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Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group
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10.1063/1.2345196
/content/aip/journal/jcp/125/14/10.1063/1.2345196
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/14/10.1063/1.2345196

Figures

Image of FIG. 1.
FIG. 1.

Standard block configuration in DMRG. From left to right, , , , and .

Image of FIG. 2.
FIG. 2.

Geometries of chemical systems used in the LDMRG study in Sec. IV.

Image of FIG. 3.
FIG. 3.

All-trans-polyenes: active space correlation energy from MP2, CCSD, CCSD(T), and LDMRG(250) as a function of polyene chain length. On the scale of the graph, the LDMRG and CC results nearly overlap.

Image of FIG. 4.
FIG. 4.

All-trans-polyenes: active space correlation energy at CCSD, CCSD(T), and LDMRG(250) level of theory per additionally introduced unit.

Image of FIG. 5.
FIG. 5.

All-trans-polyenes: relative errors in the active space correlation energies for LDMRG with various [compared to the exact LDMRG(250) results]. The black marked curves are the errors of MP2, CCSD, and CCSD(T) as reference. The plot shows absolute magnitudes in logarithmic scale.

Image of FIG. 6.
FIG. 6.

chains (circles) and all-trans-polyenes (squares): asymptotic timing data (i.e., total time per sweep) of LDMRG with (filled marks) and (unfilled marks) for screening in log-log representation with linear fit.

Image of FIG. 7.
FIG. 7.

All-trans-polyenes: convergence of the relative errors in the active space correlation energies for LDMRG as a function of [compared to the exact LDMRG(250) results]. The main plot shows magnitudes in logarithmic scale over (with linear fit); the inlay shows them over .

Image of FIG. 8.
FIG. 8.

Symmetric dissociation of : potential energy curves from RHF, MP2, and exact LDMRG. On the scale of the graph, the few available CCSD, and CCSD(T) data points were indistinguishable from the LDMRG data.

Image of FIG. 9.
FIG. 9.

Symmetric dissociation of : relative errors in the correlation energies at MP2, CCSD, CCSD(T), and different LDMRG levels of theory (compared to the exact LDMRG results) in logarithmic scale.

Image of FIG. 10.
FIG. 10.

Asymmetric dissociation of : potential energy curves from RHF, MP2, and exact LDMRG. On the scale of the graph, the LDMRG, CCSD, and CCSD(T) curves are indistinguishable.

Image of FIG. 11.
FIG. 11.

Asymmetric dissociation of : relative errors in the correlation energies at MP2, CCSD, CCSD(T), and different LDMRG levels of theory (compared to the exact LDMRG results) in logarithmic scale.

Image of FIG. 12.
FIG. 12.

Asymmetric dissociation of : half cross section of the LDMRG -one-particle density matrix at orbital No. 25.

Tables

Generic image for table
Table I.

Time, memory, and disk costs associated with the two-index operators in the original DMRG and screened LDMRG algorithms. The two-index operators determine the asymptotic computational costs of the algorithm.

Generic image for table
Table II.

All-trans-polyenes: dimension of the FCI determinant space, total RHF energy, and RHF active space electronic energy; active space correlation energies at MP2, CCSD, CCSD(T), and different LDMRG levels of theory. All energies are given in hartrees.

Generic image for table
Table III.

-chains: dimension of the FCI determinant space, total RHF energy, and RHF electronic energy; correlation energies at MP2, CCSD, CCSD(T), and LDMRG(50) levels of theory. All energies are given in hartrees.

Generic image for table
Table IV.

Asymptotic scaling exponents (with standard error) of LDMRG depending on and the screening threshold.

Generic image for table
Table V.

All-trans-polyenes: active space correlation energies from LDMRG(250) with screening thresholds of and ; absolute and relative errors of screening (compared to the exact results from screening). All energies are given in hartrees.

Generic image for table
Table VI.

Symmetric dissociation of : total RHF energy and RHF electronic energy; correlation energies at MP2, CCSD, CCSD(T), and various LDMRG levels of theory. All energies are given in hartrees.

Generic image for table
Table VII.

Asymmetric dissociation of : total RHF energy and RHF electronic energy; correlation energies at MP2, CCSD, CCSD(T), and various LDMRG levels of theory. All energies are given in hartrees.

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/content/aip/journal/jcp/125/14/10.1063/1.2345196
2006-10-09
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/14/10.1063/1.2345196
10.1063/1.2345196
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