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Multicomponent density functional theory study of the interplay between electron-electron and electron-proton correlation
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10.1063/1.4709609
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1 Department of Chemistry, 104 Chemistry Building, Pennsylvania State University, University Park, Pennsylvania 16802, USA
J. Chem. Phys. 136, 174114 (2012)
/content/aip/journal/jcp/136/17/10.1063/1.4709609
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/17/10.1063/1.4709609
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Tables

Table I.

Electron-electron and electron-proton correlation energies for the [He-H-He]+ system at a fixed He−He distance of 1.955 Å. The cc-pVDZ electronic basis set and a single s-type Gaussian nuclear basis function with a variationally optimized exponent were used. The NEO-DFT calculations were performed using the EPC2 electron-proton correlation functional with three different electronic exchange-correlation functionals: B3LYP, BLYP, and PBE. The correlation energies E corr(ee), E corr(ep), and E corr(ee, ep) are defined as the differences between the NEO-DFT(ee), NEO-DFT(ep), and NEO-DFT(ee,ep) energies, respectively, and the NEO-HF energy. The additivity error is defined as σadditivity = E corr(ee, ep) − E corr(ee) − E corr(ep). Energies are reported in atomic units.

Table II.

Vibrational frequencies in cm−1 corresponding to the hydrogen vibrational stretching motion calculated with the NEO-HF, NEO-DFT, and FGH methods for the [He-X-He]+ system with X = H, D, or T at a fixed He−He distance of 1.955 Å. The cc-pVDZ electronic basis set was used for all calculations, and the NEO-HF and NEO-DFT calculations utilized a single s-type Gaussian nuclear basis function with a variationally optimized exponent. The NEO-DFT calculations were performed using the EPC1, EPC2, and EPC2-KE electron-proton correlation functionals with the electronic exchange-correlation functional chosen to be the Hartree-Fock exchange. The FGH frequencies were obtained from the splitting between the relevant vibrational states, and the NEO frequencies were obtained from the variationally optimized exponent of the Gaussian nuclear basis function.

Table III.

Vibrational frequencies in cm−1 corresponding to the hydrogen vibrational stretching motion calculated with the NEO-DFT and FGH methods for the [He-X-He]+ system with X = H, D, or T at a fixed He−He distance of 1.955 Å. The cc-pVDZ electronic basis set was used for all calculations, and the NEO-DFT calculations utilized a single s-type Gaussian nuclear basis function with a variationally optimized exponent. The NEO-DFT calculations were performed using the EPC1, EPC2, and EPC2-KE electron-proton correlation functionals with the electronic exchange-correlation functionals B3LYP, BLYP and PBE. The FGH frequencies were obtained from the splitting between the relevant vibrational states, and the NEO frequencies were obtained from the variationally optimized exponent of the Gaussian nuclear basis function.

Table IV.

Decomposition of the electron-proton correlation energy, E epc , into its kinetic and potential energy components, T epc and V epc , respectively, for the EPC2 and EPC2-KE functionals. These values were calculated for the [He-H-He]+ system at a fixed He−He distance of 1.955 Å with the cc-pVDZ electronic basis set and a single s-type Gaussian nuclear basis function with a variationally optimized exponent. The results are given for Hartree-Fock exchange and the B3LYP, BLYP, and PBE electronic exchange-correlation functionals. Energies are reported in atomic units.

/content/aip/journal/jcp/136/17/10.1063/1.4709609
2012-05-04
2014-04-19

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