Nonadiabatic core polarization and penetration correction in alkali-like atoms: Model computations on excited states of helium

Correlation between the motion of a highly excited outer electron and that of the remaining ionic “core” of an atom is generally treated in an adiabatic approximation, in which it is assumed that the outer electron affects the core in the same way as a stationary point charge. An alternative approach to this correlation problem which avoids the adiabatic approximation is tested here on the 1s2p, 1s3d, and 1s4f states of helium. The results provide the first accurate test of the adiabatic approximation and of a simple correction for the nonzero velocity of the outer electron. The approach used here is based on neglect, in the “correlation” part of the wave function, of the possibility that the outer electron comes closer to the nucleus than any core electron (“penetration”). A correction for this neglect is derived and tested on a version of the adiabatic approximation that likewise neglects penetration.     

Electronic correlation studies. III. Self-correlated field method. Application to 2S ground state and 2P excited state of three-electron atomic systems

The self-correlated field method is based on the insertion in the group product wave function of pair functions built upon a set of correlated “local” functions and of “nonlocal” functions. This work is an application to three-electron systems. The effects of the outer electron on the inner pair are studied. The total electronic energy and some intermediary results such as pair energies, Coulomb and exchange “correlated” integrals, are given. The results are always better than those given by conventional SCF computations and reach the same level of accuracy as those given by more laborious methods used in correlation studies.     

Die horizontale Korrelation in π-Elektronensystemen und ihre Beschreibung durch Elektronenpaarfunktionen

Different types of pair functions (geminal products and their linear combinations) are tested with respect to their ability to describe the “horizontal correlation” of the π-electrons of butadiene. The validity of the π-electron approximation is not discussed and “full configuration interaction” within the limited LCAO basis is used as the standard to which the model calculations are referred. An APSG-function (APSG = antisymmetrized product of strongly orthogonal geminals) built up from equivalent (localized) geminals, which contains only one variational parameter is able to account for about 90% of the “horizontal correlation energy”. Both APSG and APIG functions constructed from delocalized geminals, are much less favorable. Criteria of the goodness of an approximate wave function are a) the energy b) comparison of its one- and two-particle density matrices with those obtained from “full CI”. The good results with the localized APSG function are related to the fact that electron correlation between electrons of opposite spin is (in this molecule) essential only within either of the “double bonds” of the “canonical structure”. The pertinent results are quite insensitive to different parametrization of the integrals.     

Theory of correlation measurements of resonance light scattering

The boson nature of radiation is shown to give rise to a purely quantum mechanical exchange contribution to the intensity-intensity correlation function for resonant light scattering by an atomic or molecular system. The exchange contribution can be decomposed into three components, one involving the intensity correlation for a pair of coherently scattered photons (“resonant Raman” processes), another for a pair of incoherently scattered ones (“resonance fluorescence”), and the last involving the exchange correlation one of each. The intensity correlation measurements of Kimble et al., on optically pumped atomic beams of sodium atoms are interpreted with the theory, producing values of the decay rate of the excited sodium atoms and of the coherence time of the exciting radiation in good agreement with expectations.     

Characteristics of antiaromatic ring pi multi-hydrogen bonds in (H2O)n-C4H4 (n = 1, 2) complexes

By counterpoise-corrected optimization method, the six antiaromatic ring pi multi-hydrogen bond structures with diversiform shapes for (H2O)n-C4H4 (n = 1,2) have been obtained at the MP2/aug-cc-pVDZ level. At the CCSD(T)/aug-cc-pVDZ level, the interaction energy obtained mainly depends on the numbers of H2O and fold numbers of the pi multi-hydrogen bond. The interaction energy order is -2.342 (1a with pi mono-hydrogen) < -2.777 (1b with pi bi-hydrogen) < -4.683 (2a with pi bi-hydrogen) < -4.734 (2b with pi tri-hydrogen) < -4.782 (2c with pi tri-hydrogen) < -5.009 kcal/mol (2d with pi tetra-hydrogen bond). Strangely, why is the interaction energy of the pi bi-hydrogen bond in 1b close to that of the pi mono-hydrogen bond in 1a (their difference is only 15.7%)? The reason is that a pi-type H-bond (as an accompanying interaction) between two lone pairs of the O-atom and a near pair of H-atoms of C4H4 exists shoulder by shoulder in structures 1a, 2a, 2b, and 2c and contributes to the interaction energy. Another accompanying interaction, a repulsive interaction between the pi H-bond (using the H-atom(s) of H2O) and the near pair of H-atoms of C4H4, is also found. For the structures and interaction energies, the pi-type H-bond produces four effects: bending the strong pi H-bond, attracting the pair of H-atoms of C4H4 so that they deviate from the C4 ring plane, showing the interaction energy contribution, and bringing the larger electron correlation contribution. The repulsive interaction also produces four effects: pushing the pair of H-atoms of C4H4 so that they deviate from its ring plane, elongating the distance of the pi H-bond, promoting the formation of pi-type H-bond, and slightly influencing the interaction energy. In the present paper, one C=C bond with two H2O (over and below the ring plane) forms a pi H-bond link in two ways: a strong-weak pi H-bond link and a strong-strong pi H-bond link. The stability contribution of the former is more favorable than the latter. One H2O forms a pi H-bond with C4H4 in two ways. One strong pi H-bond part (over or below the ring plane) always is accompanied by another H-bond part. The accompanying part is either a weak pi H-bond or pi-type H-bond.     

Toward a Consistent Interpretation of the QTAIM: Tortuous Link between Chemical Bonds,Interactions, and Bond/Line Paths

Currently, bonding analysis of molecules based on the Quantum Theory of Atoms in Molecules (QTAIM) is popular; however, “misinterpretations” of the QTAIM analysis are also very frequent. In this contribution the chemical relevance of the bond path as one of the key topological entities emerging from the QTAIM’s topological analysis of the one‐electron density is reconsidered. The role of nuclear vibrations on the topological analysis is investigated demonstrating that the bond paths are not indicators of chemical bonds. Also, it is argued that the detection of the bond paths is not necessary for the “interaction” to be present between two atoms in a molecule. The conceptual disentanglement of chemical bonds/interactions from the bonds paths, which are alternatively termed “line paths” in this contribution, dismisses many superficial inconsistencies. Such inconsistencies emerge from the presence/absence of the line paths in places of a molecule in which chemical intuition or alternative bonding analysis does not support the presence/absence of a chemical bond. Moreover, computational QTAIM studies have been performed on some “problematic” molecules, which were considered previously by other authors, and the role of nuclear vibrations on presence/absence of the line paths is studied demonstrating that a bonding pattern consistent with other theoretical schemes appears after a careful QTAIM analysis and a new “interpretation” of data is performed.     

Electron correlation and the compton profile of atomic neon

The radial momentum distribution I_o(p) and the Compton profile J_o(q) are determined for atomic neon from several restrictid Hartree-Fock (RHF) wavefunctions and two configuration interaction (CI) wavefunctions. The CI functions are the well correlated (full“second-order”) function of Viers, Schaeffer and Harris, and the Ahlrichs-Hinze multi-configuration Hartree-Fock (MCHF) function which includes only L-shell correlation. It is found for this completely closed shell system that the effects of electron correlation are quite small. This contrasts with the results for systems such as Be(²S) and B(²P) where the semi-internal and internal correlation effects were responsible for significant discrepancies between the RHF and CI results. These results indicate that a wavefunction which carefully includes the semi-internal, orbital polarization, and internal correlations beyond the RHF wavefunction (i.e., a “first-order” or “charge-density” function), should account for the principal correlation effects on the Compton profiles and momentum distributions.     

Aromaticity: an ab initio evaluation of the properly cyclic delocalization energy and the pi-delocalization energy distortivity of benzene

A complete active space self-consistent field (CASSCF) calculation of the pi system of a conjugated molecule enables one to define optimal valence pi and pi* molecular orbitals (MOs). One may define from them a set of atom-centered orthogonal pi orbitals, one per carbon atom, and the resulting upper multiplet is used to define the pi-electron delocalization energy. This quantity is confirmed to be slightly distortive, i.e., to prefer bond-alternated geometries. One may also define strongly localized bond MOs corresponding to a Kekule structure and then perturb the associated strongly localized single determinant under the effect of the delocalization between the bonds and of the electronic correlation. The third order of perturbation introduces the contribution of the cyclic circulation of the electrons around the benzene ring, i.e. the aromatic energy contribution. Its value is about 1.5 eV. It is antidistortive, but remains important under bond alternation. The cyclic correlation effects are of minor importance.     

eaq− hydration energy and photoemission threshold potentials for mercury in contact with aqueous electrolytes

The meaning of the “red limit” potential in photoemission experiments is discussed. For mercury in contact with aqueous electrolytes, the energy of a photoemitted electron at the “red limit” is 0.6 eV higher than the solvation energy of e_aq^?. This difference is attributed to the solvent reorganization energy contribution to the hydration energy of e_aq^?.     

Time-dependent photocurrents in polyethylene

A detailed study of the photocurrents in low-density polyethylene at wavelengths of 350 nm, 300 nm, and 240 nm has confirmed that the current is a linear function of intensity and has established that the observed decrease of current depends on the integrated flux of quanta at the metal–polymer interface, and is independent of intensity and pulse repetition rate. Comparison with electron excitation experiments shows that in the present case, optical ionization occurs within a few angstroms of the interface. Connections between the present results and known photodegradation data are explored, but no firm correlation can be obtained either for the initial “fast transient” or for the “slow transient” which occurs only in the shorter wavelength region. Possible models for hole injection are presented.     

Photoinduced electron transfer processes of fullerene rotaxanes containing various electron-donors

The photosensitized electron-transfer processes in the rotaxane hybrids composed with electron-accepting fullerenes and various electron-donors placed in the rotaxanes are revealed with time-resolved fluorescence and absorption spectral methods. Porphyrins are most useful as light-harvesting donors and photosensitizing donors. In addition, aromatic amines and ferrocene act as electron-donor and also hole-shifting reagents in multi-component rotaxanes. In the rotaxanes with spatially placed donor-acceptor molecules, the role of triplet states becomes important compared with the covalently connected donor–acceptor molecular systems, which may be related to the “through-space” and “through-bond” electron transfer, respectively. In the designed multi-component rotaxanes which maintain mechanically or topologically the electron-acceptor, electron-donor, and hole-shifter, the photoinduced electron transfer, hole-shift, electron–hole recombination are established. As a whole, contribution of the triplet excited states is prominent compared with the covalently bonded molecules and supramolecular systems constructed with coordination bonds.     

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.     

Elastic Scattering of fast Electrons by Highly Polar Molecules

In this paper, peculiarities are considered of the angular dependence of the intensity of elastic scattering of fast electrons by dipolar LiH molecules, calculated in the isst Born approximation using Ransil's wavefunction. The molecular component of the scattering intensity is determined. lt is shown that the contribution of chemical bond effects to the intensity of electron scattering by molecules featuring highly polar bonds includes the part which is formally analogous to the structure dependent part of the intensity. Numerical integration of the Fourier transform of the molecular electron density was utilized to calculate the intensity of elastic electron scattering by LIH, LiF and LhO molecules, using HartreeùFock molecular wavefunctions. The major portion of the contribution of chemical bond effects to the intensity of electron scattering by the highly polar (ionic) LiF and Li20 molecules is made up by the ǒioniǒ contribution due to a redistribution of electrons between atoms making up an ionic molecule. A model is suggested of independent ions in a molecule, which correctly describes the “ionic” contribution of chemical bond effects to the intensity of electron scattering by highly polar molecules and is suitable for practical utilization for interpreting electron-diffraction patterns.     

Substituent effect on exo stereoselectivity in the 1,3-Dipolar cycloaddition reaction of tulipalin A with nitrile ylides

1,3-Dipolar cycloaddition reactions of dihydro-3-methylene-2(3H)-furanone (tulipalin A) with various benzonitrile(p-X-benzylide) ylides prefer formation of exo-cycloadducts in the extent corresponding to an increasing electron donor character of the substituent X in the para-position of the benzylide phenyl ring of the 1,3-dipolar reagent. The substituent effect on diastereoselectivity of the 1,3-DC reaction is rationalized in terms of CH/pi interaction between the dipole and the dipolarophile in an exo-transition state. The determining role of such an interaction is demonstrated by the correlation of the observed diastereoselectivities with substituent Hammett sigma constants, which shows a small negative rho value. A certain contribution of CO/pi interaction between the lactone carbonyl and the substituted phenyl ring to mediation of the substituent effect is also discussed. The energy profiles of both reaction pathways were analyzed using DFT and RI-MP2 theoretical approaches. Calculated energy and structural differences between located transition states are consistent with reaction diastereoselectivities.     

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     

Steric effects-II: Relationship between topology and the steric parameter. E's—topology as a tool for the correlation and prediction of steric effects

The steric effect of alkyl groups as characterized by the revised Taft E'_s parameter is analysed using an approach based on the DARC topological system and its PELCO correlation method. This approach involves an analysis of the systemativ variation of E'_s in a topological dequencing of alkyl groups and shows the existence of three regions of distinct behaviour: R I, a “normal” behaviour region (ca 6 E'_s units) in which the contribution of the introduction of successive Me groups to the overall steric effect _{increases monotonically} (groups with 1 to 7 carbons); R II, a region, in which a “levelling” effect is observed, i.e. the contribution diminishes and becomes nil (groups with 8 and 9 carbons); and R III, where this contribution changes sign, “inversion” effect (groups with 10 carbons).Using a series of successive approximations, topological models are developed and tested. The conditions under which the topology may be used to represent the topography (i.e. the real 3-dimensional structure) are considered. The correlation of existing E'_s values and the reliable prediction of experimentally unavailable steric effects are direct consequences of this treatment.     

Structure of fibers drawn from polyethylene single crystals

Transmission electron microscopy and electron diffraction were used to study the molecular structure of fibers drawn from polyethylene single crystals at 77, 293, and 383°K. The results suggest that the formation of the fibers occurs by a two-step process. The first step is the breaking off of single blocks of folded chains from the single crystals so that a “string-of-pearls” structure is obtained. If the temperature is sufficiently high this process is followed by the thermally activated rearrangement of the molecules in the drawn fibers so that a “bamboo” structure results.     

分形等离激元黑金的热电子催化性能

借鉴电镀工业中过电流“烧焦”现象, 在过电流沉积条件下一步制备出等离激元黑金. 扫描电子显微镜、 透射电子显微镜、 X射线衍射和紫外-可见-近红外吸收光谱等表征结果显示, 该黑金是具有三维分形结构的多晶纳米金, 可以在 400~1800 nm宽波段范围内吸收光. 电催化甲醇结果显示, 黑金在宽波长光照下可以将甲醇的电催化效率提高 15.2%, 其主要贡献来源于等离激元生成的热电子, 而一小部分来自环境热. 在不同的单色光照条件下, 黑金的催化效率差别不大, 表明其对光能的利用没有明显的波长选择性.     

Quantification of electron correlation effects: Quantum Information Theory vs Method of Increments

Understanding electron correlation is crucial for developing new concepts in electronic structure theory, especially for strongly correlated electrons. We compare and apply two different approaches to quantify correlation contributions of orbitals: Quantum Information Theory (QIT) based on a Density Matrix Renormalization Group (DMRG) calculation and the Method of Increments (MoI). Although both approaches define very different correlation measures, we show that they exhibit very similar patterns when being applied to a polyacetelene model system. These results suggest one may deduce from one to the other, allowing the MoI to leverage from QIT results by screening correlation contributions with a cheap (“sloppy”) DMRG with a reduced number of block states. Or the other way around, one may select the active space in DMRG from cheap one-body MoI calculations.     

Pure through‐bond state in organic molecules for analysis of the relationship between intramolecular interactions and total energy

Ab initio configuration interaction through‐space/bond interaction analysis was proposed for the examination of specific intramolecular interactions including the effect of electron correlations. To test the effectiveness of our method, we applied it to rotational barrier in ethane. The results of our test suggest that the insensitivity of the ethane barrier to geometric relaxations is intimately connected with the cancellation of interactions through orbital overlaps and other factors. The orbital overlaps include exchange repulsion and hyperconjugation; other factors include classic Coulomb interaction and changes in bond orbital energy. The rotational state without the barrier (pure through‐bond state) can be achieved by deleting not only the “vicinal” interactions between the C? H bonds that belong to different methyl groups but also the “geminal” interactions within the methyl groups. Our mixing analysis of molecular orbitals supports the superiority of the staggered conformer by hyperconjugation. Moreover, it was demonstrated that our treatment could be applied to excited states as well as to the ground state, including electron correlation effects. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003