Abstract: Publication date: Available online 16 May 2019Source: Advances in Quantum ChemistryAuthor(s): Pierre-François Loos, Anthony Scemama, Michel Caffarel We describe a method for imposing the correct electron–nucleus (e-n) cusp in molecular orbitals expanded as a linear combination of (cuspless) Gaussian basis functions. Enforcing the e-n cusp in trial wave functions is an important asset in quantum Monte Carlo calculations as it significantly reduces the variance of the local energy during the Monte Carlo sampling. In the method presented here, the Gaussian basis set is augmented with a small number of Slater basis functions. Note that, unlike other e-n cusp-correction schemes, the presence of the Slater function is not limited to the vicinity of the nuclei. Both the coefficients of these cuspless Gaussian and cusp-correcting Slater basis functions may be self-consistently optimized by diagonalization of an orbital-dependent effective Fock operator. Illustrative examples are reported for atoms (H, He, and Ne) as well as for a small molecular system (BeH2). For the simple case of the He atom, we observe that, with respect to the cuspless version, the variance is reduced by one order of magnitude by applying our cusp-corrected scheme.

Abstract: Publication date: Available online 10 May 2019Source: Advances in Quantum ChemistryAuthor(s): Ion Mitxelena, Mario Piris, Jesus M. Ugalde The basic concepts relevant to the approximate natural orbital functional (NOF) theory are presented. We discuss in detail the reconstruction that leads to Piris NOF (PNOF) approximations focusing on the electron pairing, namely, the independent pair model PNOF5 and the inter-pair electron correlation model PNOF7. It is shown that PNOF7 is an ideal candidate to study model systems for strong correlation such as the Hubbard model and hydrogen rings. Analytic first- and second-order energy derivatives are presented for any given nuclear perturbation. Results for equilibrium geometries and harmonic vibrational frequencies corresponding to a selected set of molecules are reported.

Abstract: Publication date: Available online 10 May 2019Source: Advances in Quantum ChemistryAuthor(s): Florian A. Bischoff Multiresolution analysis (MRA), and specifically multiwavelets, can be used to compute properties of molecules accurately with defined error control. The truncation error induced by using only a finite mathematical basis for the quantum molecular wave function, which is a major source of inaccuracy in computations, can be controllably removed with MRA. A large variety of molecular properties can be computed, including ground-state properties and excited states, first- and second-order properties (dipole moments, nuclear gradients, vibrational frequencies) using density functional theory (pure and hybrid functionals) as well as correlated methods (second-order perturbation theory and Coupled-Cluster).

Abstract: Publication date: Available online 9 May 2019Source: Advances in Quantum ChemistryAuthor(s): Milagros F. Morcillo, Enrique F. Borja, José M. Alcaraz-Pelegrina, Antonio Sarsa The stability of a spherically confined atomic system when confinement is removed is studied. We consider s, p, d, and f states of the Hydrogen atom confined by a finite barrier. The stability is characterized in terms of the ionization probability of the atom when confinement is removed. The ionization probability presents different sharply peaked, nonsymmetric maxima as a function of the confinement radius that can be explained in terms of tunneling and retunneling of the confined bound states. The spatial structure of the confined bound state plays a key role in the stability of the atom. Different measures arising from information theory, such as information entropy, disequilibrium indices, and complexity measures, have been calculated to characterize quantitatively the structure of the confined state. A direct relationship between the complexity of a confined state and its stability when it is released from confinement has been found.

Abstract: Publication date: Available online 5 April 2019Source: Advances in Quantum ChemistryAuthor(s): Artur Lisoń, Monika Musiał, Stanisław A. Kucharski The Fock space coupled cluster theory provides a description of the states obtained by attachment of one ((1,0) sector) or two ((2,0) sector) electrons to the reference system. If the reference is assumed to be a doubly ionized cation then the results relate to a cation or a neutral molecule, respectively. In the current work the above scheme is applied to extensive ab initio calculations of the potential energy curves (PECs), and the spectroscopic constants of NaH and its cation for the eight lowest lying states, adopting as a reference system the doubly ionized structure, i.e., NaH2+. Such a computational strategy relies on the fact that the closed shell reference (NaH2+) dissociates into the closed shell fragments. This is advantageous since the restricted Hartree–Fock function can be used as the reference in the whole range of interatomic distances. This scheme offers a first principle size-extensive method without any model or effective potential parameters for the description of the bond breaking processes. The computed PECs and spectroscopic constants stay very close to the experimental values, with accuracy exceeding that of other theoretical approaches (in most cases) including those based on the effective core potentials.

Abstract: Publication date: Available online 7 September 2018Source: Advances in Quantum ChemistryAuthor(s): Liliana Mammino Hyperguinones A and B are prenylated acylphloroglucinols of natural origin, found in Hypericum species and exhibiting antioxidant activity. Their molecules differ only by the R chain in the COR group (ethyl and isopropyl, respectively). Their structure is better outlined by numbering the C atoms of the benzene ring. Considering the C atom to which the COR group is attached at C1, an OH is attached to C2, a pyranoid ring is fused between C3 and C4, a prenyl chain is attached at C5 and a keto O is attached at C6.Complexes of these molecules with a Cu2+ ion were calculated at the DFT level, with the B3LYP functional, the 6-31+G(d,p) basis set for the light atoms and the LANL2DZ pseudopotential for the Cu2+ ion, considering all the sites to which Cu2+ might bind (including simultaneous coordination to two geometrically suitable sites). Complexes of a third structure, in which R is an isobutyl, were also calculated to obtain more information for comparative consideration of possible influences by basically close R chains. The results show that Cu2+ prefers to bind simultaneously to two sites of the molecule and that the charge of the ion is reduced from +2 to +1 in the complexes, thanks to an electron transfer from the molecule to the ion. This is consistent with the proven antioxidant activity of the two hyperguinones. The effects of complexation on relevant molecular properties, including its intramolecular hydrogen bond, are analyzed in detail.

Abstract: Publication date: Available online 23 August 2018Source: Advances in Quantum ChemistryAuthor(s): Mitsuo Shoji, Hiroshi Isobe, Shusuke Yamanaka, Yasufumi Umena, Keisuke Kawakami, Nobuo Kamiya, Kizashi Yamaguchi Atmospheric oxygenation and evolution of aerobic life on our earth are a result of water oxidation by oxygenic photosynthesis in photosystem II (PSII) of plants, algae, and cyanobacteria. The water oxidation in the oxygen-evolving complex (OEC) of PSII is expected to proceed through five oxidation states, known as the Si (i = 0, 1, 2, 3, and 4) states in the Kok cycle, with the S1 being the most stable state in the dark. The OEC in PSII involves the active catalytic site made of four Mn ions and one Ca ion, namely the CaMn4O5 cluster. Past decades, molecular structures of the CaMn4O5 cluster in OEC of PSII have been investigated by the extended X-ray absorption fine structure (EXAFS). The magnetostructural correlations were extensively investigated by EPR spectroscopy. Recently, Kamiya and Shen groups made a great breakthrough for determination of the S1 structure of OEC of PSII by the X-ray diffraction (XRD) and X-ray free electron laser (XFEL) experiments, providing structural foundations that are crucial for theoretical investigations of structure and reactivity of the CaMn4O5 cluster. Large-scale QM/MM calculations starting from the XRD structures elucidated geometrical, electronic, and spin structures of the CaMn4O5 cluster, indicating an important role of the Jahn–Teller (JT) effect of Mn(III) ions. This review fully examines our theoretical formulae for estimation of the Jahn–Teller deformations of the CaMn4O5 cluster in OEC of PSII. Scope and applicability of the JT deformation formulae are elucidated in relation to several different structures of the CaMn4O5 cluster proposed by XRD, XFEL, EXAFS, and other experiments. Subtle differences among XRD, XFEL, and EXAFS structures in the S1 state are examined in relation to environmental effects for the CaMn4O5 cluster in OEC of PSII. The X-ray damage of the serial femtosecond crystallography (SFX) by XFEL is also examined in relation to the damage-free low-dose (LD) XRD structure. The JT deformation formulae are also applied to theoretical analysis of the S3 structures by SFX. Implications of the computational results are discussed for further refinements of geometrical parameters of the CaMn4O5 cluster in OEC of PSII and possible mechanisms of water oxidation in OEC of PSII.

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 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 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.