Authors:W. Grant Cooper Pages: 19 - 120 Abstract: Publication date: Available online 9 April 2018 Source:Advances in Quantum Chemistry Author(s): W. Grant Cooper Quantum information processing is an active field in which quantum entanglement properties of superposition states are exploited to enhance speed, versatility, and performance of measuring quantum information and executing resulting instructions. This report reviews recent studies implying the relatively rapid emergence of sustainable life on planet Earth—~4.1 billion years ago—is a consequence of EPR-generated entangled proton qubits populating duplex segments of primordial RNA–ribozyme systems. Survival of ribozyme–RNA duplex segments required selection of “Grover’s-type” quantum processors, where quantum probability measurements of the 20-different available entangled proton qubit states yielded quantum entanglement origins of the triplet code, utilizing 43 codons for ~22 l-amino acids. Analyses imply Grover’s-type enzyme quantum processor measurements of EPR-generated entangled proton “qubit pairs” can simulate dynamic evolution, and further, identify entangled proton “qubit pairs” as the smallest “measurable” genetic informational unit, specifying evolution instructions with “measured” quantum information.

Authors:Hazel Cox; Adam L. Baskerville Pages: 201 - 240 Abstract: Publication date: Available online 19 March 2018 Source:Advances in Quantum Chemistry Author(s): Hazel Cox, Adam L. Baskerville In this contribution we discuss how the series solution method can be used effectively to probe the bound state stability of three-particle systems. We demonstrate the versatility of the method by presenting results of a variational method for calculating the threshold values of particle mass or particle charge for the formation of a bound state. By treating all the particles on an equal footing, we explore the effects of nuclear motion in diatomic ions and electron correlation in two-electron atomic systems.

Authors:Svetlana A. Malinovskaya; Gengyuan Liu Pages: 241 - 294 Abstract: Publication date: Available online 16 March 2018 Source:Advances in Quantum Chemistry Author(s): Svetlana A. Malinovskaya, Gengyuan Liu The adiabatic passage-based control methods have been developed to advance a cutting-edge research area of ultracold physics. We studied the controlled excitation of Rydberg atoms, population inversion within hyperfine states of alkali atoms, and the control of internal degrees of freedom in diatomic polar molecules. We have developed an optical frequency comb-based method for creation of ultracold molecules. These works are in demand due to an urgent need in the novel methods for the production of ultracold molecules and for ultracold quantum control. We make use of chirped pulses and optical frequency combs with modulation in the form of the sinusoidal function. This allowed us to achieve the adiabatic regime of excitations, which is a robust approach for experimental realization. The novelty of the implementation of optical frequency combs for the formation of ultracold molecules relies on the creation of a quasi-dark state leading to insignificant population of the transitional, vibrational state manifold and, thus, to efficient mitigation of decoherence in the system. Moreover, the parity of the chirp of the incident electromagnetic field was shown to be an important factor in achieving a predetermined quantum yield.

Authors:Remigio Cabrera-Trujillo; Jens Oddershede Pages: 295 - 315 Abstract: Publication date: Available online 1 March 2018 Source:Advances in Quantum Chemistry Author(s): Remigio Cabrera-Trujillo, Jens Oddershede In this work, the effects of an endohedral cavity on the hydrogen dipole oscillator strength sum rule, S k , and its logarithmic version, L k , are studied. The approach is based on a finite-differences numerical solution to the Schrödinger equation for the hydrogen atom spectrum under a cavity confinement model. Endohedral effects are accounted for by means of a shell-like cavity of inner radius R 0 and thickness Δ with a penetrable potential height V 0. To analyze the cavity discontinuity, a Woods–Saxon potential is used for different values of the smoothness at the inner and outer cavity radii. Small values of the smoothness parameter allow one to simulate the discontinuity of a square-well model potential. The dipole oscillator strength sum rules S k and L k are investigated as a function of the cavity potential depth V 0. We use the values of R 0 and Δ that describe a fullerene cage. One finds that the sum rules are fulfilled within the numerical precision for low potential height conditions. However, when the well depth is V 0 = 0.7 a.u., corresponding to the first avoiding crossing between the 1s and 2s states, the sum rule differs from its closure relation and it is this well depth for which the effects of the potential discontinuity are strongest. As the S −2 sum rule is the static dipole polarizability, the results are compared to available data in the literature showing excellent agreement. We also show that inclusion of all bound and continuum excited states in the sum over states are necessary in order to obtain accurate sum rules.

Authors:Tamaz Kereselidze; John F. Ogilvie Pages: 391 - 421 Abstract: Publication date: Available online 8 March 2018 Source:Advances in Quantum Chemistry Author(s): Tamaz Kereselidze, John F. Ogilvie We survey methods elaborated for the solution of the hydrogen-atom problem in prolate spheroidal coordinates for the discrete spectrum. The expressions of Coulomb spheroidal functions and Coulomb Sturmian functions defined in spheroidal coordinates are collected and presented in a convenient form for their facile application in various calculations. Exploring the properties of spheroidal Sturmians, we show that they are the most appropriate functions for calculations on diatomic molecules. For the continuous spectrum Coulomb spheroidal functions are obtained through an exact solution of the appropriate one-dimensional equations, which are shown to be Heun's confluent equations. The derived functions are a natural generalization of the well-known Coulomb wave functions of the continuous spectrum obtained in spherical polar coordinates.

Authors:Milan Abstract: Publication date: Available online 13 December 2017 Source:Advances in Quantum Chemistry Author(s): Milan Randić This chapter reviews numerical characterization of aromaticity in polycyclic benzenoid systems solely on the basis of structural concepts. In contrast to most approaches, the characterization of aromaticity was based on selected molecular properties as descriptors of aromaticity. Our basic premises for characterization of aromaticity are Clar aromatic sextets as the carriers of aromaticity. In early 1970s Clar introduced his approach in a booklet: Aromatic Sextet Theory, in which he elaborated on the experimental support for his approach. Unfortunately a great limitation of Clar's approach is that his theory is qualitative. It is based on Clar formulas having aromatic sextets, “migrating” sextets, and “empty rings.” However, several years ago a numerical characterization of Clar's structural formulas was proposed, which opened a route to quantitative Clar aromatic sextet theory. In this chapter we have illustrated quantitative Clar aromatic sextet on a collection of smaller benzenoid hydrocarbons. Observe that all current approaches to the aromaticity, by using molecular properties as descriptors, may characterize relative aromaticity of compounds, but fail to answer the question: “What is Aromaticity.” Our structural approach to aromaticity is based on August Kekulé structural formulas and Eric Clar's aromatic sextets. Novel ingredients are the numerical characterizations of Clar's formulas for which we use the ring bond orders, recent generalization of Linus Pauling CC bond orders to rings.

Authors:Kousik Samanta; Tsednee Tsogbayar; Song Bin Zhang; Danny L. Yeager Abstract: Publication date: Available online 12 October 2017 Source:Advances in Quantum Chemistry Author(s): Kousik Samanta, Tsednee Tsogbayar, Song Bin Zhang, Danny L. Yeager Electron atom/molecule resonances are temporary bound states in the continuum. We have developed and used some complex scaled multiconfigurational methods for the determination of resonance parameters for electron–atom and electron–molecule systems including open-shell initial and/or final states and highly correlated (nondynamical correlation) atoms and molecules. In the first part of this chapter we present the theoretical background of complex scaling method to study for electron–atom/molecule resonances. Then we discuss the complex scaled multiconfigurational self-consistent field (CMCSCF) method, the complex scaled multiconfigurational spin-tensor electron propagator (CMCSTEP) method, the complex scaled multiconfigurational time-dependent Hartree–Fock (CMCTDHF) method, and a complex scaled multireference configuration interaction (CMR-CI) method. In the second part we discuss our results and compare them with other available theoretical methods and experimental data. CMCSTEP, CMCTDHF, and our CMR-CI all initially use a CMCSCF state. In real space the multiconfigurational spin-tensor electron propagator (MCSTEP) method gives very accurate and reliable ionization potentials and electron affinities. Similar good results for resonances are determined in complex space. We have developed and used CMCTDHF, a complex scaled version of the real space multiconfigurational time-dependent Hartree–Fock (MCTDHF) method to study the electronic excitation energies, transition moments, oscillator strengths, polarizabilities, and other linear response properties for atomic and molecular systems. We also have developed and used a CMR-CI, which employs the multireference orbitals and may be optimized with a CMCSCF state for the bound initial state and somewhat separates “bound” and “continuum” configurations.

Authors:Monika Musiał; Anna Bewicz; Patrycja Skupin; Stanisław A. Kucharski Abstract: Publication date: Available online 30 September 2017 Source:Advances in Quantum Chemistry Author(s): Monika Musiał, Anna Bewicz, Patrycja Skupin, Stanisław A. Kucharski The EA-EOM (electron-attachment equation-of-motion) coupled cluster approach provides a description of the states obtained by attachment of a single electron to the reference system. If the reference is assumed to be a doubly ionized cation then the results relate to the cation. In the current work the above scheme is applied to the calculations of potential energy curves for the LiK+ and NaK+ molecular ions adopting as a reference system the doubly ionized structure, i.e., LiK+2 and NaK+2. Such computational strategy benefits from the fact that the closed shell reference (LiK+2 or NaK+2) dissociates into the closed shell fragments (LiK + 2 ⇒ Li+ + K+, NaK + 2 ⇒ Na+ + K+). This is advantageous since the RHF (restricted Hartree–Fock) function can be used as a reference in the whole range of interatomic distances. This scheme offers a first principle method without any model or effective potential parameters for the description of the bond-breaking processes. Moreover, the scalar relativistic effects are included by adding appropriate terms of the DK (Douglas–Kroll) Hamiltonian to the one-electron integrals.

Authors:James E. Avery; John S. Avery Abstract: Publication date: Available online 28 September 2017 Source:Advances in Quantum Chemistry Author(s): James E. Avery, John S. Avery We present a method for evaluating 4-center electron repulsion integrals (ERI) for Slater-type orbitals by way of expansions in terms of Coulomb Sturmians. The ERIs can then be evaluated using our previously published methods for rapid evaluation of Coulomb Sturmians through hyperspherical harmonics. Numerical investigations are made of the efficiency in 1- and 2-center cases where the exact integrals can be evaluated.

Authors:Alejandra M.P. Mendez; Darío M. Mitnik; Jorge E. Miraglia Abstract: Publication date: Available online 22 September 2017 Source:Advances in Quantum Chemistry Author(s): Alejandra M.P. Mendez, Darío M. Mitnik, Jorge E. Miraglia In this work we show the results of a numerical experiment performed on the Hartree–Fock (HF) wave functions in order to understand the relationship between the positions of the orbital nodes and the inflection points (zeros of their second derivative). This analysis is equivalent to investigating the existence of a physical one-electron local potential representing the interactions between the electrons. We found that with successive improvements in the quality of the numerical methods, the nodes and the inflection points systematically become closer. When the nodes coincide exactly with the inflection points, the existence of an effective local potential would be proven. However, this requirement cannot be fulfilled unless an explicit constraint (missing in the standard method) is incorporated into the HF procedure. The depurated inversion method (DIM) was devised to obtain detailed nl-orbital potentials for atoms and molecules. The method is based on the inversion of Kohn–Sham-type equations, followed by a further careful optimization which eliminates singularities and also ensures the fulfillment of the appropriate boundary conditions. The orbitals resulting from these potentials have their internal inflection points located exactly at the nodes. In this way, the DIM can be employed to obtain effective potentials that accurately reproduce the HF orbitals.

Authors:Michael Hehenberger Abstract: Publication date: Available online 15 September 2017 Source:Advances in Quantum Chemistry Author(s): Michael Hehenberger Per-Olov Löwdin was an influential scientific leader who created and led summer schools in the Scandinavian mountains, organized the Florida Sanibel Symposia, edited Scientific Journals, and influenced a generation of students and fellow quantum chemists. Despite spending “only” 10 years close to him, the remaining professional life of the author, outside Quantum Chemistry, was highly impacted by Löwdin's charismatic personality. Even when working on engineering problems and formulating IBM's cheminformatics and bioinformatics initiatives, the author was constantly reminded of lessons learned during his years as a junior member of the Uppsala Quantum Chemistry Group. In particular, Löwdin had a rare ability to attract outstanding scientists to his events. After a few remarks regarding IBM's historic contributions to information technology, the author finally introduces a newly started High Mountain Genetics project. The project promises to combine Per-Olov Löwdin's and the author's shared love for the mountains with their passion for science. This chapter also includes a number of rare photographs, featuring Löwdin, taken during the years 1975–78.

Authors:María Belén Ruiz; Robert Tröger Abstract: Publication date: Available online 31 August 2017 Source:Advances in Quantum Chemistry Author(s): María Belén Ruiz, Robert Tröger Configuration Interaction (CI) calculations on the ground state of the C-atom are carried out using a small basis set of Slater orbitals [7s6p5d4f3g]. The configurations are selected according to their contribution to the total energy. One set of exponents is optimized for the whole expansion. Using some computational techniques to increase efficiency, our computer program is able to perform partially parallelized runs of 1000 configuration term functions within a few minutes. With the optimized computer program we were able to test a large number of configuration types and chose the most important ones. The energy of the 3P ground state of carbon atom with a wave function of angular momentum L =1 and M L =0 and spin eigenfunction with S =1 and M S =0 leads to −37.83526523h, which is millihartree accurate. We discuss the state of the art in the determination of the ground state of the carbon atom and give an outlook about the complex spectra of this atom and its low-lying states.

Authors:Jessica A. Del Punta; Gustavo Gasaneo; Lorenzo U. Ancarani Abstract: Publication date: Available online 23 August 2017 Source:Advances in Quantum Chemistry Author(s): Jessica A. Del Punta, Gustavo Gasaneo, Lorenzo U. Ancarani We investigate the two-body Coulomb radial problem, providing extensions of known results and establishing a novel connection to orthogonal polynomials. The expansion in Laguerre-type functions of positive energy Coulomb solutions allows one to separate out the radial coordinate from the physical parameters. For the regular Coulomb wave function analytical coefficients are known to be directly connected to Pollaczek polynomials. It turns out that, simultaneously for the attractive and repulsive case, they can also be related to Meixner–Pollaczek polynomials. This allows us to provide a novel interpretation of these coefficients; considering the charge as a variable, we are able to establish orthogonality and completeness properties for these charge functions. We also investigate analytically Laguerre-type expansions of the irregular, incoming and outgoing Coulomb solutions; through a careful limit process we provide the expansion coefficients in closed form.

Authors:Avram Sidi Abstract: Publication date: Available online 18 August 2017 Source:Advances in Quantum Chemistry Author(s): Avram Sidi In this chapter, we discuss some recently obtained asymptotic expansions related to problems in numerical analysis and approximation theory. • We present a generalization of the Euler–Maclaurin (E–M) expansion for the trapezoidal rule approximation of finite-range integrals ∫ a b f ( x ) d x , when f(x) is allowed to have arbitrary algebraic–logarithmic endpoint singularities. We also discuss effective numerical quadrature formulas for so-called weakly singular, singular, and hypersingular integrals, which arise in different problems of applied mathematics and engineering. • We present a full asymptotic expansion (as the number of abscissas tends to infinity) for Gauss–Legendre quadrature for finite-range integrals ∫ a b f ( x ) d x , where f(x) is allowed to have arbitrary algebraic–logarithmic endpoint singularities. • We present full asymptotic expansions, as n → ∞ , (i) for Legendre polynomials P n (x), x ∈ (−1, 1), (ii) for the integral ∫ c d f ( x ) P n ( x ) d x , − 1 < c < d < 1, and (iii) for Legendre series coefficients e n [ f ] = ( n + 1 / 2 ) ∫ − 1 1 f ( x ) P n ( x ) d x , when f(x) has arbitrary algebraic–logarithmic (interior and/or endpoint) singularities in [−1, 1].

Authors:Alessandro Roggero; Francesco Pederiva Abstract: Publication date: Available online 9 August 2017 Source:Advances in Quantum Chemistry Author(s): Alessandro Roggero, Francesco Pederiva We present an extension of the configuration interaction Monte Carlo (CIMC) method to the computation of the ground-state properties of atoms and molecules. In particular we make use of orthonormalized Gaussian basis sets and compute the coupled clusters at the singles-doubles level (CCSD) wave function to be used as importance function in the imaginary-time propagation. We present a few results for first-row atoms and some simple molecules. In particular we will show a substantial independence of results when the CCSD wave function is truncated at second-order perturbation theory level, thereby confirming the possible use of CIMC as a viable accelerator of CC calculations given the more favorable scaling with the electron number.

Authors:Patrick J. Lestrange; Mark R. Hoffmann; Xiaosong Li Abstract: Publication date: Available online 26 July 2017 Source:Advances in Quantum Chemistry Author(s): Patrick J. Lestrange, Mark R. Hoffmann, Xiaosong Li Dynamic electric properties are most commonly determined by applying linear and nonlinear response theory. This is often a sequential process as each order of response depends on the solution for the previous lower order. Response theory is a perturbative approach and is not directly amenable to modeling time-resolved spectroscopies or experiments involving exotic pulse shapes. Nonperturbative interaction between a system and an electric field can be modeled explicitly in time. This makes it possible to more easily resolve higher-order properties and highly nonlinear processes. Time-dependent configuration interaction has asserted itself as a powerful tool for accurately modeling electronic dynamics. We have implemented time-dependent configuration interaction using the graphical unitary group approach in order to study the dynamics of open-shell systems while retaining spin as a good quantum number. This approach has been used to resolve linear and nonlinear electric properties of molecular systems. Important considerations when modeling dynamic electric properties in the time-domain are presented as well as comparisons to properties of broken symmetry solutions.

Authors:John C. Morrison; Jacek Kobus Abstract: Publication date: Available online 14 July 2017 Source:Advances in Quantum Chemistry Author(s): John C. Morrison, Jacek Kobus The Hartree–Fock theory for diatomic molecules and a theoretical approach for performing many-body calculations are described. Using single-electron wave functions and energies produced by a numerical Hartree–Fock program, the Goldstone diagrams that arise in a perturbation expansion of the energy are evaluated by expressing the Goldstone diagrams in terms of pair functions that are the solution of first-order pair equations. The relevant pair equations are discretized and solved using the spline collocation method with a basis of third-order Hermite splines. Both the Hartree–Fock theory and many-body theory are more complex for diatomic molecules than they are for atoms. While the Hartree–Fock equations for atoms involve a single radial variable and the two-electron pair equation for atoms involve two radial variables, the Hartree–Fock equations for diatomic molecules involve two independent variables and the pair equation for diatomic molecules involves five independent variables. To deal with these problems of higher-dimensionality, we have developed numerical methods for dividing the variable space into smaller subregions in which the equations can be solved independently. This domain decomposition theory is described and numerical results are given for a single-electron model problem and for many-body calculations for diatomic molecules. Because the long-range goal of our work is to develop an extensive program for doing numerical coupled-cluster calculations on molecules, we will take special care to show how each part of our numerical approach is tested.

Authors:Bastien Mussard; Emanuele Coccia; Roland Assaraf; Matthew Otten; Cyrus J. Umrigar; Julien Toulouse Abstract: Publication date: Available online 11 July 2017 Source:Advances in Quantum Chemistry Author(s): Bastien Mussard, Emanuele Coccia, Roland Assaraf, Matthew Otten, Cyrus J. Umrigar, Julien Toulouse We present the extension of variational Monte Carlo (VMC) to the calculation of electronic excitation energies and oscillator strengths using time-dependent linear-response theory. By exploiting the analogy existing between the linear method for wave function optimization and the generalized eigenvalue equation of linear-response theory, we formulate the equations of linear-response VMC (LR-VMC). This LR-VMC approach involves the first- and second-order derivatives of the wave function with respect to the parameters. We perform first tests of the LR-VMC method within the Tamm–Dancoff approximation using single-determinant Jastrow–Slater wave functions with different Slater basis sets on some singlet and triplet excitations of the beryllium atom. Comparison with reference experimental data and with configuration-interaction-singles (CIS) results shows that LR-VMC generally outperforms CIS for excitation energies and is thus a promising approach for calculating electronic excited-state properties of atoms and molecules.

Authors:Eduardo V. Ludeña; Darío Arroyo; Edison X. Salazar; Jorge Vallejo Abstract: Publication date: Available online 10 July 2017 Source:Advances in Quantum Chemistry Author(s): Eduardo V. Ludeña, Darío Arroyo, Edison X. Salazar, Jorge Vallejo We deal with different representations of the noninteracting kinetic energy functional for the purpose of examining their effect upon the generation of shell structure in atoms. We decompose the noninteracting functional into a Weizsacker term plus a Pauli term where the latter is written as a product of the Thomas–Fermi ρ5/3 (r) times the Pauli enhancement factor F p [ρ]. We examine the behavior of F p [ρ] when it is given in terms of a Hartree–Fock orbital representation, of density-dependent orbitals generated through local-scaling transformations, and of the Liu–Parr power series expansion. In the latter, we compare the cases when the expansion coefficients have been expanded in an all-shell vs a shell-by-shell procedure. We apply these approximations to the aluminum atom. In particular, for this case, we examine in these different approximations, the role of the Pauli enhancement factor for the production of shell structure.

Authors:Daniel Gebremedhin; Charles Weatherford Abstract: Publication date: Available online 5 July 2017 Source:Advances in Quantum Chemistry Author(s): Daniel Gebremedhin, Charles Weatherford A single-particle pseudo-potential that splits the effect of the electron–electron repulsive potential of Helium (He) atom into two noninteracting identical particle potentials is numerically computed. This is done by minimizing the expectation value of the difference between the approximate and exact Hamiltonians over the Hilbert space of He atom. The one-particle potential is expanded in a spatial basis set which leads to an overdetermined system of linear equation that was solved using a least square approximation. The method involves a self-consistent iterative scheme where a converged solution valid for any state of the atom can be calculated. The total ground state energy for these two noninteracting particles under the calculated potential is found to be − 2.861 68, which is the Hartree–Fock limit for the He atom.

Authors:Carlos F. Bunge Abstract: Publication date: Available online 5 July 2017 Source:Advances in Quantum Chemistry Author(s): Carlos F. Bunge Configuration interaction (CI) starts from a matrix-eigenvalue equation involving an atomic or molecular electronic Hamiltonian represented by a complete set of Slater determinants made up of a given orbital basis. Full CI scales unfavorably with number of orbitals and number of electrons relative to all other orbital methods. Recent work on 10-electron systems (Ne and H2O ground states, the latter at many internuclear distances), and using large orbital bases, shows that up to sextuply excited configurations can be selected a priori, quantitatively and very efficiently by means of Brown's formula, leading to unsurpassed accuracy and understanding. Selected CI (SCI) suggests an array of promising and unexplored models and calls for new vistas demanding new algorithms. Here I review SCI with truncation energy error in the light of new software suitable for considerably larger systems.

Authors:Mateusz Witkowski; Szymon Śmiga; Ireneusz Grabowski Abstract: Publication date: Available online 3 July 2017 Source:Advances in Quantum Chemistry Author(s): Mateusz Witkowski, Szymon Śmiga, Ireneusz Grabowski The extensive study of the spin-resolved second-order Møller–Plesset method in the context of the electron density is performed. It was found the well-defined proportionality of the same- and opposite-spin parts of the MP2 correlated electronic density. We have rationalized the value of the scaling parameter used in the foundation of the SOS-MP2 (Jung et al., 2004) method from the density point of view. Our analysis is complemented by the calculations of the dipole moments using differently parameterized spin-resolved MP2 methods.

Authors:Diego R. Alcoba; Alicia Torre; Luis Lain; Ofelia B. Oña; Gustavo E. Massaccesi; Pablo Capuzzi Abstract: Publication date: Available online 27 June 2017 Source:Advances in Quantum Chemistry Author(s): Diego R. Alcoba, Alicia Torre, Luis Lain, Ofelia B. Oña, Gustavo E. Massaccesi, Pablo Capuzzi In this work we project the Hamiltonian of an N-electron system onto a set of N-electron determinants cataloged by their seniority numbers and their excitation levels with respect to a reference determinant. We show that, in open-shell systems, the diagonalization of the N-electron Hamiltonian matrix leads to eigenstates of the operator Ŝ 2 when the excitation levels are counted in terms of spatial orbitals instead of spin-orbitals. Our proposal is based on the commutation relations between the N-electron operators seniority number and spatial excitation level, as well as between these operators and the spin operators Ŝ 2 and Ŝ z . Energy and 〈 Ŝ 2 〉 expectation values of molecular systems obtained from our procedure are compared with those arising from the standard hybrid configuration interaction methods based on seniority numbers and spin-orbital-excitation levels. We analyze the behavior of these methods, evaluating their computational costs and establishing their usefulness.

Authors:Frank E. Harris Abstract: Publication date: Available online 19 June 2017 Source:Advances in Quantum Chemistry Author(s): Frank E. Harris The Hylleraas-CI (Hy-CI) method is conventionally defined as based on superposition-of-configurations (also called configuration interaction) wave functions in which each term (configuration) is built from an orbital product to which is appended at most one linear factor r ij , where r ij is the distance between particles i and j. The functions comprising an orbital product are usually chosen to be Slater-type orbitals that include spherical-harmonic angular dependence. We consider here both the conventional definition and its generalization (called extended Hy-CI or E-Hy-CI) in which the correlation factor r ij is replaced by a more general function f(r ij ). The present communication reviews the mathematical methods presently available for the fully analytical treatment of the integrals arising when these types of explicitly correlated wave functions are used within the framework of both the usual and extended Hylleraas-CI to study atomic and more general single-center systems. The analysis includes novel elements that may improve the efficiency of computations; the chapter also calls attention to new formulas for treating kinetic-energy integrals in Hy-CI methods.

Authors:Nabil Joudieh; Ali Bağcı; Philip E. Hoggan Abstract: Publication date: Available online 24 April 2017 Source:Advances in Quantum Chemistry Author(s): Nabil Joudieh, Ali Bağcı, Philip E. Hoggan A formalism to evaluate susceptibility tensors in molecules χ and those of nuclear shielding σ k is developed using GIAO (gauge-including AOs). It uses the coupled-perturbed Hartree–Fock formalism. Originality resides in the definition of local susceptibilities. An in-house MOPAC code provides an NDDO approximation to this molecular site approach which has also been used for chemical shift determination within the GAUSSIAN suite of programs.

Authors:Abul K.F. Haque; Malik Maaza; Md. M. Haque; Md. A.R. Patoary; Md. A. Uddin; Md. I. Hossain; Md. S. Mahbub; Arun K. Basak; Bidhan C. Saha Abstract: Publication date: Available online 20 April 2017 Source:Advances in Quantum Chemistry Author(s): Abul K.F. Haque, Malik Maaza, Md. M. Haque, Md. A.R. Patoary, Md. A. Uddin, Md. I. Hossain, Md. S. Mahbub, Arun K. Basak, Bidhan C. Saha Calculations of electron-impact ionization cross sections (EIICS) for L-subshell of neutral atoms with atomic number Z = 14–92 and also for M-subshell targets, having atomic number Z = 35–92 for incident energies E threshold ≤ E ≤ 106 keV, have been reported. This review comprises the results of our two easy-to-use models, capable of reproducing very closely the experimental EIICS data. We also show systematically how these models can be implemented easily to generate accurate data as demanded by various model applications. The choice of the range of atomic number Z for both L- and M-subshell targets was made possible by the wealth of the EIICS data in literature either from experiments or from rigorous quantal calculations. The detailed findings due to our XMCN and XMUIBED models are compared with the experimental and other theoretical results. Present results describe the experimental data quite well for the L- and M-subshell for various atomic targets over a wider range of projectile energy.