New efficient numerical method for solving pair correlation equations for diatomic molecules

A new method for solving correlation pair equations for diatomics is presented and followed by numerical results for the H₂ and LiH molecules. The essential feature of the new approach is a numerical representation of both basis two-electron functions and Coulomb and exchange potentials in pair equations. It is shown that this significantly simplifies the pair function optimization procedure.     

Electron correlation study for two-electron atoms by a simple correlated wave function

The difference in the electron correlation between H^- and other two-electron atoms is clarified by the introduction of the r₁₂ term in the wave function. By using the expansion of r₁₂, a certain modification of the usual electron correlation factor 1 + Cr₁₂ is introduced and its effectiveness is examined. Calculations are carried out for the ground state and the three lowest excited states (2³S, 2³P and 2¹P). The peculiar electron correlation in the ground state of H^? is shown by looking at the Coulomb hole for closed- and open-shelf models in comparison with those for other two-electron atoms.     

Application of the distinguishable electron method

In order to make a better assessment of the distinguishable electron method developed by Kirtman and co-workers, we have applied the method to some two-electron atoms and to H₂ and LiH. Our results lend support to the contention held by Kirtman and co-workers that the distinguishable electron method is a practical way of calculating reasonably accurate physical properties.     

Information distance analysis of molecular electron densities

The information‐theoretic basis of the Hirshfeld partitioning of the molecular electronic density into the densities of the “stockholder” atoms‐in‐molecules (AIM) is summarized. It is argued that these AIM densities minimize both the directed divergence (Kullback–Leibler) and divergence (Kullback) measures of the entropy deficiency between the AIM and their free atom analogs of the promolecule. The local equalization of the information distance densities of the Hirshfeld components, at the local value of the corresponding global entropy deficiency density, is outlined and several approximate relations are established between the alternative local measures of the missing information and the familiar function of a difference between the molecular and promolecule densities. Various global (of the system as a whole) and atomic measures of the entropy deficiency or the displacements relative to the isoelectronic promolecule, defined for densities or probabilities (shape functions) in both the local resolution and the Hirshfeld AIM discretization, are introduced and tested. This analysis is performed also for the valence electron (frozen‐core) approximation. Illustrative results for representative linear molecules, including diatomics, triatomics, and tetraatomics, are reported. They are interpreted as complementary characteristics of changes in the net AIM charge distribution and of the displacements in the information content of the electron distributions of bonded atoms. These numerical results confirm the overall similarity of the stockholder AIM to their free atom analogs and reflect the information displacements due to the AIM polarization and charge transfer in molecules. They also demonstrate the semiquantitative nature of the approximate relations established between the entropy deficiency densities and the related functions involving the density difference function. This development extends the range of interpretations based on the density difference diagrams into probing the associated information displacements in a molecule accompanying the formation of the chemical bonds. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002     

Charge Localization of Some Highly Polarizable Systems

In this work we discuss some close analogies among various intramolecular charge-transfer systems with high polarizability. They range from sudden-polarization systems concerning two-electron localization to valence-hole and core-hole systems involving only one-electron localization, and the combined situation of valence electron-core hole pair localization. The high polarizability of a two-site (a, b) system is shown to be correlated to the weakness of the electronic coupling integral <a|H|b> between the sites. The hole localization in core-hole states and van der waals ions is compared with that of molecular ions due to solvation effect. The electron-hole pair localization in the core-hole state of the mixed valence system is compared with that in the Π_g,a state of H₂ due to electron correlation behavior.     

Nonempirical parameters of the nonlocal core pseudopotential for the second and third row elements

For the core pseudopotential (CP) model constructed in terms of Bonifacic-Huzinaga nonlocal CP theory, parameters of the local component of CP are calculated for the second-and third-row elements. The resulting CP are associated with the Coulomb, exchange, and correlation potentials created by the nuclear charge and electron density of the core electrons. The electronic structure and potential energy surface are calculated for the hydrides of the second-row elements (LiH, CH₄, NH₃, H₂O, HF); the calculations are performed by the nonempirical nonlocal CP method. The results of these calculations agree well with those of SCF MO LCAO ab initio calculations and with experimental data.     

Model universal coulomb hole function for many-electron systems

In the framework of the homogeneous electron gas theory we give a model function G_c of the Coulomb hole that can be considered as an approximate universal correlation function for many-electron systems. The function G_c reflects the right asymptotic behavior of the correlation function of an electron gas in high and low density limits and enables one to reproduce experimental correlation energies of a number of atoms of the first and second periods in a local density approximation with the relative error 0.3–4.2%. The estimate of contributions of electrons with parallel or antiparallel spins into correlation energy shows that in the domain of densities typical for atoms of the first and second periods, the Coulomb correlation of electrons with parallel spins is in high extent suppressed by the Fermi correlation.     

Statistical electron correlation — coefficients and — holes in molecules

Summary Electron correlation in the H₂, LiH and BH molecules has been analyzed in terms of the statistical correlation coefficients introduced by Kutzelnigg, Del Re, and Berthier. Angular, radial (in-out), longitudinal (left-right) and transverse correlation coefficients have been evaluated from both self-consistent-field (SCF) and configuration interaction (CI) wave functions. It has been found that these coefficients reflect fairly well the correlation behavior in the molecular system. The lack of spherical symmetry in molecular densities adds new features to these correlation coefficients and this information can be useful for the study of electronic structure in molecules. The correlation hole function, Fermi and Coulomb holes in these systems have also been calculated and discussed.Dedicated to Professor Werner Kutzelnigg on the occasion of his sixtieth birthday     

Stockholder projector analysis: a Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

A previously introduced partitioning of the molecular one-electron density matrix over atoms and bonds [D. Vanfleteren et al., J. Chem. Phys. 133, 231103 (2010)] is investigated in detail. Orthogonal projection operators are used to define atomic subspaces, as in Natural Population Analysis. The orthogonal projection operators are constructed with a recursive scheme. These operators are chemically relevant and obey a stockholder principle, familiar from the Hirshfeld-I partitioning of the electron density. The stockholder principle is extended to density matrices, where the orthogonal projectors are considered to be atomic fractions of the summed contributions. All calculations are performed as matrix manipulations in one-electron Hilbert space. Mathematical proofs and numerical evidence concerning this recursive scheme are provided in the present paper. The advantages associated with the use of these stockholder projection operators are examined with respect to covalent bond orders, bond polarization, and transferability.     

Electronic charge density and mean kinetic energy of lithium orbitals in LiH,LiH+, Li2, Li2+, LiH2+, and Li2H+

The electron density near the lithium nucleus in the species LiH, LiH⁺, Li₂, Li₂⁺, LiH₂⁺, and Li₂H⁺ was analyzed by transforming the SCF molecular orbitals into a sum of atomic contribnutions, for both core and valence orbitals. These “hybrid-atomic” orbitals were used to compare: electron densities, orbital polarizations, and orbital mean kinetic energies with the corresponding lithium atom quantities. Core-orbital electron densities at the lithium nucleus were observed to increase by up to 0.5% relative to the lithium atom 1s orbital. Lithium cores also exhibited polarization but, surprisingly, in the direction away from the internuclear region. Similar dramatic changes were seen in the electron densities of the valence orbitals of lithium: The electron density at the nucleus for these orbitals increased two-fold for homonuclear species and twenty-fold for heteronuclear triatomic species relative to the electron density at the nucleus in lithium atom. The polarization of the valence orbital electronic charge, in the vicinity of the lithium nucleus, was also away from the internuclear region. The mean “hybrid-atomic” orbital kinetic energies associated with the lithium atom in the molecules also showed changes relative to the free lithium atom. Such changes, accompanying bond formation, were relatively small for the lithium core orbitals (within 0.2% of the value for lithium atom). The orbital kinetic energies for the lithium valence electrons, however, increased considerably relative to the lithium atom: By a factor of about 2 in homonuclear diatomics, by a factor of 7 in heteronuclear diatomics, and by a factor of 11 in the triatomic species. In summary, the total electronic density (core plus valence) at the lithium nucleus remained remarkably constant for all of the species studied, regardless of the effective charge on lithium. Thus, the drastic changes noted in the individual lithium orbitals occurred in a cooperative fashion so as to preserve a constant total electron density in the vicinity of the lithium nucleus. In all cases, bond formation was accompanied by an increase in the orbital kinetic energy of the lithium valence orbital. We suggest that these two observations represent important and significant features of chemical bonding which have not previously been emphasized.     

Deformation Density Study of KMnO4

The electron density distribution of KMnO₄ is studied by the X-ray diffraction method. Potassium permanganate crystalizes in an orthorhombic space group Pbnm with cell parameters a=7.3661(7), b=9.0610(9), c=5.6458(3)Å, Z=4. The molecular symmetry is C_S with the Mn atom and two oxygen atoms located on the plane perpendicular to the c-axis. A set of accurate diffraction data were measured at 115K. Subsequent refinements and Fourier syntheses were performed. The electron density distribution is expressed in terms of the deformation density. The Mn-O bondings are well characterized, the lone pair electron density at the oxygen atoms is also observed. The density near the Mn nucleus seems to be very sensitive to changes of the scale factor and extinction coefficient. Several types of extinction corrections were made. The features of the Mn-O bond are comparable to the theoretical density calculated at the ab-initio level, and to the experimental density of the isoelectronic compound K₂CrO₄. However, the experimental density of KMnO₄ is not so well reproduced in the vicinity of Mn nucleus.     

Dynamic electron transfers in B2H6 and Cu(PH3)2(BH4)

In order to investigate the coupling of molecular vibrations and electron distribution, dynamic electron transfers in B₂H₆ and Cu(PH₃)₂(BH₄) are lated by using a new variational method. In both molecules, the dynamic electron density near bridging hydrogen atoms decreases to form the density valley by exciting specific vibrational modes. On the other hand, in both sides of the valley density hills grow up. For these molecules, similar contour maps are given by the modes with different symmetry which have large contribution of the bridging ligands. While the dynamic electron transfer of B₂H₆ arises in symmetric form, the vibrational modes of the Cu complex gives the asymmetric redistribution of the dynamic electron density. This is attributed to the difference of the symmetry between the two molecules.     

Performance of parallel TURBOMOLE for density functional calculations

The parallelization of density functional treatments of molecular electronic energy and first-order gradients is described, and the performance is documented. The quadrature required for exchange correlation terms and the treatment of exact Coulomb interaction scales virtually linearly up to 100 nodes. The RI-J technique to approximate Coulomb interactions (by means of an auxiliary basis set approximation for the electron density) even shows superlinear speedup on distributed memory architectures. The bottleneck is then linear algebra. Demonstrative application examples include molecules with up to 300 atoms and 3000 basis functions that can now be treated in a few hours per geometry optimization cycle in C₁ symmetry. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1746–1757, 1998     

Ab initio quantum-chemical calculations of interactions of ions and hydrides of alkali metals with C3H6 and C4H8 molecules

Calculations of the C₃H₆ · LiH, C₄H₈ · M⁺, and C₄H₈ · MH systems and of C₂H₂ · MH complexes (M = Li or Na) were carried out by the unrestricted Hartree-Fock-Roothaan (UHF) method with partial optimization of the geometry using fixed geometric parameters of the C₃H₆ and C₄H₈ molecules. The standard 3-21G and 6-31G* basis sets were used. Unlike the C₃H₆ · LiH structure, the C₄H₈ · M⁺ and C₄H₈ · MH systems are typical complexes. It was found that the C₄H₈ · M⁺, C₄H₈ · MH, and C₂H₂ · MH complexes are similar in coordination of M⁺ ions and MH molecules by carbon atoms in spite of considerable differences in the interatomic distances (–1 A) between these atoms in the C₄H₈ and C₂H₂ molecules. The heats of formation (Q), which were calculated in the UHF/6-31G* approximation and using second- and fourth-order Möller-Plesset perturbation theory taking into account the electron correlation energy in the MP2/6-31G*. MP4(SDQ)/6-31G*, and MP4(SDTQ)/6-31G* approximations, satisfy the following relationships: Q(C₂H₃ · MH) < Q(C₄H₈ · MH) < Q(C₄H₈ · M⁺). It was observed that in going from Li to Na the corresponding values of Q tend to decrease.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya. No. 7, pp. 1636–1640, July, 1996.     

1:1 Adduct of (S,S)‐4‐amino‐3,5‐bis­(1‐hydroxy­ethyl)‐1,2,4‐triazole with (S,S)‐1,2‐bis­(2‐hydroxy­propionyl)­hydrazine stabilized by eight hydrogen bonds

The structure of the cocrystallized 1:1 adduct of (S,S)‐4‐amino‐3,5‐bis­(1‐hydroxy­ethyl)‐1,2,4‐triazole and (S,S)‐1,2‐bis­(2‐hydroxy­propionyl)­hydrazine, C₆H₁₂N₄O₂·C₆H₁₂N₂O₄, has tetra­gonal symmetry. All eight O‐ and N‐bound H atoms are involved in inter­molecular hydrogen bonds, resulting in infinite zigzag chains of the triazole mol­ecules, with the hydrazine mol­ecules filling the gaps between the chains and completing a three‐dimensional hydrogen‐bonded array.     

A simple model of hydrogen bonding with particular application to trends in hydrogen‐bonded dimers

A simple model has been proposed to explain trends in the computed interaction energy, bond length changes, frequency shifts and infrared intensities for the chlorofluoromethanes CF_nCl_mH, FH and FArH on complexation with the isoelectronic diatomics BF, CO, N₂ and the rare gas atoms Kr, Ar, Ne to form a series of linear or nearly linear hydrogen‐bonded complexes. The dipole moment derivative of the proton donor (with respect to the stretching coordinate) and the chemical hardness of the hydrogen‐bonded atom of the proton acceptor are identified as two useful parameters for rationalizing the changes in some of the molecular properties of the proton donor when the hydrogen bond is formed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009