Energy levels in self-assembled quantum arbitrarily shaped dots

A model to determine the electronic structure of self-assembled quantum arbitrarily shaped dots is applied. This model is based principally on constant effective mass and constant potentials of the barrier and quantum dot material. An analysis of the different parameters of this model is done and compared with those which take into account the variation of confining potentials, bands, and effective masses due to strain. The results are compared with several spectra reported in literature. By considering the symmetry, the computational cost is reduced with respect to other methods in literature. In addition, this model is not limited by the geometry of the quantum dot.     

Development of novel statistical potentials describing cation-pi interactions in proteins and comparison with semiempirical and quantum chemistry approaches

Novel statistical potentials derived from known protein structures are presented. They are designed to describe cation-pi and amino-pi interactions between a positively charged amino acid or an amino acid carrying a partially charged amino group and an aromatic moiety. These potentials are based on the propensity of residue types to be separated by a certain spatial distance or to have a given relative orientation. Several such potentials, describing different kinds of correlations between residue types, distances, and orientations, are derived and combined in a way that maximizes their information content and minimizes their redundancy. To test the ability of these potentials to describe cation-pi and amino-pi systems, we compare their energies with those computed with the CHARMM molecular mechanics force field and with quantum chemistry calculations at the Hartree-Fock level (HF) and at the second order of the M?ller-Plesset perturbation theory (MP2). The latter calculations are performed in the gas phase and in acetone, in order to mimic the average dielectric constant of protein environments. The energies computed with the best of our statistical potentials and with gas-phase HF or MP2 show correlation coefficients up to 0.96 when considering one side-chain degree of freedom in the statistical potentials and up to 0.94 when using a totally simplified model excluding all side-chain degrees of freedom. These potentials perform as well as, or better than, the CHARMM molecular mechanics force field that uses a much more detailed protein representation. The good performance of our cation-pi statistical potentials suggests their utility in protein structure and stability prediction and in protein design.     

Semiclassical approach to model quantum fluids using the statistical associating fluid theory for systems with potentials of variable range

Thermodynamic properties of quantum fluids are described using an extended version of the statistical associating fluid theory for potentials of variable range (SAFT-VR) that takes into account quantum corrections to the Helmholtz free energy A, based on the Wentzel-Kramers-Brillouin approximation. We present the theoretical background of this approach (SAFT-VRQ), considering two different cases depending on the continuous or discontinuous nature of the particles pair interaction. For the case of continuous potentials, we demonstrate that the standard Wigner-Kirkwood theory for quantum fluids can be derived from the de Broglie-Bohm formalism for quantum mechanics that can be incorporated within the Barker and Henderson perturbation theory for liquids in a straightforward way. When the particles interact via a discontinuous pair potential, the SAFT-VR method can be combined with the perturbation theory developed by Singh and Sinha [J. Chem. Phys. 67, 3645 (1977); and ibid. 68, 562 (1978)]. We present an analytical expression for the first-order quantum perturbation term for a square-well potential, and the theory is applied to model thermodynamic properties of hydrogen, deuterium, neon, and helium-4. Vapor-liquid equilibrium, liquid and vapor densities, isochoric and isobaric heat capacities, Joule-Thomson coefficients and inversion curves are predicted accurately with respect to experimental data. We find that quantum corrections are important for the global behavior of properties of these fluids and not only for the low-temperature regime. Predictions obtained for hydrogen compare very favorably with respect to cubic equations of state.     

Studies on some singular potentials in quantum mechanics

A simple methodology is suggested for the efficient calculation of certain central potentials having singularities. The generalized pseudospectral method used in this work facilitates nonuniform and optimal spatial discretization. Applications have been made to calculate the energies, densities, and expectation values for two singular potentials of physical interest, viz., (i) the harmonic potential plus inverse quartic and sextic perturbation and (ii) the Coulomb potential with a linear and quadratic term for a broad range of parameters. The first 10 states belonging to a maximum of ?? = 8 and 5 for (i) and (ii) have been computed with good accuracy and compared with the most accurate available literature data. The calculated results are in excellent agreement, especially in light of the difficulties encountered in these potentials. Some new states are reported here for the first time. This offers a general and efficient scheme for calculating these and other similar potentials of physical and mathematical interest in quantum mechanics accurately. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Implementation of dynamical nucleation theory with quantum potentials

A method is implemented within the context of dynamical nucleation theory in order to efficiently determine the ab initio water dimer evaporation rate constant. The drive for increased efficiency in a Monte Carlo methodology is established by the need to use relatively expensive quantum mechanical interaction potentials. A discussion is presented illustrating the theory, algorithm, and implementation of this method to the water dimer. Hartree–Fock and second order Møller–Plesset perturbation theories along with the Dang–Chang polarizable classical potential are utilized to determine the ab initio water dimer evaporation rate constant. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

Energy landscapes of quantum Lennard-Jones solids

To generalize inherent structure analysis to understand structural changes in quantum liquids and solids, differences between classical (V(x)) and quantum-corrected (U(qeff)(x)) energy landscapes are estimated as a function of the de Boer parameter (Λ). Path integral simulations of quantum Lennard-Jones solids are performed at zero pressure and a dimensionless reduced temperature of 0.123, corresponding to an absolute temperature of 4.2K. At constant temperature and pressure, Λ is increased from the classical limit of zero to Λ = 0.28, corresponding to para-H(2). Increasing quantum delocalization effects result in a continuous decrease in density and local order but without a transition to a disordered, liquid state. The inherent structure landscape of bulk systems is strongly dependent on density with the energy and stability of crystalline minima decreasing relative to that of amorphous packing minima as the system is stretched. For Λ ≈ 0.23, the volume fluctuations in quantum solids are sufficient to result in sampling of disordered minima while for Λ = 0.28, the underlying classical inherent structures are completely disordered, indicating that the topography of U(qeff)(x) and V(x) are qualitatively different for such values of Λ. To assess the nature of the quantum-corrected energy landscape, effective pair potentials are defined by u(qeff)(r) = -kT ln g(r) using the pair correlation function (g(r)) of the quantum system in the neighborhood of the first peak. Our results show that as Λ increases, the pair potentials become increasingly softer, shallower, and of increasing range with a shifting of the potential minimum to larger distances. For example, the reduction of the entropy of fusion and melting temperatures of quantum solids with increasing Λ are analogous to the changes in thermodynamics of melting seen in classical solids with increasing range and softness of interactions. The energy landscapes associated with such coarse-grained potentials should be useful as predictors of structural transformations in quantum systems, analogous to their use in understanding phase diagrams of complex fluids.     

Nonlinear coupling in the quantum statistical theory of proton transfer dynamics

The possible role of the nonlinear coupling on the character of the dynamics of particle transfer process is investigated. The analysis and solutions of the kinetic equation indicate that nonlinear coupling causes symmetry breaking of particle transfer potential and determines possible equilibrium structure of the system. Dissipative coupling characterizes the rate of the system to reach thermodynamic equilibrium and along with nonlinear coupling and parameters of the system determines in a unique way the resulting equilibrium structure of the system.     

On the mapping of time-dependent densities onto potentials in quantum mechanics

The mapping of time-dependent densities on potentials in systems of identical quantum mechanical particles is examined. This mapping is of significance ever since Runge and Gross [Phys. Rev. Lett. 52, 997 (1984)] established its uniqueness, forming the theoretical basis for time-dependent density functional theory. Beyond uniqueness there are two important issues: existence, often called v-representability, and stability. We show that v-representability for localized densities in turn-on situations is not assured and we give a simple example of nonexistence. As for stability, we discuss an inversion procedure and by computing its Lyapunov exponents we demonstrate that the mapping is unstable with respect to fluctuations in the initial state. We argue that such instabilities will plague any inversion procedure.     

Thermostability of salt bridges versus hydrophobic interactions in proteins probed by statistical potentials

The temperature dependence of the interactions that stabilize protein structures is a long-standing issue, the elucidation of which would enable the prediction and the rational modification of the thermostability of a target protein. It is tackled here by deriving distance-dependent amino acid pair potentials from four datasets of proteins with increasing melting temperatures (Tm). The temperature dependence of the interactions is determined from the differences in the shape of the potentials derived from the four datasets. Note that, here, we use an unusual dataset definition, which is based on the Tm values, rather than on the living temperature of the host organisms. Our results show that the stabilizing weight of hydrophobic interactions (between Ile, Leu, and Val) remains constant as the temperature increases, compared to the other interactions. In contrast, the two minima of the Arg--Glu and Arg--Asp salt bridge potentials show a significant Tm dependence. These two minima correspond to two geometries: the fork--fork geometry, where the side chains point toward each other, and the fork--stick geometry, which involves the N(epsilon) side chain atom of Arg. These two types of salt bridges were determined to be significantly more stabilizing at high temperature. Moreover, a preference for more-compact salt bridges is noticeable in heat-resistant proteins, especially for the fork--fork geometry. The Tm-dependent potentials that have been defined here should be useful for predicting thermal stability changes upon mutation.     

Cyclodextrin modified quantum dots with tunable liquid-like behaviour

Supermolecular quantum dots (QDs) nanofluids have been firstly proposed and synthesized by virtue of the strong inclusion interactions between α-cyclodextrin (α-CD) and polyethylene glycol (PEG) chains, resulting in tunable liquid-like behaviour, and controllable assembly of single QDs.     

Efficient silicon surface and cluster modeling using quantum capping potentials

A one-electron, silicon quantum capping potential for use in capping the dangling bonds formed by artificially limiting silicon clusters or surfaces is developed. The quantum capping potentials are general and can be used directly in any computational package that can handle effective core potentials. For silicon clusters and silicon surface models, we compared the results of traditional hydrogen atom capping with those obtained from capping with quantum capping potentials. The results clearly show that cluster and surface models capped with quantum capping potentials have ionization potentials, electron affinities, and highest occupied molecular orbital-lowest unoccupied molecular orbital gaps that are in very good agreement with those of larger systems. The silicon quantum capping potentials should be applied in cases where one wishes to model processes involving charges or low-energy excitations in silicon clusters and surfaces consisting of more than ca. 150 atoms.     

Optical potentials in time dependent quantum systems: evaluation ofQ space probabilities

The time dependent extension of the Feshbach formalism allows the discussion of a set of nonunitary coupled channel equations in a given model space. We show how global and exclusive transition probabilities into states of the complementary space can be extracted from the solution of the model space problem.     

Extension of the quantum virial and Hellmann–Feynman theorems to the quantum statistical averages

In the present article, we extended the quantum virial and Hellmann–Feynman theorems to the quantum statistical averages, that is, to the thermal states. We obtained some new formulas which make possible expressing the thermodynamical observables of the system as functions of the moments of coordinates, as we see in a short example relating to the pseudoharmonical oscillator. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 159–165, 1998     

Energy conserving approximations to the quantum potential: dynamics with linearized quantum force

Solution of the Schrodinger equation within the de Broglie-Bohm formulation is based on propagation of trajectories in the presence of a nonlocal quantum potential. We present a new strategy for defining approximate quantum potentials within a restricted trial function by performing the optimal fit to the log-derivatives of the wave function density. This procedure results in the energy-conserving dynamics for a closed system. For one particular form of the trial function leading to the linear quantum force, the optimization problem is solved analytically in terms of the first and second moments of the weighted trajectory distribution. This approach gives exact time-evolution of a correlated Gaussian wave function in a locally quadratic potential. The method is computationally cheap in many dimensions, conserves total energy and satisfies the criterion on the average quantum force. Expectation values are readily found by summing over trajectory weights. Efficient extraction of the phase-dependent quantities is discussed. We illustrate the efficiency and accuracy of the linear quantum force approximation by examining a one-dimensional scattering problem and by computing the wavepacket reaction probability for the hydrogen exchange reaction and the photodissociation spectrum of ICN in two dimensions.     

Additivity of statistical moments in the exponentially modified Gaussian model of chromatography

A homologous series of saturated fatty acids ranging from C₁₀ to C₂₂ was separated by reversed-phase capillary liquid chromatography. The resultant zone profiles were found to be fit best by an exponentially modified Gaussian (EMG) function. To compare the EMG function and statistical moments for the analysis of the experimental zone profiles, a series of simulated profiles was generated by using fixed values for retention time and different values for the symmetrical (σ) and asymmetrical (τ) contributions to the variance. The simulated profiles were modified with respect to the integration limits, the number of points, and the signal-to-noise ratio. After modification, each profile was analyzed by using statistical moments and an iteratively fit EMG equation. These data indicate that the statistical moment method is much more susceptible to error when the degree of asymmetry is large, when the integration limits are inappropriately chosen, when the number of points is small, and when the signal-to-noise ratio is small. The experimental zone profiles were then analyzed by using the statistical moment and EMG methods. Although care was taken to minimize the sources of error discussed above, significant differences were found between the two methods. The differences in the second moment suggest that the symmetrical and asymmetrical contributions to broadening in the experimental zone profiles are not independent. As a consequence, the second moment is not equal to the sum of σ² and τ², as is commonly assumed. This observation has important implications for the elucidation of thermodynamic and kinetic information from chromatographic zone profiles.     

FRET-based modified graphene quantum dots for direct trypsin quantification in urine

A versatile nanoprobe was developed for trypsin quantification with fluorescence resonance energy transfer (FRET). Here, fluorescence graphene quantum dot is utilized as a donor while a well-designed coumarin derivative, CMR2, as an acceptor. Moreover, bovine serum albumin (BSA), as a protein model, is not only served as a linker for the FRET pair, but also a fluorescence enhancer of the quantum dots and CMR2. In the presence of trypsin, the FRET system would be destroyed when the BSA is digested by trypsin. Thus, the emission peak of the donor is regenerated and the ratio of emission peak of donor/emission peak of acceptor increased. By the ratiometric measurement of these two emission peaks, trypsin content could be determined. The detection limit of trypsin was found to be 0.7 μg/mL, which is 0.008-fold of the average trypsin level in acute pancreatitis patient's urine suggesting a high potential for fast and low cost clinical screening.     

On the statistical behaviour of molecular vibronic energy levels

Electronic spectra of polyatomic molecules often exhibit a high density of complicated energy levels, making a detailed analysis of the individual levels unfavourable. In these cases, statistical tests provide an appropriate means for analysing the spectra. Fluctuation measures are presented and evaluated for calculated and experimental molecular spectra as examples. The results are compared with the predictions of random matrix theory.     

Energy levels for perturbed Morse oscillators

The energy levels and perturbation expansions for the expectation values of arbitrary powers of position for a perturbed Morse oscillator are obtained by application of the hypervirial and Hellmann–Feynman theorems, solely in terms of the unperturbed energy. We obtain expressions for the first-order corrections for (1 ? e^?aq )^m for 4 ? m ? 8 and the expressions to second and third order for the quartic perturbation. A numerical application to the CO molecule is made.