1990_mayo et al._dreiding a generic force field for molecular simulations

8/13/2019 1990_Mayo Et Al._dreIDING a Generic Force Field for Molecular Simulations

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J . Phys. Chem. 1990, 94, 8897-8909DREIDING: A Generic Fo rce Field for Molecular Simulations

8897

Stephen L. Mayo, Barry D. Olafson, and William A. Goddard III**BioDesign, Inc . . 199 South Los Robles (Suite 540 ), Pasadena, California 91 101 (Received: October 2, 1989;I n Final Form: February 2, 1990)

We report th e param eters for a new gen eric force field, DREI DIN G, that we find useful for predicting structures and dy namicsof organic, biological, and main-gr oup inorganic molecules. The philosophy in DREI DIN G is to use general force constantsand geometry parameters based on simple hybridization considerations rather than individual force constants and geometricparameters that depend on the particular combination of atoms involved in the bond, angle, or torsion terms. Thu s all bonddistances are derived from atomic radii, and there is only one force constant each for bonds, angles, and inversions and onlysix different values for torsional barriers. Parameters are defined for all possible combinations of atom s and new atoms canbe added to the force field rather simply. This paper reports the parameters for the "nonmetallic" main-group elements(B, C, N, 0, F columns for the C , Si, Ge, and Sn rows) plus H and a few metals (N a, Ca, Zn, Fe). The accuracy of theDR ElD lN G force field is tested by comparing with i ) 76 accurately determined crystal str uctures of organic compoundsinvolving H , C, N, 0, F, P, S, CI, and Br, i i ) rotational barriers of a number of molecules, and (iii) relative conformationalenergies and barriers of a number of molecules. We find excellent results for these systems.

I . IntroductionA great deal of progress has been made over the last two decadesi n developing force fields suitable for predicting the structuresand dynamics of molecules. Examples include the MM 2/ MM P2force fields of Allinger and co-workers,2 which have been usefulfor a variety of organic and inorganic systems, the AMBER forcefield of Kollman a nd co-w orkers3 for proteins and nucleic acids,and the C H A RM M force field of K arplus and co-workers4 forproteins and nucleic acids. In these specialized force fields, ther earc often subtle distinctions i n force constants and geometricparameters for similar atoms in slightly different environments,and it is often not clear how to generalize for new atoms or newbond types. I n order to facilitate prediction of structures formolecules where there are little or no experimental data, we havedeveloped a generic approach to force fields using parameter s thatare deliberately restricted to very simple rules. This may leadto lower accuracy for a specialized subset of molecules but hasthe virtue of allowing reasonably accurate predictions to be madefor novel combination s of elements. In this paper we discuss asimple generic force field, DREIDING, that we have found usefulfor predicting structures and dynamics of organic, biological, andmain-group inorganic molecules.

11. The DREIDINC Force FieldA . Atom Types . The elements of the DRElDlNG force fieldare the atom types. Atoms with the same atom type are treatedidentically i n the molecular mechanics force field. Each atomtype uses a five-character mnemonic label. The first two characterscorrespond to the chemical symbol (e.g., N- is nitrogen, Te istellurium), where elements with one letter have an underscore.( I ) Permanent ad dress for William A. Goddard 111: Arthur Amos NoyesLaboratory of Chem ical Physics, California In stitute of Technology, Pasadena,.C A 91125.(2 ) (a) Allinger, N. L. J . A m . Chem. SOC. 977,99, 8127. (b) Sprague,J . T.; Tai, J. C.; Yuh, Y.; Allinger, N. L. J . Compur. Chem. 1987,8,581. (c)Burkert, U.; Allinger, N. L.; Molecular Mechanics; American ChemicalSocicty: Washington, DC, 1982; ACS Monograph 177.(3) (a) Weiner, S. .; Kollman, P. A.; Case, D. A,; Singh, U. C.; Ghio, C.;Algona, G.; Profeta Jr., S.; einer, P. J . Am. Chem. Soc. 1984, 106,765. (b)Weiner, S. .; Kollmann, P. A ,; Nguyen, D.T.;Case, D. A. J . Compur. Chem.1986, 7, 230.(4) (a) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.;Swaminathan, S ; Karplus, M. J . Compur. Chem. 1983,4, 187. (b) Nillson,L . ; Karplus, M. lbid. 1986, 7, 591.

The third character indicates hybridization or geometry: 1 =linear (sp'), 2 = trigonal ( sp2), and 3 = tetrahedral (sp3). Inaddition, a n sp2 atom involved in a resonance situatio n (e.g., i nan aromatic ring) is denoted R. Thus, ethane uses C-3, ethyleneuses C-2, benzene uses C-R, while acetylene uses (2-1.The fourth character is used to indicate the number of implicithydrogens (hydrogens that are not included explicitly in thecalculations). Thu s C-32 is a tetrahedr al carbo n with two implicithydrogens. For describing folding of polyethylene polymer chains,wc could ignore the hydrogens and use only C-32.The fifth chara cter is used to indicate alternate characteristicsof the atom such as formal oxidation state.The s tandard D RE lDl NG atom types are l is ted in Table Ialong with various param eters. These rules are easy to programso that the force field types are assigned automatically fromexamining the topology of a structure.The-HB type denotes a hydrogen atom capable of forminghydrogen bonds (see section 11.1). The H-b is the bridginghydrogen of diborane.B. Form of the Force Field. The potential energy for anarbitr ary geometry of a molecule is expressed as a superpositionof valence (or bonded) interactions ( E v a l ) hat depend on thespecific connections (bonds) of the struc ture and nonbonded in-teractions ( E n b ) hat depend only on the distance between theatoms

I n DRElDlNG the valence interactions consist of bond stretch(EB,, wo-body), bond-angle bend ( E A , hree-body), dihedral angletorsion ( E T . four-body), and inversion terms ( E l , our-body)

Eva EB + EA + ET + El (2)while the nonbonded interactions consist of van der Waals ordispersion (Evdw) , lectrostatic ( E Q ) , nd explicit hydrogen bonds(Ebb) terms

The forms of these terms are described next.C Bond Stretch. DRElDlNG describes the bond stretchinteraction either as a simple harmonic oscillator

0022-3654/90/2094-8897%02.50/0 0 1990 American Chemical Society


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8898TABLE I: Geometric Valence Parameters for DREIDING

bond radius bond bond radius bondatom RP A angle, deg atom RY A angle, deg

The Journal o j Physical Chemis try , Vo l . 94, No. 26, 199(

H. 0.330 180.0 Si3 0.937 109.471H-HB 0.330 180.0 P-3 0.890H-b 0.5 O 90.0 s.3 1.040B-3 0.880 109.471 CI 0.9978-2 0.790 120.0 Ga3 1.210c- 3 0.770 109.471 Ge3 1.210C-R 0.700 120.0 As3 1.210c-2 0.670 120.0 Se3 1.210c- 0.602 180.0 Br 1.167N-3 0.702 106.7 In3 1.390N-R 0.650 120.0 Sn3 1.373N-2 0.615 120.0 S b3 1.432N-1 0.556 180.0 Te3 1.2800- 3 0.660 104.51 I- 1.3600 - R 0.660 120.0 Na 1.8600 - 2 0.560 120.0 Ca 1.9400- 0.528 180.0 Fe 1.285F. 0.61 1 180.0 Zn 1.330A13 I ,047 109.47

93.392.1180.0109.47109.47192.190.6180.0109.47109.4791.690.3180.090.090.090.0109.47

or as the Morse functionE = De[e-(onR-Rd- 1 1 2 ( s a )

The Morse function is a more acc ura te description since (5a)includes anharmonic terms near equilibrium ( R e ) nd leads to afinitc energy ( D , ) for breaking the bond. However, in manyapplications the starting geometry for new structures may be veryapproximate (say, obtained by sketching molecules on a graphicsscreen, which might lead to distances a facto r of 10 too large ortoo small) and it is essential that the force field quickly adjustto the optimum geometry. Since the Morse function (5) leadsto nearly zero forces for very large R and the harmonic functionlcads to increasingly large restoring forces as R is increased fromR,, we use the harmonic form as the default for DRElDlNG anddenote calculations using the Morse form as D REID ING /M. I nthe latter case we use the harmonic function (4a) i n the initialstage of geometry optimization and the Morse function (Sa) forrefined calculations.Writing the force constant as

k . = ( $ ) R=R.leads to

cy = [q2for the Morse scale parameter.sassume additivity of bond radiiTo predict the equilibrium bond distance RY, for bond I J , we

(6)where the bond radii RY are based on structural dat a of standardreference molecules and 6 = 0.01 A. The bond radius RY is definedin tcrms of the experimental bond length6.' of atom J to CH, (or

RYJ = R$ + RY - 6

5 ) The cubic term in the expansion of (5a) about R = Re is k : = ( P E /6 R 3 ) ~ . ~-3ak,. For comparison, the M M 2 force field2 uses a c ubic termkIc = -61,. a value we would obtain if De = k e / 8 . For k , = 700 this wouldyield D. = 8 7 . 5 .(6) (a) Landol t-Born stein, New Series I / 7; Callomon, J . H. t al., Eds.;Springer: New York, 1976. (b) Harmony, M. D., et al. J. Phys. Chem. Re/.Data 1979, 8, 619. (c) Huber, K. .; Herzberg, G . Constanis of DiatomicMolecu les; Van Nostrand-Rheinho ld New York, 1979. (d) Wells, A . F.S l r u r t u r a l Inorganic Chemistry, 5th ed.; Oxford University Press: Oxford,1984.(7) Handbook of Chemistry and Physics, 60th ed.; Weast. R. C., Astlc,M . J . , Eds.; C RC Press: Boca Raton , FL 1979.

3 Mayo et al.anothcr singlc bond to carbon) . Th e resulting radii ar e listed i nTable I .I n DRElDlNG we set all energy parameters for single bondsto

( 7 )(8 )

independent of 1,J. [For cases where atoms of two differen t bondorders arc bonded (c.g., C-3-C-2 bond of propane) the defaultis to use the parameters for a single bond.] This restriction toone force constant parameter and one bond energy is oversim-plified; however, it is well-defined for any possible pair of atomsand leads to reasonably accurate equilibrium structures.For a multiple bond with bond order n, the parameters are taken

K / J( ) = 700 (kca l /m ol ) /A2D / j (1 ) = 70 kcal/mol

asK l J( n )= n K / J ( ) (9a)D I J f l ) = nDIJ(1 (9b)

I). Angle Bend. For two bonds IJ and J K sharing a commonatom. thc three-body angle bend terms are all taken of the har-monic cosine formE I J K = hclJK[cOs O l J K - cos 31 ( 1 Oa)

whcrc 0 is the angle between bonds IJ and J K . The equilibriumanglcs 0: (see Table I ) are assumed independent of I and K , andwcrc obtained from standard reference structures of the parenthydrides.6 Where the str uctura l data were unavailable, the e J werecxtrapolated from nearby elements i n the same column of theperiodic table.Th e harmonic angle formE I J K = t / Z K I J K [ e / J K - I 1 1)

is i n common use but we prefer (loa) because ( 1 1 ) does notgenerally lead to zero slope as 0 approaches 180'.The c/JK n (loa) is related to the force constant K/JK byK IJK

(sin 09)IJK =For molecules with linear equilibrium geometries (0: = ISO'),we replace ( lo a) with2*

( 10 )The force constants for all angle bend interactions are taken as

K/jK = 100 (kcal /mol)/rad* ( 12)

E / J K = K I J K I I + cos 61JKl

independent of I , , and K .conncctcd via a common bond J K is taken of the formE . Torsion. The torsion interaction for two bonds IJ and K L

( 1 3 )where (p is the dihedral angle (angle between the IJK and J K Lplanes), nJK is the periodicity (an integ er), VJK s the barrier torotation (always positive), and p;K is the equilibrium angle. Theform of ( 1 3) is chosen so that the torsion energy is zero at theequilibrium angle and never negative. Because of symmetry (zeroslopc at 0 and 1S O 0 ) , the torsion potential must be a maximumor minimum at 0 and 180' and there a re only discrete choicesfor p jK (multip le of I 8O0/nJK) .The parameters VjK, nJK,and pya rc taken as indcpendcnt of I and L.The VjK is taken as the total barrier after adding all possibleI and L tcrms to the energy expression, but the energy is renor-malized by the total number of terms having a common J andK . Thus, for a substituted ethane (involving C-3 for J and K )VjK = 2.0 kcal/mol and the program uses a barrier of V/jKL =2 / 9 for cach of thc nine possibilities of I and L. Similarly, fora substitutcd ethylene, VjK = 45 kcal/mol and the program usesV/jK/,= 4 5 / 4 for each of the four possibilities of and L .I n DRElDlNG thc torsional parameters arc based on hy-bridization and arc independent of the particular atoms involved.

EIJKL = t / z v J K { l - cos [ n JK ( p d K ) 1 1


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DREIDING: A Generic Force FieldThe various stand ard cases are as follows:(a) A dihedral single bond involving two sp3 atoms (J ,K = X-3)V J K = 2.0 kcal/mol, n J K = 3, v ~ K 180' (or 60') (14)

(b) A dihedr al single bond involving one sp2 center and one sp3cent er {e.g., the C-C bond i n acetic acid [CH,C(O)-OH)]]: J= X-2, X-R: K = X-3)VJK= 1.0 kcal/mol, n j K = 6, K = 0 ( 1 5 )

(c) A dihedral double bon d involving two sp2 atoms ( J ,K = X-2)VJK= 45 kcal/mol, n j K = 2, V ~ K 180' (Or 0') (16)

(d) A dihedral resonance bond (bond order = 1 .5 ) involvingtwo resonant atoms ( J ,K = X-R)V J K = 25 kcal/mol, n J K = 2, v ~ K 180' (or 0 ) ( 1 7)

(e) A di hedral single bond involving two sp2or resonant atomss[e.g., the middle bond of butadiene] ( J ,K = X-2, X-R)V J K = 5 kcal /mol , n J K = 2, p y K = 180' (18)

(f) An exception to (e) is that for an exocyclic dihedral singlebond involving two aromatic atoms [e.g., a phenyl ester o r thebond between the two rings of biphenyl] ( J , K = X-R)VJK= 10 kcal/mol, n J K = 2, V ~ K 180' ( 19 )

(g) For dihedrals involving one or two spl atoms (X-I), mo-V j K = 0.0 (20)

Elements of the oxygen column (column 16) having two singlebonds are denoted as X-3; however, the rotational barriers arebest understood by thinking of the atoms in terms of the s2p4configuration, where two singly occupied p orbitals are used tomake the two bonds (with a bond angle6 o f -92' for S, Se, andTe and 104.5' for 0 ,eaving a p line pair perpendicular to thebonds (the pn lone pair). The pn lone pair is stabilized byoverlapping a singly occupied (bond) orbital on an adjacent center.As a result HSSH leads to an optimum torsion angle6 of 90.4'as does crystalline HOOH (gas-phase HOOH has an optimumtorsion angle of I 1'). Thus(h ) A d ihedral single bond involving two sp3 atoms of the oxygencolumn J , K = X-3 of column 16)

[however, the interaction with an sp3 atom o f another column isgiven in eq 14 above].(i) For dihedral bonds involving an sp 3 atom of the oxygencolumn with a n sp2 or resonant atom o f another column, the Ppair and the oxygen-like prefers to overlap the orbitals o f thesp2 ato m, leading to a planar configuration J = X-3 of column16, K = X-2,X-R)

novalent atoms (F , CI, Na, K, ...), or metals (Fe, Zn, ...)

V J K = 2.0 kcal/mol, n J K = 2, v ~ K= 90' (21)

VJK = 2.0 kcal/mol, t l j K = 2, V ~ K 180' (22)(j)An exception to the above principles is made for the caseof a dihe dral single bond involving one sp2 atom (J = X-2, X-R)and onc sp3 atom K = X-3) (for example, the single bond of

propen e). Th e problem here is that for a system such as propenethere is a 3-fold barrier with the sp3 center eclipsing the doublebond, whereas for the CC bond, say, o f acetate anion (CH3-C-00- ,hc barrier should have 6-fold character [as in ( 1 5)]. Toaccommodate this we use ( 1 5) unless I is nor an sp2 center (X-2or X-R): otherwise we use the following I X-2, X-R; J = X-2,X-R: K = X-3

VJK= 2.0 kcal/mol, l l j K = 3, ' p y ~ 180' (23)The barriers i n (14)-(23) ar e based roughly on values for thecarbon row. They should generally decrease for other rows of(8) For the exocyclic bond of an aromatic carbon to a heteroatom havinga lone pair (e.&, NH2, OH), the interaction of the lone pair with the ring leadsto the N or 0 being described as N-R or 0-R, so that (18) applies to thetorsions involving this C-R-N-R or CR -0 -R dihedral,

The Journal of Physical Chemistry, Vol. 94, No. 26, 1990 8899TABLE 11: The van der Waals Parameters for DREIDING

atom Ro A Do, kcal/mol sourceHH-bH-HBBCN0FAISiPSCIGaGCAsSCBrI nSnS bTcINu+Ca2+Fc2+Zn2+C-Rc - 3 4c - 3 3C-32C-3 I

3.1953.1953.1954.023.89833.66213.40463.47204.394.274.15004.03003.95034.394.274.154.033.954.594.474.354.234.153.1443.4724.544.544.234.23704. I5244.06773.9830

0.01520.01520.00010.0950.0950.07740.09570.07250.3 10.3 10.32000.34400.28330.400.400.410.430.370.550.550.550.570.5 10.50.050.0550.055

12.38212.38212.014.2314.03413.84313.48314.44412.012.012.012.013.86112.012.012.012.012.012.012.012.012.012.012.012.012.012.0

Implicit Hydrogens0.1356 14.0340.3016 12.00.2500 12.00. I984 12.00. I467 12.0

n-hexane crystall l ainterpolationHzO dimerinterpolationWilliamsIlaWilliams11PWilliams'ldWilliams' IbinterpolationinterpolationP4 rystalS8crystalWilliams"cinterpolationinterpolationinterpolationinterpolationinterpolationinterpolationinterpolationinterpolationinterpolationinterpolationDREIDING/AD R E I D I N G / ADREIDING/ADREIDING/Abenzene crystalCH4 crystalinterpolationinterpolationinterpolation

TABLE 111: Valence Force Constants for DREIDINGbondsn = I K = 700 (kcal /mol) /A2

II = 2 K = 1400 (kcal /mol) /A2n = 3 K = 2100 (kcal/mol)/A2angles K = 100 (kcal /mol) / rad2invcrsions:

D = 70 kcal/molD = 140 kcal/molD = 210 kcal/mol

X-2, X-R K = 40(kcal /mol) / rad2 qo= OoC-3 I K = 40(kcal /mol) / rad2 qo= 54.74Ox - 3 K = Othe periodic table. However, we eschew such subtleties here.F . Inversion. For an atom I bonded to exactly three otheratoms, J , K , L, t is often necessary to include an energy termdescribing how difficult it is to force all thre e bonds into the sam eplane (inversion) or how favorable it is to keep the bonds i n thesamc plane. Thus for planar molecules such as ethylene, the useo f bond angle terms will not in general lead to the proper restoringforce toward the planar configuration, and it is necessary to addan cxplicit four-body inversion term. Similarly for a nonplanarmolecule such as ammonia (where the barrier to inversion is 6kcal/mol), thc constants used for bond angle terms may not leadto the correct inversion barrier, requiring an explicit four-bodyterm to correctly describe the inversion energy. (In fact, forDREIDING the inversion barriers o f N H 3 , PH3 , etc., are welldescribed without explicit inversion terms.)A number of approaches have been adapted to describe suchinversion terms. Denoting the angle between the IL bond andthe J I K plane as 9, pectroscopists have often used the form

[W e define \ko so that it is zero for a normal planar molecule(where the projection of the IL bond onto the JIK plane pointsaway from the bisector o f the IJ and IL bonds).]I n the literature on biological simulations, it has been morecommon to use expressions i n which the inversion is treated asif it wcrc an (improper) torsion. Thus, the CH AR MM force field4Q n v 4 ) = Winv(d - 40)* (25)

USCS


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8900 The Journal of Physical Chemistry, Vol. 94 , No. 26, 1990TABLE IV: DREIDINC Torsion Parameters for Equivalent CentralAtoms

atom n V , . kcal /mol 0 . deeH -8-3c - 3C-Rc.2c-N-3N-RN-2VI0 - 30.R0.20-FA13SiP-3s.3CIG a3G eA53s c 3B rIn3Sn3Sb3Te3I-NaC aFeZn

332232222

333233323332

02.0 1802.0 I8025.0 I8045.0 I8002.0 18025.0 18045.0 18002.0 9025.0 18045.0 180002.0 I802.0 1802.0 1802.0 9002.0 1802.0 1802.0 1802.0 9002.0 1802.0 I802.0 1802.0 9000000

TABLE V: Hydrogen Bond Parameters for DREIDINC (Based on( H i o h )

water dimerconvention QH or Rr Dhb, E, cal/ RG..,,, OoH.for charges H, O, e kcal/mol mol 8, degcxpcrimcnt 0.33 2.75 4.0 6.13 2.94 176.1gastcigcr 0.21 2.75 7.0 -6.05 2.93 178.6no charges" 0.00 2.75 9.0 -6.03 2.92 179.9'DREIDING/A uses R h b = 2.75 A and Dhb = 9.5 kcal /mol

where 4 is the improper torsion angle of I J with respect to K Lusing the JK pseudobond dihedral (the angle between the I J Kand J K L planes). A second improper torsion approach (used i nAM BE R3) is to consider one bond (say, IL) as special and to writethe cncrgy asE?nv(B)= Y A i n v l l - COS [n(B 4dII (26)

where 19 is the angle between J I L and K I L planes and n = 2 (forplanar ccntcrs) or n = 3 (for tetrahedral centers). MM 2 uses theform2E i n v ( a ) = Y*Kinv(a- (27)

where a = 9 - 9.Although the improper torsion formulations are easier toprogram, we prefer the spectroscopic inversion because of its closecorrcspondence to chemical concepts. However, i n order that theenergy have zero slope for planar configurations (\k- 80, OO),we replace (24 ) with the form(28a)

C , = K,/(sin \kp)2 (28b)and K , is thc force consta nt. For systems with planar equilibriumgcomctrics (qp = 0') we replace (28a) wi th28

E KL= t/2CI(cos \k - cos \kp)2where

E,,,, = K,[ 1 - COS 911 ( 2 8 ~ )

Mayo et al.TABLE VI: Geometric Valence Parameters for D REIDING/A

bond radius bond bond radius bondat om RP, A angle, deg atom RP,A angle, deg

H. 0.33 0 180.0 A13 1.071 109.47H-HB 0.330 180.0 Si3 0.937 109.471c -3 0.770 109.471 P-3 0.890 109.471C.R 0.7 00 120.0 S-31 1.04 97.2c.2 0.670 120.0 s - 3 1.01 104.2c- 0.602 180.0 CI 0.997 180.03 - 3 0 700 109.471 Br 1.167 180.0N-R 0.620 120.0 Na 0.97 90.0N-2 0.620 120.0 Ca 0.99 90.0bi-I 0.388 180.0 Ti 1.31 90.00- 3 0.660 109.471 Fe 1.305 90.00.R 0.660 120.0 Zn 1.280 109.470.2 0.56 0 120.0 Ru 1.305 90.0F- 0.61 1 180.0TABLE VII: van der Waals Parameters for D REIDINC/A

atom Rn,A Dn. cal/mol atom Rn, Dn, cal/molH-H-H Bc - 3 3C-32C.3 Ic.3c - 22c-2c.2C-R2C-R IC-Rc-Ic.1h - 3 3h - 3 2h - 3Y-31\1-22N.21h-2h - R 2h _ R

3.20002.40004.18004.08003.98003.88004.08003.98003.88004.08003.98003.88003.98003.88003.99503.89503.79503.69503.89503.79703.69503.89503.7950

0.01000.0000.30500.21500. I4500.09500.2 I500.14500.09500.2 I500. I4500.09500.14500.09500.41 500.30500.2 I500.14500.30500.2 I500.14500.30500.21 50

N-RN-10 - 320 - 3 10 - 30 - 20 - R0 - R 1F-NaA13Si3P-3s - 3s - 3CIB rCaTiFeZnR u

3.69503.69503.71003.61003.51003.51003.51003.61003.28503.14404.6 1 504.43504.29504.24004.14003.91504.21 503.47204.54004.54004.54004.5400

0.14500.14500.41 500.30500.21500.21500.21 500.21 500.30500.50000.06500.09500.2 I500.30500.21500.30500.30500.05000.05500.05500.05500.0550

For X6 potentials, use ( = 12.0000.For nonplanar molecules the contribution of (28) to the barrierfor inversion is

Ebar= 2C,[sin (f/Z k7)]*For nonplanar geometries the inversion expression i n (28) treatsbond I L i n a way slightly different from bonds I J and I K , andhcncc i n DRElDlNG we add to gether all three possible inversiontcrms with cach weighted by a factor of 1 / 3 .The parameters i n (28) ar e defined only for atom s that canmake three bonds and we use force constants as follows:(a) For all planar molecules ( I = X-2,X-R)

K , = 40 (kcal /mol)/rad 2 (29)(b) For nonplanar molecules where the central atom is i n the

nitrogen column ( I = X-3), we find that the angle terms accountpropcrly for the inversion barrier in XH, without the need foradditional inversion terms. Thu s with the harmonic cos angleterm I O ) N H 3 and P H, lead to barriers of 7.4 and 29.5 kcal/molrcspcctivcly, whilc the harmonic th eta an gle term ( 1 1 ) leads to8 . and 32.6 , respectively. Sinc e these values ar e both in rca-sonable agrccmcnt with experiment (6 and >30. respective ly), wetakc K , = 0 and ignore such inversion terms.( c ) For nonplanar molecules with four or more bonds, the angleintcractions will normally prevent inversion of the center and wedo not include explicit inversion terms. Although th e energy E ( * )should havc thc symmctryE(-'P) = E + @ ) 30)

i t is sometimes useful to bias the calculations so that 30) is not


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DREIDING: A Generic Force Field The Journal of Physical Chemistry, Vol. 94, No. 26, 1990 8901

AAXTHP ABlNOSOl ACAFLR ACBUOL

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8902 The Journal of Physical Chemistry, Vol. 94, No. 26, 1990 Mayo e t al.HO

0

ACNPAClOOH0

ACPPCA ACSALAOl ACTHCP

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Figure 1. Cont inued.ADYPNL


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DREIDING: A Generic Force Field The Journal of Physical Chemistry, Vol. 94, No. 26, 1990 8903HzN Yo

AEBDOD 10

AENLANIO

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AFMSCYFigure 1. Continued.

0

AFUWOIO

0

INH2

AFUTDZIO

0

OHAFUTHU

OH

OH OH

AGALAM 10

satisfied. The most common ex ample occurs when one wants toforce a specific stereochemistry at a center while calculatingstructures or dynamics. To do this we use the form (24) whereq0 s defined so as to be positive for th e desired stereochemistry.I n this case we use K, = 40 kcal/mol to ensure retention ofstereochem istry. This is particularly importan t when implicithydrogens are used for the C, atoms of amino acids I = C-31).G . Nonbonded Interactions. The two common expressions fordescribing van der Waals nonbonded interactions9 are the Len-nard-Jone s 12-6 type expression (denoted LJ)

(31)

(32)The LJ form is simpler (two parameters rather than three) andfaster to compute (eliminating a square root and an exponenti-ation); however, our experience is that the X6 form gives asomewhat better description of sho rt-rang e interactions. Thus,DR EI DI NG allows either form and our programs permit theseforms to be interconverted. We consider the LJ as the defaultand use DR EID IN G/X 6 to denote cases where the exponential-6form is used.

~ d ~A R ~ Z BR-6

E$$ = A e X R - BR-6and the exponential-6 form (denoted X6)I0

(9) a) In order to truncate the sums over nonbonded interactions for largemolecules (>IO00 atoms), it is often convenient to replace (31), (32 ), or (37)with a function that oes smoothly to zero after some large cutoff distance(e&, R, , = 9.0 A)?. However, in this paper we calculate all nonbondInteractions. (b ) Similarly for (38) we use no distance cutoffs. [The hydrogenbond angleI O) For sufficiently small R, (32) leads to a negative energy with E ---m as R - . To avoid such unpleasant situations, we use a simple expo-nential 2 exp[-S'R] for R below the inner inflection p i n t of (32) (where thecurvature becomes negative), with 2 and S matched to the values at theinflection point. For scale parameters . 2 IO. his inflection point is far upthc repulsive wall and not important.

is restricted to be larger than 90 (linear is 180')).

yOHAGLUAM 10

0odb H

AHARFU

AHCDLA

HO-

AHDITX

I n order to better compare (31) and (32), we rewrite them as(31')LJ = Do[p-12- 2p-61

where p = R / R o s the scaled distance, Ro s the van der W aalsbond length (A ) , Do s the van der W aals well depth (k cal/mol),and {is a dimensionless scaling para mete r. Given the Ro and Doparamcters for the LJ form, there are two reasonable choices forthc scaling parameter f i n X6: (a) { = 12.0 leads to X6 havingexactly the same long-range attraction as the LJ form, and (b)f = 13.772 leads to a dimensionless force constant(33)

of K = 72 for X6,which is exactly equal to the value for LJ. Thus,with f = 13.772, the X 6 and LJ forms lead to the same descriptionncar Ro. Given the parameters for the X6 form there are tworeason abk choiccs for converting to the LJ form: (c) use the sameRo and Do.eading to a similar description near R,; (d) requirethat thc coefficient of the long range (R") term be exactly thesamc and require that the inner crossing point (Evdw= 0) be atthc samc distancc. This leads to simple equations

yeT(l-') = 1 ( 3 4 4

(34c)


8/13

8904TABLE VIII : Summary of Results for Various Options in the DREIDING Force Field

The Journal of Physical Chemistry, Vol. 94 . N o . 26, 1990 Mayo et al.

bonds harm. Morse harm. harm. harm. harm.angles theta theta cosine theta theta thetavdw L J LJ LJ x6 LJ LJ D R E l D l N G icharges no no no no e = R f = l Aatoms. A rms 0.235 0.236 0.237 0.250 0.247 0.257 0.334

avgmaxbonds, A rmsavgmax

angles, deg rmsavgmaxtorsions, deg rmsavgmax

0.2211.9530.0350.0090. I693.2370.57217.7258.9250.2228 1.972

0.2231.9420.0360.010. I683.2210.56017.698.9790.23282.083

0.2241.9440.0350.0090.1683.3560.62020.0009.0360.22582.241

which are used to find the LJ parameters ( R L ,DL ) for a givenset of X6 parameters ( R x ,Dx {).I n the current studies we use options ( a ) and (c) for inter-conversions.Nonbond interactions are not calculated between atom s bondedto each other (1,Z interactions) or atoms involved i n angle i n -teractions (1,3 interactions), since it is assumed that these i n -teractions are included i n the bond angle energy terms. Ourprograms allow the nonbond interactions between 1,4 neighborsto be included, excluded, or scaled. However, in D R E I D I N G .the default is to include the full value for all 1,4 terms.In DRE IDI NG we require that only nuclear ce nters be usedi n defining the force field. Thi s may reduce the accuracy fordescribing nonbonded interactions since there is th atuse of centers other than nuclear centers for (31) or (32) can leadto improved descriptions. However, omitting nonnuclear termsreduces the number of parameters to be defined and simplifiesextending the force field to new atoms.Consistent with the philosophy of DREIDING, we define thevan der Waals parameters only for homonuclear cases and usecombination rules to obtain the parameters for other atoms. Thestandard combination rules assume the following:( a ) a geometric mean for the A and B parameters

= [ A , i A ] ] 1 2 (35a )

(b) and an arithmetic mean for the C parameters (X6)Cij = I/zC11 + zCjj (35c)

For LJ (35ab) is equivalent to assuming the bond energies andbond distances combine as geometric means= ~ D O l l D O ~ J 1 1 i 2 (36a)

R O l ] = [ R O l ~ R O J J l I 2The use of an arithme tic mean

i n place of (36b), for combining vdw radii is more consistent withchemical practice, however, the geometric mean (36 b) has beenused in successful force fields (e.g., AMBE R3) and is more con-sistent with the X 6 form. Also for crystals, (35) allows a sim-plification i n the convergence acceleration formulas for summingthe vdw terms that speeds up the calculation ~ign ifi can tly .]~hus,DR EID ING uses (35) for X6 potentials. Ou r computer programsallow either form to be used for LJ cases: however, for DREID-ING we use (36a) with (36c) a s defaults.

I I ) (a ) Williams, D. E.; Cox, S. R. Acta Crystal logr.. Sect. B 1984, 40,404. (b) Williams, D. E.; Houpt, D. J. /bid. 986, 42, 86. (c) Williams,D. E. ; Hsu, L. Y . Acta Crysta l logr . , Sect. A 1985, 41. 296. (d) Cox,S. R.:Hsu. L . Y . ; Williams, D. E. /bid.1981, 7, 293.( 1 2 ) Jorgensen, W. J . ; Tirado-Rives. J . J . A m . Chem. Soc. 1988, 110.1657.(13) Karasawa, N . ; Goddard I l l , W. A . J . P h y s . Chem. i n press.

0.2242.0260.0330.0030. I683.0650.38916.77010.0420.28699.102

0.2311.9880.0350.0090.1653.2550.56616.2779.5330.4578 1.804 -

0.243 0.2903.501 2.4830.035 0 .0360.009 0.0040. I62 0.1393.310 3.6740.567 0.88916.576 19.54810.61 1 13.3240.576 0.25660.083 -97.569

The literature is replete with rather disparate values of van derWaals parameters. On the basis of ab initio calculation^'^ on H2dim er , CH, d im er, and (H 2)(CH 4) ,we concluded that the bestset of cnipirical van der Waals parameters are those of Williamsand co-workers. [These were based on accurate fits to a largedata base of compounds for which crystal structures and subli-mation energies were available.] Conseq uently , for DR EI DI NGu c have adopted the Williams parameters with the followingchanges.(a) Williams used the exponential-6 form, (32), whereas wealso allow LJ potentials using the same Do nd Ro.(b ) Williams used off-center locations for H (shortening theCH , NH , and OH bonds by 0.07 A) . W e use nuclear positionsfor the H van der Waals terms and reoptimized the H parametersto fit the crystal d ata on n-hexane15 (lattice constan t and subli-mation energy).(c) We did not include the extr a lone-pair centers tha t Williamsused for certain N, 0, and F atoms.( d ) W e added other atoms for the C, N , 0, and F columns byoptimizing parameters to f i t the structu res and sublimation en-ergies (using charge s based on experimental moments or on fitsto the electrostatic potentials from HartreeFock wave functions16)or by interpolation or extrapolation. W e use the same van derWaals interactions independent of hybridization of the atom (e.g.,C-3, C-R , C-2, C-1 all have the same parameters).(e) Additional atoms (Na +, Ca2+, Fe2+, Zn2+) were added withparameters appropriate for the particular situation encounteredi n biological systems.(f) Sometimes it is expedient to lump the hydrogens on carb onstogcthcr with the carbons as a single effective atom (implicithydrogens). We estimated the van der Waals paramet ers for suchcases by calculating metha ne and benzene crystals and requiringthat lattice spacing and heat of sublimation of 0 K match ex-periment (see bottom of Tab le It) . Th e final values are listedi n Tables 11-IV.H. Electrostatic Interactions. Electrostatic interactions arecalculated by using9

(37 )p = (322.0637)QiQ,/ c Rij

(14) Brusich, M . J. ; Hurley, J. N.; Lee, J . G.; Goddard I l l , W. A . Un-published results. Brusich, M. J. P h.D. Thesis, California Institute of Tech-nology, 1988. Hurley. J. N . M.S. Thesis, California Institute of Technology.1988.(15) To make this conversion we first carried out calculations using theWilliams scheme and verified his results for crystals of n-hexene and benz-e n d l a In doing these calculations we allowed the internal coordinates torespond to the fields and chose the valence force field parameters so that theobserved geometries are stable (Williams calculated only intermolecular in-tcractions). We then modified the charges in the Williams calculations tocorrespond with values from more recent stu diesi6 QH = 0.14 e) and verifiedthat this leads to negligible changes in the results. We then centered thehydrogen van der Waals and Coulomb terms on the hydrogen nuclei anddetermined parameters leading to the same net stresses i n the crystals (afterrcoptimizing valence terms to yield the observed bond distances and angles).These calculations all use the POLYGRAF program which uses periodicboundary conditions with accuracy-controlled acceleration convergence forclcctrostatic and van d er Waa ls terms (accuracy parameter of 0.01 kcal/mol).


9/13

DREIDING: A Generic Force Field The Journal of Physical Chemistry, Vol. 94, No. 26, I990 8905TABLE 1X: Errors in Calcula ting the Structures for 76 Organic Molecules Using the DREIDING Force Field'

atoms, A bonds, A angles, deg torsions, degmolecule Nat m tRM S Aatm Matm Nbnd Rbnd Abnd Mbnd Nang Rang Aang Mang Ntor R tor Ator Mtor

TOT AL 76b 0.235 0.221 1.953 1483 0.035 0.009 0.169 2174 3.224 0.566 17.750 2888 8.948 0.226 81.978A A X T H P 26A B A X E S 25ABBUMOIO 22ABlNORO2 I OABINOSOI I OABTOET 27ABZTCX 20ACADOS 22A C A F L R 17ACANlLOl I OA C A R A P 22ACBNZAOI 13ACBUOL 24A C C l T R l O 22ACDXUR 19ACENAP03 12A C F P C H 17ACFUCN 14A C G L S P 25A C G L U A l l I 5A C H G A L 17ACHlST2O 14ACHNAPIO 15ACHTARIO I OA C I M D C 4ACINDN 14A C l N S T 26A C K Y N U 18A C M B P N 24ACMEBZ 14A C M T D E 16ACNORT 31ACNPACIO 15A C N P E C 21A C O N T N I O 32ACPENCIO 15ACPPCA 12A C P R E T 03 29A C P Y N S 1 8A C R A M S 26ACSALAOI 13ACSESOIO 23A C T A N D 24ACTHBZ 22A C T H C P I OA C T O L D I IACTYSN 16A C U R I D 19A C V C H O I 2ACXMOL 22A C X M P R 14A C Y G L Y l l 8ACYTID 17ADELOXIO 28ADENOSIO 19A D F G L P I IADGSMH 29ADHELAIO 14ADMANN 12A D M H E P 14ADMINA 16A D M O P M 24A D R T A R 13ADYPNL 33AEBDODIO 22A E N L A N I O 35A F C Y D P 24AFMSCY 20AFURPOIO 13AFUTDZIO I2A F U T H U 16AGALAMIO 15AGLUAMIO 13

0.334 0.284 0.7400.112 0.105 0.1770.113 0.101 0.2080.090 0.075 0.1620.075 0.064 0.1550.414 0.343 1.3160.351 0.287 0.9150.148 0.1 I8 0.4520.147 0.1 14 0.4430.070 0.062 0.1300.340 0.296 0.8220.146 0.108 0.3250.449 0.381 0.9820.265 0.193 0.8260.141 0.126 0.2940.023 0.022 0.0330.073 0.065 0.1540.275 0.230 0.6990.341 0.287 0.7630.190 0.171 0.3790.180 0.158 0.3670.336 0.291 0.6420.078 0.066 0.1640.148 0.1 I7 0.2770.023 0.023 0.0310.072 0.067 0.1 10.244 0.207 0.6050.391 0.338 0.8520.259 0.206 0.7160.175 0.141 0.4300.254 0.211 0.6830.266 0.188 0.8470.050 0.045 0.1000.844 0.787 1.4580.184 0.160 0.4040.288 0.249 0.6690.225 0.165 0.5090.290 0.244 0.6820.263 0.235 0.5130.867 0.768 1.4240.097 0.086 0.1910.21 I 0.169 0.6080.379 0.266 1.4570.297 0.223 0.8640.093 0.077 0.2020.045 0.042 0.0860.774 0.650 1.9530.126 0.109 0.2520.109 0.085 0.2350.408 0.322 1.1030.071 0.557 1.2940.095 0.084 0.1590.202 0.190 0.3380.127 0.109 0.3000.088 0.077 0.1680.059 0.056 0.0790.340 0.284 0.9760.092 0.082 0.1690.122 0.102 0.2240.080 0.072 0.1760.061 0.054 0.1 190.677 0.610 1.3500.139 0.121 0.2640.354 0.313 0.7520.256 0.210 0.5970.420 0.309 1.5440.413 0.332 1.0980.306 0.256 0.6590.140 0.129 0.2440.247 0.204 0.5210.067 0.060 0.1430.109 0.097 0.1940.328 0.281 0.680AHA RFU 16 0.120 0.103 0.233

26 0.03928 0.03626 0.029IO 0.020I O 0.02330 0.02821 0.06424 0.02819 0.033I O 0.02622 0.03113 0.04224 0.03525 0.03020 0.03214 0.02618 0.02914 0.03425 0.03215 0.02418 0.02814 0.02416 0.0369 0.024

3 0.03015 0.04926 0.03318 0.02825 0.03314 0.03815 0.02935 0.02617 0.04021 0.03937 0.03016 0.05412 0.03732 0.03119 0.04029 0.05513 0.03926 0.03627 0.03923 0.0311 1 0.0391 1 0.03116 0.02620 0.03112 0.03123 0.03414 0.0387 0.03418 0.02432 0.02921 0.0231 2 0.03230 0.03214 0.03812 0.02714 0.02118 0.02926 0.03013 0.02437 0.03825 0.03639 0.04126 0.03322 0.02614 0.04013 0.08118 0.03215 0.02912 0.03418 0.036

0.002 0.0880.024 0.0450.015 0.0320.021 0.0340.025 0.156

0.012 -0.081

0.01 -0.0670.003 -0.0660.002 -0.0820.005 -0.0560.006 -0.0540.007 -0.0870.009 -0.0760.002 -0.0640.015 0.0520.000 0.0380.018 0.0470.005 -0.0620.012 0.0660.01 I 0.0390.005 -0.046-0.001 -0.0450.035 0.0550.007 0.0460.022 0.0380.000 -0.0870.006 -0.0580.007 -0.0520.013 0.0770.012 -0.0650.008 -0.0450.008 0.0610.005 -0.0650.009 -0.0920.019 0.060-0.016 -0.0890.024 0.0550.008 -0.0530.018 0.0760.022 0.1630.014 -0.0720.01 1 0.0720.018 0.0640.000 -0.079-0.01 7 -0.0700.012 -0.0500.005 -0.0490.002 -0.0710.007 -0.0460.01 1 0.061-0.008 -0.0660.012 0.0590.013 0.0710.020 -0.0570.007 -0.0460.013 0.0570.01 I 0.0570.022 0.0420.011 0.0430.006 0.0700.006 0.0390.013 -0.0830.003 0.0640.018 0.126-0.007 0.0670.005 -0.058

0.001 -0.089

0.000 -0.059

0.001 0.0780.025 0.1690.004 0.0650.018 0.0450.010 0.050-0.002 -0.068

36454014144333352712301731422920251934212618241 2

32238243919185325276323165227421742433116142129163320826513118451917212739175241634134202027211 527

5.4322.6301.6711.7721.4323.4703.4043.7281.9922.0555.5103.1073.3682.6203.4550.8561.8043.1165.0432.01 34.4163.4883.6254.5961.4411.9115.1713.3972.6343.9683.0324.5781.8263.1892.6406.2443.6742.8844.6262.7284.0452.9421.8162.1862.7992.0702.9 I43.3581.8973.8564.1724.0682.6002.4903.1351.9844.6992.8551.8301.6421.01 13.7552.0171.5382.3442.8683.7193.2773.51 12.5021.861I .6584.2062.701

1.1890.5040.5270.2940.5610.9350.3940.7420.1500.3281.8490.2661.1720.5560.221-0.1820.3750.21 11.7930.7461.2980.4390.5551.3520.0031.4690.1770.6660.4570.4501.1500.5410.9611.4190.3310.4051.1240.0990.5930.3910.2590.1920.4470.1480.21 1-0.1 150.41 21.2090.3890.8040.7630.6800.3490.358I .450.3320.9070.5120.3460.4140.0990.0840.5500.7350.0590.1680.309-0.09 10.4490.3210.673

-0.062

-0.132

-0.054

12.6378.9494.3193.5463.14513.280-10.74311.8934.788-4.3551 1.9476.53511.5819.0646.8834.2757.60811.2804.48011.487

10.66610.724

-1.569

-9.1 16

-1.783-3.48812.3038.5246.5478.6097.17217.750-5.1939.4351 1.60012.6598.88113.11512.698-1 2.55 19.5139.9735.4915.4767.599-4.4717.658-7.3293.77811.085-9.4497.2237.75811.1879.1063.52912.5745.4433.966-4.1 142.049-10.6445.1734.5225.61311.3509.2187.685-7.646-5.9964.2883.4598.8478.506

41 8.399 -3.060 -20.06365 3.959 0.216 10.17961 4.466 0.24 8 -10.54517 5.363 0.522 -8.29417 3.824 -0.358 6.17961 8.338 -1.120 -23.09049 5.420 -0.961 -21.87436 5.386 -0.877 -22.53512 2.675 1.468 6.05733 10.621 -3.097 -26.44719 7.879 3.715 16.99334 9 .697 -1.459 25.81559 12.712 -0.270 -38.129

41 19.440 1.097 47.904

38 4.670 0.119 11.54029 0.475 0.001 0.85333 1.514 -0.041 -4.12121 8.582 -1.471 -26.49639 6.993 -0.440 -21.17026 7.300 -0.537 -22.11533 5.313 0.987 15.56719 13.314 6.6 93 31.17532 1.798 0.026 4.2317 6.675 2.637 17.0290 0.000 0.000 0.00031 1.991 0.713 4.97347 5.35 3 2.572 15.27327 17.848 0.86 4 36.614

22 7.649 4.549 14.02078 13.897 2.797 81.97836 1.687 0.77 9 4.68629 13.905 5.504 29.653

53 9.394 -1.458 -25.83920 9.168 -1.780 -26.258

105 4.435 -0.442 10.75330 19.499 -0.222 -49.37419 11.833 -4.218 -24.08276 5.488 -0.496 12.09235 8.989 -3.022 -23.18053 15.904 -0.310 48.62419 3.524 2.196 6.67464 6.284 1.287 21.16037 9.412 2.499 28.85262 10 .152 -0.595 -48.26022 11.087 0.032 -20.84514 1.933 0.508 -4.19922 26.045 -4.720 70.21220 6.019 -2.383 -14.54024 22.925 -1.103 42.9635 3.335 -0.294 4.928

38 4.716 0.790 11.71344 10.490 1.500 25.678

35 6.044 1.698 18.94685 3.958 0.595 19.11445 2.526 0.141 8.63257 9.894 3.363 28.16525 4.795 -0.125 8.69822 4.940 0.086 - 1 1.06622 5.480 -0.632 -8.66439 2.165 0.535 -5.46452 9.020 -1.217 39.36173 8.416 -0.444 -21.92993 5.240 -0.687 -21.47348 9.313 -2.233 -29.16226 7.301 -0.286 -17.91 I24 15.706 0.267 -32.02239 2.763 0.253 -8.28326 3.804 0.597 8.02013 17.811 9.884 37.87739 4.947 0.742 -12.166

28 4.382 0.972 10.243

20 4.775 2.039 10.61765 10.084 2.446 22.160

50 7.427 1.110 15.662


10/13

8906TABLE IX (Continued)

The Journal of Physical Chemistry, Vol. 9 4 , No. 26, 1990 Mayo et al.

atoms, A bonds, A angles, deg torsions, degmolecule N a t m tRMS Aatm Matm Nbnd Rbnd Abnd Mbnd Nang Rang Aang Mang Ntor Rtor Ator Mtor

A H C D L A 14 0.075 0.067 0.141 16 0.033 0.019 -0.051 26 1 . 8 1 3 0.040 -4.555 37 3.403 0.400 8.096A H D I T X 26 0.185 0.155 0.441 30 0.037 0.009 0.076 48 1 . 8 1 7 0.279 - 5 , 8 3 3 71 5 . 5 8 8 -1.256 -22.254"Cambridge notation, see Figure 1. Here N X i s the number of terms, R X is the rms error, AX is the average error, and MX i s the maximumerror for X = atoms (aim), bonds ( bnd) , angles (ang ), a nd torsions (tor). The total rms error i n the Cartesian coordinates is indicated by trms.Bonds arc o r harmonic form (4), angles are of harmonic theta form ( I O ) , torsions are single term form ( I 3). inversions are of spectroscopic form (29).nonbonds a r c of Lennard-Jones fo rm (32), charges are not included. bNu mber of molecules.

where i and Q, are charges in electron units, R is the distancein A , c is the dielectric constant (usually c = I ) . and 332.0637converts E to kcal/m ol. Interactions are not calculated betweenatoms bonfed to each other ( 1 .2 interactions) or involved in ang leterms ( I ,3 interactions) since these are assumed to be containedi n the bond and angle interactions.A serious difficulty is how to predict the charges. For smallmolecules it has been possible to fit charges to th e electrostaticpotentials calcul ated from high-quality Hartree-Fo ck wavefunctio ns.'4 For good basis sets the results agre e with observedelectrical moments and should be the best choices moleculardynamics simulations. A method for predicting accurate chargesof large molecules is desperately needed. Some progress has beenmade;",'* however, there is not yet a general method. In this paperwe either ignore charges or use the Gasteiger" estimates forcharges.The calculations reported in this paper are all for moleculesin a vacuum or for molecular crystals, and hence we use c = 1 .In simulations of biological systems it is common to ignore solventand to use t = coRij where to s a constant, often 1 O, 4.0, or 8.0)as an approximate way to represent the effects of the solvent. Thisis needed in order to stabilize charged residues and phosphatesand to include the proper bias toward internal hydrophobic in-teraction s. As the simplest way to simulate solvation of charge dgroups by the solvent, we recommend constructing a locally neutralcluster by addition of counterions (Na+ or CI-) to charged groupsnot involved in salt bridge s. Thi s allows us to use c = 1 in (37)so that local electrostatic effects can have their full effect. (Betterof coursc is to consider the solvent explicitly.) However, i n thispaper wc omi t counterions in order t o simplify comparisons be-tween various force fields.I . Hydrogen Bonding. Within the constraint that charges andvan der Waals interactions must be centered on nuclei, it is difficultto obtain a force field that (a ) correctly predicts the structure andbond encrgy of H 2 0 imer, and (b) predicts the sublimation energyand structure of ice while (c) using the van der Waals parametersappropriate for non-hydrogen-bonded systems. As a result,DREIDING uses a special hydrogen bond term to describe theinteractions involving a hydrogen atom (denoted H-HB) on thevcrq elcctronegative atoms ( N , 0, F) associated with hydrogenbonds. When the hydrogen on such a donor is close to a n elec-tronegative acceptor atom ( N , 0, F), we (a) explicitly includeall van der Waals and electrostatic interactions corresponding tothe charges on the various atoms (including the hydrogen) andin addition, and ( b) include a CH AR MM -lik e hydrogen bondingp o t ~ n t i a l ~ ~ . ~ ~

Here O D H A is the bond angle between the hydrogen donor (D),the hydrogen (H ), and the hydrogen acceptor (A) , while R,, i5the distance between the donor and acceptor atoms i n A) .The values of Dhband Rhb depend on the convention for as-signing charges. Thus, Gasteiger charg es lead to QH 0.21 for(16) ( a ) Cox, S R. ; Williams, D. E. J . Comput. Chem. 1981. 2 . 304. ( b )Chirlian. L . E . : Francl, M. M. Ibid. 1987. 8, 894.(17 ) (a) Gasteiger, J.; Marsili, M . Tet rahedron 1980, 36, 3219. ( b ) Ex-icnded to phosphorous by Paul Saze (parameters: A = 7.40. B = 3.0, c =

I ,O). c ) For systems wi th formal charges, charges for the neutral moleculewcrc calculated first an d t h e n t h e appropriate net charge was added to thcaffcctcd a t o m s .(18) Rap#, A . K. : Goddard 1 1 1 . W . A . Charge Equilibration in MolecularDyn:imic\ Simulations. J P h j ~ h e m . To be submi t t ed for publication.

H 2 0 , whereas Hartree-Fock calculations lead to QH = 0.3416aor 0.4016b nd experiment leads to QH = 0.33. Th e resulting valuesfor Dhb and Rh b based on H 2 0dimer) are given in Table v. Notei n Table I I that the van der Waals well depth for H-HB isdifferent than for H-.J . DR EID ING IA. The initial stage of developing DR EID ING( 1984-1 985) utilized somewhat simplified energy expressions.This early force field (denoted D RE ID IN G/ A) has been usedfor a nu mber of calculations and leads to reasonable geometries.Differences from DR EID IN G are as follows.(a) Bond stretch. Only the harmonic form (4 ) was used, withK,j = lo00 (kcal/m ol)/A2 for all bonds. The atomic radii of TableV I are used.(b) Angle bend. Th e simple harmonic angle form 1 1 ) was usedwith K , j , = 100 (kc al/m ol)/ rad 2 for all angle terms. All X-3bond angles were taken as tetrahedral (0; = 109.471') except S-3and S-31 as indicated in Table VI .(c) Inversion. The CH AR M M form 2 5 ) was used with Kin"= 40 (kcal/mol)/rad2 for nonplanar molecules (X-3) and19 Kin"= 300 (kcal/mo l)/rad2 for planar molecules (X-R, X-2). TheX-2, X-R centers have 4o = 0 and X-3 centers have $o = 35.264'

i f J and K are not hydrogens and 4o = 31.4' i f J or K is ahydrogen.(d) Torsion. The form ( 1 3) was used but the barriers are takenas 20 kcal/mol for double bonds J , K = X-2 or X R ) , 1 kcal/molfor X-3-X-3 single bonds, and 0.2 kcal/mo l for other cases. N odistinction was made for the oxygen column.(e ) van der Waals. Lenna rd-Jo nes 12-6 was used (3 1) withthe parameters in Table VI 1 .(f) Electrostatics. Charges based on CH AR MM /EF 14 a wereused for peptides and nucleic acids. Charges were generallyignored Tor other sytems.(g) Hydrogen bonds. The hydrogen atoms (H-HB) bondedto electronegative atoms (N and 0) were described with thehydro en bond form (38) (using Dhb = 9.5 kcal/mol and Rhb =2.75 when close to electronegative ato ms ( N and 0 . N oexplicit charges or van d er W aals interactions were included forsuch hydrogens.111. Discussion

We consider the D RE IDI NG force field to be the simplestgeneric force field capab le of providing accurate geometries fororganic, biological, and m ain-group inorganic systems. W e havedeliberately used the fewest possible number of parameters andcouched the choices in terms of general hybridization concepts.Thus, all geometric parameters arise from either addition of bondradii or angles of the simplest hydride s (AH,, H,A-BH,). Only:I single force constant each is used for bonds, angles, and i n -versions, and only six values for torsional barriers ar e used. Th efocus hcrc has been on the B, C, N , 0, and F columns of theperiodic table, with a few other elemen ts (e.g., N a, C a, Zn , Fe)added that are commonly used for simulations of biologicalsystems. The parameters have been biased toward the first-rowclcmcnts (and carbon).The valence energies calculated here can be considered as straincncrgics and hence one could calculate heats of formation byadding in Benson's g roup additivity energies.20 We have not yetimplemented this procedure.

( 19) This value must be high enough to ensure that planar centers remainI n previous D R E I D I N G / A calculations. a value of 1000 (kcnl/lanar .moI)/rad*w a ) uacd.


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DREIDING: A Generic Force FieldTABLE Commrisons of Error (in A ) from Various Force Fields for the 76 Molecules of Figure lo

The Journal of Physical Chemistry, Vol. 94, No. 26, 1990 8907. . -

molecule standard Morse bond cosine angle exponential vdw charges f = R charges L = 1 DREIDING/A0.247 0.257 0.3320.259totalAAXTHPABAXESABBUMOIOABINORO2ABlNOSOlABTOETABZTCXACADOSACAFLR

ACAN I LO 1ACARAPACBNZAOIACBUOLACClTRlOACDXURACENAP03ACFPCHACFUCNACGLSPACGLUA I IACHGALACHlST2OACHNAPIOACHTAR 10ACIMDCACI NDNACINSTACKYNUACMBPNACMEBZACMTDEACNORTACNPACIOACNPECACONTNIOACPENC IOACPPCAACPRET03ACPYNSACRAMSACSALAOIACSESOIOACTANDACTHBZACTHCPACTOLDACTYSNACURIDACVCHOACXMOLACXMPRACYGLY I 1ACYTIDADELOXIOADENOSIOADFGLPADGSMHADHELAIOA D M A N NADM HEPADM I NAADMOPMADRTARADYPNLAEBDODIOAENLANIOAFCYDPAFMSCYAFURPO IOAFUTDZIOAFUTHUAGALAMIOAGLUAMIOAHARFUAHCDLAAHDITX

0.2350.3340.1120.1130.0900.0750.4140.3510.1480.1470.0700.3400.1460.4490.2650.1410.0230.0730.2750.3410.1900.1800.3360.0780.1480.0230.0720.2240.3910.2590.1750.2540.2660.0500.8440.1860.2880.2250.2900.2630.8670.0970.21 10.3790.2970.0930.0450.7740.1260.1090.4080.6710.0950.2020.1270.0880.0590.3400.0920.1220.0800.0610.6770.1390.3540.2560.4200.4130.3060. I400.2470.0670.1090.3280. I200.0750. I85

0.2360.3370.1190.1150.0900.0760.4200.3500.1470.1500.0700.3430.1510.49 10.2600.1410.0240.0770.2760.3570.1870.1800.3360.0800.1510.0240.0720.2380.3670.2620.1760.2580.2680.0500.8530.1940.2890.2260.2850.2630.8560.0960.2140.3810.3070.0930.0470.7730.1280.0920.4130.6650.0950.2080.1350.0910.0600.3450.0950.1200.0850.0620.670.1380.3480.2580.4320.4150.3070.I380.2470.0670.1IO0.3300.1210.0770.192

0.2380.3410.1170.1 I60.0900.0760.4270.3 120.1510.I740.0690.3420.1470.4650.2660. I350.0220.0750.2770.3550.1910.1860.3390.0860.1490.0230.0720.2510.3870.2630.1770.2460.2690.0500.8560.1960.3450.2250.2910.2730.8710.0990.2150.3800.3020.0960.0540.7710.1250.1100.41 10.6660.0970.2030. I300.0920.0580.3490.0930.1210.0820.0590.6660. I420.3540.2560.4190.4200.3070.1410.2460.0670. I090.3290. I220.0750.185

0.2480.3400.0870.0790.0850.0680.2730.4240.1580.2920.1200.3370.1900.5230.1690.1300.0240.0560.2620.2650.1790.1690.3290.0640.1440.02 10.0690.1990.2810.2500.2 IO0.2620.2520.0500.7840.1640.2900.2410.2430.2570.770.7270.2200.3840.3980.090.0700.7670.1300.0780.3930.6500.090.2000.1 IO0.7000.0540.3260.0930.1180.0700.0670.9100.1180.2820.2490.3620.3970.2830.1220.2440.0650.2950.3200.1 180.0670.I66

0.2640.11 10.1120.0850.0680.4040.3560.1410.1480.0690.3400.1680.5360.1780.1500.0230.0720.2930.3420.1740.1740.4630.0780. I480.0250.0700.2360.3910.1890.1540.2720.2650.0500.8300.I860.2880.2880.2940.3180.8980.3320.2080.3650.3050.0930.0440.7910. I280.0780.4130.5210.0930.2210.1600.6360.0520.3 150.0860.1470.0740.0600.6080.I340.3580.2650.4170.5 180.2520.1350.2440.0630.3180.2960.1390.0780.186

0.1 IO0.1120.0810.0690.4030.3520.1380.1520.0680.3440.1790.68 10.1780.1670.0230.0720.3100.3380.1840.1720.2210.0780.1730.0260.0700.2290.41 70.2430.1530.2890.2660.05 I0.8IO0.1760.3080.2940.2900.3251.0030.3230.2080.3530.3020.0930.0450.7970.1300.0770.41 80.5100.0940.2220.1850.6270.0540.3070.08 10.1510.0770.0600.6 I40.1400.3590.2700.4 I61.3250.2290.1320.2430.0620.0900.2900.1400.0790. I85

0.4170.I090.1070.1 I 10.1 I50.5570.4640.2090.3190.1500.2770.2270.7860.2990.7730.0250.2770.4000.5150.1460.1990.5370.0890.1510.0250.0780.3111.4660.3100.4870.5290.3020.0521.0830.1890.6540.4950.8450.2250.4470.4020.1780.4640.4290.1390.1600.4730.1610.2800.3 180.7920.0820.1740.1620.5580.0610.6500.1280.1560.1220.0710.4470.6590.3590.2050.4310.3510.3580.1650.230.1150.1250.5680.1600.0830.199

The standard force field has bonds of harmonic form (4), angles of harmonic theta form IO), torsions of single term form (13), inversions of spectroscopicform (29). nonbonds of Lennard-Jones form (32), and charges not included. Each other column is labeled with the chan ge from the standard.


12/13

8908 The Journal of Physical Chemi stry, Vol. 9 4 , N o . 26, 1990We envision a hierarchy of force fields2' where the simpleversions (DR IE DI NG ) allow rapid considerations of new struc-turcs and compositions while the m ore complex versions are tunedto accurately predict properties (e.g., vibrational frequencies) forparticula r systems. To describe vibrational frequencies accuratelywill certainly require more sophisticated force fields. Thu s wcmust add angle-stretch, s tretch-stretch, and angle-angle termsto the bond angle expansion (IO) and additional terms to thetorsion expression ( 1 3). Such terms are allowed in our programsand individual parameters have been optimized for specificmolecules;22however, we have not yet generalized these results

to obtain a more generic force field suitable for vibrational fre-quencies. I n addition, force constants and torsional barriersgenerally decrease going down a column of the periodic table.To treat main-group metals (Li, Be columns) and transitionmetals, the force fields must emphasize oxidation state and theinterplay of attractive Coloumb interactions with short-rangerepulsion (van der Wa als). Here the role of valence interactio ns,particularly the four-center term s (torsion and inversion), are lessimportant, while the delocalization of charge characteristic ofunsatur ated systems becomes dominant. We leave these metallicsystcms to later development^.^^IV. Applications

A . Structuresfrom the Cambridge Data Base. In order toprovide a test of its general efficacy, we used the DREIDINGforce field to predict the str ucture s of the 7 6 organic moleculesin Figure I (the first 76 structures of the Cambr idge Data Base24having R factors below 0.05). This includes a variety of bondingsituations with H, C, N , 0, F, P, S, CI, and Br (many structuresinvolve phosphates, sugars, sulfates, sulfones, nitrates, carb onates,amides, ctc.). Geometry op timizations were carried out usingB I O G R A FVersion 2.20 on the four-processor Stardent Titan Su-percomputer workstation (using Fletcher-Powell minimization)while graphics manipulations were typically carried out on theSilicon Graphics 4D/25 workstation.I n many of the 76 molecules there are strong intermolecularhydrogen bonds or salt bridges so that the structure of the freemolecule might differ from that of the crystal. On the other hand ,optimization of the structure of the molecule i n the crystal en-vironment is not a complete test of the force field because in-termolecular packing, electrostatics, and hydrogen-bonding i n -teractions will restrain the structu res from changing. Consc-quently, i n each case we extracted one complete molecule fromhe unit cell and optimized the struc ture i n a vacuum.We carried out calculations on the complete set of moleculesfor scvcral options of the DR El Dl NG force field. T he bonds weretreated either as harmonic or M orse, the angles were treated asharmonic i n either theta or cosine theta. The van der Waals termswere treated either as Lennard-Jones 12-6 or exponential-6, andthc charges were either ignored or included. When included, thecharges were calculated by using the Gasteiger" procedure andw i t h either c = 1 or c = R . The cases i n italics above wereconsidcrcd as the standard. I n each case it is the simpler option.Thc rcsults are i n Table V I I I . Thoreau would be happy. Thesimplest case leads to the most accurate result, trms = 0.235(where trms is the total rms error for all atoms of all 76 structures).Thus, usc of Morse bonds increases trms to 0.236, cosine-anglcterms increase t rms to 0.238, while X6 van der W aals increasestrms to 0.248.The simple DR EI DI NG /A force field does reasonably well,with trms = 0.332. Here the error i n bonds is about the samc(up from 0.035 to 0.036 A rms) , but the error in angles is higher(3.683 ' rms rather than 3.224") and the error in torsions is much

20) Benson, S. W. Thermochemical K inet ics ; Wiley: New York, 1976.(21) Rappe. A . K . ; Goddard 111, W . A . ; Casewit, C. . ; Mayo, S L.(22) Dasgupta, S.; Goddard 111, W. A . J . Chem. Phys. 1989, 90, 7207.(23) Li. M.; Goddard I l l W. A . The Interstitial Electron Model forMetals. Ph),s. Rev. B, i n press.(24) Kcnnard, O., et ai. Cambridge Crystalographic Data C entre, Univ-crrity Cliemical Laboratory, Lensfield Road, Cambridge, CBZ I EW, U K .

Unpublishcd results.

Mayo et al .TABLE XI: Rotational Barr iers (kcal/mol) about Single Bonds

experiment calculatedmolecule" periodicityb barrierC barrie rC Hi-C HC H 3-C H 2C HC H 3-C H2C H2C H iC H jC H I -C H IC H ,C H3-CH (CH )2C H -C H 2FC H -C H 2CIC HI-CH21C HJ-C F jC H3-CCI 3F C-C F

C H 3-C(C H3)3

C H 3-C H 2Br

C H ,-Si HC 14 j-GeH3C 14 j-C H2SiHC HJCH,-SiH3C i -Si(CH3)3CH I-N H2C H3-N H C HC H -PH,CHJ-OHCH3-SHCFj-OFC t i -OCH jC H 3 - K H 3C Hj-C H=CH2C H -C H = OC i -C(OH)=OC H -C (OCH 3 =0NH,-CH=ON (C H ),-CH=O

C H 3-N (C H ) 2

CH3-SeH

CH3-SeCH,

v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v 3v2v2

2.882 O.O1O)d3.4'3.4'3.8'3.9'4.7'3.287 (0.03)d3.68c3.68'3.623 ( 0 . 1 5 ) d3.16 0.15.10 (0.3)d3.92'1.7fI .24'2.625 O.O1)d1.979 (0.007)d1.4'1.98'3.62'4.4d1.96'0.373 (0.003)d0.445 O.OOO)d0.957 0.05)d3.900d2.630 (0.007)d2.099 (0.003)d1.498 O.OO1)d1.995'1.143d0.48 d0.284d1 8 (3 )c19.6 ( 1 . 5 )

2.8963.3763.4103.8223.9955.07 13.1723.4873.3453.3363.7684.85 15.5622.2962.0373.8052.5173.1912.0852.9163.5341.9572.1 172.3762.1833.6083.0342.9022.60i0.7530.9481.0261.03024.50621.037

"Th e dihedral pair is indicated by the single line. bSym metry as-aumcd in experimental analysis. 'The value in parentheses indicatesestimated experimental uncertainty. Reference 2 5 . Reference 26.higher ( I 3.309' rms rather than 8.948").Using cxplicit charges with t = 1 leads to worse results (0.257)while explicit charges with c = E (0.247) is worse than no charges.I t appears that the major problem with charges is that intermo-lecular electrostatics are more important than intramolecularelectrostatics. Thu s, the molecules that need charges for a gooddescription of structure need also to be treated as crystals. Thus,for these systems the acrual error i n our prediction of molecularstructure (for isolated molecules) i s probably much smaller thanthc trms quoted (which is based on the crystal structure).I n Tables IX and X we tabulate the results for DRElDlNGusing the stand ard options: the harmonic form of bond stretch( 5 ) , he harmonic theta form 1 1) for angle bend, the single termtorsional form (1 3), the sp ectroscopic inversion ( 29), th e L en-nard-Jones 12-6 nonbond form (32), and no charges.For each molecule we list the rms error i n the Cartesian co-ordinates (trms), the number of bond, angle, or torsion terms(nbnd, nang, ndih), the aoerage error for each quantity (Abn d,Aang, Adih), the rms error for each quantity (Rbnd, Rang, Rdih),and the maximum error for each quantity (Mbnd, Mang, Mdih).Th c total error s over the whole set of 76 m olecules are also listed.Thc total rms error is 0.235, while only five cases are worse than0.5: A CN PEC with 0.844, ACR AM S with 0.867, ACT YSN with0.774, A C X M P R with 0.671, and ADMOPM with.0.677. Thefirst row of Table IX lists the total errors over the ful l data set.The average error in the bonds (out of 1483) is 0.009 A , thcaveragc crror in the angles (out of 21 74) is b57', and the averagecrror in thc torsions (out of 2188) is 0.23', indicating that th egcncral scales for these quantities are appropriate. The rms errori n bonds is 0.035 A, i n angles is 3.2', an d in torsions is 8.9".Of thc five bad cases ACN PEC , ACT YSN , and ACX MPRhave intermolecular hydrogen bonds that disappear for an isolatediiiolcculc. Thu s, for the crystallin e form.29 the trms drop s from


13/13

DRE IDI NG : A Generic Force F ield The Journal of Physical Chemistry, Vol. 94, No. 26, 1990 8909TABLE XII: Conformational Energies (kcal/mol) for VariousMoleculesa TABLE XIII : Relative Energies (kcal/mol) of VariousStereoisomersa

~~ system exptlb calcdbutane, gauche/antimcthylcyclohexane. axial/equatorialphenylcyclohexane,axial/equatorialfluorocyclohexane, axial/equatorialchlorocyclohexane. axial/equatorialbromocyclohexane, axial/equatorialnitrocyclohexane, axial/equatorialcyclohcxanol, axial/equatorial1,4-dichlorocyclohexane, xial/equatorialmethyl ethyl ether, gauche/anticyclohcxane, twist-boat/chair4,4,5-trimethyl- ,3-dioxolane, axial/equat

0.76 0.751.8 (0.2) 1.293.00 4.510.20 0.330.40 0.820.50 0.521.20 I .580.50 0.250.20 1.65I .50 1.565.7 (0.3) 7.72orial 1.30 1.48

The higher energy form is listed first. bReference 270.844 o 0.372 or ACNPEC, from 0.774 o 0.257 or ACTY SN,and from 0.671 o 0.308 for ACXM P R. For ADMOP M theexperimental stru cture has a very short distance of 2.4A froma phosphate oxygen to the hydrogen on the aromatic carbonflanked by two nitrogens. Thi s suggests a very strong electr ostati cinteraction (almost a hydrogen bond) that is underestimated sinceno explicit hydrogen bond ter m is included for this interaction.Th e crystalline form of AC RA MS has extensive intermolecularring stacking tha t is lost in the isolated molecule. Thus , for thecrystalline form, trms drop s from 0.867 o 0.162.We conclude from these comparisons that the DREIDINGforce field provides useful predictions for structur es. Alth ough ,in these benchmark s, use of charge s leads to slightly worse results,we recommen d t ha t charg es be used in all studies involving in-teractions of molecules.B. Conformationsof Organic Molecules. In Table X I we showthe single-bond rotational barriers calculated with D RE lD lN Gan d com pare with e ~ p e r i m e n t . ~ ~ , ~ ~Experimental results fromthe 1982 eview (ref 25, enoted as d ), should be considered morereliable than results only contained i n the 1968 eview (ref 26,denoted as e)] DR ElD lN G uses only one value (2.0 kcal/mol)for explicit single-bond terms, b ut t he trends ar e reasonably wellreproduced. For alkanes the results are quite good (errors i nkcal/mol of 0.01 for ethane, 0.0 for propane, 0.0 for both torsionsi n butane, 0.1 for isobutane, and 0.4 or neopentane). ForCH3-CH2X , where X s a halogen, the predicted barrier is lowby 0.1 to 0.3 kcal/ mol. For C-Si an d C-Ge barriers, the predictedbarriers ar e about 50% too high, indicating that the torsionalbarrier should be smaller than 2.0 or the Si and G e rows of theperiodic table. Th e rotational barriers about peptide bonds areIO-20 high (experimental 18 and 19.6versus calculated 24.5and 21 .O, espectively).In Table XI1 we show the difference in energy for variousconfo rmatio ns of several molecules. Th e signs are always correctand th e magnitudes ar e reasonably good.In Table Xlll we show the difference in energy for variousstcrcoisomers. Th e signs are always correct and the mag nitudesare reasonably good.These results indicate that the torsional parameters are rea-sonably well-defined for organic systems and that the simple

(25) Demaison, J . et al., Molecu lar Consrants, Springer-Verlag: NewYork, 1982; Vol. 14 of Group I I Landolt-Bornstein Tables.(26) Lowe, J . P. f r o g . f h y s . Org. Chem. 1968,6, I .(27) Engler, E. M.; Andose, J . D.; Schleyer, P.V.R. J. A m. Chem. SOC.1973, 95. 8005.(28) This leads to 6E = 1/2K 6B)2or B near linear, whereas ( loa) wouldlead to bE - /8C 6Q4.(29) These calculations were carried out using periodic boundary condi-tions wi th convergence acceleration allowing all atoms to optimize.

system1,3-dimethylcyclobutane, is/transI ,2-dimethylcyclohexane, cis/trans1,3-dimethylcyclohexane, is/transI ,4-dimethylcyclohexane, cis/transI , .3.5-tetramethylcyclohexane, is/transbicyclo[3.3.0]octane, cis/transdecalin. cis/transpcrhydroanthracene, cis-transbpcrhydroanthracene, trans-anti-transbperhydroanthracene, cis-anti-cis*pcrhydroanthracene, cis-syn-cisb

exptl-0.30I .86-2.001.90-3.70-6.41 .oo2.80

4.105.608.70

calcd-0.060.98- I .341.28-4.13- I I .05I .76I .79

8.793.776.58Th e energy difference is tha t of the first species minus the second.Rclativc to trans-syn-trans.

scheme of section I IE incorporates the various features requiredfor hydrocarbons. For simplicity we have used the sa me param-eters for all other rows and columns of the periodic table. Thisia oversimplified as indicated by the increased errors for thesesystems but consistent with the DR EID ING philosophy of notreadjusting force constants for particular combinations of elements.C. Other Cases. To test the parameters for borons we cal-culatcd the structur e of diborane (B 2H6) where the bridginghydrogcn is type H-b, and B-3 and H are used for the other atoms.Assuming each B-3 is bonded to four hydrogens (no formal B-Bbond) leads to bond distances of 1.21 nd 1.39A for terminal andbridging BH bonds (experimental6b 1.201 and 1.320A). Thecalculated bond angle at the bridging H is 81.8O experimentaFb83.8) which leads to a B-B distance of .82A (experimental6b1.763A).V. Conclusions

We find that DREIDING leads to accurate geometries andreasonably accur ate barriers for various organic systems. As aresult, we expect D RE ID IN G to be useful in predicting structuresinvolving new combinations of elements and should be easilycxtendable to new atoms. The current uncertainties in predictingthe distribution of charges in molecules and in estimating the vander W aals interactions a re limitations t hat we believe are as seriousas the restricted set of parameters used in DREIDING.Th e next level of sophistication in developing gen eric force fieldsis to alter thc parameters (force constants, barriers) to changesmoothly as a function of rows and columns. We leave this fora later study.Acknowledgment. We thank Professor Anthony K. Rappt andDr. Carla J . Casewit for providing stimulating discussions andcarrying out tests of these force fields while on sabbatical atBioDesign. W e thank Drs. Walter E. Reiher 1 1 1 and Paul W .Saxe for stimulating discussions and assistance in the calculations.We thank Adria McMillan and C arol Scrivnor for typing variousversions of the text and Dr. Mar ie Ary for reformatting the textand preparing the 76 structures in the figures and the long tables(Tables VIII-XIII). Initial development of the DREl DlN G forceficld was carried out a t Caltech and supported by a g rant from

the Department of Energy, Energy Conversion and UtilizationTechnologies Program (DOE-ECUT). More recent developmentsof thc DRElDlNG force field were carried out at BioDesign.Registry No. B, 7440-42-8; C, 7440-44-0;N , 17778-88-0; 0, 17778-80-2; F. 14762-94-8; AI, 7429-90-5; Si, 7440-21-3; P, 7723-14-0; S.7704-34-9;CI. 22537-1 5-1; Ga, 7440-55-3; Ge, 7440-56-4;As, 7440-38-2:Sc. 7782-49-2: Br. 10097-32-2; In. 7440-74-6;Sn, 7440-31-5; Sb, 440-36-0; Te, 13494-80-9; 14362-44-8;Na, 7440-23-5; Ca, 7440-70-2; Fe,7439-89-6; Zn, 7440-66-6.

1990_mayo et al._dreiding a generic force field for molecular simulations

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