Natural energy orbitals and the one-particle Green's function

It is shown how the properties of the one-particle Green's function lead naturally to the definition of the so-called natural energy orbitals. These orbitals allow the fully correlated total energy of a system to be written in Hartree–Fock-like fashion and might therefore provide a bridge between sophisticated correlated wave functions and approximate theories of chemical structure and reactivity based on a Hartree–Fock-like energy expression. Moreover these orbitals form the basis for a self-consistent scheme to calculate the one-particle Green's function. The relation between these natural energy orbitals and the extended Koopmans' theorem is considered. Finally it is shown that the exactness of the lowest extended Koopmans' ionization potential implies the linear independence of the corresponding Dyson orbital from all other Dyson orbitals.     

An efficient linear scaling procedure for constructing localized orbitals of large molecules based on the one-particle density matrix

We have developed a linear-scaling algorithm for obtaining the Boys localized molecular orbitals from the one-particle density matrix. The algorithm is made up of two steps: the Cholesky decomposition of the density matrix to obtain Cholesky molecular orbitals and the subsequent Boys localization process. Linear-scaling algorithms have been proposed to achieve linear-scaling calculations of these two steps, based on the sparse matrix technique and the locality of the Cholesky molecular orbitals. The present algorithm has been applied to compute the Boys localized orbitals in a number of systems including α-helix peptides, water clusters, and protein molecules. Illustrative calculations demonstrate that the computational time of obtaining Boys localized orbitals with the present algorithm is asymptotically linear with increasing the system size.     

A study of the relationships between unpaired electron density, spin-density and cumulant matrices

This work describes the derivation of simple relationships between the density matrix of effectively unpaired electrons and the spin-density matrix in N-electron systems. The link between both devices turns out to be the one-electron matrix arising from the diagonal contraction of the cumulant matrix corresponding to the second-order reduced density matrix. We study some features of this contracted matrix, showing its usefulness to describe the electronic correlation. Numerical determinations performed in selected systems with different spin symmetries confirm the theoretical predictions.     

Polarizability as a local functional of the electron density

Expressions for the multipole polarizability and shielding factor for an atom are obtained using the model where the total electron energy is assumed to be a local functional of the electron density. This simple model correctly predicts the leading term in the 1/Z expansion of the polarizability. Further, the simple local density functional for the polarizability, when evaluated with ground-state Hartree-Fock densities, yields numerical values for atoms which are, in general, in reasonable agreement with those obtained from coupled Hartree-Fock theory.     

Calculation and properties of non-orthogonal,strictly local molecular orbitals

A general procedure to calculate non-orthogonal, strictly local molecular orbitals (NOLMOs) expanded using only a subset of the total basis set is presented. The energy of a single determinant wave function is minimised using a Newton-Raphson approach. Total energies and barriers to internal rotation for CH₄, NH₃, H₂O, CH₃CH₃, CH₃NH₂, CH₃OH, NH₂NH₂, NH₂OH and HOOH, and certain properties of the NOLMOs present in these molecules, are investigated using the 4-31G basis set.     

A spherically averaged representation of the atomic one-particle reduced density matrix

Summary A new way of representing the one-particle reduced density matrix (ODM) of closed-shell atoms in a spherically averaged manner is presented, and connections of this representation to the radial density distributionD(R) and the isotropic reciprocal form factorB(s) are shown. In this representation, certain characteristics of the angular nodal structure of the natural orbitals (NOs) are preserved. Examples of hydrogenic orbitals and near-Hartree-Fock wave functions for some closed-shell atoms are given.     

Structure, metastability, and electron density of Al lattices in light of the model of anions in metallic matrices

This paper reports a theoretical investigation of the structure, stability, and electron charge density of cubic, rhombohedral, hexagonal, and monoclinic Al lattices. The equations of state and the elastic constants are computed from total energy calculations at different volumes and unit cell strains using the density functional theory approximation. The topology of the electron density is analyzed within the crystalline implementation of the atoms in molecules formalism. The results are discussed in light of the so-called anions in metallic matrices model, which permits the interpretation of the chemical bonding and the explanation of the existence of particular symmetries of inorganic crystals. First, the Al sublattices are identified as the reference building blocks of AlX(3) (X = F, Cl, OH) compounds. The calculations reveal that the equilibrium zero-pressure Al-Al shortest distance is around 2.75 A in all of the Al matrixes, similar to the value observed in the stable face centered cubic structure of Al at room conditions. Second, at their zero-pressure equilibrium geometries, the Al sublattices are found to fulfill the mechanical stability criteria or, alternatively, to show mechanical instabilities that are compatible with the distortions observed for the structures in AlX(3) crystals. However, at the equilibrium volumes of the AlX(3) crystals, all of the Al matrices violate the spinodal condition, and the cohesion and stabilization are provided by the nonmetallic X atoms. Third, the structural anisotropy of the Al sublattices seems to be the main factor to discriminate metallic matrices able to host nonmetallic elements. The inhomogeneities of the electron charge density, which favor the arrival of nonmetallic elements and the crystal formation, are notably enhanced in passing from the fcc structure of pure Al to the less isotropic Al matrices observed in AlX(3) compounds.     

Investigation of valence orbitals of propene by electron momentum spectroscopy

The binding energy spectra and momentum distributions of all valence orbitals of propene were studied by electron momentum spectroscopy (EMS) as well as Hartree-Fock and density functional theoretical calculations. The experiment was carried out at impact energies of 1200 eV and 600 eV on the state-of-the-art EMS spectrometer developed at Tsinghua University recently. The experimental momentum profiles of the valence orbitals were obtained and compared with the various theoretical calculations. Moreover, the experiment with a new analysis method presents a strong support for the correct ordering of the orbital 8a' and 1a', i.e., 9a' < 8a' < 1a' < 7a'.     

Multireference perturbation CI III. Fast evaluation of the one-particle density matrix

Within the frame of multireference perturbation configuration interaction we have developed a fast algorithm, based on diagrammatic techniques, for the calculation of the first-order correction to the one-particle density matrix. As an example of an application we have chosen the evaluation of the dipole moment of the CO molecule, where utilization of the first-order density is shown to corroborate the variational calculation. Received: 4 August 1998 / Accepted: 21 September 1998 / Published online: 16 November 1998     

Evaluation of the electron momentum density of crystalline systems from ab initio linear combination of atomic orbitals calculations

Alternative techniques are presented for the evaluation of the electron momentum density (EMD) of crystalline systems from ab initio linear combination of atomic‐orbitals calculations performed in the frame of one‐electron self‐consistent‐field Hamiltonians. Their respective merits and drawbacks are analyzed with reference to two periodic systems with very different electronic features: the fully covalent crystalline silicon and the ionic lithium fluoride. Beyond one‐electron Hamiltonians, a post‐Hartree–Fock correction to the EMD of crystalline materials is also illustrated in the case of lithium fluoride. © 2012 Wiley Periodicals, Inc.     

Approximate density matrices and wigner distribution functions from density,kinetic energy density,and idempotency constraints

The Wigner distribution function and the corresponding density matrix are calculated using a form for the distribution function suggested by maximization of the entropy. Wigner functions and density matrices are determined by imposing conditions of idempotency on the density matrix. Exchange energies and Compton profiles calculated from density matrices obtained by imposing the idempotency constraints are compared with the results of calculations using the Hartree–Fock density matrix and a Gaussian approximation for the density matrix for H and the noble gases He through Xe. Compton profiles from Wigner functions with idempotency constraints show improvements over the Gaussian approximation for the lighter atoms, but do not show significant changes for the heavier atoms. Exchange energies from density matrices with idempotency constraints show improvements over the Gaussian approximation except for the heavier atoms Kr and Xe.     

Photoelectron spectra,penning ionization electron spectra,and character of canonical molecular orbitals

When canonical molecular orbitals are expanded in terms of a set of localized molecular orbital building blocks, called bond orbitals, the character of the canonical molecular orbitals can be characterized according to the component bond orbitals resembling the core, lone pair, and localized bond building blocks in an intuitive Lewis structure. Weinhold's natural bond orbital method can produce a unique Lewis structure with total occupancy of its occupied bond orbitals exceeding 99.9% of the total electron density for simple molecules. Two useful indices, Lewis bond order and weight of lone pair orbitals, can be defined according to the weights of the bonding and lone pair components of this unique Lewis structure. Calculation results for molecules N₂, CO, CS, NO, HCN, C₂H₂, H₂O, and H₂S show that the former index can account for the vibrational structures of photoelectron spectroscopy, whereas the latter index can account for the band intensity enhancement of Penning ionization electron spectroscopy. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 882–892, 1998     

Hartree-Fock orbitals significantly improve the reaction barrier heights predicted by semilocal density functionals

Semilocal density functional theory predictions for the barrier heights of representative hydrogen transfer, heavy-atom transfer, and nucleophilic substitution reactions are significantly improved in non-self-consistent calculations using Hartree-Fock orbitals. Orbitals from hybrid calculations yield related improvements. These results provide insight into compensating for one-electron self-interaction error in semilocal density functional theory.     

An investigation of the valence orbitals of water by high momentum resolution electron momentum spectroscopy

The momentum distributions of the valence orbitals for water well as the binding energy spectra in the region 10–45 eV have been reinvestigated with a high momentum resolution (≈0.1 a₀^?1 fwhm) binary (e.2e) spectrometer. The binding energy spectra show considerable satellite structure in the region > 25 eV which is consistent with theoretical predictions of final state configuration interaction (many-body effects) involving the (2a₁)^?1 hole state. An investigation of the momentum distribution in the satellite region confirms this assignment. This is in accord with a variety of recent theoretical studies and also consistent with earlier experiments. Differences suggested in earlier comparisons between theory and low momentum resolution experiments for the momentum distributions of the 1b₁ and 3a₁ orbitals have been verified. Several possible theoretical studies are suggested to investigate further this discrepancy between experiment and theory. Bonding effects and thenature of the molecular orbitals of H₂O in momentum space are also discussed.     

Calculation of transition density matrices by nonunitary orbital transformations

An efficient scheme for calculating one- and two-electron transition density matrices for two wave functions is described. The method applies to CAS (complete active space) wave functions and certain multireference CI expansions. The orbital sets of the two wave functions are not assumed to be equal. They are transformed to a biorthonormal basis, and the corresponding transformation of the CI coefficients is carried out directly, using the one-electron coupling coefficients.     

On the use of local basis sets for localized molecular orbitals

Two procedures are discussed for the direct variational optimization of localized molecular orbitals which are expanded in local subsets of the molecular basis set. It is shown that a Newton-Raphson approach is more efficient than an iterative diagonalization scheme. The effect of the basis-set truncation on the quality ofab-initio SCF results is investigated for Be, Li₂, HF, H₂O, NH₃, CH₄ and C₂H₆.