Energy benchmarks for methane-water systems from quantum Monte Carlo and second-order Møller-Plesset calculations.

The quantum Monte Carlo (QMC) technique is used to generate accurate energy benchmarks for methane-water clusters containing a single methane monomer and up to 20 water monomers. The benchmarks for each type of cluster are computed for a set of geometries drawn from molecular dynamics simulations. The accuracy of QMC is expected to be comparable with that of coupled-cluster calculations, and this is confirmed by comparisons for the CH4-H2O dimer. The benchmarks are used to assess the accuracy of the second-order Møller-Plesset (MP2) approximation close to the complete basis-set limit. A recently developed embedded many-body technique is shown to give an efficient procedure for computing basis-set converged MP2 energies for the large clusters. It is found that MP2 values for the methane binding energies and the cohesive energies of the water clusters without methane are in close agreement with the QMC benchmarks, but the agreement is aided by partial cancelation between 2-body and beyond-2-body errors of MP2. The embedding approach allows MP2 to be applied without loss of accuracy to the methane hydrate crystal, and it is shown that the resulting methane binding energy and the cohesive energy of the water lattice agree almost exactly with recently reported QMC values.

Energy benchmarks for water clusters and ice structures from an embedded many-body expansion.

We show how an embedded many-body expansion (EMBE) can be used to calculate accurate ab initio energies of water clusters and ice structures using wavefunction-based methods. We use the EMBE described recently by Bygrave et al. [J. Chem. Phys. 137, 164102 (2012)], in which the terms in the expansion are obtained from calculations on monomers, dimers, etc., acted on by an approximate representation of the embedding field due to all other molecules in the system, this field being a sum of Coulomb and exchange-repulsion fields. Our strategy is to separate the total energy of the system into Hartree-Fock and correlation parts, using the EMBE only for the correlation energy, with the Hartree-Fock energy calculated using standard molecular quantum chemistry for clusters and plane-wave methods for crystals. Our tests on a range of different water clusters up to the 16-mer show that for the second-order Møller-Plesset (MP2) method the EMBE truncated at 2-body level reproduces to better than 0.1 mE(h)/monomer the correlation energy from standard methods. The use of EMBE for computing coupled-cluster energies of clusters is also discussed. For the ice structures Ih, II, and VIII, we find that MP2 energies near the complete basis-set limit reproduce very well the experimental values of the absolute and relative binding energies, but that the use of coupled-cluster methods for many-body correlation (non-additive dispersion) is essential for a full description. Possible future applications of the EMBE approach are suggested.

The embedded many-body expansion for energetics of molecular crystals.

Reliable prediction of molecular crystal energetics is a vital goal for computational chemistry. Here we show that accurate results can be obtained from a monomer-based many-body expansion truncated at the two-body level, with the monomer and dimer calculations suitably embedded in a model of the crystalline environment. By including the two dominant effects--electrostatics and exchange-repulsion--we are able to capture the important nonadditive terms in the energy, and approach very closely results from full periodic second-order Møller-Plesset calculations. The advantage of the current scheme is that extension to coupled-cluster and explicitly correlated F12 methods is completely straightforward. We demonstrate the approach through calculations on carbon dioxide, hydrogen fluoride, and ice XIh and XIc. In accord with previous studies, we find these two ice polymorphs to be very close in energy, with our periodic coupled-cluster single double triple-F12 calculation giving the hexagonal structure more stable by around 0.3 kJ mol(-1).

Assessing the accuracy of quantum Monte Carlo and density functional theory for energetics of small water clusters.

We present a detailed study of the energetics of water clusters (H(2)O)(n) with n ≤ 6, comparing diffusion Monte Carlo (DMC) and approximate density functional theory (DFT) with well converged coupled-cluster benchmarks. We use the many-body decomposition of the total energy to classify the errors of DMC and DFT into 1-body, 2-body and beyond-2-body components. Using both equilibrium cluster configurations and thermal ensembles of configurations, we find DMC to be uniformly much more accurate than DFT, partly because some of the approximate functionals give poor 1-body distortion energies. Even when these are corrected, DFT remains considerably less accurate than DMC. When both 1- and 2-body errors of DFT are corrected, some functionals compete in accuracy with DMC; however, other functionals remain worse, showing that they suffer from significant beyond-2-body errors. Combining the evidence presented here with the recently demonstrated high accuracy of DMC for ice structures, we suggest how DMC can now be used to provide benchmarks for larger clusters and for bulk liquid water.

An approximate density-functional method using the Harris-Foulkes functional.

We present a method which uses the results of a molecular Kohn-Sham calculation at a reference geometry to approximate the energy at many different geometries. The Kohn-Sham electron density of the reference geometry is decomposed into atomic fragments, which move with the nuclei to approximate the density at a new geometry and the energy is evaluated with the Harris-Foulkes functional. Preliminary results for a biological quantum-mechanics/molecular-mechanics trajectory are promising: the errors of reference-geometry Harris-Foulkes (compared to full self-consistent Kohn-Sham) for the PBE exchange-correlation functional have the same magnitude as the difference between the energies of PBE and BLYP.

Comparison of the incremental and hierarchical methods for crystalline neon.

We present a critical comparison of the incremental and hierarchical methods for the evaluation of the static cohesive energy of crystalline neon. Both of these schemes make it possible to apply the methods of molecular electronic structure theory to crystalline solids, offering a systematically improvable alternative to density functional theory. Results from both methods are compared with previous theoretical and experimental studies of solid neon and potential sources of error are discussed. We explore the similarities of the two methods and demonstrate how they may be used in tandem to study crystalline solids.

High-precision calculation of Hartree-Fock energy of crystals.

When using quantum chemistry techniques to calculate the energetics of bulk crystals, there is a need to calculate the Hartree-Fock (HF) energy of the crystal at the basis-set limit. We describe a strategy for achieving this, which exploits the fact that the HF energy of crystals can now be calculated using pseudopotentials and plane-wave basis sets, an approach that permits basis-set convergence to arbitrary precision. The errors due to the use of pseudopotentials are then computed from the difference of all-electron and pseudopotential total energies of atomic clusters, extrapolated to the bulk-crystal limit. The strategy is tested for the case of the LiH crystal, and it is shown that the HF cohesive energy can be converged with respect to all technical parameters to a precision approaching 0.1 mE(h) per atom. This cohesive energy and the resulting HF value of the equilibrium lattice parameter are compared with literature values obtained using Gaussian basis sets.

Extension of molecular electronic structure methods to the solid state: computation of the cohesive energy of lithium hydride.

We describe a simple strategy for calculating the cohesive energy of certain kinds of crystal using readily available quantum chemistry techniques. The strategy involves the calculation of the electron correlation energies of a hierarchy of free clusters, and the cohesive energy E(coh) is extracted from the constant of proportionality between these correlation energies and the number of atoms in the limit of large clusters. We apply the strategy to the LiH crystal, using the MP2 and CCSD(T) schemes for the correlation energy, and show that for this material E(coh) can be obtained to an accuracy of approximately 30 meV per ion pair. Comparison with the experimental value, after correction for zero-point energy, confirms this accuracy.

Efficient exact exchange approximations in density-functional theory.

Two approaches to approximate the Slater potential component of local exact exchange of density-functional theory are investigated. The first approach employs density fitting of the electrostatic potential integrals over two occupied orbitals and the other approach approximates the "exact" Slater potential with the potential derived from the Becke-Roussel [Phys. Rev. A. 39, 3761 (1989)] model of the exchange hole. In both cases significant time savings can be achieved for larger systems compared to the calculation of the numerical Slater potential. It is then analyzed how well the orbitals obtained from the various total exchange potentials reproduce Hartree-Fock energies and molecular properties. A large range of atoms and small molecules has been utilized, including the three DNA bases adenine, thymine, and cytosine.

Poisson equation in the Kohn-Sham Coulomb problem.

We apply the Poisson equation to the quantum mechanical Coulomb problem for many-particle systems. By introducing a suitable basis set, the two-electron Coulomb integrals become simple overlaps. This offers the possibility of very rapid linear-scaling treatment of the Coulomb contribution to Kohn-Sham theory.