On the theory of electron correlation in atoms and molecules. II. General cluster expansion theory and the general correlated wave functions method

An exact cluster expansion of many electron wave functions is derived, beginning with a finite linear combination of Slater determinants rather than the more usual single determinant. This general cluster expansion is found to apply both in the case where all possible Slater determinants from a finite set of spin orbitals are included in the linear combination, and in the case where the number of determinants is restricted. The special properties of that finite linear combination of determinants closest to the exact wave function in the least squares sense are studied. These properties lead to the derivation of a general correlated wave functions method, illustrating again the close relationship between methods of this type and cluster expansion theory. Additional approximations, necessary for practical calculations, are set out.     

孪函数N电子基向Slater多电子反对称基的展开

发展了一套孪函数多电子基向Slater行列式的展开方法,并得到展开系数的解析表达式,使得孪函数多电子基直接与Hartree-Fock从头计算相关联.     

Relativistic all-electron configuration interaction calculations on the gold atom

We present the results of relativistic and non-relativistic self-consistent field and configuration interaction calculations for the gold atom, using the spin-free no-pair Hamiltonian in a basis set expansion. A new basis set for the gold atom is discussed and its results in relativistic and non-relativistic self-consistent field calculations are compared to those of numerical Dirac-Hartree-Focic and Hartree-Fock calculations, respectively. Excitation energies, electron affinities and ionization potentials were calculated using a multi-reference configuration interaction technique and are in reasonable agreement with experiment in the relativistic case.     

Slow electron velocity-map imaging spectroscopy of the 1-propynyl radical

High resolution photoelectron spectra of the 1-propynyl and 1-propynyl-d(3) anions acquired with slow electron velocity-map imaging are presented. The electron affinity is determined to be 2.7355+/-0.0010 eV for the 1-propynyl radical and 2.7300+/-0.0010 eV for 1-propynyl-d(3). Several vibronic transitions are observed and assigned using the isotopic shifts and results from ab initio calculations. Good agreement between experimental spectra and calculations suggests a C(3v) geometry for the 1-propynyl radical. No evidence is found for strong vibronic coupling between the ground electronic state and the low-lying first excited state.     

High resolution two-dimensional dose mapping of electron beam processed polymers

The recent advances in electron beam processing of polymer samples require increasingly dose mapping techniques with depth and volume resolution capability. In this paper, the use of micro-indentation and thermo-mechanical analysis is proposed to fulfill the necessary requirements in terms of resolution and accuracy. Experimental procedures are used to acquire mechanical data that are successively converted into dose levels based on dedicated calibrated samples. Physical principles, experimental artifacts, and limitations are discussed with special focus on calibration and validation of a simulator for dosimetry in electron beam cross-linking of electrical cables.     

A finite expansion method for the calculation and interpretation of molecular electrostatic potentials

Because it is useful to have the molecular electrostatic potential as an element in a complex scheme to assess the toxicity of large molecules, efficient and reliable methods are needed for the calculation and characterization of these potentials. A multicenter multipole expansion of the molecular electron charge density calculated with a limited Gaussian basis set is shown here to have only a finite number of nonzero terms from which the molecular electrostatic potential can be calculated. The discrete contributions to the electrostatic potentials from the terms of this expansion provide a physically meaningful decomposition of the potential and a means for its characterization. With pyrrole as an example, the electrostatic potential calculated from this finite expansion of the electron density is compared to that obtained from exact calculations from the same wave function. Good agreement is obtained at distances greater than 1.5 A from any atom in the molecule. In contrast, rearrangement of the terms into an expansion corresponding only to Mulliken atomic charges and dipoles yields a decomposition that produces electrostatic potentials which agree less well with the exact potential. This discrepancy is attributable to the neglect of terms due to higher moments.     

Spectral/structural data of helium atoms with exponential‐cosine‐screened coulomb potentials

Atomic systems with exponential‐cosine‐screened Coulomb (ECSC) or static screened Coulomb (SSC) potentials have drawn considerable attention recently due to the possible applications to atoms in plasma environments. In this work, we develop a computing scheme to deal with the electron–electron correlation terms with the screened Coulomb interactions instead of the conventional expansion method using the Gegenbauer's addition theorem. Based on this approach, we investigate the helium atom with the ECSC potentials. Bypassing the complex expansion functions for electron–electron interactions, the proposed approach simplifies the calculations greatly and provides an advantage on programming. The results are found to be in good agreement with the existing data. Bound‐state energies, oscillator strengths, and multipole polarizabilities varying with the screening parameters are presented. Comparisons of the ECSC potentials are made with the SSC potentials. The influence of screening effect on the energies, oscillator strengths, and polarizabilities is discussed. © 2015 Wiley Periodicals, Inc.     

Problems in electron propagator calculations of the correlation energy

Approximations to the one-electron propagator, G(ω), are discussed asa basis for correlation energy calculations. The random-phase approximation (RPA) and second-order perturbation theory estimates of the self-energy are used to determine G(ω). Correlation energy expressions, resulting from contour integration, are compared with the standard perturbation expansion. We suggest that some of the simpler approximations to the electron propagator may be unsuited to calculations of the correlation energy.     

Resolution and mass accuracy in matrix-assisted laser desorption ionization-time-of-flight

A mathematical model of time-of-flight mass analyzers employing uniform electric fields is presented that allows “exact” calculations of flight times as functions of mass-to-charge ratio, initial velocity and position, applied voltages, and instrument geometry. An “approximate” equation based on a series expansion of the “exact” result is derived which allows focusing conditions and limits on resolution to be determined for different instrument geometries and operating conditions. The fundamental theory is applied to predicting resolution and mass accuracy in matrix-assisted laser desorption ionization-time of flight. In this case higher order velocity focusing can provide excellent correction for the initial velocity distribution of a selected mass-to-charge ratio, but the focusing is mass-to-charge ratio dependent. There is generally a trade-off between ultimate resolution at a particular mass-to-charge ratio and resolution and mass accuracy over a broad mass range. In most practical applications the latter is more important. Calculations are compared with experimental results for a particular analyzer geometry, both at theoretical optimum velocity focus and at operating conditions where ultimate resolution is sacrificed for a broader range of relatively high resolution and better mass accuracy.     

Vibrational and lifetime line broadenings in ESCA

The line profile of the narrow, symmetric 1s line from neon, recorded with the new ESCA instrument with X-ray monochromatization, is analyzed. The natural linewidth of this line is found to be 0.23 ± 0.02 eV, in good agreement with theoretical calculations of the oscillator strengths for Auger transitions and X-ray emission. Spectra from molecules show frequently asymmetric core electron lines under high resolution. This rules out previous explanations based on a chemical influence on the natural lifetime. Contrary to earlier assumptions, vibrational excitations are shown to be important in core electron spectra. For methane, the vibrational energy spacing is large enough to allow the vibrational lines to be partly resolved. Recent results from accurate PNO CI calculations on methane agree well with the experimental findings. The Franck-Condon transitions in the C1s and N1s lines from CO and N₂ are shown to be well described in the harmonic approximation and approximating the potential curves of the highly excited core hole states with the potential curve for the ground state of NO⁺, X¹ Σ⁺. Knowledge of vibrational excitations in core electron spectra is shown to be valuable in the analysis of high resolution X-ray emission spectra of free molecules.     

Experimental and theoretical charge density distribution in a host-guest system: synthetic terephthaloyl receptor complexed to adipic acid

The experimental charge density distributions in a host-guest complex have been determined. The host, 1,4-bis[[(6-methylpyrid-2-yl)amino]carbonyl]benzene (1) and guest, adipic acid (2). The molecular geometries of 1 and 2 are controlled by the presence in the complex of intermolecular hydrogen bonding interactions and the presence in the host 1 of intramolecular hydrogen bonding motifs. This system therefore serves as an excellent model for studying noncovalent interactions and their effects on structure and electron density, and the transferability of electron distribution properties between closely related molecules. For the complex, high resolution X-ray diffraction data created the basis for a charge density refinement using a pseudoatomic multipolar expansion (Hansen-Coppens formalism) against extensive low-temperature (T = 100 K) single-crystal X-ray diffraction data and compared with a selection of theoretical DFT calculations on the same complex. The molecules crystallize in the noncentrosymmetric space group P2(1)2(1)2(1) with two independent molecules in the asymmetric unit. A topological analysis of the resulting density distribution using the atoms in molecules methodology is presented along with multipole populations, showing that the host and guest structures are relatively unaltered by the geometry changes on complexation. Three separate refinement protocols were adopted to determine the effects of the inclusion of calculated hydrogen atom anisotropic displacement parameters on hydrogen bond strengths. For the isotropic model, the total hydrogen bond energy differs from the DFT calculated value by ca. 70 kJ mol(-1), whereas the inclusion of higher multipole expansion levels on anisotropic hydrogen atoms this difference is reduced to ca. 20 kJ mol(-l), highlighting the usefulness of this protocol when describing H-bond energetics.     

Density functional theory study on electron and hole transport properties of organic pentacene derivatives with electron-withdrawing substituent

Attaching electron-withdrawing substituent to organic conjugated molecules is considered as an effective method to produce n-type and ambipolar transport materials. In this work, we use density functional theory calculations to investigate the electron and hole transport properties of pentacene (PENT) derivatives after substituent and simulate the angular resolution anisotropic mobility for both electron and hole transport. Our results show that adding electron-withdrawing substituents can lower the energy level of lowest unoccupied molecular orbital (LUMO) and increase electron affinity, which are beneficial to the electron injection and ambient stability of the material. Also the LUMO electronic couplings for electron transport in these pentacene derivatives can achieve up to a hundred meV which promises good electron transport mobility, although adding electron-withdrawing groups will introduce the increase of electron transfer reorganization energy. The final results of our angular resolution anisotropic mobility simulations show that the electron mobility of these pentacene derivatives can get to several cm(2) V(-1) s(-1), but it is important to control the orientation of the organic material relative to the device channel to obtain the highest electron mobility. Our investigation provide detailed information to assist in the design of n-type and ambipolar organic electronic materials with high mobility performance.     

Molecular and crystal structures of a class of push-pull quinonoid compounds with potential nonlinear optical applications

Molecular and crystal structures of three compounds with electron donor-conjugation unit-electron acceptor framework are reported where the conjugation unit is formally a quinonoid ring. Semiempirical quantum chemical calculations indicate large hyperpolarizabilities in these push-pull molecules. Since all the crystal structures are found to belong to centrosymmetric space groups, modifications are necessary for quadratic nonlinear optical applications.     

Frozen-density embedding-based many-body expansions

Fragmentation methods allow for the accurate quantum chemical (QC) treatment of large molecular clusters and materials. Here we explore the combination of two complementary approaches to the development of such fragmentation methods: the many-body expansion (MBE) on the one hand, and subsystem density-functional theory (DFT) or frozen-density embedding (FDE) theory on the other hand. First, we assess potential benefits of using FDE to account for the environment in the subsystem calculations performed within the MBE. Second, we use subsystem DFT to derive a density-based MBE, in which a many-body expansion of the electron density is used to calculate the system's total energy. This provides a correction to the energies calculated with a conventional energy-based MBE that depends only on the subsystem's electron densities. For the test case of clusters of water and of aspirin, we show that such a density-based MBE converges faster than the conventional energy-based MBE. For our test cases, truncation errors in the interaction energies are below chemical accuracy already with a two-body expansion. The density-based MBE thus provides a promising avenue for accurate QC calculation of molecular clusters and materials.     

An adiabatic linearized path integral approach for quantum time-correlation functions II: a cumulant expansion method for improving convergence

Linearized mixed quantum-classical simulations are a promising approach for calculating time-correlation functions. At the moment, however, they suffer from some numerical problems that may compromise their efficiency and reliability in applications to realistic condensed-phase systems. In this paper, we present a method that improves upon the convergence properties of the standard algorithm for linearized calculations by implementing a cumulant expansion of the relevant averages. The effectiveness of the new approach is tested by applying it to the challenging computation of the diffusion of an excess electron in a metal-molten salt solution.     

Intraprotein electrostatics derived from first principles: divide-and-conquer approaches for QM/MM calculations

Two divide-and-conquer (DAQ) approaches for building multipole-based molecular electrostatic potentials of proteins are presented and evaluated for use in QM/MM calculations. One approach is a further development of the neutralization method of Bellido and Rullmann (J Comput Chem 1989, 10, 479-487) while the other is based on removing part of the electron density before performing the multipole expansion. Both methods create systems with integer charges without using charge renormalization. To determine their performance in terms of location of cuts and distance to QM region, the new DAQ approaches are tested in calculations of the proton affinity of N(zeta) of Lys55 in the inhibitor turkey ovomucoid third domain. Finally, the two methods are used to build a variety of MM regions, applied to calculations of the pK(a) of Lys55, and compared to other computational methodologies in which force field charges are employed.     

Intermolecular electrostatic energies using density fitting

A method is presented to calculate the electron-electron and nuclear-electron intermolecular Coulomb interaction energy between two molecules by separately fitting the unperturbed molecular electron density of each monomer. This method is based on the variational Coulomb fitting method which relies on the expansion of the ab initio molecular electron density in site-centered auxiliary basis sets. By expanding the electron density of each monomer in this way the integral expressions for the intermolecular electrostatic calculations are simplified, lowering the operation count as well as the memory usage. Furthermore, this method allows the calculation of intermolecular Coulomb interactions with any level of theory from which a one-electron density matrix can be obtained. Our implementation is initially tested by calculating molecular properties with the density fitting method using three different auxiliary basis sets and comparing them to results obtained from ab initio calculations. These properties include dipoles for a series of molecules, as well as the molecular electrostatic potential and electric field for water. Subsequently, the intermolecular electrostatic energy is tested by calculating ten stationary points on the water dimer potential-energy surface. Results are presented for electron densities obtained at four different levels of theory using two different basis sets, fitted with three auxiliary basis sets. Additionally, a one-dimensional electrostatic energy surface scan is performed for four different systems (H2O dimer, Mg2+-H2O, Cu+-H2O, and n-methyl-formamide dimer). Our results show a very good agreement with ab initio calculations for all properties as well as interaction energies.     

Ab initio electron propagators in molecules with strong electron-phonon interaction. I. Phonon averages

Ab initio electron propagators in molecular systems with strong electron-electron and electron-phonon interactions are considered to study molecular electronic properties. This research is important in electron transfer reactions where the electron transition is not considered any longer as a single electron transfer process or in temperature dependences of current-voltage characteristics in molecular wires or aggregates. To calculate electron Green's functions, the authors apply a small polaron canonical transformation that intrinsically contains strong electron-phonon effects. According to this transformation, the excitation energies of the noninteracting Hamiltonian are shifted down by the relaxation (solvation) energy for each state. The electron-electron interaction is also renormalized by the electron-phonon coupling. For some values of the electron-phonon coupling constants, the renormalized Coulomb integrals can be negative resulting in the attraction between two electrons. Within this transformation, they develop a diagrammatic expansion for electron Green's function in which the electron-phonon interaction is included into the multiple phonon correlation functions. The multiple phonon correlation functions are exactly found. It is pointed out that Wick's theorem for such correlation functions is invalid. Consequently, there is no Dyson equation for electron Green's functions. The proposed approach can be considered for future method developments for quantum chemical calculations that include strong nonadiabatic (non-Born-Oppenheimer) effects.     

Resonant dissociative electron attachments to cysteine and cystine

Shape-resonant electron attachments to cysteine and cystine and the subsequent dissociation dynamics are investigated with the single-center expansion potential scattering calculations. Selectivity of the direct bond cleavage at a given resonant state or by the specific resonant state coupling is demonstrated with the one-dimensional complex potential energy curves of the temporary anion (cysteine)(-). The wave function of the lowest shape resonant state of the temporary anion (cystine)(-) distinctly shows the localized anti-bond (S-S)* character, implying that this disulfide bond can be easily broken due to the low-energy electron resonant attachment.