Abstract: Publication date: Available online 10 August 2018Source: Advances in Quantum ChemistryAuthor(s): Erkki J. Brändas Darwinian evolution is reconsidered from a microscopic perspective commensurate with modern advanced molecular readings of our physical world and its mathematical structure. Fundamental biological processes in physical Complex Enough Systems, CES, are defined and analyzed. The material description contrives molecular events at precise temperatures and specific timescales reflecting a fundamental spatiotemporal character of a conceptual class of Correlated Dissipative Structures, CDS. The latter is subject to a higher-order statistical ensemble, the Correlated Dissipative Ensemble, CDE, reminding of Dawkins' notion of an evolution of evolvability. The ontological question is reviewed incorporating the material and the immaterial parts of Nature. The exposition integrates well-defined teleonomic processes, objectively governed by an evolved program, leading up to a self-referential hypothesis for molecular communication, Communication Simpliciter. The principal unit of selection is intrinsic to the molecular genetic level and proceeds toward an extended phenotype that implicates perception and cognition. It is explicitly proven that active and mirror neurons provide communication protocols for cellular recognition and networking. The paradox of upside-down vision is explained together with a basic and straightforward analysis of the Necker Cube and the Spinning Dancer illusions.

Abstract: Publication date: Available online 20 July 2018Source: Advances in Quantum ChemistryAuthor(s): Yuliya V. Dubrovskaya, Olga Yu Khetselius, Larisa A. Vitavetskaya, Valentin B. Ternovsky, Inga N. Serga We present a consistent relativistic theory of spectra of the exotic (pionic) atomic systems based on the Klein–Gordon–Fock equation approach and relativistic many-body perturbation theory with accounting for the fundamental electromagnetic and strong pion–nuclear interactions. The latter has been performed by means of using the advanced strong pion–nuclear optical potential model with the generalized Ericson–Ericson potential. The nuclear finite size effect is taken into consideration within the Fermi model. To take the nuclear quadrupole deformation effects on pionic processes into account we have used the model by Toki et al. The radiative corrections are effectively taken into account within the generalized Uehling–Serber approximation to treat the Lamb shift vacuum-polarization part. To take the contribution of the Lamb shift self-energy part into account we have used the generalized nonperturbative procedure, which generalizes the Mohr procedure and radiation model potential method by Flambaum–Ginges. The results of calculation of the energy and spectral parameters for pionic atoms of the 173Yb, 175Lu, 197Au, 208Pb, 238U with accounting for the radiation (vacuum polarization), nuclear (finite size of a nucleus) and the strong pion–nuclear interaction corrections are presented. The corrections to the some transition energies for the pionic atoms 175Lu, 181Ta, Tl, Pb, 238U, etc., due to the radiative (polarization of vacuum), finite nuclear size effects and the electron screening correction, provided by the 2[He], 4[Be], and 10[Ne] electron shells are separately listed. For comparison the theoretical data obtained are compared with some measured values of the Berkley, CERN, and Virginia laboratories and results of the alternative Klein–Gordon–Fock theories with taking into account a finite size of the nucleus in the model uniformly charged sphere and the standard Uehling–Serber radiation correction.

Abstract: Publication date: Available online 20 July 2018Source: Advances in Quantum ChemistryAuthor(s): Kaito Takahashi X-ray absorption spectra (XAS) were calculated for CO, H2O, and X−H2O, X = F, Cl, Br as well as Y+H2O, Y = Li, Na. Using the Franck–Condon approximation and the reflection approximation, we showed that the general features seen in the experimental XAS for CO and H2O could be obtained from the simulation of the excitation from the zero point vibration of the ground electronic state. Furthermore, the XAS for H2O shows large variation if the transition is initiated from the v = 1 symmetric OH stretching vibrational state. Next, we showed that interaction with the halide and alkali metal ion causes the cross section of the water oxygen 1S XAS to decrease. The decrease in the cross section for X−H2O X = Cl, Br can be attributed to the broadening of the peaks. Lastly, we found that the excitation of the ionic hydrogen-bonded OH stretching mode for only the F–H2O can result in a drastic change in the XAS compared with the excitation from the zero point vibration. For Y+H2O, the excitation of the symmetric OH stretching vibration can cause the largest variation in the XAS, but the changes are not as large as those for bare water case. Therefore, we conclude that the vibrational excitation has a minor effect on the XAS for most monohydrated halide and alkali metal clusters.

Abstract: Publication date: Available online 20 July 2018Source: Advances in Quantum ChemistryAuthor(s): Anna V. Ignatenko, Anna A. Buyadzhi, Vasily V. Buyadzhi, Anna A. Kuznetsova, Alexander A. Mashkantsev, Eugeny V. Ternovsky In this paper, we present the results of computational analysis and modeling nonlinear chaotic dynamics of the diatomic molecules interacting with a resonant linearly polarized electromagnetic field. We used a quantum-dynamic model for diatomic molecule in an electromagnetic field, based on the solution of the Schrödinger equation and model potential method, and a chaos theory and nonlinear analysis methods such as a correlation integral algorithm, the Lyapunov's exponents and Kolmogorov entropy analysis, prediction model, etc. We present the results of computing the dynamical and topological invariants (such as the correlation and Kaplan–Yorke dimensions, Lyapunov's exponents, Kolmogorov entropy, etc.) for polarization time series of the ZrO molecule interacting with a linearly polarized electromagnetic field. The chaotic features are realized in the nonlinear dynamics of diatomic molecule in a linearly polarized electromagnetic field that is in a reasonable agreement with the data of modeling and conclusions by Berman, Kolovskii, Zaslavsky, Zganh et al., and Glushkov et al. Nonlinear prediction method is used for the polarization time series. It is shown that even though the simple procedure is used to construct the nonlinear model, the predicted results for the ZrO polarization time series are quite satisfactory.

Abstract: Publication date: Available online 20 July 2018Source: Advances in Quantum ChemistryAuthor(s): Olga Yu Khetselius The radiative transition wavelengths and oscillator strengths for some Li-like multicharged ions are calculated within the relativistic many-body perturbation theory with the optimized Dirac–Kohn–Sham zeroth approximation and an effective taking the relativistic, exchange-correlation, nuclear, radiative effects into account. All correlation corrections of the second order and dominated classes of the higher orders diagrams have been considered (electrons screening, mass operator iterations etc). The method includes the generalized Glushkov–Ivanov–Ivanova procedure (relativistic energy approach) for generation of the optimal basis set of relativistic electron wave functions with fulfillment of the gauge invariance principle. To reach the latter, we focus on accurate consideration of the QED perturbation theory fourth-order (a second order of the atomic perturbation theory) Feynman diagrams, whose contribution into imaginary part of radiation width ImδE for the multielectron ions accounts for multibody correlation effects. A minimization of the functional ImδE leads to integral–differential Dirac–Kohn–Sham–like density functional equations. The magnetic interelectron interaction is accounted for in the lowest order on α2 (α is the fine structure constant) parameter. The Lamb shift polarization part is taken into account in the modified Uehling–Serber approximation. Comparisons of our results on the radiative transition wavelengths and oscillator strengths for some transition in spectra of the Li-like multicharged ions (the nuclear charge Z = 21–30) with other comparable theoretical and experimental results are also given and discussed.

Abstract: Publication date: Available online 20 July 2018Source: Advances in Quantum ChemistryAuthor(s): Arkadiusz Kuroś, Anna Okopińska Studying the physics of quantum correlations has gained new interest after it has become possible to measure entanglement entropies of few-body systems in experiments with ultracold atomic gases. Apart from investigating trapped atom systems, research on correlation effects in other artificially fabricated few-body systems, such as quantum dots or electromagnetically trapped ions, is currently underway or in planning. Generally, the systems studied in these experiments may be considered as composed of a small number of interacting elements with controllable and highly tunable parameters, effectively described by Schrödinger equation. In this way, parallel theoretical and experimental studies of few-body models become possible, which may provide a deeper understanding of correlation effects and give hints for designing and controlling new experiments. Of particular interest is to explore the physics in the strongly correlated regime and in the neighborhood of critical points.Particle correlations in nanostructures may be characterized by their entanglement spectrum, i.e., the eigenvalues of the reduced density matrix of the system partitioned into two subsystems. We will discuss how to determine the entropy of entanglement spectrum of few-body systems in bound and resonant states within the same formalism. The linear entropy will be calculated for a model of quasi-one dimensional Gaussian quantum dot in the lowest energy states. We will study how the entanglement depends on the parameters of the system, paying particular attention to the behavior on the border between the regimes of bound and resonant states.

Abstract: Publication date: Available online 17 July 2018Source: Advances in Quantum ChemistryAuthor(s): Vasily V. Buyadzhi, Anna A. Kuznetsova, Anna A. Buyadzhi, Eugeny V. Ternovsky, Tatyana B. Tkach In this work an advanced relativistic quantum approach to computing the important radiative and collisional characteristics of multicharged ions in the Debye plasmas is presented. The approach is based on the relativistic energy formalism (the Gell-Mann and Low formalism) and relativistic many-body perturbation theory (PT) with the Dirac–Debye shielding model Hamiltonian for electron–nuclear and electron–electron systems. The optimized one-electron representation in the PT zeroth approximation is constructed by means of the correct treating the gauge-dependent multielectron contribution of the lowest PT corrections to the radiation widths of atomic levels. The computational results for the oscillator strengths and energy shifts due to the plasmas environment effect, the effective collision strengths for the Be- and Ne-like ions of Fe, Zn, and Kr embedded to different types of plasmas environment (with temperature 0.02–2 keV and electron density 1016−1024 cm−3) are presented and analyzed.

Abstract: Publication date: Available online 17 July 2018Source: Advances in Quantum ChemistryAuthor(s): Anna A. Kuznetsova, Alexander V. Glushkov, Anna V. Ignatenko, Andrey A. Svinarenko, Valentin B. Ternovsky We present a generalization of the operator perturbation theory method for computing the Stark resonances energies and widths in a case of multielectron atoms. The known advantages of the operator perturbation theory approach are conserved. The operator perturbation theory method allows calculating sufficiently exact complex eigenenergies and resonance widths and especially is destined for investigation of the spectral region of an atom near the new continuum boundary in a strong field. The essence of the method is the inclusion of the well-known “distorted waves approximation” in the frame of the formally exact perturbation theory. The difference between the real atomic and Coulomb field is taken into consideration by using the special model potentials and introducing the quantum defects on a parabolic basis. The results of calculation of the Stark resonance energies and widths for the lithium, sodium, and rubidium atoms are listed and compared with other theoretical and experimental data.

Abstract: Publication date: Available online 17 July 2018Source: Advances in Quantum ChemistryAuthor(s): Alexander V. Glushkov The fundamentals of a consistent approach, based on a relativistic energy formalism (adiabatic Gell-Mann and Low formalism) and the multiphoton emission and absorption lines moments technique, in a resonant multiphoton spectroscopy of atomic system in a realistic laser field are presented. We focus on computing multiphoton resonances parameters in the atomic systems interacting with the Lorentzian, Gaussian, and soliton-like shape laser pulses. The effective modified technique, based on the Ivanova–Ivanov method of differential equations, for computing the infinite sums in expressions for a multiphoton resonance line moments, is schematically described. Within an energy approach in relativistic approximation, the Gell-Mann and Low formula expresses the imaginary part of an atomic level energy shift δE through the QED-scattering matrix, which includes an interaction as with a laser field as with the photon vacuum field (spontaneous radiative decay). It results in possibility of a uniform simultaneous consideration of spontaneous and (or) induced, radiative processes and their interference. The radiation atomic lines position and shape fully determine a multiphoton spectroscopy of atom in a laser field. These lines are described by moments of different orders Mn. The first moments Mn (n = 1–3) determine an atomic line centre shift, its dispersion, and the asymmetry. As illustration we list the results of calculation of the multiphoton resonance shifts and widths in the cesium (transition 6S–6F; wavelength 1059 nm) atom and compare our results with available other theoretical and experimental data by Zoller and Lompre et al. In addition, we schematically generalize the theory presented above for the case of nuclear systems interacting with a superintense laser field, and for the first time, present the estimates for the parameters of the multiphoton resonance in the nucleus of iron 57Fe.

Abstract: Publication date: Available online 21 June 2018Source: Advances in Quantum ChemistryAuthor(s): Leo F. Holroyd, Michael Bühl, Marie-Pierre Gaigeot, Tanja van Mourik We modeled the driving force for aqueous keto-to-enol tautomerization of 5-bromouracil, a mutagenic thymine analogue, by first-principles molecular dynamics simulations with thermodynamic integration. Using interatomic distance constraints to model the water-assisted (de)protonation of 5-bromouracil in a periodic water box, we show that the free energy for its enolization is lower than that of the parent compound, uracil, by around 3.0 kcal/mol (BLYP-D2 level), enough to significantly alter the relative tautomeric ratios. Assuming the energetic difference also holds in the cell, this finding is evidence for the “rare tautomer” hypothesis of 5-bromouracil mutagenicity (and, possibly, that of other base analogues).

Abstract: Publication date: Available online 6 June 2018Source: Advances in Quantum ChemistryAuthor(s): Ryuhei Harada, Yasuteru Shigeta Biological functions are closely related to structural transitions of proteins, and thus it is necessary to clarify the correlation between their dynamical ordering and function. However, the timescale that can be reached by conventional molecular dynamics simulations is shorter than the timescales of several relevant biological functions. Therefore, methodologies to sample structural changes related to the biological functions are highly required. In this short review, we present an outline of the parallel cascade selection molecular dynamics (PaCS-MD) method proposed by us and show its applications for several proteins to reveal biologically relevant phenomena.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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 Ŝ2 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 Ŝ2 and Ŝz. Energy and 〈Ŝ2〉 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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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 ML = 0 and spin eigenfunction with S = 1 and MS = 0 leads to − 37.83526523 h, 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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 77Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(s): Nabil Joudieh, Ali Bağcı, Philip E. Hoggan A formalism to evaluate susceptibility tensors in molecules χ and those of nuclear shielding σk 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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(s): Alejandra M.P. Mendez, Dario 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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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 Fp[ρ]. We examine the behavior of Fp[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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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 ∫abf(x)dx, 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 ∫abf(x)dx, where f(x) is allowed to have arbitrary algebraic–logarithmic endpoint singularities.•We present full asymptotic expansions, as n→∞, (i) for Legendre polynomials Pn(x), x ∈ (−1, 1), (ii) for the integral ∫cdf(x)Pn(x)dx, − 1 < c < d < 1, and (iii) for Legendre series coefficients en[f]=(n+1/2)∫−11f(x)Pn(x)dx, when f(x) has arbitrary algebraic–logarithmic (interior and/or endpoint) singularities in [−1, 1].

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 77Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 77Author(s): Remigio Cabrera-Trujillo, Jens Oddershede In this work, the effects of an endohedral cavity on the hydrogen dipole oscillator strength sum rule, Sk, and its logarithmic version, Lk, 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 R0 and thickness Δ with a penetrable potential height V0. 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 Sk and Lk are investigated as a function of the cavity potential depth V0. We use the values of R0 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 V0 = 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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 77Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 77Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 77Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 77Author(s): Abul K.F. Haque, Malik Maaza, Md. M. Haque, Md. Atiqur R. Patoary, Md. Alfaz Uddin, Md. Ismail Hossain, Md. Selim 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 Ethreshold ≤ 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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 77Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 77Author(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.

Abstract: Publication date: 2018Source: Advances in Quantum Chemistry, Volume 76Author(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 rij, where rij 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 rij is replaced by a more general function f(rij). 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.