Formation and energetics of head-to-head and tail-to-tail domain walls in hafnium zirconium oxide.

180 ∘ domains walls (DWs) of head-to-head/tail-to-tail (H-H/T-T) type in ferroelectric (FE) materials are of immense interest for a comprehensive understanding of the FE attributes as well as harnessing them for new applications. Our first principles calculation suggests that such DW formation in hafnium zirconium oxide (HZO) based FEs depends on the unique attributes of the HZO unit cell, such as polar-spacer segmentation. Cross pattern of the polar and spacer segments in two neighboring domains along the polarization direction (where polar segment of one domain aligns with the spacer segment of another) boosts the stability of such DWs. We further show that low density of oxygen vacancies at the metal-HZO interface and high work function of metal electrodes are conducive for T-T DW formation. On the other hand, high density of oxygen vacancy and low work function of metal electrode favor H-H DW formation. Polarization bound charges at the DW get screened when band bending from depolarization field accumulates holes (electrons) in T-T (H-H) DW. For a comprehensive understanding, we also investigate their FE nature and domain growth mechanism. Our analysis suggests that a minimum thickness criterion of domains has to be satisfied for the stability of H-H/T-T DW and switching of the domains through such DW formation.

Nonlinear Reaction Coordinate of an Enzyme Catalyzed Proton Transfer Reaction.

We present an in-depth study on the theoretical calculation of an optimum reaction coordinate as a linear or nonlinear combination of important collective variables (CVs) sampled from an ensemble of reactive transition paths for an intramolecular proton transfer reaction catalyzed by the enzyme human carbonic anhydrase (HCA) II. The linear models are optimized by likelihood maximization for a given number of CVs. The nonlinear models are based on an artificial neural network with the same number of CVs and optimized by minimizing the root-mean-square error in comparison to a training set of committor estimators generated for the given transition. The nonlinear reaction coordinate thus obtained yields the free energy of activation and rate constant as 9.46 kcal mol-1 and 1.25 × 106 s-1, respectively. These estimates are found to be in quantitative agreement with the known experimental results. We have also used an extended autoencoder model to show that a similar analysis can be carried out using a single CV only. The resultant free energies and kinetics of the reaction slightly overestimate the experimental data. The implications of these results are discussed using a detailed microkinetic scheme of the proton transfer reaction catalyzed by HCA II.

Coordination Dynamics of Zinc Triggers the Rate Determining Proton Transfer in Human Carbonic Anhydrase II.

We present, for the first time, how transient changes in the coordination number of zinc ion affects the rate determining step in the enzyme human carbonic anhydrase (HCA) II. The latter involves an intramolecular proton transfer between a zinc-bound water and a distant histidine residue (His-64). In the absence of time-resolved experiments, results from classical and QM-MM molecular dynamics and transition path sampling simulations are presented. The catalytic zinc ion is found to be present in two possible coordination states; viz. a stable tetra-coordinated state, T and a less stable penta-coordinated state, P with tetrahedral and trigonal bipyramidal coordination geometries, respectively. A fast dynamical inter-conversion occurs between T and P due to reorganization of active site water molecules making the zinc ion more positively charged in state P. When initiated from different coordination environments, the most probable mechanism of proton transfer is found to be deprotonation of the equatorial water molecule from state P and transfer of the excess proton via a short path formed by hydrogen bonded network of active site water molecules. We estimate the rate constant of proton transfer as kP=1.29×106s-1 from P and kT=4.37×104s-1 from T. A quantitative match of estimated kP with the experimental value, ( kexp∼0.8×106s-1 ) suggests that dynamics of Zn coordination triggers the rate determining proton transfer step in HCA II.

Orthogonal order parameters to model the reaction coordinate of an enzyme catalyzed reaction.

The choice of suitable collective variables in formulating an optimal reaction coordinate is a challenging task for activated transitions between a pair of stable states especially when dealing with biochemical changes such as enzyme catalyzed reactions. A detailed benchmarking study is carried out on the choice of collective variables that can distinguish between the stable states unambiguously. We specifically address the issue if these variables may be directly used to model the optimal reaction coordinate, or if it would be better to use their orthogonalized counterparts. The proposed computational scheme is applied to the rate determining intramolecular proton transfer step in the enzyme human carbonic anhydrase II. The optimum reaction coordinate is determined with and without orthogonalization of the collective variables pertinent to a key conformational fluctuation and the actual proton transfer step at the active site of the enzyme. Suitability of the predicted reaction coordinates in different processes is examined in terms of the free energy profile projected along the reaction coordinate, the rate constant of transition and the underlying molecular mechanism of barrier crossing. Our results indicate that a better agreement with earlier simulation and experimental data is obtained when the orthogonalized collective variables are used to model the reaction coordinate.

Reaction Coordinate, Free Energy, and Rate of Intramolecular Proton Transfer in Human Carbonic Anhydrase II.

The role of structure and dynamics of an enzyme has been investigated at three different stages of its function including the chemical event it catalyzes. A one-pot computational method has been designed for each of these stages on the basis of classical and/or quantum mechanical-molecular mechanical molecular dynamics and transition path sampling simulations. For a pair of initial and final states A and B separated by a high free-energy barrier, using a two-stage selection process, several collective variables (CVs) are identified that can delineate A and B. However, these CVs are found to exhibit strong cross-coupling over the transition paths. A set of mutually orthogonal order parameters is then derived from these CVs and an optimal reaction coordinate, r, determined applying half-trajectory likelihood maximization along with a Bayesian information criterion. The transition paths are also used to project the multidimensional free energy surface and barrier crossing dynamics along r. The proposed scheme has been applied to the rate-determining intramolecular proton transfer reaction of the well-known enzyme human carbonic anhydrase II. The potential of mean force, F( r), in the absence of the chemical step is found to reproduce earlier results on the equilibrium population of two side-chain orientations of key residue His-64. Estimation of rate constants, k, from mean first passage times for the three different stages of catalysis shows that the rate-determining step of intramolecular proton transfer occurs with k ≃ 1.0 × 106 s-1, in close agreement with known experimental results.