Hydrogen radial distribution function

Figure 8-6. Comparison of the radial distribution function of the ctiair, boat, and twist conformations of cyclohexane (hydrogen atoms are not considered).

FIGURE 1.32 The radial distribution function tells us the probability density for finding an electron at a given radius summed over all directions. The graph shows the radial distribution function for the 1s-, 2s-, and 3s-orbitals in hydrogen. Note how the most probable radius icorresponding to the greatest maximum) increases as n increases. 

FIGURE 1.42 The radial distribution functions for s-, p-, and cf-orbitals in the first three shells of a hydrogen atom. Note that the probability maxima for orbitals of the same shell are close to each other however, note that an electron in an ns-orbital has a higher probability of being found close to the nucleus than does an electron in an np-orbital or an nd-orbital. 

This plot shows the radial distribution function of the 3s and 3p orbitals of a hydrogen atom. Identify each curve and explain how you made your decision. 

The intensity curves I, II, III, and IV of Fig. 4 are calculated for coplanar trans models with C-H = 1.06 A., the angle H - C=C = 115°, and the angle H—C—H = 109.5°. Although these hydrogen parameters are so chosen as to agree as well as possible with minor peaks of the radial distribution function, no great reliance can be placed on them, and indeed it is likely that for this molecule the C-H bond distance is 1.09 A. The models have the following additional parameters... 

Figure 6.5 The radial distribution functions > (r) for the hydrogen-like atom.

Figure 10 O-H radial distribution function as a function of density at 2000 K. At 34 GPa, we find a fluid state. At 75 GPa, we show a covalent solid phase. At 115 GPa, we find a network phase with symmetric hydrogen bonding. Graphs are offset by 0.5 for clarity.

Thus, effects of the surfaces can be studied in detail, separately from effects of counterions or solutes. In addition, individual layers of interfacial water can be analyzed as a function of distance from the surface and directional anisotropy in various properties can be studied. Finally, one computer experiment can often yield information on several water properties, some of which would be time-consuming or even impossible to obtain by experimentation. Examples of interfacial water properties which can be computed via the MD simulations but not via experiment include the number of hydrogen bonds per molecule, velocity autocorrelation functions, and radial distribution functions. 

Figure 3 The calculated radial distribution function (RDF) between carbon atoms (a) and hydrogen atoms (b) of the /3-carotene and carbon atoms of the acetone molecules, Gc c(r) and Gu-cii"), respectively.

The MD simulations show that second shell water molecules exist and are distinct from freely diffusing bulk water. Freed s analytical force-free model can only be applied to water molecules without interacting force relative to the Gd-complex, it should therefore be restricted to water molecules without hydrogen bonds formed. Freed s general model [91,92] allows the calculation of NMRD profiles if the radial distribution function g(r) is known and if the fluctuation of the water-proton - Gd vector can be described by a translational motion. The potential of mean force in Eq. 24 is obtained from U(r) = -kBT In [g(r)] and the spectral density functions have to be calculated numerically [91,97]. 

The solvation structure around a molecule is commonly described by a pair correlation function (PCF) or radial distribution function g(r). This function represents the probability of finding a specific particle (atom) at a distance r from the atom being studied. Figure 4.32 shows the PCF of oxygen-oxygen and hydrogen-oxygen in liquid water. 

Figure 21.9 Simulated radial distribution functions (RDFs). The go(carbonyi)-H(r) is for the carbonyl oxygen and all hydrogen atoms, the go(hydroxyi)-H(ij for the hydroxyl oxygen and all hydrogen atoms, and the gH(hydroxyi)-o(r) f°r hydroxyl hydrogen and all oxygen atoms.

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