Quantum Mechanical Techniques Research Articles

D-brane dynamics and creations of open and closed strings after recombination

A quantum-mechanical technique is used within the framework of U(2) super-Yang–Mills theory to investigate what happens in the process after recombination of two D p-branes at one angle. Two types of initial conditions are considered, one of which with p=4 is a candidate of inflation mechanism. It is observed that the branes' shapes come to have three extremes due to localization of tachyon condensation. Furthermore, open string pairs connecting the decaying D-branes are shown to be created; most part of the released energy is used to create them. It also strongly suggests that creation of closed strings happens afterward. Closed strings as gravitational radiation from the D-branes are also shown to be created. A few speculations are also given on implications of the above phenomena for an inflation model.

Ab initio conformational analysis of fluoromethyl formate and difluoromethyl formate

Abstract We employed ab initio quantum mechanical techniques, such as HF, MP2, and QCISD methods, to explore the conformational spaces of fluoromethyl formate and difluoromethyl formate, HC(O)OCH 3 − n F n ( n =1,2). Three potential energy minima, two with the syn and one with the anti configuration, were located for fluoromethyl formate, while four potential energy minima, two with the syn and the other two with the anti configuration, were located for difluoromethyl formate. In addition, we characterized several rotational transition states for the rotation of the C–O single bond adjacent to the carbonyl group or that adjacent to the fluoro-substituted methyl group. The results of the energy evaluations of the rotational stationary points suggest that the syn / anti energy difference, as well as the barrier height to the syn / anti interconversion, tends to decrease monotonously on going from methyl formate to trifluoromethyl formate, via fluoromethyl formate and difluoromethyl formate.

The properties of iron under core conditions from first principles calculations

The Earth’s core is largely composed of iron (Fe). The phase relations and physical properties of both solid and liquid Fe are therefore of great geophysical importance. As a result, over the past 50 years the properties of Fe have been extensively studied experimentally. However, achieving the extreme pressures (up to 360 GPa) and temperatures (∼6000 K) found in the core provide a major experimental challenge, and it is not surprising that there are still considerable discrepancies in the results obtained by using different experimental techniques. In the past 15 years quantum mechanical techniques have been applied to predict the properties of Fe. Here we review the progress that has been made in the use of first principles methods in the study of Fe, and focus upon (i) the structure of Fe under core conditions, (ii) the high P melting behaviour of Fe, (iii) the thermodynamic properties of hexagonal close-packed (hcp) Fe, and (iv) the rheological and thermodynamic properties of high P liquid Fe.

Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework

In the context of a two-parameter (α, β) deformation of the canonical commutation relation leading to nonzero minimal uncertainties in both position and momentum, the harmonic oscillator spectrum and eigenvectors are determined by using an extension of the techniques of conventional supersymmetric quantum mechanics (SUSYQM) combined with shape invariance under parameter scaling. The resulting supersymmetric partner Hamiltonians correspond to different masses and frequencies. The exponential spectrum is proved to reduce to a previously found quadratic spectrum whenever one of the parameters α, β vanishes, in which case shape invariance under parameter translation occurs. In the special case where α = β ≠ 0, the oscillator Hamiltonian is shown to coincide with that of the q-deformed oscillator with q > 1 and its eigenvectors are therefore n-q-boson states. In the general case where 0 ≠ α ≠ β ≠ 0, the eigenvectors are constructed as linear combinations of n-q-boson states by resorting to a Bargmann representation of the latter and to q-differential calculus. They are finally expressed in terms of a q-exponential and little q-Jacobi polynomials.

New Theoretical Line List for the B ′ 2 Σ + ← X 2 Σ + System of 24 MgH

Fully quantum-mechanical techniques have been applied to compute the complete line list for the B' 2Σ+ ← X 2Σ+ system of 24MgH. The list includes transition energies and oscillator strengths over the wavelength range 11,850-32,130 cm-1, for all possible allowed transitions from the ground electronic state vibrational levels v'' = 0-11. This list was computed using the best available ab initio potential energies and dipole transition moment function, with the former adjusted to account for experimental data. The agreement of the current calculations with previous theoretical results and the line list of Kurucz is discussed. Although spectroscopic accuracy for a particular line cannot be claimed for our calculations, comparison is made with the recent astronomical measurements of Wallace et al. A line list for pure rovibrational transitions in the X 2Σ+ state is also presented.

1,2-, 1,3-dioxetanes, 그리고 1,3-cyclodisiloxane의 분자구조, 에너지와 진동주파수에 대한 순 이론 양자 역학적 연구

1,2-와 1,3-dioxetane<TEX>$(C_2O_2H_4)$</TEX>, 그리고 1,3-cyclodisiloxane<TEX>$(Si_2O_2H_4)$</TEX>에 대하여 높은 이론 수준에서 분자구조, 진동주파수, 그리고 에너지 등을 계산하였다. 위의 모든 분자들에 대하여 TZ2P CCSD(T)의 이론 수준까지 분자구조를 최적화 하였으며. 진동주파수는 여러 basis set에서 SCF 방법으로 계산하였다. 본 연구에서 최적화된 분자구조들에 대한 진동주파수가 모두 실수(real number)로 예측됨으로서, 제안된 모든 분자구조가 local minimum 구조임을 확인하였다. 1,2- 및 1,3-dioxetane들과 cyclodisiloxane이 두 분자의 aldehyde와 silanone으로 해리 될 때의 중합에너지를 zero-point vibrational energy(ZPVE)를 고려하여 계산하고, 안정성을 비교하였다. The geometrical parameters, vibrational frequencies, and relative energies for 1,2-, 1,3-dioxetanes, and 1,3-cyclodisiloxane have been investigated using high level ab initio quantum mechanical techniques with large basis sets. The geometries have been optimized at the self-consistent field(SCF), the single and double excitation configuration interaction(CISD), the coupled cluster with single and double excitation(CCSD), and the CCSD with connected triple excitations[CCSD(T)] levels of theory. The highest level of theory employed in this study is TZ2P CCSD(T). Harmonic vibrational frequencies and IR intensities are also determined at the SCF level of theory with various basis sets and confirm that all the optimized geometries are true minima. Also zero-point vibrational energies have been considered to predict the dimerization energies for 1,2- and 1,3-isomers.

Computationally efficient quantum-mechanical technique to calculate the direct tunneling gate current in metal-oxide-semiconductor structures

We propose a computationally efficient, accurate and numerically stable quantum-mechanical technique to calculate the direct tunneling (DT) gate current in metal-oxide-semiconductor (MOS) structures. Knowledge of the imaginary part Γ of the complex eigenenergy of the quasi-bound inversion layer states is required to estimate the lifetimes of these states. Exploiting the numerically obtained exponential dependence of Γ on the thickness of the gate-dielectric layer even in the sub-1-nm-thickness regime, we have simplified the determination of Γ in devices where it is too small to be calculated directly. It is also shown that the MOS electrostatics, calculated self-consistently with open boundary conditions, is independent of the dielectric layer thickness provided that the other parameters remain unchanged. Utilizing these findings, a computationally efficient and numerically stable method is developed for calculating the tunneling current–gate voltage characteristics. The validity of the proposed model is demonstrated by comparing simulation results with experimental data. Sample calculations for MOS transistors with high-K gate-dielectric materials are also presented. This model is particularly suitable for DT current calculation in devices with thicker gate dielectrics and in device or process characterization from the tunneling current measurement.

Dipole oscillator strengths, dipole properties and dispersion energies for SiF4

A recommended isotropic dipole oscillator strength distribution (DOSD) has been constructed for the silicon tetrafluoride (SiF4) molecule through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength data. The constraints are furnished by experimental molar refractivity data and the Thomas-Reiche-Kuhn sum rule. The DOSD is used to evaluate a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums and mean excitation energies for the molecule. A pseudo-DOSD for SiF4 is also presented which is used to obtain reliable results for the isotropic dipole-dipole dispersion energy coefficients C6, for the interaction of SiF4 with itself and with 43 other species and the triple-dipole dispersion energy coefficient C9 for (SiF4)3.

BlochLib: a fast NMR C++ tool kit

Computational power, speed, and algorithmic complexity are increasing at a continuing rate. As a result, scientific simulations continue to investigate more and more complex systems. Nuclear magnetic resonance (NMR) is no exception. NMR theory and language is extremely well developed, that simulations have become a standard by which experiments are measured. Nowadays, complex computations can be performed on normal workstations and workstation clusters. Basic numerical operations have also become extremely optimized and new computer language paradigms have become implemented. Currently there exists no complete NMR tool kit which uses these newer techniques. This paper describes such a tool kit, BlochLib. BlochLib is designed to be the next generation of NMR simulation packages; however, the basic techniques implemented are applicable to almost any problem. BlochLib enables the user to simulate almost any NMR idea both experimental or theoretical in nature. Both classical and quantum mechanical techniques are included and demonstrated, as well as several powerful user interface tools. The total tool kit and documentation can be found at http://waugh.cchem.berkeley.edu/blochlib/.

Quantum Mechanical ab Initio Study of Mixed SiO2-GeO2 Crystals as Reference Models for Ge-Doped Silica Glasses

In the present work, we have applied first principles quantum mechanical techniques to the study of periodic models of four silica polymorphs containing different proportions of germanium as a substitutional species: α-quartz, β-quartz, α-cristobalite, and stishovite (rutile); except for β-quartz, which is considered for the sake of completeness, these phases exist both in the pure silicon and pure germanium forms. Computations have been performed using both the Hartree−Fock (HF) approximation and the gradient corrected density functional PWGGA technique. A triple-ζ plus polarization basis set has been used. All geometries have been fully optimized at the HF level. Equilibrium structure, stability, and electronic properties of the mixed phases are analyzed with reference to the pure systems. It is shown that the two species are completely miscible for all crystalline structures in all proportions. The properties of the mixed crystals vary smoothly with the impurity content. No localized defect states ass...

Metal island growth and dynamics on molybdenite surfaces

In order to understand the adsorption mechanism of metal atoms to semiconducting surfaces, we have studied, as a model system, the vapor phase adsorption of Ag, Au, and Cu on the (001) surface of molybdenite (MoS 2) and the subsequent surface diffusion of these adsorbates. Our scanning tunneling microscopy (STM) images show that, depending on the type of metal atom that is adsorbed, islands of a characteristic size (2 nm for Ag, 8 to 10 nm for Cu, two distinct sizes of 2 nm and 8 to 10 nm for Au), shape (well rounded in the lateral extension) and thickness (one monolayer for Ag, 1 to 1.5 nm for Cu) are formed during the initial stages of deposition. Whole islands are observed to surface diffuse without loss of size or shape. Despite the relatively large size of the copper islands on molybdenite, these islands surface diffuse extensively, suggesting that the Cu-S interaction is weak. Surface diffusion is only hindered once individual islands start to coalesce. As copper islands accumulate, the size and shape of the original islands can still be recognized, supporting the conclusion that these characteristics are constant and that monolayer growth occurs by the aggregation of islands across the surface. The strength and the nature of the Ag-S(MoS 2) bond were further investigated by using molecular orbital calculations, ultraviolet photoelectron spectroscopy (UPS) and scanning tunneling spectroscopy (STS). By applying quantum mechanical approaches using a two-dimensional periodic molybdenite slab and hexagonal MoS 2 clusters of different sizes with metal atoms adsorbed to them, it is possible to calculate the electron transfer between the mineral surface and the metal atom as well as the adsorption energy as a function of surface coverage. In addition, we used the results from the quantum mechanical runs to derive empirical potentials that model the characteristics of the forces within the crystal, within the adsorbed islands, and the metal and mineral surface. The combination of quantum mechanical calculations and empirical force field calculations explain the electronic structure and the highest stability of Ag islands that have seven atoms in diameter, which exactly agrees with the size of experimentally observed islands. UPS results also suggest that a specific new state is formed (approximately 4.5 eV into the valence band) which may describe the Ag-S bond because it does not occur in pure silver or molybdenite. This study shows how the combination of microscopic (STM), spectroscopic (STS, UPS), compositional (X-ray photoelectron spectroscopy, XPS) and molecular modeling (quantum mechanical and empirical) techniques is a useful approach to understand the nature of the metal to sulfide bond. Further insights may be gained concerning the natural association of certain metals with sulfides.

Trade-offs in the quantum search algorithm

Quantum search is a quantum mechanical technique for searching N possibilities in only sqrt(N) steps. This has been proved to be the best possible algorithm for the exhuastive search problem in the sense the number of queries it requires cannot be reduced. However, as this paper shows, the number of non-query operations, and thus the total number of operations, can be reduced. The number of non-query unitary operations can be reduced by a factor of log N/alpha*log(log N) while increasing the number of queries by a factor of only (1+(log N)^{-alpha}). Various choices of alpha yield different variants of the algorithm. For example, by choosing alpha to be O(log N/log(log N)), the number of non-query unitary operations can be reduced by 40% while increasing the number of queries by just two.

Potential curves and spectroscopic properties for the ground state of ClO and for the ground and various excited states of ClO−

The potential curves and dissociation energies for the ground states of ClO(2Π) and ClO−(1Σ+) and possible low lying excited states (1Π, Π3, Σ−3, Σ+3, Δ1, etc.) of ClO− have been investigated using sophisticated ab initio quantum mechanical techniques with large basis sets including diffuse functions. The equilibrium bond distance and vibrational frequency for the ground state (1Σ+) of ClO− are predicted to be 1.688 Å and 660 cm−1 at the coupled-cluster single double (triple) [CCSD(T)]/aug-cc-pVQZ level of theory. The lowest excited singlet state of ClO− is predicted to be the open-shell Π1 state, which is 2.43 eV higher in energy than the ground state, while the lowest triplet state (3Π) of ClO− has a potential with well depth of 0.32 eV. The adiabatic electron detachment energy from ClO− is predicted to be 2.29 eV including zero-point vibrational energy (ZPVE) at the CCSD(T)/aug-cc-pVQZ level of theory. The spin allowed vertical electronic transition (1Σ+–1Π) of ClO− is predicted to be 3.13 eV including ZPVE. The dissociation energies (D0) of ClO− to Cl−(1S)+O(3P), Cl−(1S)+O(1D), and Cl(2P)+O−(2P) are predicted to be 1.40, 3.46, and 3.61 eV, respectively, including ZPVE.

Dipole oscillator strength properties and dispersion energies for SiH4

A recommended isotropic dipole oscillator strength distribution (DOSD) has been constructed for the silane (SiH4) molecule through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength data. The constraints are furnished by experimental molar refractivity data and the Thomas–Reiche–Kuhn sum rule. The DOSD is used to evaluate a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for the molecule. A pseudo-DOSD for SiH4 is also presented which is used to obtain reliable results for the isotropic dipole–dipole dispersion energy coefficients C6, for the interaction of silane with itself and with forty-four other species, and the triple–dipole dispersion energy coefficient C9 for ðSiH4Þ 3 . 2002 Elsevier Science B.V. All rights reserved.

Dipole oscillator strength properties and dispersion energies for CI2

A recommended isotropic dipole oscillator strength distribution (DOSD) has been constructed for the chlorine molecule through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength and molar refractivity data. It has been used to evaluate a variety of dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for the molecule. A pseudo-DOSD for C12 is also presented which is used to obtain reliable results for the isotropic dipole-dipole dispersion energy coefficients C6, for the interaction of Cl2 with itself and forty-two other species, and the triple-dipole dispersion energy coefficient C9 for (Cl2)3.

Structural Effects in the Addition–Fragmentation Reaction of Allylic Onium Salts

Allylic onium salts with different hetero-atoms and various substituent groups at the allylic double bond have been shown to be very efficient initiators for cationic polymerization. When attacked by a radical, they become radical cations, which are highly unstable species, and undergo fragmentation into smaller radical cations called onium radical cations. The reaction mechanism involves radical formation, addition and fragmentation. In our previous work, radical initiators generated in the same way and under the same conditions are studied experimentally for their ability to affect the polymerization efficiency. Here, the factors affecting the polymerization efficiency are discussed theoretically using semi-empirical quantum mechanical techniques. The type of radical species, substituent group at the allylic side, the heteroatom at the onium side and the onium group itself are analyzed separately. For this purpose, the geometries of different onium radical cations to be fragmented are optimized and the strength of the C–heteroatom bond to be broken and the size of the radical cations after fragmentation are considered.

Entropy Loss of Hydroxyl Groups of Balanol upon Binding to Protein Kinase A

This article describes a short project for an undergraduate to learn several techniques for computer-aided drug design. The project involves estimating the loss of the rotational entropy of the hydroxyl groups of balanol upon its binding to the enzyme protein kinase A (PKA), as the entropy loss can significantly influence PKA–balanol binding affinity. This work employs semiempirical quantum mechanical techniques for estimating the potential energy curves for the rotation of the hydroxyl groups of balanol in vacuum and in PKA, and solves the Poisson equation to correct the potential energy curves for hydration effects. Statistical mechanical principles are then applied to estimate the desired entropy loss from the potential energy curves. The analysis examines the influence of hydration effects on the rotational preference of the hydroxyl groups and the significance of the rotational entropy in determining binding affinity.

Interpreting Molecular Crystal Disorder in Plumbocene, Pb(C5H5)2: Insight from Theory

Plane-wave density functional theory has been applied in a novel way to help interpret the molecular crystal structure disorder observed in the orthorhombic zigzag phase of plumbocene, Pb(C5H5)2. A crystal lattice comprising uniformly staggered C5H5 rings was found to be lower in energy by 2.8 kJ mol-1 per unit cell, compared to a uniformly eclipsed packing arrangement. This energy difference has been attributed to the difference in the strength of intermolecular interactions between the Pb(C5H5)2 chains for the two different lattices. The calculations performed allowed the determination of the crystallographic occupancy factors by a quantum mechanical technique for the first time.

A combined classical/quantum study of the photodissociation dynamics of NeBr 2(B) near the Br 2(B) dissociation limit

Techniques of quantum and nonlinear classical mechanics are employed to study the photodissociation dynamics of NeBr 2(B) near the Br 2 dissociation threshold. A time-dependent treatment is used to obtain the absorption spectrum for the B←X transition. As energy increases up to 3600 cm −1 , the spectrum shows a progressive congestion but narrow peaks appear again close to the Br 2 dissociation limit. These peaks are associated with long lived resonances that develop nodes along the minimum energy path of the linearization. Periodic orbit (PO) analysis in two dimensions is carried out for the van der Waals NeBr 2 system and POs that emerge from saddle-node bifurcations are found to be related to the structure of the above resonances.

Classical analog of quantum search

Quantum search is a quantum-mechanical technique for searching N possibilities in only $\sqrt{N}$ steps. A similar algorithm applies in a purely classical setting when there are N oscillators, one of which is of a different resonant frequency. We could identify which one this is by measuring the oscillation frequency of each oscillator, a procedure that would take about N cycles. We show, how by coupling the oscillators together in a very simple way, it is possible to identify the different one in only $\sqrt{N}$ cycles. In case there are multiple oscillators of a different frequency, we can estimate the number of these in a time which is the square root of that required by the sampling method. The analog also leads to some energy routing algorithms for mechanical systems.