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Pulay forces from localized orbitals optimized in situ using a psinc basis set
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Image of FIG. 1.
FIG. 1.

Convergence of the forces with respect to the kinetic energy cutoff and the NGWF radius. Left: force acting on an oxygen atom in CO2 along the covalent bond. Right: force acting on a hydrogen atom in H2O dimer along the hydrogen bond. The first row corresponds to the Hellmann-Feynman force, the second to the Pulay force, and the third are the Pulay-corrected (PC) total forces (Hellmann-Feynman forces plus Pulay). R refers to the NGWF radii.

Image of FIG. 2.
FIG. 2.

Egg-box effect on the energy (top) and force along the covalent bond (bottom) of a CO2 molecule with SZ (red circles), DZP (blue squares), and TZDP (green diamonds) PAO basis sets and NGWFs (black triangles).

Image of FIG. 3.
FIG. 3.

Convergence of the maximum absolute value of the force during geometry optimization of the adenine-thymine DNA base pair with NGWF radii of 3.70 Å (top) and 7.94 Å (bottom). The convergence threshold was 0.015 eV/Å.

Image of FIG. 4.
FIG. 4.

Convergence of the binding energy in the adenine-thymine complex with increasing NGWF radii. The calculations that use structures obtained with Pulay-corrected forces show systematic convergence (blue squares) with increasing NGWF radius. In contrast, the calculations with structures obtained with uncorrected Hellmann-Feynman forces (red circles) lack of convergence and show large variations of the binding energy. The calculations represented with black crosses show convergence of the binding energy with increasing NGWF radius. They are based on fixed molecular geometries obtained with Pulay-corrected forces and NGWF radius of 3.70 and 7.94 Å.

Image of FIG. 5.
FIG. 5.

Convergence of the maximum force during the BFGS geometry optimization of the tennis-ball dimer using Hellmann-Feynman forces (top left molecule) and Pulay-corrected forces (top right).

Image of FIG. 6.
FIG. 6.

Convergence of the maximum value of the force during the geometry optimization of the DNA molecule using NGWFs and DZP and TZDP PAO basis sets.


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Table I.

Geometry optimization of adenine-thymine using ONETEP for different localization radii R α with HF forces and PC forces. Results show the hydrogen bond lengths, the maximum absolute value of the force, |F|max, and the number of BFGS steps required.

Generic image for table
Table II.

Length of the two hydrogen bonds in the adenine-thymine complex obtained with different PAO multiple-ζ basis sets of different localization radius, R, given in Å. The total forces converged to 0.015 Å/eV.

Generic image for table
Table III.

Structural parameters of the optimized 1045 atom DNA fragment as optimized by ONETEP. N⋯H(4), N⋯H(8), and N⋯H(12) correspond to the hydrogen bond of the fourth, eighth, and twelfth pairs, respectively, that involve a nitrogen atom.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Pulay forces from localized orbitals optimized in situ using a psinc basis set