Ruben Pauncz

Analytical calculation of atomic and molecular electrostatic potentials from the Poisson equation

Abstract An analytic formulation is given for the total potential in atomic and molecular systems, based on the electrostatic approach from the Hellmann-Feynman theorem. The potential function is obtained from the analytic solution of the Poisson equation using charge densities expressed as a superposition of gaussian functions. The method is independent of the specific LCAO approximation used for the calculation of the charge distribution function. The calculation of the potential and its derivatives to a rapid algorithm form, which can be used for the evaluation of various electronic properties and the treatment of experimental situation, even for large molecular systems.

Theoretical Interpretation of Hund's Rule

Publisher Summary This chapter discusses a comprehensive treatment of some recent developments in the interpretation of Hunds rule. This rule can be considered as an ordering principle for the ground configuration, or at best, as a criterion for the lowest term of any configuration. The maximal formulation attempts to use the Hunds rule as a general ordering principle for any configuration. Experimentally, Hunds rule is highly reliable so far as the ground state is concerned. It is, however, not nearly as dependable for the ordering of higher terms in the configuration. The most restrictive formulation of Hunds rule states that in a configuration of equivalent electrons the deepest lying term corresponds to the highest possible value of the total spin. Generalizations of this rule to the ground state corresponding to configurations of nonequivalent electrons, as well as using it to predict the ordering of all the terms corresponding to a given configuration have been discussed. In order to illustrate quantitatively the results of scaling with reference to the interpretation of Hunds rule, the ground configuration of the carbon atom using Slater-type orbitals are reviewed.

Localized Molecular Orbitals

Publisher Summary The chapter presents different aspects of the problem of finding localized orbitals. The N-electron wavefunction of an atomic or molecular system is usually considered, within the formalism of quantum chemistry, to be the most appropriate description of such a system. The interelectronic interaction energy expression for a wavefunction consisting of a doubly occupied single Slater determinant may be written in terms of the one-electron density matrix. There are two main procedures leading to the determination of localized orbitals through the maximization of the sum of orbital self-interaction energies. Once the Hartree–Fock functional space has been determined, a series of unitary transformations can be performed among the occupied orbitals. Then the set of energy-localized functions can be obtained through an iterative procedure. The Edmiston–Ruedenberg method of localization has turned out to be an important contribution to the investigation of the electronic structure of molecular systems. Because local orbital populations are affected by orthogonal transformations, their numerical values can be used to define localizing orthogonal transformations.

The symmetric group in quantum chemistry

The Quantum Mechanical Background: Introduction. Spin-free Hamiltonian. The Antisymmetry Principle. Atomic and Molecular Orbitals. Slater Determinant. The Self-consistent-field Method. Configuration Interaction Method. Slater-Condon Rules. Lowdin Rules. The Symmetric Group: Introduction. Permutations. The Symmetric Group. Cyclic Permutation. Classes of the Symmetric Group. Subgroups of the Symmetric Group. Double Cosets. Representation of SN: Reps of the Symmetric Group. Young 1.

Studies on the Alternant Molecular Orbital Method. IV. Generalization of the Method to States with Different Multiplicities

A general formulation of the alternant molecular orbital method, applicable to states of different multiplicities in systems with an even number of atoms, is presented. The treatment is formulated in such a way that the same integral sums appear in the energy expression for the states belonging to different multiplicities. The resultant energy expressions show a simple dependence on the mixing parameter λ.Application to cyclic systems shows that the best λ values decrease slowly with increasing multiplicity. Comparison with the configuration interaction treatment reveals that the AMO method corresponds to a restricted CI treatment, but it is capable of yielding a considerable part of the energy improvement obtained by the latter method.

Studies on the Alternant Molecular Orbital Method. V. A Many‐Parameter Energy Expression for States with Different Multiplicities; Application to Benzene

Within the framework of the refined alternant molecular orbital method, a general energy expression is derived for the lowest state of any desired multiplicity of an arbitrary system with closed‐shell structure. A numerical analysis of the lowest singlet, triplet, and quintet state of the pi‐electron sextet in benzene reveals that the many‐parameter alternant molecular orbital wavefunction does, in each case, account for better than 90% of the energy improvement obtained in a full configuration interaction treatment. A detailed comparison of the AMO and CI wavefunctions for both triplet and quintet state is presented. Both methods yield a singlet—triplet separation that is too low, which suggests a basic deficiency in the customary approach to the quantum chemistry of conjugated hydrocarbons.

Efficient evaluation of the algebrants of VB wave functions using the successive expansion method. I. SpinS = 0,

An efficient expansion method for the evaluation of VB matrix elements is introduced. The overlaps of VB wave functions of N electrons can be treated as algebrants, i.e., generalized determinants, of N × N matrices. An algebrant can be expanded with subalgebrants of lower orders in a successive way. By choosing Rumer spin bases and appropriately arranging the expansion, it is found that the number of unique subalgebrants involved in the expansion increases in a quite moderate way with N. In contrast to the traditional symmetric group approach, which explicitly utilizes all N! representation matrices, the new strategy incorporates the group theoretical factors in a simple way in the successive expansion. As only the unique subalgebrants are further expanded, the computational effort required by the new strategy scales in a very acceptable manner with the increasing number of electrons.

Molecular orbital set determined by a localization procedure

A starting set of molecular maximum overlap orbitals is localized by means of an external procedure, using local density maximization as transformation criterion. For a group of hydride molecules (LiH, BH, BH3) improved localization of the starting orbitals leads to a set having increased overlap with LCAO SCF calculated molecular wave functions and improved molecular energies. The possible use of the easily obtained localized orbitals as a starting set for more elaborate calculations is considered.

Some definitions of atomic regions in molecules and solids

Abstract Mathematical formulations are presented for the construction of two different partitioning surfaces in molecular and solid systems. A surface which divides the electron charge density ϱ into atomic or fragmental regions is obtained by proceeding from a local minimum in the direction defined by the requirement for minimal ▿ϱ at each equidensity curve. An alternative partitioning into regions containing equal numbers of electrons and positive charges is shown to be obtained by a surface constructed in the direction of ▿ U , where U the electrostatic potential generated by the system. The method is exemplified for the simple cases of LiF, HF and LiH. Practical applications for the proposed surfaces and the additivity of the resulting fragments are discussed.

The concept of quasispin and its use for the study of physical and chemical properties of alternant conjugated hydrocarbons

The concept of quasispin is introduced in an elementary way in order to study the physical and chemical properties of alternant conjugated hydrocarbons in the Pariser–Parr–Pople and Hubbard models. The physical interpretation of quasispin is presented. Further, it is shown how the number of states of a given spin, quasispin, and ionization level can be enumerated. Finally, methods for the construction of simultaneous eigenfunctions of spin and quasispin are discussed in full detail for the case of hexatriene.