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Administrator • A single point calculation at a saddle point provides information about the transition state of the model. • A single point energy calculation at any other point on the potential energy surface provides information about that particular geometry, not a stable conformation or transition state. Single point energy calculations can be performed before or after performing an optimization. NOTE: Do not compare values from different methods. Different methods rely on different assumptions about a given molecule. Geometry Optimization Geometry optimization is used to locate a stable conformation of a model. This should be performed before performing additional computations or analyses of a model. Locating global and local energy minima is often accomplished through energy minimization. Locating a saddle point is optimizing to a transition state. The ability of a geometry optimization to converge to a minimum depends on the starting geometry, the potential energy function used, and the settings for a minimum acceptable gradient between steps (convergence criteria). Geometry optimizations are iterative and begin at some starting geometry as follows: 1. The single point energy calculation is performed on the starting geometry. 2. The coordinates for some subset of atoms are changed and another single point energy calculation is performed to determine the energy of that new conformation. 3. The first or second derivative of the energy (depending on the method) with respect to the atomic coordinates determines how large and in what direction the next increment of geometry change should be. 4. The change is made. 5. Following the incremental change, the energy and energy derivatives are again determined and the process continues until convergence is achieved, at which point the minimization process terminates. The following illustration shows some concepts of minimization. For simplicity, this plot shows a single independent variable plotted in two dimensions. The starting geometry of the model determines which minimum is reached. For example, starting at (b), minimization results in geometry (a), which is the global minimum. Starting at (d) leads to geometry (f), which is a local minimum.The proximity to a minimum, but not a particular minimum, can be controlled by specifying a minimum gradient that should be reached. Geometry (f), rather than geometry (e), can be reached by decreasing the value of the gradient where the calculation ends. Often, if a convergence criterion (energy gradient) is too lax, a first-derivative minimization can result in a geometry that is near a saddle point. This 130•Computation Concepts CambridgeSoft Computational Methods Overview
occurs because the value of the energy gradient near a saddle point, as near a minimum, is very small. For example, at point (c), the derivative of the energy is 0, and as far as the minimizer is concerned, point (c) is a minimum. First derivative minimizers cannot, as a rule, surmount saddle points to reach another minimum. NOTE: If the saddle point is the extremum of interest, it is best to use a procedure that specifically locates a transition state, such as the CS MOPAC Pro Optimize To Transition State command. You can take the following steps to ensure that a minimization has not resulted in a saddle point. • The geometry can be altered slightly and another minimization performed. The new starting geometry might result in either (a), or (f) in a case where the original one led to (c). • The Dihedral Driver can be employed to search the conformational space of the model. For more information, see “Tutorial 5: Mapping Conformations with the Dihedral Driver” on page 38. • A molecular dynamics simulation can be run, which will allow small potential energy barriers to be crossed. After completing the molecular dynamics simulation, individual geometries can then be minimized and analyzed. For more information see Appendix 9: “MM2 and MM3 Computations” You can calculate the following properties with the computational methods available through Chem3D using the PES: • Steric energy • Heat of formation • Dipole moment • Charge density • COSMO solvation in water • Electrostatic potential • Electron spin density • Hyperfine coupling constants • Atomic charges • Polarizability • Others, such as IR vibrational frequencies Molecular Mechanics Theory in Brief Molecular mechanics describes the energy of a molecule in terms of a set of classically derived potential energy functions. The potential energy functions and the parameters used for their evaluation are known as a “force-field”. Molecular mechanical methods are based on the following principles: • Nuclei and electrons are lumped together and treated as unified atom-like particles. • Atom-like particles are typically treated as spheres. • Bonds between particles are viewed as harmonic oscillators. • Non-bonded interactions between these particles are treated using potential functions derived using classical mechanics. • Individual potential functions are used to describe the different interactions: bond stretching, angle bending, and torsional (bond twisting) energies, and through-space (non-bonded) interactions. • Potential energy functions rely on empirically derived parameters (force constants, equilibrium values) that describe the interactions between sets of atoms. • The sum of interactions determine the spatial distribution (conformation) of atom-like particles. ChemOffice 2005/Chem3D Computation Concepts • 131 Molecular Mechanics Theory in Brief
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A Guide to CambridgeSoft Manuals An
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Chapter 31: Changes and Audit Trail
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Administrator Tutorial 7: Docking M
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Administrator Connection Table . .
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Administrator Specifying Properties
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Administrator Undoing Changes . . .
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Administrator Chapter 28: Introduci
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Administrator Atom Properties . . .
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CONSULTING & Consulting & Services
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