Monte carlo simulation of molecules and ions in liquid water

MONTE CARLO SIMULATION OF MOLECULES AND IONS IN LIQUID WATER MICHAEL YUDISTIRA PATUWO NATIONAL UNIVERSITY OF SINGAPORE 2011 MONTE CARLO SIMULATION OF MOLECULES AND IONS IN LIQUID WATER MICHAEL YUDISTIRA PATUWO (B.Sc.(Hons), NUS) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN SCIENCE DEPARTMENT OF CHEMISTRY NATIONAL UNIVERSITY OF SINGAPORE 2011 Abstract heriv—tion of re—™tion free energy of ™hemi™—l pro™esses in —queous environments ™—n ˜e —ided ˜y the knowledge of hydr—tion free energyF wonte g—rlo simul—E tion ™—n ˜e done in ™onjun™tion with the thermodyn—mi™ pertur˜—tion methodD ˜y me—ns of fennett9s —™™ept—n™e r—tioD in order to o˜t—in the free energyF „he solute mole™ule w—s –morphed9 from — nonEinter—™ting –ghost9 mole™ule inside — ˜ox ™ont—ining „s€Q€G„s€R€ w—ter mole™ules under the periodi™ ˜ound—ry ™onditions to its full potenti—l fun™tionsD ˜y su˜je™ting the two endpoint systems —nd interE medi—te systems with softE™ore soluteEsolvent inter—™tion potenti—ls to sep—r—te wg simul—tionsF ell wg simul—tions were performed using — homegrown portr—nWH proE gr—m th—t —llowed ™hoi™e of solvent models —nd ™ustom inter—™tion fun™tionsD —nd w—s wellEt—ilored for morphing oriented worksF e good de—l of —ttention w—s put on the potenti—l fun™tions used for soluteEsolvent inter—™tionF ‡hile empiri™—l fun™tions were usedD they —re l—rgely ™onsistent with est—˜lished theoreti™—l —rguments —nd ™onstru™tsF Acknowledgments pirst —nd foremostD s would like to th—nk my supervisor —nd mentorD esso™F €rofF ‚y—n €F eF fettensD for his guid—n™e —nd ™ounsel in ˜oth my undergr—du—te —nd gr—du—te ye—rsD for nurturing my interest in the (eld of physi™—l —nd ™omput—tion—l ™hemistryD —nd for ˜eing — ™onst—nt sour™e of inspir—tion for meF s —lso th—nk every le™turer s9ve h—d the honour to ˜e t—ught ˜y in the p—st seven ye—rsD who h—d ˜rought me where s —m right nowD hrF edri—n wF vee for m—king me —n —™qu—int—n™e to the (eld of qu—ntum ™hemistry —nd for his —™—demi™ guid—n™eD —nd esso™F €rofF p—n ‡—i ‰ip —nd esso™F €rofF u—ng rw—y ghu—nD who were the ex—miners for the qu—li(™—tion ex—m for my €hFhF ™—ndid—tureD for giving me — w—keEup sl—p —nd put me ˜—™k on tr—™kF ‡ithout —ll of you s would not h—ve loved ghemistry the w—y s right nowD —nd s would not h—ve ™ome this f—rF w—nyD m—ny th—nks to my junior —nd friend ve r—i enh ‚yoD whose resour™efulE ness —nd determin—tion were inv—lu—˜le to meY qod ˜less her in her future ende—vE oursF wy undergr—du—te —nd gr—du—te friends who h—d ˜een here in the s—me l—˜ together with me through thi™k —nd thinX urishn—nD gl—r—D ƒ—ndr—D rui ti—D emeli—D it would h—ve ˜een so dull without —ll of youF s would —lso extend my th—nks to vow ti— inD my —™qu—int—n™e sin™e se™ond—ry s™hool —nd — gre—t friend throughout my ye—rs in x…ƒF feing — ™hemistry m—jor would not h—ve ˜een the s—me without youF s —lso th—nk everyone who h—d helped me during my €hFhF ™—ndid—ture ye—rs in v—rious w—ysD wiss ƒuri—w—ti finte ƒ—9—d for her help in nonE—™—demi™ m—ttersD esso™F €rofF „horsten ‡ohl—nd for his ide—s —nd initi—tive ™on™erning the gr—du—te m—ttersD ‰ung ƒhing qene —nd the gƒiD for —llowing me to use their m—™hines to — signi(™—nt p—rt of my workD —nd everyone else who h—d helped me in w—ys th—t s m—y not ˜e —w—re of or h—ve forgottenF s —m honoured to ˜e — student of x…ƒD —nd s —m forever gr—teful for the gr—du—te rese—r™h s™hol—rship th—t s w—s o'eredF ‡ithout itD it would h—ve ˜een impossi˜le for me to my gr—du—te studies in ƒing—poreF „h—nk you my p—rentsD for en™our—ging me in the —™—demi™ p—th th—t s h—ve ™hosenD —nd ƒte'y —nd €ris™y for —lw—ys ˜elieving in their ˜ig ˜rotherF w—mi —nd €—piD s love you so mu™hF „h—nk you fennyD for sti™king with me —fter we9ve moved out of x…ƒ residenti—l h—llsF „h—nk you iu ˆunD for sitting those physi™s le™tures with meD uennyD my h—ll friend —nd g—ming m—teD —ll the ™ool people who were under eƒiex s™hol—rship with me ˜—™k in the d—ysD my xtg ™l—ssm—tesD my friends in xt ghor—le —nd ‚eson—n™e old —nd youngF „hese four ye—rs would h—ve ˜een so di'erent without your friendshipF vooking ˜—™kD s not —nd will never regret the de™ision of ™oming to ƒing—pore —nd doing my €hFhF work in x…ƒF „he tre—sured memories will forever st—y with meD wh—tever the future m—y ˜eF Contents Summary List of Tables List of Figures List of Symbols The Dynamics of Molecular Systems IFI IFP IFQ IFR sntermole™ul—r por™es"e €re—m˜le F F F F F F F F F F F F F F ile™trost—ti™ inter—™tions F F F F F F F F F F F F F F F F F F F F IFPFI wultipole moments —nd mole™ule in —n ele™tri™ (eld IFPFP ile™trost—ti™ inter—™tions ˜etween mole™ules F F F F F IFPFQ histri˜uted multipoles F F F F F F F F F F F F F F F F F xonEele™trost—ti™ inter—™tions F F F F F F F F F F F F F F F F F IFQFI sndu™tion energy F F F F F F F F F F F F F F F F F F F F IFQFP hispersion energy F F F F F F F F F F F F F F F F F F F F IFQFQ ix™h—ngeErepulsion energy F F F F F F F F F F F F F F F €relimin—ry g—l™ul—tions F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F gomputer ƒimul—tion wethods F F F F PFIFI wetropolis elgorithm F F F F F PFIFP €eriodi™ found—ry gonditions F PFIFQ iw—ld ƒumm—tion wethod F F PFIFR NpT ensem˜le F F F F F F F F F PFIFS pree inergy F F F F F F F F F F F PFIFT e™™ept—n™e ‚—tio wethod F F F PFIFU worphing F F F F F F F F F F F F PFIFV ƒoftE™ore potenti—l F F F F F F F „he MC €rogr—m F F F F F F F F F F F F PFPFI qener—l )ow of the progr—m F F PFPFP €rep—r—tive steps F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F SS F TP F TT F UH F UV F VI F VR F VW F WR F WW F IHR F IHT xitrogen F F F F weth—ne F F F F weth—nol F F F g—r˜on dioxide fut—ne F F F F F fenzene F F F F ith—noi™ —™id F ith—n—mide F F gon™lusion F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F Molecular Monte Carlo Simulation PFI PFP Simulation of Neutral Molecules QFI QFP QFQ QFR QFS QFT QFU QFV QFW i iv vii ix F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F I U V IQ IW PS PT QI QW RH 55 111 III IPI IPV IQU IRH IRT ISP ISV ITQ Simulation of Zwitterions RFI RFP RFQ RFR qener—l ™omments F F F el—nine F F F F F F F F F esp—r—gine F F F F F F F xeur—minid—se inhi˜itors RFRFI —n—mivir F F F F RFRFP €er—mivir F F F F Conclusion Bibliography A Spherical harmonics B Multipole moments F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F 167 ITU ITV IUS IVQ IVS IVW 193 197 209 213 fFI yper—tors F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F PIQ fFP qeometry ™onversions for multipole moments F F F F F F F F F F F F F PIR fFQ gh—nging the origin of multipole moments F F F F F F F F F F F F F F F PIS C Interaction functions D Program and Auxiliary Files 219 223 hFI MC F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F PPQ hFP Bennett_1000 F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F PPT hFQ shell F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F PPU 214 Appendix B Multipole moments y™topoles ˆ Oαβγ = qi i rα rβ rγ − |r|2 (rα δβγ + rβ δγα + rγ δαβ ) 2 @fFRA sf αD β D —nd γ —re distin™tX ˆ Oααα = 3 rα − |r|2 rα 2 qi i ˆ Oααβ = qi i ˆ Oαβγ = rα rβ − |r|2 rβ 2 qi i rα rβ rγ B.2 Geometry conversions for multipole moments Table B.1: Conversions between spherical and Cartesian geometry up to rank ƒpheri™—l to g—rtesi—n g—rtesi—n to spheri™—l ˆ M00 =q ˆ ˆ M10 = pz ˆ ˆ M11c = px ˆ ˆ M11s = py ˆ ˆ M20 ˆ = Ozz ™ontinuedFFF B.3 Changing the origin of multipole moments 215 „—˜le fFI !™ontinued ƒpheri™—l to g—rtesi—n g—rtesi—n to spheri™—l √ ˆ M21c = √ ˆ Ozx ˆ Ozx = ˆ M21s = √ ˆ Ozy ˆ Ozy = ˆ M22c = √ ˆ Oxx ˆ = − M20 + ˆ M22s = √ ˆ Oyy ˆ = − M20 − ˆ Oxy = ˆ ˆ Oxx − Oyy ˆ Oxy ˆ M30 ˆ M21c √ ˆ M21s √ ˆ M22c √ ˆ M22c √ ˆ M22s ˆ = Ozzz ˆ M31c = ˆ Ozzx ˆ Ozzx = ˆ M31c ˆ M31s = ˆ Ozzy ˆ Ozzy = ˆ M31s ˆ M32c = ˆ M32s =2 ˆ Oxyz ˆ Oxyz = ˆ 12 M32s ˆ M33c = √1 10 ˆ ˆ Oxxx − 3Oxyy ˆ Ozxx = ˆ 12 M32c ˆ M33s = √1 10 ˆ ˆ 3Oxxy − Oyyy ˆ Ozyy =− ˆ Oxxx = ˆ M33c − ˆ M31c ˆ Oxxy = ˆ M33s − ˆ 24 M31s ˆ Oxyy = ˆ M33c − ˆ 24 M31c ˆ Oyyy = ˆ M33s − ˆ M31s ˆ ˆ Ozxx − Ozyy ˆ − M30 ˆ 12 M32c ˆ − M30 ˆ ˆ (k) sn gener—lD Mk0 = Mzz z B.3 Changing the origin of multipole moments „he st—nd—rd —ddition theorem for regul—r spheri™—l h—rmoni™s is written —s su™h ‘PP“X l l1 l2 δl1 +l2 ,l (−1)l+m Rlm (a + b) = l1 ,l2 m1 =−l1 m2 =−l2 (2l + 1)! (2l1 )!(2l2 )! 216 Appendix B Multipole moments   l2 l  l1  × Rl1 m1 (a)Rl2 m2 (b)   m1 m2 −m   where the ‡igner QEj ™oe0™ient  @fFSA  l1 l2 l m1 m2 −m   is rel—ted to gles˜™hEqord—n ™oe0™ients —s followsX   l2 l   l1 l −l −m l1 m1 , l2 m2 |lm   = (−1) √ 2l + m1 m2 m @fFTA ‡e see th—t the term δl1 +l2 ,l ™rosses out —ny term where l1 + l2 = lD —nd hen™e we ™—n rewrite the —˜ove equ—tion —s su™hX l1 l Rlm (a + b) = l1 =0 m1 =−l1 l+m l−m l1 + m1 l1 − m1 pin—llyD if we t—ke position ve™tor Rl1 m1 (a)Rl−l1 ,m−m1 (b) a to ˜e the initi—l origin @fFUA O of the multipole moments —nd c = −b —s the position ve™tor of the new origin C @refer to (gure fFIAD we h—veX L l C MLM = l=0 m=−l L+M L−M l+m l−m O Mlm RL−l,M −m (−c) @fFVA …nfortun—telyD there is no ™on™ise w—y to express the new multipole terms in its re—l O formD —nd —t the ™losest it would require the ™omplex forms of the unshifted Mlm —nyw—yF ‚eg—rdlessD this tr—nsform—tion is useful in ™—ses su™h —s where distri˜uted multipoles —re used in order to des™ri˜e the ele™tri™ (eld of — mole™uleD —nd whenever it m—kes more sense to de(ne the origin —t the new site @su™h —s —t the ™entre of ™h—rge of the mole™uleD or —t — spe™i(™ —tomFA B.3 Changing the origin of multipole moments 217 Figure B.1: Change of origin for multipole moments expansion A new origin can be placed at the site where a set of multipole moments are dened, such as at the centre of an atom, if distributed multipoles were to be used instead of a central one 219 Appendix C Interaction functions sn „—˜le gFI is — list of inter—™tion fun™tions T ab in spheri™—l tensor formD su™h th—t the ele™trost—ti™ r—miltoni—n is given ˜yX ˆ ˆ Mla κ1 Mlb κ2 Tlab ,l2 κ2 1κ HEL = @gFIA l1 ,l2 κ1 κ2 „his t—˜le is t—ken from The Theory of Intermolecular Forces ˜y eF tF ƒtone ‘IPU“D p—ges PQQEPRHD —nd is in™luded here solely for illustr—tion purposesD —s the s—me inter—™tion fun™tions —re used with ™riti™—l import—n™e in the progr—m MC ˜y ‚F €F eF fettensF xo ˜l—t—nt ™opying is intended ! s —pologise in —dv—n™e for —ny o'en™e ™—used ˜y the in™lusion of this m—teri—lF „he not—tions used in the t—˜le —re derived from the rel—tive orient—tions of the inter—™tion mole™ules —™™ording to their lo™—l —xesD —s illustr—ted in pigure gFIF „—king ea , ea , ea —s the unit ve™tors de(ning the lo™—l —xes of site — —nd simil—rly x y z eb , eb , eb for site ˜D then cαβ = ea · eb D where α —nd β m—y repl—™e xD y D or z F elsoD x y z α β a t—king eab —s the unit ve™tor in the dire™tion of r(b) − r(a)D then rα = ea · eab —nd α b rβ = −eb · eab F β st should —lso ˜e noted th—t the multipole terms with su˜s™ripts IHD II™D —nd IIsD —re respe™tively equiv—lent to IzD IxD —nd Iy @refer to „—˜le fFIAF 220 Appendix C Interaction functions Figure C.1: Demonstration of local axes systems of interacting molecules for formulating interaction functions Not shown in the gure is the global axes system, which is the axes system of the laboratory Table C.1: List of interaction functions up to l , l l1 κ1 l2 κ2 4πε0 Tlab ,l2 κ2 1κ 00 00 R−1 1α 00 R−2 × a rα 20 00 R−3 × a2 (3rz 21c 00 R−3 × 21s 00 R−3 × 22c 00 R−3 × 22s 00 R−3 × ™ontinuedFFF √ − 1) a a 3rz rx √ a a 3rz ry √ a2 a2 3(rx − ry ) √ a a 3rx ry =2 221 „—˜le gFI !™ontinued l1 κ1 l2 κ2 4πε0 Tlab ,l2 κ2 1κ 1α 1β R−3 × a b (3rα rβ + cαβ ) 20 1β R−4 × a2 b (15rz rβ 21c 1β R−4 × 21s 1β R−4 × 22c 1β R−4 × 22s 1β R−4 × a a a a b 3(ry czβ + cyβ rz + 5rz ry rβ ) √ a2 a2 b a a 3(5(rx − ry )rβ + 2rx cxβ − 2ry cyβ ) √ a a b a a 3(5rx ry rβ + rx cyβ + ry cxβ ) 20 20 R−5 × a2 b (35rz rz 20 21c R−5 × R−5 × 2czx czz ) √ a2 b b b b a b a b 3(35rz rz ry −5rz ry +10rz ry czz +10rz rz czy + R−5 × 2czy czz ) √ a2 b2 b2 a b a b 3((35rz −5)(rx −ry )+20rz rx czx +rz ry czy + R−5 × 2c2 − 2c2 ) zy zx √ a2 b b a b a b 3((35rz − 5)rx ry + 10rz rx czy + rz ry czx + 20 20 20 21s 22c 22s √ √ a b + 6rz czβ − 3rβ ) a a a a b 3(rx czβ + cxβ rz + 5rz rx rβ ) √ a b a b − 5rz − 5rz + 20rz rz czz + 2c2 + 1) zz a b b b b a b a b 3(35rz rz rx −5rz rx +10rz rx czz +10rz rz czx + 2czx czy ) 21c 21c R−5 × a a b b a b a b a b (35rz rx rz rx + 5rx rx czz + 5rx rz czx + 5rz rx cxz + a b 5rz rz cxx + czz cxx + czx cxz ) 21c 21s R−5 × a a b b a b a b a b (35rz rx rz ry + 5rx ry czz + 5rx rz czy + 5rz ry cxz + a b 5rz rz cxy + czz cxy + czy cxz ) 21c 22c R−5 × a a b2 (35rz rx (rx b a b a b − ry ) + 10rx rx czx − 10rx ry czy + a b a b 10rz rx cxx − 10rz ry cxy + 2cxx czx − 2cxy czy ) ™ontinuedFFF 222 Appendix C Interaction functions „—˜le gFI !™ontinued l1 κ1 l2 κ2 4πε0 Tlab ,l2 κ2 1κ 21c 22s R−5 × a a b b a b a b a b (35rz rx rx ry + 5rx rx czy + 5rx ry czx + 5rz rx cxy + a b 5rz ry cxx + czy cxx + czx cxy ) 21s 21s R−5 × a a b b a b a b a b (35rz ry rz ry + 5ry ry czz + 5ry rz czy + 5rz ry cyz + a b 5rz rz cyy + czz cyy + czy cyz ) 21s 22c R−5 × a a b2 (35rz ry (rx b a b a b − ry ) + 10ry rx czx − 10ry ry czy + a b a b 10rz rx cyx − 5rz ry cyy + 2czx cyx − 2czy cyy ) 21s 22s R−5 × a a b b a b a b a b (35rz ry rx ry + 5ry rx czy + 5ry ry czx + 5rz rx cyy + a b 5rz ry cyx + czy cyx + czx cyy ) 22c 22c R−5 × a2 (35(rx b a − ry )(rx 2 a b b − ry ) + 20rx rx cxx − a b a b a b 20rx ry cxy −20ry rx cyx +20ry ry cyy +2c2 −2c2 − xx xy 2c2 + 2c2 ) yy yx 22c 22s R−5 × b b a2 (35rx ry (rx a a b a b − ry ) + 10rx rx cxy + 10rx ry cxx − a b a b 10ry rx cyy − 10ry ry cyx + 2cxx cxy − 2cyx cyy ) 22s 22s R−5 × a a b b a b a b a b (35rx ry rx ry + 5rx rx cyy + 5rx ry cyx + 5ry rx cxy + a b 5ry ry cxx + cxx cyy + cxy cyx ) 223 Appendix D Program and Auxiliary Files et the ˜—™k of this thesis is — gh ™ont—ining the (les th—t were used extensively during the ™ourse of this rese—r™hD —rr—nged in dire™toriesF sn this se™tion short des™riptions of the —forementioned (les —re givenF D.1 MC euthorsX fettensD ‚F €F eFY veD rF eFY —nd €—tuwoD wF ‰F sn this dire™tory —re the sour™e ™odes @in portr—nUU —nd portr—nWHAD exe™ut—E ˜lesD s—mple input —nd summ—ry output (les for the simul—tion progr—m MC version 1.4.01.MF „he output d—t— (le ™ont—ining soluteEsolvent energy during — morphing run @to ™ompute solv—tion free energy using the fennett e™™ept—n™e ‚—tioA is too l—rge to ˜e in™luded in this listingD —nd hen™e is omitted out from the ghF ‚e—d the m—nu—l MC_Manual.docx for — thorough des™ription of (les of this typeF pile n—me hes™ription alanine4.in ƒ—mple input (leF ™ontinuedFFF 224 Appendix D Program and Auxiliary Files „—˜le hFI !™ontinued pile n—me hes™ription alanine4.out ƒ—mple output (le ™ont—ining summ—ry of simE ul—tion runD gener—ted from alanine4.in —nd iC_4EL000.datF constants.f90 ƒour™e (leF wodule ™ont—ins physi™—l ™onst—nts —nd ™onversion f—™torsF electroEn.f90 ƒour™e (leF wodule ™—l™ul—tes ele™trost—ti™ energy ˜eE tween —ny two mole™ules using ™entr—l or distri˜uted multipolesF ewald.f90 ƒour™e (leF wodule sets up kEve™tors —nd ™—l™ul—tes the re—lD re™ipro™—lD selfD intr—mole™ul—rD —nd v—™uum energy terms of the iw—ld9s summ—tion fun™tion for ele™trost—ti™ energyF globals.f90 ƒour™e (leF wodule de™l—res most glo˜—l v—ri—˜les —nd —rr—ysF input.f90 ƒour™e (leD written ˜y ƒtoneD eFtF @PHHSAF €—™k—ge ™omplements io.f90 ˜y f—™ilit—ting re—ding of input (lesF iC_4EL000.dat ƒ—mple —™™omp—nying input (leF gont—in initi—l ™onE (gur—tion d—t— for solvent mole™ulesF io.f90 ƒour™e (leF wodule re—ds input —nd writes form—tted output (lesF Makefile w—ke(leF „o ˜e used with pgf95 portr—n ™ompilerF MC_1404M ixe™ut—˜leF „his (le exe™utes the progr—m MCD version 1.4.01.MF ™ontinuedFFF D.1 225 MC „—˜le hFI !™ontinued pile n—me hes™ription mc.f90 „opElevel sour™e (leF gont—ins the m—in ˜ulk of the progr—mF MC_Manual.docx wi™rosoft ‡ord PHHU do™ument (leF gont—ins the m—nu—l of the progr—mF multi.f90 ƒour™e (leF wodule de™l—res roots of integerD —rr—ys for multipole momentsD h—ndles their ™onversion ˜eE tween g—rtesi—n —nd spheri™—l ™oordin—te systemsD —nd ™he™ks for their tr—™elessnessF numRec.f portr—nUU sour™e (leF €—™k—ge ™ont—ins numeri™—l re™ipesD su™h —s the erf —nd erf™ fun™tionsF parameters.f90 ƒour™e (leF wodule de™l—res sever—l ™ontrol v—ri—˜lesD their m—ximum sizesD —nd de(nes —tom n—mesF random.f90 ƒour™e (leD written ˜y w—™l—renD xFwF@IWWPAF wodE ule ™ont—ins fun™tion dprand() th—t gener—tes r—nE dom num˜er ˜etween H —nd IF ƒeed is stored in random.dataF timing.f90 ƒour™e (leD written ˜y ƒtoneD eFtF @PHHSAF wodule tr—™ks ™pu time spent during — jo˜ runF tip4p.f90 ƒour™e (leF wodule de(nes p—r—meters for „s€Q€ —nd „s€R€ w—ter models —nd ™ont—ins su˜routines —sso™iE —ted with solvent energyF ™ontinuedFFF 226 Appendix D Program and Auxiliary Files „—˜le hFI !™ontinued pile n—me hes™ription vector.f90 ƒour™e (leF wodule ™ont—ins su˜routines for ve™tor norm—lis—tionD ™ross produ™tD —nd gener—tion of rot—E tion m—trixF Table D.1: Files in MC directory, listed alphabetically Unless specied otherwise, all source les are compatible with the Fortran90 language (.f90 extension) D.2 Bennett_1000 euthorsX fettensD ‚F €F eFD modi(ed ˜y €—tuwoD wF ‰F sn this dire™tory —re the sour™e ™odes @in portr—nWHAD exe™ut—˜lesD —nd s—mE ple output (les for the progr—m Bennett_1000D designed to ™—l™ul—te the estim—te ™h—nge in free energy using one of the output (les gener—ted ˜y MC during — morE phing run —s inputF es mentioned ˜eforeD this (le is not —v—il—˜le in the gh —s it is too l—rgeF pile n—me hes™ription Bennett_1000 ixe™ut—˜leF „his (le exe™utes the progr—m Bennett_1000D whi™h re—ds soluteEsolvent inter—™tion energy d—t— every IDHHH timesteps to estim—te the solE v—tion free energyF ™ontinuedFFF D.3 227 shell „—˜le hFP !™ontinued pile n—me hes™ription bennett_1000.f90 „opElevel sour™e (leF gont—ins the m—in ˜ulk of the progr—mF constants.f90 ƒee „—˜le hFIF EL_ala4.out ƒ—mple output (le for morphing of ele™trost—ti™ potenE ti—l with λEL = 0.25 @systems vi to xAF globals.f90 (Obsolete) input.f90 ƒee „—˜le hFIF io.f90 ƒour™e (leF wodule re—ds input —nd writes form—tted ƒee „—˜le hFIF output (lesF LJ_ala4.out ƒ—mple output (le for morphing of nonEele™trost—ti™ potenti—l with λLJ = 0.25 @systems i to vAF Makefile w—ke(leF „o ˜e used with pgf95 portr—n ™ompilerF parameters.f90 ƒee „—˜le hFIF timing.f90 ƒee „—˜le hFIF Table D.2: Files in Bennett_1000 directory, listed alphabetically D.3 shell euthorX €—tuwoD wF ‰F sn this dire™tory —re the sour™e ™odes @in portr—nWHAD exe™ut—˜lesD s—mple input —nd output (les for the progr—m shellD designed to —n—lyse the r—di—l distri˜ution of solvent mole™ules using the ™on(gur—tion dump (les gener—ted ˜y MC —s inputF 228 Appendix D Program and Auxiliary Files pile n—me hes™ription dmpxxxx.gjf ƒ—mple input (lesF gont—ins ™oordin—tes of —ll solvent mole™ules in the simul—tion ˜oxF Shell ixe™ut—˜leF „his (le exe™utes the progr—m ShellD whi™h ™—l™ul—tes the density of spe™i(™ —toms —round — requested ™oordin—te —t regul—r dist—n™esF shell.f90 ƒour™e (leF shell.in ƒ—mple input ™ontrol (leF yptions for the progr—m —re spe™i(ed hereF Table D.3: Files in Shell directory, listed alphabetically ... MONTE CARLO SIMULATION OF MOLECULES AND IONS IN LIQUID WATER MICHAEL YUDISTIRA PATUWO (B.Sc.(Hons), NUS) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN SCIENCE DEPARTMENT OF. .. Regardless, magnetic interactions due to both electronic and nuclear spin are generally too small to be considered in the context of intermolecular forces, and they are often safely and reasonably... the sum of the p—irwise inter—™tionsF „his isD of ™ourseD — m—jor ™on™ern th—t often pl—gues simul—tions of very l—rge —ssem˜liesF gorre™tions of su™h s™—le would ™onsume — l—rge —mount of ™omput—tion—l