Shalom Srebrenik

A misconception concerning the electronic density distribution of an atom

It is shown that the electronic charge density of a ground-state atom decreases monotonically as a function of radial distance from the nucleus, contrary to the widespread belief that the shell structure is reflected by relative maxima in the density. Any proposed relationship between chemical bonding and the maxima in the radial density functions of atoms should therefore be regarded with caution. It is proven that the electrostatic potential of an atom must be monotonically decreasing. The changes in charge distribution upon molecule formation are also discussed.

Towards the development of the quantum mechanics of a subspace

The development of the quantum mechanics for a subspace of a total system is pursued via the derivation or introduction of the following: (1) the variational principle for a subspace; (2) the relationship between the time dependent subspace average of an operator and its associated commutator; (3) the unique set of quantum properties found for a subspace bounded by a surface of zero flux as defined by ∇ρ (r) ⋅n (r) =0, ‐r‐S (r), and denoted as a ’’virial fragment’’; (4) the special variational properties of the zero‐flux boundaries in one‐electron systems; (5) operators which cause the energy integral to be stationary over a subspace; (6) the fragment virial theorem; (7) the importance of the scaling of the coordinates of a single electron in the determination of subspace properties; (8) a reformulation of the total Hamiltonian for a many‐particle system as a sum of single‐particle Hamiltonians through the use of a complete set of virial sharing operators; (9) new interpretation of the energy of the equil...

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.

Subspace quantum mechanics and the variational principle

This work is a continuation and extension of the delineation of the properties of a quantum subspace—a region of the real space of a molecular system bounded by a surface through which the flux in the gradient of the (observable) charge density is zero. Such subspaces are of interest as they constitute a basis for theoretical definitions of chemical concepts as obtained through experiment. The subspace stationary state variational principle, which was previously used to define this particular class of subspaces, reveals a close interrelationship between the hypervirial theorem and the variational property of the energy. By exploiting this interrelationship, one may obtain a variational solution to Schrodinger’s equation with the zero‐flux surface requirement serving as a variational constraint. The connection between the statement of the subspace variational principle and the result of perturbation theory is established at the level of the first‐order correction to the total energy. The statement of the g...

Subspace quantum dynamics and the quantum action principle

Schwinger’s quantum action principle is used to obtain a quantum mechanical description of a subspace and its properties. The subspaces considered are those regions (Ω) of real space as defined by a property of the system’s charge distribution ρ (r), namely, that they be bounded by a surface S (r) through which the flux in ∇ρ (r) is zero at every point on S (r). Through the variation of the action integral, expressed in terms of the appropriately defined Lagrangian integral operator for a subspace, one obtains the quantum equations of motion and an expression for the change in the subspace action integral operator, ΔW (Ω). This expression obeys a principle of stationary action, and thus, as for a system with boundaries at infinity, it defines the generators of infinitesimal unitary transformations. The change in a subspace property O (Ω) as induced by such an infinitesimal unitary transformation is investigated and related to the corresponding change as described by the calculus of variations. The latte...

Sufficient conditions for fragment and regional virial theorems

Sufficient theoretical conditions are derived for the satisfaction of the molecular fragment virial theorem of Bader and Beddall [J. Chem. Phys. 56, 3320 (1972)] and of the regional virial theorem of Mazziotti, Parr, and Simons [J. Chem. Phys. 59, 939 (1973)].

Quantum Chemical Studies of Morphine-Like Opiate Narcotics: Effect of Polar Group Variations

Narcotic analgesics, typified by morphine, may be defined as central nervous system (CNS) depressants that relieve or abolish pain without, at the same time, inducing loss of consciousness. There is good evidence that they act at specific sites in the CNS. This class of drugs has diverse pharmacological action and side effects, the most undesirable of which are the development of tolerance and addiction involving both physical and psychological dependence on the drug, characteristics which seriously limit their clinical use as analgesics.

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.

A theoretical model study of the comparative effectiveness of atropine and scopolamine action in the central nervous system

Abstract The molecular structural factors related to the action of atropine and scopolamine at a common biological receptor, with different apparent potencies, are studied from a theoretical viewpoint. The model molecules representing the two cholinergic antagonists are shown to possess the ability to generate an electrostatic potential field which is compatible with the “interaction pharmacophore” of acetylcholine-like molecules. A common site of action for the two types of drugs is rationalized on this basis. The effect of the differences in the molecular structure of the drugs, on their penetration ability and lipid solubility, is analyzed through the proton affinity of model compounds in the gas phase and in solution. These indicate the nature of the stronger solute-solvent interaction of scopolamine. Results from a comparative calculation of the protonation affinity of the solvated drugs are shown to reproduce the correct ratio of protonated versus free base concentrations for the two molecules, from which the reasons for the lower pK a of scopolamine and higher lipophilicity of atropine (free base) can be understood.

Formulation of molecular forces and their analytical calculation

A general definition of forces in a molecular system is considered, with the Hellmann‐Feynmann relation representing the special case for the Born‐Oppenheimer approximation. Analytic formulas are given for the calculation of forces within the fixed nuclei approximation. Derived from the analytic formulation of electrostatic potential, this calculation procedure remains valid for other average values of the form 〈r−|n|〉.