Richard F. W. Bader

The characterization of atomic interactions

The theory of molecular structure determined by the gradient vector field of the charge density ρ identifies the set of atomic interactions present in a molecule. The interactions so defined are characterized in terms of the properties of the Laplacian of the charge density ∇2ρ(r). A scalar field is concentrated in those regions of space where its Laplacian is negative and depleted in those where it is positive. An expression derived from the quantum mechanical stress tensor relates the sign of the Laplacian of ρ to the relative magnitudes of the local contributions of the potential and kinetic energy densities to their virial theorem averages. By obtaining a map of those regions where ∇2ρ(r)<0, the regions where electronic charge is concentrated, one obtains a map of the regions where the potential energy density makes its dominant contributions to the energy of a system. It is demonstrated that atomic interactions fall into two broad general classes, closed‐shell and shared interactions, each characteri...

Calculation of magnetic response properties using a continuous set of gauge transformations

Abstract A new method is described for the calculation of the magnetic susceptibility and nuclear magnetic shielding tensors using a separate gauge origin for each point in space to calculate the magnetically induced current. The method yields accurate three-dimensional induced molecular current distributions and correspondingly accurate values for the magnetic response properties. The method is easily implemented within existing coupled-perturbed Hartree—Fock programs.

Quantum Theory of Atoms in Molecules–Dalton Revisited

Publisher Summary This chapter deals with the quantum mechanical definition of the average properties of an atom. It is demonstrated that the topological property that defines the atom determines the definition of its average properties. It reviews only the basic topological properties of a charge distribution in this chapter. Their role in the definition of molecular structure and its change has been recently reviewed in detail. A bound atom is an example of an open quantum system. A quantum description of subsystems must be developed, free to exchange charge and momentum with their environment across boundaries that are defined in real space and that in general change with time. The chapter also reviews that the quantum mechanics has been shown to account for the properties of isolated atoms and for the total properties of a molecular system. The increased understanding that would result from the discovery of a firm theoretical basis for Daltons theory has not been obtained because of a lack of a quantum definition of an atom in a molecule.

Virial Field Relationship for Molecular Charge Distributions and the Spatial Partitioning of Molecular Properties

Arguments and numerical examples are presented which suggest that the distribution of electronic charge in a molecular system can be related to the total virial of all the forces exerted on each element of the charge density. Further numerical evidence is given indicating that it is possible to partition a molecular system in such a way that the same virial relationship between the average kinetic and potential energies observed for a total molecular system is found to hold for the individual fragments. This partitioning scheme is based on an observable property of the charge distribution. The proposals presented here provide a basis for the understanding and prediction of molecular charge distributions and their properties.

A topological theory of molecular structure

A theory of molecular structure is presented. The theory demonstrates that the concepts of atoms and bonds may be rigorously defined and given physical expression in terms of the topological properties of the observable distribution of charge for a molecular system. As a consequence of these definitions, one in turn obtains a definition of structure and a predictive theory of structural stability. The theory is linked to quantum mechanics by demonstrating that the atoms so defined represent a class of open quantum subsystems with a unique set of variationally defined properties.

Calculation of magnetic response properties using atoms in molecules

Abstract A new method (IGAIM — individual gauges for atoms in molecules) is presented for relatively accurate ab initio calculations of molecular magnetic response properties. The current density induced within an atom in a molecule by an external magnetic field is well described by the coupled, perturbed Hartree—Fock method when the gauge origin of the vector potential is placed at its nucleus, the natural origin for the free atom, even though it may be poorly described in the rest of the molecule. Since the molecular magnetic susceptibility and nuclear magnetic shielding tensors can be expressed in terms of the induced current density as a sum of separately determined atomic contributions, these properties are, in general, accurately predicted even with basis sets that are insufficient for conventional CPHF.

An analysis of the hydrogen bond in BASE-HF complexes using the theory of atoms in molecules

The nature, energetics and mechanism of BASE-HF hydrogen bonding (where BASE = OC, SC, N2, HCN, H3N, O3, SCO, CO2, N2O, SO2, H2CO, H2O, HF, H3P, H2S and HCl) are examined using the theory of atoms in molecules. The results are obtained from RHF/6-311 + +G**//6-31 G** calculations. A quantitative description of the electron redistribution and changes in atomic properties, including populations, energies, volumes and moments upon hydrogen bond formation are given by the theory, information which in turn provides a qualitative understanding of the hydrogen bond. A hydrogen bond results from the interaction of two closed-shell systems and the theory quantifies the concept of the mutual penetration of the van der Waals envelopes of the acid and base molecules. It is found that the extent of this penetration and the factors which govern it are of paramount importance in determining the strength of the interaction.

Prediction of the structures of hydrogen-bonded complexes using the laplacian of the charge density

The laplacian of the charge density is used to predict the structures and geometries of hydrogen-bonded gas-phase complexes of the type BASE-HF. The bases used are N2, OC, SC, OCO, SCO, HCN, N2O, HCP, H2O, H2S, H3N, H3P, O3, OSO, H2CO, HF, HCl, N2S and H2CS. Many of the weaker complexes have not been characterized experimentally, and so, results of full 6–31 G** geometry optimizations are presented. The laplacian of the charge density, ∇2ρ, determines where charge is locally concentrated and depleted. The point where ∇2ρ attains its maximum magnitude in a region of charge concentration in the base defines the site of electrophilic attack by the acidic H of HF. The angle of electrophilic attack predicted in this manner is compared with the ab initio equilibrium angle that the hydrogen of HF makes with the base. In general, the angles predicted using the laplacian are in good agreement with the ab initio and experimental results. The present results are also compared with those obtained from electrostatic m...

Quantum topology of molecular charge distributions. III. The mechanics of an atom in a molecule

The variation of the atomic action integral yields Schrodinger’s equations‐of‐motion and an atomic statement of the variational principle. The atom and its average properties are defined by the variational principle together with the requirement that they satisfy the Heisenberg equation‐of‐motion. Schrodinger’s equations define the components of the energy‐momentum tensor. The divergence equations satisfied by the spatial components of this tensor, the stress tensor, yield an expression for the resultant force exerted on a single electron at a given point in space and at a given time by the average motion of the other particles in the system. The integration of this force density over the space of an atom yields an equation‐of‐motion for an atom in a molecule identical to that determined by the generalized variational principle. Thus the action principle yields a local description of the mechanical properties of an atom and a definition of their average values. The force density is expressible in terms of...

Properties of atoms in molecules: Dipole moments and transferability of properties

This paper uses the theory of atoms in molecules to investigate the origin of molecular dipole moments. The dipole moment is given by a sum over the net charge and first moment of every atom in a molecule. The first term leads to a charge transfer contribution μc, the second to an atomic polarization contribution μa. It is shown that both terms are, in general, of equal importance in determining both the static molecular dipole moment and the moment induced by a nuclear displacement. Models which imploy only point charges and corresponding bond moments which follow rigidly the nuclear framework, i.e., models which approximate μc and ignore μa, are shown to lead to results that are incompatible with the changes that are found to occur in a molecular charge distribution during a nuclear vibration. The dipole moment is shown to be another group property that is transferable between molecules in the normal hydrocarbons, This property, along with the net charge, the energy, the correlation energy (expressed as...