Four-dimensional density and energy density functional

The relations based on an external one-electron operator V( r ) are examined from two view-points, i.e., from the Hohenberg–Kohn approach and the four-dimensional density concept introduced by Wilson and Frost, and extensively studied by Parr and Politzer. The object being to obtain, with the help of the Hellmann–Feynman theorem, new formulas for the energy of atoms and molecules, and to discuss the construction of the universal energy density functional on the basis of the four-dimensional density.     

Theory of time-resolved photoelectron imaging. Comparison of a density functional with a time-dependent density functional approach

Time-resolved photoelectron differential cross sections are computed within a quantum dynamical theory that combines a formally exact solution of the nuclear dynamics with density functional theory (DFT)-based approximations of the electronic dynamics. Various observables of time-resolved photoelectron imaging techniques are computed at the Kohn-Sham and at the time-dependent DFT levels. Comparison of the results serves to assess the reliability of the former method and hence its usefulness as an economic approach for time-domain photoelectron cross section calculations, that is applicable to complex polyatomic systems. Analysis of the matrix elements that contain the electronic dynamics provides insight into a previously unexplored aspect of femtosecond-resolved photoelectron imaging.     

Approximately N-representable density functional density matrices

For the first time, we obtain practical density matrices approximately N-representable by correlated-determinant wave functions, which are functionals of the electron density and entirely defined by information obtainable from the X-ray coherent diffraction experiment. © 1994 John Wiley & Sons, Inc.     

Method of local-scaling transformations and density functional theory in quantum chemistry. III. The energy density functional: Spin-restricted approach

The rigorous derivation of the energy density functional is proposed within the framework of the spinfree, or spin-restricted formulation of the energy density functional theory. It is shown particularly that the kinetic energy density functional is given by a sum of the Weizsacker term and the so-called “modified” Thomas–Fermi one. The variational principle is formulated for the energy density functional theory in terms of the Euler–Lagrange equation, and the virial theorem is proposed.     

Interfacial colloidal sedimentation equilibrium. II. Closure-based density functional theory

In Part I [R. E. Beckham and M. A. Bevan, J. Chem. Phys. 127, 164708 (2007)], results were presented for the sedimentation equilibrium of concentrated colloidal dispersions using confocal scanning laser microscopy experiments, Monte Carlo (MC) simulations, and a local density approximation perturbation theory. In this paper, we extended the modeling effort on those systems to include nonlocal density functional theory (DFT), which is capable of predicting the microstructure of the sediment at length scales comparable to the colloidal particle dimension. Specifically, we use a closure-based DFT formulation to predict interfacial colloidal sedimentation equilibrium density profiles. The colloid-colloid and colloid-surface interactions were modeled with DLVO screened electrostatic potentials using parameters taken directly from the experimental work. The DFT profiles were compared to the experimental and MC results from Part I. Good agreement was found for relatively dilute interfacial colloidal fluids, but agreement was less satisfactory as interfacial layering became more pronounced for conditions approaching the onset of interfacial crystallization. We also applied DFT in an inverse sense using the measured colloid density profile to extract the underlying colloid-surface potential; this can be thought of as a microscopic analog to the well-known procedure of using the macroscopic (coarse-grained) density profile to extract the osmotic equation of state. For the dilute interfacial fluid, the inverse DFT calculations reproduced the true colloid-surface potential to within 0.5kT at all elevations.     

Density functional theory: Approximating quasiparticle density functional

A constructive approach for deriving the approximating quasiparticle energy density functional is proposed. As a matter of fact, the proposed approach is the direct development of the Kohn–Sham quasiparticle concept and the Levy–Valone approach. The approach presented takes into account a pseudopotential character of the exchange-correlation part of the density functional and results in a system of functional equations to obtain ground-state energies of many-electron systems.     

Orbital-corrected orbital-free density functional theory

A new implementation of density functional theory (DFT), namely orbital-corrected orbital-free (OO) DFT, has been developed. With at most two non-self-consistent iterations, OO-DFT accomplishes the accuracy comparable to fully self-consistent Kohn-Sham DFT as demonstrated by its application on the cubic-diamond Si and the face-centered-cubic Ag systems. Our work provides a new impetus to further improve orbital-free DFT method and presents a robust means to significantly lower the cost associated with general applications of linear-scaling Kohn-Sham DFT methods on large systems of thousands of atoms within different chemical bonding environment.     

Pseudospectral time-dependent density functional theory

Time-dependent density functional theory (TDDFT) is implemented within the Tamm-Dancoff approximation (TDA) using a pseudospectral approach to evaluate two-electron repulsion integrals. The pseudospectral approximation uses a split representation with both spectral basis functions and a physical space grid to achieve a reduction in the scaling behavior of electronic structure methods. We demonstrate here that exceptionally sparse grids may be used in the excitation energy calculation, following earlier work employing the pseudospectral approximation for determining correlation energies in wavefunction-based methods with similar conclusions. The pseudospectral TDA-TDDFT method is shown to be up to ten times faster than a conventional algorithm for hybrid functionals without sacrificing chemical accuracy.     

Silabutadienes. Internal rotations and pi-conjugation. A density functional theory study

The potential energy surfaces (PESs) for internal rotation around the central single bond of nine silabutadienes, which include all possible mono-, di-, tri-, and tetrasilabutadienes, are investigated computationally by using DFT with the B3LYP functional and the 6-311+G(d,p) basis set. For 1-silabutadiene (3), 2-silabutadiene (4), 1,4-disilabutadiene (5), 2,3-disilabutadiene (6), and 1,3-disilabutadiene (7), the s-trans rotamer is the most stable. For 1,2-disilabutadiene (8), 1,2,3-trisilabutadiene (9), and 1,2,4-trisilabutadiene (10), all having a trans-bent SiSi double bond, the most stable conformers are those having an antiperiplanar (ap) structure. For tetrasilabutadiene (11), the global minimum is the gauche rotamer. The internal rotation barriers (RB) (relative to the global minimum) follow the order (kcal/mol) 5 (10.0) > 3 (7.4) > 1,3-butadiene (12, (6.6)) > 10 (4.9) > or = 7 (4.4) > or = 4 (4.0) approximately = 8 (3.9) > 9 (2.7) approximately = 6 (2.6) > 11 (2.4). The barriers are slightly smaller at CCSD(T)/cc-PVTZ, but the trend remains the same. The size of the rotation barrier is mainly dictated by the length of the central single bond; that is, it is the largest for dienes with the shorter C-C central bond (5, 3, and 12), and it is smaller for dienes with the longer Si-C and Si-Si central bonds. The strength of pi-conjugation in the s-trans conformers of silabutadienes was estimated by resonance stabilization energies (RE) calculated by using the Natural Bond Orbital (NBO) and Block Localized Wave function (BLW) methods and bond separation equations. A linear correlation is found between the barrier heights for internal rotation and pi-conjugation energies. The calculated RBs are significantly smaller than the corresponding REs, indicating that pi-resonance energies are not the only factor that dictate the RB, and therefore, RBs, although suitable for estimating trends in pi-conjugation in a series of compounds, cannot be used for estimating absolute resonance energies.     

Perspective on density functional theory

Density functional theory (DFT) is an incredible success story. The low computational cost, combined with useful (but not yet chemical) accuracy, has made DFT a standard technique in most branches of chemistry and materials science. Electronic structure problems in a dazzling variety of fields are currently being tackled. However, DFT has many limitations in its present form: too many approximations, failures for strongly correlated systems, too slow for liquids, etc. This perspective reviews some recent progress and ongoing challenges.     

Gas-phase acidity of D-glucose. A density functional theory study

The gas-phase acidity of D-glucopyranose was studied by means of B3LYP calculations combined with 6-31G(d,p) or 6-31+G(d,p) standard basis sets. For each anomer, deprotonation of the various primary and secondary hydroxyl groups was considered. As in solution, the anomeric hydroxyl is found to be the most acidic for both anomers, but only when the 6-31+G(d,p) basis set is used for geometry optimization. Deprotonation of the anomeric hydroxyl induces an important C(1)--O endocyclic bond elongation and subsequently promotes an energetically favored ring-opening process as attested by the very small calculated activation barriers. The results also suggest that interconversion between the various deprotonated alpha- and beta-anomers may easily occur under slightly energetic conditions. B3LYP/6-311+G(2df,2p) calculations led to the an absolute gas-phase acidity of deltaacidGo(298)(alpha-D-glucose) = 1398 kJ mol(-1). This estimate matches well the only experimental value available to date. Finally, this study again confirms that the use of diffuse functions on heavy atoms is necessary to describe anionic systems properly and to achieve good relative and absolute gas-phase acidities.     

Fully numerical Hartree-Fock and density functional calculations. II. Diatomic molecules

We present the implementation of a variational finite element solver in the HelFEM program for benchmark calculations on diatomic systems. A basis set of the form is used, where (μ, ν, φ) are transformed prolate spheroidal coordinates, B _n(μ) are finite element shape functions, and are spherical harmonics. The basis set allows for an arbitrary level of accuracy in calculations on diatomic molecules, which can be performed at present with either nonrelativistic Hartree-Fock (HF) or density functional (DF) theory. Hundreds of DFs at the local spin density approximation (LDA), generalized gradient approximation (GGA), and the meta-GGA level can be used through an interface with the Libxc library; meta-GGA and hybrid DFs are not available in other fully numerical diatomic program packages. Finite electric fields are also supported in HelFEM , enabling access to electric properties. We introduce a powerful tool for adaptively choosing the basis set by using the core Hamiltonian as a proxy for its completeness. HelFEM and the novel basis set procedure are demonstrated by reproducing the restricted open-shell HF limit energies of 68 diatomic molecules from the first to the fourth period with excellent agreement with literature values, despite requiring orders of magnitude fewer parameters for the wave function. Then, the electric properties of the BH and N₂ molecules under finite field are studied, again yielding excellent agreement with previous HF limit values for energies, dipole moments, and dipole polarizabilities, again with much more compact wave functions than what were needed for the literature references. Finally, HF, LDA, GGA, and meta-GGA calculations of the atomization energy of N₂ are performed, demonstrating the superb accuracy of the present approach.     

Differentiability of Lieb functional in electronic density functional theory

A solid understanding of the Lieb functional F_L is important because of its centrality in the foundations of electronic density functional theory. A basic question is whether directional derivatives of F_L at an ensemble‐V‐representable density are given by (minus) the potential. A widely accepted purported proof that F_L is Gâteaux differentiable at EV‐representable densities would say, “yes.” But that proof is fallacious, as shown here. F_L is not Gâteaux differentiable in the normal sense, nor is it continuous. By means of a constructive approach, however, we are able to show that the derivative of F_L at an EV‐representable density ρ₀ in the direction of ρ₁ is given by the potential if ρ₀ and ρ₁ are everywhere strictly greater than zero, and they and the ground state wave function have square integrable derivatives through second order. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Molecular fragments in density functional theory

The second-order density functional approach to the partitioning of the molecular density of Cedillo, Chattaraj, and Parr (Int. J. Quantum Chem. 2000, 77, 403-407) is used, together with a local assumption for the function that projects the total density into its components, to show that the distribution function adopts a stockholders form, in terms of the local softness of the isolated fragments, and that the molecular Fukui function is distributed in the molecular fragments in the same proportion as the electronic density.     

Geometry optimization in density functional methods

The geometry optimization in delocalized internal coordinates is discussed within the framework of the density functional theory program deMon. A new algorithm for the selection of primitive coordinates according to their contribution to the nonredundant coordinate space is presented. With this new selection algorithm the excessive increase in computational time and the deterioration of the performance of the geometry optimization for floppy molecules and systems with high average coordination numbers is avoided. A new step selection based on the Cartesian geometry change is introduced. It combines the trust radius and line search method. The structure of the new geometry optimizer is described. The influence of the SCF convergence criteria and the grid accuracy on the geometry optimization are discussed. A performance analysis of the new geometry optimizer using different start Hessian matrices, basis sets and grid accuracies is given.