Hartree-Fock soft Coulomb hole to estimate correlation energies in atoms, molecules and polymers

We have shown that the empirical correction introduced into the Hartree-Fock method to calculate correlation energies for atoms and therefore to remove the error caused by the so-called Coulomb hole can be extended from atoms to molecules and polymers. A reformulation was required of the necessary parameter representation. The reparametrization has been performed staying as close as possible to the original expressions for atoms reported by Chakravorty and Clementi (S.J. Chakravorty and E. Clementi, Phys. Rev. A, 39 (1989) 2290). In addition to their work, where the correlation energy has been calculated with the self-consistent Hartree-Fock wavefunction and the correction integrals, we have performed investigations, including the perturbation operator in the Fock operator, so that the total energy also contains the correlation energy. The applications of this approach to atoms and molecules show that the total electron correlation energies and ionization potentials calculated as differences of total energies can be obtained very satisfactorily. On the basis of the reported calculations it turns out that one obtains better agreement with reference values of more sophisticated calculations when the correction integrals are used to build up the Fock matrix. Furthermore we have found that the magnitude of the correlation energy depends only weakly on the size of the basis sets, which makes this empirical method very attractive for its application to large molecular and polymeric systems.     

Generalized electron number distribution functions: real space versus orbital space descriptions

The algebraic expressions previously derived to compute the electron number distribution functions (EDF) for exhaustive partitions of the physical space into sharp-boundary atoms are generalized to allow for the use of fuzzy atoms and orbital-based partitions. In some of the latter, the atomic overlap matrix required to obtain the EDF is analytical. This makes them attractive alternatives to other definitions, as the one based on the atomic basins of the quantum theory of atoms in molecules (QTAIM), which are more physically sound but also much more demanding computationally. We will compute the EDF for a series of test molecules using different fuzzy and orbital-based partitions and compare them to QTAIM EDF. The effects of electron correlation and the use of the core approximation on the EDF will also be explored.     

Hartree-Fock与密度泛函混合处理中的电子自相关和自旋平行相关问题

电子气近似中的电子相关能与量子化学中的Hartree-Fock相关能在定义上不相互等同。作者从假想的、含N个电子的"有限电子气"出发, 通过比较这类体系与无限电子气在物理模型上的差异, 合理地把电子气相关能定量地分解为单电子自相关、电子自旋平行相关以及Hartree-Fock相关三个部分。并阐明了各组分的构成随N的变化规律。在此基础上建立的Hartree-Fock与密函混合处理方案, 无须借助任何经验参数, 仅通过简捷的计算即可实现原子和分子的相关能校正。平均误差为4.2%, 优于CI-SD和MP4等Hartree-Fock处理的结果。     

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.     

Shannon information entropy of fractional occupation probability as an electron correlation measure in atoms and molecules

A new method to determine electron correlation energy is presented for atoms and molecules. This method is based on Shannon information entropy that is obtained by fractional occupation probabilities of natural atomic orbitals. It is indicated that the Shannon entropy increases as the number of electrons increases and thus can be considered as a possible measure for the electron correlation in atomic and molecular systems. For neutral atoms and singly charged positive ions we proposed an expression for correlation energy with explicit dependence on the Shannon entropy and atomic number. The obtained correlation energies have been used to compute the first ionization potentials of the ground state of the main group elements from hydrogen through krypton. The calculated ionization potentials are in reasonably good agreement with their corresponding experimental values.We also developed the additivity scheme to find a connection between Shannon entropy and molecular correlation energy. The estimated molecular correlation energies show an excellent agreement with those obtained by elaborate G3 method with R² = 0.990.     

Aromatic Superhalogens

No organic molecules with electron affinities near or above those of halogens are known. We show for the first time that aromaticity rules can be used to design molecules with electron affinities far exceeding those of halogen atoms either by tailoring the ligands of cyclopentadienyl or by multiple benzoannulations of cyclopentadienyl in conjunction with the substitution of CH groups with isoelectronic N atoms. Results based on density functional theory revealed that the electron affinities of some of these organic molecules can reach as high as 5.59 eV, thus opening the door to new class of superhalogens that contain neither a metal nor a halogen atom.     

Towards benchmark second-order correlation energies for large atoms: Zn2+ revisited

To provide very accurate reference results for the second-order M?ller-Plesset (MP2) energy and its various components for Zn(2+), which plays for 3d-electron systems a similar role as Ne for smaller atoms and molecules, we have performed extensive calculation by two completely different implementations of the MP2 method: the finite element method (FEM) and the variation-perturbation (VP) method. The FEM and VP calculations yield partial wave contributions up to l(max)=45 and 12, respectively. Detailed comparison of all FEM and VP energy components for l(max)=12 has disclosed an extraordinary similarity, which justifies using the present results as benchmarks. The present correlation energies are compared with other works. The dependability of an earlier version of FEM, already applied to very large closed-shell atoms, is confirmed. It has been found that for larger atoms the accuracy of the analytical Hartree-Fock results has an impact on the accuracy of the MP2 energies greater than for smaller atoms. Fields of applications of the present results in studies of various electron correlation effects in 3d-electron atoms and molecules are indicated.     

Pulsradiolyse organischer Halogenverbindungen I. Nachweis kurzlebiger Charge-Transfer Komplexe mit Chloratomen

In a solution of benzene in carbon tetrachloride a transient absorption in the visible part of the spectrum could be detected. It appears within less than 0.3 μs after the irradiation by a high-energy electron pulse, and it can be shown to be due to the charge-transfer complex between the chlorine atoms as electron acceptors and benzene molecules as electron donors. A variety of aromatic hydrocarbons also yield similar absorption bands in the visible. They show a linear correlation between the absorption energy and the ionisation potential of the aromatic molecules, which is typical for charge-transfer complexes. A minimum value for the equilibrium constant of complex formation is given. The equilibrium is almost fully shifted to the complex side. An estimated G value for the charge-transfer complex indicates that the complex is actually part of a main reaction in the radiation-induced mechanism. The decay of the charge-transfer complex is mostly pseudo-first order with a half life of a few microseconds.     

Correlation energies in the spin-density functional formalism

It has been shown recently that dynamical correlation effects can be adequately described by using an electron-gas expression for correlation between electrons of different spins. In this paper the method is applied to the calculation of excitation energies for the first- and second-row atoms and to the determination of ground-state properties for small polyatomic molecules, such as CH₂, CH₄, CH ₄ ⁺ , CH ₅ ⁺ . Additionally, deficiencies of the method for cases with few electrons and strongly varying electron density are investigated and an empirical correction to the electron-gas approximation is proposed. This correction is based on atomic data and gives an overall improvement for test molecules with two to four electrons.     

Elastic scattering of low and intermediate-energy electrons by Kr and Xe atoms

The many-body correlation forces, which act between the impinging electron and the bound electrons of the two heaviest rare gas atoms, are treated here using a newly developed correlation-polarisation potential that originates from the calculation of correlation energies in electronic bound-states of atoms and molecules. The new formulation of such forces, already tested by us for the lighter atomic targets, is particularly effective for the present systems and can be implemented very easily even for heavy atomic targets. The calculations reported in this paper show clearly that very good accord is obtained with more sophisticated theoretical treatments and with several experimental data on integral cross sections, momentum transfer cross sections and angular distributions.Von Humboldt — Prize Awardee 1992     

ERKALE—A flexible program package for X‐ray properties of atoms and molecules

ERKALE is a novel software program for computing X‐ray properties, such as ground‐state electron momentum densities, Compton profiles, and core and valence electron excitation spectra of atoms and molecules. The program operates at Hartree–Fock or density‐functional level of theory and supports Gaussian basis sets of arbitrary angular momentum and a wide variety of exchange‐correlation functionals. ERKALE includes modern convergence accelerators such as Broyden and ADIIS and it is suitable for general use, as calculations with thousands of basis functions can routinely be performed on desktop computers. Furthermore, ERKALE is written in an object oriented manner, making the code easy to understand and to extend to new properties while being ideal also for teaching purposes. © 2012 Wiley Periodicals, Inc.     

A recipe for designing molecules with ever-increasing electron affinities

Halogens possess among the highest electron affinities of elements in the periodic table. Superhalogen molecules with electron affinities higher than those of halogen atoms have been known to form when a metal atom is surrounded with halogen atoms. Recently, it was discovered that a new class of molecules called hyperhalogens with electron affinities higher than those of superhalogens can form when the latter serve as the building block. By use of density functional theory and B3LYP hybrid exchange-correlation functional we show that molecules with electron affinities even higher can be formed by using hyperhalogens as building blocks. We demonstrate this by using Na and Li as metal atoms and F, BF(4), and Na(BF(4))(2) as halogen, superhalogen, and hyperhalogen building blocks. The predicted electron affinities of Na[Na(BF(4))(2)](2) and Li[Li(BF(4))(2)](2) are 9.18 and 9.01 eV, which are, respectively, 0.85 and 0.5 eV higher than those of their hyperhalogen [Na(BF(4))(2) and Li(BF(4))(2)] counterparts.     

On trends in total cross sections for electron (positron) scattering on atoms and molecules at intermediate energies

An examination of total electron and positron scattering cross sections in a large variety of atoms and molecules reveals a trend related to ground state target dipole polarizability. Some correlations of total cross section with diamagnetic susceptibility and the number of target electrons have also been noted. Experimental positron and electron cross sections between 100 and 500 eV can be reasonably well described by a simple formula based on polarizability and energy correlation.     

Application of the quantum theory of atoms in molecules to selected physico-chemical and biophysical problems: focus on correlation with experiment

This article reviews how the quantum theory of atoms in molecules (QTAIM) can be used to predict experimental physico-chemical properties of molecules of biologic interest: the amino acids, the polycyclic aromatic hydrocarbons (PAH), and the opiates, for example, morphine and PEO. The predicted experimental properties are as diverse as the partial molar volumes, the free energies of hydration, the second code-letter in the genetic code, the resonance energies, and the proton spin-spin coupling constants. Recent examples of the utilization of QTAIM to construct excellent statistical models (with squared correlation coefficients (r(2)) > 0.9) correlating properties of the electron density and of the pair density to experiment are reviewed. Some new results on the solvent effects on electron delocalization are also presented.     

Accurate calculation of core-electron binding energies: multireference perturbation treatment

Multireference perturbation theory (MRPT) with multiconfigurational self-consistent field (MCSCF) reference functions is applied to the calculations of core-electron binding energies (CEBEs) of atoms and molecules. Orbital relaxations in a core-ionized state and electron correlation are both taken into account in a conventional MCSCF-MRPT procedure. In the MCSCF calculation, the target core ionized state is directly optimized as an excited state and this treatment can completely prevent a variational collapse. Multireference Moller-Plesset perturbation theory and multiconfigurational self-consistent field reference quasidegenerated perturbation theory were used to treat electron correlation. The present method quite accurately reproduced the 1s CEBEs of CH4, NH3, H2O, and FH; the average deviation from the experimental data is 0.11 eV using Ahlrichs' VTZ basis set. The C 1s and O 1s CEBEs of formic acid and acetic acid were calculated and the results are consistent with the bonding characters of the atoms in these molecules. The present procedure can also be applied to CEBEs of higher angular momentum orbitals by including spin-orbit coupling. The calculated CEBEs of Ar 2p, HCl 2p, Kr 3d, and HBr 3d are in reasonable agreement with the available experimental values. In the calculation of the 3d CEBEs, a relativistic correction significantly improves the agreements. The effect of polarization functions is also discussed.     

Unusual halogen-bonded complex FBrdelta+...delta+BrF and hydrogen-bonded complex FBrdelta+...delta+HF formed by interactions between two positively charged atoms of different polar molecules

Using ab initio calculations, the authors' predicted for the first time that the halogen-bonded complex FBrdelta+...delta+BrF and hydrogen-bonded complex FBrdelta+...delta+HF formed by the interactions between two positively charged atoms of different polar molecules can be stable in gas phase. It shows that halogen bond or hydrogen bond not only exists between oppositely charged atoms but also between like-charged atoms. That the attraction arising from the special halogen bond or hydrogen bond can exceed the electrostatic repulsion between two contact positively charged atoms stabilizes the complex. Of course, from the point of view of physics they can consider the interactions in FBrdelta+...delta+BrF and FBrdelta+...delta+HF as mainly the sum of the long range molecular interactions, namely, electrostatic, induction, and dispersion with some short-range repulsion. They found that the intermolecular electron correlation contribution representing dispersion interaction plays a crucial role in the stabilities of seemingly repulsive complexes FBrdelta+...delta+BrF and FBrdelta+...delta+HF.     

Relativistic and electron‐correlation effects on magnetizabilities investigated by the Douglas‐Kroll‐Hess method and the second‐order Møller‐Plesset perturbation theory

Isotropic and anisotropic magnetizabilities for noble gas atoms and a series of singlet and triplet molecules were calculated using the second‐order Douglas‐Kroll‐Hess (DKH2) Hamiltonian containing the vector potential A and in part using second‐order generalized unrestricted Møller‐Plesset (GUMP2) theory. The DKH2 Hamiltonian was resolved into three parts (spin‐free terms, spin‐dependent terms, and magnetic perturbation terms), and the magnetizabilities were decomposed into diamagnetic and paramagnetic terms to investigate the relativistic and electron‐correlation effects in detail. For Ne, Kr, and Xe, the calculated magnetizabilities approached the experimental values, once relativistic and electron‐correlation effects were included. For the IF molecule, the magnetizability was strongly affected by the spin‐orbit interaction, and the total relativistic contribution amounted to 22%. For group 17, 16, 15, and 14 hydrides, the calculated relativistic effects were small (less than 3%), and trends were observed in relativistic and electron‐correlation effects across groups and periods. The magnetizability anisotropies of triplet molecules were generally larger than those of similar singlet molecules. The so‐called relativistic‐correlation interference for the magnetizabilities computed using the relativistic GUMP2 method can be neglected for the molecules evaluated, with exception of triplet SbH. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009