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.

The hydrated proton was studied at the water liquid/vapor interface using the multistate empirical valence bond (MS-EVB) methodology, which enables the migration of the excess proton to and about the interface through the fluctuating bond topology described by the Grotthuss shuttle mechanism. It was found in our model that the hydrated excess proton displays a marked preference for water liquid/vapor interfaces. The resulting stable surface structures can be explained through an examination of the bond network formed between the water/proton moiety and solvating water. These results suggest the excess proton can effectively behave as an amphiphile, displaying both hydrophobic and hydrophilic character.In this communication, interesting new results are reported for the excess proton at the water liquid/vapor interface. These results are at odds with the conventional concepts of ionic solvation and have their origin in the strong solvation asymmetry of the hydronium cation. In particular, the water liquid/vapor interface for the H + (H 2 O) 1000 Cl -system, constituting a "slab" 1,2 geometry for the water molecules and the two ions, was studied via molecular dynamics (MD) simulations using rectangular periodic boundaries at 300 K and a constant volume of dimensions 31.2 × 31.2 × 75.0 Å 3 . Starting configurations were generated from a constant temperature trajectory after an initial equilibration of 500 ps with the Nose-Hoover thermostat. Ten independent microcanonical trajectories were then collected, for a total of 2.5 ns of simulation time, using MD simulations performed with the MS-EVB2 model, 3,4 and the Ewald summation method was implemented for all electrostatic interactions. The MS-EVB2 model has been successfully used to treat proton transport in bulk liquids and several biological systems. [5][6][7][8] The important distinction in this approach is that the definition of the protonated species can change during the dynamical process; that is, the proton can hop along an optimal conformation of water molecules consistent with the Grotthuss mechanism of proton transfer. 9,10 As a result of the present simulation, it was found that the proton was preferentially distributed on the surface of the water/vacuum interface. This surface localization of the hydronium was also evident for a simple "classical" model of the cation, that is, one which is unable to participate in Grotthuss hopping (see Figure 1). The orientation of the hydrated proton is such that the lone-pair side was directed away from the aqueous portion of the interface. A representative structure from an MS-EVB2 trajectory is shown in Figure 2 with the hydronium (orange) located at the interface and the counterion, in this case chloride (green), visible several molecules below the surface. Although not discussed here in detail, it is worth noting that the simulated chloride ion's radial distribution, diffusion, and coordination are in agreement with previously published values. 11,12 While the phenomenon of the "surface" excess proton observed in ...

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.