1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Spin-adaptation and redundancy in state-specific multireference perturbation theory
Rent:
Rent this article for
USD
10.1063/1.4795436
/content/aip/journal/jcp/138/12/10.1063/1.4795436
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4795436

Figures

Image of FIG. 1.
FIG. 1.

Errors of second order SS-MRPT energies for the ground state of the HF system in cc-pVDZ basis. 52 Reference function is CAS(2,2), active orbitals are naturals. Full CI values are subtracted from total SS-MRPT energies. Partitioning is either MP or EN. Label “thresh=1E-8” corresponds to omitting model space CSF's with coefficients smaller than 10−8 in absolute value. No such treatment is applied for label “no thresh.”

Image of FIG. 2.
FIG. 2.

Errors of second order SS-MRPT energies for the ground state of the HF system. Active orbitals are pseudo-canonicals. Full CI values are subtracted from total SS-MRPT energies. Basis set, reference function, and partitionings agree with that of Fig. 1 . Key legends: “” refers to the redundant parametrization of μ with direct spectators included, “, no dir spec” applies the parametrization of Eq. (7) without direct spectators, “ ” uses the non-redundant parametrization of .

Image of FIG. 3.
FIG. 3.

Errors of second order SS-MRPT energies for the ground state of the LiH molecule in Dunning's DZP basis. 53 Reference function is CAS(2,5), active orbitals are pseudo-canonicals. Full CI values are subtracted from total SS-MRPT energies. Partitioning is either MP or EN. See Fig. 2 for key legends.

Image of FIG. 4.
FIG. 4.

The largest singular value of the coefficient sensitivity matrix of SS-MRPT energy (Eq. (18) ) and relaxed coefficients (Eq. (19) ) for the ground state of the HF molecule. Basis set, reference function, and partitioning agrees with Fig. 2 . Key legends are also given at Fig. 2 .

Image of FIG. 5.
FIG. 5.

The largest singular value of the coefficient sensitivity matrix of SS-MRPT energy (Eq. (18) ) and relaxed coefficients (Eq. (19) ) for the ground state of the LiH molecule. Basis set, reference function, and partitioning agrees with Fig. 3 . Key legends are given at Fig. 2 .

Image of FIG. 6.
FIG. 6.

Errors of second order SS-MRPT energies in MP partitioning for the ground state of the HF system. Full CI values are subtracted from total SS-MRPT energies. Basis set and reference function agrees with that of Fig. 2 . Key legends: “, no dir spec” applies the parametrization of Eq. (7) without direct spectators, “ canonical ort” uses the non-redundant parametrization of with the functions of Tables I and III , “ , alternative ort” uses the non-redundant parametrization of with the functions described in Table I of the supplementary material, 48 , drop out” refers to the method where terms of μ of Eq. (7) are dropped to set the parametrization non-redundant, “det” refers to the determinantal approach.

Image of FIG. 7.
FIG. 7.

Errors of second order SS-MRPT energies in MP partitioning for the ground state of the LiH system. Full CI values are subtracted from total SS-MRPT energies. Basis set and reference function agree with that of Fig. 3 . Legends “ ” refers to the non-redundant parametrization of , see Fig. 6 for other key legends.

Tables

Generic image for table
Table I.

Overlapping sets of normalized excited functions and their orthonormalized counterparts for single excitations. Excitation operators based on the orthogonalized functions and the respective amplitudes of cluster operator are also tabulated. Model function ϕ is two-determinantal open-shell as given by Eq. (8) , is assumed. See text for labeling convention.

Generic image for table
Table II.

Relation between cluster amplitudes in the redundant parametrization Eq. (7) of μ and the orthogonal parametrization Eq. (9) of . Case of single excitations. Model function ϕ is two-determinantal open-shell, as given by Eq. (8) . See text for labeling convention.

Generic image for table
Table III.

Overlapping sets of normalized excited functions and their orthonormalized counterparts for double excitations. Excitation operators based on the orthogonalized functions and the respective amplitudes of cluster operator are also tabulated. Model function ϕ is two-determinantal open-shell, according to Eq. (8) . Index ordering < , < , and is assumed. See text for labeling convention. Notation () stands for the parity of the permutation ordering the pair ().

Generic image for table
Table IV.

Relation between cluster amplitudes in the redundant parametrization Eq. (7) of μ and the orthogonal parametrization Eq. (9) of . Case of double excitations. Model function ϕ is two-determinantal open-shell, as given by Eq. (8) . See text for labeling convention. Index ordering < , < , and is assumed. Notation () stands for the parity of the permutation ordering the pair ().

Generic image for table
Table V.

Elements of Eq. (15) , for core → virtual excitation, . Abbreviations: “cs” – closed-shell, “os” – open-shell. Indices and are left blank, when not applicable. Virtual function is assumed normalized. See text for labeling convention and the definition of .

Generic image for table
Table VI.

Elements of Eq. (15) , for core → active excitations, . Abbreviations: “cs” – closed-shell, “os” – open-shell. Indices and are left blank, when not applicable. Virtual function is assumed normalized. See text for labeling convention and the definition of .

Generic image for table
Table VII.

Elements of Eq. (15) , for active → virtual excitations, i.e., . Abbreviations: “cs” – closed-shell, “os” – open-shell. Virtual functions are assumed normalized. See text for for labeling convention and the definition of .

Generic image for table
Table VIII.

Elements of Eq. (15) , for non-coupled double excitations, i.e., = . Values of are collected for the possible combinations of with reference functions, ϕ. Admissible types for CSF ν agree with types listed for μ. Description of CSF μ is indicated in the rows, indices and are given in column headers. Abbreviations: “cs” – closed-shell, “os” – open shell, “n.a.” – not applicable. Shorthand stands for . See text for the definition of . Virtual functions are assumed normalized.

Generic image for table
Table IX.

Matrix of Eq. (15) , for core, active → 2 active excitations, (, ) → (, ). Description of CSF μ is indicated in the rows, together with index , when applicable. Characterization of CSF ν is given in column headers, together with index , when applicable. Abbreviations: “cs” – closed-shell, “os” – open shell. Shorthand stands for . See text for the definition of . Virtual functions are assumed normalized.

The table applies for the core, active → active, virtual excitations also, with substituted for . Column and row referring to a is not applicable in this case.

Loading

Article metrics loading...

/content/aip/journal/jcp/138/12/10.1063/1.4795436
2013-03-28
2014-04-23
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spin-adaptation and redundancy in state-specific multireference perturbation theory
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4795436
10.1063/1.4795436
SEARCH_EXPAND_ITEM