Electron Domains and the VSEPR Model of Molecular Geometry

The valence shell electron pair repulsion (VSEPR) model—also known as the Gillespie–Nyholm rules—has for many years provided a useful basis for understanding and rationalizing molecular geometry, and because of its simplicity it has gained widespread acceptance as a pedagogical tool. In its original formulation the model was based on the concept that the valence shell electron pairs behave as if they repel each other and thus keep as far apart as possible. But in recent years more emphasis has been placed on the space occupied by a valence shell electron pair, called the domain of the electron pair, and on the relative sizes and shapes of these domains. This reformulated version of the model is simpler to apply, and it shows more clearly that the Pauli principle provides the physical basis of the model. Moreover, Bader and his co-workers' analysis of the electron density distribution of many covalent molecules have shown that the local concentrations of electron density (charge concentrations) in the valence shells of the atoms in a molecule have the same relative locations and sizes as have been assumed for the electron pair domains in the VSEPR model, thus providing further support for the model. This increased understanding of the model has inspired efforts to examine the electron density distribution in molecules that have long been regarded as exceptions to the VSEPR model to try to understand these exceptions better. This work has shown that it is often important to consider not only the relative locations and sizes, but also the shapes, of both bonding and lone pair domains in accounting for the details of molecular geometry. It has also been shown that a basic assumption of the VSEPR model, namely that the core of an atom underlying its valence shell is spherical and has no influence on the geometry of a molecule, is normally valid for the nonmetals but often not valid for the metals, including the transition metals. The cores of polarizable metal atoms may be nonspherical because they include nonbonding electrons or because they are distorted by the ligands, and these nonspherical cores may have an important influence on the geometry of a molecule.     

Changing Rules of Bonding Electron Pair Correlation Energies of CH3X （X = F, OH, NH2） Systems

1 INTRODUCTION It has been known that the electron correlation energy of molecular systems was, and still is, one of the most serious bottleneck problems to the chemis- try accuracy of computational quantum chemistry. Since L鰓din[1] gave the definition …     

Adjacent Lone Pair (ALP) Effect: A Computational Approach for Its Origin

The adjacent lone pair (ALP) effect is an experimental phenomenon in certain nitrogenous heterocyclic systems exhibiting the preference of the products with lone pairs separated over other isomers with lone pairs adjacent. A theoretical elucidation of the ALP effect requires the decomposition of intramolecular energy terms and the isolation of lone pair–lone pair interactions. Here we used the block‐localized wavefunction (BLW) method within the ab initio valence bond (VB) theory to derive the strictly localized orbitals which are used to accommodate one‐atom centered lone pairs and two‐atom centered σ or π bonds. As such, interactions among electron pairs can be directly derived. Two‐electron integrals between adjacent lone pairs do not support the view that the lone pair–lone pair repulsion is responsible for the ALP effect. Instead, the disabling of π conjugation greatly diminishes the ALP effect, indicating that the reduction of π conjugation in deprotonated forms with two σ lone pairs adjacent is one of the major causes for the ALP effect. Further electrostatic potential analysis and intramolecular energy decomposition confirm that the other key factor is the favorable electrostatic attraction within the isomers with lone pairs separated.     

Bending the Curve: Molecular Manifestations of Electron Antisymmetry

As very light fermions, electrons are governed by antisymmetric wave functions that lead to exchange integrals in the evaluation of the energy. Here we use the localized representation of orbitals to decompose the electronic energy in a fashion that isolates the enigmatic exchange contributions and characterizes their distinctive control over electron distributions. The key to this completely general analysis is considering the electrons in groups of three, drawing attention to the curvatures of pair potentials, rather than just their amplitudes and slopes. We show that a positive curvature at short distances is essential for the mutual distancing of electrons and a negative curvature at longer distances is essential to account for the influence of lone pairs on bond torsion. Neither curvature is available in the absence of the exchange contributions. Thus, although exchange energies are much shorter range than Coulomb energies, their influence on molecular geometry is profound and readily understood.     

Evaluation of scintillators and semiconductor detectors to image three-photon positron annihilation for positron emission tomography

Positron emission tomography (PET) is rapidly becoming the main nuclear imaging modality of the present century. The future of PET instrumentation relies on semiconductor detectors because of their excellent characteristics. Three-photon positron annihilation has been recently investigated as a novel imaging modality, which demands the crucial high energy resolution of semiconductor detector. In this work the evaluation of the NaI(Tl) scintillator and HPGe and CdZTe semiconductor detectors, to construct a simple three-photon positron annihilation scanner has been explored. The effect of detector and scanner size on spatial resolution (FWHM) is discussed. The characteristics: energy resolution versus count rate and point-spread function of the three-photon positron annihilation image profile from triple coincidence measurements were investigated.     

A measure of electron localizability

A functional of the same‐spin electron pair density is proposed as a measure of electron localizability. This functional yields the average number of same‐spin electron pairs in a region Ω enclosing a fixed charge. The functional equals zero if the fixed charge in Ω originates from one electron only, with all other same‐spin electrons outside the region Ω. Then, the correlation of the electronic motion in Ω and thus the localizability of an electron is high. If the motion of the same‐spin electrons becomes less correlated, more electrons participate in the fixed charge contained in Ω, the average number of same‐spin electron pairs (the functional) increases. In the Hartree–Fock approximation the Taylor expansion of the proposed localizability functional can be related to the electron localization function of Becke and Edgecombe without using an arbitrary reference to the uniform electron gas. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Detecting polarized gamma-rays by pair production

Recently, a GEANT Monte Carlo code was used to design an outline of the geometry and to simulate the performance of a high energy (10 MeV–10 GeV) gamma-ray detector (Depaola, 1997. Monte Carlo simulation of the ARGO. Nuclear Instruments and Methods A 342, 302–307). It was shown that the incident direction and energy of the incoming photons can be determined from the tracks of the produced electrons–positron pairs. A natural follow-up problem is to study whether this system can be used to detect linearly polarized gamma-rays. In principle, this can be done by measuring the azimuthal distribution of the produced pairs since the cross-section has a dependence with the vector polarization direction. In this work we first determine the azimuthal angular distribution from the differential cross-section for pair production. We then show that the azimuthal distribution of the produced pairs has a very simple angular dependence and can be approximated very accurately by cross-section for coplanar events. Finally, we use the simplified cross-section to simulate the performance of the detector.     

An experimental and theoretical study of double photoionization of CF4 using time-of-flight photoelectron-photoelectron (photoion-photoion) coincidence spectroscopy

Single photon double ionization of CF4 has been studied by means of a time-of-flight photoelectron-photoelectron coincidence technique, which has very recently been extended towards ion detection, with energy analysis for the electrons and mass analysis for the ions. The complete single photon double ionization electron spectrum of CF4 up to a binding energy of approximately 51 eV is presented and discussed, also with the aid of accurate ab initio Green's function calculations. From ion detection in coincidence with the ejected electrons, we derive fragmentation pathway-selected double ionization electron spectra of CF4. From the same data we extract the yield of each doubly charged ion or ion pair as a function of the double ionization energy.     

Photon polarization and spin asymmetry in the elementary process of bremsstrahlung

Experimental and theoretical results are reviewed concerning the photon polarization and spin asymmetry in the elementary process of bremsstrahlung. In electron–photon coincidence experiments using an unpolarized primary beam (300 keV) the electron–nucleus bremsstrahlung was found to be almost completely linearly polarized. The same behavior was found in electron–electron bremsstrahlung. By using a transversely polarized electron beam the photon emission asymmetry was measured for fixed direction of the outgoing electrons.     

Measurement of coincidence timing resolution of scintillation detectors compared to semiconductor detectors to image three-photon positron annihilation

The coincidence timing resolution is a critical parameter for triple coincidence to measure the three photon positron annihilation yield. The yield is inversely proportional to the concentration of oxygen which acts as a quenching agent within the tissue and, therefore, provides important information about the state of the cancerous tumor. A comparison between scintillation and semiconductor detectors with respect to their timing properties for triple coincidence measurements and imaging was carried out. The coincidence timing resolution for example for HPGe detectors was found to vary between 35.4±0.02 and 42.8±0.02 ns. A comparison of all detector characteristics with respect to HPGe is presented.     

Light‐Harvesting Ytterbium(III)–Porphyrinate–BODIPY Conjugates: Synthesis,Excitation‐Energy Transfer,and Two‐Photon‐Induced Near‐Infrared‐Emission Studies

Based on a donor–acceptor framework, several conjugates have been designed and prepared in which an electron‐donor moiety, ytterbium(III) porphyrinate (YbPor), was linked through an ethynyl bridge to an electron‐acceptor moiety, boron dipyrromethene (BODIPY). Photoluminescence studies demonstrated efficient energy transfer from the BODIPY moiety to the YbPor counterpart. When conjugated with the YbPor moiety, the BODIPY moiety served as an antenna to harvest the lower‐energy visible light, subsequently transferring its energy to the YbPor counterpart, and, consequently, sensitizing the Yb^III emission in the near‐infrared (NIR) region with a quantum efficiency of up to 0.73 % and a lifetime of around 40 μs. Moreover, these conjugates exhibited large two‐photon‐absorption cross‐sections that ranged from 1048–2226 GM and strong two‐photon‐induced NIR emission.     

Study on Pair Correlation Energies of Isoelectronic Systems F^－, HF and H2F^＋

The intrapair and interpair correlation energies of F-, HF and H2F^ systems are calculated and analyzed using MP2-OPT2 method of MELD program with cc-PVSZ^* basis set. From the analysis of pair correlation energies of these isoelectronlc sysoterns, it is found that the 1sF^2 pair correlation energy is trans-ferable in these three isociectronic systems. According to the definition of pair correlation contribution of one electron pair to a system, the pair correlation contribution values of these three systems are calculated. The correlation contribution values of inner electron pairs and H—F bonding electron pair in HF molecule with those in H2F^ system are compared. The results indicate that the bonding effect of a molecule is one of the im-portant factors to influence electron correlation energy of the system. The comparison of correlation energy contributions in-cluding triple and quadruple excitations with those only includ-ing singles and doubles calculated with 6-311 G(d) basis set shows that the higher.excitation correlation energy contribution gives more than 2 % of the total correlation energy for these sys-tems.     

Unimolecular Reaction Mechanism of an Imidazolin‐2‐ylidene: An iPEPICO Study on the Complex Dissociation of an Arduengo‐Type Carbene

The photoionization and dissociative photoionization of Im(iPr)₂, 1,3‐diisopropylimidazolin‐2‐ylidene, was investigated by imaging photoelectron photoion coincidence (iPEPICO) with vacuum ultraviolet (VUV) synchrotron radiation. A lone‐pair electron of the carbene carbon atom is removed upon ionization and the molecular geometry changes significantly. Only 0.5 eV above the adiabatic ionization energy, IE_ad=7.52±0.1 eV, the carbene cation fragments, yielding propene or a methyl radical in parallel dissociation reactions with appearance energies of 8.22 and 8.17 eV, respectively. Both reaction channels appear at almost the same photon energy, suggesting a shared transition state. This is confirmed by calculations, which reveal the rate‐determining step as hydrogen‐atom migration from the isopropyl group to the carbene carbon center forming a resonance‐stabilized imidazolium ion. Above 10.5 eV, analogous sequential dissociation channels open up. The first propene‐loss fragment ion dissociates further and another methyl or propene is abstracted. Again, a resonance‐stabilized imidazolium ion acts as intermediate. The aromaticity of the system is enhanced even in vertical ionization. Indeed, the coincidence technique confirms that a real imidazolium ion is produced by hydrogen transfer over a small barrier. The simple analysis of the breakdown diagram yields all the clues to disentangle the complex dissociative photoionization mechanism of this intermediate‐sized molecule. Photoelectron photoion coincidence is a promising tool to unveil the fragmentation mechanism of larger molecules in mass spectrometry.     

Diversified Excited-State Relaxation Pathways of Donor–Linker–Acceptor Dyads Controlled by a Bent-to-Planar Motion of the Donor

Herein, we introduce the cyclic 8π-electron (C8π) molecule N,N′-diaryl-dihydrodibenzo[a,c]phenazine ( DPAC ) as a dual-functional donor to establish a series of new donor–linker–acceptor (D–L–A) dyads DLA1 – DLA5 . The excited-state bent-to-planar dynamics of DPAC regulate the energy gap of the donor, while the acceptors A1 – A5 are endowed with different energy gaps and HOMO/LUMO levels. As a result, the rate and efficiency of the excited-state electron transfer vs. energy transfer can be finely harnessed, which is verified via steady-state spectroscopy and time-resolved emission measurements. This comprehensive approach demonstrates, for the first time, the manifold of excited-state properties governed by bifunctional donor-based D–L–A dyads, including bent-to-planar, photoinduced electron transfer (PET) from excited donor to acceptor (oxidative-PET), fluorescence resonance energy transfer (FRET), bent-to-planar followed by electron transfer (PFET), and PET from donor to excited acceptor (reductive-PET).     

Count rate characteristics and count loss correction of Positologica II: a whole body positron emission tomograph

This paper describes evaluation and correction of count rate characteristics of POSITOLOGICA II, a multi-slice whole body positron emission tomography system. The present study was performed using three phantoms; a 5 cm inner diameter, water-filled lucite cylinder, a 20 cm inner diameter, water-filled lucite cylinder and a chest phantom. After injection of high activity (about 1.85 GBq (50 mCi] of 13N ammonia into each phantom, rates of true coincidence, random coincidence and single photon detections were measured during decay of the isotope through more than two orders of magnitude of activity. At very high levels of activity, count rate characteristics of the system were saturated and limited to 660 kcps of total coincidence rate, which was the sum of rates in on-time and off-time windows, by the FIFO (first-in first-out) output frequency. Below those levels of activity the relationship between count loss and true coincidence rate was not unique but depended on the phantom configurations, suggesting that count loss correction using the above relationship was inadequate for quantitative study. However, the relationship between count loss and single rate was almost independent of the phantom configurations. Thus in conclusion count loss could be corrected using single rate for POSITOLOGICA II. A practical method of count loss correction was also proposed.     

Mechanism for nuclear excitation during positron annihilation using Coulomb wave functions

We have calculated cross sections for the process of nuclear excitation during positron annihilation on any bound electron. We used Coulomb wave functions for the electron and positron.     

Study of simulation method of time evolution of atomic and molecular systems by quantum electrodynamics

We discuss a method to follow step‐by‐step time evolution of atomic and molecular systems based on quantum electrodynamics. Our strategy includes expanding the electron field operator by localized wavepackets to define creation and annihilation operators and following the time evolution using the equations of motion of the field operator in the Heisenberg picture. We first derive a time evolution equation for the excitation operator, the product of two creation or annihilation operators, which is necessary for constructing operators of physical quantities such as the electronic charge density operator. We, then, describe our approximation methods to obtain time differential equations of the electronic density matrix, which is defined as the expectation value of the excitation operator. By solving the equations numerically, we show “electron‐positron oscillations,” the fluctuations originated from virtual electron‐positron pair creations and annihilations, appear in the charge density of a hydrogen atom and molecule. We also show that the period of the electron‐positron oscillations becomes shorter by including the self‐energy process, in which the electron emits a photon and then absorbs it again, and it can be interpreted as the increase in the electron mass due to the self‐energy. © 2014 Wiley Periodicals, Inc.     

Tseng's calculations of low energy pair production

We review the theoretical work 1971–1997 of H.K. Tseng on low energy pair production. In this work numerical calculations were performed in independent particle approximation in a screened self-consistent central potential, expanding the S-matrix element in partial waves and multipoles. Sampling techniques in partial waves and multipoles were used to extend the calculations to higher energies (up to 10 Mev). Total cross sections, the positron energy spectrum, the positron angular distributions, and the positron–photon polarization correlations were studied. Agreement was obtained with most experiments, although some anomalies remained at the lowest energies (particularly at 1082 keV). Atomic screening of the nuclear charge decreases cross sections at higher energies, as described by a form factor in the momentum transfer to the nucleus. In an intermediate energy regime point Coulomb results in a shifted energy spectrum may be used. At low energies screening increases cross sections, and this is characterized in terms of a normalization screening factor which describes the change in magnitude of electron and positron wave functions at small distances. In this low energy regime angular distribution shapes and polarization correlations are independent of screening.     

Comparison of the intermolecular energy surfaces of amino acids: orientation-dependent chiral discrimination

In the present work, we compare the intermolecular energy surfaces of the alanine molecule in its neutral and zwitterionic state using ab initio theory (HF/6-311++G) as a function of mutual orientation. Starting from the optimized structures of the nonbonded homochiral (l-l) and heterochiral (d-l) pairs of molecules, the energy surfaces are studied with rigid geometry by varying the distance and orientation. The potential energy surfaces of the l-l and d-l pairs are found to be dissimilar and reflect the underlying chirality of the homochiral pair and racemic nature of the heterochiral pair. The intermolecular energy surface of the l-l pair is more favorable than the corresponding energy surface of the d-l pair. The study, for the first time, reveals clear homochiral preference without use of parameters, which was unobserved in previous detailed simulations but predicted by theory. The electrostatic interaction further augments the chiral discrimination. The basis set superposition error (BSSE) corrected results show enhanced discrimination. Use of higher-level M?ller-Plesset perturbation theory (MP2) and further BSSE correction do not change the conclusions made at the Hartree-Fock (HF) level. The major conclusions based on HF and MP2 level calculations remain unaltered when the calculations of the potential energy surfaces for the neutral and zwitterionic pairs are repeated using the density functional theory (DFT) (B3LYP/6-311++G). The observed orientation dependence has significance in the biological chiral recognition as well as peptide synthesis at the peptidyl transferase center where the amino terminal and peptidyl terminal undergo mutual rotatory motion.