Eric Schwegler

Towards an assessment of the accuracy of density functional theory for first principles simulations of water

A series of Car-Parrinello (CP) molecular dynamics simulations of water are presented, aimed at assessing the accuracy of density functional theory in describing the structural and dynamical properties of water at ambient conditions. We found negligible differences in structural properties obtained using the Perdew-Burke-Ernzerhof or the Becke-Lee-Yang-Parr exchange and correlation energy functionals; we also found that size effects, although not fully negligible when using 32 molecule cells, are rather small. In addition, we identified a wide range of values of the fictitious electronic mass (micro) entering the CP Lagrangian for which the electronic ground state is accurately described, yielding trajectories and average properties that are independent of the value chosen. However, care must be exercised not to carry out simulations outside this range, where structural properties may artificially depend on micro. In the case of an accurate description of the electronic ground state, and in the absence of proton quantum effects, we obtained an oxygen-oxygen correlation function that is overstructured compared to experiment, and a diffusion coefficient which is approximately ten times smaller.

Linear scaling computation of the Hartree–Fock exchange matrix

Thresholding criteria are introduced that enforce locality of exchange interactions in Cartesian Gaussian‐based Hartree–Fock calculations. These criteria are obtained from an asymptotic form of the density matrix valid for insulating systems, and lead to a linear scaling algorithm for computation of the Hartree–Fock exchange matrix. Restricted Hartree–Fock/3‐21G calculations on a series of water clusters and polyglycine α‐helices are used to demonstrate the O(N) complexity of the algorithm, its competitiveness with standard direct self‐consistent field methods, and a systematic control of error in converged total energies.

Linear scaling computation of the Fock matrix

Computation of the Fock matrix is currently the limiting factor in the application of Hartree-Fock and hybrid Hartree-Fock/density functional theories to larger systems. Computation of the Fock matrix is dominated by calculation of the Coulomb and exchange matrices. With conventional Gaussian-based methods, computation of the Fock matrix typically scales as ∼N2.7, where N is the number of basis functions. A hierarchical multipole method is developed for fast computation of the Coulomb matrix. This method, together with a recently described approach to computing the Hartree-Fock exchange matrix of insulators [J. Chem. Phys. 105, 2726 (1900)], leads to a linear scaling algorithm for calculation of the Fock matrix. Linear scaling computation the Fock matrix is demonstrated for a sequence of water clusters at the restricted Hartree-Fock/3-21G level of theory, and corresponding accuracies in converged total energies are shown to be comparable with those obtained from standard quantum chemistry programs. Restri...

LINEAR SCALING COMPUTATION OF THE FOCK MATRIX. II. RIGOROUS BOUNDS ON EXCHANGE INTEGRALS AND INCREMENTAL FOCK BUILD

A new linear scaling method for computation of the Cartesian Gaussian-based Hartree-Fock exchange matrix is described, which employs a method numerically equivalent to standard direct SCF, and which does not enforce locality of the density matrix. With a previously described method for computing the Coulomb matrix [J. Chem. Phys. 106, 5526 (1997)], linear scaling incremental Fock builds are demonstrated for the first time. Microhartree accuracy and linear scaling are achieved for restricted Hartree-Fock calculations on sequences of water clusters and polyglycine α-helices with the 3-21G and 6-31G basis sets. Eightfold speedups are found relative to our previous method. For systems with a small ionization potential, such as graphitic sheets, the method naturally reverts to the expected quadratic behavior. Also, benchmark 3-21G calculations attaining microhartree accuracy are reported for the P53 tetramerization monomer involving 698 atoms and 3836 basis functions.

The solvation of Na+ in water: First-principles simulations

First-principles molecular dynamics simulations have been performed on the solvation of Na+ in water. Consistent with the available experimental data, we find that the first solvation shell of Na+ contains on average 5.2 water molecules. A significant number of water exchanges between the first and second solvation shells are observed. However, the simulations are not long enough to reliably measure the rate of water exchange. Contrary to several previous studies, we do not find any effect of Na+ on the orientation of water molecules outside of the first solvation shell. Furthermore, the complete set of structural properties determined by first-principles molecular dynamics is not predicted by any of the known classical simulations.First-principles molecular dynamics simulations have been performed on the solvation of Na+ in water. Consistent with the available experimental data, we find that the first solvation shell of Na+ contains on average 5.2 water molecules. A significant number of water exchanges between the first and second solvation shells are observed. However, the simulations are not long enough to reliably measure the rate of water exchange. Contrary to several previous studies, we do not find any effect of Na+ on the orientation of water molecules outside of the first solvation shell. Furthermore, the complete set of structural properties determined by first-principles molecular dynamics is not predicted by any of the known classical simulations.

A quantum fluid of metallic hydrogen suggested by first-principles calculations.

It is generally assumed that solid hydrogen will transform into a metallic alkali-like crystal at sufficiently high pressure. However, some theoretical models have also suggested that compressed hydrogen may form an unusual two-component (protons and electrons) metallic fluid at low temperature, or possibly even a zero-temperature liquid ground state. The existence of these new states of matter is conditional on the presence of a maximum in the melting temperature versus pressure curve (the ‘melt line’). Previous measurements of the hydrogen melt line up to pressures of 44 GPa have led to controversial conclusions regarding the existence of this maximum. Here we report ab initio calculations that establish the melt line up to 200 GPa. We predict that subtle changes in the intermolecular interactions lead to a decline of the melt line above 90 GPa. The implication is that as solid molecular hydrogen is compressed, it transforms into a low-temperature quantum fluid before becoming a monatomic crystal. The emerging low-temperature phase diagram of hydrogen and its isotopes bears analogies with the familiar phases of 3He and 4He (the only known zero-temperature liquids), but the long-range Coulomb interactions and the large component mass ratio present in hydrogen would result in dramatically different properties.

Fast assembly of the Coulomb matrix: A quantum chemical tree code

Fast methods based on a representation of the electron charge density in a Hermite Gaussian basis are introduced for constructing the Coulomb matrix encountered in Hartree‐Fock and density functional theories. Simplifications that arise from working in a Hermite Gaussian basis are discussed, translations of such functions are shown to yield rapidly convergent expansions valid in both the near‐ and far‐field, and the corresponding truncation errors are derived in compact form. The relationship of such translations to hierarchical multipole methods is pointed out and a quantum chemical tree code related to the Barnes‐Hut method is developed. Novel methods are introduced for the independent thresholding of ‘‘bra’’ and ‘‘ket’’ distributions as well as for screening out insignificant multipole interactions. Recurrence relations for computing the Cartesian multipole tensor are used to efficiently calculate far‐field electrostatic interactions using high‐order expansions. Application of the quantum chemical tree...

Evidence for a first-order liquid-liquid transition in high-pressure hydrogen from ab initio simulations

Using quantum simulation techniques based on either density functional theory or quantum Monte Carlo, we find clear evidence of a first-order transition in liquid hydrogen, between a low conductivity molecular state and a high conductivity atomic state. Using the temperature dependence of the discontinuity in the electronic conductivity, we estimate the critical point of the transition at temperatures near 2,000 K and pressures near 120 GPa. Furthermore, we have determined the melting curve of molecular hydrogen up to pressures of 200 GPa, finding a reentrant melting line. The melting line crosses the metalization line at 700 K and 220 GPa using density functional energetics and at 550 K and 290 GPa using quantum Monte Carlo energetics.

A first principles molecular dynamics simulation of the hydrated magnesium ion

Abstract First principles molecular dynamics has been used to investigate the solvation of Mg2+ in water. In agreement with experiment, we find that the first solvation shell around Mg2+ contains six water molecules in an octahedral arrangement. The electronic structure of first solvation shell water molecules has been examined with a localized orbital analysis. We find that water molecules tend to asymmetrically coordinate Mg2+ through one of the oxygen lone pair orbitals and that the first solvation shell dipole moments increase by 0.2 Debye relative to pure liquid water.

Melting of ice under pressure

The melting of ice under pressure is investigated with a series of first-principles molecular dynamics simulations. In particular, a two-phase approach is used to determine the melting temperature of the ice-VII phase in the range of 10–50 GPa. Our computed melting temperatures are consistent with existing diamond anvil cell experiments. We find that for pressures between 10 and 40 GPa, ice melts as a molecular solid. For pressures above ≈45 Gpa, there is a sharp increase in the slope of the melting curve because of the presence of molecular dissociation and proton diffusion in the solid before melting. The onset of significant proton diffusion in ice-VII as a function of increasing temperature is found to be gradual and bears many similarities to that of a type-II superionic solid.