First-order gradient correction for the exchange-energy density functional for atoms

Summary Spurred by earlier discoveries by Deb and others that a first-order correction in the kinetic energy functional leads to an improved kinetic energy, a first-order gradient term is studied as a component of the gradient-corrected functional for atomic exchange energy. This term is shown to improve the local density approximation to the exchange energy more than does the usual second-order gradient correction. The imperative of systematically deriving this gradient correction is discussed but not resolved.     

Electronic band structure and optical properties of titanium oxyphosphates Li0.50Co0.25TiO(PO4) single crystals: An ab-initio calculations

From the refined atomic positions obtained by Belmal et al. (2004) [1] using X-ray diffraction for Li_0.50Co_0.25TiO(PO₄), we have performed a structural optimization by minimizing the forces acting on the atoms keeping the lattice parameters fixed at the experimental values. With this relaxed (optimized) geometry we have performed a comprehensive theoretical study of electronic properties and dispersion of the linear optical susceptibilities using the full potential linear augmented plane wave (FP-LAPW) method. The generalized gradient approximation (GGA) exchange-correlation potential was applied. In addition, the Engel-Vosko generalized gradient approximation (EVGGA) was used for comparison with GGA because it is known that EVGGA approach yields better band splitting compared to the GGA. We have calculated the band structure, and the total and partial densities of states. The electron charge densities and the bonding properties were analyzed and discussed. The complex dielectric optical susceptibilities were discussed in detail.     

Deformation Potentials: Towards a Systematic Way beyond the Atomic Fragment Approach in Orbital-Free Density Functional Theory

This work presents a method to move beyond the recently introduced atomic fragment approximation. Like the bare atomic fragment approach, the new method is an ab initio, parameter-free, orbital-free implementation of density functional theory based on the bifunctional formalism that treats the potential and the electron density as two separate variables, and provides access to the Kohn–Sham Pauli kinetic energy for an appropriately chosen Pauli potential. In the present ansatz, the molecular Pauli potential is approximated by the sum of the bare atomic fragment approach, and a so-called deformation potential that takes the interaction between the atoms into account. It is shown that this model can reproduce the bond-length contraction due to multiple bonding within the list of second-row homonuclear dimers. The present model only relies on the electron densities of the participating atoms, which themselves are represented by a simple monopole expansion. Thus, the bond-length contraction can be rationalized without referring to the angular quantum numbers of the participating atoms.     

Information distance analysis of molecular electron densities

The information‐theoretic basis of the Hirshfeld partitioning of the molecular electronic density into the densities of the “stockholder” atoms‐in‐molecules (AIM) is summarized. It is argued that these AIM densities minimize both the directed divergence (Kullback–Leibler) and divergence (Kullback) measures of the entropy deficiency between the AIM and their free atom analogs of the promolecule. The local equalization of the information distance densities of the Hirshfeld components, at the local value of the corresponding global entropy deficiency density, is outlined and several approximate relations are established between the alternative local measures of the missing information and the familiar function of a difference between the molecular and promolecule densities. Various global (of the system as a whole) and atomic measures of the entropy deficiency or the displacements relative to the isoelectronic promolecule, defined for densities or probabilities (shape functions) in both the local resolution and the Hirshfeld AIM discretization, are introduced and tested. This analysis is performed also for the valence electron (frozen‐core) approximation. Illustrative results for representative linear molecules, including diatomics, triatomics, and tetraatomics, are reported. They are interpreted as complementary characteristics of changes in the net AIM charge distribution and of the displacements in the information content of the electron distributions of bonded atoms. These numerical results confirm the overall similarity of the stockholder AIM to their free atom analogs and reflect the information displacements due to the AIM polarization and charge transfer in molecules. They also demonstrate the semiquantitative nature of the approximate relations established between the entropy deficiency densities and the related functions involving the density difference function. This development extends the range of interpretations based on the density difference diagrams into probing the associated information displacements in a molecule accompanying the formation of the chemical bonds. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002     

Atomic radii scales and electron properties deduced from the charge density

A procedure to represent Hartree-Fock electron densities in atoms [L. Fernandez Pacios, J. Comp. Chem., 14 , 410 (1993)] defines ρ(r) as a reduced expansion of exponential functions. These analytically modeled densities (AMDs) are used in this article to develop a simple computational procedure for analyzing different atomic radii scales implemented in the commercial software system MATHEMATICA. The analysis is focused on the physical information associated to a given atomic radius as deduced from calculations depending on ρ(r). The amount of electron charge contained in the sphere of the given radius as well as the distinct contributions to the potential energy integrated up to that radius are obtained within the AMD formulation for main-group atoms H—Kr. The ASCII file needed to run the procedure within MATHEMATICA is also presented. © 1995 by John Wiley & Sons, Inc.     

Electron momentum density and band structure calculations of α- and β-GeTe

We have measured isotropic experimental Compton profile of α-GeTe by employing high energy (662 keV) γ-radiation from a ¹³⁷Cs isotope. To compare our experiment, we have also computed energy bands, density of states, electron momentum densities and Compton profiles of α- and β-phases of GeTe using the linear combination of atomic orbitals method. The electron momentum density is found to play a major role in understanding the topology of bands in the vicinity of the Fermi level. It is seen that the density functional theory (DFT) with generalised gradient approximation is relatively in better agreement with the experiment than the local density approximation and hybrid Hartree–Fock/DFT.     

Analytical method for the representation of atoms-in-molecules densities

We present analytic refinements and applications of the deformed atomic densities method [Fernández Rico, J.; López, R.; Ramírez, G. J Chem Phys 1999, 110, 4213-4220]. In this method the molecular electron density is partitioned into atomic contributions, using a minimal deformation criterion for every two-center distributions, and the atomic contributions are expanded in spherical harmonics times radial factors. Recurrence relations are introduced for the partition of the two-center distributions, and the final radial factors are expressed in terms of exponential functions multiplied by polynomials. Algorithms for the practical implementation are developed and tested, showing excellent performances. The usefulness of the present approach is illustrated by examining its ability to describe the deformation of atoms in different molecular environments and the relationship between these atomic densities and some chemical properties of molecules.     

Diminished gradient dependence of density functionals: constraint satisfaction and self-interaction correction

The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation for the exchange-correlation energy functional has two nonempirical constructions, based on satisfaction of universal exact constraints on the hole density or on the energy. We show here that, by identifying one possible free parameter in exchange and a second in correlation, we can continue to satisfy these constraints while diminishing the gradient dependence almost to zero (i.e., almost recovering the local spin density approximation or LSDA). This points out the important role played by the Perdew-Wang 1991 nonempirical hole construction in shaping PBE and later constructions. Only the undiminished PBE is good for atoms and molecules, for reasons we present, but a somewhat diminished PBE could be useful for solids; in particular, the surface energies of solids could be improved. Even for atoms and molecules, a strongly diminished PBE works well when combined with a scaled-down self-interaction correction (although perhaps not significantly better than LSDA). This shows that the undiminished gradient dependence of PBE and related functionals works somewhat like a scaled-down self-interaction correction to LSDA.     

Subshell fitting of relativistic atomic core electron densities for use in QTAIM analyses of ECP-based wave functions

Scalar-relativistic, all-electron density functional theory (DFT) calculations were done for free, neutral atoms of all elements of the periodic table using the universal Gaussian basis set. Each core, closed-subshell contribution to a total atomic electron density distribution was separately fitted to a spherical electron density function: a linear combination of s-type Gaussian functions. The resulting core subshell electron densities are useful for systematically and compactly approximating total core electron densities of atoms in molecules, for any atomic core defined in terms of closed subshells. When used to augment the electron density from a wave function based on a calculation using effective core potentials (ECPs) in the Hamiltonian, the atomic core electron densities are sufficient to restore the otherwise-absent electron density maxima at the nuclear positions and eliminate spurious critical points in the neighborhood of the atom, thus enabling quantum theory of atoms in molecules (QTAIM) analyses to be done in the neighborhoods of atoms for which ECPs were used. Comparison of results from QTAIM analyses with all-electron, relativistic and nonrelativistic molecular wave functions validates the use of the atomic core electron densities for augmenting electron densities from ECP-based wave functions. For an atom in a molecule for which a small-core or medium-core ECPs is used, simply representing the core using a simplistic, tightly localized electron density function is actually sufficient to obtain a correct electron density topology and perform QTAIM analyses to obtain at least semiquantitatively meaningful results, but this is often not true when a large-core ECP is used. Comparison of QTAIM results from augmenting ECP-based molecular wave functions with the realistic atomic core electron densities presented here versus augmenting with the limiting case of tight core densities may be useful for diagnosing the reliability of large-core ECP models in particular cases. For molecules containing atoms of any elements of the periodic table, the production of extended wave function files that include the appropriate atomic core densities for ECP-based calculations, and the use of these wave functions for QTAIM analyses, has been automated.     

Atomic properties of selected biomolecules: quantum topological atom types of hydrogen,oxygen, nitrogen and sulfur occurring in natural amino acids and their derivatives

Molecular electron densities are generated at B3LYP/6-311+G(2d,p)//HF/6-31G(d) level for 57 molecules, including one conformation of each naturally occurring amino acid and smaller derived molecules. The electron densities are partitioned into atomic fragments according to the approach of quantum chemical topology (QCT). A set of 547 unique topological atoms is obtained, containing 421 hydrogens, 63 oxygens, 57 nitrogens and 6 sulfurs. Each atom is described by seven properties: volume, kinetic energy, monopole, dipole, quadrupole, octupole and hexadecapole moment. Cluster analysis groups atoms into atom types based on their similarity expressed in the discrete 7D space of atomic properties. Using a separation criterion we distinguish seven hydrogen, six oxygen, two nitrogen and six sulfur atom types.     

Density functional calculation of intermolecular potentials

Calculations of intermolecular potentials following the density functional theory (DFT) turn out to be very complicated without using some appropriate approximations. Most often the following three approximations have been considered. In one approximation the disturbed charge distributions during collisions are reduced to sums of undisturbed charge distributions from the colliding species. In another approximation, the so-called local density approximation (LDA), one neglects the fact that the intermolecular potentials that depend on charge densities also depend on gradients in the densities. In a third approximation one assumes that the intermolecular potential can be considered as a sum of two terms: a term for the long-range geometry and a term for the short-range geometry. In this Article the three approximations mentioned will be discussed for numerical accuracy for calculations of potentials between inert gas atoms and for calculations of potentials between surfaces and inert gas atoms. In the discussion a few other approximations will be mentioned too.     

Generalized Born model with a simple, robust molecular volume correction

Generalized Born (GB) models provide a computationally efficient means of representing the electrostatic effects of solvent and are widely used, especially in molecular dynamics (MD). A class of particularly fast GB models is based on integration over an interior volume approximated as a pairwise union of atom spheres-effectively, the interior is defined by a van der Waals rather than Lee-Richards molecular surface. The approximation is computationally efficient, but if uncorrected, allows for high dielectric (water) regions smaller than a water molecule between atoms, leading to decreased accuracy. Here, an earlier pairwise GB model is extended by a simple analytic correction term that largely alleviates the problem by correctly describing the solvent-excluded volume of each pair of atoms. The correction term introduces a free energy barrier to the separation of non-bonded atoms. This free energy barrier is seen in explicit solvent and Lee-Richards molecular surface implicit solvent calculations, but has been absent from earlier pairwise GB models. When used in MD, the correction term yields protein hydrogen bond length distributions and polypeptide conformational ensembles that are in better agreement with explicit solvent results than earlier pairwise models. The robustness and simplicity of the correction preserves the efficiency of the pairwise GB models while making them a better approximation to reality.     

Generalized Hirshfeld Partitioning with Oriented and Promoted ProatomsSCI北大核心CSCD

In this study, we show how to generalize Hirshfeld partitioning methods to possibly include non-spherical proatom densities. While this generalization is numerically challenging(requiring global optimization of a large number of parameters), it is conceptually appealing because it allows the proatoms to be pre-polarized, or even promoted, to a state that more closely resembles the atom in a molecule. This method is based on first characterizing the convex set of proatom densities associated with the degenerate ground states of isolated atoms and atomic ions. The preferred orientation of the proatoms' densities are then obtained by minimizing the information–theoretic distance between the promolecular and molecular densities. If contributions from excited states(and not just degenerate ground states) are included in the convex set, this method can describe promoted atoms. While the procedure is intractable in general, if one includes only atomic states that have differing electron-numbers and/or spins, the variational principle becomes a simple convex optimization with a single unique solution.     

LocalSCF method for semiempirical quantum-chemical calculation of ultralarge biomolecules

A linear-scaling semiempirical method, LocalSCF, has been proposed for the quantum-chemical calculations of ultralarge molecular systems by treating the large-scale molecular task as a variational problem. The method resolves the self-consistent field task through the finite atomic expansion of weakly nonorthogonal localized molecular orbitals. The inverse overlap matrix arising from the nonorthogonality of the localized orbitals is approximated by preserving the first-order perturbation term and applying the second-order correction by means of a penalty function. This allows for the separation of the orbital expansion procedure from the self-consistent field optimization of linear coefficients, thereby maintaining the localized molecular orbital size unchanged during the refinement of linear coefficients. Orbital normalization is preserved analytically by the variation of virtual degrees of freedom, which are orthogonal to the initial orbitals. Optimization of linear coefficients of localized orbitals is performed by a gradient procedure. The computer program running on a commodity personal computer was applied to the GroEL-GroES chaperonin complex containing 119,273 atoms.     

Quantum similarity measures under atomic shell approximation: First order density fitting using elementary Jacobi rotations

The elementary Jacobi rotations technique is proposed as a useful tool to obtain fitted electronic density functions expressed as linear combinations of atomic spherical shells, with the additional constraint that all coefficients are kept positive. Moreover, a Newton algorithm has been implemented to optimize atomic shell exponents, minimizing the quadratic error integral function between ab initio and fitted electronic density functions. Although the procedure is completely general, as an application example both techniques have been used to compute a 1S-type Gaussian basis for atoms H through Kr, fitted from a 3-21G basis set. Subsequently, molecular electronic densities are modeled in a promolecular approximation, as a simple sum of parameterized atomic contributions. This simple molecular approximation has been employed to show, in practice, its usefulness to some computational examples in the field of molecular quantum similarity measures. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2023–2039, 1997     

Relativistic virial theorem for atoms

A relativistic virial theorem is derived for atoms in a general manner. The virial ratio consists of the usual V/T term and a correction term W/T, where T, V, and W are the kinetic energy, the potential energy, and correction terms, respectively. Explicit forms of W are presented for four specific nuclear potential models. Numerical calculations for a uniform nuclear charge model show that the magnitude of the correction term W/T increases with increasing atomic numbers and that it modifies the ratio V/T considerably for atoms with large atomic numbers in particular. Received: 21 November 2000 / Accepted: 8 January 2001 / Published online: 3 April 2001     

Resonance structures of the amide bond: the advantages of planarity

Delocalization indexes based on magnitudes derived from electron-pair densities are demonstrated to be useful indicators of electron resonance in amides. These indexes, based on the integration of the two-electron density matrix over the atomic basins defined through the zero-flux condition, have been calculated for a series of amides at the B3LYP/6-31+G* level of theory. These quantities, which can be viewed as a measure of the sharing of electrons between atoms, behave in concordance with the traditional resonance model, even though they are integrated in Bader atomic basins. Thus, the use of these quantities overcomes contradictory results from analyses of atomic charges, yet keeps the theoretical appeal of using nonarbitrary atomic partitions and unambiguously defined functions such as densities and pair densities. Moreover, for a large data set consisting of 24 amides plus their corresponding rotational transition states, a linear relation was found between the rotational barrier for the amide and the delocalization index between the nitrogen and oxygen atoms, indicating that this parameter can be used as an ideal physical-chemical indicator of the electron resonance in amides.