• journal/journal.article
• aip/jcp
• /content/aip/journal/jcp/136/15/10.1063/1.3703894
• jcp.aip.org
1887
No data available.
No metrics data to plot.
The attempt to plot a graph for these metrics has failed.
Density functional theory with fractional orbital occupations
USD
10.1063/1.3703894
By Jeng-Da Chai1,a)
View Affiliations Hide Affiliations
Affiliations:
1 Department of Physics, Center for Theoretical Sciences, and Center for Quantum Science and Engineering, National Taiwan University, Taipei 10617, Taiwan
a) Electronic mail: jdchai@phys.ntu.edu.tw.
J. Chem. Phys. 136, 154104 (2012)
/content/aip/journal/jcp/136/15/10.1063/1.3703894
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/15/10.1063/1.3703894

## Figures

FIG. 1.

Potential energy curves (in total energy) for the ground state of H2, calculated by both the spin-restricted and spin-unrestricted formalisms of the HF theory and KS-DFT (with LDA and B3LYP functionals). The exact potential energy curve is calculated by the CCSD theory.

FIG. 2.

Potential energy curves (in relative energy) for the ground state of H2, calculated by the spin-restricted HF theory and KS-DFT (with various XC functionals). The exact potential energy curve is calculated by the CCSD theory. The zeros of energy are set at the respective spin-unrestricted dissociation limits.

FIG. 3.

Potential energy curves (in total energy) for the ground state of H2, calculated by spin-restricted TAO-LDA (with various θ). The θ = 0 case corresponds to spin-restricted KS-LDA.

FIG. 4.

Same as Fig. 3 but in relative energy. The zeros of energy are set at the respective spin-unrestricted dissociation limits.

FIG. 5.

Occupation numbers of the 1σ g orbital for the ground state of H2 as a function of the internuclear distance R, calculated by spin-restricted TAO-LDA (with various θ). The θ = 0 case corresponds to spin-restricted KS-LDA. The reference data are the FCI NOONs.37

FIG. 6.

Potential energy curves (in relative energy) for the ground state of H2, calculated by the spin-restricted (with and without the entropy contributions) and spin-unrestricted TAO-LDA (θ = 40 mHartree), where the zeros of energy are set at the spin-unrestricted dissociation limit. The entropy contributions (in total energy) as a function of the internuclear distance R, calculated by spin-restricted TAO-LDA (θ = 40 mHartree), are also shown.

FIG. 7.

Same as Fig. 6 but for θ = 7 mHartree.

FIG. 8.

Potential energy curves (in total energy) for the ground state of N2, calculated by spin-restricted TAO-LDA (with various θ). The θ = 0 case corresponds to spin-restricted KS-LDA.

FIG. 9.

Same as Fig. 8 but in relative energy. The zeros of energy are set at the respective spin-unrestricted dissociation limits.

FIG. 10.

Occupation numbers of the 3σ g orbital for the ground state of N2 as a function of the internuclear distance R, calculated by spin-restricted TAO-LDA (with various θ). The θ = 0 case corresponds to spin-restricted KS-LDA. The reference data are the MRCI NOONs.77

FIG. 11.

Same as Fig. 10 but for the 1π ux orbital.

FIG. 12.

Potential energy curves (in relative energy) for the ground state of N2, calculated by the spin-restricted (with and without the entropy contributions) and spin-unrestricted TAO-LDA (θ = 40 mHartree), where the zeros of energy are set at the spin-unrestricted dissociation limit. The entropy contributions (in total energy) as a function of the internuclear distance R, calculated by spin-restricted TAO-LDA (θ = 40 mHartree), are also shown.

FIG. 13.

Torsion potential energy curves (in relative energy) for the ground state of twisted ethylene as a function of the HCCH torsion angle, calculated by spin-restricted TAO-LDA (with various θ). The zeros of energy are set at the respective minimum energies. The θ = 0 case corresponds to KS-LDA.

FIG. 14.

Occupation numbers of the π (1b2) orbital for the ground state of twisted ethylene as a function of the HCCH torsion angle, calculated by spin-restricted TAO-LDA (with various θ). The θ = 0 case corresponds to spin-restricted KS-LDA. The reference data are the half-projected NOONs of CASSCF method (HPNO-CAS).79

FIG. 15.

Torsion potential energy curves (in relative energy) for the ground state of twisted ethylene as a function of the HCCH torsion angle, calculated by the spin-restricted (with and without the entropy contributions) and spin-unrestricted TAO-LDA (θ = 15 mHartree), where the zeros of energy are set at the respective minimum energies. The entropy contributions (in total energy) as a function of the HCCH torsion angle, calculated by spin-restricted TAO-LDA (θ = 15 mHartree), are also shown.

FIG. 16.

Pentacene, consisting of 5 linearly fuzed benzene rings, is designated as 5-acene.

FIG. 17.

Singlet-triplet energy gap as a function of the acene length, calculated by spin-unrestricted KS-DFT (with LDA, BLYP, and B3LYP functionals), using the 6-31G* basis set. The experimental data are taken from Refs. 80 to 83, and the DMRG data are taken from Ref. 88.

FIG. 18.

Singlet-triplet energy gap as a function of the acene length, calculated by spin-unrestricted TAO-LDA (with various θ), using the 6-31G* basis set. The θ = 0 case corresponds to spin-unrestricted KS-LDA. The experimental data are taken from Refs. 80 to 83.

FIG. 19.

Singlet-triplet energy gap as a function of the acene length, calculated by spin-unrestricted TAO-LDA (θ = 7 mHartree), using both the 6-31G* and 6-31G basis sets.

FIG. 20.

HOMO occupation numbers for the lowest singlet states of n-acenes as a function of the acene length, calculated by spin-restricted TAO-LDA (with various θ)/6-31G*. The θ = 0 case corresponds to spin-restricted KS-LDA. Reference data are the NOONs of the active-space variational 2-RDM method.95

FIG. 21.

Active orbital occupation numbers (HOMO-6, …, HOMO-1, HOMO, LUMO, LUMO+1, …, and LUMO+6) for the lowest singlet states of n-acenes as a function of the acene length, calculated by spin-restricted TAO-LDA (θ = 7 mHartree)/6-31G*.

## Tables

Table I.

Statistical errors (in kcal/mol) of the reaction energies of 30 chemical reactions, Ref. 20, calculated by TAO-LDA (with various θ (in mHartree)). The θ = 0 case corresponds to KS-LDA.

Table II.

Statistical errors (in Å) of EXTS,74 calculated by TAO-LDA (with various θ (in mHartree)). The θ = 0 case corresponds to KS-LDA.

Table III.

Singlet-triplet energy gaps (ST gaps) of n-acenes in the polymer limit (n → ∞), obtained by nonlinear least-squares fittings of 3 different data sets (20- to 74-acene, 30- to 74-acene, and 40- to 74-acene) of the ST gaps calculated by spin-unrestricted TAO-LDA (θ = 7 mHartree)/6-31G, using a power-law fitting function of the form a + bn c . Here, the coefficient of determination R 2 is a statistical measure of the goodness-of-fit (R 2 = 1, for a perfect fit).

/content/aip/journal/jcp/136/15/10.1063/1.3703894
2012-04-17
2014-04-16

Article
content/aip/journal/jcp
Journal
5
3

### Most cited this month

More Less
This is a required field