Improved partition–expansion of two‐center distributions involving slater functions

The calculation of the electronic structure of large systems is facilitated by the substitution of the two‐center distributions by their projections on auxiliary basis sets of one‐center functions. An alternative is the partition–expansion method in which one first decides what part of the distribution is assigned to each center, and next expands each part in spherical harmonics times radial factors. The method is exact, requires neither auxiliary basis sets nor projections, and can be applied to Gaussian and Slater basis sets. Two improvements in the partition–expansion method for Slater functions are reported: general expressions valid for arbitrary quantum numbers are derived and the efficiency of the procedure is increased giving analytical solutions to integrals previously computed by numerical quadrature. The efficiency of the new version is assessed in several molecules and the advantages over the projection methods are pointed out. © 2013 Wiley Periodicals, Inc.     

Analytical method for the representation of atoms-in-molecules densities

We present analytic refinements and applications of the deformed atomic densities method [Fernández Rico, J.; López, R.; Ramírez, G. J Chem Phys 1999, 110, 4213-4220]. In this method the molecular electron density is partitioned into atomic contributions, using a minimal deformation criterion for every two-center distributions, and the atomic contributions are expanded in spherical harmonics times radial factors. Recurrence relations are introduced for the partition of the two-center distributions, and the final radial factors are expressed in terms of exponential functions multiplied by polynomials. Algorithms for the practical implementation are developed and tested, showing excellent performances. The usefulness of the present approach is illustrated by examining its ability to describe the deformation of atoms in different molecular environments and the relationship between these atomic densities and some chemical properties of molecules.     

Electrostatic potentials and fields from density expansions of deformed atoms in molecules

The exact representation of the molecular density by means of atomic expansions, consisting in spherical harmonics times analytical radial factors, is employed for the calculation of electrostatic potentials, fields, and forces. The resulting procedure is equivalent to an atomic multipolar expansion in the long-range regions, but works with similar efficiency and accuracy in the short-range region, where multipolar expansions are not valid. The performances of this procedure are tested on the calculation of the electrostatic potential contour maps and electrostatic field flux lines of water and nitrobenzene, computed from high-quality molecular electron densities obtained with Slater basis sets.     

Entropic measures of Rydberg‐like harmonic states

The Shannon entropy, the desequilibrium and their generalizations (Rényi and Tsallis entropies) of the three‐dimensional single‐particle systems in a spherically symmetric potential V(r) can be decomposed into angular and radial parts. The radial part depends on the analytical form of the potential, but the angular part does not. In this article, we first calculate the angular entropy of any central potential by means of two analytical procedures. Then, we explicitly find the dominant term of the radial entropy for the highly energetic (i.e., Rydberg) stationary states of the oscillator‐like systems. The angular and radial contributions to these entropic measures are analytically expressed in terms of the quantum numbers which characterize the corresponding quantum states and, for the radial part, the oscillator strength. In the latter case, we use some recent powerful results of the information theory of the Laguerre polynomials and spherical harmonics which control the oscillator‐like wavefunctions.     

On the accuracy of the potential harmonic functions

The matrix elements of the correlation function between symmetric potential harmonics are simplified into the analytical summations of the grand angular momenta by smartly using the recurrence and coupling relations of the potential harmonics. The correlation-function potential-harmonic and generalized-Laguerre-function method (CFPHGLF) , recently developed by us, is applied to the S states of the helium-like systems for Z = 2 to 9. The results exhibit good convergence with the bases in terms of both the angular and radial directions. The final eigen-energies agree excellently with the best s-limits of the variational configuration interaction (CI) method for the involved low-lying S states. The accuracy of the potential harmonic (PH) expansion scheme is discussed relative to the exact Hylleraas CI results (HCI), and Hartree-Fock results. Moreover, suggestion is given for the future improvement of the PH scheme.     

Electrostatic potentials,fields and field gradients from a general crystalline charge density

Explicit expressions for the electrostatic potential, the electric field and the electric field gradient at the nuclear positions of a crystalline lattice are presented. They are derived for a charge density given as an expansion in terms of spherical harmonics around the nuclear sites and as a Fourier series in the interstitial. These expressions can be decomposed into contributions from the spherical region centered around the lattice site of interest, from spherical regions surrounding all the other lattice sites and a contribution from the interstitital region.     

Translation of STO charge distributions

Barnett and Coulson's zeta-function method (M. P. Barnett and C. A. Coulson, Philos. Trans. R. Soc., Lond. A 1951, 243, 221) is one of the main sources of algorithms for the solution of multicenter integrals with Slater-type orbitals. This method is extended here from single functions to two-center charge distributions, which are expanded at a third center in terms of spherical harmonics times analytical radial factors. For s-s distributions, the radial factors are given by a series of factors corresponding to the translation of s-type orbitals. For distributions with higher quantum numbers, they are obtained from those of the s-s distributions by recurrence. After analyzing the convergence of the series, a computational algorithm is proposed and its practical efficiency is tested in three-center (AB/CC) repulsion integrals. In cases of large basis sets, the procedure yields about 12 correct significant figures with a computational cost of a few microseconds per integral.     

Parametrization of the radial distribution function of a Yukawa fluid

We give semi-empirical expressions for five terms in an inverse temperature expansion of the radial distribution function of a Yukawa fluid. The parameters in these terms are chosen to fit what we believe should be an accurate equation of state when either the energy or pressure routes is used. Thus, a measure of self consistency is achieved. The equation of state which is the basis of our fit is the inverse temperature expansion of the Yukawa fluid free energy, obtained from the mean spherical approximation but modified to give reasonable results at low densities.     

Configuration interaction benchmark for Be ground state

A set of 432 energy-optimized Slater-type radial orbitals together with spherical harmonics up to ? = 30 is used to approximate the corresponding full configuration interaction (CI) expansion for Be ground state. An analysis of radial and angular patterns of convergence for the energy yields a basis set incompleteness error of 8.7 μhartree of which 85% comes from radial basis truncations for ? ≤ 30. Select-divide-and-conquer CI (Bunge in J Chem Phys 125:014107, 2006; Bunge and Carbó-Dorca in J Chem Phys 125:014108, 2006) produces an energy upper bound 0.02(1) μhartree above the full CI limit. The energy upper bound E = ?14.6673473 corrected with these two truncation energy errors yields E = ?14.6673560 a.u. (Be) in fair agreement with the latest explicitly correlated Gaussian results of E = ?14.66735646 a.u. (Be). The new methods employed are discussed. It is acknowledged that at this level of accuracy traditional atomic CI has reached a point of diminishing returns. Modifications of conventional (orbital) CI to seek for significantly higher accuracy without altering a strict one-electron orbital formalism are proposed.     

高阶FMSA展开研究缔合流体界面张力

结合一阶平均球近似(First-order mean-spherical approximation, FMSA)与重整化群(Renormalization group, RG)变换计算了流体全局性相行为. 应用FMSA理论解析得到的径向分布函数(Radial distribution function, RDF)和直接相关函数(Direct correction function, DCF)建立密度泛函方法, 并在其展开项中考虑了高阶微扰项作用, 即考虑了主体流体密度不一致性, 避免原有方法在计算密度分布时存在难以收敛、误差大等问题. 将高阶展开扩展应用到缔合流体, 计算表明, 和分子模拟数据相比, 界面密度分布和界面张力较之原有的密度泛函方法均有了明显改善.     

Order of stabilities in water nanoclusters: Insight from some recent double‐hybrid functionals

In the present work, the applicability of some of the recently proposed and modern double‐hybrid (DH) models and other density functional theory (DFT) approximations has been analyzed for a difficult test, the order of stability in low‐energy isomers of water nanoclusters. In particular, we aim to systematically investigate for these functionals the role played by several factors such as dispersion correction, integrand functions upon which the DHs are based, and different spin scaling for the perturbative term in DH calculations of the relative energies for various isomers of water nanoclusters (H₂O)₂₀. From the obtained results, the superior performance of DHs with respect to the functionals from previous rungs is confirmed. It is shown that the dispersion corrected DHs perform better than noncorrected counterparts. Plus, the DH models based on cubic integrand (CI) and quadratic integrand (QI) functions are nearly equivalent in performance. We also find that using only contributions of electron pairs with opposite spin for the perturbative correlation part through scaled opposite spin scheme does not represent a significant improvement on accuracy of the results. Putting all the results together, the dispersion corrected parameterized DHs and parameter‐free DH models involving CI and QI functions outperform other approximations for relative energies of water 20‐mers. Altogether, predicting the correct order of the stability in water nanoclusters may be considered as another Achilles' heel in DFT calculations, although more analyses in this context are still needed. © 2016 Wiley Periodicals, Inc.     

Structure and adsorption of a hard-core multi-Yukawa fluid confined in a slitlike pore: grand canonical Monte Carlo simulation and density functional study

Because of the increasing interest in studying the phenomenon exhibited by charge-stabilized colloidal suspensions in confining geometry, we present a density functional theory (DFT) for a hard-core multi-Yukawa fluid. The excess Helmholtz free-energy functional is constructed by using the modified fundamental measure theory and Rosenfeld's perturbative method, in which the bulk direct correlation function is obtained from the first-order mean spherical approximation. To validate the established theory, grand canonical ensemble Monte Carlo (GCMC) simulations are carried out to determine the density profiles and surface excesses of multi-Yukawa fluid in a slitlike pore. Comparisons of the theoretical results with the GCMC data suggest that the present DFT gives very accurate density profiles and surface excesses of multi-Yukawa fluid in the slitlike pore as well as the radial distribution functions of the bulk fluid. Both the DFT and the GCMC simulations predict the depletion of the multi-Yukawa fluid near a nonattractive wall, while the mean-field theory fails to describe this depletion in some cases. Because the simple form of the direct correlation function is used, the present DFT is computationally as efficient as the mean-field theory, but reproduces the simulation data much better than the mean-field theory.     

Influence of electronic correlation in monoelectronic density in p-space

The radial molecular monoelectronic density and their orbital contributions have been calculated in the momentum space. For these purposes, densities for the ground state of several atoms and molecules, using a cc-pVTZ basis set at HF level, as well as some post-HF and DFT methods are computed. The difference between the radial monoelectronic density computed with each method and that using the HF wave function is used as a tool to study the influence of the electronic correlation in the momentum space. Densities obtained with post HF calculations show a similar behavior around p = 1.0 and 2.0, that are different from the DFT results. Radial momentum densities (p-densities) are more influenced by the electronic correlation than the exchange part of the DFT methods. CISD p-density is more affected than DFT p-density when the intermolecular distance increases. An analysis of the powers of moments calculated with different methods has been carried out. Contribution to the Serafin Fraga Memorial Issue.     

受限于纳米狭缝中的四缔合Lennard-Lones流体的相平衡和界面张力研究

分别用改进的基础测量理论和平均球近似理论表达短程作用和长程作用对四缔合Lennard-Jones流体的过剩自由能的贡献. 在密度函泛理论的框架下, 研究了平均密度等温线, 密度分布, 未缔合分子在平衡汽相和液相中的分布, 相平衡以及平衡时的界面张力等热力学性质. 分析了缔合能量, 流体-固体作用和孔宽对受限于纳米狭缝中的四缔合Lennard-Jones流体相行为的影响.     

Scaling relations,virial theorem,and energy densities for long‐range and short‐range density functionals

Decomposition of the Coulomb electron–electron interaction into a long‐range and a short‐range part is described within the framework of density functional theory, deriving some scaling relations and the corresponding virial theorem. We study the behavior of the local density approximation in the high‐density limit for the long‐range and the short‐range functionals by carrying out a detailed analysis of the correlation energy of a uniform electron gas interacting via a long‐range‐only electron–electron repulsion. Possible definitions of exchange and correlation energy densities are discussed and clarified with some examples. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Kirkwood-Buff integrals and density fluctuations in aqueous solution of caffeine

The Kirkwood-Buff theory is applied to caffeine aqueous solution. The integrals of radial distribution functions are calculated from the osmotic coefficient, density and sound velocity data at 25°C. The results are discussed in terms of density fluctuations of two components and the correlation between them. It is found that the concentration dependence of Kirkwood-Buff integrals reflects the association tendency of caffeine and its strong influence on the properties of the solvent.     

Intrinsic minimal atomic basis representation of molecular electronic wavefunctions

The problem of finding an effective minimal atomic basis that spans the exact occupied wavefunctions of a mean‐field theory at a given molecular geometry, which has a number of special properties, is studied and a new general procedure is developed that (1) solves for a raw minimal set of strongly atom‐centered functions—products of spherical harmonics and molecule‐optimized radial parts—that approximately span the occupied molecular wavefunctions and minimize the sum of their energies, (2) uses projection operators to get a new set of deformed atom‐centered functions that exactly span the occupied space and fall into core and valence subsets, (3) applies a new zero‐bond‐dipole orthogonalization scheme to the core‐orthogonalized valence subset so that for each two‐center product of these functions the projection of its dipole moment along the line going through the two centers is zero. The resulting effective minimal atomic basis is intrinsic to the molecular problem and does not need a free‐atoms input. Some interesting features of the zero‐bond‐dipole orthogonalization are showing up in the atomic population analysis of a diverse set of molecules. The new procedure may be useful for the interpretation of electronic structure, for the construction of model Hamiltonians in terms of transferable molecular integrals, and for the definition of active valence space in the treatment of electron correlation. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

On the stability of metal–aminoacid complexes in water based on water–ligand exchange reactions and electronic properties: Detailed study on iron–glycine hexacoordinated complexes

Thermodynamic stability of metal–aminoacid complexes in water is discussed in terms of the Gibbs free energy of water–ligand exchange processes, and the electronic stabilizing factors thoroughly investigated by means of 1‐electron and 2‐electron density properties. Hexacoordinated complexes formed between iron cations and glycine molecules acting as monodentate or bidentate ligands have been chosen as targets for the current study. Results agree with experimental findings, and complexes formed with bidentate ligands are found to be more stable than those formed with monodentate ones. The larger the number of the coordinated glycine molecules the more stable is the complex. Fe(III) complexes are more stable than Fe(II) ones, but differences are small and the Fe³⁺/Fe²⁺ exchange process appears to be energetically feasible for these complexes. Formation of the second glycine–iron interaction involving the amino nitrogen in the bidentate ligands is enthalpycally unfavorable but takes place due to the large entropy rise of the process. The larger stability of Fe(III) complexes is due however to the balance between energetic and solvation terms, which is favorable to these complexes. Electron density properties account satisfactorily for the electronic energy changes along the complex formation in terms of ligand–metal electron transfer and covalent bond orders. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Correlation energy,correlated electron density,and exchange‐correlation potential in some spherically confined atoms

We report correlation energies, electron densities, and exchange‐correlation potentials obtained from configuration interaction and density functional calculations on spherically confined He, Be, Be²⁺, and Ne atoms. The variation of the correlation energy with the confinement radius R_c is relatively small for the He, Be²⁺, and Ne systems. Curiously, the Lee–Yang–Parr (LYP) functional works well for weak confinements but fails completely for small R_c. However, in the neutral beryllium atom the CI correlation energy increases markedly with decreasing R_c. This effect is less pronounced at the density‐functional theory level. The LYP functional performs very well for the unconfined Be atom, but fails badly for small R_c. The standard exchange‐correlation potentials exhibit significant deviation from the “exact” potential obtained by inversion of Kohn–Sham equation. The LYP correlation potential behaves erratically at strong confinements. © 2016 Wiley Periodicals, Inc.