Hydrogen, diffusion functions

One or two plus signs can also be added, such as 6—31+G or 6—31++G. A single plus sign indicates that diffuse functions have been added to atoms other than hydrogen. The second plus sign indicates that diffuse functions are... 

Fig. 16. Hydrogen diffusion coefficient as a function of inverse temperature.

The general strategy embodied by this table is to select the most accurate calculation that is computationally practical for a given size system. Note that for the lower-cost methods, you will also need to add diffuse functions and/or additional polarization functions on the hydrogen atoms as appropriate for the systems you are studying. 

The 6-31+G(d) basis set is the 6-31G(d) basis set with diffuse functions added to heavy atoms. The double plus version, 6-31++G(d), adds diffuse functions to the hydrogen atoms as well. Diffuse functions on hydrogen atoms seldom make a significant difference in accuracy. 

Even larger basis sets are now practical for many systems. Such basis sets add multiple polarization functions per atom to the triple zeta basis set. For example, the 6-31G(2d) basis set adds two d functions per heavy atom instead of just one, while the 6-311++G(3df,3pd) basis set contains three sets of valence region functions, diffuse functions on both heavy atoms and hydrogens, and multiple polarization functions 3 d functions and 1 f function on heavy atoms and 3 p functions and 1 d function on hydrogen atoms. Such basis sets are useful for describing the interactions between... 

The values in red are within O.OlA of the experimental value. Using the 6-31G basis set, including diffuse functions on the hydrogen atom, improves the result over that obtained with diffuse functions only on the fluorine atom, although the best result with this basis set is obtained with no diffuse functions at all. 

Hydrogen diffusivity as a function of temperature. The effective diffusivity data of X52 and X65 pipeline steels obtained under gaseous hydrogen charging conditions are compared with the compiled results for the literature. (After Alefeld, G. and Volkl, J. Hydrogen in Metals I—Basic Properties, Springer, New York, 1978.)... 

Fig. 19. Hydrogen diffusion coefficient, measured at 240°C, as a function of phosphine and diborane gas phase doping level, deduced from the data in Fig. 17. The dependence on dangling bond density is indicated on the top horizontal scale (Street el al., 1987b).

Exposure of bulk GaAs Si wafers to a capacitively coupled rf deuterium plasma at different temperatures generates deuterium diffusion profiles as shown in Fig. 1. These profiles are close to a complementary error function (erfc) profile. At 240°C, the effective diffusion coefficient is 3 x 10 12 cm2/s. The temperature dependence of the hydrogen diffusion coefficient is given by (Jalil et al., 1990) ... 

Table 1. Atomization energies and electron affinities (kcal/mol) for LiH at QCISD/MG3 geometries for methods that do not involve diffuse functions on hydrogen.

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