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Quantum Monte Carlo study of Jastrow perturbation theory. I. Wave function optimization
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10.1063/1.3220631
/content/aip/journal/jcp/131/10/10.1063/1.3220631
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/10/10.1063/1.3220631

Figures

Image of FIG. 1.
FIG. 1.

Effect of cumulant representations on the standard error of matrix elements for energy and variance minimization. Results are shown for the Ne atom with Hartree–Fock reference wave function and a matrix element with respect to the two basis functions Eq. (41) vs the number of Monte Carlo sample points. (a) Upper part: relative standard error of the matrix element Eq. (35) (solid line), Eq. (36) (dotted line) and Eq. (37) (dashed line) for Newton’s method. Lower part: relative standard error of the matrix element Eq. (38) (solid line), Eq. (39) (dotted line) and Eq. (40) (dashed line) of the JPTE-I equation. (b) Relative standard error of the corresponding matrix element for JPTV-I (30) (solid line), JPTV-II (31) (dotted line) and Newton’s method (32) (dashed line).

Image of FIG. 2.
FIG. 2.

Ratios of variational correlation energies for Jastrow factors with respect to the exact ground state (upper part) and fixed-node DMC (lower part) energies. Energy optimized correlation functions from the first iteration step of the JPTE-I , JPTE-II and Newton’s method are compared with fully converged FOPIM based on the JPTE-I equation.

Image of FIG. 3.
FIG. 3.

Convergence behavior of JPTE-I (○), JPTE-II (◻), and Newton’s method (◇) for energy optimization with respect to the number of iterations for the (a) Ne atom and (b) .

Image of FIG. 4.
FIG. 4.

Convergence of FOPIM based on the JPTE-I equation, in the case of the Ne atom, for an initial reference wave function with prescribed electron-electron cusp (47). For comparison convergence is shown for a Hartree–Fock wave function as an initial guess.

Image of FIG. 5.
FIG. 5.

Convergence to the ground state energy of for different bond lengths starting from a RHF reference wave function. Results are shown for FOPIM with JPTE-I, JPTE-II, and Newton’s method. The bond length varies from the equilibrium bond length up to . For each method, results are shown only for those bond lengths at which convergence has been achieved.

Image of FIG. 6.
FIG. 6.

Removal of polar configurations by the Jastrow factor for at bond length . (a) RHF and (b) Jastrow wave functions are plotted along the bond axis, i.e., . The nuclei are located at .

Image of FIG. 7.
FIG. 7.

Convergence of the standard deviation of the local energy for the Ne atom with different basis sets for the correlation function. Results are shown for FOPIM with JPTV-I (○), JPTV-II (◇), and Newton’s method . Three different basis sets have been studied: (a) 7 term basis, (b) 17 term basis, (c) 92 term basis. The 7 and 17 term bases were taken from Ref. 33. A Hartree–Fock reference wave function has been taken as an initial guess, except for Newton’s method where in (b) and (c) the JPTV-I result from the first iteration step was chosen.

Tables

Generic image for table
Table I.

Variational energies (Hartree) and standard deviations of the local energy for first row atoms and the molecules and . Jastrow factors have been optimized by FOPIM for energy and variance minimization based on JPTE-I, JPTV-I, and JPTV-II, respectively. Hartree–Fock orbitals have been used for the Slater determinant. For comparison we have also listed fixed-node DMC and “exact” energies.

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/content/aip/journal/jcp/131/10/10.1063/1.3220631
2009-09-10
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Quantum Monte Carlo study of Jastrow perturbation theory. I. Wave function optimization
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/10/10.1063/1.3220631
10.1063/1.3220631
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