Effective Atomic Orbitals: A Tool for Understanding Electronic Structure of Molecules

It is discussed that one can obtain effective atomic orbitals (AOs) in quite different theoretical frameworks of Hilbert-space and three-dimensional (3D) analyses. In all cases, one can clearly distinguish between the orbitals of an effective minimal basis set and orbitals which are only insignificantly occupied. This observation makes a solid theoretical basis beyond our qualitative picture of molecular electronic structure, described in terms of minimal basis AOs having decisive participation in bonding, and may be considered as a quantum chemical manifestation of the octet rule. For strongly positive atoms like the hypervalent sulfur, some weakly occupied orbitals reflecting "back donation" can also be identified. From the conceptual point of view, it is very important that AOs of characteristic shape can be obtained even by processing the results of plane wave calculations in which no atom-centered basis orbitals were applied. The different types of analyses (Hilbert-space and 3D) can be done on equal footing, performing quite analogous procedures, and they exhibit an unexpected interrelation, too. (C) 2014 Wiley Periodicals, Inc

Hermitian "chemical" Hamiltonian: an alternative ab initio method

Some previous results of the present author are combined in order to develop a Hermitian version of the "Chemical Hamiltonian Approach." In this framework the second quantized Born-Oppenheimer Hamiltonian is decomposed into one-and two-center components, if some finite basis corrections are omitted. (No changes are introduced into the one-and two-center integrals, while projective expansions are used for the three-and four-center ones, which become exact only in the limit of complete basis sets.) The total molecular energy calculated with this Hamiltonian can then presented as a sum of the intraatomic and diatomic energy terms which were introduced in our previous "chemical energy component analysis" scheme. The corresponding modified Hartree-Fock-Roothaan equations are also derived; they do not contain any three-and four-center integrals, while the non-empirical character of the theory is conserved. This scheme may be useful also as a "layer" in approaches like ONIOM

Covalent Bonding: The Role of Exchange Effects

It is stressed that the two-center exchange energy componen ts lead to a significant lowering of the total molecular energy becau se of ex- clusion of self-repulsion, and this is inevitable for coval ent bond for- mation. The success of the two-center bond order index relie s on the fact that it gives a qualitative estimate of this important p henomenon

Lokális tulajdonságok kvantumkémiai analízise és számítása = Quantum chemical analysis and computation of local properties

- Általánosítottuk az effektív atompályák fogalmát az ún. 3-dimenziós (fuzzy atom, Bader atom) analízis esetére. A hagyományos atompálya-képet alá lehet támasztani akár síkhullám-számítások eredményei alapján is. - Kötésrend-számítások síkhullám-szá | - The concept of effective atomic orbitals has been generalized for the case of the 3-dimensional analysis (fuzzy atoms, Bader's atoms). The classical picture of atomic orbitals can be corroborated even based on the results of plane-wave calculations

The atomic orbitals of the topological atom

The effective atomic orbitals have been realized in the framework of Bader’s atoms in molecules theory for a general wavefunction. This formalism can be used to retrieve from any type of calculation a proper set of orthonormalized numerical atomic orbitals, with occupation numbers that sum up to the respective Quantum Theory of Atoms in Molecules (QTAIM) atomic populations. Experience shows that only a limited number of effective atomic orbitals exhibit significant occupation numbers. These correspond to atomic hybrids that closely resemble the core and valence shells of the atom. The occupation numbers of the remaining effective orbitals are almost negligible, except for atoms with hypervalent character. In addition, the molecular orbitals of a calculation can be exactly expressed as a linear combination of this orthonormalized set of numerical atomic orbitals, and the Mulliken population analysis carried out on this basis set exactly reproduces the original QTAIM atomic populations of the atoms. Approximate expansion of the molecular orbitals over a much reduced set of orthogonal atomic basis functions can also be accomplished to a very good accuracy with a singular value decomposition procedure

Energiakomponensek számítása molekulákban és reagáló rendszerekben = Calculation of energy components in molecules and in reacting systems

Konceptuálisan új Hartree-Fock szintű energiapartíciós módszereket javasoltunk a molekulák elektronszerkezetének mind Hilbert-térbeli analízise, mind a háromdimenzós térben végzett analízise keretében. Bevezettünk egy új elméleti fogalmat, az ''atomi egységfelbontást'', (atomic decompositions of identity), amely lehetővé teszi, hogy a legkülönbözőbb populációs analízis és energiadekompozíciós módszereket egy közös általános formalizmus keretében vizsgáljuk. Az atomi egységfelbontás segítségével végrehajtottuk az MP2 szintű energia felbontását is. Megoldottuk a DFT szinten számolt energiafelbontást is; ehhez definiáltunk egy új mennyiséget, a ''kötésrendsűrűséget''. Részletesen vizsgáltuk azt a dilemmát, hogy a kinetikus energia integrálok kezelésétől függően a kétatomos energiakomponensek vagy a ''kémiai'' energiatartománybe esnek az egyensúlyi magkonfigurációknál vagy intuitíve helyes távolságfüggést mutatnak. Megoldottuk az várható érték fizikailag korrekt partícióját. | Conceptually new energy partitioning schemes have been introduced at the Hartree-Fock level of theory for both Hilbert-space and three-dimensional space analyzes of the molecular electronic structure. A new theoretical concept, the ""atomic decomposition of identity"" has been introduced, permitting to treat the most different problems of population analysis and energy decomposition in the framework of a common general formalism. Using the atomic decomposition of identity, the partitioning of the MP2 energy has been also accomplished. The problem of decomposing the DFT energy has also been solved; a new quantity, the ""bond order density"" has been defined for that purpose. We have studied in detail the dilemma that - depending on the way of treating the kinetic energy integrals - one gets diatomic energy components which either are on the ""chemical scale"" at the equilibrium molecular conformations or exhibit intuitively correct distance dependence. The physically correct partitioning of the expectation value has also been accomplished

The influence of cations on the dipole moments of neighboring polar molecules

It is shown that the dipole moment of polar (water, methanol, formamide, acetone and acetonitrile) molecules in the neighborhood of a cation is increased primarily by polarization from the bare electrostatic charge of the cation, although the effective value of the latter is somewhat reduced by "back donation" of electrons from neighbouring polar molecules. In other words, the classical picture may be viewed as if a point charge slightly smaller than the nominal charge of the cation would be placed at the cation site. It was found that the geometrical arrangement of the polar molecules in the first solvation shell is such that their mutual polarization reduces the dipole moments of individual molecules, so that in some cases they become smaller than the dipole moment of the free protic or aprotic molecule. We conjecture that this behavior is essentially a manifestation of the Le Chatellier-Braun principle