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Assessment of a simple correction for the long-range charge-transfer problem in time-dependent density-functional theory
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10.1063/1.2197829
/content/aip/journal/jcp/124/21/10.1063/1.2197829
http://aip.metastore.ingenta.com/content/aip/journal/jcp/124/21/10.1063/1.2197829

Figures

Image of FIG. 1.
FIG. 1.

Schematic representation of the (uncorrected) coupling matrix for a system consisting of two fragments with a large separation. Left: full coupling matrix in the basis of all occupied (o1/o2)-virtual (v1/v2) orbital pairs for fragments 1 and 2. Right: coupling matrix after the removal of the orbital pairs corresponding to CT excitations. The white areas correspond to matrix elements that will be (close to) zero due to a zero differential overlap.

Image of FIG. 2.
FIG. 2.

Excitation energies for the system He⋯Be as a function of the internuclear distance from SAOP/TZ2P calculations [fcorr: corrected according to Eq. (4)]. CISD data from Ref. 9 are given for comparison.

Image of FIG. 3.
FIG. 3.

Isosurface plots of orbitals around the HOMO-LUMO gap involved in some of the low-lying CT excitations of the ethylene-tetrafluoroethylene complex (ascending orbital energies from left to right; distance: ).

Image of FIG. 4.
FIG. 4.

Adiabatic excited-state potential energy curves (solid lines) for irrep of the ethylene-tetrafluoroethylene complex (SAOP/TZP; zero point: ground-state energy at ). Top: no kernel correction; bottom: kernel correction applied. Labels correspond to the character of the excitation at a distance of ; the character of the excitations may change due to avoided crossings. In the lower diagram, also a pure -like curve for the state (dotted line; shifted by for clarity of presentation) as well as “intuitive” diabatic states are shown. The latter curves connect data points of states with similar characters (dashed lines; shifted by for clarity of presentation).

Image of FIG. 5.
FIG. 5.

Adiabatic excited-state potential energy curves for irrep of the ethylene-tetrafluoroethylene complex (SAOP/TZP; zero point: ground-state energy at ). Top: no kernel correction; bottom: kernel correction applied. Labels correspond to the characters of the excitation at a distance of ; the character of the excitations may change due to avoided crossings.

Image of FIG. 6.
FIG. 6.

Adiabatic excited-state potential energy curves (solid lines) for irrep of the ethylene-tetrafluoroethylene complex (CC2/TZVP; zero point: ground-state energy at ). We also show a pure -like curve for the CT-state (dotted line; shifted by for clarity of presentation) as well as the “intuitive” diabatic potential energy curve for the lowest CT-like transition (dashed lines; shifted by for clarity of presentation). For short distances, the character of this excitation spreads over the three lowest excitations in this irrep (indicated by additional dashed lines).

Image of FIG. 7.
FIG. 7.

Isosurface plots of the orbitals of the ethylene-tetrafluoroethylene complex showing a pronounced mixing for a distance of .

Image of FIG. 8.
FIG. 8.

Excitation energies obtained for different numbers of optimized states in irrep of the ethylene-tetrafluoroethylene complex. Left: default guess (orbital energy differences) used to construct guesses for the lowest excitations; right: corrected guess [Eq. (16)] applied.

Image of FIG. 9.
FIG. 9.

Structure of the acetone-water cluster and isosurface plot of one of the orbitals with a partial lone pair character .

Image of FIG. 10.
FIG. 10.

Spectra (SAOP/TZP/DZ) of the acetone∙20 cluster shown in Fig. 9 from a conventional TDDFT calculation (“no correction”) as well as from two calculations using the asymptotic correction to the coupling matrix with different values of the switching parameter . The spectra are modeled by applying a Gaussian broadening of (dotted lines) and (solid lines). For the spectra with a half width of , also the positions of the maxima are indicated.

Tables

Generic image for table
Table I.

Number of matrix-vector products needed to converge roots (irrep ) in the TDDFT calculation. A: default zero-order guess used to construct lowest-energy eigenvectors and preconditioner; B: guess vectors based on corrected guess energies [Eq. (16)]; and C: guess vectors and preconditioner based on Eq. (16). Note that scheme A converges to eigenvalues different from those obtained in schemes B and C for small (see Fig. 8).

Generic image for table
Table II.

Excitation energies (SAOP/TZP/DZ; in units of eV) of the lowest transitions of the acetone-water cluster shown in Fig. 9 from a conventional TDDFT calculation (“conv.”) and calculations with the asymptotic correction. In the latter case, we either used the default switching parameter or a larger value of . Also given are the oscillator strengths (in a.u.) from the conventional calculation and the dominant orbital contributions; the orbitals are characterized in Table III.

Generic image for table
Table III.

Characterization of the orbitals (SAOP/TZP/DZ) of the acetone-water cluster shown in Fig. 9.

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/content/aip/journal/jcp/124/21/10.1063/1.2197829
2006-06-01
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Assessment of a simple correction for the long-range charge-transfer problem in time-dependent density-functional theory
http://aip.metastore.ingenta.com/content/aip/journal/jcp/124/21/10.1063/1.2197829
10.1063/1.2197829
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