Thermodynamic integration , complex interactions

Potential energy surfaces of weakly bound dimers and trimers are the key quantities needed to compute transition frequencies in the high resolution spectra, (differential and integral) scattering cross sections or rate coefficients describing collisional processes between the molecules, or some thermodynamic properties needed to derive equations of state for condensed phases. However, some other quantities governed by weak intermolecular forces are needed to describe intensities in the spectra or, more generally, infrared and Raman spectra of unbound (collisional complexes) of two molecules, and dielectric and refractive properties of condensed phases. These are the interaction-induced (or collision-induced) dipole moments and polarizabilities. 

The thermodynamic analyses most often used, particularly fhe van t Hoff mefhod, require that measurements be made at steady-state conditions. In the case of radioligand binding determination of equilibrium constants, fhe time required for fhe protein-ligand interaction to reach steady state depends on fhe incubation temperature, and, therefore, the equilibrium constant must be determined for each temperature studied. For the most accurate results, fhe determination needs to be made at more than two temperatures in order to detect non-linearity. The integrated form of the van t Hoff equation takes fhe simple form fhat is commonly used only if ATT and AS° for the interaction are not temperature dependent otherwise, non-linearity in the van t Hoff plot can arise. Meaningful information can StiU be obtained in such cases, but more complex analysis is required. 

A self-assembly reaction that involves the connection of individual building blocks via noncovalent interactions permits the rational integration of desired functional groups into the resulting molecules. Transition metal coordination bonds have been exploited in the synthesis of numerous metal-based supramolecular architectures in recent years. Complexation of metal ions to multidentate ligands generates equilibrium mixtures of various structures based on numerous possible combinations of metals and ligands.In the situation of thermodynamic control (see Thermodynamics Laws), the... 

With the molecular dynamics method the differential equations describing the classical equations of motion for interacting atoms are solved by step-by-step numerical integration. These differential equations involve derivatives of the energy and, hence, force fields. The solution to the differential equations gives the position and momenta of each atom at each time step (typically a femtosecond) over a total time interval (typically 10 ps-10 ns) limited by the computational speed of the computer, the complexity of the force field, and the size of the molecular system. Thermodynamic properties are obtained from the time and ensemble average of appropriate molecular properties. 

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