Basis Of Quantum Mechanics Research Articles

Direct Space Decomposition of ELI-D: Interplay of Charge Density and Pair-Volume Function for Different Bonding Situations

The topological features, i.e., gradients and curvatures of the same-spin electron pair restricted electron localizability indicator (ELI-D) in position space are analyzed in terms of those of the electron density and the pair-volume function. The analysis of the topology of these constituent functions and their interplay on ELI-D attractor formation for a number of molecules representing chemically different bonding situations allows distinguishing between different chemical bonding scenarios on a quantum mechanical basis without the recourse to orbitals. The occurrence of the Laplacian of the electron density in the expression for the Laplacian of ELI-D allows us to establish a physical link between electron localizability and electron pairing as displayed by ELI-D and the role of Laplacian of the density in this context.

Revealing the Beauty of Molecules

Revealing the Beauty of Molecules

Characterization of asphaltene structure using atomic force microscopy

In this study, at the first stage, asphaltene was extracted. The roughness of asphaltene coating at different rpm was studied using an image analysis confocal microscopy. The basics of quantum mechanics and statistical thermodynamics are used to predict the potential energy and the intermolecular forces of asphaltene molecules. The functional forms for the potential energy and intermolecular forces are evaluated. Our final goal is to be able to observe and determine the surface structures of asphaltene micelles with scanning probe microscopes. So, the focus of the work on these unusual molecules is to characterize their structure, dynamics and thermodynamics and to establish the relationship between these properties and petroleum fluid behaviour. The existence of various nanostructures of asphaltene in petroleum has been extensively discussed. A set of fitted data is used to check the validity of the calculated results. The good agreement between the proposed models and the data is promising.

Deformed quantum mechanics and q-Hermitian operators

Starting on the basis of the non-commutative q-differential calculus, we introduce a generalized q-deformed Schrödinger equation. It can be viewed as the quantum stochastic counterpart of a generalized classical kinetic equation, which reproduces at the equilibrium the well-known q-deformed exponential stationary distribution. In this framework, q-deformed adjoint of an operator and q-Hermitian operator properties occur in a natural way in order to satisfy the basic quantum mechanics assumptions.

CHARACTERIZATION OF ASPHALTENE USING POTENTIAL ENERGY AND NANOCALCULATION

The basics of quantum mechanics and statistical thermodynamics were used to predict the potential energy and intermolecular forces of asphaltene molecules. The parameters associated with the chemical structure were also estimated for a specific asphaltene molecule to predict the Mie potential function. Based on the structural results, a new form of the Virial EOS with Peneloux correction was developed to estimate the density, solubility parameter and a correction factor that accounts for the structural effect of asphaltene. In this way, asphaltenes were considered as polymer-like compounds consisting of aggregates of a monodisperse. Finally, three new correlations were developed to predict the key parameters of asphaltenes, namely structural coefficient, density and solubility as functions of temperature and molecular weight. The correlations facilitate the calculation of the numerical methods of these parameters. These parameters were also compared successfully with the results found by the Soave Redlich Kwong equation of state. Meanwhile, at first the stage asphaltene was extracted and the roughness of the asphaltene coating in different rpm was studied by using of image analysis confocal microscopy.

Topics and methods in condensed matter theory: from basic quantum mechanics to the frontiers of research

I-Introductory Many-Body Physics.- Basic Many-Body Quantum Mechanics.- Adiabatic Switching and Time-Ordered series.- Atomic Shells and Multiplets.- Green's Functions as Thought Experiments.- Hopping Electron Models: an Appetizer.- Many-body Effects in Electron Spectroscopies.- Symmetry in Quantum Physics.- Group Representations for Physicists.- Simpler Uses of Group Theory.- Product of Representations and Further Physical Applications.- More on Green Function Techniques.- Equations of Motion and Further Developments.- Feynman Diagrams for Condensed Matter Physics.- Many-Body Effects and Further Theory.- Non-Equilibrium Theory.- Non-Perturbative Approaches and Applications.- Some Recursion Techniques with Applications.- Aspects of Nonlinear Optics and Many-Photon Effects.- Selected Exact Results in Many-Body Problems.- Quantum Phases.- Pairing from repulsive interactions.- Algebraic Methods.- Appendices.- Appendix 1: Zero-point Energy in a Pillbox.- Appendix II-Character Tables.- Proof of the Wigner-Eckart Theorem.

An Optimized Algebraic Basis for Molecular Potentials

The computation of vibrational spectra of diatomic molecules through the exact diagonalization of algebraically determined matrices based on powers of Morse coordinates is made substantially more efficient by choosing a properly adapted quantum mechanical basis, specifically tuned to the molecular potential. A substantial improvement is achieved while still retaining the full advantage of the simplicity and numerical light-weightedness of an algebraic approach. In the scheme we propose, the basis is parametrized by two quantities which can be adjusted to best suit the molecular potential through a simple minimization procedure.

The GRW model and Bell-like inequalities**This work was supported in part by the Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Italy.

The basics of quantum mechanics with spontaneous localization (GRW model) are rediscussed in the framework of a quantum stochastic process introduced by Ford and Lewis and originated by instantaneous fuzzy space-localization processes superimposed upon an otherwise reversible Schrödinger time evolution.

Towards a possible ab initio molecular mechanics. Transferability of density matrix elements

AbstractMolecular structures are characterized by a large degree of additivity and transferability of various intramolecular interactions determining the shape and energetics of molecules. This property is constantly utilized by the different “molecular mechanics” (MM) schemes which allow one to obtain quite reliable molecular geometries and relative energy values for a wide range of molecular systems, which is especially remarkabke in the light of the simplicity of the assumptions made. Numerous MM schemes presented in the literature use different sets of parameters (force fields, etc.), which are adjusted empirically. The known success of MM models poses two important questions: first, one wishes to understand why do they work at all, and, second, one would like to develop schemes, in which the parameters of MM can be determined theoretically. Such an analysis could also give some deeper insight permitting to predict whether the given MM scheme is expected to be successful if applied to the class of problems actually at hand. From a more pragmatic point of view, having a bridge connecting a quantum mechanical (QM) description of molecular structure with a classical moldel (MM) can help to improve hybrid QM/MM methods by providing a systematic derivation of the form of the junction between the subsystems treated by MM and QM, respectively and by giving a priori estimates of the junction parameters. Our previous studies based on the semiempirical quantum chemical Hamiltonians of MINDO and MNDO types permitted us to draw the conclusion that the success of MM can indeed be understood on the basis of quantum mechanics. The analysis of the geminal‐type wave functions constructed by making use of oriented hybrid orbitals showed that the parameters of the wave function and the energy contributions of the individual bonds are indeed well transferable, in good agreement with the simple chemical picture of the systems studied. It seems to be desirable to develop a similar analysis also at the ab initio level of the theory, because that would connect together the chemical and physical description of molecules and explain the observed transferability of molecular interactions more rigorously than semiempirical theories can do it. On the other hand this treatment might be also useful for developing QM/MM junctions in the cases when the QM part of the systems are described at the ab initio level. We report here results of the first step of this analysis: the geminal parameters expressed in a symmetrically orthogonalized optimized minimal basis set exhibit a degree of stability similar to that observed in the semiempirical case. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

Computational analysis of ordering in higher homologous series of nBAC: The effect of a dielectric medium

A computational analysis of ordering in higher homologous series of p-n-alkylbenzoic acids (nBAC) that have 7 (7BAC) and 9 (9BAC) carbon atoms in the alkyl chain has been carried out on the basis of quantum mechanics and intermolecular forces. The molecular geometry of 7BAC and 9BAC has been constructed on the basis of published crystallographic data with the standard values of bond lengths and bond angles. The evaluation of atomic charge and dipole moment at each atomic center has been carried out through the complete neglect differential overlap (CNDO/2) method. The configurational energy has been computed via the Rayleigh-Schrodinger perturbation method. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration in a dielectric medium at the nematic-isotropic-transition temperature through the use of the Maxwell-Boltzmann formula. It has been observed that there is a considerable rise in the probability of interactions, although the order of preference remains the same. The present article offers theoretical support to the experimental observations. In addition, this provides a new way of looking at the liquid-crystalline molecules in a dielectric medium.

One Hundred Years of Light Quanta (Nobel Lecture)

The Nobel Prize in Physics 2005 falls in the realm of light (see picture; a) classical and b) quantum physics observation of light), and it is awarded to three scientists: Roy Glauber, John Hall and Theodor Hänsch. Roy Glauber succeeded in describing a general method for observing photons. He formulated a theory that gives optics a quantum-mechanical basis.

Dissipative process under a boundary perturbation

A dissipative process in systems subjected to a boundary perturbation is analyzed on the basis of quantum mechanics. We show that the response of the system to the perturbation can be expressed in terms of the first-passage time defined appropriately by quantum mechanics. In other words, the first-passage-time distribution plays the role of the response function in the linear response theory. We apply this formalism to the one-dimensional Anderson model in which a current is introduced at one end of the system and the other is connected to an absorbing wall. We find that the frequency-dependent oscillations of the susceptibility reflect the narrowness of the first-passage-time distribution in disordered systems.

QSAR studies on 1-phenylbenzimidazoles as inhibitors of the platelet-derived growth factor

This work is devoted to the development of quantitative structure–activity relationship (QSAR) models of the biological activity of 123 1-phenylbenzimidazoles as inhibitors of the PDGF receptor. The molecular features are represented by chemical descriptors that have been calculated on geometrical, topological, quantum mechanical, and electronic basis by using CODESSA PRO. The obtained models, linear (multilinear regression) and nonlinear (artificial neural network), are aimed to link the structures to their reported activity log 1/IC 50. The former model can be used for physico-chemical interpretation, while the latter possesses a superior predictive ability.

ORDERING OF A THERMOTROPIC MESOGEN AT PHASE TRANSITION TEMPERATURE — A STATISTICAL APPROACH BASED ON QUANTUM MECHANICS

The molecular ordering of a thermotropic mesogen, 4-alkenyl bicyclohexylnitrile (ALKBCHN), has been carried out on the basis of quantum mechanics and intermolecular forces. The evaluation of atomic charges and dipole moment at each atomic centre has been done through the Complete Neglect Differential Overlap (CNDO/2) method. The configurational energy has been computed using the Rayleigh-Schrodinger perturbation method. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration in a dielectric medium (i.e. non-interacting and non-mesogenic solvent, benzene) at phase transition temperature (364.7 K) using the Maxwell–Boltzmann formula. It has been observed that in dielectric medium the energies/probabilities are redistributed and there is a considerable rise in the probability of interactions, although the order of preference remains the same. An attempt has been made to develop a new and interesting model of mesogen in a dielectric medium. The present article offers a theoretical support to the experimental observations.

Atomic orbitals and their representation: can 3-D computer graphics help conceptual understanding?

Quantum mechanics is a non-intuitive subject. For example, the concept of orbital seems too difficult to be mastered by students who are starting to study it. Various investigations have been done on student's difficulties in understanding basic quantum mechanics. Nevertheless, there are few attempts at probing how student's understanding is influenced by appropriate visualization techniques, which are known to help conceptual understanding. ''Virtual Water'' is a 3-D virtual environment we have designed and built to support the learning of Physics and Chemistry at final high school and first-year university levels. It focuses on the microscopic structure of water and explores, among others, atomic and molecular orbitals. Having asked a group of first-year students of Sciences and Engineering courses at the University of Coimbra, Portugal, to describe how they conceive electrons in atoms we found some common misconceptions. We have tried, with partial success, to overcome them by making students explore our virtual environment. The most relevant characteristics of the virtual environment which contributed to student's conceptual understanding were 3-D perception and navigation.

Atomic orbitals and their representation: can 3-D computer graphics help conceptual understanding?

Quantum mechanics is a non-intuitive subject. For example, the concept of orbital seems too difficult to be mastered by students who are starting to study it. Various investigations have been done on student's difficulties in understanding basic quantum mechanics. Nevertheless, there are few attempts at probing how student's understanding is influenced by appropriate visualization techniques, which are known to help conceptual understanding. ''Virtual Water'' is a 3-D virtual environment we have designed and built to support the learning of Physics and Chemistry at final high school and first-year university levels. It focuses on the microscopic structure of water and explores, among others, atomic and molecular orbitals. Having asked a group of first-year students of Sciences and Engineering courses at the University of Coimbra, Portugal, to describe how they conceive electrons in atoms we found some common misconceptions. We have tried, with partial success, to overcome them by making students explore our virtual environment. The most relevant characteristics of the virtual environment which contributed to student's conceptual understanding were 3-D perception and navigation.

Quantum mechanical basis of conceptual chemistry

Quantum mechanical basis of conceptual chemistry

Quantum mechanics of phase-sensitive amplification in a fiber

In a recent paper [C.J. McKinstrie, S. Radic, Opt. Express 12 (2004) 4973], four schemes were described, which produce phase-sensitive amplification in fibers: Degenerate scalar and vector four-wave mixing (FWM), and phase conjugation (PC) combined with frequency conversion (FC), in either order. In this paper, the basic quantum mechanics of these schemes are discussed. For each scheme, formulas are derived for the field-quadrature and photon-number variances. The effects of polarization misalignment on vector FWM, and the effects of unbalanced conversion on PC combined with FC, are studied. Moderate amounts of these imperfections do not degrade significantly the performances of the aforementioned schemes.

Cognitive and neuropsychological basis for quantum mechanics: Part III

PurposeThis is a continuation of Parts I and II of the paper. In this part it is suggested that microscopic particles behave similarly to macroscopic objects: Features of two entangled particles, having the same “dimension” (kind of feature), may interchange and migrate from one particle to the other while their wave function collapses. In the particular case of electrically charged particles, like an electron and a proton, the migrating features that are interchanged between the particles, may be the electrical charges (that have the same “dimension”). This implies that each atom of matter has some very small probability to be an atom of antimatter, and it may be annihilated if it collides with an atom of matter. The purpose of this study is to suggest how this hypothesis may be tested empirically.Design/methodology/approachThe cooler are the molecules of gases, the slower they are. Therefore, according to Heisenberg's principle of uncertainty, the probability that gaseous molecules will collide increases when the gas is cooled.FindingsWe may expect that when gases are cooled there is a higher than usual probability that gaseous molecules of matter and antimater will collide and will annihilate each other, emitting photons of gamma rays. Such findings has been reported by Molchadzki, but not explained. The same is true regarding other situations in which the probability of collisions of gaseous molecules is higher than the usual, like the colliding of gaseous molecule at the center of an imploding bubble of gas.Originality/valueIf a procedure that increases the number of collisions between gaseous molecules considerably will be developed, it may be that this procedure will be applicable for obtaining clean energy by annihilations of matter and antimatter.

Role of dielectric medium on mesogenic compounds (BCHs) at phase transition temperature: A comparative computational analysis

A comparative computational analysis on two liquid crystalline disubstituted biphenylcyclohexanes (BCHs) of general formula R-C6H10-C6H4-X with R: C3H7; X: H (BCH30) and R: C5H11; X: CN (BCH5CN) has been carried out on the basis of quantum mechanics and intermolecular forces. The evaluation of atomic charge and dipole moment at each atomic centre has been carried out through an all-valence electron (CNDO/2) method. The configurational energy has been computed using the Rayleigh-Schrodinger perturbation method. The total interaction energy values obtained were used to calculate the probability of each configuration in dielectric medium (i.e. non-interacting and non-mesogenic solvent, benzene) at room temperature, transition temperature and above transition temperature using the Maxwell-Boltzmann's formula. The flexibility of various interacting configurations has been studied in terms of variation of probability due to small departures from the most probable configurations. Further, the various possible geometrical arrangements between a molecular pair during the different modes of interactions have been considered. An attempt has been made to develop a new and interesting model for mesogenic compounds in a dielectric medium. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)