Comparing theory with experiment molecular properties

8 Comparing theory with experiment molecular properties 

The focus so far has been on obtaining the molecular wavefunction or electron density, and the associated energy of an optimized structure. Energy is undoubtedly a fundamental quantity, but experimental methods often characterize molecules by their properties, which arise as responses of the system to external 

First-order Nuclear position Nuclear force 

Third-order Nuclear position Nuclear position Nuclear position Anharmonic coupling 

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We cannot stress enough the importance of benchmarking your calculated results to experimental data. The experimental data can be in the form of structural, chemical, or other information. However, in real-world research problems, there may be no experimental data for corroborating your calculations on the molecules you want to treat. If possible, test the computational method on a similar molecule for which accurate experimental data are available. Ascertain to your satisfaction that the method is reliable. If even this test is not possible, we recommend aiming to use the best level of theory possible for your problem because you will have no way to detect systematic or other errors. The highest level of theory that is practical has a better chance of agreeing with experiment than a lower one. Lower level quantum methods can sometimes predict molecular properties adequately when comparing similar molecules in which effects of systematic errors are minimized. 

For molecules of chemical interest it is not possible to calculate an exact many-electron wave function. As a result, we have to make certain approximations. The most commonly made approximation is the molecular orbital approximation, which is outlined in the next section. Within such a framework, it is useful to define various levels of computational method, each of which can be applied to give a unique wave function and energy for any set of nuclear positions and number of electrons. If such a model is clearly specified and if it is sufficiently simple to apply repeatedly, it can be used to generate molecular potential energy surfaces, equilibrium geometries, and other physical properties. Each such theoretical model can then be explored and the results compared in detail with experiment. If there is sufficient consistent success, some confidence can then be acquired in its predictive power. Each such level of theory therefore should be thoroughly tested and characterized before the significance of its prediction is assessed. 

Another route to find AG is what is usually called the theimodynamic or phenomenological approach. In this, we assume an appropriate expression for AG on the basis of experiments or some theoretical considerations and evaluate the parameters involved from a set of relevant equilibrium data. We then apply the expression of AG so determined to calculate other equilibrium properties and compare the results with the corresponding experimental data. The comparison will show us how adequate the chosen AG is and how it should be modified for better agreement with experiment. Thus, in principle, it is possible to approach step by step a more correct AG of the system under study. Being purely empirical, this method may not be appealing for those who are primcirily interested in events at the molecular level. However, it often allows us to know what thermodynamic factors play a role in controlling the phenomena concerned. The availablity of such information is indeed essential for theoreticians who want to make a more accurate formulation of AG by statistical mechanical theory. 

Vibrational Corrections In order to compare theoretically calculated spectroscopic parameters to experiment, one must consider the effect of molecular vibrations. This is because the properties alluded to above depend upon the structure of the molecule and therefore must be averaged over the vibrational motion of the system under consideration. Force field evaluations in conjimction with vibrational perturbation theory allow the estimation of zero-point vibrational corrections to molecular properties. 

In this chapter, we have presented the fundamentals of molecular theory for the viscoelasticity of flexible homogeneous polymers, namely the Rouse/Zimm theory for dilute polymer solutions and unentangled polymer melts, and the Doi-Edwards theory for concentrated polymer solutions and entangled polymer melts. In doing so, we have shown how the constitutive equations from each theory have been derived and then have compared theoretical prediction with experiment. The material presented in this chapter is very important for understanding how the molecular parameters of polymers are related to the rheological properties of homopolymers. 

This article reviews the following solution properties of liquid-crystalline stiff-chain polymers (1) osmotic pressure and osmotic compressibility, (2) phase behavior involving liquid crystal phasefs), (3) orientational order parameter, (4) translational and rotational diffusion coefficients, (5) zero-shear viscosity, and (6) rheological behavior in the liquid crystal state. Among the related theories, the scaled particle theory is chosen to compare with experimental results for properties (1H3), the fuzzy cylinder model theory for properties (4) and (5), and Doi s theory for property (6). In most cases the agreement between experiment and theory is satisfactory, enabling one to predict solution properties from basic molecular parameters. Procedures for data analysis are described in detail. 

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