Using molecular similarity to construct accurate semiempirical electron structure theories

Ab initio electronic structure methods give accurate results for small systems, but do not scale well to large systems. Chemical insight tells us that molecular functional groups will behave approximately the same way in all molecules, large or small. This molecular similarity is exploited in semiempirical methods, which couple simple electronic structure theories with parameters for the transferable characteristics of functional groups. We propse that high-level calculations on small molecules provide a rich source of parametrization data. In principle, we can select a functional group, generate a large amount of ab initio data on the group in various small-molecule environments, and "mine" this data to build a sophisticated model for the group's behavior in large molecules. This work details such a model for electron correlation: a semiempirical, subsystem-based correlation functional that predicts a subsystem's two-electron density as a functional of its one-electron density. This model is demonstrated on two small systems: chains of linear, minimal-basis (H-H)5, treated as a sum of four overlapping (H-H)2 subsystems; and the aldehyde group of a set of HOC-R molecules. The results provide an initial demonstration of the feasibility of this approach.Comment: The following article appeared in the Journal of Chemical Physics, 121 (12), 5635-5645 (2004) and may be found at http://jcp.aip.org

Long-range-corrected hybrids including RPA correlation

We recently demonstrated a connection between the random phase approximation (RPA) and coupled cluster theory [J. Chem. Phys. 129, 231101 (2008)]. Based on this result, we here propose and test a simple scheme for introducing long-range RPA correlation into density functional theory. Our method provides good thermochemical results and models van derWaals interactions accurately.Comment: Accepted version of the manuscrip

Well-Tempered Metadynamics Simulations Predict the Structural and Dynamic Properties of a Chiral 24-Atom Macrocycle in Solution

Inspired by therapeutic potential, the molecular engineering of macrocycles is garnering increased interest. Exercising control with design, however, is challenging due to the dynamic behavior that these molecules must demonstrate in order to be bioactive. Herein, the value of metadynamics simulations is demonstrated: the free-energy surfaces calculated reveal folded and flattened accessible conformations of a 24-atom macrocycle separated by barriers of c.a. 6 kT under experimentally relevant conditions. Simulations reveal that the dominant conformer is folded-an observation consistent with a solid-state structure determined by X-ray crystallography and a network of rOes established by 1H NMR. Simulations suggest that the macrocycle exists as a rapidly interconverting pair of enantiomeric, folded structures. Experimentally, 1H NMR shows a single species at room temperature. However, at lower temperature, the interconversion rate between these enantiomers becomes markedly slower, resulting in the decoalescence of enantiotopic methylene protons into diastereotopic, distinguishable resonances due to the persistence of conformational chirality. The emergence of conformational chirality provides critical experimental support for the simulations, revealing the dynamic nature of the scaffold-a trait deemed critical for oral bioactivity

Deriving Extended DFT+U From Multiconfigurational Wavefunction Theory

This work derives a modified Hubbard correction to density functional theory (DFT+U), as a well-defined approximation to a multiconfigurational wavefunction-in-DFT method. One projects the electron-electron interaction operator onto the atomic states used in DFT+U, introduces the projected interaction into the noninteracting Kohn-Sham reference system, introduces a valence-bond (VB)-type approximation for the reference system's multideterminant wavefunction, and approximates the formally exact projected-interacting exchange-correlation (XC) functional using a generalized self-interaction correction. The reference system's correlation energy can be expressed en terms of the projected state occupation numbers and a promotion energy for the VB configurations. All of this can be done exactly for asymptotically separated minimal-basis hydrogen atoms, exactly recovering the flat-plane condition. Simple approximations to the promotion energy accurately model spin-splitting energies of iron spin-crossover complexes, without introducing excessive delocalization error in iron atom

Systematically Improvable Generalization of Self-Interaction Corrected Density Functional Theory

Perdew-Zunger self-interaction correction (PZSIC) reintroduces an exact constraint to approximate density functional theory (DFT), but can paradoxically degrade performance and is not systematically improvable. We use the Adiabatic Projection formalism to derive PZSIC in terms of a reference system experiencing only electron self-interaction. Generalization introduces correlation into the reference system, systematically bridging from PZSIC to exact wavefunction theory. Minimal active spaces resolve the PZSIC paradox, accurately treating near-equilibrium and strongly-correlated systems.Comment: 10 pages, 2 figure

Unification of Perdew-Zunger Self-Interaction Correction, DFT+U, and Rung 3.5 Density Functionals

We unify the Perdew-Zunger self-interaction correction (PZSIC) to approximate density functional theory (DFT), the Hubbard correction DFT+U, and Rung 3.5 functionals within the Adiabatic Projection formalism. We modify the Kohn-Sham reference system, introducing electron self-interaction in selected states. Choosing those states as localized orbitals, localized atomic states, or states at each point in space recovers PZSIC, DFT+U, and Rung 3.5. Typical Hubbard U parameters approximate scaled-down PZSIC. A Rung 3.5 variant of DFT+U opens a band gap in the homogeneous electron gas

Projected Hybrid Density Functionals: Method and Application to Core Electron Ionization

This work presents a new class of hybrid density functional theory (DFT) approximations, incorporating nonlocal exact exchange in predefined states such as core atomic orbitals (AOs). These projected hybrid density functionals are a flexible generalization of range-separated hybrids. This work derives projected hybrids using the Adiabatic Projection formalism. One projects the electron-electron interaction operator onto the chosen predefined states, reintroduces the projected operator into the noninteracting Kohn-Sham reference system, and introduces a density functional approximation for the remaining electron-electron interactions. Projected hybrids are readily implemented existing density functional codes, requiring only a projection of the one-electron density matrices and exchange operators entering existing routines. This work also presents a first application: a core-projected Perdew-Burke-Ernzerhof hybrid PBE0c70, in which the fraction of nonlocal exact exchange is increased from 25% to 70% in core AOs. Automatic selection of the projected AOs provides a black-box model chemistry appropriate for both core and valence electron properties. PBE0c70 predicts core orbital energies that accurately recover core-electron binding energies of second- and third-row elements, without degrading PBE0's good performance for valence-electron properties

Testing Exact Upper Bounds to Exact Exchange

The exact exchange energy and its energy density are useful but computationally expensive ingredients in density functional approximations for Kohn–Sham density functional theory. We present detailed tests of some exact nonempirical upper bounds to exact exchange. These “Rung 3.5” upper bounds contract the Kohn–Sham one-particle density matrix with model density matrices used to construct semilocal model exchange holes and invoke the Cauchy–Schwarz inequality. The contraction automatically eliminates the computationally expensive long-range component of the exact exchange hole. Numerical tests show that the exchange upper bounds underestimate total exchange energies while predicting other properties with accuracy approaching standard hybrid approximations