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Higher-order symplectic integration in Born–Oppenheimer molecular dynamics
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10.1063/1.3268338
/content/aip/journal/jcp/131/24/10.1063/1.3268338
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/24/10.1063/1.3268338

Figures

Image of FIG. 1.
FIG. 1.

Total energy for a molecular dynamics simulation of an molecule with three different integration methods (XL-BOMD with symplectic Verlet shown with a dotted line in blue, linear extrapolation shown with a dashed line in green, and XL-BOMD fourth order shown with a black solid line). The number of SCF cycles in the SCF optimization is 4 for all methods and the time step is chosen for each method such that the computational cost is the same per unit time of the simulation.

Image of FIG. 2.
FIG. 2.

Error amplitude, Eq. (9), for a molecule for different numbers of SCF cycles vs increasing values of . Shown are 1 SCF per time step in blue, 3 SCF:s per time step in red, and 5 SCF:s per time step in black. The integrator used is McLachlan and Atela’s fourth order integrator for which the optimized -value is 4.617. The time step is .

Image of FIG. 3.
FIG. 3.

Error amplitude as function of the number of force evaluations per period for the and molecules for the second order optimal and fourth order McLachlan and Atela integrators.

Image of FIG. 4.
FIG. 4.

Error amplitude as function of the number of force evaluations per period for the molecule and all third order integrators.

Image of FIG. 5.
FIG. 5.

Error amplitude as function of the number of force evaluations per period for the molecule and all fourth order integrators.

Image of FIG. 6.
FIG. 6.

Error amplitude as function of the number of force evaluations per period for the molecule and all sixth order integrators.

Image of FIG. 7.
FIG. 7.

Error amplitude as function of the number of force evaluations per period for all orders for the molecule.

Image of FIG. 8.
FIG. 8.

Error amplitude as function of the number of force evaluations per femtosecond for all orders for the molecule.

Image of FIG. 9.
FIG. 9.

Leapfrog. .

Image of FIG. 10.
FIG. 10.

Optimal second order. .

Image of FIG. 11.
FIG. 11.

Optimal third order. .

Image of FIG. 12.
FIG. 12.

Fourth order Blanes and Moan. .

Image of FIG. 13.
FIG. 13.

Fifth order. .

Image of FIG. 14.
FIG. 14.

Sixth order Blanes and Moan 1. .

Image of FIG. 15.
FIG. 15.

The Blanes and Moan sixth order methods with 1 SCF cycle.

Tables

Generic image for table
Table I.

The symplectic integrators investigated in this work with their order, number of intermediate steps, , and their optimized values.

Generic image for table
Table II.

Coefficients for symplectic integrators.

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/content/aip/journal/jcp/131/24/10.1063/1.3268338
2009-12-28
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Higher-order symplectic integration in Born–Oppenheimer molecular dynamics
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/24/10.1063/1.3268338
10.1063/1.3268338
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