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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.