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A linear- and sublinear-scaling method for calculating NMR shieldings in atomic orbital-based second-order Møller-Plesset perturbation theory
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10.1063/1.4801084
/content/aip/journal/jcp/138/17/10.1063/1.4801084
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/17/10.1063/1.4801084

Figures

Image of FIG. 1.
FIG. 1.

Absolute value of C-NMR shielding difference (in ppm) between the first carbon atom of various alkanes and the first carbon in CH at HF level and the correlation contribution at MP2 level (cc-pVTZ basis; MP2 results were calculated with the program package ).

Image of FIG. 2.
FIG. 2.

Similarities of the sparsity patterns of the matrices ( ) and ( ) for the molecule CH (STO-3G basis). Elements are signed by different colours dependent on their sizes: value >10 yellow, >10 red, >10 green, >10 cyan, >10 blue, and >10 white.

Tables

Generic image for table
Table I.

Correlation contribution to C-NMR shieldings (in ppm) at MP2 level in dependence of the number of Laplace points. In addition, the difference to the MO-MP2 shieldings is given in parentheses (6-311G** basis for CH, CHCH, and CHCH, and 3-21G for the other systems).

Generic image for table
Table II.

Correlation contribution to H-NMR shieldings (in ppm) at MP2 level in dependence of the number of Laplace points. In addition, the difference to the MO-MP2 shieldings is given in parentheses (6-311G** basis for CH, CHCH, and CHCH, and 3-21G for the other systems).

Generic image for table
Table III.

Number of significant elements and scaling behavior (in parentheses) of transformations and contractions involving the perturbed pseudo-densities as shown in Eqs. (9) and (17) (for calculating C-NMR shieldings of the first and sixth C-atom of CH or CH, respectively; one Laplace point; ϑ = 10; basis set STO-3G; perturbations and ). For comparison also the scaling behavior of the perturbed and unperturbed pseudo-densities is listed.

Generic image for table
Table IV.

Screening influence on C-NMR shieldings for the first C-atom of alkanes (STO-3G basis) as compared to the exact value (deviation in ppm) by using five terms of the Eqs. (33) and (34) (labeled 5×) and ten terms (denoted 10×). For a description of the approximations see text. The first threshold applies to selecting significant elements in the matrix product and the second to used integral products and . The data apply to one Laplace point.

Generic image for table
Table V.

The first two rows show the number of significant elements and scaling behavior (in parentheses) of the contributing products within the matrix multiplication of the second derivative of the pseudo-densities with the R-matrices (see Eq. (28) ). Furthermore, the effect of a preliminary preselection using the 5×-screening (discussed in text) is shown: The number of preselected significant elements and scaling behavior (in parentheses) in the R-matrices and in the contraction products of two-electron integrals to form the R-matrices [Eq. (7) ] is listed for different thresholds (C-NMR shieldings of the first C-atom of different alkanes; one Laplace point; basis set STO-3G).

Generic image for table
Table VI.

Number of significant elements and scaling behavior (in parentheses) of the Z-vector for avoiding and the contractions with the two-electron integrals (). For comparison also the unfavorable scaling behavior of and of its contractions is shown, which are avoided in our present formulation (C-NMR shieldings of the first C-atom of different alkanes; one Laplace point; ϑ = 10; basis set STO-3G; perturbation and ).

Generic image for table
Table VII.

Number of significant elements and scaling behavior (in parentheses) of the Z-vector employed for avoiding and the contractions with the two-electron integrals. Different thresholds are listed (C-NMR shieldings of the first C-atom of different alkanes, one Laplace point; basis set STO-3G; thresholds for the R-matrices: 10 for the matrices, 10 for the contractions).

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/content/aip/journal/jcp/138/17/10.1063/1.4801084
2013-05-01
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A linear- and sublinear-scaling method for calculating NMR shieldings in atomic orbital-based second-order Møller-Plesset perturbation theory
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/17/10.1063/1.4801084
10.1063/1.4801084
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