We present ONETEP (order-N electronic total energy package), a density functional program for parallel computers whose computational cost scales linearly with the number of atoms and the number of processors. ONETEP is based on our reformulation of the plane wave pseudopotential method which exploits the electronic localization that is inherent in systems with a nonvanishing band gap. We summarize the theoretical developments that enable the direct optimization of strictly localized quantities expressed in terms of a delocalized plane wave basis. These same localized quantities lead us to a physical way of dividing the computational effort among many processors to allow calculations to be performed efficiently on parallel supercomputers. We show with examples that ONETEP achieves excellent speedups with increasing numbers of processors and confirm that the time taken by ONETEP as a function of increasing number of atoms for a given number of processors is indeed linear. What distinguishes our approach is that the localization is achieved in a controlled and mathematically consistent manner so that ONETEP obtains the same accuracy as conventional cubic-scaling plane wave approaches and offers fast and stable convergence. We expect that calculations with ONETEP have the potential to provide quantitative theoretical predictions for problems involving thousands of atoms such as those often encountered in nanoscience and biophysics.

The partitioning of the energy in ab initio quantum mechanical calculations into its chemical origins (e.g., electrostatics, exchange-repulsion, polarization, and charge transfer) is a relatively recent development; such concepts of isolating chemically meaningful energy components from the interaction energy have been demonstrated by variational and perturbation based energy decomposition analysis approaches. The variational methods are typically derived from the early energy decomposition analysis of Morokuma [Morokuma, J. Chem. Phys., 1971, 55, 1236], and the perturbation approaches from the popular symmetry-adapted perturbation theory scheme [Jeziorski et al., Methods and Techniques in Computational Chemistry: METECC-94, 1993, ch. 13, p. 79]. Since these early works, many developments have taken place aiming to overcome limitations of the original schemes and provide more chemical significance to the energy components, which are not uniquely defined. In this review, after a brief overview of the origins of these methods we examine the theory behind the currently popular variational and perturbation based methods from the point of view of biochemical applications. We also compare and discuss the chemical relevance of energy components produced by these methods on six test sets that comprise model systems that display interactions typical of biomolecules (such as hydrogen bonding and π-π stacking interactions) including various treatments of the dispersion energy.

We present a reformulation of the plane-wave pseudopotential method for insulators. This new approach allows us to perform density-functional calculations by solving directly for ''nonorthogonal generalized Wannier functions'' rather than extended Bloch states. We outline the theory on which our method is based and present test calculations on a variety of systems. Comparison of our results with a standard plane-wave code shows that they are equivalent. Apart from the usual advantages of the plane-wave approach such as the applicability to any lattice symmetry and the high accuracy, our method also benefits from the localization properties of our functions in real space. The localization of all our functions greatly facilitates the future extension of our method to linear-scaling schemes or calculations of the electric polarization of crystalline insulators.

We study the hydration of the actinyl cations, uranyl UO 2 2+ and plutonyl PuO 2 2+ , by performing KohnSham Density Functional Theory calculations using a new quantum chemistry codesMAGIC. The calculations have been performed on the separate uranyl and plutonyl species, and on the complexes AcO 2 2+ ‚nH 2 O (Ac ) U, Pu and n ) 4, 5, and 6), in the gas and aqueous phases. The liquid-state environmental effects are included via a simple cavity model and by using the self-consistent reaction field method. The calculations find that the solvent effects are crucial. By this, we mean that a simple cavity model, alone, will be incapable of giving insight into the chemical behavior of such molecules. The short-ranged interactions between the actinyls and their closest water molecules are very strong and involve an appreciable amount of charge transfer, an effect that cannot be included in cavity models. The actinyls form strongly bound complexes with the surrounding water molecules, with n ) 5 being the most stable. Thus, the short-range solvent effects are important. The binding energies of the complexes are very large, and in the gas phase they are about twice as large as in the aqueous phase. Thus, the bulk solvent effects are also important. Any reactivity of the actinyls with other species will thus be impeded by the existence of such strongly bound complexes, and the solvent will play an actiVe role in such phenomena. Regarding the chemical behavior of the actinyls in aqueous solution, our studies provide preliminary evidence that there will be no qualitative and very little quantitative difference between the uranium and plutonium species.

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We present an implicit solvent model for ab initio electronic structure calculations which is fully self-consistent and is based on direct solution of the nonhomogeneous Poisson equation. The solute cavity is naturally defined in terms of an isosurface of the electronic density according to the formula of Fattebert and Gygi (J. Comp. Chem. 23, 6 (2002)). While this model depends on only two parameters, we demonstrate that by using appropriate boundary conditions and dispersionrepulsion contributions, solvation energies obtained for an extensive test set including neutral and charged molecules show dramatic improvement compared to existing models. Our approach is implemented in, but not restricted to, a linear-scaling density functional theory (DFT) framework, opening the path for self-consistent implicit solvent DFT calculations on systems of unprecedented size, which we demonstrate with calculations on a 2615-atom protein-ligand complex.

The VV10 and rVV10 nonlocal correlation functionals are consistently implemented and assessed, with the goal of determining if the rVV10 nonlocal correlation functional can replace the VV10 nonlocal correlation functional in the recently developed B97M-V density functional, to give the B97M-rV density functional. Along the way, four density functionals are simultaneously tested: VV10, rVV10, B97M-V, and B97M-rV. An initial assessment is carried out across the S22 data set, and the short-range damping variable, b, is varied for all four density functionals in order to determine the sensitivity of the functionals to the empirical parameter. The results of this test indicate that a value of b = 6 (fortuitously the same as that in B97M-V) is suitable for B97M-rV. The functionals are then compared across an extensive database of interaction energies, and it is demonstrated that B97M-rV either matches or outperforms B97M-V for all of the tests considered. Finally, the optimization of b across the S22 data set is extended to two range-separated hybrid density functionals, ωB97X-V and ωB97M-V, and a value of b = 6.2 is recommended for both ωB97X-rV and ωB97M-rV.

Linear-scaling electronic structure methods are essential for calculations on large systems. Some of these approaches use a systematic basis set, the completeness of which may be tuned with an adjustable parameter similar to the energy cut-off of plane-wave techniques. The search for the electronic ground state in such methods suffers from an ill-conditioning which is related to the kinetic contribution to the total energy and which results in unacceptably slow convergence. We present a general preconditioning scheme to overcome this ill-conditioning and implement it within our own first-principles linear-scaling density functional theory method. The scheme may be applied in either real space or reciprocal space with equal success. The rate of convergence is improved by an order of magnitude and is found to be almost independent of the size of the basis.