Born-Oppenheimer Dynamics Research Articles

Ab initio molecular dynamics: Propagating the density matrix with gaussian orbitals. IV. Formal analysis of the deviations from born‐oppenheimer dynamics

AbstractIn the context of the recently developed Atom‐centered Density Matrix Propagation (ADMP) approach to ab initio molecular dynamics, a formal analysis of the deviations from the Born—Oppenheimer surface is conducted. These deviations depend on the fictitious mass and on the magnitude of the commutator of the Fock and density matrices. These quantities are found to be closely interrelated and the choice of the fictitious mass provides a lower bound on the deviations from the Born—Oppenheimer surface. The relations are illustrated with an example calculation for the Cl−(H2O)25 cluster. We also show that there exists a direct one‐to‐one correspondence between approximate Born—Oppenheimer dynamics, where SCF convergence is restricted by a chosen threshold value for the commutator of the Fock and density matrices, and extended Lagrangian dynamics performed using a finite value for the fictitious mass. The analysis is extended to the nuclear forces used in the ADMP approximation. The forces are shown to be more general than those standardly used in Born—Oppenheimer dynamics, with the addition terms in the nuclear forces depending on the commutator mentioned above.

Ab initio molecular dynamics: Propagating the density matrix with Gaussian orbitals. III. Comparison with Born–Oppenheimer dynamics

In a recently developed approach to ab initio molecular dynamics (ADMP), we used an extended Lagrangian to propagate the density matrix in a basis of atom centered Gaussian functions. Results of trajectory calculations obtained by this method are compared with the Born–Oppenheimer approach (BO), in which the density is converged at each step rather than propagated. For NaCl, the vibrational frequency with ADMP is found to be independent of the fictitious electronic mass and to be equal to the BO trajectory result. For the photodissociation of formaldehyde, H2CO→H2+CO, and the three body dissociation of glyoxal, C2H2O2→H2+2CO, very good agreement is found between the Born–Oppenheimer trajectories and the extended Lagrangian approach in terms of the rotational and vibrational energy distributions of the products. A 1.2 ps simulation of the dynamics of chloride ion in a cluster of 25 water molecules was used as a third test case. The Fourier transform of the velocity–velocity autocorrelation function showed the expected features in the vibrational spectrum corresponding to strong hydrogen bonding in the cluster. A redshift of approximately 200 cm−1 was observed in the hydroxyl stretch due to the presence of the chloride ion. Energy conservation and adiabaticity were maintained very well in all of the test cases.

Ab initio molecular dynamics: Propagating the density matrix with Gaussian orbitals. II. Generalizations based on mass-weighting, idempotency, energy conservation and choice of initial conditions

A generalization is presented here for a newly developed approach to ab initio molecular dynamics, where the density matrix is propagated with Gaussian orbitals. Including a tensorial fictitious mass facilitates the use of larger time steps for the dynamics process. A rigorous analysis of energy conservation is presented and used to control the deviation of the fictitious dynamics trajectory from the corresponding Born–Oppenheimer dynamics trajectory. These generalizations are tested for the case of the Cl−(H2O)25 cluster. It is found that, even with hydrogen atoms present in the system, no thermostats are necessary to control the exchange of energy between the nuclear and the fictitious electronic degrees of freedom.

Large Timesteps in First-Principles Molecular Dynamics Simulations

A number of first-principles molecular dynamics simulations of biologically important systems, e.g. molecular liquids and biomolecules in aqueous solution, are emerging in the past few years. Since these calculations are computationally very demanding, clever use of CPU time is crucial. One way to accelerate the simulations is to use the largest possible timestep, which is mainly limited by the highest vibrational frequency of the system. In the systems mentioned above, the highest frequencies arise from stretching motion of the covalent bonds, which are only weakly coupled to other modes in most cases. Therefore, by freezing these fast modes, we can use much larger timesteps without changing the long-time behavior of the system. Bond-angle constraints, on the other hand, will not be considered in this article, since they can significantly alter the properties of the system, with little gain in efficiency. Although the constrained molecular dynamics (CMD) is a well-established technique for classical simulations, its applications within the first-principles calculations are limited to the estimation of free-energy differences associated with chemical reactions. In these simulations, constraints were imposed only on the reaction coordinates, and the time evolution of the system was followed by the fictitious dynamics. In contrast, CMD has rarely been used for the Born-Oppenheimer dynamics (BOD), in which the electronic ground state is reached at every ionic step. In general, the number of iterations for electronic minimization increases for larger timesteps in BOD, since the quality of the extrapolated wavefunctions deteriorates. Therefore, it is not obvious if CMD provides any improvement of the performance. In this article, we investigate the efficiency of CMD within BOD as well as the effects of using deuterium atoms in place of hydrogen atoms. We have implemented CMD within our first-principles molecular dynamics code, FEMTECK, along the lines of RATTLE algorithm. Note that the computational efforts to calculate the constraint forces are negligible compared with those for the (unconstrained) ionic forces in the first-principles calculations. Therefore, we solve the nonlinear equations for the bond lengths (eqs. (A1) and (A3) of ref. 15) by the Newton-Raphson method, which, at the cost of inverting small matrices,

Thermal properties of Na8 microclusters.

We present results of isothermal molecular-dynamics calculations for Na 8 microclusters. The Born-Oppenheimer dynamics is calculated using a many-body potential developed by Tomanek and coworkers. We analyzed the system in a temperature range from 25 to 1500 K. The Na 8 cluster seems to undergo two phase transitions, a solid-glass transition at ≃100 K, and a melting transition at T≃800 K

Phase transitions in Na7-Na9 microclusters.

We present a wide range of properties of ${\mathrm{Na}}_{7}$--${\mathrm{Na}}_{9}$ microclusters determined in the framework of our improved molecular-dynamics approach at fixed temperature. The Born-Oppenheimer dynamics was treated by means of an effective many-body potential, used previously for clusters, surface, and bulk properties. We have computed rotational, vibrational, and potential energies and corresponding specific heats, momenta of inertia, shapes parameters, and bond lengths of the Na microclusters over a wide range of temperatures, from 25 to 1500 K. We have determined that sodium microclusters undergo two ``phase transitions,'' one around 100 K from a crystal to a glassy or molten state, and a second one around 800 K, to a fluid state of the cluster. At low temperatures Na microclusters are essentially incompressible, but relatively easy to deform. At high temperatures Na clusters become extremely soft, and evaporation of atoms sets in.

Born–Oppenheimer dynamics using density-functional theory: Equilibrium and fragmentation of small sodium clusters

The properties of small neutral and positively charged sodium clusters and the fragmentation dynamics of Na++4 are investigated using a simulation technique which combines classical molecular dynamics on the electronic Born–Oppenheimer ground-state potential surface with electronic structure calculations via the local spin-density functional method. Results for the optimal energies and structures of Nan and Na+n (n≤4) are in quantitative agreement with previous studies and experimental data. Fission of Na++4 on its ground state Born–Oppenheimer potential-energy surface, following sudden ionization of selected configurations of an Na+4 (or Na4) cluster, whose vibrational energy content corresponds to 300 K, is found to occur on a picosecond time scale. The preferred fission channel is found to be Na+3+Na+, with an interfragment relative translational kinetic energy of ∼2 eV, and a vibrationally excited Na+3. The dynamics of the fragmentation process is analyzed.