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2016
The MD functionality implemented in ONETEP is founded on the Born-Oppenheimer approximation which states that the electrons are much lighter than nuclei, the dynamics of electrons is much faster compared to the dynamics of the nuclei. As a consequence, the former can be considered to react instantaneously to the motion of the latter. The forces acting on the nuclei are derived from the ground state electronic configuration by means of the Hellmann-Feynamn theorem. The motion of the nuclei is described by the laws of classical mechanics
Handbook of Materials Modeling, 2005
R. Car et al. elements such as hydrogen; classical or ab initio path integral approaches can then be applied, albeit at a higher computational cost. The use of Newton's equations of motion for the nuclear evolution implies that vibrational degrees of freedom are not quantized, and will follow a Boltzmann statistics. This approximation becomes fully justified only for temperatures comparable with the highest vibrational level in the system considered.
An accelerated polynomial expansion scheme to construct the density matrix in quantum mechanical molecular dynamics simulations is proposed. The scheme is based on recursive density matrix expansions, e.g. [Phys. Rev. B. 66 (2002), p. 155115], which are accelerated by a scale-and-fold technique [J. Chem. Theory Comput. 7 (2011), p. 1233]. The acceleration scheme requires interior eigenvalue estimates, which may be expensive and cumbersome to come by. Here we show how such eigenvalue estimates can be extracted from the recursive expansion by a simple and robust procedure at a negligible computational cost. Our method is illustrated with density functional tight-binding Born-Oppenheimer molecular dynamics simulations, where the computational effort is dominated by the density matrix construction. In our analysis we identify two different phases of the recursive polynomial expansion, the conditioning and purification phases, and we show that the acceleration represents an improvement of the conditioning phase, which typically gives a significant reduction of the computational cost.
Accounts of Chemical Research - ACCOUNT CHEM RES, 2006
Electronically nonadiabatic or non-Born-Oppenheimer (non-BO) chemical processes (photodissociation, charge-transfer, etc.) in- volve a nonradiative change in the electronic state of the system. Molecular dynamics simulations typically treat nuclei as moving classically on a single adiabatic potential energy surface, and these techniques are not immediately generalizable to non-BO systems due to the inherently quantum mechanical nature of electronic transitions. Here we generalize the concept of a single-surface molecular dynamics trajectory to that of a coupled-surface non- BO trajectory that evolves "semiclassically" under the influence of two or more electronic states and their couplings. Five non-BO trajectory methods are discussed. Next, we summarize the results of a series of systematic studies using a database of accurate quantum mechanical reaction probabilities and internal energy distributions for several six-dimensional model bimolecular scat- tering collisions. ...
Physical Review Letters, 2006
We present a time-reversible Born-Oppenheimer molecular dynamics scheme, based on selfconsistent Hartree-Fock or density functional theory, where both the nuclear and the electronic degrees of freedom are propagated in time. We show how a time-reversible adiabatic propagation of the electronic degrees of freedom is possible despite the non-linearity and incompleteness of the selfconsistent field procedure. Time-reversal symmetry excludes a systematic long-term energy drift for a microcanonical ensemble and the number of self-consistency cycles can be kept low (often only 2-4 cycles per nuclear time step) thanks to a good initial guess given by the adiabatic propagation of the electronic degrees of freedom. The time-reversible Born-Oppenheimer molecular dynamics scheme therefore combines a low computational cost with a physically correct time-reversible representation of the dynamics, which preserves a detailed balance between propagation forwards and backwards in time.
The Journal of Chemical Physics, 2012
Born-Oppenheimer molecular dynamics simulations with long-term conservation of the total energy and a computational cost that scales linearly with system size have been obtained simultaneously. Linear scaling with a low pre-factor is achieved using density matrix purification with sparse matrix algebra and a numerical threshold on matrix elements. The extended Lagrangian Born-Oppenheimer molecular dynamics formalism [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] yields microcanonical trajectories with the approximate forces obtained from the linear scaling method that exhibit no systematic drift over hundreds of picoseconds and which are indistinguishable from trajectories computed using exact forces.
International Journal of Quantum Chemistry, 1994
The content of an ab-inddo time-dependent theory of quantm molecular dynamics of electrons and atomic nuclei is presented. Employing the time-dependent variational principle and a family of approximate state vectors yields a set of dynamical equations approximating the time-dependent SchrOdinger equation. These equations govern the time evolution of the relevant state vector parameters as molecular orbital coefficients, nuclear positions and momenta. This approach does not impose the Born-Oppenheimer approximation, does not use potential energy a. surfaces and takes into account elecow-nuclear coupling. Basic cnservation laws are fully ' obeyed. The simplest model of the theory employs a single determinantal state for the electrons CL and classical nuclei and is implemented in the computer code ENDyne. Results from this ab-. _ kio theory are reported for ion-atom and ion-molecule collisions.
The Journal of chemical physics, 2014
Extended Lagrangian Born-Oppenheimer molecular dynamics based on Kohn-Sham density functional theory is generalized in the limit of vanishing self-consistent field optimization prior to the force evaluations. The equations of motion are derived directly from the extended Lagrangian under the condition of an adiabatic separation between the nuclear and the electronic degrees of freedom. We show how this separation is automatically fulfilled and system independent. The generalized equations of motion require only one diagonalization per time step and are applicable to a broader range of materials with improved accuracy and stability compared to previous formulations.
Reviews of Modern Physics, 1994
An overview is presented of methods for time-dependent treatments of molecules as systems of electrons and nuclei. The theoretical details of these methods are reviewed and contrasted in the light of a recently developed time-dependent method called electron-nuclear dynamics. Electron-nuclear dynamics (END) is a formulation of the complete dynamics of electrons and nuclei of a molecular system that eliminates the necessity of constructing potential-energy surfaces. Because of its general formulation, it encompasses many aspects found in other formulations and can serve as a didactic device for clarifying many of the principles and approximations relevant in time-dependent treatments of molecular systems. The END equations are derived from the time-dependent variational principle applied to a chosen family of efhciently parametrized approximate state vectors. A detailed analysis of the END equations is given for the case of a single-determinantal state for the electrons and a classical treatment of the nuclei. The approach leads to a simple formulation of the fully nonlinear time-dependent Hartree-Fock theory including nuclear dynamics. The nonlinear END equations with the ab initio Coulomb Hamiltonian have been implemented at this level of theory in a computer program, ENDyne, and have been shown feasible for the study of small molecular systems. Implementation of the Austin Model 1 semiempirical Hamiltonian is discussed as a route to large molecular systems. The linearized END equations at this level of theory are shown to lead to the random-phase approximation for the coupled system of electrons and nuclei. The qualitative features of the general nonlinear solution are analyzed using the results of the linearized equa-918 918 920 920 921 921 922 922 922 923 923 923 923 924 924 925 925 926 928 928 928 929 929 930 931 931 933 935 935 937 937 937 940 941 atomic orbitals nal basis of trav-B. Nonorthogonal representation 1. Derivation in an orthonormal basis a. Metric b. Density matrix c. Energy 2. Derivation in the atomic-orbital basis a. Definition of parameters b. Dynamic orbitals c. Metric d. Density matrix e. Energy 3. Details of semiempirical approaches References 950 950 959
Arxiv preprint arXiv: …, 2011
Abstract. Born-Oppenheimer dynamics is shown to provide an accurate approximation of time-independent Schrödinger observables for a molecular system with an electron spectral gap, in the limit of large ratio of nuclei and electron masses, without assuming that the ...
Journal of Chemical Theory and Computation, 2020
Extended Lagrangian Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 100, 123004 (2008)] is presented for Hartree-Fock theory, where the extended electronic degrees of freedom are represented by a density matrix that accounts for fractional occupation numbers at elevated electronic temperatures. A 4th-order metric tensor, T ≡ K T K, is used in the generalized extended harmonic oscillator of the Lagrangian that generates the dynamics of the electronic degrees of freedom. The kernel, K, is given in terms of an inverse Jacobian of a matrix residual function and appears in the equation of motion for the extended harmonic oscillator. A tunable low-rank approximation of this 4th-order kernel is used for the integration of the electronic degrees of freedom. In contrast to regular direct Born-Oppenheimer molecular dynamics simulations, no iterative self-consistent field optimization is required prior to the force evaluations. The formulation and algorithms provide a general guide to implement extended Lagrangian Born-Oppenheimer molecular dynamics for quantum chemistry, density functional theory, and semiempirical methods using a density matrix formalism.
Chemical Physics Letters, 2001
We examine the eect of the diagonal Born±Oppenheimer correction on dynamics in two simple systems ± the Hooke's atom in an external harmonic potential and the collinear hydrogen exchange reaction. The transmission probability for the Hooke's atom, calculated within the Born±Oppenheimer approximation, is simply shifted in energy with respect to the exact result, and this is corrected by the diagonal adiabatic contribution. The reaction probability for the H 3 system re¯ects the fact, that the diagonal Born±Oppenheimer correction raises the barrier to the reaction by approximately 70 cm À1 . Ó
ESAIM: Mathematical Modelling and Numerical Analysis, 2007
We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for higher order corrections. We also present a new elementary derivation of the correct second-order time-dependent Born-Oppenheimer approximation and discuss as applications the dynamics near a conical intersection of potential surfaces and reactive scattering.
Physical Review Letters, 2008
A new "on the fly" method to perform Born-Oppenheimer ab initio molecular dynamics (AIMD) is presented. Inspired by Ehrenfest dynamics in time-dependent density functional theory, the electronic orbitals are evolved by a Schrödinger-like equation, where the orbital time derivative is multiplied by a parameter. This parameter controls the time scale of the fictitious electronic motion and speeds up the calculations with respect to standard Ehrenfest dynamics. In contrast to other methods, wave function orthogonality needs not be imposed as it is automatically preserved, which is of paramount relevance for large scale AIMD simulations. 71.15.Pd, 31.15.Ew Ab initio molecular dynamics (AIMD) on the ground state Born-Oppenheimer (gsBOMD) potential energy surface for the nuclei has become a standard tool for simulating the conformational behaviour of molecules, bioand nano-structures and condensed matter systems from first principles [1]. However, gsBOMD (in the DFT [2] picture) requires that the Kohn-Sham (KS) energy functional be minimized for each value of the nuclei positions. As this minimization can be very demanding, Car and Parrinello (CP) proposed an elegant and efficient "on the fly" scheme in which the KS orbitals are propagated with a fictitious dynamics that mimics gsBOMD. The CP method has had a tremendous impact in many scientific areas . Nevertheless, the numerical cost of AIMD hinders the application of the method to large scale simulations, such as those of interest in biochemistry or material science. Recently, new methods that allow larger systems and longer simulation times to be studied have been reported [6], but the cost associated with the wave function orthogonalization is still a potential bottleneck for both gsBOMD and CP.
Journal of the Mexican Chemical Society
A new method for pressure control in first-principle molecular dynamics simulations for finite systems is presented. The extended Lagrangian methodology is applied to generate the equations of motion and the system’s volume is obtained by a purely geometrical procedure, which is inexpensive in terms of computational cost. The implementation of all discussed algorithms was carried out in the program deMon2k where a robust machinery for auxiliary density functional theory calculations exists. The here described methodology extend our effort on property calculations beyond the polyatomic ideal gas approximation on the basis of first-principle electronic structure calculations.
Journal of General Physiology, 2010
The Journal of Chemical Physics, 2017
Physical Review B, 2012
As the processing power available for scientific computing grows, first principles Born-Oppenheimer molecular dynamics simulations are becoming increasingly popular for the study of a wide range of problems in materials science, chemistry and biology. Nevertheless, the computational cost of Born-Oppenheimer molecular dynamics still remains prohibitively large for many potential applications. Here we show how to avoid a major computational bottleneck: the self-consistent-field optimization prior to the force calculations. The optimization-free quantum mechanical molecular dynamics method gives trajectories that are almost indistinguishable from an "exact" microcanonical Born-Oppenheimer molecular dynamics simulation even when low pre-factor linear scaling sparse matrix algebra is used. Our findings show that the computational gap between classical and quantum mechanical molecular dynamics simulations can be significantly reduced.
The Journal of Chemical Physics, 2011
An important element determining the time requirements of Born-Oppenheimer molecular dynamics (BOMD) is the convergence rate of the self-consistent solution of Roothaan equations (SCF). We show here that improved convergence and dynamics stability can be achieved by use of a Lagrangian formalism of BOMD with dissipation (DXL-BOMD). In the DXL-BOMD algorithm, an auxiliary electronic variable (e.g., the electron density or Fock matrix) is propagated and a dissipative force is added in the propagation to maintain the stability of the dynamics. Implementation of the approach in the self-consistent charge density functional tight-binding method makes possible simulations that are several hundred picoseconds in lengths, in contrast to earlier DFT-based BOMD calculations, which have been limited to tens of picoseconds or less. The increase in the simulation time results in a more meaningful evaluation of the DXL-BOMD method. A comparison is made of the number of iterations (and time) required for convergence of the SCF with DXL-BOMD and a standard method (starting with a zero charge guess for all atoms at each step), which gives accurate propagation with reasonable SCF convergence criteria. From tests using NVE simulations of C 2 F 4 and 20 neutral amino acid molecules in the gas phase, it is found that DXL-BOMD can improve SCF convergence by up to a factor of two over the standard method. Corresponding results are obtained in simulations of 32 water molecules in a periodic box. Linear response theory is used to analyze the relationship between the energy drift and the correlation of geometry propagation errors.
Theoretical and Computational Chemistry, 1999
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