Parameterizing a Forcefield

We can now consider putting actual numbers, kstretch, leq, kbend, etc., into Eqs. 3.2, 3.3, 3.4 and 3.5, to give expressions that we can actually use. The process of finding these numbers is called parameterizing (or parametrizing) the forcefield. The set of molecules used for parameterization, perhaps 100 for a good forcefield, is called the training set. In the purely illustrative example below we use just ethane, methane and butane. 

Parameterizing the Bond Stretching Term A forcefield can be parameterized by reference to experiment (empirical parameterization) or by getting the numbers from high-level ab initio or density functional calculations, or by a combination of both approaches. For the bond stretching term of Eq. 3.2 we need stretch ancl 4q-Experimentally, stretch could be obtained from IR spectra, as the stretching frequency of a bond depends on the force constant (and the masses of the atoms involved) [8], and Zeq could be derived from X-ray diffraction, electron diffraction, or microwave spectroscopy [9], 

Let us find kstretch for the C/C bond of ethane by ab initio (Chapter 5) calculations. Normally high-level ab initio calculations would be used to parameterize a forcefield, but for illustrative purposes we can use the low-level but fast STO-3G method [10], Equation 3.2 shows that a plot of Estretch against (l—leq)2 should be linear with a slope of kstretch. Table 3.1 and Fig. 3.7 show the variation of the energy 

Similarly, the CH bond of methane was stretched using ab initio STO-3G calculations the results are 

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Why does parameterizing a forcefield for transition states present special problems ... 

What advantages or disadvantages are there to parameterizing a forcefield with the results of high-level calculations rather than the results of experiments ... 

Molecular mechanics is essentially empirical, while methods like PPP, CNDO, and AM1/PM3 are semiempirical. What are the analogies in PPP etc. to MM procedures of developing and parameterizing a forcefield Why are PPP etc. only. sY mz empirical ... 

To properly parameterize a molecular mechanics forcefield by calculations only high-level ab initio (or density functional) calculations would actually be used, but this does not affect the principle being demonstrated... 

Accurate force constants etc. can be obtained from high-level ab initio (Chapter 5) or DFT (Chapter 7) calculations. If we use these for a forcefield, then we are parameterizing to match reality only to the extent that the high-level calculations match experiment. Apart from a possible philosophical objection, which we essentially dismissed, there is the question of the trustworthiness of the ab initio or DFT results. For normal molecules, that is, species which are not in some way exotic [1], these calculations do indeed deliver quite reliable results. The advantages they offer over experimental acquisition of the required parameters is that these quantities (1) can be obtained for a wide variety of compounds without regard to synthetic difficulties or commercial availability, (2) are offered up transparently... 

The analogies in semiempirical (SE) methods to MM procedures for developing a forcefield arise from the need to fit experimental values to parameters in equations. In SE parameterization heats of formation, geometric parameters, etc. are used to adjust the values of integrals in the Hamiltonian of quantum-mechanical equations. In MM vibrational frequencies, geometric parameters, etc. are used to... 

One-way, bottom-up interfaces. These involve a one-way, often one-time transfer of information from a lower level of modelling to a higher level. Examples include using a QM calculation to parameterize an MM forcefield, or using an MM simulation to parameterize a CG potential. 

Using an inappropriate forcefield a field parameterized for one class of compounds is not likely to perform well for other classes. 

For each of the three Estretch(X-Y) terms, kstretch(X-Y) and leq(X-Y) are needed, for a total of 6 parameters. For each of the three Ebend(XYZ) terms, kbend(XYZ) and aeq(XYZ) are needed, for a total of 6 parameters. The torsional curve likely requires at least 5 parameters (see chapter 3, section 3.2.2) for reasonable accuracy. This makes a total of 6 + 6 + 5 = 17 parameters. But this would be a very stunted forcefield it has no parameters for nonbonded interactions and so is not suitable for molecules with bulky groups, and it is parameterized only for the atom types sp3 C, H, and Cl. It cannot handle other kinds of carbon and other elements, and it has no special parameters for electrostatic interactions. 

MM methods provide a simpler representation of molecules, in which the fine detail of the electrons represented implicitly via partial charges and, is some cases, molecular polarisabilities. MM models represent molecules as a collection of atoms interacting through classical potentials. There are several MM models (or forcefields), and they dilfer in the functional forms of the interaction potential used between atoms, and in the means by which these interaction potentials are parameterized. Several good recent reviews of MM forcefields have been produced. Several MM forcefields have been developed for application to biomolecular systems. The most popular of these are the CHARMM, AMBER, ... 

Two-way dynamic parameterisation methods. These involve a dynamic transfer of information between separate classical and quantum calculations, e.g. using successive QM calculations to dynamically re-parameterize the classical potentials the QM atoms of an MM forcefield during a live simulation. 

These classical interaction potentials must be parameterized, e.g. the magnitude of the partial charges on each atom in the molecule must be assigned, and the equilibrium bond length and size of the harmonic force constant must be attached to each bond. In the early biomolecular MM forcefields, these parameters were developed to produce molecular models that could reproduce known experimental properties of the bulk system. For example, several MM water models have been developed. ° One of the earliest successful models, TIP3P, was parameterized such that simulations of boxes of TIP3P molecules reproduced known thermodynamic properties of water, such as liquid density and heats of vaporisation. Such a parameterisation scheme is to be applauded, as it ties the molecular model closely to experiment. Indeed many of the common MM models of amino acids were developed by comparison to experiment, e.g. OPLS. Indeed it is such a good... 

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