On the local representation of the electronic momentum operator in atomic systems

The local quantum theory is applied to the study of the momentum operator in atomic systems. Consequently, a quantum-based local momentum expression in terms of the single-electron density is determined. The limiting values of this function correctly obey two fundamental theorems: Kato's cusp condition and the Hoffmann-Ostenhof and Hoffmann-Ostenhof exponential decay. The local momentum also depicts the electron shell structure in atoms as given by its local maxima and inflection points. The integration of the electron density in a shell gives electron populations that are in agreement with the ones expected from the Periodic Table of the elements. The shell structure obtained is in agreement with the higher level of theory computations, which include the Kohn-Sham kinetic energy density. The average of the local kinetic energy associated with the local momentum is the Weizsacker kinetic energy. In conclusion, the local representation of the momentum operator provides relevant information about the electronic properties of the atom at any distance from the nucleus.     

Atomic shell structure and electron numbers

The electron localization function (ELF) was calculated for the atoms Li to Sr. The ELF maxima reveal the atomic shell structure for all these atoms. The shells are separated from each other by ELF minima. The integration of the electron density in a shell gives electron numbers. For the valence shell those are in good agreement with the ones expected from the Periodic Table of Elements. © 1996 John Wiley & Sons, Inc.     

Electron correlation effects on the shape of the Kohn–Sham molecular orbital

Even systems in which strong electron correlation effects are present, such as the large near-degeneracy correlation in a dissociating electron pair bond exemplified by stretched H₂, are represented in the Kohn–Sham (KS) model of non-interacting electrons by a determinantal wavefunction built from the KS molecular orbitals. As a contribution to the discussion on the status and meaning of the KS orbitals we investigate, for the prototype system of H₂ at large bond distance, and also for a one-dimensional molecular model, how the electron correlation effects show up in the shape of the KS σ _g orbital. KS orbitals φ^HL and φ^FCI obtained from the correlated Heitler-London and full configuration interaction wavefunctions are compared to the orbital φ^LCAO, the traditional linear combination of atomic orbitals (LCAO) form of the (approximate) Hartree-Fock orbital. Electron correlation manifests itself in an essentially non-LCAO structure of the KS orbitals φ^HL and φ^FCI around the bond midpoint, which shows up particularly clearly in the Laplacian of the KS orbital. There are corresponding features in the kinetic energy density t _s of the KS system (a well around the bond midpoint) and in the one-electron KS potential v _s (a peak). The KS features are lacking in the Hartree-Fock orbital, in a minimal LCAO approximation as well as in the exact one. Received: 11 December 1996 / Accepted: 10 January 1997     

Calculation of core-level electron spectra of ionic liquids

On the example of 40 ion pairs (5 cations times 8 anions), this study demonstrates how the core-level binding energy values can be calculated and used to plot theoretical spectra at low computational cost using density functional theory methods. Three approaches for obtaining the binding energy values are based on delta Kohn–Sham (ΔKS) calculations, 1s KS orbital energies, and atomic charges. The ΔKS results show reasonable agreement with the available experimental X-ray photoelectron data. The 1s KS orbital energies correlate well with the ΔKS results. Atomic charge correlation with ΔKS is improved by accounting for the charges of neighboring atoms. Assignment of binding energies to atoms and the applicability of the mentioned methods to model systems of ionic liquids are discussed.     

Atomic calculations with an effective one-body potential

The accuracy of a new effective one-body potential is assessed by the study of the electronic structure of atoms from He to Kr. The exchange part of this potential is obtained from a local approximation. Several simplified representations of the electronic density which lead to analytic Coulomb potentials are tested. It is shown that the introduction of the shell structure of the density is necessary, at least for third row atoms. The screening parameters of the potential are variationally optimized with respect to the total energy of the atom. With the most elaborate form of the Coulomb potential which contains one screening parameter for each shell, the comparison of the results with exact Hartree–Fock calculations is very promising. The relative difference is on the order of 10^?5 for the total energy and on the order of 10^?2 for the orbital energies. Multiplet splitting is reproduced accurately and F^? is predicted to be stable (in contrast some others local potentials) by an amount of 0.046 a.u., compared with 0.050 a.u. for an exact Hartree–Fock calculation.     

On the transferability of Fock matrix elements

The transferability of Fock matrix elements in the linear combination of atomic orbitals molecular orbital scheme is analysed using localized orbitals. It is shown that this transferability is dependent on the transferability of these localized orbitals and the neglect of long-range contributions from partially cancelling Coulomb nuclear attraction and electron repulsion terms. A theoretical basis is thus provided for the simulated ab initio molecular orbital and related methods. Various corrections previously introduced in an ad hoc manner are shown to be justified. Transferability in both the closed shell and open shell schemes is analysed.     

Electron localization functions and local measures of the covariance

The electron localization measure proposed by Becke and Edgecombe is shown to be related to the covariance of the electron pair distribution. Just as with the electron localization function, the local covariance does not seem to be, in and of itself, a useful quantity for elucidating shell structure. A function of the local covariance, however, is useful for this purpose. A different function, based on the hyperbolic tangent, is proposed to elucidate the shell structure encapsulated by the local covariance; this function also seems to work better for the electron localization measure of Becke and Edgecombe. In addition, we propose a different measure for the electron localization that incorporates both the electron localization measure of Becke and Edgecombe and the Laplacian of the electron density; preliminary indications are that this measure is especially good at elucidating the shell structure in valence regions. Methods for evaluating electron localization functions directly from the electron density, without recourse to the Kohn-Sham orbitals, are discussed.     

Potential of mean force of hydrophobic association: dependence on solute size

The potentials of mean force (PMFs) were determined for systems involving formation of nonpolar dimers composed of methane, ethane, propane, isobutane, and neopentane, respectively, in water, using the TIP3P water model, and in vacuo. A series of umbrella-sampling molecular dynamics simulations with the AMBER force field was carried out for each pair in either water or in vacuo. The PMFs were calculated by using the weighted histogram analysis method (WHAM). The shape of the PMFs for dimers of all five nonpolar molecules is characteristic of hydrophobic interactions with contact and solvent-separated minima and desolvation maxima. The positions of all these minima and maxima change with the size of the nonpolar molecule, that is, for larger molecules they shift toward larger distances. The PMF of the neopentane dimer is similar to those of other small nonpolar molecules studied in this work, and hence the neopentane dimer is too small to be treated as a nanoscale hydrophobic object. The solvent contribution to the PMF was also computed by subtracting the PMF determined in vacuo from the PMF in explicit solvent. The molecular surface area model correctly describes the solvent contribution to the PMF together with the changes of the height and positions of the desolvation barrier for all dimers investigated. The water molecules in the first solvation sphere of the dimer are more ordered compared to bulk water, with their dipole moments pointing away from the surface of the dimer. The average number of hydrogen bonds per water molecule in this first hydration shell is smaller compared to that in bulk water, which can be explained by coordination of water molecules to the hydrocarbon surface. In the second hydration shell, the average number of hydrogen bonds is greater compared to bulk water, which can be explained by increased ordering of water from the first hydration shell; the net effect is more efficient hydrogen bonding between the water molecules in the first and second hydration shells.     

Unpaired electrons at the second‐order reduced density matrix level: Covalent bonding,and coulomb and fermi correlations in closed shell systems

The usual one‐electron populations in atomic orbitals of closed shell systems are split into unpaired and paired at the (spin‐dependent) second‐order reduced density matrix level. The unpaired electron in an orbital is defined as the “simultaneous occurrence of an electron and an electron hole of opposite spins in the same spatial orbital,” which for simplicity is called “electropon.” The electropon population in a given orbital reveals whether and to what degree the Coulomb correlations, and hence, the chemical bonding between this orbital and the remaining orbitals of the system are globally favorable or unfavorable. The interaction of two electropons in two target orbitals reveals the quality (favorable or unfavorable) and the strength of the covalent bonding between these orbitals; this establish a bridge between the notion of “unpaired electrons” and the traditional covalent structure of valence‐bond (VB) theory. Favorable/unfavorable bonding between two orbitals is characterized by the positive/negative (Coulomb) correlation of two electropons of opposite spins, or alternatively, by the negative/positive (Fermi) correlation of two parallel spin electropons. A spin‐free index is defined, and the relationship between the electropon viewpoint for chemical bonding and the well‐known two‐electron Coulomb and Fermi correlations is established. Benchmark calculations are achieved for ethylene, hexatriene, benzene, pyrrole, methylamine, and ammonia molecules on the basis of physically meaningful natural orbitals. The results, obtained in the framework of both orthogonal and nonorthogonal population analysis methods, provide the same conceptual pictures, which are in very good agreement with elementary chemical knowledge and VB theory. © 2013 Wiley Periodicals, Inc.     

Role of electron correlation in the quantum-mechanical calculations of the coulomb interaction energy in the DNA base pairs

The intermolecular electronic correlation contributions to the Coulomb component of the nucleic acid base interaction energy are estimated. The Coulomb energy is evaluated with the use of atomic monopoles, which are determined from the π-electronic densities calculated by the SCF method and by employing partially or completely optimized APSG wave functions. When the correlation is thus taken into account, a systematic decrease in atomic charges occurs; this effect is considerable only if an optimized orbital set is used. As a result, the Coulomb interaction energy due to the π-electronic atoms decreases from ?1.13 to ?0.85 kcal/mol for the AT pair and from ?7.15 to ?4.61 kcal/mol for the GC pair.     

2,3-Diphenylbutadiene and donor-acceptor functionalized derivatives: exploring the competition between conjugation paths in branched pi-systems

2,3-Diphenylbutadiene and its donor-acceptor functionalized derivatives represent branched pi systems consisting of three overlapping linearly conjugated units, namely a 1,3-butadiene and two phenylethene subsystems. The evaluation of pi conjugation using a scheme based on the natural bond orbital analysis shows that the details of the structure of these compounds is governed by electron delocalization. The potential energy surface of 2,3-diphenylbutadiene shows two minima, each one representing a distinct combination of conjugation patterns. These minima are shown to be connected by a low-energy path with transition structures that have one conjugation path fully activated, while conjugation is completely disrupted along the other path. We will show that, in response to donor-accptor functionalization, the 2,3-diphenylbutadiene backbone will switch to other conformations, which come along with substantial changes in the electronic structure.     

More on the melting of Lennard-Jones clusters

The melting of 13-atom clusters interacting via Lennard-Jones potentials has been revisited using molecular dynamics coupled to steepest descent quenches. A procedure was devised to account for the fraction of times the global and local minima of the potential energy surface are accessed during a long trajectory. This quantity presents a sigmoid shape. A phenomenological model of melting is given in terms of a correlated walk that maps the short time excursions among the global and local minima in configuration space. Comparison between the simulation results and the theoretical model shows that the melting transition is well described in terms of the temperature changes of the fraction of high energy minima accessed during the cluster trajectory. Cooperativity is clear from the S shape of this quantity, i.e., the access to a local minimum favours the access to other local minima.     

Tight-binding density functional theory: an approximate Kohn-Sham DFT scheme

The DFTB method is an approximate KS-DFT scheme with an LCAO representation of the KS orbitals, which can be derived within a variational treatment of an approximate KS energy functional. But it may also be related to cellular Wigner-Seitz methods and to the Harris functional. It is an approximate method, but it avoids any empirical parametrization by calculating the Hamiltonian and overlap matrices out of DFT-derived local orbitals (atomic orbitals, AO's). The method includes ab initio concepts in relating the Kohn-Sham orbitals of the atomic configuration to a minimal basis of the localized atomic valence orbitals of the atoms. Consistent with this approximation, the Hamiltonian matrix elements can strictly be restricted to a two-center representation. Taking advantage of the compensation of the so-called "double counting terms" and the nuclear repulsion energy in the DFT total energy expression, the energy may be approximated as a sum of the occupied KS single-particle energies and a repulsive energy, which can be obtained from DFT calculations in properly chosen reference systems. This relates the method to common standard "tight-binding" (TB) schemes, as they are well-known in solid-state physics. This approach defines the density-functional tight-binding (DFTB) method in its original (non-self-consistent) version.     

Fast noniterative orbital localization for large molecules

We use Cholesky decomposition of the density matrix in atomic orbital basis to define a new set of occupied molecular orbital coefficients. Analysis of the resulting orbitals ("Cholesky molecular orbitals") demonstrates their localized character inherited from the sparsity of the density matrix. Comparison with the results of traditional iterative localization schemes shows minor differences with respect to a number of suitable measures of locality, particularly the scaling with system size of orbital pair domains used in local correlation methods. The Cholesky procedure for generating orthonormal localized orbitals is noniterative and may be made linear scaling. Although our present implementation scales cubically, the algorithm is significantly faster than any of the conventional localization schemes. In addition, since this approach does not require starting orbitals, it will be useful in local correlation treatments on top of diagonalization-free Hartree-Fock optimization algorithms.     

Shannon entropy as a predictor of avoided crossing in confined atoms

Avoided crossing is one of the unique spectroscopic features of a confined atomic system. Shannon information entropy of the ground state and some of the excited states of confined H atom as a predictor of avoided crossing is studied in this work. This is accomplished by varying the strength of the confinement and examining structure properties like ionization energy and Shannon information entropy. Along with the energy level repulsion at the avoided crossing, Shannon information entropy is also exchanged between the involved states. This work also addresses a question: In addition to that regarding localization, what other property of the system can be extracted from Shannon entropy? Insightful connection is discovered between Shannon entropy and the average value of confinement potential, Coulomb potential, and kinetic energy.     

Tensor factorizations of local second-order Møller-Plesset theory

Efficient electronic structure methods can be built around efficient tensor representations of the wavefunction. Here we first describe a general view of tensor factorization for the compact representation of electronic wavefunctions. Next, we use this language to construct a low-complexity representation of the doubles amplitudes in local second-order M?ller-Plesset perturbation theory. We introduce two approximations--the direct orbital-specific virtual approximation and the full orbital-specific virtual approximation. In these approximations, each occupied orbital is associated with a small set of correlating virtual orbitals. Conceptually, the representation lies between the projected atomic orbital representation in Pulay-Saeb? local correlation theories and pair natural orbital correlation theories. We have tested the orbital-specific virtual approximations on a variety of systems and properties including total energies, reaction energies, and potential energy curves. Compared to the Pulay-Saeb? ansatz, we find that these approximations exhibit favorable accuracy and computational times while yielding smooth potential energy curves.     

New results for phase transitions from catastrophe theory

Catastrophe theory predicts that in certain limits universal relations should exist between barrier heights, curvatures and the positions of local maxima and minima on a potential or free energy surface. In the present work we investigate these relations for both first- and second-order phase transitions, revealing that the ideal ratios often hold quite well over a wide range of conditions. This elementary catastrophe theory is illustrated for the melting transition of an atomic cluster, the isotropic-to-nematic transition in a liquid crystal, and the ferromagnetic-to-paramagnetic phase transition in the two-dimensional Ising model.     

On the electronic shell structure of metallic spheres and circular discs

The electronic shell structure of spherical and circular potential wells of finite depth is examined as an extension of the work of Balian and Bloch. We obtain analytical expressions for the electronic density of states, which are in good agreement with numerical results. The position of the maxima and minima in the density of states depends strongly on the depth of the potential via the quantummechanical scattering phases. For circular discs the oscillating structure in the density of states shows a different supershell pattern than for spheres. This is a consequence of the difference in the effective quantummechanical multiplicity of closed paths, which determine the oscillating structure.     

电负性研究(Ⅱ)—氢的电负性

氢的电负性值是氢元素性质的重要参数，１９３２年Pauling犤１～３犦定量确定氢的相对电负性值等于２．１，１９６１年Allred犤４，５犦用更准确的实验数据对Paul－ing电负性标度进行了修正，氢的电负性值被确定为２．２，目前这两个数值都在采用。元素的电负性值是与元素的性质紧密相关的，一个合适的电负性标度应该至少反映所有重要元素的电负性值，氢的化合物比任何其它元素都多，理应有一个基本的准确电负性值，然而一些电负性标度中却缺乏这样的数据。在Murphy等四人犤６犦最近发表的论文中，对Pauling电负性标度又进行了深入考查与…