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A natural orbital analysis of the long range behavior of chemical bonding and van der Waals interaction in singlet H2: The issue of zero natural orbital occupation numbers
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10.1063/1.4801431
/content/aip/journal/jcp/138/16/10.1063/1.4801431
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/16/10.1063/1.4801431

Figures

Image of FIG. 1.
FIG. 1.

The interaction potential between two H atoms from full CI (FCI) calculations in three basis sets compared to the Kołos and Wolniewicz 19 reference curve, plus two limited CI calculations in NO basis. 8 NO: only CSFs from (1σ g )2, (1σ u )2, (2σ g )2, (2σ u )2, (1π g )2, (1π u )2 configurations. 2 NO: only CSFs from (1σ g )2, (1σ u )2 configurations.

Image of FIG. 2.
FIG. 2.

The total interaction potential V(R) and the chemical bonding contribution V ChB (R) = E MCSCF (R) − E MCSCF (∞) for singlet H2. The dynamical correlation contribution in the singlet state, as well as the dynamical correlation contribution in the triplet state, are also shown. All calculations based on MCSCF (HF) or FCI in aug-cc-pV6Z basis.

Image of FIG. 3.
FIG. 3.

The interaction potential as function of 1/R 2 over the R interval from R = 11 bohrs (1/R 2 = 0.0083) till R = 13 bohrs (1/R 2 = 0.0059). The least squares fit to a straight line, gives C 6 ≈ −6.27 ± 0.01 and C 8 ≈ −161.99 ± 1.60.

Image of FIG. 4.
FIG. 4.

The CI coefficient of the determinant |nσ u αnσ u β|, C n > C k , kn, in various basis sets.

Image of FIG. 5.
FIG. 5.

All CI coefficients for the |nσ u αnσ u β| determinants except |1σ u α1σ u β| (C 1 tends to ). The red dashed line indicates, as a guide to the eye, in which NOs the p character mostly resides.

Tables

Generic image for table
Table I.

The energy E with respect to two isolated H atoms (i.e., V(R)) and the dynamical correlation energy (the van der Waals bonding) with full CI and with limited CI (in a basis of 8 NOs) from calculations in aug-cc-pV6Z basis. Energies in μH.

Generic image for table
Table II.

The contribution of atomic 2p and 3p orbitals to selected σ u and π g(y/x) orbitals. The 1σ u (not in the figure) is always approximately and has occupation number close to 1. At 4 and 5 bohrs the 3σ u is the second NO with negative occupancy amplitude, at 6 bohrs and beyond the orbital with sizable positive occupancy amplitude is the 2σ u .

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/content/aip/journal/jcp/138/16/10.1063/1.4801431
2013-04-22
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A natural orbital analysis of the long range behavior of chemical bonding and van der Waals interaction in singlet H2: The issue of zero natural orbital occupation numbers
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/16/10.1063/1.4801431
10.1063/1.4801431
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