Fundamental importance of the Coulomb hole sum rule to the understanding of the Colle-Salvetti wave function functional

In this paper we consider the general form of the correlated-determinantal wave function functional of Colle and Salvetti (CS) for the He atom. The specific form employed by CS is the basis for the widely used CS correlation energy formula and the Lee-Yang-Parr correlation energy density functional of Kohn-Sham density functional theory. We show the following: (i) The key assumption of CS for the determination of this wave function functional, viz., that the resulting single-particle density matrix and the Hartree-Fock theory Dirac density matrix are the same, is equivalent to the satisfaction of the Coulomb hole sum rule for each electron position. The specific wave function functional derived by CS does not satisfy this sum rule for any electron position. (ii) Application of the theorem on the one-to-one correspondence between the Coulomb hole sum rule for each electron position and the constraint of normalization for approximate wave functions then proves that the wave function derived by CS violates charge conservation. (iii) Finally, employing the general form of the CS wave function functional, the exact satisfaction of the Coulomb hole sum rule at each electron position then leads to a wave function that is normalized. The structure of the resulting approximate Coulomb holes is reasonably accurate, reproducing both the short- and the long-range behavior of the hole for this atom. Thus, the satisfaction of the Coulomb hole sum rule by an approximate wave function is a necessary condition for constructing wave functions in which electron-electron repulsion is represented reasonably accurately.     

Magnetic and conduction properties in 1D organic radical materials: an ab initio inspection for a challenging quest

The chemical control of magnetic and conduction properties for organic radicals is mainly based on t, the resonance integral, and U, the on-site repulsion, used in the Hubbard model. A qualitative analysis based on the competition between the kinetic and the Coulomb contribution, and the expression of the magnetic exchange coupling suggests that U should be roughly 800 cm(-1) while the resonance integral |t| should be 200 cm(-1) to reach bifunctionality. Ab initio wavefunction-based calculations allowed us to quantitatively measure those quantities for several organic materials considered as 1D systems starting from their reported crystal structures. The extraction of t and U parameters from the exchange coupling constants between neighbouring radicals allowed us to anticipate a possible metallic behaviour. Finally, the impact of chemical changes in the constitutive units is measured to rationalize the macroscopic behaviour modifications. It is shown that the intriguing regime characterized by simultaneous itinerant and localized electrons might be achieved by molecular engineering.     

Tunnel coupled dangling bond structures on hydrogen terminated silicon surfaces

We study both experimentally and theoretically the electronic behavior of dangling bonds (DBs) at a hydrogen terminated Si(100)-2×1 surface. Dangling bonds behave as quantum dots and, depending on their separation, can be tunnel coupled with each other or completely isolated. On n-type highly doped silicon, the latter have a net charge of -1e, while coupled DBs exhibit altered but predictable filling behavior derived from an interplay between interdot tunneling and Coulomb repulsion. We found good correlation between many scanning tunneling micrographs of dangling bond structures and our theoretical results of a corresponding extended Hubbard model. We also demonstrated chemical methods to prevent tunnel coupling and isolate charge on a single dangling bond.     

Quartic lattice interactions,soliton‐like excitations,and electron pairing in one‐dimensional anharmonic crystals

In this study, it is shown that two added, excess electrons with opposite spins in one‐dimensional crystal lattices with quartic anharmonicity may form a bisolectron, which is a localized bound state of the paired electrons to a soliton‐like lattice deformation. It is also shown that when the Coulomb repulsion is included, the wave function of the bisolectron has two maxima, and such a state is stable in lattices with strong enough electron (phonon/soliton)–lattice coupling. Furthermore, the energy of the bisolectron is shown to be lower than the energy of the state with two separate, independent electrons, as even with account of the Coulomb repulsion the bisolectron binding energy is positive. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Accuracy of second order perturbation theory in the polaron and variational polaron frames

In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous analysis of the regimes of validity of the polaron transformation is still lacking. Here we provide such a benchmark, comparing second order perturbation theory results in the original untransformed frame, the polaron frame, and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix. Equilibrium quantities allow a direct comparison of the three methods without invoking any further approximations as is usually required in deriving master equations. It is found that the second order results in the original frame are accurate for weak system-bath coupling; the results deteriorate when the bath cut-off frequency decreases. The full polaron results are accurate for the entire range of coupling for a fast bath but only in the strong coupling regime for a slow bath. The variational method is capable of interpolating between these two methods and is valid over a much broader range of parameters.     

Theoretical study of the CS2+ dication

The potential energy and spin-orbit coupling functions of 11 lowest electronic states of CS(2+) dication have been calculated using internally contracted multireference configuration method. Using these functions, the positions and widths of the corresponding vibronic levels have been evaluated by means of the stabilization and log-phase-amplitude methods. The states governing the second step in the sequential pathway CS2(3+)-->S++CS2+-->S++C++S+ of the overall three-body Coulomb explosion of CS(2)3+ have been determined.     

Electron correlation: the many-body problem at the heart of chemistry

The physical interactions among electrons and nuclei, responsible for the chemistry of atoms and molecules, is well described by quantum mechanics and chemistry is therefore fully described by the solutions of the Schr?dinger equation. In all but the simplest systems we must be content with approximate solutions, the principal difficulty being the treatment of the correlation between the motions of the many electrons, arising from their mutual repulsion. This article aims to provide a clear understanding of the physical concept of electron correlation and the modern methods used for its approximation. Using helium as a simple case study and beginning with an uncorrelated orbital picture of electronic motion, we first introduce Fermi correlation, arising from the symmetry requirements of the exact wave function, and then consider the Coulomb correlation arising from the mutual Coulomb repulsion between the electrons. Finally, we briefly discuss the general treatment of electron correlation in modern electronic-structure theory, focussing on the Hartree-Fock and coupled-cluster methods and addressing static and dynamical Coulomb correlation.     

Role of electrostatic interactions in two-dimensional self-assembly of tobacco mosaic viruses on cationic lipid monolayers

We explore two-dimensional self-assembly of tobacco mosaic viruses (TMVs) on a substrate-supported, fluid lipid monolayer by manipulating the electrostatic interactions, with specific focus on the effects of the cationic lipid concentration in the monolayer and the presence of Ca(2+) ions in the surrounding bulk solution. The TMV assemblies were characterized by grazing-incidence X-ray scattering and atomic force microscopy, and the inter-particle interaction quantified through X-ray scattering data analysis. In the absence of Ca(2+) ions, we found that higher charge densities on the lipid monolayer led to poorer in-plane order, which may be attributed to faster adsorption kinetics, due to the surface potential that increases with charge density. At the same time, higher lipid-charge densities also resulted in weaker repulsion between TMVs, due to partial screening of Coulomb repulsion by mobile cationic lipids in the monolayer. The lipid-charge dependence was diminished with increasing concentration of Ca(2+) ions, which also led to tighter packing of TMVs. The results indicate that Ca(2+) ions strengthen the screening of Coulomb repulsion between TMVs and consequently enhance the role of attractive forces. Control experiments involving Na(+) ions suggest that the attractive inter-TMV interaction has contributions from both the van der Waals force and the counter-ion-induced attraction that depends on ion valence.     

Gaussian and finite-element Coulomb method for the fast evaluation of Coulomb integrals

The authors propose a new linear-scaling method for the fast evaluation of Coulomb integrals with Gaussian basis functions called the Gaussian and finite-element Coulomb (GFC) method. In this method, the Coulomb potential is expanded in a basis of mixed Gaussian and finite-element auxiliary functions that express the core and smooth Coulomb potentials, respectively. Coulomb integrals can be evaluated by three-center one-electron overlap integrals among two Gaussian basis functions and one mixed auxiliary function. Thus, the computational cost and scaling for large molecules are drastically reduced. Several applications to molecular systems show that the GFC method is more efficient than the analytical integration approach that requires four-center two-electron repulsion integrals. The GFC method realizes a near linear scaling for both one-dimensional alanine alpha-helix chains and three-dimensional diamond pieces.     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Magnetic properties in three electrons under Rashba spin-orbit interaction and magnetic field

In this work, we study three-electron magnetic susceptibility in quantum dots under Rashba spin-orbit interaction (SOI) and magnetic field by an analytical methodology. The Hamiltonian of the system is separated to center of mass and relative terms using the Jacobi transformations and the hyperspherical coordinates. By solving Schrodinger equation, energy levels and thereby the susceptibility are calculated using canonical ensemble. At zero temperature, the magnetization reduces with increasing magnetic field with and without Rashba SOI in three-electron-quantum dot without electron-electron (e-e) interaction. Also, SOI slightly changes the magnetization for three-electron-quantum dot without e-e interaction. At nonzero temperature, the magnetization shows a paramagnetic peak when the magnetic field increases. This peak position changes under the SOI. In the presence of e-e interaction, the susceptibility enhances with raising magnetic field and it shows a maximum. The susceptibility at low magnetic field is negative and then it becomes positive. The susceptibility with e-e interaction and without SOI is always diamagnetic and its magnitude reduces with enhancing magnetic field. The susceptibility shows a transition between diamagnetic and paramagnetic with e-e interaction and SOI.     

Theory and calculation for the electronic coupling in excitation energy transfer

Excitation energy transfer (EET) is a process where the electronically excitation is transferred from a donor to an acceptor. EET is widely seen in both natural and in artificial systems, such as light‐harvesting in photosynthesis, the fluorescence resonance energy transfer technique, and the design of light‐emitting molecular devices. In this work, we outline the theories describing both singlet and triplet EET (SEET and TEET) rates, with a focus on the physical nature and computational methods for the electronic coupling factor, an important parameter in predicting EET rates. The SEET coupling is dominated by the Coulomb coupling, and the remaining short‐range coupling is very similar to the TEET coupling. The magnitude of the Coulomb coupling in SEET can vary much, but the contribution of short‐range coupling has been found to be similar across different excited states in naphthalene. The exchange coupling has been believed to be the major physical contribution to the short‐range coupling, but it has been pointed out that other contribution, such as the orbital overlap effect is similar or even larger in strength. The computational aspects and the subsequent physical implication for both SEET and TEET coupling values are summarized in this work. © 2013 The Authors. International Journal of Quantum Chemistry Published by Wiley Periodicals, Inc.     

Charge loss in gas-phase multiply negatively charged oligonucleotides

In an attempt to shed light on the mechanism by which gaseous samples of negatively charged oligonucleotides undergo extremely slow (i.e., over 1-1000 s) charge loss, we have carried out molecular dynamics simulations on an oligonucleotide anion, T(5)(3-), containing five thymine, deoxyribose, and phosphate units in which the first, third, and fifth phosphates are negatively charged. The study is aimed at determining the rate at which an electron is detached from such a trianion by way of an internal Coulomb repulsion induced event. In this process, the intrinsic 5.0-5.1 eV electron binding strength of each phosphate site is reduced by the repulsive Coulomb potentials of the other two negative sites. As geometrical fluctuations cause the distances among the three negative phosphate sites to change, this causes the Coulomb repulsion energies at these sites to fluctuate. Once the Coulomb potential at any phosphate site exceeds ca. 5 eV, the electron on that site is able to undergo autodetachment. Although such an electron must tunnel through a barrier to escape, it is shown that the tunneling rate is not the rate-limiting step in electron loss; instead, it is the rate at which geometrical fluctuations cause the Coulomb potentials to exceed 5 eV that determines the rate of electron loss. Because these rates are extremely slow, special techniques had to be introduced to allow results of dynamics simulations on more flexible models of T(5)(3-) to be extrapolated to predict the behavior of the actual T(5)(3-).     

Salt-regulated attraction and repulsion of spherical polyelectrolyte brushes towards polyelectrolyte multilayers

Adsorption of colloidal particles presents an interesting alternative to the modification of surfaces using covalent coupling or physisorption of molecules. However, to tailor the properties of these materials full control over the effective particle-substrate interactions is required. We present a systematic investigation of the adsorption of spherical polyelectrolyte brushes (SPB) onto polyelectrolyte multilayers (PEM). A brush layer grafted from colloidal particles allows the incorporation of various functional moieties as well as the precise adjustment of their adsorption behaviour. In the presence of oppositely charged surfaces the amount of adsorbed SPB monotonically increases with the ionic strength, whereas equally charged substrates efficiently prevent colloidal attachment below a threshold salt concentration. We found that the transition from the osmotic to the salted brush regime at approximately 100 mM coincided with a complete loss of substrate selectivity. In this regime of high ionic strength, attractive secondary interactions become dominant over electrosteric repulsion. Due to the soft polyelectrolyte corona a surface coverage exceeding the theoretical jamming limit could be realized. Both the adsorption kinetics and the resulting thin film morphologies are discussed. Our study opens avenues for the production of two-dimensional arrays and three-dimensional multilayered structures of SPB particles.     

The effect of the polarization electric field on helix-unwinding in a planar chiral smectic C liquid-crystal cell

The effect of the polarization electric field on helix-unwinding in a thin planar chiral smectic C liquid-crystal cell is studied by using the nematic-like expression for the elastic deformation free-energy density. It is found that the elongation of the helical pitch when the cell thickness decreases is greater when the spontaneous polarization is larger. This is due to the Coulomb repulsion between polarization charges concentrated at ± 2π disclinations.     

Copper-mediated domino process for the synthesis of tetraiodinated di(perylene bisimide)

Tetraiodinated di(perylene bisimide) has been prepared from tetrabrominated perylene bisimide by the combination of Ullmann-type coupling, C-H transformation, and halogen-exchange. The crystal structure analysis confirmed that the aromatic core is quite distorted because of the electrostatic repulsion and steric encumbrance of iodine substituents in the bay regions.     

On the calculation of arbitrary multielectron molecular integrals over Slater‐type orbitals using recurrence relations for overlap integrals. II. Two‐center expansion method

Using expansion formulas for the charge‐density over Slater‐type orbitals (STOs) obtained by the one of authors [I. I. Guseinov, J Mol Struct (Theochem) 1997, 417, 117] the multicenter molecular integrals with an arbitrary multielectron operator are expressed in terms of the overlap integrals with the same screening parameters of STOs and the basic multielectron two‐center Coulomb or hybrid integrals with the same operator. In the special case of two‐electron electron‐repulsion operator appearing in the Hartree–Fock–Roothaan (HFR) equations for molecules the new auxiliary functions are introduced by means of which basic two‐center Coulomb and hybrid integrals are expressed. Using recurrence relations for auxiliary functions the multicenter electron‐repulsion integrals are calculated for extremely large quantum numbers. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 117–125, 2001