1 contentsbenedick.rutgers.edu/software-manuals/forcefield.pdfcharmm®, discover®, and the open...

Forcefield-Based Simulations/September 1998 i

1 Contents

1. Introduction 1Who should use this documentation 2What can simulation engines do? 2

Energy minimization 2Molecular dynamics 3Other forcefield-based calculations 3

What are forcefields and simulation engines? 4Using this guide 5Additional information 6Typographical conventions 7

2. Forcefields 9The potential energy surface 10Empirical fit to the potential energy surface 11

The forcefield 12The energy expression 16

Forcefields supported by MSI forcefield engines 19Main types of forcefields 20Advantages of having several forcefields 23Primary uses of each MSI forcefield 24

Second-generation forcefields accurate for many properties 26CFF91, PCFF, CFF, COMPASS—consistent forcefields 28MMFF93, the Merck molecular forcefield 34

Rule-based forcefields broadly applicable to the periodic table 35ESFF, extensible systematic forcefield 36UFF, universal forcefield 42VALBOND 44Dreiding forcefield 51

Classical forcefields 53AMBER forcefield 53CHARMm forcefield 56CVFF, consistent valence forcefield 57

Special-purpose forcefields 61

ii Forcefield-Based Simulations/September 1998

1. Contents

Glass forcefield 62MSXX forcefield for polyvinylidene fluoride 64Zeolite forcefields 65Forcefields for sorption on zeolites 67Forcefields for Cerius2•Morphology module 67

Archived and untested forcefields 68

3. Preparing the Energy Expression and the Model 73Using forcefields 75Selecting forcefields 78Assigning forcefield atom types and charges 78

What are atom types in forcefields? 79Assigning atom types to a model 79Assigning charges 81

Parameter assignment 84Determination of which parameters are used with which

atom types 84Automatic assignment of values for missing parameters 86Manual parameter assignment 89

Using alternative forms of energy terms 92Removing terms from the energy expression 93Scaling or editing any selected type of term 94Alternative bond terms 94Scaled torsion terms 95Inversion terms 96Nonbond functional form 96Hydrogen bonds and hydrogen-bond terms 96Bond–angle cross terms vs. Urey–Bradley terms 98

Applying constraints and restraints 98When to use constraints/restraints 100Fixed atom constraints 102Template forcing, tethering, quartic droplet restraints, and

consensus conformations 103General internal-coordinate restraints 106Distance and NOE restraints 106Distance and angle constraints in dynamics simulations 109Angle restraints 110Torsion restraints 110Inversion, out-of-plane, and chiral restraints 112Plane and other geometrical constraints and restraints 112

Modeling periodic systems 113Minimum-image model 115Explicit-image model 117Crystal simulations 119Bonds across boundaries 120

Handling nonbond interactions 120

Forcefield-Based Simulations/September 1998 iii

Combination rules for van der Waals terms 124The dielectric constant and the Coulombic term 125Nonbond cutoffs 127Cell multipole method 138Ewald sums for periodic systems 143

4. Minimization 153General minimization process 155

Specific minimization example 155Line search 157

Minimization algorithms 160Steepest descents 161Conjugate gradient 164Newton–Raphson methods 166

General methodology for minimization 173Minimizations with MSI simulation engines 174When to use different algorithms 176Convergence criteria 178Significance of minimum-energy structure 180

Energy and gradient calculation 181Vibrational calculation 182

Application of minimization to vibrational theory 183Vibrational frequencies 185General methodology for vibrational calculations 187

5. Molecular Dynamics 189Integration algorithms 192

Introduction 192Criteria of good integrators in molecular dynamics 193Integrators in MSI simulation engines 194

The choice of timestep 197Integration errors 198

Example 1—Two colliding hydrogen atoms 199Example 2—Energy conservation of a harmonic oscillator

204Statistical ensembles 205

NVE ensemble 207NVT ensemble 208NPT and NST ensembles 208NPH and NSH ensembles 209Equilibrium thermodynamic properties 210

Temperature 211How temperature is calculated 212How temperature is controlled 214

iv Forcefield-Based Simulations/September 1998

1. Contents

Pressure and stress 220Units and sign conventions for pressure and stress 221How pressure and stress are calculated 222How pressure and stress are controlled 225

Types of dynamics simulations 229Quenched dynamics 232Simulated annealing 232Consensus dynamics 233Impulse dynamics 233Langevin dynamics 234Stochastic boundary dynamics 234Multibody order-N dynamics 234

Constraints during dynamics simulations 235The SHAKE algorithm 236The RATTLE algorithm 237

Dynamics trajectories 238General methodology for dynamics calculations 238

Stages and duration of dynamics simulations 239Dynamics with MSI simulation engines 241Restarting a dynamics simulation 246

6. Free Energy 251Relative free energy—theory and implementation 251

Finite difference thermodynamic integration (FDTI) 251Relative free energy—methodology 255

Absolute free energy 258Theory and implementation 258Example: Fentanyl 264Analysis of results 270

A. References 273

B. Forcefield Terms and Atom Types 283Forcefield term definitions 284AMBER atom types 287

Standard AMBER forcefield 287Homan’s carbohydrate forcefield 290

CFF91 atom types 291CHARMm atom types 294COMPASS atom types 297CVFF atom types 302CVFF_aug atom types 305

Forcefield-Based Simulations/September 1998 v

ESFF atom types 307PCFF—additional atom types 312

vi Forcefield-Based Simulations/September 1998

1. Contents

Forcefield-Based Simulations/October 1997 1

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) mod-ules, which are run through the molecular modeling programs (i.e., graphical interfaces) shown in Table 1.

Table 1. Simulation enginesa within MSI’s molecular modeling programsb

Molecular modeling program and release

number

Simulation engine

CHARMm Discoverc OFF

Cerius2™ 4.0 √ √d √Insight® II 4.0.0 √Insight® II 97.0 √ √QUANTA® √standalonee √ √

aSee definitions under What are forcefields and simulation engines?.bDiscover 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 Cerius2, and is used only in spe-cialized modules in Insight II.cDiscover 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 Dis-cover programs have different capabilities. FDiscover and CDiscover (in Insight II) are accessed through the Discover and Discover_3 modules, respectively.dCDiscover only.eCHARMm and Discover can also be run without the assistance of a graph-ical molecular modeling program.

2 Forcefield-Based Simulations/October 1997

1. Introduction

Who should use this documentation

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.

Prerequisites 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 (Cerius2, Insight, and/or QUANTA).

Your workstation should have:

♦ A licensed copy of Cerius2, 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 Cerius2™ or Insight®.

♦ Repairing poor geometries occurring at splice points during homology building of protein structures.

♦ Mapping the energy barriers for geometric distortions and con-formational transitions using “torsion forcing” to obtain Ram-achandran-type contour plots for proteins or RIS statistical weights for polymers.

What can simulation engines do?


♦ Evaluating whether a molecule can adopt a template conforma-tion 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 pro-tein loops.

♦ Producing sets of 3D structures consistent with distance and torsion constraints deduced from NMR experiments (simu-lated annealing).

♦ Calculating free energies of binding, including solvation and entropy effects.

♦ Probing the locations, conformations, and motions of mole-cules 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 fre-quencies.

♦ 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 poly-mer matrix.

♦ Calculating thermal expansion coefficients of amorphous poly-mers.

♦ Calculating the radial distribution of liquids and amorphous polymers.


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?

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 deriva-tives 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 “engine” defined

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.)

“Forcefield” and “energy expression” defined

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 parame-ters for all combinations of atoms for which it was parameterized, as well as a defined, summed functional form for the bond-stretch-ing 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).

Importance of the force-field in simulations

It is important to understand that the forcefield—both the func-tional form and the parameters themselves—represents the single largest approximation in molecular modeling. The quality of the

Using this guide


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.

Moledular modeling pro-grams

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 sup-plied by MSI include Cerius2, 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 com-pares 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 algo-rithms that these programs can use; how, in general, to carry out minimization calculations; and the applicability of minimi-zation 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 calcula-tions.


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 Guides are available for every simulation engine and modeling program that MSI provides, including these:

♦ MSI Forcefield Engines: CDiscover.

♦ Cerius2 Forcefield Engines: OFF.

♦ MSI Forcefield Engines: FDiscover.

♦ MSI Forcefield Engines: CHARMm.

♦ Cerius2 Modeling Environment.

♦ Insight II.

♦ QUANTA documentation set.

On-screen help In addition to the task-oriented documentation for each simula-tion engine, on-screen help is available within the Cerius2, Insight, and QUANTA environments. Please see the documentation for the specific program for how to access the help.

Supplemental documen-tation

Additional information on using the Cerius2, 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 program-mers and system administrators is contained in installation/administration guides. Supplemental information that may be of general interest (including additional information on the elec-tronic documentation) is contained in release notes.

MSI’s website The URL for the documentation and customer support areas of MSI’s website are :

http://www.msi.com/doc/http://www.msi.com/support/

Information relevant to forcefields, simulation engines, and mod-eling programs can be found.

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 addi-tion, slashes (/) are used to separate a menu item from a sub-menu 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 exam-ple:

Enter 0.001 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.


1. Introduction


2 Forcefields

This chapter focuses specifically on the forcefields supported by MSI’s simulation engines.

Who should read this chapter

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.

This chapter explains 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 simu-lations. You need to read it to optimize how you set up your sim-ulation. The general procedure for forcefield-based calculations is outlined under Using forcefields.

The atom types defined for each forcefield are listed under Force-field 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.


2. Forcefields

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 relativ-istic 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 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 elec-trons are several thousands of times lighter than the nuclei and

Table 2. Finding information in Forcefields section

If you want to know about: Read:

The theory behind forcefields. The potential energy surface; Empirical fit to the potential energy surface.

What a forcefield is. The forcefield; The energy expression.Characteristics of forcefields. Main types of forcefields.What forcefields are available in which

MSI modeling programs.Table 3. Primary uses of forcefields provided in MSI prod-

ucts (Page 1 of 2).Choosing the best forcefield for your

calculation.Table 3. Primary uses of forcefields provided in MSI prod-

ucts (Page 1 of 2). followed by one or more of the descriptive subsections starting under Second-genera-tion forcefields accurate for many properties.

HΨ R r,( ) EΨ R r,( )=



therefore move much faster, Born and Oppenheimer (1927) pro-posed 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:

Equation for electronic motion, or the potential energy surface

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.

Equation for nuclear motion on the potential energy surface

The second equation then describes the motion of the nuclei on this potential energy surface E(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.


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 sur-face. 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:

Hψ r R;( ) Eψ r R;( )=

HΦ R( ) EΦ R( )=


2. Forcefields

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 struc-tures, transition states, relative energies, and harmonic vibrational frequencies.

The forcefield

Components of a force-field

The forcefield contains the necessary building blocks for the calcu-lations of energy and force:

♦ A list of atom types.

♦ A list of atomic charges (if not included in the atom-type infor-mation).

♦ 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.

Coordinates, terms, func-tional forms

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 sur-face 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.

RddV

– mt2

2

d

d R=



Purpose of forcefields 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 mod-els. Some forcefields aim for high accuracy for a limited set of ele-ment types, thus enabling good prediction of many molecular properties. Other forcefields aim for the broadest possible cover-age of the periodic table, with necessarily lower accuracy.

Physical significance 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”.

Quantum and mechani-cal descriptions of bonds

Covalent bonds can, to a first approximation, be described by a harmonic oscillator, both in quantum and classical mechanical the-ory. 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 poten-tial energy to kinetic energy and achieving a maximum velocity as it passes the minimum. Its velocity (kinetic energy) is then con-verted 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 mechan-ical 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 plot-ted 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-


2. Forcefields

ability that the quantum mechanical ball will be at a given point on the parabola can be quantified. The quantum mechanical probabil-ity 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 sys-tem (tunneling). Both these properties can be attributed to the uncertainty principle.

Utility of the forcefield approach

With such a different qualitative picture of fundamental physical principles, is it reasonable to use a mechanical approach for obvi-ously quantum mechanical entities like bonds? In practice, many experimental properties such as vibrational frequencies, sublima-

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 low-est, and there is a finite probability that the particle can be found outside the classical limits (pale vertical lines).

classical harmonic oscil-lator

quantum harmonic os-cillator

3.0

0.0

3.0

0.0-2 2 -2 2



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. Never-theless, it is important to appreciate the fundamental limitations of a mechanical approach.

Limitations of the force-field approach

Applications beyond the capability of most forcefield methods include:

♦ Electronic transitions (photon absorption).

♦ Electron transport phenomena.

♦ Proton transfer (acid/base reactions).

The power of the force-field approach

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 magni-tude faster (and cheaper) than quantum-based calculations. Forcefield-based simulations can be used for studying con-densed-phase molecules, macromolecules, crystal morphology, inorganic and organic interphases, etc., where the properties of interest are not sensitive to quantum effects (e.g., phase behav-ior, 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 hydro-gen 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.)


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:

Valence interactions The energy of valence interactions is generally accounted for by diagonal terms, namely, bond stretching (Ebond), valence angle bending (Eangle), dihedral angle torsion (Etorsion), and inversion (also called out-of-plane interactions) (Einversion or Eoop) terms, which are part of nearly all forcefields for covalent systems. A Urey–Bradley term (EUB) may be used to account for interactions between atom pairs involved in 1–3 configurations (i.e., atoms bound to a common atom):

Evalence = Ebond + Eangle + Etorsion + Eoop + EUB Eq. 5

Valence crossterms 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 Force-field Terms and Atom Types.)

Nonbond interactions The energy of interactions between nonbonded atoms is accounted for by van der Waals (EvdW), electrostatic (ECoulomb), and (in some older forcefields) hydrogen bond (Ehbond) terms:

Enonbond = EvdW + ECoulomb + Ehbond Eq. 6

Restraints Restraints that can be added to an energy expression include dis-tance, 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

Etotal Evalence Ecrossterm Enonbond+ +=



and use, see Preparing the Energy Expression and the Model in this documentation set and also the documentation for the particular simulation engine.

Example energy expres-sion for water

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:

Eq. 7

where Koh, b0oh, Khoh, and θ0hoh 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 coor-dinates).

♦ The parameters (the force constants Koh and Khoh, as well as the reference values b0oh and θ0hoh).

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.

Example forcefield func-tion

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:

V R( ) Koh b boh0

–( )2

Koh b ′ boh0

–( )2

Khoh θ θhoh0

–( )2

+ +=


2. Forcefields

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 repul-sive and attractive Lennard–Jones terms as well as Coulombic terms, all of which are a function of the distance rij between atom pairs. The forcefield defines the functional form of each term in this equation as well as the parameters such as Db, α, and b0. 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 gen-eral 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 inter-actions. Thus, a true energy expression might actually use a list of allowed interactions rather than the full summation implied in Eq. 8.

V R( ) Db 1 exp a b b0–( )–( )–[ ] 2

b

∑ Hθ θ θ0–( )2θ

∑ Hφ 1 s nφ( )cos+[ ]φ

∑+ +=

Hχχ2

χ

∑ Fbb ′ b b0–( ) b′ b ′0–( )b ′

∑b

∑ Fθθ′ θ θ0–( ) θ′ θ′0–( )θ′

∑θ

∑+ + +

Fbθ b b0–( ) θ θ0–( )

θ

∑b

∑ Fθθ′φθ′

∑ θ θ0–( ) θ′ θ′0–( ) φcosθ

∑+ +

Fχχ′ χχ′

χ′

∑χ

∑ Aijrij12-------Bijrij

6------–

qiqjrij

---------+

j i>

∑i

∑+ +




The results of any mechanics or dynamics calculation depend cru-cially on the forcefield. The quality of the description of both the system and the particular properties being analyzed is of para-mount 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.

Contents of this section This section gives a general comparison of the forcefields that are available in MSI products and presents the reasoning behind mak-ing 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.

Forcefield descriptions Complete descriptions of each forcefield follow in subsequent sec-tions:

Second-generation force-fields

CFF91, PCFF, CFF, COMPASS—consistent forcefields

MMFF93, the Merck molecular forcefield

Broadly applicable force-fields

ESFF, extensible systematic forcefield

UFF, universal forcefield

VALBOND

Dreiding forcefield

Classical forcefields Standard AMBER forcefield

Homans’ carbohydrate forcefield

CHARMm forcefield

CVFF, consistent valence forcefield

Special-purpose force-fields

Glass forcefield

MSXX forcefield for polyvinylidene fluoride

Zeolite forcefields

Forcefields for sorption on zeolites

Forcefields for Cerius2•Morphology module


2. Forcefields

Other forcefields Archived and untested forcefields

Related information The atom types defined by each forcefield are listed under Force-field 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

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 peri-odic table.

♦ Classical, first-generation forcefields applicable mainly to bio-chemistry.

♦ Special-purpose forcefields that are narrowly applicable to par-ticular applications or types of models.

A complete list of these forcefields, their main uses, and the simu-lation engine that handles them is given in Table 3.

In addition, we supply (but do not support) several older or untested forcefields.

Second-generation force-fields

♦ The CFF family of forcefields (CFF91, PCFF, CFF, COMPASS) 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 com-pounds containing H, C, N, O, S, P, halogen atoms and ions, alkali metal cations, and several biochemically important diva-lent 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 cover-age of organic polymers, (inorganic) metals, and zeolites. COMPASS is a new version of PCFF.

The CFF family of forcefields have been shown to reproduce experimental results more accurately than classical forcefields such as CVFF and AMBER.

♦ 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 recep-tors 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 rule-based forcefield that was developed at MSI.

The goal of this forcefield is to provide the widest possible cov-erage of the periodic table, enabling both the structures of iso-lated molecules and crystals to be reproduced. Its scope does not extend to highly accurate vibrational frequencies or other properties such as conformational energies.

♦ The Universal forcefield (Rappé et al. 1992) is an excellent gen-eral-purpose forcefield. All the Universal forcefield parameters are generated from a set of rules based on element, hybridiza-tion, and connectivity.

The Universal forcefield was parametrized for the full periodic table and has been carefully validated for main-group com-pounds (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 bet-ter results for non-hypervalent structures where the geometry of ligands around a central atom is unknown.


2. Forcefields

♦ The Dreiding forcefield (Mayo et al. 1990) is a good, robust, all-purpose forcefield. While a specialized forcefield is more accu-rate 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 experimen-tal data.

It can be used for structure prediction and dynamics calcula-tions on organic, biological, and main-group inorganic mole-cules.

Classical forcefields ♦ The AMBER forcefield Weiner et al. 1984, 1986) was parameter-ized 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 Macromolecu-lar mechanics) is packaged in a highly flexible molecular mechanics and dynamics engine originally developed in the laboratory of Dr. Martin Karplus at Harvard University. It has been widely used and can be considered well tested and char-acterized (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 simu-lated using CHARMm.

♦ The CVFF forcefield is a classic forcefield having some anhar-monic 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.

Special-purpose force-fields

♦ In addition to some standard forcefields, the Cerius2•Open Force Field module provides several smaller forcefield param-eter 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 Cerius2•Morphology module.

Advantages of having several forcefields

The ability to choose among several forcefields has several advan-tages:

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 parame-ters for all functional groups appropriate for protein simula-tions.

2. Identical calculations with two or more independent forcefields can be compared to assess the dependence of the results on the forcefield:

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 gen-erally more complex and therefore require more resources.)

Different energy terms can be compared. For example, approx-imations such as a distance-dependent dielectric constant or scaling of 1–4 nonbond interactions can be assessed.


2. Forcefields

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 con-tinues to provide more accurate and more broadly applicable forcefields. As experience is gained in parameterizing force-fields and as new experimental data become available, the range of both properties and systems fit by these newer force-fields 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:

Table 3. Primary uses of forcefields provided in MSI products (Page 1 of 2)

Type and use of forcefieldForcefield

name Simulation engine Forcefield filename(s)Docu-

mented

Second-generation, general-purpose

CFF91 Discover; OFFa cff91.frc; cff91_950_1.01

here

CFF95b Discover; OFF cff95.frc; cff95_950_1.01

here

CFF Discover, OFF cff.frc; cff1.01 hereMMFF93 CHARMmc mmff_setup.STR here

2nd-generation, poly-mers

PCFF, COM-PASS, COMPASS982

Discover; OFF pcff.frc; pcff_300_1.01, compass.frc; COMPASS1.0, compass98.frc; Compass98.01

here

Rule-based, broadly applicable, general-purpose

ESFF Discoverd esff.frc hereUniversal OFF UNIVERSAL1.02 hereUFF-VAL-

BONDOFF UFF_VALBOND1.01 here

Dreiding OFF DREIDING2.21 here

Classical, general-pur-pose (biochemistry)

AMBER Discover, OFFe amber.frc hereCHARMm CHARMmf hereCVFF Discover; OFF cvff.frc; cvff_950_1.01g here



Additional information Additional information about forcefields included with Cerius2 is printed to the text window when you load a forcefield. Alterna-

Special-purpose:Inorganic oxide glasses Glass OFF glassff_1.01, glassff_

2.01here

Morphology module of Cerius2

Lifson OFF morph_lifson1.11 hereMomany OFF morph_momany1.1 hereScheraga OFF morph_scheraga1.1 hereWilliams OFF morph_williams1.01 here

Polyvinylidene fluoride polymers

MSXX OFF msxx_1.01 here

Zeolites BKS OFF bks1.01 hereBurchart OFF burchart1.01 hereBurchart–

DreidingOFF burchart1.01-

DREIDING2.21here

Burchart–Universal

OFF burchart1.01-UNIVERSAL1.02

here

CVFF_aug Discover; OFF cvff_300_1.01 hereZeolite sorption Yashonath OFF sor_yashonath1.01 here

Demontis OFF sor_demontis1.01 herePickett OFF sor_pickett1.01 hereWatanabe–

AustinOFF watanabe-austin1.01 here

Older, archived, misc. several Discover; OFF gifts/*, archive/* here

Untested, misc. several OFF untested/ here

aOFF = the Open Force Field module of Cerius2.bMarketed as an add-on forcefield, not present in Discover or OFF by default.cCHARMm as run through the Cerius2•MMFF module, not in QUANTA or standard CHARMm.dIn CDiscover, not FDiscover; in other words, in the Cerius2•Discover and the Insight•Discover_3 modules, not the Insight•Discover module.eIn the Insight•Discover_3 and the Insight•Discover modules but not the Cerius2•Discover module. An older version of AMBER is accessible through the Cerius2•OFF module.fCHARMm is both the name of a forcefield and the name of a simulation engine that handles the CHARMm forcefield.gCVFF differs slightly in versions 3.0.0 and 95.0 of Insight II—both versions are included in Cerius2•OFF.

Table 3. Primary uses of forcefields provided in MSI products (Page 2 of 2)

Type and use of forcefieldForcefield

name Simulation engine Forcefield filename(s)Docu-

mented


2. Forcefields

tively, you can click the Show information action button in the Load Force Field control panel.

Additional information about forcefields included with Insight 4.0.0 can be obtained with the Forcefield/FF_Info parameter block, which is accessed through the Builder and other modules. (It is not included in Insight 97.0.)

Second-generation forcefields accurate formany properties

Availability Second-generation forcefields provided or developed by MSI include CFF91, CFF, PCFF, COMPASS, and MMFF93:

♦ The CFF family of forcefields (CFF91, PCFF, CFF, COMPASS—consistent forcefields) are run via the Discover program, which is available in the Insight•Discover_3, Insight•Discover, and Cerius2•Discover modules. They can also be used by the Cerius2•Open Force Field module. Discover is also used implicitly by other modules in Insight II (such as some in the Polymer suite of products). The CFF and COMPASS forcefields are separately licensed (that is, not present by default within Discover).

♦ MMFF93 (MMFF93, the Merck molecular forcefield) is run via a version of CHARMm that supports the Cerius2•MMFF mod-ule.

Characteristics The topography of an energy surface is usually very complex, especially for large and/or complex models, with many energy minima and barriers and regions of greatly varying energy and curvature. Nevertheless, the forcefield expression must be as accu-rate and complete as possible, to avoid spurious or misleading results. The newer, second-generation forcefields meet this requirement through their greater complexity than the classical forcefields, having expanded analytic energy expressions that include additional terms.

Parameterization The complexity of second-generation forcefields requires the use of a large number of forcefield parameters. There are almost always far more parameters than can be inferred from experiment, such as by microwave or infrared spectroscopy. However, modern



quantum mechanical methods can generate enough quantum observables so that all the necessary parameters can be accurately determined by fitting the energy expression to these observables.

Quantum calculations of the energy surfaces of a series of model compounds (equilibrium structures, models at conformational energy barriers, and distorted structures) yield energies as well as their derivatives with respect to atomic coordinates (i.e., the sur-face gradients and curvatures) (Maple et al. 1994a, b). Many atomic partial charges are also determined quantum mechanically.

Intermolecular or nonbond parameters are computed by fitting to experimental crystal lattice constants and sublimation energies of crystals (Hagler et al. 1979a, b).

Since quantum mechanics (Hartree–Fock approximation with the 6-31G* basis set) yields results that differ consistently from exper-iment, the parameterized forcefield is then fit to experimental data by parameterizing a small number of scaling factors (Hwang et al. 1994).

The CFF family of forcefields (within Discover) can use automatic parameters (Automatic assignment of values for missing parameters) when no explicit parameters are present. These are noted in the output file from the calculation.

Advantages of deriving forcefields from quantum calculations

The use of quantum calculations in the development of second-generation forcefields has the advantages that:

♦ Sufficient data are available for accurately determining all the forcefield parameters.

♦ The resulting forcefield may be broad in terms of the types of molecules and molecular environments that may be modeled, since no recourse to experiment is required, even for unusual or transient species. Properties can be modeled for:

Isolated small molecules (structure, thermodynamics, spectros-copy).

Condensed phases (crystal structure, sublimation energies, heats of vaporization).

Macromolecular systems.

♦ The resulting forcefield is consistent, since all parameters, func-tional groups, and molecular species are modeled in the same


2. Forcefields

way. This is in contrast to forcefields whose parameters are derived empirically, since the experimental data for different molecules necessarily come from greatly differing sources and types of measurements, and are sometimes of questionable accuracy.

♦ Fewer atom types are necessary.

CFF91, PCFF, CFF, COMPASS—consistent forcefields

Functional form

All the CFF forcefields (CFF91, CFF, PCFF, COMPASS) have the same functional form, differing mainly in the range of functional groups to which they were parameterized (and therefore, having slightly different parameter values). These differences can be examined by using the forcefield editing capabilities of Cerius2 and Insight or in the forcefield files. Atom equivalences for assign-ment of parameters to atom types may also differ, as may some combination rules for nonbond terms (see Preparing the Energy Expression and the Model for explanation of these processes, which occur during forcefield setup).

The analytic expressions used to represent the energy surface are shown in Eq. 9. Both anharmonic diagonal terms and many cross-terms are necessary for a good fit to a variety of structures and rel-ative energies, as well as to vibrational frequencies.

The CFF forcefields employ quartic polynomials for bond stretch-ing (Term 1) and angle bending (Term 2) and a three-term Fourier expansion for torsions (Term 3). The out-of-plane (also called inversion) coordinate (Term 4) is defined according to Wilson et al. (1980). All the crossterms up through third order that have been found to be important (Terms 5–11) are also included—this gives a forcefield equivalent to the best used in a formate anion test case (Maple et al. 1990). Term 12 is the Coulombic interaction between the atomic charges, and Term 13 represents the van der Waals interactions, using an inverse 9th-power term for the repulsive part rather than the more customary 12th-power term.

No explicit special atom types are used for carbons in strained three- and four-membered rings. The quartic angle potential, com-bined with crossterms, enables accurate description of normal



alkanes, cyclobutane, and cyclopropane with one set of parame-ters.

Note

Eq. 9

Because the Wilson out-of-plane definition is used in the CFF family of forcefields, results calculated with CDiscover, FDiscover, and Cerius2•OFF should agree exactly.


2. Forcefields

K2 b b0–( )2 K3 b b0–( )3 K4 b b0–( )4+ +[ ]

b

∑

2 θ θ0–( )2 H3 θ θ0–( )3 H4 θ θ0–( )4+ +

V1 1 φ φ10

–( )cos–[ ] V2 1 2φ φ20

–( )cos–[ ] V3 1 3φ φ30

–(cos–[+ +[∑

χχ2 Fbb ′ b b0–( ) b′ b ′0–( )

b ′

∑b

∑ Fθθ′ θ θ0–( ) θ′ θ–(θ′

∑θ

∑+ +

Fbθ b b0–( ) θ θ0–( )

θ

∑ b b0–( ) V1 φcos V2 2φcos V+ +[φ

∑b

∑+

b′ b ′0–( ) V1 φcos V2 2φcos V3 3φcos+ +[ ]

φ

∑

θ θ0–( ) V1 φcos V2 2φcos V3 3φcos+ +[ ]

φ

∑

Kφθθ′ φcos θ θ0–( ) θ′ θ′0–( )

θ′

∑θ

∑ qiqjεrij---------i j>

∑ Aijrij9------Bijrij

6------–

i j>

∑+ +

(1)

(2)

(3)

(5) (6)

(7) (8)

(9)

(10)

(11) (12) (13)



CFF91 forcefield

Applicability CFF91 is useful for hydrocarbons, proteins, protein–ligand interac-tions. For small models it can be used to predict: gas-phase geom-etries, vibrational frequencies, conformational energies, torsion barriers, crystal structures; for liquids: cohesive energy densities; for crystals: lattice parameters, rms atomic coordinates, sublima-tion energies; for macromolecules: protein crystal structures.

It has been parameterized explicitly (based on quantum mechan-ics calculations and molecular simulations, see Parameterization) for acetals, acids, alcohols, alkanes, alkenes, amides, amines, aro-matics, esters, and ethers (Maple 1994a, Hwang 1994).

The functional form of CFF91 is exactly as shown in Eq. 9.

Atom types CFF91 has parameters for functional groups that consist of H, Na, Ca, C, Si, N, P, O, S, F, Cl, Br, I, and/or Ar. The atom types of the CFF91 forcefield are listed in Table 27.

Partial charges The bond increment section of the .frc file for CFF91 enables partial charges to be determined whenever the Discover program or the Cerius2•OFF module is able to assign automatic atom types.

CFF forcefield

Applicability CFF (formerly CFF95) was parameterized for additional func-tional groups beyond CFF91 (Maple et al. 1994a, b, Hwang et al. 1994, Hagler & Ewig 1994). It is recommended for all life sciences applications and for organic polymers such as polycarbonates and polysaccharides.

Almost all types of computations within Insight or Cerius2 life sci-ence modules may be performed using CFF. These include inter-molecular and intramolecular energies and forces, optimization of model structures, and molecular dynamics simulations. CFF is not currently implemented for relative free-energy perturbations or for applications in the Docking module of Insight.

Atom types The atom types of the CFF forcefield are listed in the separate doc-umentation for CFF (below).

Additional information Additional information on CFF, which is sold as a separately licensed product, is contained in the MSI Forcefields:CFF book (published separately by MSI).


2. Forcefields

PCFF forcefield for polymers and other materials

Applicability PCFF was developed based on CFF91 and is intended for applica-tion to polymers and organic materials. It is useful for polycarbon-ates, melamine resins, polysaccharides, other polymers, organic and inorganic materials, about 20 inorganic metals, as well as for carbohydrates, lipids, and nucleic acids and also cohesive ener-gies, mechanical properties, compressibilities, heat capacities, elastic constants. It handles electron delocalization in aromatic rings by means of a charge library rather than bond increments.

Validation Parameterization, testing, and validation of PCFF included the compounds listed for CFF91 and these functional groups: carbon-ates, carbamates, phosphazene, urethanes, siloxanes, silanes, ureas (Sun et al. 1994, Sun 1994, 1995), and zeolites (Hill and Sauer 1994). Metal parameters (listed below) were derived by fitting to crystal structures and elastic constants.

Atom types PCFF has parameters for functional groups that consist of those listed for CFF91 and also He, Ne, Kr, Xe. In addition, it includes Lennard–Jones parameters for the metals Li, K, Cr, Mo, W, Fe, Ni, Pd, Pt, Cu, Ag, Au, Al, Sn, Pb. Atom type coverage in PCFF includes those listed for CFF91 (Table 27) and the atoms listed here.

COMPASS forcefield for organic and inorganic materials

A high quality general forcefield

COMPASS (Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies) represents a technology break-through in forcefield method. It is the first ab initio forcefield that enables accurate and simultaneous prediction of gas-phase prop-erties (structural, conformational, vibrational, etc.) and con-densed-phase properties (equation of state, cohesive energies, etc.) for a broad range of molecules and polymers. It is also the first high quality forcefield to consolidate parameters of organic and inorganic materials.

Parameterization COMPASS is an ab initio forcefield — most parameters were derived based on ab initio data. Generally speaking, the parame-terization procedure can be divided into two phases: ab initio parameterization and empirical optimization. In the first phase, partial charges and valence parameters were derived by fitting to ab initio potential energy surfaces. At this point, the van der Waals parameters were fixed to a set of initial approximated parameters.



In the second phase, emphasis is on optimizing the forcefield to yield good agreement with experimental data. A few critical valence parameters were adjusted based on the gas phase experi-mental data. More importantly, the van der Waals parameters were optimized to fit the condensed-phase properties. For cova-lent molecular systems, this refinement was done based on molec-ular dynamics simulations of liquids; for inorganic systems, this is based on energy minimization on crystals.

Validation The parameters for covalent molecules have been thoroughly val-idated using various calculation methods including extensive MD simulations of liquids, crystals, and polymers. (Sun 1998, Sun et al., 1998, Rigby et al. 1998). For the inorganic materials, validations of COMPASS were performed based on energy minimization method.

Applicability The COMPASS forcefield has broad coverage in covalent mole-cules including most common organics, small inorganic mole-cules, and polymers. For these molecular systems, the COMPASS forcefield has been parameterized to predict various properties for molecules in isolation and in condensed phases. The properties include molecular structures, vibrational frequencies, conforma-tion energies, dipole moments, liquid structures, crystal struc-tures, equations of state, and cohesive energy densities. The latest development in COMPASS extended the coverage to include inor-ganic materials - metals, metal oxides, and metal halides using various non-covalent models. Currently, some of these materials have been parameterized. COMPASS is able to predict various solid-state properties: unit cell structures, lattice energies, elastic constants, and vibrational frequencies. The combination of param-eters for organics and for inorganics opens up the possibility of future study of interfacial and mixed systems.

License The COMPASS forcefield is licensed and related files are encrypted. You must have a license for this forcefield in order to use it. The parameters of encrypted forcefields may be viewed with the forcefield editor, but it is not possible to save changes made to the forcefield.

More information For more information about the COMPASS forcefield, please see the COMPASS user guide.


2. Forcefields

MMFF93, the Merck molecular forcefield

The Merck molecular forcefield is derived largely from ab initio calculations and can be accurately applied to a variety of con-densed-phase and aqueous systems. It uses a unique functional form for describing the van der Waals interactions (Halgren 1992) and employs novel combination rules that systematically correlate van der Waals parameters with those that describe experimentally characterized interactions involving rare-gas atoms. Electrostatic interactions are scaled to mimic solution effects.

Applicability Conformational energies, geometries, and vibrational frequencies of small organic molecules.

Functional form The MMFF93 energy expression is similar to that of MM2 and MM3:

Eq. 10

Where:

Ebij

Quartic bond stretching term.

Eaijk

Cubic angle bending term (cosine when the refer-ence angle is ≅ 180°).

Ebaijk

Stretch–bend crossterm.

Eoopijk;l

Term for out-of-plane motion at tri-coordinate cen-ters, using the Wilson definition of the out-of-plane angle.

Etijkl

Torsion twisting term.

EvdWij

Buffered 14–7 van der Waals interaction term.

Eqij

Buffered Coulombic term for electrostatic interac-tions. Use of a distance-dependent dielectric “constant” is supported.

To allow straightforward application to condensed-phase simula-tions employing implicit solvent molecules, MMFF93 includes a dielectric constant in its electrostatic interaction terms.

EMMFF Ebi jEaijk

Ebaijk

Eoop Et EvdW Eq∑+∑+∑+∑+∑+∑+∑=



Charges are implemented via bond increments (similar to CVFF or the CFF family of forcefields) that are included as part of the force-field.

Missing parameters are supplied via a generic step-down and equivalency typing scheme (see Preparing the Energy Expression and the Model).

The terms of the energy expression are calculated in kcal mol-1. They are described in detail by Halgren (1992, 1996a–d, Halgren & Nachbar, 1996).

Rule-based forcefields broadly applicable to theperiodic table

Availability Rule-based forcefields provided by MSI with generally broad applicability across the periodic table include ESFF, the Universial forcefield, and the Dreiding forcefield:

♦ The ESFF forcefield (ESFF, extensible systematic forcefield) is run via the CDiscover program, which is available in the Insight•Discover_3 module.

♦ UFF-VALBOND (VALBOND) is available via the Cerius2 Open Force Field module.

♦ The Universal (UFF, universal forcefield) and Dreiding (Dreiding forcefield) forcefields are accessible through the Cerius2•Open Force Field module.

Parameterization Although the second-generation (Second-generation forcefields accu-rate for many properties) and classical (Classical forcefields) forcefields derive the forcefield parameters by fitting ab initio and/or exper-imental data sets, these rule-based forcefields rely on atomic param-eters coupled with theoretically and empirically derived rules for generating explicit forcefield parameters. The rules embody phys-ical reality (electronegativity, hardness, atomic radii for UFF and ESFF, simple hybridization for Dreiding) and therefore tend to break redundancies and guarantee transferability. As much as pos-sible, the atomic parameters are directly determined from experi-ment or calculated rather than fit.


2. Forcefields

Characteristics ESFF can be used for structure prediction of organic, inorganic, and organometallic systems in gas or condensed phases. It covers all elements in the periodic table up to Rn. Its scope does not extend to highly accurate vibrational frequencies or conforma-tional energies (Shi et al., no date).

UFF covers all elements in the periodic table and is the default forcefield in Cerius2. It is recommended for any system that is not covered by the more accurate special-purpose forcefields. It gives better structures than the Dreiding forcefield but may not be as accurate for properties that depend on intermolecular interactions.

In the VALBOND formalism, hybrid orbital strength functions are used as the basis for a molecular expression of molecular shapes. These functions are suitable for accurately describing the energet-ics of distorted bond angles not only around the energy minimum, but also for very large distortions.

The Dreiding forcefield predicts bulk material properties that depend on intermolecular interactions better than does UFF, but it is not as widely applicable to the periodic table. It is not as accurate as the special-purpose forcefields for the materials for which they are applicable.

ESFF, extensible systematic forcefield

Derivation

ESFF was derived using a mixture of DFT calculations on dressed atoms to obtain polarizabilities, gas-phase and crystal structures, etc. The training set included primarily organic and organometal-lic compounds and a few inorganic compounds. The focus was on crystal structures and sublimation energies. The training set included models containing each element in the first 6 periods up to lead (Z = 82) (except for the inert gases), Sr, Y, Tc, La, and the lan-thinides (except for Yb).

Parameters and charges are generated on-the-fly, based on the model configuration, the local environment, and the derived rules.



Functional form

Valence energy The analytic energy expressions for the ESFF forcefield are pro-vided in Eq. 11. Only diagonal terms are included.

Bond energy The bond energy is represented by a Morse functional form, where the bond dissociation energy D, the reference bond length r0, and the anharmonicity parameters are needed. In constructing these parameters from atomic parameters, the forcefield utilizes not only the atom types and bond orders, but also considers whether the bond is endo or exo to 3-, 4-, or 5-membered rings.

The rules themselves depend on the electronegativity, hardness, and ionization of the atoms as well as atomic anharmonicities and the covalent radii and well depths. The latter quantities are fit parameters, and the former three are calculated.


2. Forcefields

Eq. 11

Angle types The ESFF angle types are classified according to ring, symmetry, and π-bonding information into five groups:

♦ The normal class includes unconstrained angles as well as those associated with 3-, 4-, and 5-membered rings. The ring angles are further classified based on whether one (exo) or both bonds (endo) are in the ring. Additionally, angles with only central atoms in a ring are also differentiated.

♦ The linear class includes angles with central atoms having sp hybridization, as well as angles between two axial ligands in a metal complex.

(5)(4)

(3)

(2)

(1)

Epot Db 1 eα– rb rb

0–( )( )

–2

b

∑=Ka

θa0

sin2---------------- θacos θa

0cos–( )2

a

∑

2Ka θacos 1+( )

a

∑Ka

θa θacos2

a

∑2Kan2

--------- 1 nθa( )cos–( ) 2Kaβ r13 ρa–( )–( )+

a

∑

+

(normal)

(linear)

(perpendicular)

(equatorial)

Dτθ1sin

2 θ2sin2

θ10

sin2 θ20

sin2-------------------------------- sign

θ1sinn θ2sin2

θ10

sinn θ20

sinn-------------------------------- nτ[ ]cos+

τ

∑+

Doχ2

o

∑ AiBj AjBi+rnb9---------------------------- 3BiBjrnb

6----------–

nb

∑ qiqjrnb---------nb

∑+ + +(6)



♦ The perpendicular class is restricted to metal centers and includes angles between axial and equatorial ligands around a metal center.

♦ The equatorial class includes angles between equatorial ligands of square planar (sqp), trigonal bipyramidal (tbp), octahedral (oct), pentagonal bipyramidal (pbp), and hexagonal bipyrami-dal (hbp) systems.

♦ The π system class includes angles between pseudoatoms. This class is further differentiated in terms of normal, linear, perpen-dicular, and equatorial types.

The rules that determine the parameters in the functional forms depend on the ionization potential and, for equatorial angles, the periodicity. In addition to these calculated quantities, the parame-ters are functions of the atomic radii and well depths of the central and end atoms of the angle, and, for planar angles, two overlap quantities and the 1–3 equilibrium distances.

Torsions To avoid the discontinuities that occur in the commonly used cosine torsional potential when one of the valence angles approaches 180°, ESFF uses a functional form that includes the sine of the valence angles in the torsion. These terms ensure that the function goes smoothly to zero as either valence angle approaches 0° or 180°, as it should. The rules associated with this expression depend on the central bond order, ring size of the angles, hybridization of the atoms, and two atomic parameters for the central atom which is fit.

Out-of-plane centers The functional form of the out-of-plane energy is the same as in CFF91, where the coordinate (φ) is an average of the three possible angles associated with the out-of-plane center. The single parame-ter that is associated with the central atom is a fit quantity.

Nonbond energy

Partial charges The charges are determined by minimizing the electrostatic energy with respect to the charges under the constraint that the sum of the charges is equal to the net charge on the molecule. This is equiva-lent to equalization of electronegativities.

Derivation The derivation of the rule begins with the following equation for the electrostatic energy:


2. Forcefields

Eq. 12

where χ is the electronegativity and η the hardness. The first term is just a Taylor series expansion of the energy of each atom as a function of charge, and the second is the Coulomb interaction law between charges. The Coulomb law term introduces a geometry dependence that ESFF for the time being ignores, by considering only topological neighbors at effectively idealized geometries.

Atomic charges Minimizing the energy with respect to the charges leads to the fol-lowing expression for the charge on atom i:

Eq. 13

where λ is the Lagrange multiplier for the constraint on the total charge, which physically is the equalized electronegativity of all the atoms. The ∆χ term contains the geometry-independent rem-nant of the full Coulomb summation.

Adjustment to chemical reality

Eqns. 12 and 13 give a totally delocalized picture of the charges in a relatively severe approximation. To obtain reasonable charges as judged by, for example, crystal packing calculations, some modifi-cations to the above picture have been made. Metals and their immediate ligands are treated with the above prescription, sum-ming their formal charges to get a net fragment charge. Delocal-ized π systems are treated in an analogous fashion. And σ systems are treated using a localized approach in which the charges of an atom depend simply on its neighbors. Note that this approach, unlike the straightforward implementations based on the equal-ization of electronegativity, does include some resonance effects in the π system.

Electronegativity and hardness obtained by DFT

The electronegativity and hardness in the above equations must be determined. In earlier forcefields they were often determined from experimental ionization potentials and electron affinities; how-ever, these spectroscopic states do not correspond to the valence states involved in molecules. For this reason, ESFF is based on electronegativities and hardnesses, calculated using density func-tional theory as implemented in DMol. The orbitals are (fraction-

E Ei0 χiqi

12---η iqi2+ +

i

∑ BqiqjRij---------i j>

∑+=

qiλ χ i– χi∆–

η i----------------------------=



ally) occupied in ratios appropriate for the desired hybridization state, and calculations are performed on the neutral atom as well as on positive and negative ions.

van der Waals interactions ESFF uses the 6–9 potential for the van der Waals interactions. Since the van der Waals parameters must be consistent with the charges, they are derived using rules that are consistent with the charges.

Derivation Starting with the London formula:

Eq. 14

where α is the polarizability and IP the ionization potential of the atoms, the polarizability, in a simple harmonic approximation, is proportional to n / IP where n is the number of electrons. Across any one row of the periodic table, the core electrons remain unchanged, so that the following form is reasonable:

Eq. 15

where a′ and b′ are adjustable parameters that should depend on just the period, and neff is the effective number of (valence) elec-trons. Further assuming that α is proportional to R3 and that another equivalent expression to that in Eq. 14 is:

Eq. 16

where ε is a well depth, the following forms are deduced for the rules for van der Waals parameters:

Rules for van der Waals parameters Eq. 17

The van der Waals parameters are affected by the charge of the atom.

Modification for metal atoms

In ESFF we found it sufficient to modify the ionization potential (IP) of metal atoms according to their formal charge and hardness:

Eq. 18

Bi α i2 IP⋅∼( )

α a′IP------

b ′neffIP

-------------+=

Bi εR6∼

Ria

IP( )1 3/------------------

b neff1 3/⋅

IP( )1 3/------------------+= and εi c IP( )=

IP IP( )0 qη i+=


2. Forcefields

Treatment of nonmetals and for nonmetals to account for the partial charges when calculat-ing the effective number of electrons.

ESFF atom types

ESFF atom types (Table 32) are determined by hybridization, for-mal charge, and symmetry rules (Atom-typing rules in ESFF). In addition, the rules may involve bond order, ring size, and whether bonds are endo or exo to rings. For metal ligands the cis–trans and axial–equatorial positionings are also considered. The addition of these latter types affects only certain parameters (for example, bond order influences only bond parameters) and thus are not as powerful as complete atom types. In one sense they provide a fur-ther refinement of typing beyond atom types.

Coverage of the periodic table

The ESFF forcefield has been parameterized to handle all elements in the periodic table up to radon. It is recommended for organome-tallic systems and other systems for which other forcefields do not have parameters. ESFF is designed primarily for predicting rea-sonable structures (both intra- and intermolecular structures and crystals) and should give reasonable structures for organic, biolog-ical, organometallic and some ceramic and silicate models. It has been used with some success for studying interactions of mole-cules with metal surfaces. Predicted intermolecular binding ener-gies should be considered approximate.

UFF, universal forcefield

Cerius2 contains a full implementation of the Universal forcefield, including bond order assignment. The Cerius2 implementation has been rigorously tested and results are in agreement with pub-lished work on this forcefield (Rappé et al. 1992, Casewit et al. 1992a, b, Rappé et al. 1993).

Parameter generation is based on physically realistic rules.

Functional form UFF is a purely diagonal, harmonic forcefield. Bond stretching is described by a harmonic term, angle bending by a three-term Fou-rier cosine expansion, and torsions and inversions by cosine–Fou-rier expansion terms. The van der Waals interactions are described by the Lennard–Jones potential. Electrostatic interactions are described by atomic monopoles and a screened (distance-depen-dent) Coulombic term.



Atom types The Universal forcefield’s atom types are denoted by an element name of one or two characters followed by up to three other char-acters:

♦ The first two characters are the element symbol (for example, N_ for nitrogen or Ti for titanium).

♦ The third character (if present) represents the hybridization state or geometry (for example, 1 = linear, 2 = trigonal, R = an atom involved in resonance, 3 = tetrahedral, 4 = square planar, 5 = trigonal bipyramidal, 6 = octahedral).

♦ The fourth and fifth characters (if present) indicate characteris-tics such as the oxidation state (for example, Rh6+3 represents octahedral rhodium in the +3 formal oxidation state; H_ _ _b indicates a diborane bridging hydrogen type; and O_3_z is a framework oxygen type suitable for zeolites).

Coverage of the periodic table

UFF has full coverage of the periodic table. UFF is moderately accurate for predicting geometries and conformational energy dif-ferences of organic molecules, main-group inorganics, and metal complexes. It is recommended for organometallic systems and other systems for which other forcefields do not have parameters.

Parameterization The Universal forcefield includes a parameter generator that calcu-lates forcefield parameters by combining atomic parameters. Thus, forcefield parameters for any combination of atom types can be generated as required.

The atomic parameters are combined using a prescribed set of equations (rules) that generate forcefield parameters for bond, angle, torsion, inversion (i.e., out-of-plane), and van der Waals and Coulombic energy terms. For further details, including the gener-ator equations, see Rappé et al. (1992).

Dummy atoms are used in π-complexation and are associated with explicit parameters.

ImportantTo obtain correct results when using UFF, calculate fractional bond orders after atom typing the structure and before setting up the energy expression. Cerius2 does this correctly by default, and you need not worry about it unless you change the default behavior.


2. Forcefields

Charges in the Universal forcefield

The Universal forcefield was developed in conjunction with the charge equilibration (Rappé & Goddard 1991) method. Therefore this method of electrostatic charge calculation is highly recom-mended for use with the Universal forcefield. For more on the charge equilibration calculation, see the documentation supplied with Cerius2•OFF).

Versions UNIVERSAL1.02 is the most up-to-date, and recommended, ver-sion of the UFF. It includes full bond-order correction. (UFF 1.02 differs from UFF 1.01 in that some explicit torsion parameters were corrected and one of the oxygen atom-typing rules was modified.)

UFF-VALBOND is UFF with a different function to calculate the angle energy, so most things which are true for UFF, are true for UFF-VALBOND.

The burchart1.01–UNIVERSAL1.02 forcefield combines UFF with the Burchart forcefield. See burchart1.01-UNIVERSAL1.02 for more information.

VALBOND

Introduction

Most molecular mechanics methods attempt to describe accurate potential energy surfaces by using a variant of the general valence forcefield, and a large number of parameters. These simple force-fields are not accurate outside the proximity of the energetic min-ima and often are difficult to apply to the different shapes and higher coordination numbers of transition metal complexes.

In the VALBOND formalism, hybrid orbital strength functions are used as the basis for a molecular expression of molecular shapes. These functions are suitable for accurately describing the energet-ics of distorted bond angles not only around the energy minimum, but also for very large distortions.

The combination of these functions with simple valence bond ideas leads to a simple scheme for predicting molecular shapes.

Structures and vibrational frequencies calculated by the VAL-BOND method agree well with experimental data for a variety of molecules from the main group of the periodic table.



UFF-VALBOND is a combination of the original VALBOND method described by Root et al. (1993), augmented with non-orthogonal strength functions taken from Root (1997) and the Uni-versal Forcefield of Rappé et al. (1992).

Validation

Although the original VALBOND was developed for use with the CHARMM forcefield (Brooks et al., 1983), the table below shows that the quality of the new UFF-VALBOND forcefield is compara-ble to the original, and similar to popular forcefields.

Table 4

Molecule Item Calc Ref Diff ExpRef-Exp

Cal-Exp

Ethane H-C-H 108.7 108.3 0.4 107.5 0.8 1.2Ethane C-C-H 110.2 110.6 -0.4 111.2 -0.6 -1.0Propane C-C-C 112.9 112.0 0.9 112.0 0.0 0.9Propane H-C-H 107.6 107.2 0.4 107.8 -0.6 -0.2Butane C-C-C 112.9 112.0 0.9 113.3 -1.3 -0.4Isobutane C-C-C 111.3 110.7 0.6 110.8 -0.1 0.5Cyclopentane C2-C1-C5 104.4 103.7 0.7 103.0 0.7 1.4Cyclopentane C1-C2-C3 106.0 104.9 1.1 104.2 0.7 1.8Cyclopentane C2-C3-C4 106.8 106.4 0.4 105.9 0.5 0.9Cyclohexane C-C-C 111.9 110.7 1.2 111.4 -0.7 0.5Cyclohexane H-C-H 107.4 107.7 -0.3 107.5 0.2 -0.1Methyl-Cyclo-

hexaneC-C-C(exo) 111.5 110.9 0.6 112.1 -1.2 -0.6

Norbornane C1-C2-C3 102.5 102.4 0.1 102.7 -0.3 -0.2Norbornane C2-C1-C6 110.6 109.0 1.6 109.0 0.0 1.6

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