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Analysis of electron-positron wavefunctions in the nuclear-electronic orbital framework
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10.1063/1.4704124
/content/aip/journal/jcp/136/16/10.1063/1.4704124
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/16/10.1063/1.4704124

Figures

Image of FIG. 1.
FIG. 1.

Dependence of the PsH NEO-XCHF radial (a) electron density, (b) positron density, and (c) electron-positron contact density on the number of terms in the GTG expansion for N gem = 0−8. The dashed lines denote NEO-HF results, and the solid lines denote NEO-XCHF results for varying values of N gem. For electron density, the solid lines for different values of N gem are indistinguishable. For the positron and contact densities, increasing the value of N gem increases the magnitude of the maximum until convergence at N gem = 2 for the positron density and N gem ≈ 7 for the contact density.

Image of FIG. 2.
FIG. 2.

Dependence of the PsH NEO-XCHF radial electron-positron intracule density on the number of terms in the GTG expansion for N gem = 0−8. (a) I ep without integration over angular coordinates and (b) I ep with integration over angular coordinates (i.e., multiplication of part (a) by 4πr 2 for this spherically symmetric system). The dashed lines denote NEO-HF results, and the solid lines denote NEO-XCHF results for varying values of N gem, where increasing the value of N gem increases the magnitude of the maximum until convergence.

Image of FIG. 3.
FIG. 3.

Comparison of the radial PsH electron density (blue), positron density (red), and electron-positron contact density (black) calculated with the NEO-XCHF (solid lines) and ECG44 (dashed lines) methods. Contact densities have been scaled by a factor of 10.

Image of FIG. 4.
FIG. 4.

Comparison of the LiPs electron density (blue) and positron density (red) calculated with the NEO-XCHF (solid lines) and SVM29 (dashed lines) approaches. Square roots of the densities have been plotted for more detailed representation of the valence electron portion of the electron density.

Image of FIG. 5.
FIG. 5.

Comparison of the LiPs (a) electron-positron contact density (black) and (b) electron density (blue) and positron density (red) calculated with the NEO-XCHF (solid lines) and NEO-HF (dashed lines) methods. The contact densities have been normalized. Square roots of the electron and positron densities have been plotted for more detailed representation of the valence electron portion of the electron densities.

Image of FIG. 6.
FIG. 6.

Electron density for e+LiH along the Li—H axis calculated with the NEO-XCHF (solid blue line) and ECG25 (dashed blue line) methods. The origin of the x axis is at the midpoint between the Li and H nuclei, and the circles indicate the positions of the Li (left circle) and H (right circle) nuclei. Note that the solid and dashed lines are virtually indistinguishable everywhere except at the Li and H nuclei.

Image of FIG. 7.
FIG. 7.

Positron density for e+LiH along the Li—H axis calculated with the NEO-XCHF and NEO-HF (solid lines) and ECG25 and HF11 methods by Strasburger (dashed lines). The NEO-XCHF and ECG curves are blue, while the HF-level curves are red. The origin of the x axis is at the midpoint between the Li and H nuclei, and the circles indicate the positions of the Li (left circle) and H (right circle) nuclei. Blue tick marks on the x axis represent the positions of the positron basis function centers in the NEO-XCHF calculations for this system.

Image of FIG. 8.
FIG. 8.

Electron-positron contact density for e+LiH along the Li—H axis calculated with the NEO (solid lines) and ECG25 (dashed line) methods. The NEO contact densities were calculated at the NEO-HF level and at the NEO-XCHF level with N gem = 2 and N gem = 8. The magnitudes of the maxima increase as the number of GTG functions increases. The origin of the x axis is at the midpoint between the Li and H nuclei, and the circles indicate the positions of the Li (left circle) and H (right circle) nuclei.

Image of FIG. 9.
FIG. 9.

Comparison of electron-positron contact densities for e+LiH along the Li—H axis calculated with the ECG method25 (black dashed line) and at the HF level11 (blue solid line) by Strasburger, as well as with the NEO-HF method (red solid line). The HF-level contact densities have been scaled by 24 (Strasburger) and 20 (NEO-HF) and are very similar on this plot. The origin of the x axis is at the midpoint between the Li and H nuclei, and the circles indicate the positions of the Li (left circle) and H (right circle) nuclei.

Tables

Generic image for table
Table I.

Total energies (au), annihilation rates (ns−1), and GTG function parameters, with γ given in units of au, calculated for PsH using the even-tempered 6s/6s positronic basis set. For each separate calculation, the energy and annihilation rate are given in the row corresponding to N gem, the number of terms used in the GTG expansion (i.e., the energy and annihilation rate in a given row are associated with the column for which this row presents the last set of GTG function parameters).

Generic image for table
Table II.

Annihilation rates (ns−1), radial expectation values (au), and average electron-electron, electron-positron, and electron-electron-positron contact densities (au) calculated for PsH with the NEO-HF, NEO-XCHF, SVM, and ECG approaches. The ⟨δ ep ⟩ values for SVM and ECG have been multiplied by a factor of 2 to facilitate comparison of spin-projected quantities to NEO expectation values.

Generic image for table
Table III.

Annihilation rates (ns−1) for PsH, LiPs, and e+LiH calculated with the NEO-HF, NEO-XCHF, SVM, and ECG approaches. In order to provide consistent comparisons, the constants used to calculate NEO annihilation rates with Eq. (9) were obtained from the corresponding SVM and ECG references for each system. These specific values for in Eq. (9) used to calculate the NEO annihilation rates are listed below after the corresponding reference in units of .

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/content/aip/journal/jcp/136/16/10.1063/1.4704124
2012-04-25
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Analysis of electron-positron wavefunctions in the nuclear-electronic orbital framework
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/16/10.1063/1.4704124
10.1063/1.4704124
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