Authors:Stine T. Olsen; Asbjørn Bols; Thorsten Hansen; Kurt V. Mikkelsen Pages: 53 - 102 Abstract: Publication date: 2017 Source:Advances in Quantum Chemistry, Volume 75 Author(s): Stine T. Olsen, Asbjørn Bols, Thorsten Hansen, Kurt V. Mikkelsen We consider two different theoretical methods for investigating molecules sandwiched between electrodes and nanoparticles. One method is a heterogeneous and structured dielectric model for describing the physical situation of a molecule located between electrodes where the molecule is described by quantum mechanics and the electrodes as heterogeneous dielectric media. The interactions between the quantum subsystem and the dielectric media are given by polarization terms that are included in the quantum mechanical equations. The second method is a theoretical method that describes the effects of nanoparticles on molecular properties of molecules, and it is based on a quantum mechanical/molecular mechanics (QM/MM) response method. This method enables us to calculate frequency-dependent molecular properties of molecules interacting with nanoparticles having specific structures. Thereby, we are able to investigate how the specific structures of the nanoparticles affect the molecular properties of the molecules located next to or between nanoparticles. These methods enable us to perform calculations of different electronic and redox states of molecules and their molecular properties between nanoparticles or electrodes. The presented methods make it possible to investigate electron transport in molecular devices.

Authors:John W. Perram Pages: 103 - 116 Abstract: Publication date: 2017 Source:Advances in Quantum Chemistry, Volume 75 Author(s): John W. Perram For mechanical systems subject to time dependent, holonomic constraints, the principle of virtual work is apparently required to derive D'Alembert's equations of motion. This is in contrast to situations where the constraints are time independent, where the equations of motion can be derived by standard arguments using vector calculus and linear algebra. Attempts to apply this method when some of the constraints have an explicit time dependence lead extra terms in the equations of motion. These apparent terms are removed by appealing to the principle of virtual work. In this work we show that, for the cases of universal, revolute, and telescopic joints between two rigid bodies of which one's motion is specified externally, these terms apparently vanish identically when the computer algebra system Mathematica is used. This leads us to provide lengthy but elementary analytic proofs that the extra terms vanish identically for the three cases which, we believe, are exhaustive for real mechanical system.

Authors:Michael Sabio; Sid Topiol Pages: 147 - 174 Abstract: Publication date: 2017 Source:Advances in Quantum Chemistry, Volume 75 Author(s): Michael Sabio, Sid Topiol X-ray structures for ligand-modulated GPCRs were not available until 2007 and were limited to class A GPCRs. The recent availability of X-ray structures for mGluR5, a class C GPCR, provides a valuable tool for understanding drug action. For mGluR5, pairs of extremely closely related ligands have been shown to have opposite (activating PAM vs inactivating NAM) pharmacological switching effects, which have defied understanding in drug-discovery studies. Using MM and QM calculations, we have identified a cluster of mGluR5 residues that provide a pressure point that is sensitive to these small NAM/PAM differences. These residues reside in the extracellular side of the transmembrane region of the mGluR5 protein on helices 5 and 6, which for class A GPCRs are known to require conformational changes in the intracellular region for activation to occur. We also find that docking studies presented herein provide a clear explanation for the highly efficient mGluR5-NAM MPEP in terms of its interactions with the protein.

Authors:Eric A. Buchanan; Zdeněk Havlas; Josef Michl Pages: 175 - 227 Abstract: Publication date: 2017 Source:Advances in Quantum Chemistry, Volume 75 Author(s): Eric A. Buchanan, Zdeněk Havlas, Josef Michl After a brief review of electronic aspects of singlet fission, we describe a systematic simplification of the frontier orbital (HOMO/LUMO) model of singlet fission and Davydov splitting in a pair of rigid molecules. In both instances, the model includes electron configurations representing local singlet excitation on either chromophore, charge transfer in either direction, and triplet excitation in both chromophores (biexciton). The resulting equations are simple enough to permit complete searches for local extrema of the square of the electronic matrix element and to evaluate the effect of intermolecular interactions on the exoergicity of singlet fission and on the biexciton binding energy in the six-dimensional space of rigid dimer geometries. The procedure is illustrated on results for the six best geometries for dimers of ethylene and of an indigoid heterocycle with 24 carbon, nitrogen, and oxygen atoms.

Authors:Jens Oddershede; John F. Ogilvie; Stephan P.A. Sauer; John R. Sabin Pages: 229 - 241 Abstract: Publication date: 2017 Source:Advances in Quantum Chemistry, Volume 75 Author(s): Jens Oddershede, John F. Ogilvie, Stephan P.A. Sauer, John R. Sabin Calculations of the continuum contributions to dipole oscillator sum rules for hydrogen are performed using both exact and basis-set representations of the stick spectra of the continuum wave function. We show that the same results are obtained for the sum rules in both cases, but that the convergence toward the final results with increasing excitation energies included in the sum over states is slower in the basis-set cases when we use the best basis. We argue also that this conclusion most likely holds also for larger atoms or molecules.

Authors:Jan Linderberg Pages: 243 - 266 Abstract: Publication date: 2017 Source:Advances in Quantum Chemistry, Volume 75 Author(s): Jan Linderberg Properties of electronic systems are a principal concern for quantum chemical theory and calculations and are succinctly expressed in terms of various Green functions, also termed propagators or response functions. Spherical symmetry offers simplifications and analytical options that will be explored in this chapter. A proper many-electron theory in the relativistic form is lacking, but the use of the Dirac equation and four-component functions provides certain advantages in the formulation of the electron propagator. Energy functionals are developed for an inhomogeneous system with spherical symmetry. It is also shown how approximate response functions can be obtained for electric and magnetic perturbations.

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

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

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

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

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

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

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

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

Authors:Barak Hirshberg; R. Benny Gerber Abstract: Publication date: Available online 7 March 2017 Source:Advances in Quantum Chemistry Author(s): Barak Hirshberg, R. Benny Gerber Methods that can accurately describe the quantum dynamics of large molecular systems have many potential applications. Since numerical solution of the time-dependent Schrödinger equation is only possible for systems with very few atoms, approximate methods are essential. This paper describes the development of such methods for this challenging time-dependent many-body quantum mechanical problem. Specifically, we focus on the development of mean-field theories, to which Mark Ratner has contributed greatly over the years, such as the time-dependent self-consistent field method, mixed quantum–classical methods, and the classical separable potentials method. The advantages and limitations of the different variants of mean-field theories are highlighted. Recent developments, aimed at applying mean-field methods for large systems, and their applications are presented. Issues where further methodological advancement is desirable are discussed. Examining the tools available so far, and the recent progress, we conclude there are promising perspectives for future development of mean-field theories for quantum dynamics with applications to realistic systems in important chemical and physical processes.

Authors:Isidore Last; Joshua Jortner Abstract: Publication date: Available online 24 February 2017 Source:Advances in Quantum Chemistry Author(s): Isidore Last, Joshua Jortner Novel features of analysis and control of nanoplasma dynamics are manifested in elemental and molecular clusters irradiated by a near-infrared intense ultraintense laser pulse, where the laser energy pumped to the nanoplasma electrons is transferred to the cluster ions by Coulomb explosion (CE) and by electron–ion impact mechanisms. The contribution of the electron–ion impact was studied by a microscopic model, together with molecular dynamics simulations of the electron–ion kinetic energy transfer in the course of the electron–ion collision events. The simulations were performed for ionic (He+)N, (Ne+)N, and (Ne4+)N clusters containing weakly charged ions, as well as for (H+)N and (He2+)N clusters consisting of bare nuclei and electrons. The clusters were subjected to femtosecond (τ =30fs) laser pulses with peak intensities of I M =1015–1017 Wcm−2. The force F imp, generated by the electron impact kinetic energy transfer was found to decrease strongly with the exploding cluster radius R, i.e., F imp ∝ R − η , with η ~4–6. The electron impact energy transferred to the periphery ions of clusters (in the size domain of N =104–106) made up less than 2.5% of the maximal ion energy. The laser energy transfer to the nanoplasma involves the dominating contribution of the Coulomb energy and a minor contribution of the electron impact, with the cluster expansion and decay being governed by the CE mechanism.

Authors:Adam P. Ashwell; Mark A. Ratner; George C. Schatz Abstract: Publication date: Available online 15 February 2017 Source:Advances in Quantum Chemistry Author(s): Adam P. Ashwell, Mark A. Ratner, George C. Schatz We present a detailed study of the impact of ligand passivation on the electronic structures and optical properties of plasmonic Ag nanoclusters using density functional theory (DFT) and time-dependent density functional theory (TD-DFT). The clusters studied are A g 13 5 + , A g 25 S H 18 − , A g 25 N H 2 18 − , A g 32 14 + , and A g 44 S H 30 4 − . We find that the highest occupied ligand orbitals from S (3p) and N (2p) appear just above the conduction band, and this leads to significant ligand-to-metal charge transfer transitions at high energies. Dielectric screening associated with ligand passivation results in reduced HOMO–LUMO gaps and in an increased gap between the HOMO and the valence band associated with the Ag 4d orbitals. Ligand field effects result in splitting of plasmonic peaks, leading to reduced mixing between nearby single-particle excitations. The magnitude of these effects is found to decrease when thiolate ligands are replaced with amine ligands. We also find that, in the case of the A g 44 S H 30 4 − cluster, the ligands localize plasmonic excitations into the core of the cluster.

Authors:Arie Landau; Debarati Bhattacharya; Idan Haritan; Anael Ben-Asher; Nimrod Moiseyev Abstract: Publication date: Available online 7 December 2016 Source:Advances in Quantum Chemistry Author(s): Arie Landau, Debarati Bhattacharya, Idan Haritan, Anael Ben-Asher, Nimrod Moiseyev Situations in which a molecule in a given configuration is electronically bound while in another configuration is autoionized are widespread in nature. In these situations, the change in molecular configuration due to nuclear dynamics is the reason the molecule emits free electrons to the surrounding, ie, autoionizes. Such a situation may even happen to molecules in their ground electronic state, for example, it can happen to H 2 − : at some bond lengths, the molecule is autoionized, at some bond lengths its ground state is bound, and at sufficiently large internuclear distances a stable hydrogen atom and a stable negative charged hydrogen, H−, in their ground electronic states, are obtained. In addition, such situations can be seen in electronic scattering from molecules and in cold molecular collisions. For example, in a collision between electronically excited helium atom and a hydrogen molecule in its ground state, metastable complex He*–H2 is formed. As time passes this complex decays to helium in its ground state, H 2 + , and a free electron. In all these cases the molecular dynamics play a key role as the molecules are autoionized. This poses a problem, since the Born–Oppenheimer (BO) approximation is applicable only when the decay process due to ionization is ignored. Therefore, in order to study molecular dynamics and take autoionization into consideration, one should calculate the potential energy surfaces (PES) by imposing outgoing boundary conditions (OBCs) on the electronic wavefunctions. Doing so, the electronic molecular spectrum will be discrete (no continuum), where the PES will be either real (bound electronic states) or complex (metastable molecules that ionize). These complex potential energy surfaces (CPES) are what enables one to take into consideration the electronic autoionization in the molecular dynamics. Nevertheless, calculating CPES by standard quantum chemistry packages (SQCPs) is not a trivial task, since they were designed to calculate bound electronic excited states. Bound states lie on the real plane, unlike metastable states (resonances); therefore, explicit calculation of resonances requires modification of SQCPs. Several different possibilities for calculating CPES by modifying SQCPs are discussed in this review. Yet, the holy grail is to be able to use SQCPs, which are highly efficient codes, for calculating resonances without changing the codes. The main focus of this review will be on new methods, we have developed, that enable calculating CPESs from SQCPs, ie, without any modifications of standard codes. Such methods allow the calculations of polyatomic CPESs, as indicated by our preliminary results.

Authors:Vipin Srivastava; Suchitra Sampath Abstract: Publication date: Available online 5 October 2016 Source:Advances in Quantum Chemistry Author(s): Vipin Srivastava, Suchitra Sampath We present some initial results to show that Löwdin's two orthogonalization schemes, namely Symmetric and Canonical, can help us to understand certain important aspects of the brain's competence to learn and memorize. We propose that these orthogonalizations may constitute the physiological actions that the brain may perform to deal with certain types of memories.

Authors:Ingvar Lindgren Abstract: Publication date: Available online 12 September 2016 Source:Advances in Quantum Chemistry Author(s): Ingvar Lindgren A new form of time-dependent perturbation theory has been developed based upon the covariant-evolution operator (CEO), previously introduced by us. This has made it possible to combine time-dependent perturbations, like the quantum-electrodynamical (QED) perturbations, with time-independent interactions, like the Coulomb interaction (electron correlation) in a single perturbation expansion. For the first time quantum-electrodynamical perturbations can then be combined with electron correlation beyond second order. The experimental accuracy is in many cases so high that these effects have become significant. A numerical scheme has been developed where first-order QED effects are combined with the electron correlation and applied to highly charged helium-like ions. This scheme contains the dominating part of the higher-order QED effects and has been applied to highly charged helium-like ions, for which effects beyond second order (two-photon effects) have for the first time been evaluated. The calculations have been performed using Feynman as well as Coulomb gauge. In evaluating effects beyond second order involving radiative QED it was necessary to employ the Coulomb gauge.

Authors:Orlando Tapia Abstract: Publication date: Available online 30 August 2016 Source:Advances in Quantum Chemistry Author(s): Orlando Tapia The photonic scheme provides an abstract perspective to describing chemical and physical processes; it is well adapted for biologically sustained processes too. The scheme is used to help analyze semiclassic pictures in order for a deeper understanding of natural processes to arise. A q-state is not an object (eg, a molecule) but convoluted with a photon field, it hangs somehow on sensitive surfaces revealing an image constructed from q-events: these q-events are joint q-energy and angular momentum bridging probe-to-probing systems. Exchanges between physical states and probing ones establish a reality for a q-state. Thus, in the photonic scheme, a q-state may emerge as an image if appropriately recorded via q-events. Initially collected q-events seem to indicate a random process. However, after gathering these q-events in sufficient numbers, as in a two-slit example, a supportive image develops corresponding more and more to what is known as an interference pattern. Moreover, the unlocking of a spin-triplet state is used to illustrate applications: for instance, the opening required a path starting from a parent spin-singlet excited electronic state. A low-frequency multiphoton mechanism regulated by conservation laws permits the description of a triplet state activation. Of course, the materiality sustaining a q-state must transfer information that is richer than that a classical particle impact would convey. The use we make of quantum mechanics is basically the same that everyone does though without current interpretations; inclusion of photon fields makes the difference by providing quantum mechanisms to accomplish measurements.

Authors:Karen Abstract: Publication date: Available online 25 August 2016 Source:Advances in Quantum Chemistry Author(s): Dževad Belkić, Karen Belkić High-resolution quantitative signal analysis using the fast Padé transform (FPT) is applied to a specific problem (cerebral asphyxia) within magnetic resonance spectroscopy (MRS) for in vivo pediatric neurodiagnostics. Potential broader implications for the presented methodology are indicated for interdisciplinary research, including quantum chemistry. An iterative averaging procedure is introduced and validated, which could be automatically built-in, to provide denoised spectra, so vitally needed in clinical MRS. The full equivalence of nonparametrically and parametrically generated total shape spectra in the FPT is demonstrated. With subsequent parametric analysis, exceedingly dense component spectra are reliably reconstructed, both with the mixture of absorption and dispersion components (“usual” mode) and by setting the reconstructed phases to zero, in order to eliminate interference effects (“ersatz” mode). Via the ersatz components, the consequences and extent of the said interference effect are distinctly visualized for every overlap of closely located resonances or hidden resonances. Practical implementation of Padé-optimized MRS from in vivo encoded time signals in the clinical setting is hereby demonstrated.

Authors:Sven Larsson Abstract: Publication date: Available online 3 August 2016 Source:Advances in Quantum Chemistry Author(s): Sven Larsson Thirty years after the discovery of high temperature (HT) superconductivity (SC), no by all accepted theory exists. The Bardeen, Cooper, Schrieffer (BCS) model, hewed into the Bloch theory for metals, is unfit for local systems such as cuprates and organic superconductors. In this chapter, we will use a theory that dates back to Landau and Pekar, but we will avoid the effective mass approach by using a total free energy model, as designed for electron transfer problems by Marcus and Jortner. A diffusion equation is used to derive the resistivity in the local case. The original definition of Hubbard U by Mott as a metal-to-metal (or molecule-to-molecule) charge transfer energy will be updated by including the neglected negative terms. It will be shown that the absorption at 2eV in the cuprates is indeed due to Cu–Cu charge transfer, identical to the Hubbard U or Mott transition. The model accounts for bond-length fluctuations due to occupancy of d-orbitals (extended over the ligands), or in the molecular case the π orbitals, and this makes it necessary to make a distinction between adiabatic and vertical Hubbard U. U vert =1.5–3eV while U ad may be a few hundred times smaller. Organic SC in aromatic hydrocarbons will be shortly reviewed and found consistent with the general model. Finally, we will discuss SC in tungsten bronzes discovered in 1964 by Matthias.

Authors:Marcelo Hidalgo Cardenuto; Kaline Coutinho; Sylvio Canuto Abstract: Publication date: Available online 26 July 2016 Source:Advances in Quantum Chemistry Author(s): Marcelo Hidalgo Cardenuto, Kaline Coutinho, Sylvio Canuto Combining Statistical Mechanics and Quantum Chemistry it is possible to study solvent effects in spectroscopy and understand chemical reactivity in solution. However, once the thermodynamic condition can be incorporated, it is possible to advance in other important regions of the phase diagram. Hence supercritical fluids with temperature and pressure beyond the critical point can be studied. Supercritical fluids are of interest both for their remarkable physical chemical properties and the industrial interests. The critical point, however, is apparently not a thermodynamic condition amenable to quantum chemical calculations. This is because it is characterized by intense fluctuations and density inhomogeneity. The correlation length becomes infinite at the critical point. But for points close enough to the critical point the fluctuations disappear, and it is possible to get very close to this rather interesting point in the phase diagram. In this work we review some results for the spectroscopy of molecular systems in the supercritical region and the static dipole polarizability and the refractive index of Ar only 2K above the critical point. The refractive index presents some peculiarities, but it is well behaved as we pass at the critical point. The numerical value obtained of 1.083 is in very good agreement with the experimental value of 1.086. We contend that the proximity of the critical point is amenable to theoretical quantum mechanical studies possibly accessing new physical phenomena.

Authors:Lawrence J. Dunne; Erkki J. Brändas; Hazel Cox Abstract: Publication date: Available online 25 July 2016 Source:Advances in Quantum Chemistry Author(s): Lawrence J. Dunne, Erkki J. Brändas, Hazel Cox In this chapter we give a selective review of our work on the role of electron correlation in the theory of high-temperature superconductivity (HTSC). The question of how electronic repulsions might give rise to off-diagonal long-range order (ODLRO) in high-temperature superconductors is currently one of the key questions in the theory of condensed matter. This chapter argues that the key to understanding the occurrence of HTSC in cuprates is to be found in the Bohm–Pines Hamiltonian, modified to include a polarizable dielectric background. The approach uses reduced electronic density matrices and discusses how these can be used to understand whether ODLRO giving rise to superconductivity might arise from a Bohm–Pines-type potential which is comprised of a weak long-range attractive tail and a much stronger short-range repulsive Coulomb interaction. This allows time-reversed electron pairs to undergo a superconducting condensation on alternant cuprate lattices. Thus, a detailed summary is given of the arguments that such interacting electrons can cooperate to produce a superconducting state in which time-reversed pairs of electrons effectively avoid the repulsive hard-core of the interelectronic Coulomb interaction but reside on average in the attractive well of the effective potential. In a superconductor the plasma wave function becomes the longitudinal component of a massive photon by the Anderson–Higgs mechanism. The alternant cuprate lattice structure is the key to achieving HTSC in cuprates with d x 2 − y 2 symmetry condensate symmetry.

Authors:David A. Micha Abstract: Publication date: Available online 1 July 2016 Source:Advances in Quantum Chemistry Author(s): David A. Micha The subject of this contribution is how projection operators can be constructed to treat a variety of time-dependent phenomena involving interacting molecules, and to treat the dissipative dynamics of a localized subsystem in a large environment. It develops partitioning methods in a functional space of wavefunctions introduced to construct molecular effective potentials and long-lived states from distortion, adiabatic, and fast motion states. It also gives a treatment starting from the statistical density operator, for partitioning in a many-atom system undergoing dissipative dynamics, and shows how to construct contracted density operators with selected total system states, or reduced density operators for localized phenomena in a primary region. The presentation displays related mathematical procedures useful for partitioning of both wavefunctions and density operators and for derivation of their equations of motion.

Authors:Héctor H. Corzo; J.V. Ortiz Abstract: Publication date: Available online 1 July 2016 Source:Advances in Quantum Chemistry Author(s): Héctor H. Corzo, J.V. Ortiz Electron propagator theory is an efficient means to accurately calculating electron binding energies and associated Dyson orbitals that is systematically improvable and easily interpreted in terms of familiar concepts of valence theory. After a brief discussion of the physical meaning of the poles and residues of the electron propagator, the Dyson quasiparticle equation is derived. Practical approximations of the self-energy operator in common use are defined in terms of the elements of the Hermitian superoperator Hamiltonian matrix. Methods that retain select self-energy terms in all orders of the fluctuation potential include the two-particle-one-hole Tamm–Dancoff approximation, the renormalized third-order method, the third-order algebraic diagrammatic construction, and the renormalized, nondiagonal second-order approximation. Methods based on diagonal second-order and third-order elements of the self-energy matrix, such as the diagonal second-order, diagonal third-order, outer valence Green's function, partial third-order, and renormalized partial third-order approximations, provide efficient alternatives. Recent numerical tests on valence, vertical ionization energies of representative, small molecules, and a comparison of arithmetic and memory requirements provide guidance to users of electron propagator software. A survey of recent applications and extensions illustrates the versatility and interpretive power of electron propagator methodology.

Authors:Berrondo Abstract: Publication date: Available online 25 June 2016 Source:Advances in Quantum Chemistry Author(s): M. Berrondo, J. Récamier The energy transfer between vibrational and translational degrees of freedom during an inelastic collision between two molecules induces quantum squeezing in the vibrational molecular coordinate under very diverse circumstances. In this chapter, we present the relevant calculation for the very simple case of an atom–diatomic collinear transition, the Landau–Teller model. Both the uncertainty of the vibrational coordinate and the Husimi function show clear evidence of quantum squeezing. Our model treats the relative translation of the colliding species as a classical variable. The vibrational motion of the diatomic molecule is treated quantum mechanically in terms of the evolution operator and coherent states. The corresponding classical and quantum equations of motion are coupled. We first consider the squeezing of a coherent vibrational state where we include the dynamic evolution of the Husimi function. The second case corresponds to an initial thermal distribution of vibrational states where we plot the position uncertainty for the squeezed vibrational state.

Authors:Jan Linderberg; Yngve Erkki John Sabin Abstract: Publication date: Available online 14 June 2016 Source:Advances in Quantum Chemistry Author(s): Jan Linderberg, Yngve Öhrn, Erkki J. Brändas, John R. Sabin

Authors:Carlos F. Bunge Abstract: Publication date: Available online 8 June 2016 Source:Advances in Quantum Chemistry Author(s): Carlos F. Bunge Per-Olov Löwdin was an inspiring and compelling teacher. His most prominent papers were written more than 50 years ago, whereas since then quantum chemistry, its software, and its computers have changed almost beyond recognition. In accurate calculations with truncation energy errors, an important part of Per-Olov’s themes and thoughts appears highly relevant today in applications to atoms and small molecules. My purpose here is to place projection operators, natural orbitals, error bounds, and the variational theorem for finite Hermitian matrices, in the light of current challenges in the field.

Authors:Jan Linderberg Abstract: Publication date: Available online 2 June 2016 Source:Advances in Quantum Chemistry Author(s): Jan Linderberg Attempting to survey and review some developments in the design and use of atomic basis sets for molecular electronic structure calculations from the perspective of Per-Olov Löwdin's contributions this chapter is offered as a contribution to the celebration of the centennial of his birth.

Authors:Yngve Abstract: Publication date: Available online 31 May 2016 Source:Advances in Quantum Chemistry Author(s): Yngve Öhrn This account of the time-dependent variational principle is presented in memory of Per-Olov Löwdin on the occasion of the centenary of his birth. The material presented here has been published as part of a book chapter, 1 and is reintroduced here in recognition of Löwdin's interest in this topic. 2 Also the importance of the use of coherent state parameters as functions of time is emphasized, as well as the connection to the electron nuclear dynamics (END) theory. 3

Authors:Cleanthes A. Nicolaides Abstract: Publication date: Available online 30 April 2016 Source:Advances in Quantum Chemistry Author(s): Cleanthes A. Nicolaides I start by thanking Erkki Brändas and Jack Sabin for inviting me to contribute to this special volume commemorating the 100th birthday of Per-Olov Löwdin. Their initiative adds to previous ones involving conferences and books that have been dedicated to him, all expressing the respect and admiration that Löwdin inspired throughout his scientific career in his associates and professional colleagues. Although there are many people who are better qualified to comment on Löwdin's personality and achievements, I take this opportunity to state briefly my impressions of him. I met Löwdin only a few times during the 1970s and 1980s, in conferences and in Sanibel symposia, starting with the conference on “The Future of Quantum Chemistry” that was held in Dalseter, Norway, Sept. 1–5, 1976, organized by J.-L. Calais and O. Goscinski to celebrate his 60th birthday. Those encounters (which included a couple of cocktail parties and soccer games where he played goalie) led to a nice rapport, even though I was much younger. They were sufficient to leave me with the best of impressions about his openness, about his interest in assisting young scientists from all over the world, and about his scientific inquisitiveness and aim for mathematical clarity and justification. Löwdin's scientific and organizational achievements were instrumental in advancing the cause of quantum chemistry in Sweden as well as internationally, especially during the 1950s and 1960s. For example, the Uppsala summer schools and the Sanibel winter symposia became institutions. He is remembered with respect and affection not only for his research papers but also for his exceptional activity which accelerated the recognition of quantum chemistry as a distinct scientific discipline with a diverse community of theoretical scientists. As a member of this community, I feel lucky for the opportunity given to me by the Editors to contribute the paper which follows. The paper summarizes elements of theories and computational methods that we have constructed and applied over the years for the nonperturbative solution of many-electron problems (MEPs), in the absence or presence of strong external fields, concerning resonance/nonstationary states with a variety of electronic structures. Using brief arguments and comments, I explain how these MEPs are solvable in terms of practical time-independent or time-dependent methods, which are based on single- or multistate Hermitian or non-Hermitian formulations. The latter result from the complex eigenvalue Schrödinger equation (CESE) theory. The CESE has been derived, for field free as well as for field-induced resonances, by starting from Fano's 1961 discrete-continuum standing-wave superposition, and by imposing outgoing-wave boundary conditions on the resulting solution. Regularization is effected via the use of complex coordinates for the orbitals of the outgoing electron(s) in each channel. The Hamiltonian coordinates remain real. The computational framework emphasizes the use of appropriate forms of the trial wavefunctions and the choice of function spaces according to the state- and property-specific methodology, using either nonrelativistic or relativistic Hamiltonians. In most cases, the bound part of excited wavefunctions is obtained via state-specific “HF or MCHF plus selected parts of electron correlation” schemes. This approach was first introduced to the theory of multiply excited and inner-hole autoionizing states in 1972, and its feasibility was demonstrated even in cases of multiply excited negative-ion scattering resonances. For problems of states interacting with strong and/or ultrashort pulses, the many-electron time-dependent Schrödinger equation is solved via the state-specific expansion approach. Applications have produced a plethora of numerical data that either compare favorably with measurements or constitute testable predictions of properties of N-electron field-free and field-induced nonstationary states.