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Using force-matching to reveal essential differences between density functionals in ab initio molecular dynamics simulations
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10.1063/1.3591374
/content/aip/journal/jcp/134/19/10.1063/1.3591374
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/19/10.1063/1.3591374

Figures

Image of FIG. 1.
FIG. 1.

Comparison of the water RDFs from BLYP-340 (red), BLYP-1100 (blue), and HCTH-340 (green) CPMD simulations.

Image of FIG. 2.
FIG. 2.

Short-ranged components of the effective atom-atom forces [panel (a)] and respective potentials [panel (b)] in liquid water by the FM method as functions of interatomic separation from same simulations as in Fig. 1.

Image of FIG. 3.
FIG. 3.

Effective total nonbonded atom-atom forces [panel (a)] and respective potentials [panel (b)] in liquid water by the FM method as functions of interatomic separation from same simulations as in Fig. 1.

Image of FIG. 4.
FIG. 4.

Bonded components of the effective atom-atom forces in liquid water by FM method as functions of interatomic separation from same simulations as in Fig. 1.

Image of FIG. 5.
FIG. 5.

Panel (a): Errors in force Eq. (20) vs time. Instant values of ΔF are shown in black lines for oxygen (left) and hydrogen (right), and cyan line for total error (right). White lines show corresponding running time averages 〈ΔF t (dashed line is for the 〈ΔF tot t ). Panel (b): Distributions of errors PF) for oxygen (solid/thin), hydrogen (dashed), and total (solid/thick).

Image of FIG. 6.
FIG. 6.

Average temperature within last 100 ps segment of trajectories and respective running averages from FF(BLYP,340) (upper curve) and SPC/Fw (Ref. 36) (lower curve) models.

Image of FIG. 7.
FIG. 7.

Comparison of water RDFs from BLYP-340 simulation (red) with that of the FF(BLYP,340) model (blue) and its polynomial fit (Table III) (green).

Image of FIG. 8.
FIG. 8.

Comparison of water RDFs from BLYP-1100 simulation (red), and simulations using the spline (blue) and polynomial (Table IV) (green) fits of the FF(BLYP,1100) model.

Image of FIG. 9.
FIG. 9.

Comparison of water RDFs from HCTH-340 simulation (red) with those from the FF(HCTH,340) model after 500 ps (blue) and after the first 15 ps (green). The g OO using the polynomial fit of the FF(HCTH,340) model (Table V) is also shown (black dashed).

Tables

Generic image for table
Table I.

Structural and dynamical properties of liquid water from different CPMD simulations and experiment. D self , self-diffusion coefficient (for the BLYP-340 and HCTH-340 simulations, the second number is from Ref. 16); , position of a first maximum in the g OO; (g OO) max , value of a first maximum in the g OO; , average HOH angle.

Generic image for table
Table II.

Partial charges, intramolecular potentials, and molecular properties in a gas-phase monomer of the various FM models. q O, q H, partial charges on oxygen and hydrogens; k OH(HH), , intramolecular potential constants; (∠HOH)0, equilibrium HOH angle; μ0, molecular dipole moment. SPC/E model and experimental data are also shown for comparison.

Generic image for table
Table III.

Coefficients of the least-squares fit of the short-ranged forces f ij (r) of the FF(BLYP,340) model using the expansion in Eq. (17) with n max = 18. Atomic units for force and distance were used. At small separations r < r core , the f ij (r) was extrapolated as in Eq. (16). The following core radii were used: a.u., a.u., a.u. The cutoff of 0.79 nm must be applied to this expansion.

Generic image for table
Table IV.

Coefficients of the least-squares fit of the short-ranged forces f ij (r) of the FF(BLYP,1100) model using the expansion in Eq. (17) with n max = 18. Atomic units were used. At small separations r < r core , the f ij (r) was extrapolated as in Eq. (16). The following core radii were used: a.u., a.u., a.u. The cutoff of 0.9 nm must be applied to this expansion.

Generic image for table
Table V.

Coefficients of the least-squares fit of the short-ranged forces f ij (r) of the FF(HCTH,340) model using the expansion in Eq. (17) with n max = 18. Atomic units were used. At small separations r < r core , the f ij (r) was extrapolated as in Eq. (16). The following core radii were used: a.u., a.u., a.u. The cutoff of 1.0 nm must be applied to this expansion.

Generic image for table
Table VI.

Coefficients of the least-squares fit of the short-ranged forces f ij (r) of the FF(HCTH,340) model using the expansion in the truncated Chebyshev series Eqs. (18) and (19) with n max = 18. The following radii, , were used in Eq. (19): a.u, a.u., a.u., and a.u. Atomic units were used. At small separations, r < r core , the f ij (r) was extrapolated as in Eq. (16). A cutoff of 0.95 nm must be applied to this expansion.

Generic image for table
Table VII.

Binding energy U pot , equilibrium O-O distance R OO, total dipole moment , and average molecular dipole moment μmean of the gas-phase dimer from the FM models and the corresponding ab initio calculations using a plane wave basis with cutoff of 80 Ry. Data from the SPC/E model and the experiment are given for a comparison.

Generic image for table
Table VIII.

Properties of different FM water models. All properties reported from NPT simulation unless otherwise noted. “Spl.” and “Pol.” denote representations of short-ranged forces by spline and polynomial expansions, respectively. Polynomial expansion is in powers of 1/r for the FF(BLYP,340) and the FF(BLYP,1100) models (see Tables III and IV) and in the Chebyshev series for the FF(HCTH,340) model (see Table VI). , position of first maximum in the g OO; (g OO) max , value of the first maximum in the g OO; D self , self-diffusion coefficient; U pot , average configuration energy; U inter , average intermolecular energy; , average HOH angle; , average molecular dipole moment; ρ, density; C V , isochoric heat capacity; α P , thermal expansion coefficient; and κ T , isothermal compressibility.

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/content/aip/journal/jcp/134/19/10.1063/1.3591374
2011-05-18
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Using force-matching to reveal essential differences between density functionals in ab initio molecular dynamics simulations
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/19/10.1063/1.3591374
10.1063/1.3591374
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