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Analysis of the nuclear-electronic orbital method for model hydrogen transfer systems
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10.1063/1.1940634
/content/aip/journal/jcp/123/1/10.1063/1.1940634
http://aip.metastore.ingenta.com/content/aip/journal/jcp/123/1/10.1063/1.1940634

Figures

Image of FIG. 1.
FIG. 1.

One-dimensional proton potential energy curves and the corresponding ground state nuclear wavefunctions for the system with HeHe distances of (a) 1.8, (b) 2.2, and (c) 2.6 Å. These curves were calculated on a one-dimensional grid along the HeHe axis at the full CI/6-31G level, and the proton vibrational wavefunctions were calculated with the FGH method.

Image of FIG. 2.
FIG. 2.

NEO-full CI ground state energies as functions of the HeHe distance for (a) and (b) . All energies are relative to the minimum of the system.

Image of FIG. 3.
FIG. 3.

NEO-full CI ground state energy as a function of the hydrogen basis function separation for two (solid) and three (dashed) hydrogen basis functions, where the third basis function center is placed at the midpoint. The results are given for the (a) system with HeHe distance of 2.6 Å and (b) system with HeHe distance of 1.8 Å.

Image of FIG. 4.
FIG. 4.

Full CI ground state energy as a function of the distance between the He nucleus and a “ghost” hydrogen electronic basis function center for the He atom (solid) and the cation (dashed). Note that the intramolecular BSSE is much larger for the He atom. The energies are relative to the energy of the He and atoms in the absence of the “ghost” hydrogen electronic basis function center.

Image of FIG. 5.
FIG. 5.

A schematic representation of the system used to estimate the intramolecular BSSE for NEO-HF calculations on the system with a HeHe distance of 2.6 Å. The X’s represent the nuclear basis function centers, and the open circles represent the electronic basis function centers. In (a), the proton and electronic basis function centers are identical, as in typical NEO calculations. The separation between basis function centers is 1.60 Å on the left and 0.928 Å on the right. In (b), two additional electronic basis function centers are included, so each calculation includes four electronic and two nuclear basis function centers. The additional electronic basis function centers ensure a consistent electronic basis set. The intramolecular BSSE is estimated to be the difference between the relative energies of the configurations in (a) and (b).

Tables

Generic image for table
Table I.

Optimized nuclear basis function center separations for a range of relatively short HeHe distances in the system. The two hydrogen basis function center positions were optimized variationally at the NEO-full CI level. The smallest eigenvalue from diagonalization of the electronic overlap matrix is also given for each HeHe distance.

Generic image for table
Table II.

Energy differences between the lowest two vibronic states corresponding to the hydrogen stretch for the system with a HeHe distance of 1.9 Å. The numbers in parentheses indicate the number of hydrogen basis function centers. The DZSPDN nuclear basis set includes two each of -, and -type Gaussians, resulting in a total of 20 nuclear basis functions per hydrogen center. The DZSNB (or DZSPNB) include only - (or - and -) type Gaussians, and the nuclear basis set includes two each of - and -type Gaussians and one set of -type Gaussians. The grid calculations were performed with the FGH method3,20 for a one-dimensional grid potential obtained at the full CI level. The 6-31G electronic basis set was used for all calculations.

Generic image for table
Table III.

Energy differences between the lowest two vibronic states for the system with a HeHe distance of 1.6 Å. Two hydrogen basis function centers were used for the NEO calculations. The DZSPDN nuclear basis set includes two each of -, and -type Gaussians, resulting in a total of 20 nuclear basis functions per hydrogen center. The DZSNB (or DZSPNB) include only - (or - and -) type Gaussians. The grid calculations were performed with the FGH method3,20 for a one-dimensional grid potential obtained at the full CI level. The 6-31G electronic basis set was used for all calculations.

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/content/aip/journal/jcp/123/1/10.1063/1.1940634
2005-07-08
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Analysis of the nuclear-electronic orbital method for model hydrogen transfer systems
http://aip.metastore.ingenta.com/content/aip/journal/jcp/123/1/10.1063/1.1940634
10.1063/1.1940634
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