We propose and implement an alternative approach to the original Car–Parrinello method where the density matrix elements (instead of the molecular orbitals) are propagated together with the nuclear degrees of freedom. Our new approach has the advantage of leading to an O(N) computational scheme in the large system limit. Our implementation is based on atom-centered Gaussian orbitals, which are especially suited to deal effectively with general molecular systems. The methodology is illustrated by applications to the three-body dissociation of triazine and to the dynamics of a cluster of a chloride ion with 25 water molecules.

In a recently developed approach to ab initio molecular dynamics ͑ADMP͒, 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 ͑BO͒, 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, H 2 CO→H 2 ϩCO, and the three body dissociation of glyoxal, C 2 H 2 O2→H 2 ϩ2CO, 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 Ϫ1 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.

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 Ϫ ͑H 2 O͒ 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.

Advances in the computation of the Coulomb, exchange, and correlation contributions to Gaussian-based Hartree–Fock and density functional theory Hamiltonians have demonstrated near-linear scaling with molecular size for these steps. These advances leave the O(N3) diagonalization bottleneck as the rate determining step for very large systems. In this work, a conjugate gradient density matrix search (CG-DMS) method has been successfully extended and computationally implemented for use with first principles calculations. A Cholesky decomposition of the overlap matrix and its inverse is used to transform to and back from an orthonormal basis, which can be formed in near-linear time for sparse systems. Linear scaling of CPU time for the density matrix search and crossover of CPU time with diagonalization is demonstrated for polyglycine chains containing up to 493 atoms and water clusters up to 900 atoms.