The aromaticity and antiaromaticity of the ground state (S 0), lowest triplet state (T 1), and first singlet excited state (S 1) of benzene, and the ground states (S 0), lowest triplet states (T 1), and the first and second singlet excited states (S 1 and S 2) of square and rectangular cyclobutadiene are assessed using various magnetic criteria including nucleus-independent chemical shifts (NICS), proton shieldings, and magnetic susceptibilities calculated using complete-active-space self-consistent field (CASSCF) wave functions constructed from gauge-including atomic orbitals (GIAOs). These magnetic criteria strongly suggest that, in contrast to the well-known aromaticity of the S 0 state of benzene, the T 1 and S 1 states of this molecule are antiaromatic. In square cyclobutadiene, which is shown to be considerably more antiaromatic than rectangular cyclobutadiene, the magnetic properties of the T 1 and S 1 states allow these to be classified as aromatic. According to the computed magnetic criteria, the T 1 state of rectangular cyclobutadiene is still aromatic, but the S 1 state is antiaromatic, just as the S 2 state of square cyclobutadiene; the S 2 state of rectangular cyclobutadiene is nonaromatic. The results demonstrate that the well-known "triplet aromaticity" of cyclic conjugated hydrocarbons represents a particular case of a broader concept of excited-state aromaticity and antiaromaticity. It is shown that while electronic excitation may lead to increased nuclear shieldings in certain low-lying electronic states, in general its main effect can be expected to be nuclear deshielding, which can be substantial for heavier nuclei.

The levels of aromaticity of the most important geometries on the ground-state (S(0)), lowest triplet-state (T(1)), and first singlet excited-state (S(1)) potential energy surfaces (PESs) for cycloocta-1,3,5,7-tetraene (COT) are assessed using a wide range of magnetic criteria including nucleus-independent chemical shifts (NICSs), proton shieldings, and magnetic susceptibilities calculated using complete-active-space self-consistent-field (CASSCF) wave functions constructed from gauge-including atomic orbitals (GIAOs). It is shown that the ground state of D(8h) COT (transition state for the pi-bond-shift process on the S(0) PES) is markedly antiaromatic, even more so than the classical example of an antiaromatic system, the ground state of square cyclobutadiene. The CASSCF-GIAO magnetic properties of the ground state of D(4h) COT (transition state for the ring-inversion process on the S(0) PES) strongly suggest that it is much less antiaromatic than the ground state of D(8h) COT, whereas those of the ground state of D(2d) COT (local minimum on the S(0) PES) indicate that it is decidedly nonaromatic. The lowest triplet state and the first singlet excited state of D(8h) COT (local minima on the T(1) PES and the S(1) PES, respectively) exhibit surprisingly similar magnetic properties. These, in turn, are very close to the magnetic properties of benzene, which is a strong indication of a high degree of aromaticity.

Aromaticity, antiaromaticity, and their effects on chemical bonding in the ground states (S), lowest triplet states (T), and the first and second singlet excited states (S and S) of benzene (CH) and square cyclobutadiene (CH) are investigated by analyzing the variations in isotropic magnetic shielding around these molecules in each electronic state. All shieldings are calculated using state-optimized π-space complete-active-space self-consistent field (CASSCF) wave functions constructed from gauge-including atomic orbitals (GIAOs), in the 6-311++G(2d,2p) basis. It is shown that the profoundly different shielding distributions in the S states of CH and CH represent aromaticity and antiaromaticity "fingerprints" which are reproduced in other electronic states of the two molecules and allow classification of these states as aromatic (S and S for CH, T and S for CH) or antiaromatic (S and S for CH, T and S for CH). S CH is predicted to be even more aromatic than S CH. As isotropic shielding isosurfaces and contour plots show very clearly the effects of aromaticity and antiaromaticity on chemical bonding, these can be viewed, arguably, as the most succinct visual definitions of the two phenomena currently available.

The spin-coupled (SC) theory of molecular electronic structure is introduced as the modern development of classical valence bond (VB) theory. Various important aspects of the SC wave function are described. Attention is particularly focused on the construction and properties of different sets of N-electron spin functions in different spin bases, such as the Kotani, Rumer and Serber. Applications of the SC description to a range of different kinds of chemical problems are presented, beginning with simple examples: the H2 and CH4 molecules. This is followed by the description offered by the SC wave function of more complex situations such as the insertion reaction of H2 into CH2(lA1), the phenomenon of hypervalence as displayed by molecules such as diazomethane, CH2N2, SF6 and XeF2. The SC description of the ground and excited states of benzene is briefly surveyed. This is followed by the SC description of antiaromatic systems such as C4H4 and related molecules.

Aromaticity and bonding in furan, pyrrole, and thiophene are investigated through the behavior of the isotropic shielding σiso(r) within the regions of space surrounding these molecules. HF-GIAO/6-311++G(d,p) and MP2-GIAO/6-311++G(d,p) (Hartree-Fock and second-order Møller-Plesset perturbation theory utilizing gauge-including atomic orbitals) σiso(r) contour plots are constructed using regular two-dimensional 0.05 Å grids in the molecular plane, in horizontal planes 0.5 and 1 Å above it, and in a vertical plane through the heteroatom. The nucleus-independent chemical shifts (NICS) calculated at the ring centers and at 0.5 Å and 1 Å above these centers, NICS(0), NICS(0.5), and NICS(1), respectively, support the widely accepted order of aromaticities thiophene > pyrrole > furan. The results suggest that accurate NICS calculations benefit more from the use of an extended basis set than from the inclusion of dynamical electron correlation effects. The different extents of σiso(r) delocalization observed in the horizontal contour plots and other features of σiso(r) are also consistent with an aromaticity reduction of the order thiophene > pyrrole > furan. It is suggested that the extent of σiso(r) delocalization in σiso(r) contour plots in planes 1 Å above the molecular plane could be used for comparing the relative aromaticities of a wide range of aromatic systems.