Molecule degrees of freedom

Algorithms that explicitly consider water molecules degrees of freedom during docking carmot reliably improve the virtual screening results thus, responsibility for the treatment of explicit water molecules remains largely in the hand of the modeler, who needs to decide which water molecules to retain in the binding pocket. The... 

This formula arises from the fact that each atom is capable of motion in each of three dimensions (the x, y, and z axes of the Cartesian coordinate system). Thus, n atoms will have 3ra total degrees of freedom, but of these 3 correspond to motion of the molecule as a whole through space (translation) and 3 to rotation of the molecule as a whole about its 3 (2 for a linear molecule) principal axes. This leaves 3w-6 (3w-5 for a linear molecule) degrees of freedom for motions of the atoms with respect to each other (vibration). 

Although a diatomic molecule can produce only one vibration, this number increases with the number of atoms making up the molecule. For a molecule of N atoms, 3N-6 vibrations are possible. That corresponds to 3N degrees of freedom from which are subtracted 3 translational movements and 3 rotational movements for the overall molecule for which the energy is not quantified and corresponds to thermal energy. In reality, this number is most often reduced because of symmetry. Additionally, for a vibration to be active in the infrared, it must be accompanied by a variation in the molecule s dipole moment. 

All gases below their critical temperature tend to adsorb as a result of general van der Waals interactions with the solid surface. In this case of physical adsorption, as it is called, interest centers on the size and nature of adsorbent-adsorbate interactions and on those between adsorbate molecules. There is concern about the degree of heterogeneity of the surface and with the extent to which adsorbed molecules possess translational and internal degrees of freedom. 

An interesting point is that infrared absorptions that are symmetry-forbidden and hence that do not appear in the spectrum of the gaseous molecule may appear when that molecule is adsorbed. Thus Sheppard and Yates [74] found that normally forbidden bands could be detected in the case of methane and hydrogen adsorbed on glass this meant that there was a decrease in molecular symmetry. In the case of the methane, it appeared from the band shapes that some reduction in rotational degrees of freedom had occurred. Figure XVII-16 shows the IR spectrum for a physisorbed H2 system, and Refs. 69 and 75 give the IR spectra for adsorbed N2 (on Ni) and O2 (in a zeolite), respectively. 

In an ideal molecular gas, each molecule typically has translational, rotational and vibrational degrees of freedom. The example of one free particle in a box is appropriate for the translational motion. The next example of oscillators can be used for the vibrational motion of molecules. 

Consider a gas of N non-interacting diatomic molecules moving in a tln-ee-dimensional system of volume V. Classically, the motion of a diatomic molecule has six degrees of freedom—tln-ee translational degrees corresponding to the centre of mass motion, two more for the rotational motion about the centre of mass and one additional degree for the vibrational motion about the centre of mass. The equipartition law gives (... 

These results do not agree with experimental results. At room temperature, while the translational motion of diatomic molecules may be treated classically, the rotation and vibration have quantum attributes. In addition, quantum mechanically one should also consider the electronic degrees of freedom. However, typical electronic excitation energies are very large compared to k T (they are of the order of a few electronvolts, and 1 eV corresponds to 10 000 K). Such internal degrees of freedom are considered frozen, and an electronic cloud in a diatomic molecule is assumed to be in its ground state f with degeneracy g. The two nuclei A and... 

The direct dissociation of diatomic molecules is the most well studied process in gas-surface dynamics, the one for which the combination of surface science and molecular beam teclmiques allied to the computation of total energies and detailed and painstaking solution of the molecular dynamics has been most successful. The result is a substantial body of knowledge concerning the importance of the various degrees of freedom (e.g. molecular rotation) to the reaction dynamics, the details of which are contained in a number of review articles [2, 36, 37, 38, 39, 40 and 41]. 

Consider the collision of an atom (denoted A) with a diatomic molecule (denoted BC), with motion of the atoms constrained to occur along a line. In this case there are two important degrees of freedom, the distance R between the atom and the centre of mass of the diatomic, and the diatomic intemuclear distance r. The Flamiltonian in tenns of these coordinates is given by ... 

Variational RRKM theory is particularly important for imimolecular dissociation reactions, in which vibrational modes of the reactant molecule become translations and rotations in the products [22]. For CH —> CHg+H dissociation there are tlnee vibrational modes of this type, i.e. the C—H stretch which is the reaction coordinate and the two degenerate H—CH bends, which first transfomi from high-frequency to low-frequency vibrations and then hindered rotors as the H—C bond ruptures. These latter two degrees of freedom are called transitional modes [24,25]. C2Hg 2CH3 dissociation has five transitional modes, i.e. two pairs of degenerate CH rocking/rotational motions and the CH torsion. 

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