Non‐born–oppenheimer nuclear and electronic densities for a hooke‐coulomb model for a four‐particle system

Based on the exact solutions for a non‐Born–Oppenheimer (nBO) Hooke‐Coulomb model for a four‐particle system (J. Chem. Phys. 2005, 123, 024102), we present here nBO nuclear and electron one‐particle densities for this system. We examine the effect on the topology of the one‐particle densities that arises from the selection of different reference points for the densities. In addition, we analyze the behavior of these densities as a function of the mass ratio between light and heavy particles. We conclude from these results that molecular structure is not univocally related to the topology of the one‐particle densities in a nBO regime. © 2012 Wiley Periodicals, Inc.     

Analysis of approximations and errors in equations of motion method calculations

We analyze a number of fundamental questions associated with the use of a finite one-particle orbital basis in equations of motion (EOM) method calculations of excitation energies etc., of atomic and molecular systems. This approximation yields an approximate n_e-electron ground state and say, N excited states, while there are (N + 1)² different possible basis operators for EOM calculations. We show that sets of at most 2N basis operators can contribute to the EOM calculations. Any set of 2N basis operators, satisfying certain conditions, provides the exact EOM energies which are equivalent to complete configuration interaction results within the same orbital basis. We investigate the use of particle-particle shifting operators which are not employed in EOM calculations in model calculations on He with operator bases smaller than the complete 2V to consider the convergence of the expansion. The dependence of EOM calculations on the quality of the approximate ground state wavefunction is studied through calculations for Be where additional support is provided for the frequent need for multiconfigurational zeroth order reference functions (as corrected perturbatively). Excited state EOM wavefunctions from EOM calculations are shown to not necessarily be orthogonal to either the exact or approximate ground state wavefunction, suggesting implications in the use of EOM methods to evaluate excited state properties. The He and Be examples and a simple two-level problem are also utilized to illustrate questions concerning the use of the EOM equations to obtain an iteratively improved ground state wavefunction.     

三元体系H3BO3-MgCl2-H2O在308.15K和323.15K稳定相平衡研究

采用等温溶解法研究了三元体系H3BO3 - MgCl2 - H2O在308.15 K和323.15 K的稳定相平衡;测定了上述体系液相中各组分的平衡溶解度及液相密度,并绘制了相应相图和平衡溶液密度组成图.结果表明,该体系在308.15 K和323.15 K时有一个共饱点、两条饱和溶解度曲线和两个结晶相区,无复盐及固溶体...     

Generalized k-particle brillouin conditions and their use for the construction of correlated electronic wavefunctions

The variational form of the Schrödinger equation is shown to be equivalent to a set of generalized Brillouin conditions in terms of arbitrary antihermitean operators R. For a special choice of these R in second-quantization language, k-particle Brillouin conditions are derived that are a generalization of the “generalized one-particle Brillouin conditions” of Levy and Berthier. The application of these conditions to one-particle and two-particle hamiltonians is discussed. A two-particle generalization of the Fock operator is derived and an iterative variational pair-cluster scheme is derived. It is shown that CEPA and SCEP methods satisfy an approximate rather than an exact set of Brilouin conditions.     

Body frames in the separation of collective angles in quantum N-body problems

The application of the concept of body-fixed reference frames, proposed by C. Eckart [Phys. Rev. 47, 552 (1935)], to the problem of the separation of three collective angles in quantum N-body problems is analyzed based on the technique recently developed by Meremianin and Briggs [Phys. Rep. 384, 121 (2003)]. Special attention is paid to the body frame defined by the "second Eckart condition" which minimizes vibro-rotational couplings near the equilibrium position. The important case of the Eckart frame for three-body systems is considered in detail. The connection of the basis vectors of the Eckart frame with Jacobi vectors is derived. All results of this work are valid for an arbitrary choice of internal (body-frame) coordinates.     

The chemical potential for dilute hard-sphere mixtures

Accurate Monte Carlo evaluation of the probability of inserting an additional particle of arbitrary size into a hard-sphere fluid at various densities allows a quantitative check on the scaled particle interpolation formula for this probability, which is rigorously known when the added particle is either very small or very large. The simple scaled particle formula is remarkably accurate due to a favorable choice of the functional dependence of the surface tension on curvature. The biggest deviation occurs at liquid-like densities where the insertion probability is about 20% larger for larger particles, indicating a larger probability of occurrence of larger density fluctuations, and resulting in a smaller (3%) excess chemical potential than the simple theory predicts. On the other hand, at lower densities the insertion probability for large particles is slightly smaller than the theory predicts.     

H2-H2 revisited. orthogonalization,polarization and delocalization effects within a bond-orbital scheme

The bond-orbital approach to short-range intermolecular interactions is extended to include polarization and delocalization effects using second-order perturbation theory. Ab initio calculations on H₄ show that results based on a nonorthogonal BO SCF wavefunction closely approach the full MO ones, whereas different orthogonalizatkm procedures give corrections which depend heavily on the accuracy of the one-configuration result.     

Monodisperse and core-shell-structured SiO2@YBO3:Eu3+ spherical particles: synthesis and characterization

Y0.9Eu0.1BO3 phosphor layers were deposited on monodisperse SiO2 particles of different sizes (300, 570, 900, and 1200 nm) via a sol-gel process, resulting in the formation of core-shell-structured SiO2@Y0.9Eu0.1BO3 particles. X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), transmission electron microscopy (TEM), photoluminescence (PL), and cathodoluminescence (CL) spectra as well as lifetimes were employed to characterize the resulting composite particles. The results of XRD, FE-SEM, and TEM indicate that the 800 degrees C annealed sample consists of crystalline YBO3 shells and amorphous SiO2 cores, in spherical shape with a narrow size distribution. Under UV (240 nm) and VUV (172 nm) light or electron beam (1-6 kV) excitation, these particles show the characteristic 5D0-7F1-4 orange-red emission lines of Eu3+ with a quantum yield ranging from 36% (one-layer Y0.9Eu0.1BO3 on SiO2) to 54% (four-layer Y0.9Eu0.1BO3 on SiO2). The luminescence properties (emission intensity and color coordinates) of Eu3+ ions in the core-shell particles can be tuned by the coating number of Y0.9Eu0.1BO3 layers and SiO2 core particle size to some extent, pointing out the great potential for these particles applied in displaying and lightening fields.     

Nuclear Coordinate dependence of electronic transition moments in orbitally forbidden transitions: A new interpretation of deuterium isotope effects

The nuclear coordinate dependence of electronic transtion moments has been investigated for the purpose of finding new interpretations of deuterium isotope effects on spectral intensities and radiative decay rates in orbitally forbidden electronic transitions. By using “AO following nuclei” wavefunctions as the building block for the electronic wavefunction in the adiabatic BO vibronic wavefunction, the spin-free hamiltonian is diagonalized to generate eigenfunctions and eigen-energies. It is found that the electronic transtion moments based on these eigenfunctions show dependences upon the vibrational modes which are not directly involved in vibronic coupling. This leads to interpretations of the deuterium isotope effects in T₁ → S₀ radiative transitions of aromatic hydrocarbons and S₀ → S₁ absorption in pyrazine which are not based on the conventional Herzberg—Teller or non-BO coupling.     

On the validity range of the Born-Oppenheimer approximation: a semiclassical study for all-particle quantization of three-body Coulomb systems

The validity range of the Born-Oppenheimer (BO) approximation is studied with respect to the variation of the mass (m) of negatively charged particle by substituting an electron (e) with muon (mu) and antiproton (p) in hydrogen molecule cation. With the use of semiclassical quantization applied to these (ppe), (ppmu), and (ppp) under a constrained geometry, we estimate the energy difference of the non-BO vibronic ground state from the BO counterpart. It is found that the error in the BO approximation scales to the power of 3/2 to the mass of negative particles, that is, m(1.5). The origin of this clear-cut relation is analyzed based on the original perturbation theory due to Born and Oppenheimer, with which we show that the fifth order term proportional to m(5/4) is zero and thereby the first correction to the BO approximation should arise from the sixth order term that is proportional to m(6/4). Therefore, the validity range of the Born-Oppenheimer approximation is wider than that often mistakenly claimed to be proportional to m(1/4).     

Levy Constrained Search in Fock Space: An Alternative Approach to Noninteger Electron NumberSCI北大核心CSCD

By extending the Levy wavefunction constrained search to Fock Space,one can define a wavefunction constrained search for electron densities in systems having noninteger number of electrons.For pure-state v-representable densities,the results are equivalent to what one would obtain with the zero-temperature grand canonical ensemble.In other cases,the wavefunction constrained search in Fock space presents an upper bound to the grand canonical ensemble functional.One advantage of the Fock-space wavefunction constrained search functional over the zero-temperature grand-canonical ensemble constrained search functional is that certain specific excited states(i.e.,those that are not ground-statev-representable) are the stationary points of the Fock-space functional.However,a potential disadvantage of the Fock-space constrained search functional is that it is not convex.     

Application of Exact Analytic Total Energy Functional for Hooke’s Atom to He, Li+ and Be++: An Examination of the Universality of the Energy Functional in DFT

We employ the recently generated energy density functional for Hooke’s atom [Ludeña EV et al (2004) Intern J Quantum Chem 99:297], to which we introduce a simplification for the kinetic energy term, to evaluate the total energy of the helium atom and of the two-electron ions Li⁺ and Be⁺⁺. Using accurate representations for the one-particle densities of these systems we show that the energy density functional for Hooke’s atom leads, in these cases, to energy values that are below the exact ones. We discuss the implication of this finding with respect to the existence of a universal energy functional in DFT.     

The diffusion-limited reaction A + A →0 in the steady state: influence of correlations in the source

We study theoretically the kinetics of the diffusion-limited reaction + →0 in the steady state. We consider the effect of an external source which adds correlated pairs of particles. We show that in dimensions below 2 and in the low-density limit spatial self-organization of reactants occurs and is controlled by the correlation in the source term. At higher densities there is a crossover to a regime similar to the random landing case, exhibiting a non-classical order of reaction.     

Effect of cosurfactant on the free-drainage regime of aqueous foams

We report results of drainage in aqueous foams of small bubble size D (D=180 microm) prepared with SDS-dodecanol solutions. We have performed free-drainage experiments in which local drainage rates are measured by electrical conductivity and by light scattering techniques. We have investigated the role of the surfactant-cosurfactant mass ratio on the drainage regime. The results confirm that a drainage regime corresponding to a high surface mobility can indeed be found for such small bubbles, and show that an increase in the cosurfactant content can induce a transition to a low surface mobility drainage regime. We show that the transition is not linked to variations of the bulk properties, but rather to variations of the interfacial properties. However, the results show that the added amount of dodecanol to trigger the transition is quite high, evidencing that the relevant control parameter for drainage regimes includes both bubble size and interfacial contributions.     

Computer simulation study of the phase behavior and structural relaxation in a gel-former modeled by three-body interactions

We report a computer simulation study of a model gel-former obtained by modifying the three-body interactions of the Stillinger-Weber potential for silicon. This modification reduces the average coordination number and consequently shifts the liquid-gas phase coexistence curve to low densities, thus facilitating the formation of gels without phase separation. At low temperatures and densities, the structure of the system is characterized by the presence of long linear chains interconnected by a small number of three coordinated junctions at random locations. At small wave vectors the static structure factor shows a nonmonotonic dependence on temperature, a behavior which is due to the competition between the percolation transition of the particles and the stiffening of the formed chains. We compare in detail the relaxation dynamics of the system as obtained from molecular dynamics with the one obtained from Monte Carlo dynamics. We find that the bond correlation function displays stretched exponential behavior at moderately low temperatures and densities, but exponential relaxation at low temperatures. The bond lifetime shows an Arrhenius behavior, independent of the microscopic dynamics. For the molecular dynamics at low temperatures, the mean squared displacement and the (coherent and incoherent) intermediate scattering function display at intermediate times a dynamics with ballistic character and we show that this leads to compressed exponential relaxation. For the Monte Carlo dynamics we always find an exponential or stretched exponential relaxation. Thus we conclude that the compressed exponential relaxation observed in experiments is due to the out-of-equilibrium dynamics.     

Impact of network topology on cationic diffusion and hardness of borate glass surfaces

The connection between bulk glass properties and network topology is now well established. However, there has been little attention paid to the impact of network topology on the surface properties of glass. In this work, we report the impact of the network topology on both the transport properties (such as cationic inward diffusion) and the mechanical properties (such as hardness) of borate glasses with modified surfaces. We choose soda lime borate systems as the object of this study because of their interesting topological features, e.g., boron anomaly. An inward diffusion mechanism is employed to modify the glass surface compositions and hence the surface topology. We show that accurate quantitative predictions of the hardness of the modified surfaces can be made using topological constraint theory with temperature-dependent constraints. Experimental results reveal that Ca(2+) diffusion is most intense in glasses with lowest BO(4) fraction, whereas Na(+) diffusion is only significant when nonbridging oxygens start to form. These phenomena are interpreted in terms of the atomic packing and the local electrostatic environments of the cations.     

Single electron densities: a new tool to analyze molecular wavefunctions

A new partitioning scheme for the electron density of a many-electron wavefunction into single electron densities is proposed. These densities are based on the most probable arrangement of the electrons in an atom or molecule. Therefore, they contain information about the electron-electron interaction and, most notably, the Fermi hole due to the antisymmetry of the many-electron wavefunction. The single electron densities overlap and can be combined to electron pair distributions close to the qualitative electron pairs that represent, for instance, the basis of the valence shell electron pair repulsion model. Single electron analyses are presented for the water, ethane, and ethene molecules. The effect of electron correlation on the single electron and pair densities is investigated for the water molecule.     

Non-Born-Oppenheimer molecular structure and one-particle densities for H2D+

We show that the nonadiabatic (non-Born-Oppenheimer) ground state of a three-nuclei system can be effectively calculated with the use of an explicitly correlated Gaussian basis set with floating centers. Sample calculations performed for the H2D+ system with various basis set sizes show good convergence with respect to both the total energy and the expectation values of the internuclear distances (molecular geometry), the distances between the nuclei and the electrons, and between the electrons. We also provide a derivation of the formulas for one-particle density calculations and some density plots showing the spatial distribution of the H2D+ nuclear and electronic densities.