Simple relationship between total molecular correlation energies and LMO sizes

As an alternative to the density functional approach to estimating total molecular correlation energies, the equation E_corr=?0.06593 ∑ R, where R_i=〈r²〉${}_{\text{i}}^{\text{½}}$ and i runs over the localized molecular orbitals was fitted to 25 STO -3G data points with a root-mean-square error of 0.025 hartree. Other more general equations were tried but no significant improvement was observed in the fit.     

A relationship between the sizes and energies of localized molecular orbitals. I. A study of selected first-row hydrides

Ab initio calculations have been performed on selected first-row hydrides with a large Gaussian basis set. Energy localized molecular orbitals (LMO 'S ) were computed and analysed in terms of their sizes and shapes. The total molecular electronic energy was partitioned into components which may be associated with an MO , and the relationship between the sizes and energies of such orbitals was examined. It was found that a simple energy–size relationship exists for core LMO 'S but only approximately holds for bond LMO 'S .     

A relationship between atomic correlation energy and Tsallis entropy

A new relationship between electron correlation energy and Tsallis entropy is presented. This relationship is a generalization of previous equations which correlate the atomic correlation energy and the Shannon entropy. The results, relatively to the atoms with atomic number 2 < Z < 29, put in evidence the crucial role of the p‐parameter in terms of representation of the long‐range interaction contribution in the correlation energy. Moreover, the p‐values, which reproduce the experimental values of the correlation energy, indicate that the atomic wave functions are more localized with respect to those calculated in the limit of p → 1. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Accurate all-electron correlation energies for the closed-shell atoms from Ar to Rn and their relationship to the corresponding MP2 correlation energies

All-electron correlation energies E(c) are not very well-known for atoms with more than 18 electrons. Hence, coupled-cluster calculations in carefully designed basis sets are combined with fully converged second-order M?ller-Plesset perturbation theory (MP2) computations to obtain fairly accurate, nonrelativistic E(c) values for the 12 closed-shell atoms from Ar to Rn. These energies will be useful for the evaluation and parameterization of density functionals. The results show that MP2 overestimates ∣E(c)∣ for heavy atoms. Spin-component scaling of the MP2 correlation energy is used to provide a simple explanation for this overestimation.     

脂肪胺、醇HOMO能级与质子亲和能关系

20世纪 70年代前后 ,随着离子回旋共振 (ＩＣＲ)实验技术的发展 ,在气相条件下能够进行有机化合物质子亲和能的测定 ,摆脱了复杂溶剂化作用的干扰 ,可以直接研究分子结构与有机化合物气相酸碱性的关系 ,加深了人们对取代基效应的认识 ,为进一步研究溶剂化效应对有机化合物性能的影响奠定了基础 .因此 ,分子结构与气相酸碱性的关系研究成为人们感兴趣的课题之一 .迄今 ,在探讨有机同系物气相碱相与分子结构关系问题的研究方面 ,大体分为两类 :一类是采用经验或半经验参数 (如取代基电子效应参数 )与质子亲和能相关联[1,2 ] ;另一类是利用量子…     

On the relation between core electron binding energies of ions in solution and their solvation energies

Experimental and computational results from the study of positive and negative ions in solution are presented. The importance of short-range interactions between ion and solvent is studied with regard to core ionization of the ion. Exchange repulsion is found to be a significant factor in the interpretation of data for both cations and anions. Experimental results are presented for the core ionization of the OH^? ion in solution. The data show a strong similarity with corresponding data for the F^? ion, resulting in a large negative solvation energy for the final core hole state. The Be²⁺ ion shows large solvation energies for both ground- and core-ionized states, which is interpreted as due to charge transfer effects between solvent and ion.     

Density functional theory studies on the dissociation energies of metallic salts: relationship between lattice and dissociation energies

The formation and physicochemical properties of polymer electrolytes strongly depend on the lattice energy of metal salts. An indirect but efficient way to estimate the lattice energy through the relationship between the heterolytic bond dissociation and lattice energies is proposed in this work. The heterolytic bond dissociation energies for alkali metal compounds were calculated theoretically using the Density Functional Theory (DFT) of B3LYP level with 6‐311+G(d,p) and 6‐311+G(2df,p) basis sets. For transition metal compounds, the same method was employed except for using the effective core potential (ECP) of LANL2DZ and SDD on transition metals for 6‐311+G(d,p) and 6‐311+G(2df,p) calculations, respectively. The dissociation energies calculated by 6‐311+G(2df,p) basis set combined with SDD basis set were better correlated with the experimental values with average error of ca. ±1.0% than those by 6‐311+G* combined with the LANL2DZ basis set. The relationship between dissociation and lattice energies was found to be fairly linear (r>0.98). Thus, this method can be used to estimate the lattice energy of an unknown ionic compound with reasonably high accuracy. We also found that the dissociation energies of transition metal salts were relatively larger than those of alkaline metal salts for comparable ionic radii. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 827–834, 2001     

Linear relationship between activation energies and reaction energies for coverage-dependent dissociation reactions on rhodium surfaces

Evidence of a relationship between activation energies and enthalpy changes of various dissociation reactions on transition metals has been reported recently. A reconsideration of density functional theory results for dissociation energies of oxygen and NO on different rhodium surfaces (low-index and stepped) and their dependencies on oxygen precoverage reveal that also here a linear Br?nsted-Evans-Polanyi (BEP) relationship exists. The establishment of such a general concept would be of tremendous importance for the development of detailed, elementary-step reaction mechanisms, because the activation energies of reaction steps as well as their coverage dependencies could be estimated based on the adsorption energies calculated by means of DFT.     

A relationship between atomic correlation energy of neutral atoms and generalized entropy

In a previous article, hereafter named as Paper I, we have showed a relationship between atomic correlation energy of neutral atoms with 2 < Z < 29 and Tsallis entropy. In this article, we generalize this relation showing the link between the atomic correlation energy and a general form of entropy obtained from deformed algebra. The results evidence the role of both q and Δ parameters of the general entropy, in terms of contribution of the long‐range interactions in the correlation energy. The q and Δ values, obtained as best fit of the atomic correlation energies 2 < Z < 29, indicate that this general form of entropy reduces to the Tsallis one, reproducing well the trend of the correlation energy for low Z. Moreover, as a consequence of these values of the parameters, the state atomic wave function is more localized with respect to the wave function calculated in the limit of Shannon entropy. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

The influence of electron correlation on reaction energies. The dimerization energies of BH3 and LiH

Results of rigorous computations employing extended Gaussian-type basis sets are reported for BH₃, B₂H₆, LiH, and Li₂H₂ in their respective equilibrium geometries. The dimerization energy of BH₃ is calculated as −20.7 kcal/mol within the Hartree-Fock approximation and as −36.6 kcal/mol if electron correlation is included. The corresponding results for the dimerization of LiH are −47.3 kcal/mol and −48.3 kcal/mol. Partitioning of the correlation energy contributions allows to attribute the effect of electron correlation to the increase of next neighbour bond interactions on the dimerization of BH₃ and LiH. The difficulties of accurate computations of reaction energies are discussed in detail.     

Derivation of the linear relationship between SWCNTs functionalization energies and sidewall curvature

A simple linear relationship between the functionalization reaction energies for the exohedral monovalent addition on the surface of an ideal, infinitely long, single-walled carbon nanotube (SWCNT) and the reciprocal SWCNT radius has been derived employing the hard?Csoft acid basis principle and the tight binding model. The slope of the derived linear relationship is a function of the effective number of valence electrons involved in the functionalization reaction. The intercept of the derived linear relationship, equal to the reaction energies on a planar graphite surface, is a function of the electrophilicity of the monovalent addend and of the condensed Fukui function of its reacting atom. The theoretical predictions of this simple formula are coherent with the computational density functional theory data reported in the literature.     

The relationship between adsorption energies of methyl on metals and the metallic electronic properties: a first-principles DFT study

A theoretical study of CH3 adsorbed on the (111) surface of some transition and noble metal surfaces M (M = Cu, Ni, Rh, Pt, Pd, Ag, Au) and on the Fe(100) is presented. We find that the hollow site is preferred more than the top one for Fe, Ni, Rh, and Cu, but it is the other way for Pt, Pd, Au, and Ag. In addition, a good linear relationship was observed between the chemisorption energy and d-band center for Group VIII metals or the square of the coupling matrix element for Group IB metals at the hollow site. Interestingly, with a detailed comparison of the adsorption energies at the top and hollow sites, we find that the adsorption energies among each group are very similar on the top site, which supports the theoretical model of Hammer and Norskov that the coupling between the HOMO of adsorbate and sp states of the metal is dominant and almost equal, and that the second coupling to the d-band contributes less but reflects the change of the adsorption energy. It confirms that the coupling to the d band comprises two opposite factors, that is, the d-band center was attractive and the square of the coupling matrix element was repulsive, such that the contributions from the two factors can counteract each other at the top site.     

The relationship between thermodynamic stabilities of carbenium ions in the gas phase and in aqueous solution: A wide scope study

The thermodynamics of the reaction involving R_ref = tert-butyl and 21 carbenium ion/alcohol systems has been studied at the MP2/6-311+G(3d, 2p)//MP2/6-311+G(d, p) level. The results have been compared to the experimental data for the same systems in solution. The range of structural effects spans 102 kcal mol⁻¹ in the gas phase and is the widest ever examined. A physically meaningful correlation has been found. Phenyl-substituted systems are among the most important exceptions.     

The computation of accurate correlation energies using “strong-orthogonal” correlation functions

Correlation energies are computed for the ground state of He, using various Hylleraas-type correlation factors, according to E′ = E - E_O, where E refers to the total energy and E_O to the energy computed in the single determinant approximation, involving the same orbitals used for the computation of E. It is shown that this procedure, provides accurate estimates of the correlation energy, when the correlation functions are “strong orthogonal” to the corresponding uncorrelated wavefunctions.     

Dispersion self-free energies and interaction free energies of finite-sized ions in salt solutions

The role for many-body dipolar (dispersion) potentials in ion-solvent and ion-solvent-interface interactions is explored. Such many-body potentials, accessible in principle from measured dielectric data, are necessary in accounting for Hofmeister specific ion effects. Dispersion self-energy is the quantum electrodynamic analogue of the Born electrostatic self-energy of an ion. We here describe calculations of dispersion self-free energies of four different anions (OH-, Cl-, Br-, and I-) that take finite ion size into account. Three different examples of self-free energy calculations are presented. These are the self-free energy of transfer of an ion to bulk solution, which influences solubility; the dispersion potential acting between one ion and an air-water interface (important for surface tension calculations); and the dispersion potential acting between two ions (relevant to activity coefficient calculations). To illustrate the importance of dispersion self-free energies, we compare the Born and dispersion contributions to the free energy of ion transfer from water to air (oil). We have also calculated the change in interfacial tension with added salt for air (oil)-water interfaces. A new model is used that includes dispersion potentials acting on the ions near the interface, image potentials, and ions of finite size that are allowed to spill over the solution-air interface. It is shown that interfacial free energies require a knowledge of solvent profiles at the interface.     

The correlation potential for two-electron atomic ions

The correlation potential is computed for two electron atomic ions with atomic numbers from 1 to 10 using the charge density reconstructed from a natural orbital expansion of a Kinoshita-like atomic wave function. Over the wide range of densities involved, the correlation potentials are not even approximately a local function of the density.     

Investigation of correlation between impact sensitivities and bond dissociation energies in benzenoid nitro compounds

The geometries of ten benzenoid energetic materials are fully optimized by employing B3LYP and B3P86 methods with the 6–31G** basis set. Bond dissociation energies (BDEs) for the removal of the NO₂ group in benzenoid molecules are calculated at the same level. The calculation results show that the insertion of an electron withdrawing group increases the stability of the molecules, while the insertion of an electron donating group reduces the stability of the molecules. In addition, the relationship between the impact sensitivities and the weakest BDE values is examined. There exists a good linear correlation between the impact sensitivity and the ratio of the BDE value to the molecular total energy.     

A discussion on the energies involved in specific adsorption of ions

The change in specific adsorption of I^? ions on the series of metals Au, Hg, Bi, Pb, Cd, and Ga is analyzed using data of specifically adsorbed charge and shift in potential of zero charge. Factors determining the change in adsorbability are discussed in the light of previous formulations. It is shown that the work connected with water desorption as an ion becomes adsorbed, usually neglected or underestimated in previous discussions, is very likely to be the main factor determining the change in adsorbability along the series of metals. A rough estimation of energies involved in water desorption suggests that metal—water surface bonds are probably weak on sp-metals so that they are unable to affect the reactivity of metal surfaces with respect to the gas phase as strong covalent surface bonds are involved, for instance in the hydrogen evolution reaction. Conversely, the strong effect of water desorption on the specific adsorption of ions may be an indication of ion—metal interactions to be substantially independent of the nature of the metal. This suggests that covalent contributions to the surface bond are apparently minor for metals more electropositive than Au.     

Approximate exchange and electrostatic interaction energies of deformed ions

Computation of exchange-polarization and electrostatic-polarization interaction energies between ions is the most expensive step in ab initio investigations of the properties of perfect and imperfect ionic crystals. In the present paper approximate formulas are proposed for these quantities. They save about 95% of the computation time and give these values with an error less than 0.2 kcal mol^?1 as compared to ab initio results. The formulas for the exchange- and electrostatic-polarization energies involve the generalized overlap integral between the one-determinantal wave functions of the deformed ions. The approximations are tested in the calculations of the interactions of deformed ions in LiF and NaF crystals.