Atomic Charge Transfer-counter Polarization Effects Determine Infrared Ch Intensities Of Hydrocarbons: A Quantum Theory Of Atoms In Molecules Model.

Atomic charge transfer-counter polarization effects determine most of the infrared fundamental CH intensities of simple hydrocarbons, methane, ethylene, ethane, propyne, cyclopropane and allene. The quantum theory of atoms in molecules/charge-charge flux-dipole flux model predicted the values of 30 CH intensities ranging from 0 to 123 km mol(-1) with a root mean square (rms) error of only 4.2 km mol(-1) without including a specific equilibrium atomic charge term. Sums of the contributions from terms involving charge flux and/or dipole flux averaged 20.3 km mol(-1), about ten times larger than the average charge contribution of 2.0 km mol(-1). The only notable exceptions are the CH stretching and bending intensities of acetylene and two of the propyne vibrations for hydrogens bound to sp hybridized carbon atoms. Calculations were carried out at four quantum levels, MP2/6-311++G(3d,3p), MP2/cc-pVTZ, QCISD/6-311++G(3d,3p) and QCISD/cc-pVTZ. The results calculated at the QCISD level are the most accurate among the four with root mean square errors of 4.7 and 5.0 km mol(-1) for the 6-311++G(3d,3p) and cc-pVTZ basis sets. These values are close to the estimated aggregate experimental error of the hydrocarbon intensities, 4.0 km mol(-1). The atomic charge transfer-counter polarization effect is much larger than the charge effect for the results of all four quantum levels. Charge transfer-counter polarization effects are expected to also be important in vibrations of more polar molecules for which equilibrium charge contributions can be large.

Quantum theory of the far-off-resonance continuous-wave Raman laser: Heisenberg-Langevin approach

We present the quantum theory of the far-off-resonance continuous-wave Raman laser using the Heisenberg-Langevin approach. We show that the simplified quantum Langevin equations for this system are mathematically identical to those of the nondegenerate optical parametric oscillator in the time domain with the following associations: pump pump, Stokes signal, and Raman coherence idler. We derive analytical results for both the steady-state behavior and the time-dependent noise spectra, using standard linearization procedures. In the semiclassical limit, these results match with previous purely semiclassical treatments, which yield excellent agreement with experimental observations. The analytical time-dependent results predict perfect photon statistics conversion from the pump to the Stokes and nonclassical behavior under certain operational conditions.

Extreme Observables and Optimal Measurements in Quantum Theory

Optimization of quantum measurement processes has a pivotal role in carrying out better, more accurate or less disrupting, measurements and experiments on a quantum system. Especially, convex optimization, i.e., identifying the extreme points of the convex sets and subsets of quantum measuring devices plays an important part in quantum optimization since the typical figures of merit for measuring processes are affine functionals. In this thesis, we discuss results determining the extreme quantum devices and their relevance, e.g., in quantum-compatibility-related questions. Especially, we see that a compatible device pair where one device is extreme can be joined into a single apparatus essentially in a unique way. Moreover, we show that the question whether a pair of quantum observables can be measured jointly can often be formulated in a weaker form when some of the observables involved are extreme. Another major line of research treated in this thesis deals with convex analysis of special restricted quantum device sets, covariance structures or, in particular, generalized imprimitivity systems. Some results on the structure ofcovariant observables and instruments are listed as well as results identifying the extreme points of covariance structures in quantum theory. As a special case study, not published anywhere before, we study the structure of Euclidean-covariant localization observables for spin-0-particles. We also discuss the general form of Weyl-covariant phase-space instruments. Finally, certain optimality measures originating from convex geometry are introduced for quantum devices, namely, boundariness measuring how ‘close’ to the algebraic boundary of the device set a quantum apparatus is and the robustness of incompatibility quantifying the level of incompatibility for a quantum device pair by measuring the highest amount of noise the pair tolerates without becoming compatible. Boundariness is further associated to minimum-error discrimination of quantum devices, and robustness of incompatibility is shown to behave monotonically under certain compatibility-non-decreasing operations. Moreover, the value of robustness of incompatibility is given for a few special device pairs.

π-dimerization of pleiadiene radical cations at low temperatures revealed by UV–vis spectroelectrochemistry and quantum theory

One-electron oxidation of the non-alternant polycyclic aromatic hydrocarbon pleiadiene and related cyclohepta[ c,d]pyrene and cyclohepta[c,d]fluoranthene in THF produces corresponding radical cations detectable in the temperature range of 293–263 K only on the subsecond time scale of cyclic voltammetry. Although the EPR-active red-coloured pleiadiene radical cation is stable according to the literature in concentrated sulfuric acid, spectroelectrochemical measurements reported in this study provide convincing evidence for its facile conversion into the green-coloured, formally closed shell and, hence, EPRsilent π-bound dimer dication stable in THF at 253 K. The unexpected formation of the thermally unstable dimeric product featuring a characteristic intense low-energy absorption band at 673 nm (1.84 eV; logεmax=4.0) is substantiated by ab initio calculations on the parent pleiadiene molecule and the PF6 − salts of the corresponding radical cation and dimer dication. The latter is stabilized with respect to the radical cation by 14.40 kcal mol−1 (DFT B3LYP) [37.64 kcal mol−1 (CASPT2/DFT B3LYP)]. An excellent match has been obtained between the experimental and TDDFT- calculated UV–vis spectra of the PF6 − salt of the pleiadiene dimer dication, considering solvent (THF) effects.

Investigating the Nature of Noble Gas-Copper Bonds by the Quantum Theory of Atoms in Molecules

We investigated noble gas copper bonds in linear complexes represented by the NgCuX general formula in which Ng and X stand for a noble gas (neon, argon, krypton, or xenon) and a halogen (fluorine, chlorine or bromine), respectively, by coupled cluster methods and modified cc-pVQZ basis sets. The quantum theory of atoms in molecules (QTAIM) shows a linear relation between the dissociation energy or noble gas-copper bonds and the amount of electronic charge transferred mainly from the noble gas to copper during complexation. Large changes in the QTAIM quadrupole moments of copper and noble gases resulting from this bonding and a comparison between NgCuX and NgNaCl systems indicate that these noble gas-copper bonds should be better interpreted as predominantly covalent. Finally, QTAIM atomic dipoles of noble gases in NgNaCl systems agree satisfactorily with atomic dipoles given by a simple model for these NgNa van der Waals bonds.

Two definitions of the electric polarizability of a bound system in relativistic quantum theory

For the electric polarizability of a bound system in relativistic quantum theory, there are two definitions that have appeared in the literature. They differ depending on whether or not the vacuum background is included in the system. A recent confusion in this connection is clarified. © 1999 American Associations of Physics Teachers.

A quantum theory for the excitation spectrum of a rectangular Andreev billiard

We consider a N - S box system consisting of a rectangular conductor coupled to a superconductor. The Green functions are constructed by solving the Bogoliubov-de Gennes equations at each side of the interface, with the pairing potential described by a step-like function. Taking into account the mismatch in the Fermi wave number and the effective masses of the normal metal - superconductor and the tunnel barrier at the interface, we use the quantum section method in order to find the exact energy Green function yielding accurate computed eigenvalues and the density of states. Furthermore, this procedure allow us to analyze in detail the nontrivial semiclassical limit and examine the range of applicability of the Bohr-Sommerfeld quantization method.

Electrostatic potentials and polarization effects in proton-molecule interactions by means of multipoles from the quantum theory of atoms in molecules

Some atomic multipoles (charges, dipoles and quadrupoles) from the Quantum Theory of Atoms in Molecules (QTAIM) and CHELPG charges are used to investigate interactions between a proton and a molecule (F2, Cl2, BF, AlF, BeO, MgO, LiH, H2CO, NH3, PH3, BF3, and CO2). Calculations were done at the B3LYP/6-311G(3d,3p) level. The main aspect of this work is the investigation of polarization effects over electrostatic potentials and atomic multipoles along a medium to long range of interaction distances. Large electronic charge fluxes and polarization changes are induced by a proton mainly when this positive particle approaches the least electronegative atom of diatomic heteronuclear molecules. The search for simple equations to describe polarization on electrostatic potentials from QTAIM quantities resulted in linear relations with r-4 (r is the interaction distance) for many cases. Moreover, the contribution from atomic dipoles to these potentials is usually the most affected contribution by polarization what reinforces the need for these dipoles to a minimal description of purely electrostatic interactions. Finally, CHELPG charges provide a description of polarization effects on electrostatic potentials that is in disagreement with physical arguments for certain of these molecules. (c) 2012 Wiley Periodicals, Inc.

Waves, analytical signals, and some postulates of quantum theory

In this paper we apply the formalism of the analytical signal theory to the Schrödinger wavefunction. Making use exclusively of the wave-particle duality and the rinciple of relativistic covariance, we actually derive the form of the quantum energy and momentum operators for a single nonrelativistic particle. Without using any more quantum postulates, and employing the formalism of the characteristic function, we also derive the quantum-mechanical prescription for the measurement probability in such cases.

Quantum theory of spin waves in finite chiral spin chains

We calculate the effect of spin waves on the properties of finite-size spin chains with a chiral spin ground state observed on biatomic Fe chains deposited on iridium(001). The system is described with a Heisenberg model supplemented with a Dzyaloshinskii-Moriya coupling and a uniaxial single ion anisotropy that presents a chiral spin ground state. Spin waves are studied using the Holstein-Primakoff boson representation of spin operators. Both the renormalized ground state and the elementary excitations are found by means of Bogoliubov transformation, as a function of the two variables that can be controlled experimentally, the applied magnetic field and the chain length. Three main results are found. First, because of the noncollinear nature of the classical ground state, there is a significant zero-point reduction of the ground-state magnetization of the spin spiral. Second, there is a critical external field from which the ground state changes from chiral spin ground state to collinear ferromagnetic order. The character of the two lowest-energy spin waves changes from edge modes to confined bulk modes over this critical field. Third, in the spin-spiral state, the spin-wave spectrum exhibits oscillatory behavior as function of the chain length with the same period of the spin helix.

Modern quantum theory.

Includes bibliography.