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Atomic relaxation was stopped when the forces on atoms were less than 0.01eV/Å.
For the molecules whose fingerprint layers of some atoms were less than six, the character "A" was added manually to the missing layers of the atoms in those molecules to meet the requirement of quantitative calculation.
Geometry optimizations were carried out until the force on each atom and the maximum displacements of the atoms were less than the threshold values of 0.002 a.u. and 0.005 Å.
The relaxation was stopped when the forces on each atoms were less than 5 × 10−4 eV Å−1 and each component of the stress tensor was smaller than 0.05 GPa.
Amino acid sites within each of the structural clusters were in close proximity to each other (for example, their proximal carbon atoms were less than 4 Å distant, against an average distance of 40 Å between all pairs of amino acids).
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Mechanical oscillators have been made from silicon at dimensions of 10 × 100 nanometres, where more than 10percentt of the atoms are less than one atomic distance from the surface.
The number of groups that can accept hydrogen atoms to form hydrogen bonds (estimated by the sum of oxygen and nitrogen atoms) is less than 10.
Therefore, the α-hydrogen atoms are less positively charged in the ethanol dication than in the methanol dication, as evident in the Mulliken population analysis of doubly-charged ethanol (Supplementary Fig. 11).
Moreover, if the attached atoms are less electronegative than the carbon atom, this can also lead to an increase in the singlet-triplet energy gap, and thus to further stabilization of the triplet state.
A conflict is detected when the distance between two atoms is less than 0.4 Å.
The final forces on the atoms are less than 0.01 eV/Å.
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