1 Contents. 1. Contents i. 1. Introduction Forcefields 9

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1 1 Contents 1. Contents i 1. Introduction 1 Who should use this documentation What can simulation engines do? Energy minimization Molecular dynamics Other forcefield-based calculations What are forcefields and simulation engines? Using this guide Additional information Typographical conventions Forcefields 9 The potential energy surface Empirical fit to the potential energy surface The forcefield The energy expression Forcefields supported by MSI forcefield engines Main types of forcefields Advantages of having several forcefields Primary uses of each MSI forcefield Second-generation forcefields accurate for many properties27 CFF91, PCFF, CFF consistent forcefields MMFF93, the Merck molecular forcefield Rule-based forcefields broadly applicable to the periodic table 35 ESFF, extensible systematic forcefield UFF, universal forcefield VALBOND Dreiding forcefield Classical forcefields AMBER forcefield CHARMm forcefield Forcefield-Based Simulations/September 1998 i

2 1. Contents CVFF, consistent valence forcefield Special-purpose forcefields Glass forcefield MSXX forcefield for polyvinylidene fluoride Zeolite forcefields Forcefields for sorption on zeolites Forcefields for Cerius 2 Morphology module Archived and untested forcefields Preparing the Energy Expression and the Model 73 Using forcefields Selecting forcefields Assigning forcefield atom types and charges What are atom types in forcefields? Assigning atom types to a model Assigning charges Parameter assignment Determination of which parameters are used with which atom types Automatic assignment of values for missing parameters86 Manual parameter assignment Using alternative forms of energy terms Removing terms from the energy expression Scaling or editing any selected type of term Alternative bond terms Scaled torsion terms Inversion terms Nonbond functional form Hydrogen bonds and hydrogen-bond terms Bond angle cross terms vs. Urey Bradley terms Applying constraints and restraints When to use constraints/restraints Fixed atom constraints Template forcing, tethering, quartic droplet restraints, and consensus conformations General internal-coordinate restraints Distance and NOE restraints Distance and angle constraints in dynamics simulations. 109 Angle restraints Torsion restraints Inversion, out-of-plane, and chiral restraints Plane and other geometrical constraints and restraints112 Modeling periodic systems Minimum-image model Explicit-image model ii Forcefield-Based Simulations/September 1998

3 Crystal simulations Bonds across boundaries Handling nonbond interactions Combination rules for van der Waals terms The dielectric constant and the Coulombic term Nonbond cutoffs Cell multipole method Ewald sums for periodic systems Minimization 153 General minimization process Specific minimization example Line search Minimization algorithms Steepest descents Conjugate gradient Newton Raphson methods General methodology for minimization Minimizations with MSI simulation engines When to use different algorithms Convergence criteria Significance of minimum-energy structure Energy and gradient calculation Vibrational calculation Application of minimization to vibrational theory Vibrational frequencies General methodology for vibrational calculations Molecular Dynamics 189 Integration algorithms Introduction Criteria of good integrators in molecular dynamics. 193 Integrators in MSI simulation engines The choice of timestep Integration errors Example 1 Two colliding hydrogen atoms Example 2 Energy conservation of a harmonic oscillator 204 Statistical ensembles NVE ensemble NVT ensemble NPT and NST ensembles NPH and NSH ensembles Equilibrium thermodynamic properties Forcefield-Based Simulations/September 1998 iii

4 1. Contents Temperature How temperature is calculated How temperature is controlled Pressure and stress Units and sign conventions for pressure and stress How pressure and stress are calculated How pressure and stress are controlled Types of dynamics simulations Quenched dynamics Simulated annealing Consensus dynamics Impulse dynamics Langevin dynamics Stochastic boundary dynamics Multibody order-n dynamics Constraints during dynamics simulations The SHAKE algorithm The RATTLE algorithm Dynamics trajectories General methodology for dynamics calculations Stages and duration of dynamics simulations Dynamics with MSI simulation engines Restarting a dynamics simulation Free Energy 251 Relative free energy theory and implementation Finite difference thermodynamic integration (FDTI).251 Relative free energy methodology Absolute free energy Theory and implementation Example: Fentanyl Analysis of results A. References 273 B. Forcefield Terms and Atom Types 283 Forcefield term definitions AMBER atom types Standard AMBER forcefield Homan s carbohydrate forcefield CFF91 atom types CHARMm atom types CVFF atom types iv Forcefield-Based Simulations/September 1998

5 CVFF_aug atom types ESFF atom types PCFF additional atom types Index Forcefield-Based Simulations/September 1998 v

6 1. Contents vi Forcefield-Based Simulations/September 1998

7 1 Introduction This Forcefield-Based Simulations documentation is a general guide to all MSI s simulation engines, that is, software products whose computational work is based on a forcefield. These include CHARMm, Discover, and the Open Force Field (OFF) modules, which are run through the molecular modeling programs (i.e., graphical interfaces) shown in Table 1. Table 1. Simulation engines a within MSI s molecular modeling programs b Molecular modeling Simulation engine program and release number CHARMm Discover c OFF Cerius d Insight II Insight II 97.0 QUANTA standalone e a See definitions under What are forcefields and simulation engines?. b Discover and OFF each offer a choice of several forcefields (see Table 3); the CHARMm program gives access only to the CHARMm forcefield in QUANTA and standalone, only to MMFF in Cerius 2, and is used only in specialized modules in Insight II. c Discover exists in two versions: one written in FORTRAN (series 2.8.x, 2.9.x and earlier ; referred to as FDiscover) and the other in C (series 3.0, 3.1, 3.0.0, 4.0.0, 95.0, 96.0, 97.0; referred to as CDiscover). CDiscover and FDiscover are specified in this documentation only where the FORTRAN and C Discover programs have different capabilities. FDiscover and CDiscover (in Insight II) are accessed through the Discover and Discover_3 modules, respectively. d CDiscover only. e CHARMm and Discover can also be run without the assistance of a graphical molecular modeling program. Forcefield-Based Simulations/October

8 1. Introduction Who should use this documentation Prerequisites This guide is written mainly for the typical scientist-user of MSI s simulation engines. Although these programs are written to run with reasonable default values for basic simulations, you should read this guide if you want to make efficient use of the programs, obtain the best results possible, and understand the results. You should already be familiar with: The system and windowing software on your workstation. How to use the particular MSI molecular modeling program that contains the desired simulation engine (Cerius 2, Insight, and/or QUANTA). Your workstation should have: A licensed copy of Cerius 2, Insight, and/or QUANTA as well as of the appropriate simulation engine. A directory in which you have write permission. What can simulation engines do? Energy minimization Typical uses of energy minimization include: Optimizing initial geometries of models constructed in a molecular modeling program such as Cerius 2 or Insight. Repairing poor geometries occurring at splice points during homology building of protein structures. Mapping the energy barriers for geometric distortions and conformational transitions using torsion forcing to obtain Ramachandran-type contour plots for proteins or RIS statistical weights for polymers. 2 Forcefield-Based Simulations/October 1997

9 What can simulation engines do? Evaluating whether a molecule can adopt a template conformation consistent with a pharmacophoric or catalytic site model ( template forcing ). Molecular dynamics Typical uses of molecular dynamics include: Searching the conformational space of alternative amino acid sidechains in site-specific mutation studies. Identifying likely conformational states for highly flexible polymers or for flexible regions of macromolecules such as protein loops. Producing sets of 3D structures consistent with distance and torsion constraints deduced from NMR experiments (simulated annealing). Calculating free energies of binding, including solvation and entropy effects. Probing the locations, conformations, and motions of molecules on catalyst surfaces. Running diffusion calculations. Other forcefield-based calculations In addition, simulation engines can be routinely used for: Calculating normal modes of vibration and vibrational frequencies. Analyzing intramolecular and intermolecular interactions in terms of residue residue or molecule molecule interactions, energy per residue, or interactions within a radius. Calculating diffusion coefficients of small molecules in a polymer matrix. Calculating thermal expansion coefficients of amorphous polymers. Calculating the radial distribution of liquids and amorphous polymers. Forcefield-Based Simulations/October

10 1. Introduction Performing rigid-body rms comparisons between minimized conformations of the same or similar structures or between simulated and experimentally observed structures. What are forcefields and simulation engines? Simulation engine defined Forcefield and energy expression defined Importance of the forcefield in simulations The fundamental computation at the core of a forcefield-based simulation is the calculation of the potential energy for a given configuration of atoms (and cells, if requested and possible). The calculation of this energy, along with its first and second derivatives with respect to the atomic coordinates (and cell coordinates), yields the information necessary for minimization, harmonic vibrational analysis, and dynamics simulations. This calculation is actually performed by the simulation engine, or forcefield-based program. Simulation engines are the computational packages that handle the application of forcefields in minimization, dynamics, and other molecular mechanics simulations. Currently, MSI-supplied simulation engines include CHARMm, Discover, and OFF. (CHARMm is the name for both a simulation engine and for the forcefield included in that engine.) The functional form of the potential energy expression and the entire set of parameters needed to fit the potential energy surface constitute the forcefield (Ermer 1976). The energy expression is the specific equation set up for a particular model and including (or not) any optional terms. For example, a forcefield would contain bond-stretching parameters for all combinations of atoms for which it was parameterized, as well as a defined, summed functional form for the bond-stretching term. The corresponding energy expression would contain bond-stretching parameters for only those combinations of bonded atoms actually found in the model being studied, as well as the specific bond-stretching terms for the number and types of bonds in that model (see example under Example energy expression for water). It is important to understand that the forcefield both the functional form and the parameters themselves represents the single largest approximation in molecular modeling. The quality of the 4 Forcefield-Based Simulations/October 1997

11 Using this guide Moledular modeling programs forcefield, its applicability to the model at hand, and its ability to predict the particular properties measured in the simulation directly determine the validity of the results. Molecular modeling programs are the graphical user interfaces (UIFs or GUIs) that can be used to prepare models, set up forcefields, and access the simulation engines. Some simulation engines can also be run in standalone mode, that is, outside the graphical molecular modeling program. Molecular modeling programs currently supplied by MSI include Cerius 2, Insight, and QUANTA. Using this guide This guide contains background information on forcefields, the theories involved in their use, and how they are implemented in MSI s simulation engines, as well as general methodology and strategies for performing the various types of calculation most commonly done with these programs: Forcefields presents the concept of an energy surface and compares the forcefields available to MSI s simulation engines, including their functional forms and atom types. Different forcefields have been developed specifically for different types of models or computational experiments. Preparing the Energy Expression and the Model concerns concepts such as periodic boundary conditions, nonbond interactions, restraints, and constraints. You typically need to refine both the model and the energy expression that you intend to set up, in order to optimize your calculation conditions. Minimization includes information on the minimization algorithms that these programs can use; how, in general, to carry out minimization calculations; and the applicability of minimization in energy and vibration calculations. Molecular Dynamics covers the dynamics algorithms in these programs, thermodynamic ensembles, control of temperature and pressure, and constraints during dynamics. Free Energy presents relative and absolute free energy calculations. Forcefield-Based Simulations/October

12 1. Introduction References contains the scientific references cited in this guide. Atom types and forcefield terms are listed under Forcefield Terms and Atom Types. Additional information Available documentation On-screen help Supplemental documentation MSI s website Guides are available for every simulation engine and modeling program that MSI provides, including these: MSI Forcefield Engines: CDiscover. Cerius 2 Forcefield Engines: OFF. MSI Forcefield Engines: FDiscover. MSI Forcefield Engines: CHARMm. Cerius 2 Modeling Environment. Insight II. QUANTA documentation set. In addition to the task-oriented documentation for each simulation engine, on-screen help is available within the Cerius 2, Insight, and QUANTA environments. Please see the documentation for the specific program for how to access the help. Additional information on using the Cerius 2, Insight, and QUANTA interfaces, including building models and writing scripts for automated running, is contained in their respective guides. Technical information that is mainly of use to programmers and system administrators is contained in installation/ administration guides. Supplemental information that may be of general interest (including additional information on the electronic documentation) is contained in release notes. The URL for the documentation and customer support areas of MSI s website are : Information relevant to forcefields, simulation engines, and modeling programs can be found. 6 Forcefield-Based Simulations/October 1997

13 Typographical conventions Typographical conventions Unless otherwise noted in the text, Forcefield-Based Simulations uses these typographical conventions: Terms introduced for the first time are presented in italic type. For example: Instructions are given to the software via control panels. Keywords in the interface are presented in bold type. In addition, slashes (/) are used to separate a menu item from a submenu item. For example: Select the View/Colors menu item means to click the View menu item, drag the cursor down the pulldown menu that appears, and release the mouse button over the Colors item. Words you type or enter are presented in bold type. For example: Enter in the Convergence entry box. UNIX command dialog and file samples are represented in a typewriter font. For example, the following illustrates a line in a.grf file: CERIUS Grapher File Words in italic represent variables. For example: discovery input_file In this example, the name of the file from which data are read in replaces input_file. Forcefield-Based Simulations/October

14 1. Introduction 8 Forcefield-Based Simulations/October 1997

15 2 Forcefields Who should read this chapter This chapter explains This chapter focuses specifically on the forcefields supported by MSI s simulation engines. You should read this chapter if you want to know: What a forcefield is. What a potential energy surface is. How to choose the best forcefield for your system. The potential energy surface Empirical fit to the potential energy surface Forcefields supported by MSI forcefield engines Second-generation forcefields accurate for many properties Rule-based forcefields broadly applicable to the periodic table Classical forcefields Special-purpose forcefields Archived and untested forcefields Related information Preparing the Energy Expression and the Model presents information on how the functional forms of forcefields are used for real simulations. You need to read it to optimize how you set up your simulation. The general procedure for forcefield-based calculations is outlined under Using forcefields. The atom types defined for each forcefield are listed under Forcefield Terms and Atom Types. Illustrations of various types of cross terms are also included. The files that specify the forcefields are described in the separate documentation for each simulation engine. Forcefield-Based Simulations/October

16 2. Forcefields Table 2. Finding information in Forcefields section If you want to know about: The theory behind forcefields. What a forcefield is. Characteristics of forcefields. What forcefields are available in which MSI modeling programs. Choosing the best forcefield for your calculation. Read: The potential energy surface; Empirical fit to the potential energy surface. The forcefield; The energy expression. Main types of forcefields. Table 3. Primary uses of forcefields provided in MSI products. Table 3. Primary uses of forcefields provided in MSI products. followed by one or more of the descriptive subsections starting under Second-generation forcefields accurate for many properties. The potential energy surface The complete mathematical description of a molecule, including both quantum mechanical and relativistic effects, is a formidable problem, due to the small scales and large velocities. However, for this discussion, these intricacies are ignored and the focus is on general concepts, because molecular mechanics and dynamics are based on empirical data that implicitly incorporate all the relativistic and quantum effects. Since no complete relativistic quantum mechanical theory is suitable for the description of molecules, this discussion starts with the nonrelativistic, time-independent form of the Schrödinger description: The Schrödinger equation HΨ( Rr, ) = EΨ( Rr, ) Eq. 1 where H is the Hamiltonian for the system, Ψ is the wavefunction, and E is the energy. In general, Ψ is a function of the coordinates of the nuclei (R) and of the electrons (r). The Born Oppenheimer approximation Although this equation is quite general, it is too complex for any practical use, so approximations are made. Noting that the electrons are several thousands of times lighter than the nuclei and 10 Forcefield-Based Simulations/October 1997

17 Empirical fit to the potential energy surface Equation for electronic motion, or the potential energy surface Equation for nuclear motion on the potential energy surface therefore move much faster, Born and Oppenheimer (1927) proposed what is known as the Born Oppenheimer approximation: the motion of the electrons can be decoupled from that of the nuclei, giving two separate equations. The first equation describes the electronic motion: Hψ( rr ; ) = Eψ( rr ; ) Eq. 2 and depends only parametrically on the positions of the nuclei. Note that this equation defines an energy E(R), which is a function of only the coordinates of the nuclei. This energy is usually called the potential energy surface. The second equation then describes the motion of the nuclei on this potential energy surface E(R): HΦ( R) = EΦ( R) Eq. 3 The direct solution of Eq. 2 is the province of ab initio quantum chemical codes such as Gaussian, CADPAC, Hondo, GAMESS, DMol, and Turbomole. Semiempirical codes such as ZINDO, MNDO, MINDO, MOPAC, and AMPAC also solve Eq. 2, but they approximate many of the integrals needed with empirically fit functions. The common feature of these programs, though, is that they solve for the electronic wavefunction and energy as a function of nuclear coordinates. In contrast, simulation engines provide an empirical fit to the potential energy surface. Empirical fit to the potential energy surface Solving Eq. 3 is important if you are interested in the structure or time evolution of a model. As written, Eq. 3 is the Schrödinger equation for the motion of the nuclei on the potential energy surface. In principle, Eq. 2 could be solved for the potential energy E, and then Eq. 3 could be solved. However, the effort required to solve Eq. 2 is extremely large, so usually an empirical fit to the potential energy surface, commonly called a forcefield (V), is used. Since the nuclei are relatively heavy objects, quantum mechanical effects are often insignificant, in which case Eq. 3 can be replaced by Newton s equation of motion: Forcefield-Based Simulations/October

18 2. Forcefields 2 dv dr = m dr d t 2 Eq. 4 Molecular dynamics and mechanics The solution of Eq. 4 using an empirical fit to the potential energy surface E(R) is called molecular dynamics. Molecular mechanics ignores the time evolution of the system and instead focuses on finding particular geometries and their associated energies or other static properties. This includes finding equilibrium structures, transition states, relative energies, and harmonic vibrational frequencies. The forcefield Components of a forcefield Coordinates, terms, functional forms The forcefield contains the necessary building blocks for the calculations of energy and force: A list of atom types. A list of atomic charges (if not included in the atom-type information). Atom-typing rules. Functional forms for the components of the energy expression. Parameters for the function terms. For some forcefields, rules for generating parameters that have not been explicitly defined. For some forcefields, a defined way of assigning functional forms and parameters. This total package for the empirical fit to the potential energy surface is the forcefield. The forcefields commonly used for describing molecules employ a combination of internal coordinates and terms (bond distances, bond angles, torsions, etc.), to describe part of the potential energy surface due to interactions between bonded atoms, and nonbond terms to describe the van der Waals and electrostatic (etc.) interactions between atoms. The functional forms range from simple quadratic forms to Morse functions, Fourier expansions, Lennard Jones potentials, etc. 12 Forcefield-Based Simulations/October 1997

19 Empirical fit to the potential energy surface Purpose of forcefields Physical significance Quantum and mechanical descriptions of bonds The goal of a forcefield is to describe entire classes of molecules with reasonable accuracy. In a sense, the forcefield interpolates and extrapolates from the empirical data of the small set of models used to parameterize the forcefield to a larger set of related models. Some forcefields aim for high accuracy for a limited set of element types, thus enabling good prediction of many molecular properties. Other forcefields aim for the broadest possible coverage of the periodic table, with necessarily lower accuracy. The physical significance of most of the types of interactions in a forcefield is easily understood, since describing a model s internal degrees of freedom in terms of bonds, angles, and torsions seems natural. The analogy of vibrating balls connected by springs to describe molecular motion is equally familiar. However, it must be remembered that such models have limitations. Consider for example the difference between such a mechanical model and a quantum mechanical bond. Covalent bonds can, to a first approximation, be described by a harmonic oscillator, both in quantum and classical mechanical theory. Consider the classic oscillator in Figure 1. A ball poised at the intersection of the pale horizontal line with the parabolic energy surface (thick line) would begin to roll down, converting its potential energy to kinetic energy and achieving a maximum velocity as it passes the minimum. Its velocity (kinetic energy) is then converted back into potential energy until, at the exact same height as it had started, it would pause momentarily before rolling back. The interchange of kinetic and potential energy in such a mechanical system is familiar and intuitive. The probability of finding the ball at any point along its trajectory is inversely proportional to its velocity at that point (which is opposite to the probability for a real atom). This probability is plotted above the parabolic curve (thin line, Figure 1). The probability is greatest near the high-energy limits of its trajectory (where it is moving slowly) and lowest at the energy minimum (where it is moving quickly). Because the total energy cannot exceed the initial potential energy defined by the starting point, the probability drops to zero outside the limit defined by the intersection of the total energy (pale horizontal line) with the parabola. Describing a quantum mechanical trajectory is impossible, because the uncertainty principle prevents an exact, simultaneous specification of both position and momentum. However, the prob- Forcefield-Based Simulations/October

20 2. Forcefields classical harmonic oscillator quantum harmonic oscillator Figure 1. Energy and probability of a mechanical and quantum particle in a harmonic energy well The energy is indicated by the heavy lines and probability by the thin lines. The total energy of the system is indicated by the pale horizontal line. The classical (mechanical) probability is highest when the particle reaches it maximum potential energy (zero velocity) and drops to zero between these points. The quantum mechanical probability is highest where the potential energy is lowest, and there is a finite probability that the particle can be found outside the classical limits (pale vertical lines). Utility of the forcefield approach ability that the quantum mechanical ball will be at a given point on the parabola can be quantified. The quantum mechanical probability function plotted in the right panel of Figure 1 is very different from the mechanical system. First, the highest probability is at the energy minimum, which is the opposite of the mechanical case. Second, the quantum mechanical ball can actually be found beyond the classical limits imposed by the total energy of the system (tunneling). Both these properties can be attributed to the uncertainty principle. With such a different qualitative picture of fundamental physical principles, is it reasonable to use a mechanical approach for obviously quantum mechanical entities like bonds? In practice, many experimental properties such as vibrational frequencies, sublima- 14 Forcefield-Based Simulations/October 1997

21 Empirical fit to the potential energy surface Limitations of the forcefield approach The power of the forcefield approach tion energies, and crystal structures can be reproduced with a forcefield, not because the systems behave mechanically, but because the forcefield is fit to reproduce relevant observables and therefore includes most of the quantum effects empirically. Nevertheless, it is important to appreciate the fundamental limitations of a mechanical approach. Applications beyond the capability of most forcefield methods include: Electronic transitions (photon absorption). Electron transport phenomena. Proton transfer (acid/base reactions). The true power of the atomistic description of a model embodied in the energy expression lies in three major areas: The first is that forcefield-based simulations can handle large systems, since these simulations are several orders of magnitude faster (and cheaper) than quantum-based calculations. Forcefield-based simulations can be used for studying condensed-phase molecules, macromolecules, crystal morphology, inorganic and organic interphases, etc., where the properties of interest are not sensitive to quantum effects (e.g., phase behavior, equations of state, bond energies, etc.). The second is the analysis of the energy contributions at the level of individual or classes of interactions. For instance, you can decompose the energy into bond energies, angle energies, nonbond energies, etc. or even to the level of a specific hydrogen bond or van der Waals contact, in order to understand a physical observable or to make a prediction. The third area, which is described under Applying constraints and restraints, lies in the modification of the energy expression to bias the calculation. You can impose constraints (absolute conditions), such as fixing an atom in space and not allowing it to move. You can also add extra terms to the energy expression to restrain or force the system in certain ways. For instance, by adding an extra torsion potential to a particular bond, you can force the torsion angle toward a desired value. (You can apply constraints also for quantum-based energy calculations.) Forcefield-Based Simulations/October

22 2. Forcefields The energy expression The actual coordinates of a model combined with the forcefield data create the energy expression (or target function) for the model. This energy expression is the equation that describes the potential energy surface of a particular model as a function of its atomic coordinates. The potential energy of a system can be expressed as a sum of valence (or bond), crossterm, and nonbond interactions: E total = E valence + E crossterm + E nonbond Valence interactions The energy of valence interactions is generally accounted for by diagonal terms, namely, bond stretching (E bond ), valence angle bending (E angle ), dihedral angle torsion (E torsion ), and inversion (also called out-of-plane interactions) (E inversion or E oop ) terms, which are part of nearly all forcefields for covalent systems. A Urey Bradley term (E UB ) may be used to account for interactions between atom pairs involved in 1 3 configurations (i.e., atoms bound to a common atom): E valence = E bond + E angle + E torsion + E oop + E UB Eq. 5 Valence crossterms Nonbond interactions Modern (second-generation) forcefields generally achieve higher accuracy by including cross terms to account for such factors as bond or angle distortions caused by nearby atoms. Crossterms can include the following terms: stretch stretch, stretch bend stretch, bend bend, torsion stretch, torsion bend bend, bend torsion bend, stretch torsion stretch. (These are illustrated under Forcefield Terms and Atom Types.) The energy of interactions between nonbonded atoms is accounted for by van der Waals (E vdw ), electrostatic (E Coulomb ), and (in some older forcefields) hydrogen bond (E hbond ) terms: E nonbond = E vdw + E Coulomb + E hbond Eq. 6 Restraints Restraints that can be added to an energy expression include distance, angle, torsion, and inversion restraints. Restraints are useful if you, for example, are interested in the structure of only part of a model. For information on restraints and their implementation and use, see Preparing the Energy Expression and the Model in this 16 Forcefield-Based Simulations/October 1997

23 Empirical fit to the potential energy surface Example energy expression for water documentation set and also the documentation for the particular simulation engine. As a simple example of a complete energy expression, consider the following equation, which might be used to describe the potential energy surface of a water model: 0 VR ( ) K oh ( b b oh ) 2 0 K oh ( b b oh ) 2 0 = + + K hoh ( θ θ hoh ) 2 Eq. 7 Example forcefield function where K oh, b 0 oh, K hoh, and θ 0 hoh are parameters of the forcefield, b is the current bond length of one O H bond, b is the length of the other O H bond, and θ is the H O H angle. In this example, the forcefield defines: The coordinates to be used (bond lengths and angles). The functional form (a simple quadratic in both types of coordinates). The parameters (the force constants K oh and K hoh, as well as the reference values b 0 oh and θ 0 hoh). The reference O H bond length and reference H O H angle are the values for an ideal O H bond and H O H angle at zero energy, which is not necessarily the same as their equilibrium values in a real water molecule. Eq. 7 is an example of an energy expression as set up for a simple molecule. Eq. 8 is an example of the corresponding general, summed forcefield function: Forcefield-Based Simulations/October

24 2. Forcefields VR ( ) = D [ b 1 exp( ab ( b 0 )) ] 2 + H ( θ θ θ ) H φ [ 1 + scos( nφ) ] b θ + H χ χ 2 + F bb ( b b 0 ) ( b b ) 0 + F θθ ( θ θ 0 )( θ θ 0 ) χ b b + F bθ ( b b 0 )( θ θ 0 ) + F θ θ θθ φ ( 0) ( θ θ 0 ) cosφ b θ + F χχ χχ + χ χ i j > i A ij r12 ij θ θ B ij r6 ij q i q j r ij Eq. 8 The first four terms in this equation are sums that reflect the energy needed to stretch bonds (b), bend angles (θ) away from their reference values, rotate torsion angles (φ) by twisting atoms about the bond axis that determines the torsion angle, and distort planar atoms out of the plane formed by the atoms they are bonded to (χ). The next five terms are cross terms that account for interactions between the four types of internal coordinates. The final term represents the nonbond interactions as a sum of repulsive and attractive Lennard Jones terms as well as Coulombic terms, all of which are a function of the distance r ij between atom pairs. The forcefield defines the functional form of each term in this equation as well as the parameters such as D b, α, and b 0. The forcefield also defines internal coordinates such as b, θ, φ, and χ as a function of the Cartesian atomic coordinates, although this is not explicit in Eq. 8. We should note that the energy expression in Eq. 8 is cast in a general form. The true energy expression for a specific model includes information about the coordinates that are included in each sum. For example, it is common to exclude interactions between bonded and 1 3 atoms in the summation representing the nonbond interactions. Thus, a true energy expression might actually use a list of allowed interactions rather than the full summation implied in Eq. 8. θ θ φ 18 Forcefield-Based Simulations/October 1997

25 Forcefields supported by MSI forcefield engines Forcefields supported by MSI forcefield engines Contents of this section Forcefield descriptions Second-generation forcefields Broadly applicable forcefields Classical forcefields Special-purpose forcefields The results of any mechanics or dynamics calculation depend crucially on the forcefield. The quality of the description of both the system and the particular properties being analyzed is of paramount importance. Accurate, specific parameters generally give better results than automatic, generic parameters. Choosing the correct forcefield is vitally important in getting reasonable results from energy calculations. This section gives a general comparison of the forcefields that are available in MSI products and presents the reasoning behind making a wide variety of forcefields available to our customers. It should enable you to make at least a preliminary choice of which forcefield to use. Complete descriptions of each forcefield follow in subsequent sections: CFF91, PCFF, CFF consistent forcefields MMFF93, the Merck molecular forcefield ESFF, extensible systematic forcefield UFF, universal forcefield VALBOND Dreiding forcefield Standard AMBER forcefield Homans carbohydrate forcefield CHARMm forcefield CVFF, consistent valence forcefield Glass forcefield MSXX forcefield for polyvinylidene fluoride Zeolite forcefields Forcefields for sorption on zeolites Forcefields for Cerius 2 Morphology module Forcefield-Based Simulations/October

26 2. Forcefields Other forcefields Related information Archived and untested forcefields The atom types defined by each forcefield are listed under Forcefield Terms and Atom Types, and the types of parameters used in the forcefields are described in the documentation for each simulation engine. Main types of forcefields Second-generation forcefields MSI provides four main types of forcefields: Second-generation forcefields capable of predicting many properties. Rule-based forcefields applicable to a broad range of the periodic table. Classical, first-generation forcefields applicable mainly to biochemistry. Special-purpose forcefields that are narrowly applicable to particular applications or types of models. A complete list of these forcefields, their main uses, and the simulation engine that handles them is given in Table 3. In addition, we supply (but do not support) several older or untested forcefields. The CFF family of forcefields (CFF91, PCFF, CFF) are closely related second-generation forcefields (Maple et al. 1988, 1994a, b, Dinur and Hagler 1991, Waldman and Hagler 1993, Hill and Sauer 1994, Hwang et al. 1994, Hagler and Ewig 1994, Sun et al. 1994, Sun 1994, 1995). The CFF family of forcefields were parameterized against a wide range of experimental observables for organic compounds containing H, C, N, O, S, P, halogen atoms and ions, alkali metal cations, and several biochemically important divalent metal cations. CFF has slightly more atom types than CFF91 (Forcefield Terms and Atom Types). PCFF is based on CFF91, extended so as to have a broad coverage of organic polymers, (inorganic) metals, and zeolites. 20 Forcefield-Based Simulations/October 1997

27 Forcefields supported by MSI forcefield engines The CFF family of forcefields have been shown to reproduce experimental results more accurately than classical forcefields such as CVFF and AMBER. COMPASS stands for Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies. COMPASS is MSI's breakthrough forcefield technology for materials science. It is the first ab initio forcefield that enables accurate and simultaneous prediction of structural, conformational, vibrational, and thermophysical properties for a broad range of molecules in isolation and in condensed phases. It is also the first high quality forcefield that consolidates parameters for organic and inorganic materials previously found in different forcefields. COMPASS is developed from PCFF, a CFF type forcefield for organic materials and polymers. In addition to the high-quality prediction of molecular properties that PCFF offers, COMPASS has been specifically optimized to yield high accuracy predictions of condensed-phase properties of many organic liquids and polymers, making possible, for example, detailed studies of the temperature dependence of solubility parameters of polymers and small molecule liquids. In addition to broad coverage in organics, small inorganic molecules, and polymers, this forcefield has been augmented with new functional forms, to include coverage of inorganic materials - metal oxides, metals, and metal halides. Detailed information about the COM- PASS forcefield can be found in the COMPASS user guide. The Merck molecular forcefield (MMFF93), developed by T. A. Halgren at the Merck Research Laboratories (1992, Halgren & Nachbar, 1996) is designed to be used with a large variety of chemical models. The main application of MMFF93 is to the study of receptor ligand interactions involving proteins or nucleic acids as receptors and a wide range of chemical structures as ligands. The forcefield can describe ligands and receptors in isolation as well as in the bound state. Rule-based forcefields The ESFF forcefield (extensible systematic forcefield) is a rulebased forcefield that was developed at MSI. The goal of this forcefield is to provide the widest possible coverage of the periodic table, enabling both the structures of isolated molecules and crystals to be reproduced. Its scope does Forcefield-Based Simulations/October

28 2. Forcefields not extend to highly accurate vibrational frequencies or other properties such as conformational energies. The Universal forcefield (Rappé et al. 1992) is an excellent general-purpose forcefield. All the Universal forcefield parameters are generated from a set of rules based on element, hybridization, and connectivity. The Universal forcefield was parametrized for the full periodic table and has been carefully validated for main-group compounds (Casewit et al. 1992b), organic molecules (Casewit et al. 1992a), and metal complexes (Rappé et al. 1993). VALBOND is a combination of the UFF, universal forcefield, and the VALBOND method for the angle energy. This forcefield combines the advantages of a general forcefield with the strengths of the VALBOND method and may give better results for non-hypervalent structures where the geometry of ligands around a central atom is unknown. The Dreiding forcefield (Mayo et al. 1990) is a good, robust, allpurpose forcefield. While a specialized forcefield is more accurate for predicting a limited number of structures, the Dreiding forcefield allows reasonable predictions for a very much larger number of structures, including those with novel combinations of elements and those for which there is little or no experimental data. It can be used for structure prediction and dynamics calculations on organic, biological, and main-group inorganic molecules. Classical forcefields The AMBER forcefield Weiner et al. 1984, 1986) was parameterized against a limited number of organic models. It has been widely used for proteins, DNA, and other classes of molecules and may be considered well characterized. The standard AMBER forcefield is mainly useful for proteins and nucleic acids. The Homans (1990) carbohydrate forcefield is based on AMBER, but extended to polysaccharides. It is not generally recommended for use in materials science studies. The CHARMm forcefield (Chemistry at HARvard Macromolecular mechanics) is packaged in a highly flexible molecular mechanics and dynamics engine originally developed in the 22 Forcefield-Based Simulations/October 1997

29 Forcefields supported by MSI forcefield engines Special-purpose forcefields laboratory of Dr. Martin Karplus at Harvard University. It has been widely used and can be considered well tested and characterized (e.g., Brooks et al. 1983, Momany and Rone 1992). A variety of systems, from isolated small molecules to solvated complexes of large biological macromolecules, can be simulated using CHARMm. The CVFF forcefield is a classic forcefield having some anharmonic and cross term enhancements. As the traditional default forcefield in the Discover program, it has been used extensively and can be considered well tested and characterized. CVFF was parameterized to reproduce peptide and protein properties. In addition to some standard forcefields, the Cerius 2 Open Force Field module provides several smaller forcefield parameter files for more specialized work. These include separate forcefields for glasses, zeolites, and polyvinylidene fluoride, as well as some forcefields that are intended only for use in the Cerius 2 Morphology module. Advantages of having several forcefields The ability to choose among several forcefields has several advantages: 1. A broader range of systems can be treated: Some classical forcefields were originally created for modeling proteins and peptides, others for DNA and RNA. Some have been extended to handle more general systems having similar functional groups. The rule-based forcefields have extended the range of forcefield simulations to a broader range of elements. The second-generation forcefields currently include parameters for all functional groups appropriate for protein simulations. 2. Identical calculations with two or more independent forcefields can be compared to assess the dependence of the results on the forcefield: Forcefield-Based Simulations/October

30 2. Forcefields For example, amino acid parameters are defined in the AMBER, CHARMm, CVFF, CFF, and MMFF93 forcefields, so peptide and protein calculations with these forcefields can be compared to assess the effect of the forcefields. 3. The different functional forms used in the various energy expressions increase the flexibility of the Discover program and the Open Force Field module: You can balance the requirements of high accuracy vs. available computational resources. (Highly accurate forcefields are generally more complex and therefore require more resources.) Different energy terms can be compared. For example, approximations such as a distance-dependent dielectric constant or scaling of 1 4 nonbond interactions can be assessed. Harmonic bond terms are accurate only at bond lengths close to the reference bond length, but the Morse term can be used to model bond breaking. 4. The development of new forcefields at MSI and elsewhere continues to provide more accurate and more broadly applicable forcefields. As experience is gained in parameterizing forcefields and as new experimental data become available, the range of both properties and systems fit by these newer forcefields will increase. Primary uses of each MSI forcefield Table 3 summarizes the forcefields best suited for various types of work and lists the simulation engines that handle each one: 24 Forcefield-Based Simulations/October 1997

31 Forcefields supported by MSI forcefield engines Table 3. Primary uses of forcefields provided in MSI products (Page 1 of 2) Type and use of forcefield Second-generation, general-purpose Classical, general-purpose (biochemistry) Forcefield name Simulation engine Forcefield filename(s) CFF91 Discover; OFF a cff91.frc; cff91_950_ 1.01 CFF95 b Discover; OFF cff95.frc; cff95_950_ 1.01 CFF Discover, OFF cff.frc; cff1.01 MMFF93 CHARMm c mmff_setup.str PCFF Discover; OFF pcff.frc; pcff_300_1.01 COMPASS98 d Discover; OFF compass.frc; COMPASS1.0, compass98.frc; Compass98.01 Rule-based, broadly applicable, generalpurpose ESFF Discover e esff.frc Universal OFF UNIVERSAL1.02 UFF-VAL- OFF UFF_VALBOND1.01 BOND Dreiding OFF DREIDING2.21 AMBER Discover, OFF f amber.frc CHARMm CHARMm g CVFF Discover; OFF cvff.frc; cvff_950_1.01 h Special-purpose: Inorganic oxide glasses Glass OFF glassff_1.01, glassff_ 2.01 Morphology module of Cerius 2 Polyvinylidene fluoride polymers Lifson OFF morph_lifson1.11 Momany OFF morph_momany1.1 Scheraga OFF morph_scheraga1.1 Williams OFF morph_williams1.01 MSXX OFF msxx_1.01 Forcefield-Based Simulations/October