A relationship between correlation energies and sizes: The helium-like ions

The correlation energy (E _corr) is found to be inversely proportional to the product of the electron pair size (2>) and the square of the effective nuclear charge (Z _eff) for the helium-like ions.     

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 .     

On the relation between the formal atomic charges and total molecular energies

It is shown that the total SCF molecular energies are fairly well reproduced by the sum of electrostatic potentials exerted on the nuclei calculated in the point-charge approximation. Hence, there is a very simple relation between the total energies and formal atomic charges in molecules. The semiempirical SCC-MO charges have the same performance as the ab initio DZ ones.     

Simple molecular wavefunctions with correlation corrections

It is shown that the main deficiencies of wavefunctions of Hartree-Fock type (wrong dissociation behavior and absence of correlation between electrons of unlike spin) may be corrected by a simple method. Just sufficient CI is admitted to ensure qualitatively correct dissociation, while the short-range correlation energy is estimated with the Colle-Salvetti functional. Potential energy curves for H₂ and LiH are computed at various levels of approximation and the main features of the method are discussed.     

Simple empirical formulas and good quality estimations for electron correlation energies of molecules and molecular clusters: First-row atom molecules

Using the ab initio coupled cluster method, correlation energies were calculated for a number of molecules composed of first-row atoms. The results of computations can be fitted rather well with simple analytic formulas. The main result of the present investigation is that intraatomic part of the correlation energy is proportional to sum of squares of valence electron charges on atoms composing the molecule. The proportionality coefficient depends on the basis set used. Independently, the approximations were introduced which allow for good estimation of intraatomic correlation energy by using M øller-Plesset second-order perturbation calculations only. © 1996 John Wiley & Sons, Inc.     

Simple molecular wavefunctions with correlation corrections II

The potential curves for the ground state of Li₂ (¹ _g ⁺ ) and FH (¹ _g ⁺ ) are computed. The correlation energy is calculated using a functional of the one- and two-electron density matrices derived from an MC SCF reference wavefunction and is added to the reference energy to obtain a correlated potential curve.     

Ionization energies of homologous organic compounds and correlation with molecular size

The empirical relationship IE ∝? 1/n, between the ionization energy (IE) and molecular size (as represented by the number of atoms, n) in homologous series of organic compounds has been confirmed for n-alkanes, alkyl halides, cyclic ethers and alkyl-subsiituted cycloalkanes. For each series, the plot of IE vs. 1/n produces a line of characteristic slope. The only exception is the cycloalkanes themselves, whose IE values (from C₃ to C₈) are closely similar. The possible relationship between the IE, the polarizability of the molecules and the energy of the highest occupied molecular orbital is briefly discussed.     

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.     

A new functional for variational calculation of atomic and molecular second-order correlation energies

Second-order correlation energies for atoms and molecules are calculated with a novel variational functional that is closely related to the one used before but neglects the most time-consuming terms. Consequently much larger basis sets could be used. Results for He, Be, H₂ and LiH obtained with an explicitly correlated gaussian geminal basis are better than the best published results by 0.32, 0.06, 3.3, and 6.2% and are estimated to be accurate to within a fraction of 1%.     

Investigation on the correlation between the interaction energies of all substituted groups and the molecular stabilities of nitro compounds

A model, similar to an isodesmic reaction, is for the first time presented in this paper for describing, defining, and calculating the interaction energies of the indirectly linked groups or atoms within one molecule. Its applications to nitro substitutes of methane, benzene, and cubane verify its validity for a separate group of closely related compounds by the reasonable correlation between the calculated interaction energies of all substituted groups and the molecular stabilities or experimental impact sensitivities. Comparing with some existing rules of assessing the molecular stability, this so-called interaction energy is calculated using a model considering the chemical structures, that is, the electronic environments of compounds, and can be well related with the stabilities of nitro compounds. All investigation results show that the so-called interaction energy is a new, quantitative, and useful tool to evaluate the stabilities of nitro compounds.     

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.     

Accuracy of basis-set extrapolation schemes for DFT-RPA correlation energies in molecular calculations

We construct a reference benchmark set for atomic and molecular random phase approximation (RPA) correlation energies in a density functional theory framework at the complete basis-set limit. This set is used to evaluate the accuracy of some popular extrapolation schemes for RPA all-electron molecular calculations. The results indicate that for absolute energies, accurate results, clearly outperforming raw data, are achievable with two-point extrapolation schemes based on quintuple- and sextuple-zeta basis sets. Moreover, we show that results in good agreement with the benchmark can also be obtained by using a semiempirical extrapolation procedure based on quadruple- and quintuple-zeta basis sets. Finally, we analyze the performance of different extrapolation schemes for atomization energies.     

The correspondence between the molecular orbital and differential ionization energies methods

The correspondence between Self-Consistent Hückel MO methods and Differential Ionization Energies methods is discussed in terms of the approximations used for the diagonal matrix elements. The two methods are shown to be equivalent if electronic correlation is neglected. Ground-state properties of the hydrogen halides are calculated by these simple methods and shown to be in good overall agreement with experimental data.

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Zusammenfassung Die Übereinstimmung zwischen selbstkonsistenten Hückel MO-Methoden und Methoden der Differentiellen Ionisierungsenergien wird in Termen solcher Näherungen diskutiert, die für die diagonalen Matrixelemente benutzt werden. Es wird gezeigt, daß die beiden Methoden äquivalent sind, wenn die Elektronenkorrelation vernachlässigt wird. Grundzustandseigenschaften der hydrogen halides werden mit diesen einfachen Methoden ausgerechnet und zeigen sich in überall guter Übereinstimmung mit experimentellen Daten.

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Résumé La correspondance entre les méthodes SCF Hückel et d'énergie d'ionisation différentielle est discutée en fonction des approximations utilisées pour les éléments de matrice diagonaux. Les deux méthodes sont équivalentes si la corrélation électronique est négligée. Les propriétés de l'état fondamental des acides halogènés sont calculées par ces méthodes simples et l'on constate un accord raisonnable avec les données expérimentales.

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Work supported by the Research Corporation and the National Science Foundation (Grant GY 2657/67).     

On the correlation between polarizabilities and molecular dimensions

A correlation between electric polarizabihty and the mean linear electronic charge density is proposed and shown to exist for some homologous electrically neutral atomic and molecular species. The correlation implies an inverse relationship between molecular dimensions in these species and the charge distortion induced in them by a uniform electric field.     

A correlation between polarizabilities and atomic and molecular dimensions

A method of correlating polarizability to the volume of atoms and molecules is proposed. This method can serve to predict atomic and mean molecular polarizabilities. The standard deviation for the group of the hydrogen halides is 0.02 and for the group of the homopolar diatomic molecules 0.05. The interpolated polarizability of the N₃ molecule was found to be 3.017 A³.     

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.     

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