Molecular Hyperdynamics Coupled with the Nonorthogonal Tight-Binding Approach: Implementation and Validation

Abstract

We present the molecular hyperdynamics algorithm and its implementation to the nonorthogonal tight-binding model NTBM and the corresponding software. Due to its multiscale structure, the proposed approach provides the long time scale simulations (more than 1 s), unavailable for conventional molecular dynamics. No preliminary information about the system potential landscape is needed for the use of this technique. The optimal interatomic potential modification is automatically derived from the previous simulation steps. The average time between adjusted potential energy fluctuations provides an accurate evaluation of physical time during the hyperdynamics simulation. The main application of the presented hyperdynamics method is the study of thermal-induced defects arising in the middle-sized or relatively large atomic systems at low temperatures. To validate the presented method, we apply it to the C60 cage and its derivative C60NH2.Hyperdynamics leads to the same results as a conventional molecular dynamics, but the former possesses much higher performance and accuracy due to the wider temperature region. The coefficient of acceleration achieves 10 7 and more. Straight lines are the linear approximations of these dependencies by the Arrhenius lawwhere  is the time that is needed for the corresponding reaction, Ea is the activation energy, kB is the Boltzmann's constant, T is the temperature. Activation energies can be derived from the slopes of approximating lines. Both MD and hyperdynamics methods predict the formation of the same Stone-Wales defect imaged in Fig. 2a. We obtain the reasonably good agreement of reaction times predicted using these methods, see Fig. 2a. Corresponding activation energies are equal to 6.22 ± 0.99 and 6.44 ± 0.22 eV for MD and hyperdynamics, respectively, see Fig. 3a. They match with the previously reported corresponding energy barrier (6.48 eV 27 ). One can see the high accuracy of hyperdynamics associated with the wide available temperature range. Note, that hyperdynamics provides reaction times of 1 s and more, whereas the comparable number of MD steps can provide only tens of nanoseconds. So, the acceleration factor due to the use of hyperdynamics reaches 10 7 and more.During the studying of heated C60NH2 cage, we observe two possible events: the C-N bond fission ( Fig. 2b) and the formation of bridge configuration with tetra-coordinated nitrogen (Fig. 2c).The latter appears only at very high temperatures (T ≥ 1800 K). Thus, we ignored this scenario in the activation energy evaluation. Such example confirms the importance of accounting for the lowtemperature region to get the actual reaction mechanism. For the fission of the C-N bond, we obtain the activation energies of 3.66 ± 0.55 and 3.28 ± 0.21 eV for MD and hyperdynamics methods, respectively. These values are close to the previously reported binding energies between NH2 functional group and small carbon nanotubes (2.5 ÷ 3.5 eV depending on the tube's chirality indices 28 ). Figure 3b demonstrates reasonably well agreement ...

Probing of Neural Networks as a Bridge from Ab Initio Relevant Characteristics to Differential Scanning Calorimetry Measurements of High‐Energy Compounds

“…Even accelerated approaches such as hyperdynamics require at least thousands of time steps to obtain relevant statistics. [ 21 ] Therefore, molecular dynamics can only be applied to a limited number of compounds. More efficient HEDM preassessment methods are needed to test many candidates or even scan chemical spaces.…”

Subsurface Nitrogen Dissociation Kinetics in Lithium Metal from Metadynamics

“…Metadynamics is one such method, used for accelerating and reconstructing free energy surfaces from molecular simulations, including first-principles simulations involving chemical reactions. − ,, More recently, metadynamics has been used for directly calculating rate constants. − This approach, sometimes called “infrequent metadynamics”, accelerates the time scale of simulations by adding an artificial bias while keeping the critical transition state regions unbiased. − Under the assumptions of transition state theory, it has been shown that the addition of the artificial bias accelerates the time scale of the simulation by a factor α as defined in eq where k B is Boltzmann’s constant, T is temperature, t sim is the simulation time, which is the sum of the time steps taken in the simulation, t phys is the corresponding accelerated physical or real time, s ( t sim ) is the value of one (or more) collective variable(s) s at simulation time t sim , V ( s ( t sim ), t sim ) is the instantaneous value of the added artificial bias potential V at collective variable value s ( t sim ) and simulation time t sim , and the brackets ⟨···⟩ denote the average of the bracketed quantity over the course of the simulation. , The physical elapsed time t phys is therefore a statistical property of the simulation, depending exponentially on the added artificial bias potential. ,,, The exponential dependence of the acceleration factor on the artificial bias allows for substantial acceleration of the time scale, but also leads to potentially noisy or biased reaction rate estimates if the bias potential grows too rapidly or if the collective variables chosen are not sufficient. ,, In particular, the resulting rate estimates can be erroneous or difficult to interpret when the collective variables chosen are insufficient for describing important barriers or configurations that may exist within the initial state. , It should be noted that this “hidden barriers” problem is not unique to the context of calculating rate constants; this is also a well-known cause of error in the ordinary usage of metadynamics for reconstructing free energy surfaces. ,…”