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1 Supportng nformaton for the manuscrpt Intaton Mechansms and Knetcs for Pyrolyss and Combuston of JP Hydrocarbon Jet Fuel by Kmberly Chenoweth Adr CT van Dun Sddharth Dasgupta and Wllam A Goddard III ReaxFF Force Feld Parameter Fle Reactve MDforce feld: c/h/o combuston force feld November 6 39! Number of general parameters 5!pboc 95469!pboc 6545!pcoa 55!ptrp4 6663!ptrp3!kc 588!povun6 46!ptrp 76!povun7 3356!povun8 79!ptrp!Lower Taperradus swa!upper Taperradus swb!not used !pval7 689!plp 563!pval9 384!pval 643!not used 699!ppen 3989!ppen !ppen4!not used 57796!ptor!ptor3 9487!ptor4!not used 645!pcot 559!pvdW!Cutoff for bond order* cutoff 365!pcoa4 699!povun4 5!povun3 85!pval8!not used!not used!not used!not used 696!pcoa3 3! Nr of atoms; atomid;rosgma; Val;atom mass;rvdw;d;gamma;rop;vale alfa;gammaw;valangle;povun5;nu;cheem;etaeem;nu ropp;plp;heat ncrement;pboc4;pboc3;pboc5nu;nu povun;pval3;nu;valboc;pval5;nu;nu;nu C H O ! Nr of bonds; at;at;desgma;dep;depp;pbe;pbo5;3corr;nu;pbo6povun S

2 pbe;pbo3;pbo4;nu;pbo;pbo ! Nr of offdagonal terms at;at;d;rvdw;alfa;rosgma;rop;ropp ! Nr of angles at;at;at3;thetaoo;pval;pval;pcoa;pval7;ppen;pval ! Nr of torsons at;at;at3;at4;;v;v;v3;ptor;pcot;nu;nu ! Nr of hydrogen bonds at;at;at3;rhb;phb;phb;phb S

3 ReaxFF Potental Functons: Ths document contans all the general ReaxFFpotental functons In the current ReaxFF code all the energy contrbutons n ths document are calculated regardless of system composton All parameters that do not bear a drect physcal meanng are named after the partal energy contrbuton that they appear n For example p val and p val are parameters n the valence angle potental functon Parameters wth a more drect physcal meanng lke the torsonal rotatonal barrers V V V 3 bear ther more recognzable names Overall system energy Equaton descrbes the ReaxFF overall system energy E system = E bond lp over under val tors pen con coa H! bond C trple vdwaals Below follows a descrpton of the partal energes ntroduced n equaton Bond Order and Bond Energy Coulomb A fundamental assumpton of ReaxFF s that the bond order BO between a par of atoms can be obtaned drectly from the nteratomc dstance r as gven n Equaton In calculatng the bond orders ReaxFF dstngushes between contrbutons from sgma bonds pbonds and double p bonds BO % = BO BO BO = exp p bo $ & r r o * p bo exp p % bo3 $ / & % exp p bo5 $ & r r o r r o * * p bo4 p bo6 / / Based on the uncorrected bond orders BO derved from Equaton an uncorrected overcoordnaton Δ can be defned for the atoms as the dfference between the total bond order around the atom and the number of ts bondng electrons Val neghbours = Val $ BO 3a = S3

4 ReaxFF then uses these uncorrected overcoordnaton defntons to correct the bond orders BO usng the scheme descrbed n Equatons 4af To soften the correcton for atoms bearng lone electron pars a second overcoordnaton defnton Δ boc equaton 3b s used n equatons 4e and 4f Ths allows atoms lke ntrogen and oxygen whch bear lone electron pars after fllng ther valence to break up these electron pars and nvolve them n bondng wthout obtanng a full bond order correcton boc = Val boc neghbours BO $ 3b = f BO BO BO BO!!! = BO = BO = BO! = BO $ f!! & = $ % Val $ f $ f BO $ f! BO!! BO $ f $ f $ f BO $ f BO $ f $ f BO $ f BO Val f f f Val BO 5 5 4a Val f! f f 3 4b 3 f = expp boc $ expp boc $ 4c f 3 = % $ ln p boc $ exp p $ & boc [ exp p boc $ ] * 4d f 4 BO = expp boc3 $ p boc4 $ BO $ BO boc p boc5 4e f 5 BO = expp boc3 $ p boc4 $ BO $ BO boc p boc5 4f S4

5 A corrected overcoordnaton Δ can be derved from the corrected bond orders usng equaton 5 neghbours = Val $ BO 5 = Equaton 6 s used to calculate the bond energes from the corrected bond orders BO p be E bond = D e $ BO % $ exp p be BO & * D e $ BO D e $ BO 6 3 Lone par energy Equaton 8 s used to determne the number of lone pars around an atom Δ e s determned n Equaton 7 and descrbes the dfference between the total number of outer shell electrons 6 for oxygen 4 for slcon for hydrogen and the sum of bond orders around an atomc center neghbours e = Val e $ BO 7 = n lp = nt e & e % exp p lp * e * nt & 4 3 % / 6 $ 3 $ For oxygen wth normal coordnaton total bond order= Δ e =4 equaton 8 leads to lone pars As the total bond order assocated wth a partcular O starts to exceed equaton 8 S5

6 causes a lone par to gradually break up causng a devaton Δ lp defned n equaton 9 from the optmal number of lone pars n lpopt eg for oxygen for slcon and hydrogen lp = n lp opt! nlp 9 Ths s accompaned by an energy penalty as calculated by equaton E lp = lp p lp lp exp $75 4 Overcoordnaton For an overcoordnated atom Δ > equatons ab mpose an energy penalty on the system The degree of overcoordnaton Δ s decreased f the atom contans a brokenup lone electron par Ths s done by calculatng a corrected overcoordnaton equaton b takng the devaton from the optmal number of lone pars as calculated n equaton 9 nto account E over = nbond $ = p ovun D e BO % % lpcorr Val lpcorr & exp p ovun % lpcorr * a lpcorr = lp neghbours lp % p ovun 3 $ exp p ovun 4 $ & $ BO BO %% / * = 3 b 5 Undercoordnaton For an undercoordnated atom Δ < we want to take nto account the energy contrbuton for the resonance of the πelectron between attached undercoordnated atomc centers Ths s S6

7 done by equatons where E under s only mportant f the bonds between undercoordnated atom and ts undercoordnated neghbors partly have πbond character E under = / p ovun5 / exp exp / p lpcor p ovun6 ovun lpcor & povun7 exp$ p $ % ovun8 * lp / neghbours = BO BO!! 6 Valence Angle Terms 6 Angle energy Just as for bond terms t s mportant that the energy contrbuton from valence angle terms goes to zero as the bond orders n the valence angle goes to zero Equatons 3ag are used to calculate the valence angle energy contrbuton The equlbrum angle Θ o for Θ k depends on the sum of πbond orders SBO around the central atom as descrbed n Equaton 3d Thus the equlbrum angle changes from around 947 for sp 3 hybrdzaton πbond= to for sp πbond= to 8 for sp πbond= based on the geometry of the central atom and ts neghbors In addton to ncludng the effects of πbonds on the central atom Equaton 3d also takes nto account the effects of over and undercoordnaton n central atom as determned by equaton 3e on the equlbrum valency angle ncludng the nfluence of a lone electron par Val angle s the valency of the atom used n the valency and torson angle evaluaton Val angle s the same as Val boc used n equaton 3c for nonmetals The functonal form of Equaton 3f s desgned to avod sngulartes when SBO= and SBO= The angles n Equatons 3a3g are n radans E val [ p! BO! ] { p p } = f 7 BO f 7 BO k f8 $ val val exp 3a val o k p f 7 BO = exp p val 3 BO val 4 3b S7

8 $ f 8 = p val 5 p val 5 angle exp p val 6 $ angle angle exp p val 7 $ exp p val 6 $ 3c SBO = & neghbours 8 $ % exp $BO n $ angle $ p val 8 n lp n= * neghbors BO BO n n n= BO angle = Val angle SBO = f SBO neghbours BO n n= SBO = SBO p val 9 f < SBO < SBO = SBO p val 9 SBO = f SBO > 3d $ 3e f < SBO < = $ % $ exp $p val % $ SBO 3f { [ ]} 3g 6 Penalty energy To reproduce the stablty of systems wth two double bonds sharng an atom n a valency angle lke allene an addtonal energy penalty as descrbed n Equatons 4a and 4b s mposed for such systems Equaton 9b deals wth the effects of over/undercoordnaton n central atom on the penalty energy E pen = p pen f 9 exp $p pen BO $ [ ] exp [ $p pen BO k $ ] 4a exp p pen 4 $ exp p pen 3 $ f 9 = exp p pen 3 $ 4b 63 Threebody conugaton term The hydrocarbon ReaxFF potental contaned only a fourbody conugaton term see secton 7 whch was suffcent to descrbe most conugated hydrocarbon systems However ths term faled to descrbe the stablty obtaned from conugaton by the NO group To descrbe the stablty of such groups a threebody conugaton term s ncluded equaton 5 S8

9 E exp val exp pcoa / BO! 5 exp [! p ] [! p BO! 5 ] coa4 neghbours neghbours = exp&! 3 exp&! 3! coa pcoa pcoa BO BOn pcoa! BO k BOkn n= n= 7 Torson angle terms & coa4 k 7 Torson rotaton barrers Just as wth angle terms we need to ensure that dependence of the energy of torson angle ω kl accounts properly for BO and for BO greater than Ths s done by Equatons 6a6c E tors = f & $ V % BO BO k BO sn * kl k sn * kl 5 % * $ cos kl V exp{ ptor BO k f k } cos kl V3 cos3 kl! f BO BO k BO kl = exp p tor BO f k = & 6a [ ] [ exp p tor BO k ] exp p tor BO kl 6b exp p tor3 $ angle angle [ k ] [ ] exp p tor4 $ angle angle [ k ] exp p tor3 $ angle angle k [ ] 6c % * $ 7 Four body conugaton term Equatons 7ab descrbe the contrbuton of conugaton effects to the molecular energy A maxmum contrbuton of conugaton energy s obtaned when successve bonds have bond order values of 5 as n benzene and other aromatcs E con = f BO BO k BO kl p cot [ cos kl $ sn% k sn% kl ] 7a * $ f BO BO k BO kl = exp p cot BO & % / exp * p BO $ & cot % k / exp * p BO $ & cot % kl / 7b 8 Hydrogen bond nteractons Equaton 8 descrbed the bondorder dependent hydrogen bond term for a XH Z system as ncorporated n ReaxFF r [ ] exp p hb hb3 & E Hbond = p hb exp p hb BO XH * S9 $ o r $ HZ o / sn 8 XHZ & % r HZ r hb % 8

10 9 Correcton for C ReaxFF erroneously predcts that two carbons n the C molecule form a very strong trple bond whle n fact the trple bond would get destablzed by termnal radcal electrons and for that reason the carboncarbon bond s not any stronger than a double bond To capture the stablty of C we ntroduced a new partal energy contrbuton E C Equaton 9 shows the potental functon used to destablze the C molecule: E E C C = k = c 4 BO $ $ 4 $ 3 4 f BO $ $ 4 > f BO $ $ 4! 3 where Δ s the level of under/overcoordnaton on atom as obtaned from subtractng the valency of the atom 4 for carbon from the sum of the bond orders around that atom and k c the force feld parameter assocated wth ths partal energy contrbuton Trple bond energy correcton To descrbe the trple bond n carbon monoxde a trple bond stablzaton energy s used makng CO both stable and nert Ths energy term only affects CO bonded pars Equaton shows the energy functon used to descrbe the trple bond stablzaton energy E trp = p trp exp [/ p BO / 5 ] trp exp& / p trp4 neghbours k= % BOk / BO exp& / p * $ 5 exp [ p!! ] trp3 trp4 neghbours k= BO k / BO % * $ Nonbonded nteractons In addton to valence nteractons whch depend on overlap there are repulsve nteractons at short nteratomc dstances due to Paul prncple orthogonalzaton and attracton energes at long dstances due to dsperson These nteractons comprsed of van der Waals and Coulomb forces are ncluded for all atom pars thus avodng awkward alteratons n the energy descrpton durng bond dssocaton Taper correcton To avod energy dscontnutes when charged speces move n and out of the nonbonded cutoff radus ReaxFF employs a Taper correcton as developed by de Vos S

11 Burchart 995 Each nonbonded energy and dervatve s multpled by a Taperterm whch s taken from a dstancedependent 7 th order polynomal equaton Tap = Tap 7 r 7 Tap 6 r 6 Tap 5 r 5 Tap 4 r 4 Tap 3 r 3 Tap r Tap r Tap The terms n ths polynomal are chosen to ensure that all st nd and 3 rd dervatves of the nonbonded nteractons to the dstance are contnuous and go to zero at the cutoff boundary To that end the terms Tap to Tap 7 n equaton are calculated by the scheme n equaton where R cut s the nonbonded cutoff radus 7 Tap 7 = /R cut 6 Tap 6 = 7 /R cut 5 Tap 5 = 84 /R cut 4 Tap 4 = 35 /R cut Tap 3 = Tap = Tap = Tap = van der Waals nteractons To account for the van der Waals nteractons we use a dstancecorrected Morsepotental Equatons 3ab By ncludng a shelded nteracton Equaton 3b excessvely hgh repulsons between bonded atoms nteractons and atoms sharng a valence angle 3 nteractons are avoded 3 % E vdwaals = Tap D exp $ f 3r * $ exp & r vdw / % $ f 3r 53 * 6 43 & r vdw / 73 3a p f 3 r = r vdw & % * $ w p vdw p vdw 3b 3 Coulomb Interactons As wth the van der Waalsnteractons Coulomb nteractons are taken nto account between all atom pars To adust for orbtal overlap between atoms at close dstances a shelded Coulombpotental s used Equaton 4 S

12 E coulomb = Tap C q q [ r 3 / 3 ] 4 / 3 Atomc charges are calculated usng the Electron Equlbraton Method EEMapproach The EEM charge dervaton method s smlar to the QEqscheme; the only dfferences apart from parameter defntons are that EEM does not use an teratve scheme for hydrogen charges as n QEq and that QEq uses a more rgorous Slater orbtal approach to account for charge overlap S

13 Table Expermental data plotted n Fgure 5 Data taken from Rao RN; Kunzru D J Anal Appl Pyrolyss % Converson CH4 wt % % Converson C3 wt% % Converson C4 wt% % Converson C5 wt% S3

14 Table ReaxFF data plotted n Fgure 5 Temp Smulaton K % Converson CH4 wt % Mole Fracton Temp Smulaton K % Converson C3 wt % Mole Fracton Temp Smulaton K % Converson C4 wt % Mole Fracton Temp Smulaton K % Converson C5 wt % Mole Fracton S4