Calculation methods empirical

Interactions between hydrogen-bond donor and acceptor groups in different molecules play a pivotal role in many chemical and biological problems. Hydrogen bonds can be studied with quantum chemical calculations and empirical methods. 

Traditionally, trajectory calculations were only performed on previously calculated (or empirically estimated) potential energy surfaces. With the increased computational speed of modern computers, it has also become possible to employ direct dynamics trajectory calculations [34, 35]. In this method, a global potential energy surface is not needed. Instead, from some... 

Radmer, R.J., Kollman, P.A., Free energy calculation methods a theoretical and empirical comparison of numerical errors and a new method for qualitative estimates of free energy changes, J. Comput. Chem. 1997,18, 902-919... 

Spectroscopic methods such as IR and Raman have proven to be exceptionally powerful methods for solving many chemistry problems . However, the vibrational assignment, as well as the understanding of the relationship between the observed spectral features and molecular structure or reactivity of the sample, can be very difficult. Theoretical methods can certainly assist to obtain a deeper understanding of the vibrational spectra of new compounds. These are the well-established force field calculations, semi-empirical and ab initio methods . 

Dynamic NMR gives information on the number and symmetries of conformations present in solution and on the energy barriers separating these conformations. This is particularly true for systems with barriers between about 25 and 90 kJ mol-1, a situation which often occurs in the medium ring. The interpretation of the NMR data can be carried out by the examination of molecular models, but this is a relatively crude and sometimes misleading method. Empirical force field (or molecular mechanics) calculations are much superior, even though the parametrization of heteroatoms may be open to question. Quantum mechanical calculations are not very suitable the semiempirical type, e.g. MINDO, do not reproduce conformational properties of even cyclohexane satisfactorily, and the ab initio... 

The intramolecular 4 + 3-, 3 + 3-, 4 + 2-, and 3 + 2-cycloaddition reactions of cyclic and acyclic allylic cations have been reviewed, together with methods for their generation by thermal and photochemical routes.109 The synthetic uses of cycloaddition reactions of oxyallyl cations, generated from polybromo and some other substrates, have also been summarized seven-membered rings result from 4 + 3-cycloadditions of these with dienes.110 The use of heteroatom-stabilized allylic cations in 4 + 3-cycloaddition reactions is also the subject of a new experimental study.111 The one-bond nucleophilicities (N values) of some monomethyl- and dimethyl-substituted buta-1,3-dienes have been estimated from the kinetics of their reactions with benzhydryl cations to form allylic species.112 Calculations on allyl cations have been used in a comparison of empirical force field and ab initio calculational methods.113... 

Various PK parameters such as CL, Vd, F%, MRT, and T /2 can be determined using noncompartmental methods. These methods are based on the empirical determination of AUC and AUMC described above. Unlike compartmental models (see below), these calculation methods can be applied to any other models provided that the drug follows linear PK. However, a limitation of the noncompartmental method is that it cannot be used for the simulation of different plasma concentration-time profiles when there are alterations in dosing regimen or multiple dosing regimens are used. 

Energy calculation and minimization One of the fundamental properties of molecules is their energy content and energy level. Three major theoretical computational methods of their calculation include empirical (molecular mechanics), semiempirical, and ab initio (quantum mechanics) approaches. Energy minimization results in geometry optimization of the molecular structure. 

Depending on the type of interaction between an adsorbed particle and a solid state surface there are cases, where adsorption enthalpies can be calculated using empirical and semi-empirical relations. In the case of atoms with a noble-gas like ground-state configuration and of symmetrical molecules the binding energy (EB) to a solid surface can be calculated as a function of the polarizability (a), the ionization potential (IP), the distance (R) between the adsorbed atom or molecule and the surface, and the relative dielectric constants (e) (Method 9) [58-61] ... 

Various empirical calculation methods to standardize atomic ion quantitation have been proposed, however... 

Determination of appropriate coefficients of heat transfer is required for design calculations on heat-transfer operations. These coefficients can sometimes be estimated on the basis of past experience, or they can be calculated from empirical or theoretical equations developed by other workers in the field. Many semiempirical equations for the evaluation of heat-transfer coefficients have been published. Each of these equations has its limitations, and the engineer must recognize the fact that these limitations exist. A summary of useful and reliable design equations for estimating heat-transfer coefficients under various conditions is presented in this chapter. Additional relations and discussion of special types of heat-transfer equipment and calculation methods are presented in the numerous books and articles that have been published on the general subject of heat transfer. 

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