Potential energy intramolecular

Next come the dihedral angles (or torsions), and the contribution that each makes to the total intramolecular potential energy depends on the local symmetry. We distinguish between torsion where full internal rotation is chemically possible, and torsion where we would not normally expect full rotation. Full rotation about the C-C bond in ethane is normal behaviour at room temperature (although 1 have yet to tell you why), and the two CH3 groups would clearly need a threefold potential, such as... 

The actual calculation consists of minimizing the intramolecular potential energy, or steric energy, as a function of the nuclear coordinates. The potential-energy expressions derive from the force-field concept that features in vibrational spectroscopic analysis according to the G-F-matrix formalism [111]. The G-matrix contains as elements atomic masses suitably reduced to match the internal displacement coordinates (matrix D) in defining the vibrational kinetic energy T of a molecule ... 

The final step in the MM analysis is based on the assumption that, with all force constants and potential functions correctly specified in terms of the electronic configuration of the molecule, the nuclear arrangement that minimizes the steric strain corresponds to the observable gas-phase molecular structure. The objective therefore is to minimize the intramolecular potential energy, or steric energy, as a function of the nuclear coordinates. The most popular procedure is by computerized Newton-Raphson minimization. It works on the basis that the vector V/ with elements dVt/dxn the first partial derivatives with respect to cartesian coordinates, vanishes at a minimum point, i.e. = 0. This condition implies zero net force on each atom... 

The interaction potentials between beads were adopted from Refs. [77,78], and are briefly described below for the sake of completeness. The intramolecular potential energy of the freely diffusing protein is given by... 

In practice, the value of the reaction coordinate r is determined from the gas-phase potential energy surface of the complex. Then we use the pair-distribution function for the system (for example, determined by a Monte Carlo simulation) and the intramolecular potential energy Vjatra to calculate the relation between the two rate constants. Alternatively, one may determine the potential of mean force directly in a Monte Carlo simulation. With the example in Fig. 10.2.6 and a reaction coordinate at rj, we see that the potential of mean force is negative, which implies that the rate constant in solution is larger than in the gas phase. Physically, this means that the transition state is more stabilized (has a lower energy) than in the gas phase. If the reaction coordinate is at r, then the potential of mean force is positive and the rate constant in solution is smaller than in the gas phase. 

The intramolecular potential energy is usually not considered for simple molecules, but it should be considered for molecules like C02 because of possible bond stretching and bending [60], The third one depends on the solid nature and on the pore shape. In the case of carbon materials with slit-shaped pores, a Steele 10-4-3 potential can be used for solid-fluid interaction ... 

The intramolecular potential-energy function recently proposed by Anderson has been applied to N02 and the other bent molecules SOz and... 

The potential energy of ffie system is ffie sum of ffie intermolecular potential energy, intramolecular potential energy, and virtual bond energy for all ffie beads in the system (Eq. 1). 

Motion type (1) contributes R to the heat capacity per mole of vibrators (when excited, see Sect. 2.3.3 and 2.3.4). Types (2-4) add only R/2, but may also need some additional inter- and intramolecular potential energy contributions, making particularly the types (3) and (4) difficult to assess. This is at the root of the ease of the link of macromolecular heat capacities to molecular motion. The motion of type (1) is well approximated as will be shown next. The motion of type (2) can be described with the conformational isomers model, and more recently by empirical fit to the Ising model (see below). The contribution of types (3) and (4), which are only easy to describe in the gaseous state (see Fig. 2.9), is negligible for macromolecules. 

The two new terms (relative to Eq. (1)) describe interac ons between the particles of interest and a bath. In a stochastic simulation of local polymer dynamics in dilute solution, the polymer chain is the systmi of interest and the solvent is the bath. Bath particles are not represented explicitly. Rather, the bath damps the motion of the particles with friction terms and supplies stochastic forces Nj which mimic the effect of collisions between solvent molecules and the polymer. Energy is not conserved in the system stochastic forces exdiange energy between the bath and the chain. In principle, P should now indude a hydrodynamic interaction term [14]. In practice, this term is usually neglected in simulatiorm of local dynamics and only the intramolecular potential energy of the polymer is used to determine the force. The stochastic forces in Eq. (2) are characterized by ... 

Among the most used force fields of this kind we cite AMBER-GAFF [9, 10], OPLS [11], and CHARMM [12], all relying on intramolecular potential energy functions like the following ... 

The intramolecular potential energy is very important in determining the conformations of the macromolecules, both in the crystalline state and in the amorphous or solution state. In turn, the potential energy may be taken, in general, as a sum of terms of the kind stretching, bending, torsion, nonbonded,e1ectrostatic ... 

Now the stability of a r-mer molecule is ensured by intramolecular interactions between its elements. For the present purpose it is sufiGl-cient to assume that the corresponding valency forces are harmonic. We may therefore write the intramolecular potential energy... 

Fig. 14. The three-bond element (top). Variation of the intramolecular potential energy barrier with the angle of rotation, 0.

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