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An arbitrary order Douglas–Kroll method with polynomial cost
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10.1063/1.3068310
/content/aip/journal/jcp/130/4/10.1063/1.3068310
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/4/10.1063/1.3068310

Figures

Image of FIG. 1.
FIG. 1.

Number of matrix multiplications at different orders for the DK scheme with exponential parametrization; results of Reiher and Wolf from Ref. 27.

Image of FIG. 2.
FIG. 2.

Number of matrix multiplications at different orders of the DK scheme with exponential parametrization; our work.

Image of FIG. 3.
FIG. 3.

Accuracy of total energies of one-electron systems at different orders of the DK method with exponential parametrization. The column axis denotes the value of .

Image of FIG. 4.
FIG. 4.

Accuracy of total energies of many-electron atoms using the arbitrary order method with exponential parametrization. The column axis denotes the value of .

Tables

Generic image for table
Table I.

Number of matrix multiplications necessary for the evaluation of the Hamiltonians. The data of both special exponential and general parametrizations of the unitary transformation up to 200th order are listed. The results of Reiher and Wolf with exponential parametrization up to 14th order are given for comparison.

Generic image for table
Table II.

One-electron ground state energies for the DK scheme employing various parametrizations of the unitary transformation. All results are in atomic (Hartree) units and are obtained with an even-tempered Gaussian basis set of 50 exponents. The electron rest energy has been subtracted in all cases.

Generic image for table
Table III.

Expectation of in the one-electron ground state for the DK scheme employing various parametrizations of the unitary transformation. All results are in atomic (Hartree) units and are obtained with an even-tempered Gaussian basis set of 50 exponents.

Generic image for table
Table IV.

One-electron ground state energies and expectation values of operators , for the DK scheme employing various parametrizations of the unitary transformation. The results of the BSS method and DEQ (Dirac equation) are also presented. All results are in atomic (Hartree) units and are obtained with an even-tempered Gaussian basis set of 50 exponents.

Generic image for table
Table V.

One-electron ground state energies and expectation values of transformed operators , for the DK scheme employing the exponential type of unitary transformation. All results are in atomic (Hartree) units and are obtained with an even-tempered Gaussian basis set of 50 exponents.

Generic image for table
Table VI.

Hartree–Fock all-electron ground state energies and expectation values of and for the radon atom. A quadruple-zeta Gaussian basis set of the form (Ref. 39) and the speed of light have been used for all calculations and a point nuclear model was employed.

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/content/aip/journal/jcp/130/4/10.1063/1.3068310
2009-01-27
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: An arbitrary order Douglas–Kroll method with polynomial cost
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/4/10.1063/1.3068310
10.1063/1.3068310
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