Intro to Comp Simulation

8/6/2019 Intro to Comp Simulation

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I. Introduction o ComputerSimulationComputersimulation s abridgebetweenh99ly andex}-e ment:Computersiriulation -}"exact" rcsults or a!9l!!9!bl!ag&lComparec experimentalcsults_+testmodlCompareo theorticalptedictionsor thismodel--ttest heoriesTheorie$and nodelswill helpunderstandnd nterpretexperimentalcsultsComputersimulationislbglgg,bjqdeen nricroscooic-arrd-Erlcrolcllplgp-r9Le4tes:Computersimulation +grtqlg-*ogc, g-rarlsi e: atomicand- qlgggl-au4oJion)Microscopic details -madoscopicpropertiesComputel simulatioi canFovide information not a!-ailablg from rcal xpenmen$'-measureoents under,extrcms conditions that are experiltrentally prchibitive or difficult

:q:lli! .lT"1"":l* !!!on,g{ strTturempossible1di!]cult o studvxperimentallv-molecular eventsthat are1oo ast or to,ollow to study expe menlally'The complete mathematicnldescriptionofa system

\iL li., -l ilr i ( -/ : "NontelalivistigPchrodingerquatio-n:,rix, rlt!{R, !) *.&d.s{s- r) 0)

!/

R: coordinates f nuclei!: coordinates f electrons

'9(P't), ruuu"fun.tion for the system

H('r) - V(qr) 'L '*q(F!


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r- l6": rotalenergyofthe sYstemF('t)' Huntilto"iun ii'r thc s)'stem

H(R,!) - ' \"* + r' i+' iR'!) ' {21

7F'o), potrrtiul of i"tertttion ber*'eenal1ntclei and ekctorts

" ;-""t-*t' "*"ran

&couple theidotion of the electrons from thenucli to get

2 seDaiatequationsThe ffst descril*s tlre motiotr of til eltctrons (for fixd nuclei)

ta{:i B)d(!;s) = C.rF.}dt;a) {3)

ffo**3 4r, kinetic energiesofthe nrclei aodelctrons,respeeiiv_ly

({)'Adftie)= r.t +Y14!}

9l5s), "6",ron;" *uu,- function dependsnlyparametticallyon thepositions f the

Nclei)3'f3i,

"l".o.*i" "n.ig,v (functionol onlyhe nucleaiccoidinates)

F{8)"* b" ui"tt"d ns hepatettid cntrly suritce on rvhich tbenucler ';love'


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The secondequatioDdescribeshe mohon of the nucli on thepotential energysurface

t,{n).s*(a)*(R) - ,s4{a)

whele

.de.{s.)=:.a*+r.dn)

In Eq. I theelectronie oordrnatesreaveraged vertheelectronicwavefunclion' henucleiaremoving n theaverageield of thbelectrons'This svalid fthe electronsmovemuch asterhan henuclei. isanapproximationf'dfrom Eq. aad ncludeselectronic,vibntional,rotational,andtranslationalenergy.ThecorTespondingapproximation to the lvavefunction is

's{t,a) 'rtie)tta).4rW' und he"Eq 6lcould esolvedor th' In principle,Eq f couldbesolvedor

nuclearmotion.But solutionof tsq l requiresa largeamountof computatiol usingabinitio quantum hemistycodes uchasGaussianor semiempiricalodes uchasMNDO'

MOPAC,etc.).Thus, sually nempirical t to39a forcefield)sused'Solutionof Eq O scalled uantumdynamicsandalso equires arge mount fcomputation.Sincehenucleiare elativelyheavy' theqxantummechanicalffectsareoften nsignificant,oEq- canbe eplaced ith theNwton'squationsimotion

(5)

{61

(?)

{6)dE.,(A:^E.ynR! Er


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#i\""ult d "l".ri.al rnolaular

dyrrar,lrcs

!f we ar nol interes'ted Ir tl''e ime "volotion of$e systerntheo we c* *"W)to

;*c$lat staticpropeariesuchasquilitdarn struotr*es"tsansition ldes'la rirgis,.ta. :hisscalled molcllai m4hanies'Typicalassumprions f tlassicelmolecular yna6ics

2.nr*-li moveon d singlepotndal urfacei"' a"ltt1"lct"oni"-st"t")3. oolnrialsurfacecanbeapprgxCl-4!dy-e! rmplljlglfit4. nuclarmotioncan bedescribd ydassic"l ryh-t*

II. Molecular MechanicalPotentials(Forcefields)A.classical or.eftldcorsisls of:

Theforefreld is frt to experimentallata from a'smallstofmolecules'li{hrhegoal

that be forcefild' il l accwate{ynlerpolate odexltapola{e o others}slemsThiclassir:al forcefiells are fit to reproduceobservablssuch as structu'esand rlative


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empiricallYThe total Potntial s

(e)Y -U +V,,rr Vt+IAt+U"r-

A, Intrasolecdar (botrding)ntractronslntlamolbcular ntemalenelgy ermsaregivenby

& Weneedquaritummechanioso

describebondingaccuratelybutcanapproximatebondilgwithsimplephysicalmodels.Bondstretching ndanglebendingcanbetreatedas f atomsa connec&d

y spnngs'

Bonalstretching14=h0_eyllarmonic Potential:

. vr-trlt - *P(-o{l - a'))PMorse Potenlisl:In general,Morsepotential is more expensive but more accu@tehan

harmonlc

Disadvartages f MorsePorenLial' -allows a bond 1ostetch to an unrealistic length

-for a sltucturowith long bondsthe@w"uld bc almost no forcepulliDgthc otoms

together -rconvelgellce might be problematic or nonphysicalrcsultsmight be obtained

Disadvantae of harmonic otental)other importatrt structus could b destroyed-too large of a force at long distances-

A-oglebending!l= a.{e- 9.}'Rotatio aroun'l bonds torsion angles)


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torsionaaglecemral form:%-- fltil + ''|c'E{nd}Lhere,1.2.3.4'6

Exanrplesl y. - 0V2)lI r.o{34)l-tl,vo lefg*dral oalbofls coBledd by slnc+e bond: J trr|Ill':Ralvr= O/r&Ir - d{2#)l-doubl,eond:2 nlinima

O{t-ofdane defo'Brationof ad*aar:systmux- E;zCross erfits'couptingsbar+eendeforrnationsf iniemalcoordinates-rcquircd o eccuratelyrcproducxpeti4er*alibntional frequencies-can ecomeunst*le far romminimaAs{i-b){6'-irJf..{6 -i"Xg -$,srf{r-ot{f-4)PotxfB- Nohbooded iDleracliotrsTtienonbordddtreriorr" ."gi*n ty Yi+ EAlom-alod or site-siteapproxima(ioD:.Inreractionb"tqngEg19!,lqiust asun of in cti-Intractionsites risl3lly nterd on 1+le ugli of the riolculeExtend+datom epieseotalion:some|-!]1!?qjf1!igl!4Ei!gl}j!\atoms to which they ar bouBd G'l R@ J- \_/


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Advantages:

ejg!-'UYlryPslryqsl'- lossof stedcellects- H coonlinates rcnecessaryor someanalysis i e ' protonNMR)1.ElectrostaticCoulornbic)nteracfonsThe electrostaticntePction of two atomswith charges&and

glseparatedby r'jis o-fthe

- reduces jqP!!44!-(about half of atomsareH's)

-!|c9!$- H p".iti"". "."^lly t()t *Disadvantages:- difficult to reprfsentH-bonding

formYc= (1$)

lfletolla:Coulomb'saw:Angstroms),hepotentiul"n"tga i"

yO * S\sa!lato!-

like chargesepel, nlike charges ttract.If2 charges reseparbtedy a medium(i e ',solvent)' hen hepotntialenergyot

, ..^.V(t) - 332*kcnllmolwheres the ielectricorslanlinteractionecreases:. = 1-{00in acuurr * 2iornonpolariquid hydrocarbons. * 50for iquid vater

$q,


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nuclei, thnet oneachatom s considgrd.&,Ls!lllP1!!!!9tlo!fh--ele-cironsrenolsh.redequallybet\ een he alorns n a rnoleculeThe el'cirond;st butiondeterrDineshpartial ohargoDeachaloi_n.Thesecan bealculatd ]omputalionally using \4uliikenchatgeanal.vsis,CHelPG, RESp' etc'

r)/ Ehctrostatic potDtial euergy of interaction betrYel2 moletules-usCollombb lawbtweenparlial charges n achatom-sumoverall alomsIfigltr order moments {typically not palt ofclasrical fo'ceitelds)

."/,'^ Dipole moments$easur o{the polarity ofa molcule-vectorquaitity (magnitud and direction)-for 2 chergesofequal magtitude q but oppositesign separated-dirctionis*omj9il99Egl!ry!4e +-J-Jor multipleclBrges,addup contributionsof all cha'gesor 3 componenis

y4- @l+1$+$tt\Note that /dependson th origin for chargedspecies

\./Dipole-dipole inteiactions:simplificatbn of interaction hween 2 neutmlmoleculeswith dipole mornentsrs toapplcxirnte heeffectofall the charges n eachmolcuie lva dipolemoment

potntial nergy iinteraction betwen2 dipolut t {B) ^ x-'

1't: 'iryby a distance ;ljjl

._,,,ton-d Pole rrteractions:


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sinplificationolinteraition betrleenchargedon an'l neutmlmoleculewith dipole

moments to approximatehc efl'ectof all chalges nthenutralmoieculeby a dlpole

momentpotntial enelgyof interactionPolatizationpola ze: chalgenear molecule with no permanentdipole momentdistorts electronlc

distribu{bnofmolecule o createaninduceddipolemomentpotarizability:easurefhoweasvt is o4!:!9!99ry1!!y!jl!3ryE:lleion - induceddipole intetaction: interaction betweena charged on and polarizedmolecule

' ' " 'rssical orcefields' ut hasbeenshown o bpolarizationypically nol included n clair1\poflantExample: eed olarization ems !n order o modelhydrogen ondingand ion

dissociatio[ in water2. London-vander Waals interactions

.. . v(n)^ fi 'bet\ \eenan on anda dlpole s

Thel'ondon-vanerwaals nteractionsor?j49ryryLarat-!94ufll

v"art E

Alsocalled ennaril-Jones 2-6potential:

Yu-

04

02)"[(r)"-(;I


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welldeptb:eFti)edy{isirg rapulsive w4l atdistanestess &n tt"Bac*grouod:| ,oDdonattractioo-g{crua{o4dipqte jnduaddipole i$teraction,iu$adroheousditole {d'to fl$ctsatio{ls in+e{*or}ied*iki{te*ioo} occrrs irr one atoa:!rto'idr il$uees an oppositety dirstd dipole in atoig&oring etoorI-dwaYs.ettrshvett(r)= *S

'4foependson thepotarizalility {i.e.easeof #@alization of thededrons) of thegrcupsinvol\dvanderWaals ePulsion-all atords rmolculs pelatshortdistaatsstericpulsions){uantummechtrnical dgin: ?letronslannot eput ioto o'relectronicorbitaldiftrent simplemodelsavailablehardaplFr: ero nteractiodqrgy untilbacellto{ojfetr{')=#sofi spnere:&is poritive anddepends n bothatotr$vanderw'ads adlus: clistaJtceetlvel2 aiomswhe+eprlsionenergy starts ising.rapidlyC. Ilydrogen bonds{n sonreorcelields,hydrogeabondsarisehornslartdardandr Wsalsandlct{ostalrc


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5

tenns.Other orcefields ncludrrspecial ydrogen onding ennsvss.Backg,oundor hldrogenbonds:-H atom nteracts imultaneodslywith 2 otheratoms-enthalpYo{j}lSlmol (compatedto about400 kJ/mol for covalent bonds)-themost mportant H-boods in biological systemsoccur with O and Nl.xperimenlal rilerion thal H-bond existsberween and B-if2 atornsare closer than the sum oftheir van de. Waals radii { R 1,5,{for O) ttlen theyIa.ealmost efinitelyH-bonded

23 *3.04-ifA,B=N,O hen fAB distances a H-bond xistsH-bondbecomesweaker n aqueous olutiondue o competitionwith waterH-bondnet,rork of water:-eachwater s intemctionwith 4 tetraie&ally oriented eighbors-rct rigid(mobile)-alomalousroprties fwater:highboiling oint, ighviscosity, ighentropy fvapoizationD. Constraints nd RcstraintsTheconstraints nd restraints ermsaregivenbyLUseconstmints lld rcstraints o modify he.energyxprcssion Qbias he calculation i eto focus he calculation on a regionor confomationof interestand o setupcomputational xperiments)Constraint:an absolute estrictionRestrainl: an energeticbiasFixedafom constraiRts

n f,r*, . ' /v1@'u (-t\- lr "uLi { t


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eonst{ainaioms to 6 given locationTeflns n Se energyexpressionnlollingorly ilxed atomscan be eliminaied

_-',e!ergy

calculal;onaslerNuslber ofdegrees of ireedom ii:rLlresysem is redijced -+mini$ization anddynanricsfasterExanPlesfix ptoi-ein aJ)dBDdel wa{9rstrt}cturearoundprotein

-Fix nost ofprotin but ptdict strrctute of celtajn 'eglonsDistance estraintsfolEe tbe distancbetween 2 atoms owald a given value-simpleharFonic function:

it =Jf{., - rid'lr}r 413)

-five piecewisecontinuoxs rgio$sof hainonic function {flat-botlomtdpotential)

Y - 5l +{t1-rj}ft:rrft6-rr|:0- -I(3it11 t$t= .{ + {41 r4}ir4

r{


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!1.Hw.ra, ;ru: c ,. ir iac{ioDsl{et x Jepartte niEriictioB tssul|s rom co$bioaton ofln*don, vander Vaals'el l-. .(: .1.rcil ' ; ondingnleraclionsfiyd-.r'i, ).r;rjt: lvalei fearing{i!'tergcrion nvith \a'ate' ess ibvstattle than \tati $'ith rvatei)hyd.i.' -,\ilic: 'vater loting (strong fal'orable interactions with watet)arni.', rr :iiic: both hyrLophiiic andh;drop*robic ciraracter n thesalllemolecule; (manyami:c :cjds and.mcleotidease9 .:,^ti:.!,, ,r,i. 'l7 t ' '.i'tv.l f c,ohcbic tteraclions:,1:w d$a!!c,l]ql gqs,-enhopy'dri\'en2 hi'ckoca*on groupsR introduced into Ealer wilLclusir+lldiophobic amiro ecids n pmtein usually cluster in iderior ofp'otin' atd hydrophi'lic{cha.ge.d,polar) a{hiro aids end to be at {he surfaaeu'i}ere hey interactwith water'Polar {ipid ncdecules orm bila!r shels or membranesn \'}ater$'herc hydrocarbonparts aie buded insiCeandpo'lar ol charged parts are on the surface

Intro to Comp Simulation

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