Abstract: Publication date: Available online 23 November 2019Source: Advances in Quantum ChemistryAuthor(s): Maximilian Seel, János LadikAbstractThe aim of this paper is to review some basic ideas, concepts, and questions of today's theoretical biology and stimulate reflection on them. Possible sources of misunderstanding, confusion, and disagreement in the discussion of the foundation of biology are outlined. Major attention is given to different interpretations (and implications) of the term “explanation” and “living system.” It is argued that the concepts of present day's physics are not general enough to describe biology. As examples of possible new concepts “complexity” and “creativity” are discussed. Different definitions of “living systems” and their flaws are reviewed. It is concluded that an explanation of a living system involves both, an understanding of its parts and of the organization of these parts. This leads to a discussion of the role of quantum mechanics and non-equilibrium statistical thermodynamics in biology. Finally, the implications of some philosophical points of view and the role of Gödel's incompleteness theorem in a basic theory of biology are discussed.

Abstract: Publication date: Available online 6 November 2019Source: Advances in Quantum ChemistryAuthor(s): Yury M. Koroteev, Evgenii V. ChulkovAbstractWe present the density functional calculation results for K adsorption on the Pt(111) and Cu(111) surfaces in a (2 × 2) structure. The site preference, surface relaxation, and electron structure of these systems are analyzed. The hcp hollow position is found to be the most favorable for K adsorption on Pt(111). For the Cu(111)-(2 × 2)-K system we find that all the considered adsorption sites (hcp and fcc hollow, bridge, and top) lead to the energy difference within few meV. The calculated surface relaxations and adsorption geometry are in agreement with available experimental data. It is demonstrated that the K adsorption leads to the disappearance of a number of the substrate surface and resonance states in the energy region above − 2 eV/−3 eV (Pt/Cu) and to the appearance of new surface features, as well as bands that are significantly localized at the adsorbate. It is found that the K adsorption (1) transforms the Shockley surface state lying in the bulk band gap near the Γ point on the clean Pt and Cu surfaces into the state localized at the K adlayer and (2) and shifts this state up by energy about 0.4 eV.

Abstract: Publication date: 2019Source: Advances in Quantum Chemistry, Volume 79Author(s): Viktor N. Staroverov, Egor OspadovAbstractThe exchange-correlation potential of the Kohn–Sham density-functional scheme is the difference between the Fermi potential—an effective potential appearing in the one-electron Schrödinger equation for the square root of the electron density—and the Pauli potential, i.e., vXC(r) = vF(r) − vP(r). We show that, for a given external potential and electron number, knowledge of vF(r) alone is sufficient to generate the corresponding vP(r) and vXC(r). The Fermi potential itself can be computed from the system's interacting two-electron reduced density matrix or modeled directly. The unified treatment of these three potentials provides a practical method for accessing accurate functional derivatives of the exchange-correlation, Pauli kinetic, and Levy–Perdew–Sahni energy functionals without having to tackle functional differentiation and numerical challenges of other construction techniques.

Abstract: Publication date: Available online 29 October 2019Source: Advances in Quantum ChemistryAuthor(s): Istvan Nagy, Inigo AldazabalAbstractIn this contribution we determine the exact solution for the ground-state wave function of a two-particle correlated model atom with harmonic interactions. From that wave function, the nonidempotent one-particle reduced density matrix is deduced. Its diagonal gives the exact probability density, the basic variable of density functional theory (DFT). The one-matrix is directly decomposed, in a point-wise manner, in terms of natural orbitals and their occupation numbers, i.e., in terms of its eigenvalues and normalized eigenfunctions. The exact informations are used to fix three, approximate, independent-particle models. Next, a time-dependent external field of finite duration is added to the exact and approximate Hamiltonians and the resulting Cauchy problem is solved. The impact of the external field is investigated by calculating the energy shift generated by that time-dependent field. It is found that the nonperturbative energy shift reflects the sign of the driving field. The exact probability density and current are used, as inputs, to investigate the capability of a formally exact independent-particle modeling in time-dependent DFT as well. The results for the observable energy shift are analyzed by using realistic estimations for the parameters of the two-particle target and the external field. A comparison with the experimental prediction on the sign-dependent energy loss of swift protons and antiprotons in a gaseous He target is made.

Abstract: Publication date: Available online 6 September 2019Source: Advances in Quantum ChemistryAuthor(s): Wayne W. Hayes, Joseph R. MansonAbstractWork on theories of gas–surface interactions received a strong impetus from advances in experimental physics in the early part of the last century, notably from the work of Stern and coworkers on verifying the Maxwell–Boltzmann distribution and the work of Roberts in measuring the energy accommodation coefficient. Much of the subsequent experimental work has involved gases made up of heavy mass atoms with large incident energies and relatively high surface temperatures, which are the conditions under which the scattering can be described with classical physics. In this paper a straightforward theory of classical gas–surface scattering is considered and applied to the analysis of a wide variety of experiments. The theory depends on limited information about the nature of the actual particle–surface interaction potential but does correctly account for the necessary laws of conservation of energy and momentum. Analysis of well-controlled experiments in the classical regime involving rare gases scattering from liquid, metal, and insulator surfaces is shown to yield a great deal of information about the atom–surface interaction and also reveals limitations on what such experiments are capable of revealing about the collision process.

Abstract: Publication date: Available online 4 September 2019Source: Advances in Quantum ChemistryAuthor(s): Irina Yu. Sklyadneva, Rolf Heid, Klaus-Peter Bohnen, Evgueni V. ChulkovAbstractWe report on the first ab initio study of the electron–phonon interaction and its contribution to the lifetime broadening of excited hole (electron) surface states on the (110) surface of Ag and Cu. The calculations based on density-functional theory were carried out using a linear response approach in the mixed-basis pseudopotential representation. The calculated strength of the phonon-mediated scattering varies with the energy position of a hole (electron) state in the surface energy band while a directional anisotropy is noticeable only for occupied surface states. It is shown that the electron–phonon interaction in occupied surface states is largely determined by bulk electronic states and is weak compared to the phonon-induced coupling of excited electrons, characterized by a strong energy dependence due to significant intraband scattering. Analysis of various contributions to the electron–phonon coupling reveals that the bulk phonon modes determine the scattering of excited holes, while the surface phonon modes are more involved in the coupling of exited electrons.

Abstract: Publication date: Available online 3 September 2019Source: Advances in Quantum ChemistryAuthor(s): Vyacheslav M. Silkin, Eugene V. Chulkov, Pedro M. EcheniqueAbstractThe surface excitation spectra of the B-terminated and Mg-terminated MgB2(0001) surfaces are studied in the ab initio time-dependent density functional theory approach. The band structure of both these surfaces is fully included into evaluation of the surface response function using a linear response approach. We find that different surface electronic structures for these surface terminations result in very different surface collective electronic excitations. Due to a number of surface states and peculiarity of the MgB2 dielectric properties several surface plasmons, such as surface plasmon, interband surface plasmon, acoustic surface plasmon, and others have been found. We trace their evolution with momentum transfer change on both surfaces. Whereas at vanishing momentum transfers the plasmons in both systems can be understood considering the bulk MgB2 dielectric function, upon momentum increase the collective excitations present very different behavior. We relay such behavior to the differences in the surface electronic structure of the studied terminations.

Abstract: Publication date: Available online 19 August 2019Source: Advances in Quantum ChemistryAuthor(s): Alejandra M.P. Mendez, Darío M. Mitnik, Jorge E. MiragliaAbstractWe investigate the feasibility of using pseudopotentials to generate the bound and continuum orbitals needed in collisional calculations. By examination of several inelastic processes in the first Born approximation, we demonstrate the inconveniences of this approach. Instead, we advocate use of effective potentials obtained with the depurated inversion method (DIM). In this contribution, we extend this method to molecular systems. Calculations of single first-order photoionization and proton-impact ionization using the DIM show fair agreement with experimental results for both atoms and molecules.

Abstract: Publication date: Available online 19 August 2019Source: Advances in Quantum ChemistryAuthor(s): Johanna P. Carbone, Lan Cheng, Rolf H. Myhre, Devin Matthews, Henrik Koch, Sonia CorianiAbstractAn extensive analysis has been carried out of the performance of standard families of basis sets with the hierarchy of coupled cluster methods CC2, CCSD, CC3, and CCSDT in computing selected Oxygen, Carbon, and Nitrogen K-edge (vertical) core excitation and ionization energies within a core-valence separated scheme in the molecules water, ammonia, and carbon monoxide. Complete basis set limits for the excitation energies have been estimated via different basis set extrapolation schemes. The importance of scalar relativistic effects has been established within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e).

Abstract: Publication date: Available online 12 August 2019Source: Advances in Quantum ChemistryAuthor(s): Claudio D. Archubi, Nestor R. AristaAbstractA review of the behavior of the energy loss, mean-free path and straggling of protons, positrons, and electrons in an electron gas is performed using different dielectric models which represent the case of metals (Lindhard model for a free electron gas and wave-packet model or extended wave-packet model for bound states contributions) and the cases of semiconductors and insulators (Levine and Louie model, Brandt and Reinheimer model, and extended wave-packet model for systems with a band gap). The effects produced by the band gap of the material and by the properties of the incident particle are analyzed in detail. Significant differences related to the mass and to the indistinguishability (in the case of electrons) are described. In particular, inner-shell contributions are described for protons and correlated protons with a corresponding comparison with experimental results. Analytical expressions for the high-energy limit are displayed for all the cases using the plasmon-pole approximation.

Abstract: Publication date: Available online 12 August 2019Source: Advances in Quantum ChemistryAuthor(s): Károly TőkésiAbstractThe interaction of charged particles with materials can always be associated with the energy transfer process that results in the change of the energy of the particles. In this chapter we show examples when projectiles suffer energy loss either in ion-atom, or electron-surface and ion-surface collisions. We present classical trajectory Monte Carlo results to calculate energy losses of the projectiles in proton-hydrogen atom collisions. The obtained results verify that high order effects should be included for a proper description of electronic stopping power. Energy loss of charged particles near surfaces pose several interesting problems, among them the separation of surface from bulk effects. We analyze the possible way of the separation in electron-surface and ion-capillary collisions. We show that the correlation between the angular distribution and the energy loss of ions passing through capillaries can be used to probe the surface loss functions without the contribution of the bulk one.

Abstract: Publication date: Available online 2 August 2019Source: Advances in Quantum ChemistryAuthor(s): F. Flores, G. Chiappe, E.V. Anda, E.C. GoldbergAbstractAn ionic Hamiltonian based on the first Hund rule applied to transition metal atoms is reviewed and discussed in detail. The tunneling current between a STM-tip and a transition metal atom is analyzed by means of that Hamiltonian combined with an effective crystal-field effect. We use an equation of motion (EOM) method to calculate that inelastic tunneling current, as well as the Kondo resonance appearing at the Fermi level.We show how an accurate description of its Kondo resonance for the Co/Cu2N(100) system can be achieved by extending the EOM-calculation up to fourth-order in the atom/metal interaction that defines the parameter of expansion in the EOM-equations. These results allow us to calculate also the inelastic tunneling excitation of the atom and the dynamical fluctuations of the atomic spin from S = 3/2 to S = 1.

Abstract: Publication date: Available online 2 August 2019Source: Advances in Quantum ChemistryAuthor(s): Néstor R. Arista, Juana L. Gervasoni, Silvina Segui, Isidro Villó-Pérez, Raúl O. BarrachinaAbstractThe phenomenon of bulk and surface plasmons in solids of different geometries is analyzed in detail, giving special consideration to Ritchie's pioneering works and his relevant contributions to the advance of the knowledge in the field. A review of plasmon processes is made, illustrating the characteristics of surface and bulk modes and showing alternative formulations based on the dielectric function formalism, the hydrodynamical model, and the Hamiltonian method. The main characteristics of plasmons in infinite media, planar interfaces, cylindrical, and spherical nanostructures are discussed.

Abstract: Publication date: Available online 22 July 2019Source: Advances in Quantum ChemistryAuthor(s): Stanka V. Jerosimić, Milan Z. Milovanović, Roland Wester, Franco A. GianturcoAbstractWe report the results of fixed-nuclei calculations for the excited, dipole-supported anionic states of the C3N− anion using the multireference configuration interaction (MRCI) method with Davidson perturbative correction, plus other similar multireference methods. Within the adiabatic approximation, we find that there are several low-lying bound states of 3Σ+ and 1Σ+ symmetry that lie in energy below the neutral molecule when we employ specifically selected multiconfigurational self-consistent field (MCSCF) reference functions for the subsequent MRCI. We further find that only one set of 3Σ+ and 1Σ+ states are present when using complete active space SCF (CASSCF) reference functions. No 1,3Π states were found to be bound by the present calculations. Furthermore, when employing very diffuse basis sets, we found that there are many states lying in the vicinity of the neutral species due to the large number of the neutral virtual molecular Hartree-Fock orbitals with energies close to the zero. On the other hand, when additionally considering that the rotational constant of the parent neutral species is about 0.02 meV, only a smaller number of such states have a computed binding energy above this threshold and could therefore be considered physically viable. We therefore surmise that the present calculations are helping us to shed more light on the physical features of these, very special anionic states of the title molecule, states also present in a larger class of linear carbon chain with supercritical dipoles.

Abstract: Publication date: Available online 17 July 2019Source: Advances in Quantum ChemistryAuthor(s): Gabriel Breuil, Kaltrina Shehu, Elise Lognon, Sylvain Pitié, Benjamin Lasorne, Thibaud EtienneAbstractIn this chapter we discuss the reliability of two computational methods (numerical integration on Cartesian grids and population analysis) used for evaluating scalar quantities related to the nature of electronic transitions. These descriptors are integrals of charge density functions built from the detachment and attachment density matrices projected onto the Euclidean space using a finite basis of orbitals. While the numerical integration on Cartesian grids is easily considered to be converged for medium-sized density grids, the population analysis approximation to the numerical integration values is diagnosed using 8 tests performed on 59 molecules with a combination of 15 Gaussian basis sets and 6 exchange-correlation functionals.

Abstract: Publication date: Available online 10 July 2019Source: Advances in Quantum ChemistryAuthor(s): Luis Enrique Aguilar Suarez, R.K. Kathir, Enrico Siagri, Remco W.A. Havenith, Shirin FarajiAbstractSinglet fission has been explored as an alternative mechanism to enhance the performance of solar cells. In this work, we use a nonorthogonal configuration interaction approach to study the singlet fission process in solid 2-methylene-2H-indene, an identified potential singlet fission molecule. Results of the electronic coupling calculations in pairs of molecules show that this molecule is suitable for the efficient formation of the 1TT state (≈40 meV). We report, for the first time, a comparison of the nonorthogonal configuration interaction approach with two other theoretical methodologies: restricted active space with two spin flips and the ab initio Frenkel–Davydov exciton model.

Abstract: Publication date: Available online 10 July 2019Source: Advances in Quantum ChemistryAuthor(s): Remigio Cabrera-Trujillo, Stephan P.A. Sauer, John R. Sabin, Jens OddershedeAbstractWe present dipole oscillator strength-dependent properties such as sum rules, dipole polarizability, mean excitation energy, and stopping cross section as a function of the ionic charge of C, F, Si, and Cl atoms. The excitation spectra and the dipole oscillator strengths are obtained by means of the time-dependent Hartree–Fock approximation. We report the sum rules, Sk, from −6 ≤ k ≤ 2 and the logarithmic sum rule Lk = dSk/dk as a function of the ionic charge −1 ≤ q ≤ Z − 1 with Z being the nuclear charge. The contributions from the bound and continuum states to all sum rules are analyzed as a function of k and charge of the cation. The study allows us to determine a scaling behavior of the bound and continuum state contributions in terms of the cation number of electrons and nuclei charge for k ≤ 0. We propose a new way of determining orbital mean excitation energy as the difference between the mean excitation energy of two neighboring cationic states of an atom. This procedure allows to obtain all orbital mean excitation energy for the four atoms within the time-dependent Hartree–Fock approximation, thus effectively including electronic correlation in the orbital mean excitation energy. As a result, the mean excitation energy within a shell differs for each electron. Wherever possible, we compare with available data in the literature finding excellent agreement.

Abstract: Publication date: Available online 29 June 2019Source: Advances in Quantum ChemistryAuthor(s): Stephan P.A. Sauer, John R. Sabin, Jens OddershedeAbstractWe present a review of calculations of mean excitation energies of small molecules, atoms and their ions using the Random-Phase Approximation. We discuss the relationship with other calculations and we propose several simple rules that may be used to estimate mean excitation energies of cations and singly charged anions. We conclude that the accuracy of the mean excitation energies obtained using this method in terms of choice of basis sets and inclusion of electron correlation is enough to obtain experimental accuracy of stopping powers of gas phase small molecules, atoms and their ions.

Abstract: Publication date: Available online 27 June 2019Source: Advances in Quantum ChemistryAuthor(s): Cecilia Coletti, Vincenzo Aquilanti, Federico PalazzettiAbstractIn this survey we account for basic mathematical ingredients for dealing with quantum chemical problems. We focus on comprehensive previous work (Coletti et al., 2013, pp. 74–127, Ref. 1) documenting relationships with the Askey scheme, a classification of the orthogonal polynomials sets of hypergeometric type. A reduction of the scheme is proposed individuating nine fundamental functional sets which have their counterparts in quantum mechanics; they occur in the general Kepler–Coulomb problem: as well known basis sets for expansions of orbitals in quantum chemistry and in the treatment of specific atomic and molecular applications. A novelty of the approach, with respect to this extensively covered topic, is the establishment of this representation for Kravchuk polynomials, on the mathematical side and, correspondingly, of the spherical top wavefunctions on the physical side: the latter are explicitly connected with the Wigner's rotation matrix of angular momentum theory. Novel presentations of the Askey-type hierarchy of hypergeometrical orthonormal basis sets relevant in quantum mechanics and the relationships connecting them are established by powerful tools: from the mathematical viewpoint, the Askey duality and asymptotic analysis; from a physical viewpoint, the symmetry by transposition and semiclassical limits. A new three-by-three matrix visualization illustrates the set of correspondences to assist further work on the path connecting classical and quantum physics and discrete and continuous mathematics that is presented elsewhere (Coletti et al., 2019, Ref. 46). This is pictured as a bridge where Racah polynomials and harmonic oscillator wavefunctions are the corner stones, while the rotation matrix of Wigner is the keystone. Here, the path is illustrated as the steps of a stairway that we define as the Jacobi ladder, where going up and down is insightful for applications. Extension to the full Askey scheme, object of future work, is briefly noted: some reference is made to our recent progress in spherical to hyperspherical manifold representations involving the q-scheme of Askey and related orthogonal polynomials as possible orthonormal basis sets in quantum mechanics.

Abstract: Publication date: Available online 20 June 2019Source: Advances in Quantum ChemistryAuthor(s): Daniel Gebremedhin, Charles Weatherford, Brian WilsonAbstractIn multiple-scattering methods, overlap integrals of cluster wavefunctions for an interstitial region, which lies inside the Watson sphere and outside all the enclosed ionspheres, are discussed. When the potential inside this interstitial region is taken to be constant, and hence, obeys the Helmholtz equation, the resulting solutions are known to involve Bessel functions. Normalizing the cluster wavefuntions inside this intricate region naturally leads to two-center integrals of various Bessel-type functions. In this article, all of the numerous types of integrals that might arise are exhaustively presented. Analytical expressions that are suitable for efficient computation of the overlap integrals are worked out by employing known addition theorems for the Bessel functions. These integrals require careful attention as they otherwise lead to an artificial singularity that may not cancel.

Abstract: Publication date: Available online 19 June 2019Source: Advances in Quantum ChemistryAuthor(s): Juan Martín Randazzo, Lorenzo Ugo AncaraniAbstractSturmian functions (SF) constitute a very useful spectral tool to deal with bound states or break-up problems in atomic and molecular physics. In their standard form for the three-body case, the radial part of the wave function is proposed as an expansion in products of one-dimensional generalized SF (GSF). Here, we present an alternative spectral approach. It is based on solutions of a two-dimensional Sturmian eigenvalue problem that is solved with a finite set of one-dimensional GSF. The resulting 2DSF basis set functions depend simultaneously on two interparticle distances and possess a natural reordering. Through calculations of the Helium ground and 41F excited states energy, we compare the efficiency of the two equivalent sets of functions. The superiority of the two-dimensional approach demonstrated here should be particularly useful to reduce computational costs for applications in the continuum regime.

Abstract: Publication date: Available online 16 May 2019Source: Advances in Quantum ChemistryAuthor(s): Pierre-François Loos, Anthony Scemama, Michel CaffarelAbstractWe 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. UgaldeAbstractThe 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. BischoffAbstractMultiresolution 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 SarsaAbstractThe 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. KucharskiAbstractThe 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 MamminoAbstractHyperguinones 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 YamaguchiAbstractAtmospheric 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. BrändasAbstractDarwinian 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. SergaAbstractWe 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 TakahashiAbstractX-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. TernovskyAbstractIn 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 KhetseliusAbstractThe 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 OkopińskaAbstractStudying 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. TkachAbstractIn 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. TernovskyAbstractWe 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. GlushkovAbstractThe 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 MourikAbstractWe 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 ShigetaAbstractBiological 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.