bahudhruviy ghanata aupcharikta

bahudhruviy ghanata aupcharikta (jyala hansen-coppens aupcharikta asehi mhanatat) hii niils keey yanni prastavit kelelya electron ghanata modelingchi ksh-kiran sfatikalekhan paddhat aahe. 1978 madhye hansen aanee phillip coppens. samanyatah vaparlya jaanarya swatantra anoo pratimanapeksha vegale, hansen-coppens aupcharikta eka aspherical drushtikon sadar karate, jyamule ekhadyala kendrakabhovati electron vitaranache vegvegalya dishene swatantrapane pratirupan karata yete aanee mhanoon tapasalelya sphatikachya ekak peshitil renuchya asankhya rasayanik vaishishtyanche tapshilvar varnan karata yete.
siddhant.
swatantra anoo model.
swatantra anoo pratikruti (aay. aii. emm. mhanoon sankshipt), jyavar bahudhruviy pratikruti aadharit aahe, hii aavesh ghanata pratikrutichi eka paddhat aahe. anoochya bhovati electronche vitaran samasthanik aahe aanee tyamule aaveshachi ghanata hii keval kendrakapasoonchya antaravar avalambun aahe yaa gruhitkavar teey avalambun asate. yaa electronchya ghanateche varnan karnyasathi vaparlya jaanarya radial karyachi nivad manmani aahe, jarr tyache mool moolya maryadit asel tarr. vyavharat ektar gossian-kinwa slatter-prakar 1s-kakshiy karye vaparali jaatat.
tyachya sopya drushtikonamule, hii paddhat eka saral namuna pradan karate, jyat konatehi atirikt mapdand (sthitijanya aanee deby-waller ghatakanvyatirikt) parishkrut karanyachi aavashyakta nasate. yamule aay. aay. emm. laa samadhankarak kamgiri karata yete, tarr vivartan prayogatoon tulanene qamee pramanat mahitee upalabdh asate. tathapi, ekvachan aadhar karyacha nishchit aakar, samaroop anoo vaishishtyanche konatehi tapshilvar varnan karnyas pratibandh karato.
kappa aupcharikta.
kahee valence shale mapdand samayojit karnyasathi, kappa aupcharikta prastavit karnyat aalee hotee. heey done atirikt parishkrut mapdand sadar karateh bahya kavach loksankhya (sootra _ 1 mhanoon darshavili jaate) aanee tyacha vistar/aakunchan (sootra _ 2). tyamule, electronchi ghanata ashee tayar kelee jaateh
sootra 1, jeey aavesh pravahachya bhagasathi jababdar aahe, teey aanshik aaveshasah reshiyaritya jodalele aahe, tarr samanyikrut sootra 2 parameter scale radial samanvay sootra 6. mhanoon, sootra 2 parameter qamee kelyane bahya kavach vistarte aanee tyaulat, teey vadhavalyane teey aakunchan hote. jaree kappa aupcharikta ajunahi, katekorpane sangayache tarr, eka golakar paddhat asali taree, aadhunik drushtikon samajoon ghenyachya dishene heey eka mahattvache paul aahe kaaran yamule ekach ghatakache rasayanikdrushtya bhinn anoo vegale karata yetat.
bahudhruviy varnan.
bahudhruviy pratikrutichya varnanat, kendrakabhovatichi aavesh ghanata khaleel samikaranadvare dilee jaateh 
golakar bhag haah kappa aupchariktepasun jawaljawal aprabhedya aahe, fakt eka farak mhanje aateel kavchatil loksankhyeshi sambandhit eka mapdand. hanson-coppens aupchariktechi kharee takad samikaranachya ujavya, vikrutipoorn bhagat aahe. yethe sootra _ 9 heey kappa formalism (aspherical bhagacha vistar/aakunchan) madheel sootra _ 2 sarkhich bhoomika purn karate, tarr vaiyaktik sootra _ 11 hii nishchit golakar karye aahet, jee sootra _ 12 shhee samaan aahet. golakar harmonics sootra _ 13 (pratyek tyachya populational parameter sootra _ 14 saha), tathapi, vidyut anisotropic charge vitaranache anukaran karnyasathi sadar kele jaatat.
yaa drushtikonat, pratyek anusathi eka nishchit samanvay pranali lagoo karane aavashyak aahe. jaree pahilya drushtikshepat serve anoonsathi ekak peshivar aniyantrit aanee andadhundapane avalambun rahane vyavharik vatat asale, taree pratyek anoola tyache swatache sthanik nirdeshank niyukt karane adhik fayadeshir aahe, jyamule sankarikaran-vishisht parasparsanvadanvar laksh kendrit karata yete. hydrogenchya ekvachan sigma bandhanche varnan kahee zed-samantar seudorbitals vaparoon changle kele jaau shakate, tarr 3 putt rotational samamiti asalele xy-plain oriented multipoles sapat sugandhi sanrachanansathi adhik fayadeshir siddha hotil.
anuprayog.
hanson-coppens aupchariktecha prathamik fayda mhanje modella golakar nirbandhanpasun mukt karanyachi aanee kendrakachya sabhovatalache adhik achook varnan karanyachi tyachi kshamata. asha prakare kahee aanvik vaishishtyanche parikshan karane shakya hote, jeey samanyatah keval andaje kinwa purnapane durlakshit kele jaau shakatat.
hydrogenchi sthitee.
ksh-kiran sfatikalekhan sanshodhkala sarvoch electron ghanatechi sthitee achookpane nishchit karnyas aanee yaa mahitichya aadhare kendrakanchya sthanabaddal tark karnyas anumati dete. haah drushtikon judd (hydrogen nasalele) anoonsathi konatyahi samasyeshivay karya karato, jyanche aateel kavach electron bahya kavach electronpeksha khoopach jaast pramanat ghanata karyat yogdan detat.
tathapi, hydrogen anoonmadhye serve ghatakanmadhye eka vaishishtyapurn vaishishtya aahe-tyanchyakade agadi ekach electron asato, joou tyanchya sanyojak kavchavar dekhil asato aanee tyamule itar vividh ghatakanchya anoonsah majboot sahsanyojak bandh tayar karnyat guntalela asato. bandh tayar hott asatana, electron ghanateche jastit jaast karya kendrakapasun lakshaniyaritya door aanee itar anookade jaate. heey konatyahi golakar drushtikonatun hydrogenchi sthitee swatach yogyaritya tharvanyapasun rokhate. mhanoon, samanyatah hydrogenchya sthiticha andaj samaan renunsathi neutron chrystallography detachya aadhare lavala jaato, kinwa qamee-gunvattechya vivartan detachya babatit teey ajibat pratirupit kele jaat nahee.
neutron mojamapatoon mojamapatoon konatyahi nirbandhanpasun bandhanchi lambi sodalyanantar, hanson-coppens aupchariktecha vapar karoon hydrogen anoonchya sthananna muktapane parishkrut karane (jaree vadgrast asale taree) shakya aahe. puresha bahudhruvansaha anukaran kelele bandh kakshiy vishvasarh bandh lambi rakhoon thevatana ghanatechya vitaranache chhan varnan karate. hydrogen anoonchya anisotropic visthapan mapdandancha andaj lavane yogya asoo shakate, udaa.jee. aupchariktechi olakh karoon denyapurvi aanee bahudha bandhanchya antarachya maryada sodoon, chhaya vaparane.
bandh modelling.
renumadhil vividh parasparsanvadanchi lambi aanee samarthya yanche vishleshan karnyasathi, richard badderche 'anunmadhil anoo' pramey lagoo kele jaau shakate. yaa aspherical modeldware pradan kelelya electron kshetrachya jatil varnanamule, parasparsanvadi anoonmadhye vastavadi bandh marg sthapit karane tasech tyanche nirnayak bindu shodhane aanee tyanche vaishishtyikaran karane shakya hote. yaa mahitichi sakhol antardrushti bandhanchi takad, prakar, dhruviyata kinwa lambvartulakarta yabaddal upayukt mahitee dete aanee itar renunshi tulana kelee tarr tapasalelya sanyugachya vastavik electron sanrachanebaddal adhik samaj milate.
charge pravah.
pratyek anoochya pratyek bahudhruvasathi tyachya loksankhyeche swatantrapane shuddhikaran kele jaat asalyane, vaiyaktik shulk kvachitach purnank asateel. vastavik prakarananmadhye, electronchi ghanata renumadhun muktapane vahate aanee tee kalbahya jhalelya bohr anoo modelmule udbhavalelya aanee aay. aii. emm. madhye madhye konatyahi nirbandhanni bandhaleli nasate. tyamule eae. chya madhyamatoon.jee. achook white vishleshan, nivval anubharancha andaj lavala jaau shakato, joou tapasakhalil pranalinchi samaj adhik sakhol karnyasathi punha fayadeshir aahe.
truti aanee maryada.
jaree bahudhruviy aupcharikta heey sanrachana sudharanyache eka sope aanee saral paryayi sadhan asale, taree teey nishchitpane dosharahit nahee. samanyatah pratyek anusathi teen kinwa nauu mapdand parishkrut kele jaatat, jeey anisotropic visthapan vicharat ghetale jaat aahe qee nahee yavar avalambun asate, chauthya aanee tyanantarchya kalavadhishi sambandhit (jase qee chlorine, loh kinwa bromin) judd anoonche sampoorn bahudhruviy varnan karnyasathi 37 mapdandanparyantche shuddhikaran aavashyak asate. heey mothya asamamiteey ekak asalelya konatyahi sfatikansathi (visheshtah macromolecular sanyuge) samasyapradhan siddha hote aanee qamee darjachya mahitisathi, swatantra pratibimbanche aanee parishkrut mapdandanche asamadhankarak gunottar asalelya hanson-coppens aupchariktecha vapar karoon eka sudharana karane ashakya karate.
kahee mapdand ekach velee parishkrut kartana savadhgiri balgali pahije (i.eae. sootra _ 2 kinwa sootra _ 9, bahudhruviy loksankhya aanee aushnik mapdand), kaaran teey jordar parasparsambandhit asoo shakatat, parinami asthir sudharana kinwa unfigical parameter moolye hotat. eka renumadhil pratyek anusathi sthanik samamitimule (jyamule parishkrut bahudhruvanchi sankhya qamee hote) atirikt nirbandh lagoo karane kinwa vidyaman detabasemadhun populational parameters aayat karane dekhil eka pargamya model sadhya karnyasathi aavashyak asoo shakate. dusarikade, uparokt drushtikon prayogansathi aavashyak asalelya mahitiche praman lakshaniyaritya qamee karatat, tarr aspherical charge vitaranasandarbhat kahee pramanat tapasheel rakhoon thevatat. tyamule, samadhankarak ksh-kiran vivartan mahitee asalelya sthool aanvik sanrachananchehi ashach paddhatine aakarman kele jaau shakate.
tyanche samya asoonahi, vaiyaktik bahudhruv heey quantum gananemule gananemule laharichya aanvik kakshanchya anoo prakshepananshi sambandhit nasatat. tathapi, karbharine utkrushtapane saranshit kelyapramane, "model sphatik ghanatechi rachana, seudoatumche superposition mhanoon [...] yaat parimanatmak vaishishtye aahet jee quantum rasayanik gananevar aadharit anek parinamanchya jawal aahet. jarr anoo lahari karyanmadhil ativyapti pureshi lahan asel, udaharanarth sankraman dhatuchya sankulanmadhye hott asel, tarr anoo bahudhruv anoo sanyojak kakshanshi parasparsambandhit asoo shakatat aanee bahudhruviy gunank dhatuchya dii-kakshanchya loksankhyeshi parasparsambandhit asoo shakatat.
quantum crystallographychya wavefunction aadharit paddhatincha vapar karoon ex-reey mojalelya vivartan tivrata aanee quantum yantrik wavefunctions yanchyatil majboot parasparsambandh shakya aahe, udaharanarth ex-reey anoo kakshiy model, tathakathit prayogik wavefunction kinwa hirshfeld anoo parishkaran.

