Finite-size scaling for critical conditions for stable quadrupole-bound anions

We present finite-size scaling calculations of the critical parameters for binding an electron to a finite linear quadrupole field. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. The model Hamiltonian consists of a charge Q located at the origin of the coordinates and k charges -Q/k located at distances R(i), i=1, em leader,k. After proper scaling of distances and energies, the rescaled Hamiltonian depends only on one free parameter q=QR. Two different linear charge configurations with q>0 and q<0 are studied using basis sets in both spherical and prolate spheroidal coordinates. For the case with q>0, the finite size scaling calculations give an extrapolated critical value of q(c)=1.469 70+/-0.000 05 a.u. by using a basis set with prolate spheroidal coordinates. For the quadrupole case with q<0, we obtained an extrapolated critical value of mid R:q(c)mid R:=3.982 51+/-0.000 01 a.u. for stable quadrupole bound anions. The corresponding critical exponent for the ground state energy alpha=1.9964+/-0.0005, with E approximately (q-q(c))(alpha).     

Finite size scaling for the atomic Shannon-information entropy

We have developed the finite size scaling method to treat the criticality of Shannon-information entropy for any given quantum Hamiltonian. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. To illustrate this approach we present a study to estimate the critical exponents of the Shannon-information entropy S approximately (lambda-lambda(c))(alpha(S) ), the electronic energy E approximately (lambda-lambda(c))(alpha(E) ), and the correlation length xi approximately mid R:lambda-lambda(c)mid R:(-nu) for atoms with the variable lambda=1/Z, which is the inverse of the nuclear charge Z. This was realized by approximating the multielectron atomic Hamiltonian with a one-electron model Hamiltonian. This model is very accurate for describing the electronic structure of the atoms near their critical points. For several atoms in their ground electronic states, we have found that the critical exponents (alpha(E),nu,alpha(S)) for He (Z=2), C (Z=6), N (Z=7), F (Z=9), and Ne (Z=10), respectively, are (1, 0, 0). At the critical points lambda(c)=1/Z(c), the bound state energies become absorbed or degenerate with continuum states and the entropies reach their maximum values, indicating a maximal delocalization of the electronic wave function.     

Critical point estimation of the Lennard-Jones pure fluid and binary mixtures

The apparent critical point of the pure fluid and binary mixtures interacting with the Lennard-Jones potential has been calculated using Monte Carlo histogram reweighting techniques combined with either a fourth order cumulant calculation (Binder parameter) or a mixed-field study. By extrapolating these finite system size results through a finite size scaling analysis we estimate the infinite system size critical point. Excellent agreement is found between all methodologies as well as previous works, both for the pure fluid and the binary mixture studied. The combination of the proposed cumulant method with the use of finite size scaling is found to present advantages with respect to the mixed-field analysis since no matching to the Ising universal distribution is required while maintaining the same statistical efficiency. In addition, the accurate estimation of the finite critical point becomes straightforward while the scaling of density and composition is also possible and allows for the estimation of the line of critical points for a Lennard-Jones mixture.     

Correlation energy extrapolation by intrinsic scaling. I. Method and application to the neon atom

Remarkably accurate scaling relations are shown to exist between the correlation energy contributions from various excitation levels of the configuration interaction approach, considered as functions of the size of the correlating orbital space. These relationships are used to develop a method for extrapolating a sequence of smaller configuration interaction calculations to the full configuration-interaction energy. Calculations of the neon atom ground state with the Dunning's quadruple zeta basis set demonstrate the ability of the method to obtain benchmark quality results.     

Micellization of telechelic associative polymers: self-consistent field modeling and comparison with scaling concepts

We present numerical results from self-consistent field calculations on the micellization of telechelic associative polymers and their mono-functional analogues. These results are confronted with relatively simple scaling concepts. The proportionality of the critical micelle concentration (CMC) with the hydrophilic backbone length, as found in the calculations, shows good correspondence with a scaling argument based on the entropic penalty of loop formation. It is also shown that models for the conformation of spherical brushes can be applied to predict the structure of the flowerlike micelles formed by these telechelic polymers. Furthermore, we find good agreement between the numerical dependence of the aggregation number upon both backbone and terminal hydrophobe length and an analytical expression derived from the well-known Daoud-Cotton model by introducing a correction for the finite size of the micellar core.     

Refinement of the experimental energy levels of higher 2D Rydberg states of the lithium atom with very accurate quantum mechanical calculations

Very accurate variational non-relativistic calculations are performed for four higher Rydberg (2)D states (1s(2)nd(1), n = 8,..., 11) of the lithium atom ((7)Li). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions and finite nuclear mass is used. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The results of the calculations allow for refining the experimental energy levels determined with respect to the (2)S 1s(2)2s(1) ground state.     

Finite element method for finite-size scaling in quantum mechanics

We combined the finite-size scaling method with the finite element method to provide a systematic procedure for obtaining quantum critical parameters for a quantum system. We present results for the Yukawa potential solved with the finite element approach. The finite-size scaling approach was then used to find the critical parameters of the system. The critical values lambda c, alpha, and nu were found to be 0.83990345, 2.0002, and 1.002, respectively, for l = 0. These results compare well with the theoretically exact values for alpha and nu and with the best numerical estimations for lambda c. The finite element method is general and can be extended to larger systems.     

Nucleation near the spinodal: limitations of mean field density functional theory

We investigate the diverging size of the critical nucleus near the spinodal using the gradient theory (GT) of van der Waals and Cahn and Hilliard and mean field density functional theory (MFDFT). As is well known, GT predicts that at the spinodal the free energy barrier to nucleation vanishes while the radius of the critical fluctuation diverges. We show numerically that the scaling behavior found by Cahn and Hilliard for these quantities holds quantitatively for both GT and MFDFT. We also show that the excess number of molecules Deltag satisfies Cahn-Hilliard scaling near the spinodal and is consistent with the nucleation theorem. From the latter result, it is clear that the divergence of Deltag is due to the divergence of the mean field isothermal compressibility of the fluid at the spinodal. Finally, we develop a Ginzburg criterion for the validity of the mean field scaling relations. For real fluids with short-range attractive interactions, the near-spinodal scaling behavior occurs in a fluctuation dominated regime for which the mean field theory is invalid. Based on the nucleation theorem and on Wang's treatment of fluctuations near the spinodal in polymer blends, we infer a finite size for the critical nucleus at the pseudospinodal identified by Wang.     

Geminal model chemistry. IV. Variational and size consistent pure spin states

We present a computationally inexpensive method that yields ground state wave functions of pure spin symmetry. The method is variational and rigorously size consistent, free from adjustable parameters, and has a favorable scaling with system size. It is based on the recently introduced partially spin restricted geminal wave functions with limited spin contamination. Computations of a bond breaking, a transition metal compound, and a symmetric hydrogen cluster confirm the properties of this method.     

Calculation of accurate permanent dipole moments of the lowest 1,3Sigma+ states of heteronuclear alkali dimers using extended basis sets

Obtaining ultracold samples of dipolar molecules is a current challenge which requires an accurate knowledge of their electronic properties to guide the ongoing experiments. In this paper, we systematically investigate the ground state and the lowest triplet state of mixed alkali dimers (involving Li, Na, K, Rb, Cs) using a standard quantum chemistry approach based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective terms for core polarization effects. We emphasize on the convergence of the results for permanent dipole moments regarding the size of the Gaussian basis set, and we discuss their predicted accuracy by comparing to other theoretical calculations or available experimental values. We also revisit the difficulty to compare computed potential curves among published papers, due to the differences in the modelization of core-core interaction.     

方阱链状分子临界性质的Monte Carlo模拟

在巨正则系综下对阱宽为λ=1.5,链长分别为4、8、16的方阱链状流体实施Monte Carlo模拟,采用建立在完整标度基础上的无偏的Q-参数方法,通过histogram reweighting技术以及有限尺寸标度理论得到了热力学极限下该系列流体的临界温度和临界密度.模拟结果表明,方阱链流体的临界温度随着链长的增加而升高.并且不同链长方阱流体的临界温度均低于已报道的结果.由于本文所采用的完整标度的无偏性,我们估计的临界点更加准确.并且流体的临界温度与链长之间的关系与Flory-Huggins理论相一致.我们还预测了无限链长方阱流体的临界温度,比已有结果略高.     

Scaled opposite-spin CC2 for ground and excited states with fourth order scaling computational costs

An implementation of scaled opposite-spin CC2 (SOS-CC2) for ground and excited state energies is presented that requires only fourth order scaling computational costs. The SOS-CC2 method yields results with an accuracy comparable to the unscaled method. Furthermore the time-determining fifth order scaling steps in the algorithm can be replaced by only fourth order scaling computational costs using a "resolution of the identity" approximation for the electron repulsion integrals and a Laplace transformation of the orbital energy denominators. This leads to a significant reduction of computational costs especially for large systems. Timings for ground and excited state calculations are shown and the error of the Laplace transformation is investigated. An application to a chlorophyll molecule with 134 atoms results in a speed-up by a factor of five and demonstrates how the new implementation extends the applicability of the method. A SOS variant of the algebraic diagrammatic construction through second order ADC(2), which arises from a simplification of the SOS-CC2 model, is also presented. The SOS-ADC(2) model is a cost-efficient alternative in particular for future extensions to spectral intensities and excited state structure optimizations.     

Dynamics and scaling of polymers in a dilute solution: analytical treatment in two and higher dimensions

We consider the dynamical scaling of a single polymer chain in good solvent. In the case of two-dimensional systems, Shannon and Choy [Phys. Rev. Lett. 79, 1455 (1997)] have suggested that the dynamical scaling for a dilute polymer solution breaks down. Using scaling arguments and analytical calculations based on the Zimm model, we show that the dynamical scaling of a dilute two-dimensional polymer system holds when the relevant dynamical quantities are properly extracted from finite systems. Most important, the polymer diffusion coefficient in two dimensions scales logarithmically with system size, in excellent agreement with our extensive computer simulations. This scaling is the reason for the failure of the previous attempts to resolve the dynamical scaling of dilute two-dimensional polymer systems. In three and higher dimensions our analytic calculations are in agreement with previous results in the literature.     

HSO自由基电子基态激发态的CAS计算研究

使用CASSCF方法和ANO-L基组优化了HSO自由基的基态和3个低占据激发态的结构, 并采用包括更多电子动态相关能的CASPT2方法进行了单点能校正. 频率计算结果表明, 优化的4个几何为势能面上的稳定点. 通过电子结构的研究合理地解释了各个激发态相对于电子基态的结构变化.     

Benchmark values of Shannon entropy for spherically confined hydrogen atom

The information‐theoretic measure of confined hydrogen atom has been investigated extensively in the literature. However, most of them were focused on the ground state and accurate values of information entropies, such as Shannon entropy, for confined hydrogen are still not determined. In this work, we establish the benchmark results of the Shannon entropy for confined hydrogen atom in a spherical impenetrable sphere, in both position and momentum spaces. This is done by examining the bound state energies, the normalization of wave functions, and the scaling property with respect to isoelectronic hydrogenic ions. The angular and radial parts of Shannon entropy in two conjugate spaces are provided in detail for both free and confined hydrogen atom in ground and several excited states. The entropies in position space decrease logarithmically with decreasing the size of confinement, while those in momentum space increase logarithmically. The Shannon entropy sum, however, approaches to finite values when the confinement radius closes to zero. It is also found that the Shannon entropy sum shares same trend for states with similar density distributions. Variations of entropy for nodeless bound states are significantly distinct form those owning nodes when changing the confinement radius.