ( ) δρ( ) whee F (ρ) is he Hoheneg - Kohn univesl funcionl of DFT [35].

3 In. J. Mol. Sci., 3 34 The complee chceiion of n N picle sysem ced on y n exenl poenil v( ) equies only N nd v( ). The esponse of he sysem sujeced o chnge in N fixed v( ) is given y χ nd η while he line esponse funcion [34] mesues he esponse of he sysem when v( ) is vied consn N. If he sysem is kep unde he influence of he wek elecic field, poliiliy (α ) kes ce of he coesponding esponse. Duing molecule fomion he eleconegiviies of he peinen oms ge equlied [4,43]. A sle configuion o fvole pocess is genelly ssocied wih mximum hdness [36,37], minimum poliiliy [44-47] nd mximum enopy [48] vlues. The condiions fo mximum hdness nd enopy nd minimum poliiliy complemen he usul minimum enegy cieion fo siliy. Recenly P e. l. [49] hve defined he elecophiliciy index (W) s µ W = (5) η We lso sudy he ehvio of (1/W), vlid cndide fo he nucleophiliciy index. Noe h he quniy (1-W) will lso seve he pupose of nucleophiliciy index. I hs lso een shown ecenly [5] h he unceiny poduc o he phse spce volume (V ps ) is mesue of qunum flucuions nd hence hs eing in he sudies of qunum domin ehvio of clssiclly choic sysems. I hs een ledy demonsed [51] h in cse we focus ou enion o specific om / molecule king p in chemicl ecion he whole pocedue cn e simuled y he inecion of n om / molecule wih n exenl field of he sengh of he ode of he chemicl ecion field. A molecul ecion dynmics cn e envisged [44] y monioing he ime evoluion of he eleconegiviy of specific om fom is isoled om vlue o he equlied molecul eleconegiviy vlue s well s y sudying he dynmic pofiles of hdness nd enopy nd how hey ge mximied nd h of he minimiion of poliiliy duing he couse of he chemicl ecion. In he pesen wok we sudy he inecion of hydogen om in is gound eleconic se nd n excied eleconic se wih lse fields of diffeen colos. The effec of he fequency of he exenl lse field on he ovell eciviy of he om in is vious eleconic ses vis á vis he vlidiy of he ssocied eleconic sucue pinciples in dynmicl conex s well s he inensiies of he geneed highe ode hmonics [5] would e undesood in his sudy. Dynmics of hese eciviy pmees (η nd α ) hve een sudied [44,46,53] in he conexs of vious ime dependen pocesses. Whehe η nd α cn povide some insigh ino he qunum domin ehvio of clssiclly choic sysem is ye o e nlyed. Hydogen oms nd molecules in n oscilling elecic field hve een consideed o e veile gold mines fo exploing he qunum specs of chos [54]. Depending on he fequency nd he field inensiy, hydogen [54,55] oms in he pesence of n exenl field hve een shown o exhii egul / choic dynmics. Boh qunum fluid dynmics (QFD) [56,57] nd qunum heoy of moion (QTM) [58,59] hve povided qunum signues of chos in hydogen oms. In QFD [56] he ovell moion of he sysem unde

4 In. J. Mol. Sci., consideion is mpped ono h of poiliy fluid hving densiy (,) j (, ) nd ρ (,) nd χ (,) ( = ρ χ ) ρ nd cuen densiy unde he influence of he exenl clssicl poenil ugmened y qunum poenil [55-59] j e especively oined [55-59] fom he mpliude nd he phse of he wve funcion. In QTM [58], he wve moion is govened y he soluion o he ime dependen Schödinge equion (TDSE) nd he picle moion is followed y solving he peinen Newon s equion of moion wih foces oigining fom oh clssicl nd qunum poenils. Impon insigh ino he choic dynmics hs een oined [57] hough ρ vs χ plos which cn e consideed o e cnoniclly conjuge. In QTM i is oined [59] in ems of he disnce eween wo iniilly close Bohmin jecoies nd he ssocied Kolmogoov Sini enopy. In he pesen ppe we monio he possile egul / choic dynmics hough he ime evoluion of vious eciviy indices of hydogen om in he gound nd highly excied eleconic ses in he pesence of one colo nd wo colo lse pulses. The heoeicl ckgound of he pesen wok is povided in secion II. Secion III pesens he numeicl deils, nd he esuls nd discussions e given in secion IV. Finlly, secion V conins some concluding emks. II. Theoeicl Bckgound Clssicl inepeion of qunum mechnics is s old s he qunum mechnics iself. In he Mdelung epesenion [55] he ime dependen Schödinge equion fo single picle moving unde poenil V ( ) (in u), vi. ( ) ( ) ( ) 1 ψ, + V ψ, = i, i = 1 (6) is nsfomed ino wo fluid dynmicl equions. Susiuing he following pol fom of he wve funcion 1 v ψ, = ρ, exp iχ, (7) ( ) ( ) ( ( )) in eq. (6) nd seping he el nd he imginy ps, one oins n equion of coninuiy nd n Eule ype equion of moion υ + ρ +. j = ( υ ) υ = ( V + ) In eqs (8) he chge densiy, ρ (,) nd cuen densiy, j (, ) j (, ) ρ(, ) υ(, ) whee he velociy (,) V qu (8).. (8) is = (9) υ cn e defined in ems of he phse of he wve funcion s υ(, ) = & = χ(, ) (9) The quniy V qu ppeing in eq. (8) is clled he qunum poenil o Bohm poenil of hidden vile heoy [6] nd defined s

5 In. J. Mol. Sci., ρ V qu = (9c) 1 ρ Theefoe, in his qunum fluid dynmics [55] he ovell moion of he sysem unde consideion, υ, unde cn e hough of s moion of poiliy fluid hving densiy ρ ( ) nd velociy ( ) he influence of he exenl clssicl poenil ugmened y qunum poenil, V qu. ρ, conins ll infomion [35]. In ime Fo he gound se of mny picle sysem, ( ) dependen siuion lso he ime dependen densiy funcionl heoy [5] sses h ny physicl, j, nd hus llows us o fomule he osevle cn e expessed s funcionl of ρ ( ) nd ( ) dynmics in ems of clssicl like 3D quniies. Alhough Mdelung nsfomion in ems of, j, is no sighfowd in mny picle siuion, we cn mke use of he ime ρ ( ) nd ( ) dependen densiy funcionl heoy in consucing wo fluid dynmicl equions in 3D spce. The fomlism is emed s qunum fluid densiy funcionl heoy [61] which hs een pplied in undesnding ion om collisions [61-63], om field inecions [64,65] nd eleconegiviy [51,66], hdness [66-68] nd enopy dynmics [68] in chemicl ecion. Qunum poenil plys cucil ole in he qunum heoy of moion [58] s well. In his epesenion of qunum mechnics developed y de Boglie [69] nd Bohm [7], he ovell moion of he sysem is undesood in ems of he moion of picle expeiencing foces oigining fom he clssicl nd qunum poenils. The Newon s equion of moion fo his picle guided y ψ,, soluion o eq. (6)) cn e wien s wve (epesened y ( ) ( & ) = ( V + V qu ) = () & +. (9d) A picul insn he soluion o he ime dependen Schödinge equion (6) fixes he velociy of he picle (cf. eq. 9) nd, hence, fo given iniil posiion he picle moion cn e sudied hough he soluion () o he eq. (9). Theoies sed on qunum poenil ide hve een pplied in solving vious physico chemicl polems [58, 71-83]. Becuse of he pesence of nonlineiy nd lso he clssicl lnguge, hese heoies hve een found [57-59, 81-85] o e helpful in undesnding he qunum domin ehvio of clssiclly choic sysems which is descied s qunum chology y Bey [86]. The qunum heoy of moion, howeve, llows one o sudy he qunum chos in sysem wihou ny eso o is clssicl domin dynmics [58]. The ime dependen Schödinge equion (in u.) fo he pesen polem is ( ) ( ) ( ) 1 ψ, + V ψ, = i (1) V, is given y whee he poenil ( ) 1 V (, ) = + vex (, ). (1)

6 In. J. Mol. Sci., In eq. (1) he exenl poenil fo he monochomic nd ichomic lse pulses my e wien s v ex, = ε1, fo monochomic pulse (1c) whee nd ( ) = ε, fo ichomic pulse (1d) ( ) ε 1 = ε cos ω (1e) [ cos( ω ) ( 1) ] ε =.5ε + cos ω (1f) To hve slow oscillions duing nd fe he souce eing swiched on, ε is wien in ems of he mximum mpliude ε nd he swich on ime s ε = / fo (1g) ε = ε ohewise. (1h) I my e noed h fo mny elecon polem one my eihe solve he ssocied TDSE o he coesponding genelied nonline Schödinge equion wihin qunum fluid densiy funcionl fmewok [46,53,55,63-66,69,89], he le eing hee dimensionl even in he cse of mny elecon sysem. To consuc he hdness kenel (eq 4), we need he Hoheneg Kohn univesl funcionl F [ ρ]. Fo mny elecon sysem [ ρ] F my e ken s [53] ρ ρ F[ ρ] = 1 v v v v 1 (, ) (, ) v v ρ(, ) χ(, ) d + T[ ρ] + v v dd + Exc [ ρ] (11) whee he fis em is he mcoscopic kineic enegy, he ls em is he exchnge coelion enegy, nd T [ ρ] is he ininsic kineic enegy given y [53] 4 3 ρ / T[ ρ ] = T [ ρ] + Tw[ ρ] ( N ) λ d (11) 1 3 ρ whee T [ ρ] is he Thoms Femi funcionl [88], [ ρ] T is he Weisäcke funcionl [88], λ is consn [53], ( N ) is n N dependen pmee [53]. Fo oining he glol hdness η (eq. 3) we lso equie he Fukui funcion f ( ) he following locl fomul fo f ( ), s ( ) ( ) f = s( ) d whee he locl sofness ( ) v v Fo clculing (, ) w. We employ (11c) s is given s follows s pescied y Fuenel [89] v v v δ ( ) s( ) = v v. (11d) η (, ) η of he ove equion he following locl fom fo [ ρ] F is used [53]:

7 In. J. Mol. Sci., locl ee locl F [ ρ] = T [ ρ] + V [ ρ] (11e) whee he locl kineic enegy [9] nd he elecon elecon epulsion enegy [91] my e ken s [53] T locl 1 ρ / [ ρ ] = T [ ρ] + ( 3π ) d (11f) 1 3 4π ρ nd V locl ee 3 3 v [ ρ ] =.7937( N 1) / ρ 4 / d. (11g) Noe h he ove emen is pplicle o mny elecon sysems nd ll elecon elecon inecion ems would e sen in he cse of hydogen om. To follow he poliiliy dynmics he dynmic poliiliy is defined s [44,53] ind α ( ) = D ( ) / I ( ) (1) whee Dind () is he eleconic p of he induced dipole momen given s D v v ( ) = ρ (, ) d (1) nd I () is he - componen of he exenl field. ind The phse spce volume o he unceiny poduc V ps hs een shown [9] o e n impon dignosic of he qunum signue of clssicl chos [9] s eled o he compcness of he elecon cloud [93]. Fo he pesen polem i my e defined s V ps { < ( p } 1/ ~ < p ~ ~ ~ > ) >< ( p < p > ) >< ( ρ < ρ > ) >< ( < > ) > = ρ ρ. (13) A shp incese in V ps () implies choic moion [9] since i is mesue of he ssocied qunum flucuions [9]. To genee he hmonic specum he induced dipole momen, Dind () is Fouie nsfomed o oined d (ω ). I hs een shown [94] h he solue sque of he Fouie nsfom, ω oughly popoionl o he expeimenl hmonic disiuion. d ( ) is The Shnnon enopy is given y S == k ρ ln ρ d, (14) whee k is he Bolmnn consn. We cn genee he qunum jecoy of picle fo given iniil posiion fom equion (9). Now, we e in posiion o nlye he sensiive dependence on iniil condiion, chceisic of choic sysem. Equion (9) is solved wih wo diffeen iniil posiions of he, ~ ρ + d ~ ρ, + d, d ~ ρ = d =. 1. Iniil momenum of he picle is ken s picle, ( ~ρ ) nd ( ) ( )

8 In. J. Mol. Sci., eo in ll cses. We sudy he ime evoluion of phse spce disnce (D) fo he coesponding qunum jecoies defined s [56,59,8,83] D( ) = [( ~ ρ ] 1/ 1 ( ) ~ ρ ( )) + ( 1( ) ( )) + ( p ~ ρ ( ) p ~ ( )) + ( p ( ) p ( )) 1 ρ 1 whee ( ~ ρ, p,, ) efes o poin in phse spce. ~ρ p We lso clcule he ssocied Kolmogoov Sini enopy s defined [8,83] elow whee he Lypunov exponen is given y [8,83] Λ+ > +, (15) H = Λ, (15) 1 Λ = lim ln[ D( ) / D()] (15c) () D α Accoding o he Hmilon Jcoi fomulion of qunum mechnics, posiive KS enopy is ssocied wih choic qunum dynmics [59,87]. III. Numeicl Soluion The TDSE (eq. 1) is solved numeiclly in cylindicl pol coodines ( ~ ~ ρ, φ, ), s n iniil oundy vlue polem using n lening diecion implici mehod [95]. The soluion pocedue egins wih he ψ 1s nd ψ s nlyicl wve funcions of he hydogen om. Since he elecon densiy vies pidly ne he nucleus nd elively slowly elsewhee, we nsfom he viles s follows y = ~ ρ φ (16) nd ~ ρ = x. (16) Eq. (1) kes he following fom in he nsfomed viles once n nlyicl inegion is cied ou ove φ ~ π, 3 y 1 y y 1 y υ eff y = i. (17) 3 4 4x x 4x x x The esuling idigonl mix equion is solved using Thoms lgoihm. The mesh sies doped hee e x = =.4 u nd =.1u, ensuing he siliy of he fowd ime cenl spce ype numeicl scheme doped hee. The iniil nd oundy condiions ssocied wih his polem e y(x,) is known fo x, = (18) y(,) = = y(,), (18) y(x, ± ) = x,. (18c)

9 In. J. Mol. Sci., The numeicl scheme is sle [96] due o he pesence of i = 1. As fuhe check of he numeicl ccucy, we hve veified he consevion of nom nd enegy (in eo field cses). The wve funcion is moved fowd o he end of he simulion nd hen ken ck o is iniil posiion y evesing he ime diecion, whee he oiginl pofile is epoduced well wihin he olence limi of he pesen clculion. We hve lso solved eq. (9) using second ode Runge Ku mehod o genee he qunum jecoies of given iniil posiion. The field pmees e in omic unis unless ohewise specified. IV. Resuls nd Discussions The ime evoluion of diffeen eciviy pmees e depiced in Figues 1 1. All quniies e in omic unis. Unless ohewise specified, in ll figues nd efe o he gound se ( n=1) nd excied se (n=) of he hydogen om, especively, nd ed coloed solid line nd lue coloed solid line especively signify monochomic nd ichomic pulses. Figue 1 pesens he ime dependence of he exenl field wih diffeen fequencies nd he sme mpliude. 6 4 ε ε Figue 1: Time evoluion of he exenl elecic field: ε1 ( ) monochomic pulse, ε ( ) ichomic pulse. Field pmees: ε = 5.; ω =.5π, ω 1 = ω.

10 In. J. Mol. Sci., Tempol evoluion of he chemicl poenil is depiced in Figue. I exhiis chceisic oscillions. The oscillions in µ is no in phse wih he exenl field. I is impon o noe h he mpliude of µ - oscillions ecomes vey lge fo oh he eleconic ses nd oh monochomic nd ichomic pulses µ µ µ µ Figue : Time evoluion of chemicl poenil (µ) when hydogen om is sujeced o exenl elecic fields: Gound se; Excied se. ( ) Monochomic pulse, ( ) ichomic pulse. Field pmees: ε = 5.; ω =.5π, ω 1 = ω. Chemicl hdness ( η ) is pesened in Figue 3. Fo oh one nd wo colo cses η is much lge fo n=1 se hn h of he n= se fo he whole ime nge. This my e consideed o e dynmicl vin of he MHP. Hdness oscilles in ime in ll he cses. Howeve, he oscillion is neihe in phse no ou of phse wih espec o he oscillions in he exenl one nd wo colo fields. I is expeced ecuse of he fc h s soon s he lse is swiched on, hee ss ug of w eween he omic nucleus nd he exenl field o goven he elecon densiy disiuion. The nucleus ies o mke he densiy disiuion spheiclly symmeic owing o he cenl nue of he nucle coulom field while he cylindicl symmey of he pplied elecic field ies o cee n oscilling dipole h emis diion including highe hmonics. Ovell densiy oscillion ecomes nonline due o he ineply of wo diffeen ypes of effecs. Hdness fo he n=1 se deceses (fo oh one nd wo - colo siuions) nd ins moe o less sedy vlue he end of he simulion, which is sill lge in compison o he coesponding vlue fo he n= se. Fo oh

11 In. J. Mol. Sci., one nd wo colo siuions, η vlues elive o he coesponding vlues in sence of he field (no shown) e much lge fo he n=1 se. I ppes h elively smlle η vlue signls possile choic dynmics η η η η Figue 3: Time evoluion of hdness (η) when hydogen om is sujeced o exenl elecic fields: Gound se; Excied se. ( ) Monochomic pulse, ( ) ichomic pulse. Field pmees: ε = 5.; ω =.5π, ω 1 = ω. Poliiliy vlues s hey evolve in he couse of ime e pesened in Figue 4. I oscilles wih fequency h is doule h of he exenl field. The exem in he exenl field coesponding o he minim in α nd he le lows up when he field is eo. Hee lso if we compe he especive minimum α vlues ( α min ) fo he wo eleconic ses, α min fo he gound se is smlle hn h of he excied se which is conspicuous fo he ichomic pulse. This is in confomiy wih minimum poliiliy pinciple (MPP). The MPP evels iself in ime dependen siuion.

12 In. J. Mol. Sci., α α α α 1 1 Figue 4: Time evoluion of poliiliy (α) when hydogen om is sujeced o exenl elecic fields: Gound se; Excied se. ( ) Monochomic pulse, ( ) ichomic pulse. Field pmees: ε = 5.; ω =.5π, ω 1 = ω. Figue 5 depics he dynmics of he unceiny poduc (phse volume). As in he cses of µ ndη, V ps lso oscilles neihe in phse no ou of phse wih he exenl field. The mgniude of V ps eins is iniil (=) smll vlue fo he n=1 se whees fo he n= se i inceses quickly o vey lge vlue. Since V ps mesues he qunum flucuions, choic jecoy is genelly ssocied wih lge V ps vlues [9]. lge inceses in V ps cn e expeced o ccompny choic jecoy. Convesely, smll o modee inceses in V ps cn e evidence h given qunum mechnicl jecoy should e egded nonchoic [9]. In genel, he elecons e ighly ound nd hence he disiuion is less diffuse fo he n=1 se nd loosely ound fo he n= se nd he sysem is expeced o e hde nd less polile fo he gound se [3,34,46,53,88,93]. Agin, he elecon densiy eing moe compc in he gound se, he coesponding unceiny poduc is expeced [93] o e smll. Once he exenl field is swiched on, he gound se densiy would e disiued ove lge volume nd consequenly hee would e decese in η nd incese in α nd V ps of he sysem. Since smlle η vlue is ccompnied wih lge V ps vlue nd vice ves nd V ps is known [9] o e he signue of he clssicl chos in he coesponding qunum domin ehvio, hdness cn s well e consideed o e dignosic of he choic dynmics in qunum sysem.

13 In. J. Mol. Sci., V ps 3 1 V ps V ps V ps Figue 5: Time evoluion of phse volume (V ps ) when hydogen om is sujeced o exenl elecic fields: Gound se; Excied se. ( ) Monochomic pulse, ( ) ichomic pulse. Field pmees: ε = 5.; ω =.5π, ω 1 = ω. Figues 6 nd 7 depic especively he dynmicl pofiles of elecophiliciy nd nucleophiliciy indices especively. Boh W nd 1/W show oscillions chceisic of he esuln field of wo compeing ones fo oh he eleconic ses nd fo he one nd wo colo pulses. 3.5E+9 3.5E+9 3.E+9 3.E+9.5E+9.5E+9.E+9.E+9 w 1.5E+9 w 1.5E+9 1.E+9 1.E+9 5.E+8 5.E+8.E+ 8 6.E w 4 w Figue 6: Time evoluion of elecophiliciy index (W) when hydogen om is sujeced o exenl elecic fields: Gound se; Excied se. ( ) Monochomic pulse, ( ) ichomic pulse. Field pmees: ε = 5.; ω =.5π, ω 1 = ω.

14 In. J. Mol. Sci., /w. 1/w /w. 1/w Figue 7: Time evoluion of nucleophiliciy index (1/W) when hydogen om is sujeced o exenl elecic fields: Gound se; Excied se. ( ) Monochomic pulse, ( ) ichomic pulse. Field pmees: ε = 5.; ω =.5π, ω 1 = ω. The hmonic spec e pesened in Figue 8. The ovell domin of he spec nd hei envelopes look like hose epoed y Ehd nd Goss [5]. We found h he hmonics geneed y he monochomic nd ichomic pulses look simil nd hose geneed fom he fome is less inense hn hose esuled fom he le [5] E-3 1E-4.1 1E-3 1E-4 1E-5 1E-5 1E-6 1E-6 1E-7 1E-7 1E-8 1E-8 d(ω) 1E-9 1E-1 1E-11 1E-1 d(ω) 1E-9 1E-1 1E-11 1E-1 1E-13 1E-13 1E-14 1E-14 1E-15 1E-15 1E-16 1E-16 1E-17 1E-17 1E-18 1E-18 1E-19 1E-19 1E E ω ω E-3.1 1E-3 1E-4 1E-4 1E-5 1E-6 1E-5 1E-6 1E-7 1E-7 1E-8 1E-8 1E-9 1E-9 d(ω) 1E-1 1E-11 1E-1 d(ω) 1E-1 1E-11 1E-1 1E-13 1E-13 1E-14 1E-14 1E-15 1E-15 1E-16 1E-16 1E-17 1E-17 1E-18 1E-18 1E-19 1E-19 1E E ω ω Figue 8: d(ω) vs ω plo when hydogen om is sujeced o exenl elecic fields: Gound se; Excied se. ( ) Monochomic pulse, ( ) ichomic pulse. Field pmees: ε = 5.; ω =.5π, ω 1 = ω.

15 In. J. Mol. Sci., 3 35 Figue 9 depics he phse ( p ~ vs ρ~ ρ nd p vs ) of cses nd fo monochomic lse pulse, The fcion of he ol phse spce visied y he Bohmin jecoies is much moe fo he excied se. These plos eflec h he cse is fo egul moion whees he cse is fo choic moion p ρ p ρ p ρ p ρ Figue 9: Phse spce jecoies when hydogen om is sujeced o exenl elecic field: Gound se; Excied se. (.) Monochomic pulse. Field pmees: ε = 5.; ω =.5π, ω 1 = ω. Figue 1 depics he phse ( p ~ vs ρ~ ρ nd p vs ) plos cse nd fo ichomic lse pulse. These plos lso eflec h he cse is fo egul moion whees he cse is fo choic moion p ρ p ρ p ρ p ρ Figue 1: Phse spce jecoies when hydogen om is sujeced o exenl elecic field: Gound se; Excied se. (.) Bichomic pulse. Field pmees: ε = 5.; ω =.5π, ω 1 = ω.

16 In. J. Mol. Sci., Figue 11 depics he Kolmogoov Sini (KS) enopy fo oh gound (n=1) nd excied (n=) ses fo monochomic nd ichomic lse pulses. Fo oh monochomic nd ichomic lse pulses he KS enopy (H) eins is iniil vey smll vlue fo n=1. Fo n= cse H emins smll iniilly nd hen inceses pidly o high posiive vlue. The smll H vlue in he fome cse vis á vis he vey lge H vlue in he le povides unmiskle signue of chos in he highly excied se of he hydogen om in pesence of n exenl elecic field H H Figue 11: Time evoluion of KS enopy (H) when hydogen om is sujeced o exenl elecic fields: Gound se; Excied se. ( ) Monochomic pulse, ( ) ichomic pulse. Field pmees: ε = 5.; ω =.5π, ω 1 = ω. Shnnon enopy hs een shown in Figue 1. In he figue nd efe o he gound nd n= ses of he hydogen om especively. I inceses in he gound se nd deceses in he excied se fo oh he lse pulses, possile signue of he mximum enopy pinciple vis vis choic ioniion fom he highly excied se. I is impon o noe h he clculions hve een cied ou up o 35 u wih no chnge in he quliive ends. Plos e unced much smlle ime seps fo esy visuliion.

17 In. J. Mol. Sci., s/k s/k s/k 5. s/k Figue 1: Time evoluion of S/k, whee S is he Shnnon enopy nd k is he Bolmnn consn when hydogen om is sujeced o exenl elecic fields: Gound se; Excied se. ( ) Monochomic pulse, ( ) ichomic pulse. Field pmees: ε = 5.; ω =.5π, ω 1 = ω. V. Concluding Remks Qunum poenil sed heoies e doped o sudy he eciviy dynmics nd chos of hydogen om in is gound nd excied eleconic ses inecing wih polied lse pulses of diffeen colos. Dynmicl vins of he pinciples of eleconegiviy equliion, mximum hdness, minimum poliiliy nd mximum enopy mnifes hemselves. A ug of w eween he spheiclly symmeic nucle coulom field nd cylindiclly symmeic exenl elecic field o goven he elecon densiy disiuion is delineed hough he dynmicl pofiles of vious eciviy indices like eleconegiviy, hdness, poliliy, elecophiliciy, nucleophiliciy nd phse volume fo he exenl field nd in diffeen eleconic ses. Hmonic spec of he highe ode hmonics included in he diion emied y he esuling oscilling dipole hve een nlyed. Tempol evoluion of Bohmin jecoy, KS enopy nd Shnnon enopy hs esily diffeenied he egul nd choic ehvio of hydogen om especively in gound nd excied ses in pesence of n oscilling elecic field. Fo oh he lse pulses he incese in he unceiny poduc fo he excied se is vey lge, which implies possile choic dynmics. A lge hdness vlue, on he ohe hnd, is expeced o chceie egul ehvio.

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