Structure and Dynamics of the TIP3P, SPC, and SPC/E Water Models at 298 K

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1 9954 J. Phys. Chem. A 2001, 105, Structure nd Dynmics of the TIP3P, SPC, nd SPC/E Wter Models t 298 K Pekk Mrk nd Lennrt Nilsson* Krolinsk Institutet, Deprtment of Bioscience t NOVUM, S Huddinge, Sweden ReceiVed: August 22, 2000; In Finl Form: Mrch 21, 2001 Moleculr dynmics simultions of five wter models, the TIP3P (originl nd modified), SPC (originl nd refined), nd SPC/E (originl), were performed using the CHARMM moleculr mechnics progrm. All simultions were crried out in the microcnonicl NVE ensemble, using 901 wter molecules in cubic simultion cell furnished with periodic boundry conditions t 298 K. The SHAKE lgorithm ws used to keep wter molecules rigid. Nnosecond trjectories were clculted with ll wter models for high sttisticl ccurcy. The chrcteristic self-diffusion coefficients D nd rdil distribution functions, g OO, g OH, nd g HH for ll five wter models were determined nd compred to experimentl dt. The effects of velocity rescling on the self-diffusion coefficient D were exmined. All these empiricl wter models used in this study re similr by hving three interction sites, but the smll differences in their pir potentils composed of Lennrd- Jones (LJ) nd Coulombic terms give significnt differences in the clculted self-diffusion coefficients, nd in the height of the second pek of the rdil distribution function g OO. 1. Introduction Liquid wter, the most importnt solvent in nture, hs mny specil nd unusul properties. Mny of these specil properties re due to the bility of wter molecules to form hydrogen bonds with other wter molecules in three-dimensionl networks. The mcroscopic properties of liquid wter hve been thoroughly studied nd re now well-known, but the microscopic forces tht define wter structure re not completely understood. 1 Microscopic properties cn be nlyzed by different experimentl techniques, such s X-ry scttering 2,3 nd neutron diffrction, 2,4 which mesure the structure of liquid wter nd queous solutions. Neutron diffrction with isotopic substitution (NDIS) hs been used to mesure intermoleculr prtil pir correltion functions for liquid wter. 5-7 The self-diffusion coefficient of pure wter hs been mesured to be 2.3 ( 10-9 m 2 s -1 ) t 298 K using the diphrgm-cell technique 8 or the pulsed-grdient spin echo (PGSE) NMR method. 9 The three rdil pir distribution functions for H 2 O, g OO, g OH, nd g HH, hve generlly been used together with the self-diffusion coefficient to chrcterize the structure nd dynmics of wter t different tempertures. 6,7,10 Simultneously severl theoreticl methods hve been developed to describe the properties of wter nd queous solutions. Experimentl nd theoreticl methods re continuously being developed to give more detiled views of the microscopic properties of liquid wter, thus incresing our knowledge. In this study we use one of the theoreticl methods, moleculr dynmics simultions, to clculte the bulk properties for models of liquid wter. Mny different potentil functions for the wter monomer nd liquid wter hve been developed over the lst 30 yers The wter monomer cn be treted s rigid or s flexible, llowing ll degrees of freedom for the OH bonds nd HOH bond ngle. In rigid models the SHAKE lgorithm 24 is generlly used to constrin the bond lengths, including fictitious H-H bond, thus mking the model rigid. All wter models used here, * To whom correspondence should be ddressed. E-mil: Lennrt.Nilsson@biosci.ki.se. Fx: the TIP3P (trnsferble intermoleculr potentil 3P) (originl 11 nd modified 12 ), SPC (simple point chrge) (originl 13 nd refined 14 ), nd SPC/E (extended simple point chrge) (originl 15 ) cn be described s effective rigid pir potentils composed of Lennrd-Jones (LJ) nd Coulombic terms. All of these wter models hve three interction sites nd re similr in nture, but the Lennrd-Jones (LJ) nd Coulombic terms differ (see Tble 1) nd give significnt differences in clculted bulk properties for liquid wter. In moleculr dynmics simultions Newton s equtions of motion re numericlly integrted for ll toms, which requires the evlution of the tomic forces t ech time step. The force evlution is dominted computtionlly by the lrge number of nonbonded interctions, nd in prticulr by the long-rnge electrosttic interctions. Even with fst computers simplifying pproximtions re needed to reduce the computtionl time to n cceptble level. The necessity to use system of finite size mens tht boundry conditions must be chosen, which my lso introduce rtifcts. The fst multipole expnsion method 25 llows reltively efficient hndling of long-rnge interctions, nd for periodic systems the Ewld summtion technique s commonly implemented my be used to compute the Coulomb interctions exctly; in nonperiodic, sphericl, systems, Coulombic effects of the neglected surroundings my be treted by rection field. 26 Still the most commonly used method to chieve resonbly cost-effective computtion is to use sphericl cutoff, which reduces the number of pir wise interctions by neglecting ll interctions between prticles seprted by distnce lrger thn the cutoff. 26,28 In this pper, we compre clculted bulk properties for the TIP3P (originl 11 nd modified 12 ), SPC (originl 13 nd refined 14 ), nd SPC/E 15 wter models t 298 K. All simultions were performed under exctly the sme conditions nd using the sme system size with 901 wter molecules. The system size with 901 wter molecules ws defined lrge enough to be used lso in future simultions of smll biomolecules, such s mino cids or nucleic cid frgments. The nonbonded interctions were truncted using force shifting, 28 where the clculted forces nd /jp003020w CCC: $ Americn Chemicl Society Published on Web 10/06/2001

2 TIP3P, SPC, nd SPC/E Wter Models J. Phys. Chem. A, Vol. 105, No. 43, TABLE 1: Nonbonded Prmeters, Geometry, nd Electrosttic Properties of the Three-Point Wter Models prmeters nd units TIP3P originl TIP3P modified SPC originl SPC refined SPC/E originl dipole (debye) r OO 0 (Å) ɛ OO (kcl mol -1 ) r HH 0 (Å) ɛ HH (kcl mol -1 ) r OH 0 (Å) ɛ OH (kcl mol -1 ) q O (e units) q H (e units) b OH 0 (Å) θ HOH 0 (deg) K b (kcl mol -1 Å -2 ) K θ (kcl mol -1 rd -2 ) 55.0 energies re smoothly shifted to zero t the cutoff distnce. This scheme hs been found 29 to give similr structurl nd dynmic properties for bulk wter s when Ewld summtion is used. The nonbonded list size nd updting time re importnt when simultions t constnt energy (NVE) re performed. If the size or updting frequency of the nonbonded list is underestimted, energy conservtion is violted nd the system temperture increses, which my necessitte some kind of temperture control, commonly implemented vi velocity rescling. It should be noted tht the discontinuities introduced in the velocities by this rescling my ffect dynmic properties such s the self-diffusion coefficient. Simultions with nd without velocity rescling were compred using ll five wter models. Velocity rescling effects in moleculr dynmics simultions in generl hve been studied nd reported in the literture. 30 Our interest in this work concentrted on the bulk wter structure nd dynmics, s chrcterized by the rdil distribution functions, g OO, g OH, nd g HH nd self-diffusion coefficient D. In generl, the three-site potentils provide too little structure in g OO when compred with more complicted models, nd specificlly the TIP3P wter model is lcking the second pek. 11,21 The rdil distribution functions, g OO, g OH, nd g HH for ll wter models used in this study, except the refined SPC, re reported in the literture. 11,13,15,17,21 Self-diffusion coefficients hve been reported for the originl TIP3P wter model between 5.2 nd 7.0 ( 10-9 m 2 s -1 ), 31 for the modified TIP3P wter model between 2.3 nd 5.2 ( 10-9 m 2 s -1 ), for the originl SPC wter model between 3.6 nd 5.2 ( 10-9 m 2 s -1 ), 31 nd for the SPC/E wter model between 2.2 nd 4.4 ( 10-9 m 2 s -1 ), 31 but the self-diffusion coefficient for the refined SPC wter model ws never reported in the literture. The self-diffusion coefficient D should be esy to clculte from moleculr dynmics dt, 37 but the conflicting results for the sme wter model reported in the literture show tht is not the cse, nd set of long simultions performed nd nlyzed under identicl conditions is necessry to ccomplish meningful comprison. In this work, our first gol ws to clculte the self-diffusion coefficient nd rdil distribution functions for these wter models under identicl conditions. We lso estimte the sttisticl ccurcy of the commonly used method to clculte the selfdiffusion coefficient D, the Einstein reltion. 37 Long simultions ( ns) with ll five wter models were used to clculte the men vlue, nd the vrince of the men, for the self-diffusion coefficient. Finlly we present the effects of velocity rescling when used s temperture control method. This work, together with recently reported work by vn der Spoel et l. 31 nd experimentl dt for liquid wter, 5,8 is n importnt test for vlidting ll these five commonly used wter models. TABLE 2: Systems Simulted simultion wter model 2. Simultion Procedures simultion period (ns) temperture e (K) temperture control f 1 TIP3P originl 0.6 c / 0.5 d (1.7) yes 42/500ps g 2 b TIP3P originl 0.6 / (0.9) no 3 TIP3P modified 1.1 / (1.8) yes 95/1000ps 4 b TIP3P modified 1.7 / (1.0) no 5 SPC originl 0.6 / (1.7) yes 33/500ps 6 b SPC originl 1.0 / (1.1) no 7 SPC refined 1.1 / (1.8) yes 66/1000ps 8 b SPC refined 1.2 / (1.2) no 9 SPC/E 4.1 / (1.9) yes 40/1000ps 10 b SPC/E 4.1 / (1.4) no Nonbonded list 1 (see Methods). b Nonbonded list 2 (see Methods). c Totl time. d Time used for nlysis. e Averge clculted over the nlyzed prt of the simultion, stndrd devition (in prentheses). f Velocity rescling (see Methods). g Number of velocity rescling events over the nlyzed prt of the simultion. All different wter models, the TIP3P (originl, modified), SPC (originl, refined), nd SPC/E (originl) were compred using identicl microcnonicl (NVE) or NVT simultions. For convenience the interction prmeters nd geometries of the models re given in Tble 1. All simultions were performed t 298 K using solvent density of g/cm 3 with periodic boundry conditions in cubic box with side length 30.0 Å. The box contined 901 H 2 O molecules nd ll simultions were strted with the sme initil coordintes nd the sme initil velocity ssignments (i.e., the sme seed ws used for the rndom number genertor) for the wter molecules. In the NVT simultions the temperture ws llowed to vry (5 K round 298 K. If the verge temperture since the lst velocity scling, with the verge being tken over t lest 2 ps, drifted outside the 10 K window tom velocities were scled to give temperture of 298 K gin. The SHAKE 24 lgorithm ws used to keep wter molecules rigid. Newton s equtions of motion were integrted with the Verlet lepfrog lgorithm with time step of ps. 26,37 The dielectric constnt ws 1.0 nd the nonbonded interctions energies nd forces were smoothly shifted to zero t cutoff of 12.0 Å. The shifting function ws pplied on n tom-by-tom bsis using the force shift method. 28 Two different nonbonded lists were used: (1) 13.0 Å cutoff for the list nd updted every 20 steps or (2) 14.0 Å cutoff for the list nd updted when necessry using heuristic test. A totl of 10 simultions were performed (Tble 2). For the nlysis, coordinte sets for every 0.4 ps were used. All MD simultions nd nlysis were performed with the CHARMM progrm. 38 Self-diffusion coefficients were clculted from the men squre displcement (MSD) of ll oxygen toms using the

3 9956 J. Phys. Chem. A, Vol. 105, No. 43, 2001 Mrk nd Nilsson TABLE 3: Self-Diffusion Coefficients (10-9 m 2 s -1 ) for Three Wter Models Using Different Prts of the Slope of MSD(t) vst prt of the slope (ps) TIP3P modified Einstein reltion 37 TIP3P b modified SPC/E originl SPC/E b originl SPC refined SPC b refined Nonbonded list 1 (see Methods). b Nonbonded list 2 (see Methods). lim tf r(t + t) - r(t ) 2 ) 6Dt where r(t) is the position of the oxygen tom of the wter molecule t time t, D is the self-diffusion coefficient, nd the brckets denote verging over ll wter molecules nd time origins t. The self-diffusion coefficient ws estimted from the slope of the liner prt t long times of the men squre displcements vs time plot. The initil prt of the line is influenced by inertil effects nd should not be included in this clcultion. To mke sure tht the self-diffusion coefficient clcultions were not ffected by the inertil effects, different prts of the slope of MSD vs time were tested (Tble 3). When choosing rnge the need to void the inertil regime hs to be contrsted with the sttistics of the dt; for long time-seprtions there re only very few points vilble in the trjectory nd the sttistics for these points therefore re not s good. For the simultions without velocity scling the results re very similr for ll the tested intervls, including the shortest t 2-10 ps. Since D is temperture dependent, nd the simultions do not run t exctly the sme temperture, we lso djusted the observed diffusion coefficients to the stndrd temperture 298 K by using experimentl results t different tempertures. 8 The self-diffusion coefficients were thus djusted ccording to D(298) ) D(T) m 2 s -1 K -1 (298 - T) where T is the ctul temperture during the simultion. 3. Results The temperture in moleculr dynmics simultion is computed from the kinetic energy of the moving toms, which my exhibit both fluctutions nd drift. For precise determintion of temperture-dependent properties, such s the selfdiffusion coefficient, the temperture must be stble during the simultion, nd number of methods to control the temperture hve been described in the literture. 26 A temperture drift my be cused by pproximtions or deficiencies in the simultion protocol. We will in this section first exmine the temperture stbility of our wter simultions, nd how the stbility is influenced by different updting schemes for the nonbond list. In the following sections the self-diffusion coefficient D nd rdil distribution functions (g(r)) re clculted. Here we lso monitor how D nd g(r) re influenced by temperture control in the form of velocity scling Temperture, Stbility, nd Equilibrtion. The temperture nd potentil energy s function of time re shown in Figure 1 for ll five wter models, nd with two different nonbond list updting schemes. In the simultions using updted scheme 1, where the nonbonded list is slightly too smll so tht toms not on the list my fll within the cutoff distnce without Figure 1. The temperture nd potentil energy s function of time for ll five wter models using two different nonbonded updting schemes 1 nd 2 (see Methods). () TIP3P (originl), (b) TIP3P (modified), (c) SPC (originl), (d) SPC (refined), (e) SPC/E (originl). The potentil energy in the lower pnel is plotted in thin line for scheme 1 nd thick line for scheme 2. ctully intercting for some time until the next list updte, energy conservtion ws violted, nd the system temperture ws incresing. The temperture ws controlled using velocity rescling in ll simultions performed using scheme 1. With scheme 2, when bigger nonbonded list size ws used together with updting when necessry, energy conservtion ws not violted nd the system temperture stbilized close to the trget temperture (298 K). In generl, no velocity rescling ws needed to control the temperture with scheme 2, except when the SPC (originl nd refined) wter models were used. In the SPC systems, the temperture ws decresing slightly in the beginning of the simultion nd infrequent velocity rescling ws needed to scle-up the temperture to the trget vlue, before the trjectories without velocity rescling were produced. For the SPC (refined) wter model the temperture ws llowed to vry (10 K round 298 K when the trjectory without velocity rescling ws produced. The verge pressure nd stndrd devition (in prentheses) for the originl TIP3P wter model ws (109.6) br, nd (98.5) br with schemes 1 nd 2, respectively. For the originl SPC the corresponding vlues were (106.9) br with scheme 1 nd (123.1) br with scheme Self-Diffusion Coefficient D. Self-diffusion coefficients evluted using different rnges of the slope of MSD vs time clculted from verging over the 901 wter molecules nd the 1.0 ns trjectories (Figure 2) re shown in Tble 3. It cn be seen from Figure 2 tht there is more noise t long times,

4 TIP3P, SPC, nd SPC/E Wter Models J. Phys. Chem. A, Vol. 105, No. 43, TABLE 4: Self-diffusion Coefficients ( 10-9 m 2 s -1 ) for the Modified TIP3P Wter Model Using Three Different Lengths of the Slope of MSD(t) vs t prt of the trjectory (ps) slope (ps) slope (ps) slope (ps) slope (ps) temperture(k) (0.8) (0.9) (1.1) (1.0) (1.0) (0.9) (1.1) (0.9) (0.9) (1.0) verge std dev 5.83 (0.07) 5.85 (0.08) 5.93 (0.2) 5.91 (0.11) (0.96) The nlyzed prt of the trjectory, 200 ps. Figure 2. MSD vs time clculted from verging over the 901 wter molecules nd the 1.0 ns trjectories. TIP3P (modified) line, SPC (refined) dot, nd SPC/E (originl) dsh. () Nonbonded scheme 2 nd (b) nonbonded scheme 1. Figure 3. MSD vs time for 10 seprte 100 ps blocks of the stble simultion of TIP3P (modified). nd we cn lso see from Tble 3 tht, in the simultions with the slight temperture drift nd velocity rescling (Figure 2b), there is pronounced devition from linerity. The vrition in D obtined from these different rnges of the slope is 2% for the stble simultions (Figure 2) nd 7% for the simultions with velocity rescling (Figure 2b). Figure 3 shows MSD vs time for 10 seprte 100 ps blocks of the stble simultion, without velocity rescling, of TIP3P (modified). These plots become noisy s time increses, becuse fewer dt points re vilble of the points used to clculte MSD t long times. For given system size the ccurcy of the self-diffusion coefficient clcultion depends on which prt of the slope is used nd how long the trjectory is. When the self-diffusion coefficient is clculted with stndrd devition of the order 0.1( 10-9 m 2 s -1 ), s in this study, the upper limit of the rnge of the slope of MSD vs time hs to be restricted to bout 20% of the nlyzed trjectory length. This cn be seen from Tble 4, where different rnges of the slope of MSD vs time hve been used to clculte the self-diffusion coefficient. Similr men vlues nd stndrd devitions were obtined when the upper limit of the rnge of the slope of MSD vs time ws limited to 20% of the nlyzed trjectory length. The self-diffusion coefficient 5.85 ( 10-9 m 2 s -1 ) with stndrd devition of 0.08 ( 10-9 m 2 s -1 ) ws obtined from 100 ps trjectory pieces with the upper limit of 20 ps. When the upper limit of the used rnge of the slope ws incresed to 50 ps, the nlyzed trjectory length hd to be incresed to 200 ps for similr ccurcy. The self-diffusion coefficients determined in this mnner were similr, with similr stndrd devitions, nd there ws no drift with time (Tble 4). A similr self-diffusion coefficient ws lso obtined from 1.0 ns (Tble 3) trjectory when the upper limit of the rnge of the slope of MSD vs time ws limited to 20% of the nlyzed trjectory length. It is lso evident from Tble 4 tht 100 ps is long trjectory when compred to ll relevnt relxtion processes in the system. These evlutions of D cn be treted s independent nd we thus expect the stndrd error of D computed from the full 1 ns trjectory to decrese by 1/ , to bout 0.5%. The simultions with the SPC/E wter model were extended to 4.0 ns, with very similr results when compred with the shorter 1.0 ns simultions. The 300 ps dely needed for convergence of the self-diffusion coefficient reported by vn der Spoel et l. 31 is likely due to their method of estimting the convergence of D, which does not use the slope of the plot of MSD(t)vst, but insted uses the rtio MSD- (t)/6t. This corresponds to computing the slope strting from t ) 0, which mens tht the slope clculted in this wy is influenced by the initil, inertil phse of the MSD, n influence which pprently persists for long times, wheres if the shorttime prt of MSD(t) is neglected, the self-diffusion coefficient cn be relibly computed in 100 ps or less, depending on the system size. The resulting self-diffusion coefficients for ll five wter models t 25 C re given in Tble 5. All five wter models give rther high vlues for D when compred with the experimentl vlue, 8 nd the TIP3P, SPC, nd SPC/E, respectively, correspond to rel wter round 74, 55, nd 33 C, rther thn to the simultion temperture of 25 C. The modified versions of TIP3P nd SPC re both slightly more fluid thn the originl versions (Tble 5), nd we lso note tht the difference, m 2 s -1, is only observble in simultion

5 9958 J. Phys. Chem. A, Vol. 105, No. 43, 2001 Mrk nd Nilsson TABLE 5: Self-diffusion Coefficients ( 10-9 m 2 s -1 ) for All Wter Models Using Two Different Lengths of the Slope of MSD(t) vst wter model slope ( ps) slope ( ps) temperture c (K) D (25 C) f TIP3P originl 5.88 d (0.10) e 5.87 d (0.09) e d (1.7) e 5.67 TIP3P originl b 5.59 (0.06) 5.59 (0.08) (0.9) 5.65 TIP3P modified 5.92 (0.09) 5.92 (0.11) (1.8) 5.73 TIP3P modified b 5.83 (0.07) 5.85 (0.08) (1.0) 5.78 SPC originl 4.39 (0.05) 4.40 (0.06) (1.7) 4.22 SPC originl b 4.22 (0.06) 4.24 (0.08) (1.1) 4.20 SPC refined 4.49 (0.08) 4.48 (0.08) (1.8) 4.30 SPC refined b 4.26 (0.07) 4.24 (0.10) (1.2) 4.26 SPC/E originl 2.90 (0.06) 2.89 (0.08) (1.9) 2.75 SPC/E originl b 2.78 (0.04) 2.77 (0.06) (1.4) 2.76 exptl 8, Nonbonded list 1 (see Methods). b Nonbonded list 2 (see Methods). c Temperture of the MD simultion. d Men vlues. e Stndrd devitions. f Self-diffusion coefficients djusted to 25 C, using the slope ps. with 900 wter molecules which is run for 0.5 ns (or longer if fewer wter molecules re used). The self-diffusion coefficients clculted in this study re in good greement with the vlues reported by vn der Spoel et l. 31 (see Tble 6) for the originl TIP3P, SPC, nd SPC/E wter models, but the self-diffusion coefficient for the modified TIP3P wter model is higher thn the vlues reported in the literture Rdil Distribution Functions, g OO, g OH, nd g HH. The rdil distribution functions, g OO, g OH, nd g HH re commonly used when the structure of the liquid wter is studied. These intermoleculr prtil pir correltion functions for liquid wter t 25 C were determined from neutron diffrction dt by Soper et l. 5,7 The old 5 nd new 7 results for g OO, g OH, nd g HH re in good greement, except tht the first O-H pek t 1.8 Å is incresed by bout 14% compred to tht of previous nlysis. The differences probbly represent the currently vilble ccurcy in determining the site-site pir correltion functions for wter. The rdil distribution functions, g OO, g OH, nd g HH re esy to clculte from moleculr dynmics dt nd re generlly used when different wter models re compred with experimentl dt. The rdil distribution functions computed from our simultions for the TIP3P (modified), SPC (refined), nd SPC/E wter models re compred with experimentl dt 5 in Figure 4. Heights nd positions of the peks nd minim re given for g OO in Tble 7 nd for g OH in Tble 8. Our clculted rdil distribution functions re in good greement with the previously reported results in the literture. SPC/E gives the closest greement with experiment for g OO, but the first pek position occurs t too short distnce when compred with experiment. SPC (refined) hs similr pek positions, but the overll structure Figure 4. Rdil distribution functions: () SPC/E (originl), (b) SPC (refined), (c) TIP3P (modified) line, nd the neutron diffrction dt 5 dot. RDF curves re shifted by 2 units for clrity. is flttened when compred with SPC/E. The modified TIP3P hs the first pek position closest to the experimentl position, TABLE 6: Comprison of Different Wter Properties from Two Different Moleculr Dynmics Simultion Studies model N c r c (Å) d E pot (kj/mol) e F (g cm -3 ) f T (K) g D ( 10-9 m 2 s -1 ) h SPC/E originl (0.18) (4.4) 2.7(0.12) SPC/E b originl (0.03) (1.4) 2.8(0.06) SPC originl (0.16) (4.4) 4.2(0.08) SPC b originl (0.03) (1.1) 4.2(0.08) TIP3P originl (0.16) (4.4) 5.4(0.14) TIP3P b originl (0.02) (0.9) 5.6(0.08) TIP3P b modified (0.02) (1.0) 5.9(0.08) SPC b refined (0.03) (1.2) 4.2(0.10) exptl ,9 vn der Spoel et l. 31 b The present study. c Number of H 2O. d Cutoff distnce. e Potentil energy. Averge clculted over the nlyzed prt of the simultion, stndrd devition (in prentheses). f Density. g Temperture. Averge clculted over the nlyzed prt of the simultion, stndrd devition (in prentheses). h Self-diffusion coefficient. Averge clculted over the nlyzed prt of the simultion, stndrd devition (in prentheses).

6 TIP3P, SPC, nd SPC/E Wter Models J. Phys. Chem. A, Vol. 105, No. 43, TABLE 7: Oxygen-Oxygen Pir Distribution Functions for All Wter Models t 25 C Using the Similr MD Simultions first mximum position first mximum second mximum position second minimum third mximum position wter model (Å) g OO position (Å) (Å) g OO position (Å) (Å) g OO TIP3P originl (3.70) (4.50) (0.99) (5.80) TIP3P modified (3.80) (5.40) (1.00) (5.94) SPC originl SPC refined SPC/E originl exptl All numbers in prentheses re pproximte vlues. TABLE 8: Oxygen-Hydrogen Pir Distribution Functions for All Wter Models t 25 C Using the Similr MD Simultions first mximum position firs minimum position second mximum position wter model (Å) g OH (Å) g OH (Å) g OH TIP3P originl TIP3P modified SPC originl SPC refined SPC/E originl exptl but the height of the pek is too low nd the structure beyond the first pek is missing. Both SPC/E nd SPC (refined) hve very similr pek positions lso for g OH. The first nd the second pek positions occur t too short distnces when compred with experiment. SPC/E hs too high first pek, but for SPC (refined) the pek height is similr to experiment. Both SPC/E nd SPC (refined) hve too low second peks. TIP3P (modified) hs the right first pek position, but the height of the pek is too low. The second pek is shifted to shorter distnce nd the height of the pek is too low. The SPC (refined) model gives good greement with experiment for g HH. The SPC/E hs the significntly similr pek positions, but the first pek is too high when compred with SPC (refined). The modified TIP3P hs flttened structure; both peks re shifted inwrd nd the heights of the peks re too low. The oxygen-oxygen pir correltion functions re very similr when SPC (originl) nd SPC (refined) re compred, nd TIP3P (modified) is lso quite similr to TIP3P (originl). The modifiction of the TIP3P wter model chnges slightly the structure of the model liquid. TIP3P (originl) hs the first pek t shorter distnce thn TIP3P (modified) nd the height of the pek is lso lower. The well-documented problem for the TIP3P model, to hve too little structure beyond the first pek, is similr in both models. The refined SPC wter model gives slightly more structure when compred with the SPC (originl), nd the first pek is shifted to the sme position s the SPC/E hs. The position of the first pek for SPC (originl) is closer to experiment, but the height of the pek is lower when compred with the SPC (refined). By using long trjectories without velocity rescling (continuous dynmics), it ws possible to clculte the rdil distribution functions, g OO, g OH, nd g HH, with high sttisticl ccurcy nd the slightly different structures for the model liquids could be compred. 4. Summry nd Discussion We hve studied structurl nd dynmic properties of threesite wter models commonly used in biomoleculr simultions: TIP3P, SPC, SPC/E, nd modified versions of TIP3P nd SPC. These models were ll prmetrized using smll systems with certin schemes to hndle long-rnge electrosttic interctions. In ctul biomoleculr simultion pplictions, nd lso in studies of these models themselves, other schemes re often employed, which my ffect the results directly through the chnges introduced in the interction potentil; the effects my lso be more indirect through effects on the temperture, nd temperture stbility, of the system. All simultions in this study were performed with 12.0 Å cutoff nd the self-diffusion coefficient my be slightly different if the long-rnge interctions re clculted using other methods. With nnosecond simultions of round 1000 wter molecules the self-diffusion coefficient cn be determined with 0.5% error, if the temperture is stble. A drift in the temperture ws obtined when the size nd updting frequency of the nonbonded list ws underestimted. We hve lso shown tht temperture control by wek coupling to het bth in the form of velocity rescling cuses devition from linerity when the slope of MSD vs time ws clculted. In the prmetriztion of TIP3P (originl), Monte Crlo simultions were performed on 125 wter molecules using sphericl cutoff t 7.5 Å. Both SPC nd SPC/E were prmetrized nd tested using 216 wter molecules with moleculr dynmics simultions where the nonbonded interctions were truncted with sphericl cutoff t 9.0 Å pplied on moleculeby-molecule bsis. The refinement of the SPC wter model ws performed by wek coupling to system pressure nd potentil energy per mol (the het of vporiztion) 14 using severl different system sizes nd cutoff distnces. The bulk wter structure nd dynmics, s chrcterized by the rdil distribution functions, g OO, g OH, nd g HH, nd the self-diffusion coefficient D for the refined SPC were not included in tht study. In this study we hve shown tht different wter models hve significntly different properties when simulted under exctly the sme conditions. Our results re in good greement with recently reported dt by vn der Spoel et l. 31 (Tble 6). The bulk properties of liquid wter in moleculr dynmics simultions re ffected, for exmple, by the system size, the method used for truncting long-rnge interctions nd the method used for temperture control. When our results re compred with the results of vn der Spoel et l. 31 (Tble 6) the differences in potentil energy nd in the self-diffusion coefficients re the effects of different simultion methods used. The clculted self-diffusion coefficients re consistent with the rdil distribution functions g OO, g OH, nd g HH. The SPC/E wter model gives the best bulk wter dynmics nd structure, the SPC (originl) wter model gives less structure nd fster diffusion, wheres the TIP3P (modified) wter model gives even less structure nd fster dynmics when compred with the experimentl vlues for liquid wter. The second pek is the g OO, indicting the second hydrtion shell of wter, is relted to the self-diffusion coefficient, such tht the wter model with less defined second hydrtion shell hs lrger self-diffusion coefficient.

7 9960 J. Phys. Chem. A, Vol. 105, No. 43, 2001 Mrk nd Nilsson The modifiction of the TIP3P wter chnged the bulk wter dynmics nd structure slightly when compred with the originl TIP3P wter model. The refined SPC wter model is lso quite similr to the originl SPC model, but since the chrges re reduced the dipole moment is lso reduced, from to D. It should be noted tht the TIP3P (originl nd modified) model hs lmost the sme dipole moment s the SPC/E model, nd D, respectively. The lrger dipole moment of the SPC/E wter model, when compred with the originl SPC wter model with similr Lennrd-Jones (LJ) prmeters nd model structure, is the due to incresed point chrges. The point chrges were chnged when the originl SPC wter model ws reprmetrized with polriztion correction. 15 The bulk properties for the SPC/E model re closer to the experimentl vlues of liquid wter thn the originl SPC wter model. The lrger point chrges lso give lower potentil energy for the SPC/E model (Figure 1 nd Tble 6) when compred with the originl SPC wter model. When ll five models re compred with respect to selfdiffusion coefficients or rdil distribution functions it is cler tht they form three different groups: TIP3P (originl) nd TIP3P (modified), SPC (originl) nd SPC (refined), SPC/E. SPC remins SPC, nd TIP3P remins TIP3P, even fter the modifictions. Acknowledgment. This work ws supported by the Swedish Nturl Science Reserch Council nd by the Mgnus Bergvll Foundtion. References nd Notes (1) Neilson, G. W., Enderby, J. E., Eds. Wter nd Aqueous Solutions; Adm Hilger: Bristol, (2) Corongiu, G.; Clementi, E. J. Chem. Phys. 1992, 97, (3) Nrten, A. H.; Levy, H. A. J. Chem. Phys. 1971, 55, (4) Neilson, G. W.; Enderby, J. E. J. Phys. Chem. 1996, 100, (5) Soper, A. K.; Phillips, M. G. Chem. Phys. 1986, 107, 47. (6) Postorino, P.; Tromp, R. H.; Ricci, M.-A.; Soper, A. K.; Neilson, G. W. Nture 1993, 366, 668. (7) Soper, A. K.; Bruni, F.; Ricci, M. A. J. Chem. Phys. 1997, 106, 247. (8) Mills, R. J. Phys. Chem. 1973, 77, 685. (9) Price, W. S.; Ide, H.; Art, Y. J. Phys. Chem. A 1999, 103, 448. (10) Soper, A. K. J. Phys.: Condens. Mtter 1996, 8, (11) Jorgensen, W. L.; Chndrsekhr, J.; Mdur, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. (12) Neri, E.; Fischer, S.; Krplus, M. J. Chem. Phys. 1996, 105, (13) Berendsen, H. J. C.; Postm, J. P. M.; vn Gunsteren, W. F.; Hermns, J. In Intermoleculr Forces; Pullmn, B., Ed.; Reidel: Dordrecht, 1981, p 331. (14) Berweger, C. D.; vn Gunsteren, W. F.; Müller-Plthe, F. Chem. Phys. Lett. 1995, 232, 429. (15) Berendsen, H. J. C.; Griger, J. R.; Strtsm, T. P. J. Phys. Chem. 1987, 91, (16) Mtsuok, O.; Clementi, E.; Yoshimine, M. J. Chem. Phys. 1976, 64, (17) Wtnbe, K.; Klein, M. L. Chem. Phys. 1989, 131, 157. (18) Liu, Y.; Ichiye, T. J. Phys. Chem. 1996, 100, (19) Buch, V.; Sndler, P.; Sdlej, J. J. Phys. Chem. B 1998, 102, (20) Levitt, M.; Hirshberg, M.; Shron, R.; Lidig, K. E.; Dggett, V. J. Phys. Chem. B 1997, 101, (21) Jorgensen, W. L.; Jenson, C. J. Comput. Chem. 1998, 19, (22) Chilvo, A. A.; Cummings, P. T. J. Chem. Phys. 1996, 105, (23) Dng, L. X. J. Phys. Chem. B 1998, 102, 620. (24) Ryckert, J.-P.; Ciccotti, G.; Berendsen, H. J. C. J. Comput. Phys. 1977, 23, 327. (25) Drden, T. A.; Sgui, C. Annu. ReV. Biophys. Biomol. Struct. 1999, 28, 155. (26) vn Gunsteren, W. F.; Berendsen, H. J. C. Angew. Chem., Int. Ed. Engl. 1990, 29, 992. (27) Ewld, P. Ann. Phys. 1921, 64, 253. (28) Steinbch, P. J.; Brooks, B. R. J. Comput. Chem. 1994, 15, 667. (29) Prevost, M.; Vn Belle, D.; Lippens, G.; Wodk, S. Mol. Phys. 1990, 71, 587. (30) Hrvey, S. C.; Tn, R. K.-Z.; Chethm, T. E., III J. Comput. Chem. 1998, 19, 726. (31) vn der Spoel, D.; vn Mren, P. J.; Berendsen, H. J. C. J. Chem. Phys. 1998, 108, (32) Feller, S. E.; Pstor, R. W.; Rojnuckrin, A.; Bogusz, S.; Brooks, B. R. J. Phys. Chem. 1996, 100, (33) Tski, K.; McDonld, S.; Brdy, J. W. J. Comput. Chem. 1993, 14, 278. (34) Liu, Q.; Schmidt, R. K.; Teo, B.; Krplus, P. A.; Brdy, J. W. J. Am. Chem. Soc. 1997, 119, (35) Smith, P. E.; Bltt, H. D.; Pettitt, B. M. J. Phys. Chem. B 1997, 101, (36) Mkrov, V. A.; Feig, M.; Andrews, B. K.; Pettitt, B. M. Biophys. J. 1998, 75, 150. (37) Allen, M. P.; Tildesley, D. J. Computer Simultions of Liquids; Oxford Science: Oxford, (38) Brooks, B. R.; Bruccoleri, R. E.; Olfson, B. D.; Sttes, D. J.; Swminthn, S.; Krplus, M. J. Comput. Chem. 1983, 4, 187.