Modern semiempirical methods are of sufficient accuracy when used in the modeling of molecules of the same type as used as reference data in the parameterization. Outside that subset, however, there is an abundance of evidence that these methods are of very limited utility. In an attempt to expand the range of applicability, a new method called PM7 has been developed. PM7 was parameterized using experimental and high-level ab initio reference data, augmented by a new type of reference data intended to better define the structure of parameter space. The resulting method was tested by modeling crystal structures and heats of formation of solids. Two changes were made to the set of approximations: a modification was made to improve the description of noncovalent interactions, and two minor errors in the NDDO formalism were rectified. Average unsigned errors (AUEs) in geometry and ΔHf for PM7 were reduced relative to PM6; for simple gas-phase organic systems, the AUE in bond lengths decreased by about 5 % and the AUE in ΔHf decreased by about 10 %; for organic solids, the AUE in ΔHf dropped by 60 % and the reduction was 33.3 % for geometries. A two-step process (PM7-TS) for calculating the heights of activation barriers has been developed. Using PM7-TS, the AUE in the barrier heights for simple organic reactions was decreased from values of 12.6 kcal/mol-1 in PM6 and 10.8 kcal/mol-1 in PM7 to 3.8 kcal/mol-1. The origins of the errors in NDDO methods have been examined, and were found to be attributable to inadequate and inaccurate reference data. This conclusion provides insight into how these methods can be improved.

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Optimization of parameters for semiempirical methods VI: more modifications to the NDDO approximations and re-optimization of parameters.

Over 4000 chemically unique flavonoids have been identified in plant sources. These low-molecular-weight substances, found in all vascular plants, are phenyl- benzopyrones (phenylchromones) with an assortment of basic structures. Primarily recognized as the pigments responsible for the autumnal burst of hues and the many shades of yellow, orange and red in flowers and food (see Chapter 13), the flavonoids are found in fruits, vegetables, nuts, seeds, stems, flowers as well as tea and wine and are important constituents of the human diet.

The impact of plant flavonoids on mammalian biology: implications for immunity, inflammation and cancer

Recent progress in ESCA studies of gases

Publisher Summary This chapter provides a summary of the relativistic calculations on multielectron or multicenter problems. The Dirac–Fock Hamiltonian and the main quantum electrodynamical (QED) corrections are discussed and the atomic and bandstructure calculations are reviewed. Then the construction of relativistic molecular orbitals and the solvable one-electron molecular and solid-state models are described. The simplest possible system for studying relativistic effects in chemical bonding is H2+. Several variational linear combinations of atomic orbitals (LCAO)-type solutions of the Dirac equation for H2+ show that the relativistic effects decrease the electronic energy by about –7 ╳ 10–6 a.u. The Dirac-Fock and Dirac-Slater molecular calculations, the relativistic semiempirical methods, and the perturbation treatments of relativistic effects are also described. In relativistic treatments of several spectroscopic properties, the entire formulation must be changed if relativistic wavefunctions are used. Some of its examples are considered. The chapter also presents a preliminary account of the relativistic effects on the chemical properties of the periodic system of elements.

Relativistic Quantum Chemistry

The interaction of water with the Pt(111) surface

The general polyatomic molecule in a closed‐shell electronic state with nuclei fixed according to the Born‐Oppenheimer approximation is photoionized to form a final singlet state in which one electron is excited into the continuum. All bound orbitals are assumed identical in the initial and final states. The unbound orbital is approximated either by a plane‐wave or by a plane‐wave orthogonalized to all occupied bound orbitals. Formulations are given for cases in which bound orbitals are expressed as linear combinations of Slater‐type orbitals, orthogonalized Slater‐type orbitals, Cartesian Gaussian‐type orbitals, or Gaussian‐lobe functions. General equations are derived for the photoionization cross section of randomly oriented polyatomic molecules as a function of angle between the polarization vector of the photon beam and the propagation vector of photoejected electrons. Also derived is the photoionization cross section of the same sample as a function of angle between an unpolarized photon beam and th...

Theoretical equations for photoionization cross sections of polyatomic molecules in plane‐wave and orthogonalized plane‐wave approximations

The general equations for calculating photoionization cross sections of polyatomic molecules in the plane‐wave and orthogonalized plane‐wave approximations have been programmed for the electronic computer. Applications are described for the molecules H2, CH4, N2, CO, H2O, H2S, and H2CCH2 for incident photon energies from threshold to 1500 eV. Relative experimental photoionization band intensities for the above molecules are measured using NeI, HeI, and HeII resonance radiation. A simplified analysis of the intensities derived from electrostatic deflection analyzers is presented. The 2P3/2:2P1/2 intensity ratios of the rare gases are determined with the three modes of excitation mentioned above. An analysis of the resolution capabilities of an electrostatic deflection spectrometer as a function of electron kinetic energy is presented. Relative experimental photoionization band intensities for the above molecules obtained by ionization with the three uv sources and MgKa and A1Ka x‐ray sources are compared with computed differential cross sections. Variations in computed cross sections as a function of the kinetic energy of the photoelectrons are discussed and possible interpretations are proposed.

Calculated photoionization cross sections and relative experimental photoionization intensities for a selection of small molecules

Generalization of Dewar's half-electron method for calculating energies of open-shell electronic states

A semiempirical model has been developed for estimating spin‐orbit interactions in molecular ion states derived by ionization of closed‐shell neutral molecule states. A perturbation approach is used with an effective spin‐orbit interaction operator Hso and approximate Mulliken‐Wolfsberg‐Helmholz molecular orbital (MO) wavefunctions. Effective spin‐orbit parameters ζv were obtained by interpolation with respect to atomic charges derived from the MO calculations. The He I photoelectron spectra of the PX3(X = Cl, Br, I) and PYX3(X = Cl, Br; Y = O, S) series have been measured. Splittings observed in some of the ionization bands of this series have been successfully interpretated as spin‐orbit splittings using the newly developed model.

Frank O. Ellison

Papers

Theoretical equations for photoionization cross sections of polyatomic molecules in plane‐wave and orthogonalized plane‐wave approximations

Calculated photoionization cross sections and relative experimental photoionization intensities for a selection of small molecules

Generalization of Dewar's half-electron method for calculating energies of open-shell electronic states

Model for calculating spin‐orbit interactions with applications to photoelectron spectroscopy

ESCA: A new semi-empirical correlation between core-electron binding energy and valence-electron density☆