On the quantum mechanical propagator for driven coupled harmonic oscillators

The exact propagator beyond and at caustics for a pair of coupled and driven oscillators with different frequencies and masses is calculated using the path-integral approach. The exact wavefunctions and energies are also presented. Finally the propagator is re-calculated through an alternative method, using the δfunction. © 1992 IOP Publishing Ltd.

Quantum mechanical study of YTiO3 to the investigation of piezoelectricity

In previous articles we reported through theoretical studies the piezoelectric effect in BaTiO3, SmTiO3, and YFeO3. In this paper, we used the Douglas-Kroll-Hess (DKH) second-order scalar relativistic method to investigate the piezoelectricity in YTiO3. In the calculations we used the [6s4p] and [10s5p4d] Gaussian basis sets for the O (3P) and Ti (5S) atoms, respectively, from the literature in combination with the (30s21p16d)/[15s9p6d] basis set for the Y ( 3D) atom, obtained by generator coordinate Hartree-Fock (GCHF) method, and they had their quality evaluated using calculations of total energy and orbital energies (HOMO and HOMO-1) of the 2TiO+1 and 1YO+1 fragments. The dipole moment, the total energy, and the total atomic charges in YTiO3 in C s space group were calculated. When we analyze those properties we verify that it is reasonable to believe that YTiO3 does not present piezoelectric properties. Copyright © 2011 Raimundo Dirceu de Paula Ferreira et al.

Ab initio quantum mechanical investigation of structural and chemical-physical properties of selected minerals for minero-petrological, structural ceramic and biomaterial applications

The purpose of this thesis is the atomic-scale simulation of the crystal-chemical and physical (phonon, energetic) properties of some strategically important minerals for structural ceramics, biomedical and petrological applications. These properties affect the thermodynamic stability and rule the mineral-environment interface phenomena, with important economical, (bio)technological, petrological and environmental implications. The minerals of interest belong to the family of phyllosilicates (talc, pyrophyllite and muscovite) and apatite (OHAp), chosen for their importance in industrial and biomedical applications (structural ceramics) and petrophysics. In this thesis work we have applicated quantum mechanics methods, formulas and knowledge to the resolution of mineralogical problems ("Quantum Mineralogy”). The chosen theoretical approach is the Density Functional Theory (DFT), along with periodic boundary conditions to limit the portion of the mineral in analysis to the crystallographic cell and the hybrid functional B3LYP. The crystalline orbitals were simulated by linear combination of Gaussian functions (GTO). The dispersive forces, which are important for the structural determination of phyllosilicates and not properly con-sidered in pure DFT method, have been included by means of a semi-empirical correction. The phonon and the mechanical properties were also calculated. The equation of state, both in athermal conditions and in a wide temperature range, has been obtained by means of variations in the volume of the cell and quasi-harmonic approximation. Some thermo-chemical properties of the minerals (isochoric and isobaric thermal capacity) were calculated, because of their considerable applicative importance. For the first time three-dimensional charts related to these properties at different pressures and temperatures were provided. The hydroxylapatite has been studied from the standpoint of structural and phonon properties for its biotechnological role. In fact, biological apatite represents the inorganic phase of vertebrate hard tissues. Numerous carbonated (hydroxyl)apatite structures were modelled by QM to cover the broadest spectrum of possible biological structural variations to fulfil bioceramics applications.

Further Quantum Mechanical Evidence that Difluorotoluene does not Hydrogen Bond

Calculations were run on the methylated DNA base pairs adenine:thymine and adenine:difluorotoluene to further investigate the hydrogen-bonding properties of difluorotoluene (F). Geometries were optimized using hybrid density functional theory. Single-point calculations at the MP2(full) level were performed to obtain more rigorous energies. The functional counterpoise method was used to correct for the basis set superposition error (BSSE), and the interaction energies were also corrected for fragment relaxation. These corrections brought the B3LYP and MP2 interaction energies into excellent agreement. In the gas phase, the Gibbs free energies calculated at the B3LYP and MP2 levels of theory predict that A and T will spontaneously form an A:T pair while A:F spontaneously dissociates into A and F. Solvation effects on the pairing of the bases were explored using implicit solvent models for water and chloroform. In aqueous solution, both A:T and A:F are predicted to dissociate into their component monomers. Semiempirical calculations were performed on small sections of B-form DNA containing the two pairs, and the results provide support for the concept that base stacking is more important than hydrogen bonding for the stability of the A:F pair within a DNA helix.

Modeling of Magic Water Clusters(H20)2 and (H20)21H+ with the PM3 Quantum-Mechanical Method

The PM3 quantum-mechanical method is able to model the magic water clusters (H20),, and (H20)&+. Results indicate that the H30+ ion is tightly bound within the (H20),, cluster by multiple hydrogen bonds, causing deformation to the symmetric (HzO),, pentagonal dodecahedron structure. The structures, energetics, and hydrogen bond patterns of six local minima (H20)21H+ clusters are presented.

Quantum-Mechanical Investigation of Large Water Clusters

The PM3 quantum-mechanical method has been used to study large water clusters ranging from 8 to 42 water molecules. These large clusters are built from smaller building blocks. The building blocks include cyclic tetramers, pentamers, octamers, and a pentagonal dodecahedron cage. The correlations between the strain energy resulting from bending of the hydrogen bonds formed by different cluster motifs and the number of waters involved in the cluster are discussed. The PM3 results are compared with TIP4P potential and ab initio results. The number of net hydrogen bonds per water increases with the cluster size. This places a limit on the size of clusters that would fit the Benson model of liquid water. Many of the 20-mer clusters fit the Benson model well. Calculations of the ion cluster (H20)4o(H30+)2 reveal that the m/e ratio obtainable by mass spectrometry experiments can uniquely indicate the conformation of the 20 water pentagonal dodecahedron cage present in the larger clusters.

Quantum Mechanical Study of Sulfuric Acid Hydration: Atmospheric Implications

The role of the binary nucleation of sulfuric acid in aerosol formation and its implications for global warming is one of the fundamental unsettled questions in atmospheric chemistry. We have investigated the thermodynamics of sulfuric acid hydration using ab initio quantum mechanical methods. For H2SO4(H2O)n where n = 1–6, we used a scheme combining molecular dynamics configurational sampling with high-level ab initio calculations to locate the global and many low lying local minima for each cluster size. For each isomer, we extrapolated the Møller–Plesset perturbation theory (MP2) energies to their complete basis set (CBS) limit and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled harmonic vibrational frequencies. We found that ionic pair (HSO4–·H3O+)(H2O)n−1 clusters are competitive with the neutral (H2SO4)(H2O)n clusters for n ≥ 3 and are more stable than neutral clusters for n ≥ 4 depending on the temperature. The Boltzmann averaged Gibbs free energies for the formation of H2SO4(H2O)n clusters are favorable in colder regions of the troposphere (T = 216.65–273.15 K) for n = 1–6, but the formation of clusters with n ≥ 5 is not favorable at higher (T > 273.15 K) temperatures. Our results suggest the critical cluster of a binary H2SO4–H2O system must contain more than one H2SO4 and are in concert with recent findings(1) that the role of binary nucleation is small at ambient conditions, but significant at colder regions of the troposphere. Overall, the results support the idea that binary nucleation of sulfuric acid and water cannot account for nucleation of sulfuric acid in the lower troposphere.

Ability of the PM3 Quantum Mechanical Method to Model Intermolecular Hydrogen Bonding between Neutral Molecules

The PM3 semiempirical quantum-mechanical method was found to systematically describe intermolecular hydrogen bonding in small polar molecules. PM3 shows charge transfer from the donor to acceptor molecules on the order of 0.02-0.06 units of charge when strong hydrogen bonds are formed. The PM3 method is predictive; calculated hydrogen bond energies with an absolute magnitude greater than 2 kcal mol-' suggest that the global minimum is a hydrogen bonded complex; absolute energies less than 2 kcal mol-' imply that other van der Waals complexes are more stable. The geometries of the PM3 hydrogen bonded complexes agree with high-resolution spectroscopic observations, gas electron diffraction data, and high-level ab initio calculations. The main limitations in the PM3 method are the underestimation of hydrogen bond lengths by 0.1-0.2 for some systems and the underestimation of reliable experimental hydrogen bond energies by approximately 1-2 kcal mol-l. The PM3 method predicts that ammonia is a good hydrogen bond acceptor and a poor hydrogen donor when interacting with neutral molecules. Electronegativity differences between F, N, and 0 predict that donor strength follows the order F > 0 > N and acceptor strength follows the order N > 0 > F. In the calculations presented in this article, the PM3 method mirrors these electronegativity differences, predicting the F-H- - -N bond to be the strongest and the N-H- - -F bond the weakest. It appears that the PM3 Hamiltonian is able to model hydrogen bonding because of the reduction of two-center repulsive forces brought about by the parameterization of the Gaussian core-core interactions. The ability of the PM3 method to model intermolecular hydrogen bonding means reasonably accurate quantum-mechanical calculations can be applied to small biologic systems.

Quantum Mechanical Study of Sulfuric Acid Hydration: Atmospheric Implications

The role of the binary nucleation of sulfuric acid in aerosol formation and its implications for global warming is one of the fundamental unsettled questions in atmospheric chemistry. We have investigated the thermodynamics of sulfuric acid hydration using ab initio quantum mechanical methods. For H2SO4(H2O)n where n = 1–6, we used a scheme combining molecular dynamics configurational sampling with high-level ab initio calculations to locate the global and many low lying local minima for each cluster size. For each isomer, we extrapolated the Møller–Plesset perturbation theory (MP2) energies to their complete basis set (CBS) limit and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled harmonic vibrational frequencies. We found that ionic pair (HSO4–·H3O+)(H2O)n−1clusters are competitive with the neutral (H2SO4)(H2O)n clusters for n ≥ 3 and are more stable than neutral clusters for n ≥ 4 depending on the temperature. The Boltzmann averaged Gibbs free energies for the formation of H2SO4(H2O)n clusters are favorable in colder regions of the troposphere (T = 216.65–273.15 K) for n = 1–6, but the formation of clusters with n ≥ 5 is not favorable at higher (T > 273.15 K) temperatures. Our results suggest the critical cluster of a binary H2SO4–H2O system must contain more than one H2SO4 and are in concert with recent findings(1) that the role of binary nucleation is small at ambient conditions, but significant at colder regions of the troposphere. Overall, the results support the idea that binary nucleation of sulfuric acid and water cannot account for nucleation of sulfuric acid in the lower troposphere.

Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians

We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant.

Stability of nonrelativistic quantum mechanical matter coupled to the (ultraviolet cutoff) radiation field

We announce a proof of H-stability for the quantized radiation field, with ultraviolet cutoff, coupled to arbitrarily many non-relativistic quantized electrons and static nuclei. Our result holds for arbitrary atomic numbers and fine structure constant. We also announce bounds for the energy of many electrons and nuclei in a classical vector potential and for the eigenvalue sum of a one-electron Pauli Hamiltonian with magnetic field.

Toward a quantum-mechanical description of metal-assisted phosphoryl transfer in pyrophosphatase

The wealth of kinetic and structural information makes inorganic pyrophosphatases (PPases) a good model system to study the details of enzymatic phosphoryl transfer. The enzyme accelerates metal-complexed phosphoryl transfer 1010-fold: but how? Our structures of the yeast PPase product complex at 1.15 Å and fluoride-inhibited complex at 1.9 Å visualize the active site in three different states: substrate-bound, immediate product bound, and relaxed product bound. These span the steps around chemical catalysis and provide strong evidence that a water molecule (Onu) directly attacks PPi with a pKa vastly lowered by coordination to two metal ions and D117. They also suggest that a low-barrier hydrogen bond (LBHB) forms between D117 and Onu, in part because of steric crowding by W100 and N116. Direct visualization of the double bonds on the phosphates appears possible. The flexible side chains at the top of the active site absorb the motion involved in the reaction, which may help accelerate catalysis. Relaxation of the product allows a new nucleophile to be generated and creates symmetry in the elementary catalytic steps on the enzyme. We are thus moving closer to understanding phosphoryl transfer in PPases at the quantum mechanical level. Ultra-high resolution structures can thus tease out overlapping complexes and so are as relevant to discussion of enzyme mechanism as structures produced by time-resolved crystallography.

New insights into NO-carbon and N2O-carbon reactions from quantum mechanical calculations

Density functional theory calculations were used to investigate the mechanisms of NO-carbon and N2O-carbon reactions. It was the first time that the importance of surface nitrogen groups was addressed in the kinetic behaviors of the NO-carbon reaction. It was found that the off-plane nitrogen groups that are adjacent to the zigzag edge sites and in-plane nitrogen groups that are located on the armchair sites make the bond energy of oxygen desorption even ca. 20% lower than that of the off-plane epoxy group adjacent to zigzag edge sites and in-plane o-quinone oxygen atoms on armchair sites; this may explain the reason why the experimentally obtained activation energy of the NO-carbon reaction is ca. 20% lower than that of the O-2-carbon reaction over 923 K. A higher ratio of oxygen atoms can be formed in the N2O-carbon reaction, because of the lower dissociation energy of N2O, which results in a higher ratio of off-plane epoxy oxygen atoms. The desorption energy of semiquinone with double adjacent off-plane oxygen groups is ca. 20% less than that of semiquinone with only one adjacent off-plane oxygen group. This may be the reason why the activation energy of N2O is also ca. 20% less than that of the O-2-carbon reaction. The new mechanism can also provide a good qualitative comparison for the relative reaction rates of NO-, N2O-, and O-2-carbon reactions. The anisotropic characters of these gas-carbon reactions can also be well explained.

Long distance coupling of a quantum mechanical oscillator to the internal states of an atomic ensemble

We propose and investigate a hybrid optomechanical system consisting of a micro-mechanical oscillator coupled to the internal states of a distant ensemble of atoms. The interaction between the systems is mediated by a light field which allows the coupling of the two systems in a modular way over long distances. Coupling to internal degrees of freedom of atoms opens up the possibility to employ high-frequency mechanical resonators in the MHz to GHz regime, such as optomechanical crystal structures, and to benefit from the rich toolbox of quantum control over internal atomic states. Previous schemes involving atomic motional states are rather limited in both of these aspects. We derive a full quantum model for the effective coupling including the main sources of decoherence. As an application we show that sympathetic ground-state cooling and strong coupling between the two systems is possible.