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WIREs Comput Mol Sci
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Car–Parrinello molecular dynamics

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The Car–Parrinello (CP) method made molecular dynamics simulation with on‐the‐fly computation of interaction potentials from electronic structure theory computationally feasible. The method reformulates ab initio molecular dynamics (AIMD) as a two‐component classical dynamical system. This approach proved to be valuable far beyond the original CP molecular dynamics method. The modern formulation of Born–Oppenheimer (BO) dynamics is based on the same basic principles and can be derived from the same Lagrange function as the CP method. These time‐reversible BO molecular dynamics methods allow higher accuracy and efficiency while providing similar longtime stability as the CP method. AIMD is used in many fields of computational physics and chemistry. Its applications are instrumental in fields as divers as enzymatic catalysis and the study of the interior of planets. With its versatility and predictive power, AIMD has become a major approach in atomistic simulations. © 2011 John Wiley & Sons, Ltd.

Figure 1.

Schematic view of a Born–Oppenheimer‐type dynamical system with slow variables q, propagated initial guess fast variables x, and optimized fast variables y.

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Figure 2.

Constant of motion along a 10 ps trajectory calciulated using Born–Oppenheimer molecular dynamics. The system is 32 water molecules at 300K and experimental density. The blue line shows the result from a simulation using the always stable predictor– corrector (ASPC) integrator with K = 3. The red line is the result from a simulation using a linear extrapolation of density matrix. The convergence criteria was in both cases ϵ = 10−5 (root mean square of orbital transformation gradient48). The average number of iterations was 3 for ASPC and 4 for the linear density matrix extrapolation.

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Figure 3.

Analysis of error in forces on nuclei from a 1 ps trajectory of 64 water molecules. The error is defined as the difference between a fully converged calculation and a calculation stopped at ϵ = 10−5 (root mean square of orbital transformation gradient48). (a) Distribution of error in atomic units on hydrogen (green line), oxygen atoms (red line), and all atoms (black line). (b) Autocorrelation function for the force error vectors. (c) Distribution of angle between force error and atomic velocities.

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Electronic Structure Theory > Density Functional Theory

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