Todd A. Keith

A comparison of models for calculating nuclear magnetic resonance shielding tensors

The direct (recomputation of two‐electron integrals) implementation of the gauge‐including atomic orbital (GIAO) and the CSGT (continuous set of gauge transformations) methods for calculating nuclear magnetic shielding tensors at both the Hartree‐Fock and density functional levels of theory are presented. Isotropic 13C, 15N, and 17O magnetic shielding constants for several molecules, including taxol (C47H51NO14 using 1032 basis functions) are reported. Shielding tensor components determined using the GIAO and CSGT methods are found to converge to the same value at sufficiently large basis sets; however, GIAO shielding tensor components for atoms other than carbon are found to converge faster with respect to basis set size than those determined using the CSGT method for both Hartree‐Fock and DFT. For molecules where electron correlation effects are significant, shielding constants determined using (gradient‐corrected) pure DFT or hybrid methods (including a mixture of Hartree‐Fock exchange and DFT exchange...

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.

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.

Topological analysis of magnetically induced molecular current distributions

The topology of the first‐order current density J(1)(r) induced in a molecule by an applied magnetic field is analyzed and classified in terms of the properties of its critical points, as determined by the 3×3 coefficient matrix of the asymmetric tensor ∇J(1). The eigenvalues of this tensor yield the topological indices for classifying the possible critical points in the J(1)(r) field. The phase portraits describing the current flow associated with these critical points and their role in determining the structure of a molecular current distribution are illustrated. A molecular current distribution is a fully three‐dimensional vector field. In addition to closed loops of current, it exhibits one‐ and two‐dimensional sources and sinks which generate surfaces, spirals, and single lines of current. The nonisolated critical points lie on stagnation paths which, along with the isolated critical points, fully characterize the current distribution. The antisymmetric component of ∇J(1) is the curl of J(1) which de...

Properties of atoms in molecules: additivity and transferability of group polarizabilities

The experimental demonstration of the additivity and transferability of group properties in the hydrocarbons, that is, the establishment of additivity schemes for their molar volumes, polarizabilities and heats of formation, played a central role in establishing the concept of a functional group in chemistry. It is shown here that the theory of atoms in molecules recovers and explains the experimentally observed additivity and transferability of the group polarizabilities in the hydrocarbons, just as has been previously done for the heats of formation, electric moments and molar volumes. All of the group properties exhibit the same pattern of transferable behavior. In particular, the linear relationship between the group polarizabilities and corresponding group volumes, as defined by theory, enable one to predict the mean polarizabilities of hydrocarbons to better than one-half of one percent using readily calculated group volumes. The outer sheath of hydrogen atom charge density polarizes in the directio...

Properties of atoms in molecules: Magnetic susceptibilities

The molecular magnetic susceptibility tensor χ is expressible as a sum of atomic or group contributions. An atomic contribution consists of a basin and a surface component; the former is given by the integral of a magnetization density over the basin of the atom, and the latter, by the integral of the flux in the position weighted current density through the interatomic surfaces that the atom shares with its bonded neighbors. The surface component is obtained as a consequence of the atomic hypervirial theorem defining the average of the velocity operator. Magnetic properties are determined by the observable electron current density, and the atomic behavior of this field has been correlated with corresponding behavior of the electron density. Thus the importance of the magnetization within an atomic basin relative to the flux in current through its interatomic surfaces parallels the extent to which the electron density is localized within the individual atomic basins. For example, 77% of the pronounced ani...

Subshell Fitting of Relativistic Atomic Core Electron Densities for Use in QTAIM Analyses of ECP-Based Wave Functions

Scalar-relativistic, all-electron density functional theory (DFT) calculations were done for free, neutral atoms of all elements of the periodic table using the universal Gaussian basis set. Each core, closed-subshell contribution to a total atomic electron density distribution was separately fitted to a spherical electron density function: a linear combination of s-type Gaussian functions. The resulting core subshell electron densities are useful for systematically and compactly approximating total core electron densities of atoms in molecules, for any atomic core defined in terms of closed subshells. When used to augment the electron density from a wave function based on a calculation using effective core potentials (ECPs) in the Hamiltonian, the atomic core electron densities are sufficient to restore the otherwise-absent electron density maxima at the nuclear positions and eliminate spurious critical points in the neighborhood of the atom, thus enabling quantum theory of atoms in molecules (QTAIM) analyses to be done in the neighborhoods of atoms for which ECPs were used. Comparison of results from QTAIM analyses with all-electron, relativistic and nonrelativistic molecular wave functions validates the use of the atomic core electron densities for augmenting electron densities from ECP-based wave functions. For an atom in a molecule for which a small-core or medium-core ECPs is used, simply representing the core using a simplistic, tightly localized electron density function is actually sufficient to obtain a correct electron density topology and perform QTAIM analyses to obtain at least semiquantitatively meaningful results, but this is often not true when a large-core ECP is used. Comparison of QTAIM results from augmenting ECP-based molecular wave functions with the realistic atomic core electron densities presented here versus augmenting with the limiting case of tight core densities may be useful for diagnosing the reliability of large-core ECP models in particular cases. For molecules containing atoms of any elements of the periodic table, the production of extended wave function files that include the appropriate atomic core densities for ECP-based calculations, and the use of these wave functions for QTAIM analyses, has been automated.

Origin of dipole moment enhancement in the formation of SiF4–NH3 dimer

The dimerization of SiF4 and NH3 is accompanied by a substantial 1.63 a.u. increase in dipole moment. Theoretical analysis of the charge distribution of the SiF4–NH3 system using the theory of atoms in molecules shows that the origin of this increase is primarily the large geometrical change which occurs within the SiF4 molecule when the dimer is formed, rather than the changes in atomic polarization or interatomic or intermolecular electron transfer. The relative displacement of the highly charged fluorine atoms of SiF4 away from NH3 upon dimer formation accounts for nearly 90% of the dipole moment enhancement. This result is in agreement with predictions made recently based on experimental results.