Atom-centered Density Matrix Propagation Research Articles

Effect of time-dependent basis functions and their superposition error on atom-centered density matrix propagation (ADMP): connections to wavelet theory of multiresolution analysis.

We present a rigorous analysis of the primitive Gaussian basis sets used in the electronic structure theory. This leads to fundamental connections between Gaussian basis functions and the wavelet theory of multiresolution analysis. We also obtain a general description of basis set superposition error which holds for all localized, orthogonal or nonorthogonal, basis functions. The standard counterpoise correction of quantum chemistry is seen to arise as a special case of this treatment. Computational study of the weakly bound water dimer illustrates that basis set superposition error is much less for basis functions beyond the 6-31+G(*) level of Gaussians when structure, energetics, frequencies, and radial distribution functions are to be calculated. This result will be invaluable in the use of atom-centered Gaussian functions for ab initio molecular dynamics studies using Born-Oppenheimer and atom-centered density matrix propagation.

First-principle molecular dynamics of the Berry pseudorotation: insights on 19F NMR in SF4.

First-principles [density-functional theory (DFT)] molecular-dynamic simulations of the Berry pseudorotation mechanism in SF4 were performed using the atom-centered density-matrix propagation method. The reaction was monitored by following the chemical shieldings of the fluorine atoms, computed on snapshots along the trajectories. In particular we compared the results obtained using a standard functional based on the generalized gradient approximation with those issuing from its hybrid Hartree-Fock-DFT counterpart using a number of basis sets. Our results show that both the basis set and the functional choice rule the quality of the molecular properties monitored as well as the trajectory over the potential-energy surface.

Hybrid Ab-Initio/Empirical Molecular Dynamics: Combining the ONIOM Scheme with the Atom-Centered Density Matrix Propagation (ADMP) Approach

A new methodology to perform hybrid empirical/ab-initio molecular dynamics is presented. The method combines the well-established hybrid ONIOM scheme with the recently developed ADMP (Atom-Centered Density Matrix Propagation) approach, where the one electron density matrix expanded in an atom-centered Gaussian basis set is propagated as electronic variables along with the classical nuclear degrees of freedom via an extended Lagrangian procedure. The unified and single-valued ONIOM expressions for the energy and energy derivatives allow for an implementation of conservative dynamics. It is found that atom-centered basis sets large enough to provide good chemical accuracy can be used even when electronic embedding is adopted in the QM/MM scheme, and this does not affect the well-behaved and conservative nature of the dynamics. The method contains very appealing features for the study of biological systems, including the ability to employ accurate density functionals, the freedom to choose a periodic or a cluster boundary condition for the system under study, asymptotic O(N) scaling through established techniques, and the ability to use reasonably large time-steps through the tensorial fictitious mass scheme. The general ADMP/ONIOM formalism is illustrated through a series of test calculations. A simulated study of proton hopping inside the gramicidin A ion channel is also presented, to show the potential of the method in describing reactivity in large systems.

Atom-Centered Density Matrix Propagation (ADMP): Generalizations Using Bohmian Mechanics

We present a generalization for the atom-centered density matrix propagation (ADMP) approach to ab initio molecular dynamics that allows for a quantum-mechanical treatment of the nuclear degrees of freedom while adiabatically time-propagating the electronic degrees of freedom. This generalization uses the Bohmian approach to quantum mechanics. The regular ADMP equations are seen to arise in the special case of the ℏ → 0 limit of the current formalism. Semiclassical approximations are also discussed, and rigorous error estimates are provided to define the accuracy of the current formalism.

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.