The Basic Paradigm

Perhaps because the development of molecular force fields to date has been based almost exclusively on fitting experimental results, the term empirical is often used in reference to the nature of these force fields, in distinction from ab initio quantum mechanical calculations, which are based on first principles. However, the empirical behavior results from first principles, and, in fact, much of this review will focus on tracing empirical behavior from first principles and ab initio calculations. 

Equation [1] is believed to capture the physics of molecular systems. It should account for equilibrium structures, vibrational specta, and thermodynamic functions. The task at this point, then, is to properly specify the functional form of the various contributions to the energy and determine their characteristic constants. 

To the lowest order of approximation (which is also very popular), the valence coordinates in Eq. [1] are represented as simple harmonic springs, as implied above for the example of NaCl, characterized by their equilibrium lengths and spring or force constants. For this reason Eq. [1] is often referred to as a force field. Flowever, a polyatomic molecule is more than a collection of springs, and so more elaborate model functions are needed. (Nevertheless, the terms force constants and force field are usually retained.) A successful elucidation of the various functions in Eq. [1] should yield, desirably, the potential energy surface to within several tenths of a kilocalorie per mole in the regions near chemical equilibrium and/or low-lying torsional barriers.  

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The basic paradigm underlying the field of research broadly referred to as quantitative structure-activity relationship (QSAR) modeling is that the structure of the chemical determines its activity ... 

T.F. Quatieri and R.J. McAulay Audio Signal Processing Based on Sinusoidal Analysis/Synthesis. One of the basic paradigms of digital audio analysis, coding (i.e. analysis/synthesis) and synthesis systems is the sinusoidal model. It has been used for many systems from speech coding to music synthesis. The chapter contains the unified view of both the basics of sinusoidal analysis/synthesis and some of the applications. 

Many fundamental concepts of human health risk assessment from chemical and biological hazards have been described in Risk Assessment in the Federal Government Managing the Process (NRC, 1983). The basic paradigm developed in that report is shown in Figure 6-1, and it captures the two key components—risk assessment and risk management—that apply equally well to building protection situations. 

By the early 1990s, the basic paradigm that efficient protein folding in vivo depends on a set of highly conserved proteins termed molecular chaperones was well established (Cheng et at., 1989 Gething and... 

At this point we may go back to the basic paradigm discussed in the first section, which is our starting point for deriving empirical force fields. As stated there, empirical force fields are based on the realization that, for many needs, the physics entailed in the Schrbdinger equation can be captured without the full N... 

A core policy requirement for the development of the Part IIA regime was that it should reflect the polluter pays principle . This is internationally accepted as the basic paradigm for environmental liabilities and responsibilities. However, implementing the polluter pays principle for historic contamination is not a simple task. There may, for example, have been a considerable chain of custody for different contaminants over the time they have been in the ground. 

That said, with the provision of huger, labelled corpora, the natural progression has still been towards using machine-learning techniques to predict prominence. We should probably not be surprised to find that these techniques follow the basic paradigm used for... 

The basic paradigm of a filter instrument is that many applications may be run using a few select wavelengths. Experience has shown that most organic materials have common moieties, i.e., C-H, O-H, and N-H... 

Just as the Gaussian chain is the basic paradigm of the statistics of polymer solutions, so is its extension to the bead-spring model still basic to current work in the held of polymer dynamics. The two limiting cases of free draining (no hydrodynamic interaction between beads, characterized by the draining parameter A = 0) and non-free draining (dominant hydrodynamic interaction, A= CO, due to Rouse and Zimm, respectively, are sufficiently familiar that the approach is often known as the Rouse-Zimm model. ... 

Once the war was over in 1945, Fuoss accepted the Sterling Chair in Chemistry at Yale. The team of Onsager, Kirkwood and Fuoss made Yale the premier theoretical chemistry department in the world at this time. The focus of his work at Yale was on electrolyte solutions, polyelectrolytes and the statistical mechanics of condensed phase systems. He was elected to the National Academy of Sciences in 1951. While his interests continued to evolve after this period in directions different than the community of polymer scientists, his contribution to the period of the consolidation of the basic paradigms was seminal. The unique phenomena associated with linear polyelectrolytes stimulated much theoretical activity, both in the time of Fuoss and afterward. It remains a challenging, but rewarding, topic today. 

Multiple PESs may be of simultaneous interest based not only on physical reasons, as emphasized in the previous paragraph, but also for mathematical or computational reasons. Consider the basic paradigm of state-selective methods the nondynamical electron correlation for a specific state is calculated within a model space and then the dynamical electron correlation is calculated. The implicit assumption is that the zero-order model space many-electron basis functions (MEBFs) (e.g., MCSCF functions and MCSCF complementary space... 

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