Self-consistent Molecular Orbitals Research Articles

Electronic spectral shifts of aromatic molecule–rare-gas heteroclusters

In this paper, a semiempirical theory for the spectral shifts of the electronic origin of the S0→S1 transition of (aromatic molecule)⋅(rare-gas)n heteroclusters is advanced and applied. Neglecting the modifications of intermolecular overlap and exchange interactions upon electronic excitation, the dispersive contributions to the spectral shift are evaluated to second order, accounting for finite-size structural features of the large molecule by the utilization of the multicenter monopole representation of the intermolecular interactions. The spectral shifts for nonpolar aromatic hydrocarbons in or on rare-gas heteroclusters are represented in terms of differences between electrostatic interactions involving an electrostatic field (due to the molecular transition monopoles charge distribution) and an induced dipole (originating from the rare-gas polarizability). The transition monopoles incorporated all the one- and two-electron ππ* excitations of the aromatic molecule, which were represented by Hückel or self-consistent molecular orbitals (MO). The dispersive spectral shifts were semiempirically scaled to correct the systematic overestimate of the transition monopoles within these simple MO schemes. The red spectral shift was recast in terms of a sum of two-atom (carbon atom–rare-gas) and three-atom (carbon atom–rare-gas–carbon atom) contributions, which are subsequently summed over the contributions of all the rare-gas atoms, with each term involving products of an electronic factor and a geometric factor. The electronic factors exhibit a linear dependence of the spectral shift on the rare-gas polarizability, while the geometric factors incorporate the structural effects of the contributions of the individual rare-gas atoms to the spectral shift, predicting the nonadditivity of the spectral shift per added rare-gas atom and the exhibition of distinct spectral shifts for different structural isomers. The semiempirical theory in conjunction with structural information emerging from (pairwise) potential optimization for small and medium-sized (n=1–8) heteroclusters and from molecular dynamics simulation for medium-sized and large heteroclusters (n=5–34) was applied. The theory accounts for the spectral shifts of small and medium-sized rare-gas heteroclusters of pentacene and tetracene as well as for small, medium-sized, and large heteroclusters of 9,10 dichloroanthracene, but not for the general pattern of the spectral shifts for anthracene⋅An (A=Ar, Kr; n=1–8) and for perylene⋅Arn (n=2). The confrontation between theory and experiment for the spectral shifts of pentacene⋅Arn (n=1–8), tetracene⋅Arn (n=1–8), tetracene⋅Krn (n=1–8), 9,10 dichloroanthracene⋅Arn (n=1–34) and 9,10 dichloroanthracene⋅Krn (n=1–20), allows for the elucidation of the size dependence of spectral shifts, for the identification of structural isomers in small and medium-sized heteroclusters, and for the exploration of spectral inhomogeneous broadening in large heteroclusters.

Molecular-orbital approach to ion-atom collisions with multiply charged projectiles

In a slow collision between a multiply charged projectile ion and a neutral target atom, self-consistent molecular orbitals in the entrance channel can be defined by introducing a variational constraint which enforces the initial charge sharing and reflects the charge-equilibration process during the collision. In the present work, the interaction of an auxiliary electric field with the electronic dipole moment along the internuclear line is added to an effective single-electron Hamiltonian in order to simulate a constrained Hartree-Fock procedure. In this way, correlation diagrams for the systems ${\mathrm{N}}^{2+}$ + O and ${\mathrm{Ne}}^{4+}$ + Ne are computed. The diagrams exhibit crossings between energy curves of like symmetry. The correlations are found to be the same as in the corresponding charge-balanced (or neutral) systems and are hence consistent with existing experimental data.

The calculation of spin-restricted single-determinant wavefunctions

A procedure is described for the calculation of spin-restricted single-determinant molecular orbital wavefunctions for systems such as free radical ground states and lowest triplet states. It is a further development of ‘partitioning techniques’, which divide the available one-electron space (for a given basis) into three mutually orthogonal subspaces for doubly-occupied, singly-occupied and empty orbitals respectively. Necessary and sufficient conditions are derived for the calculated total energy to be stationary with respect to changes in these subspaces. These lead to an iterative procedure for the determination of self-consistent molecular orbitals. Some preliminary applications to hydrocarbon radicals are described and compared with corresponding spin-unrestricted results.

Magneto-optical activity: Gauge-invariant calculations in the random-phase approximation

The use of London's gauge-invariant orbitals in the calculation of magnetic rotational strengths is investigated. Self-consistent molecular orbitals at non-zero magnetic field strengths have been determined in the Pariser-Parr-Pople model and these have been employed in the calculation of excitation energies and transition moments according to the mono-excited configuration interaction and the random phase approximations. Applications to the magneto-optical activity of aniline, phenol, and benzonitrile are reported. The results are origin-independent and compare well with experimental values.

On the changes in molecular geometry with electronic excitation

In recent years, the near-ultraviolet electronic absorption spectra of a number of substituted benzene compounds have been studied under high resolution (Christoffersen et al., 1969; Bist et al., 1967; Christoffersen et aL, 1967; Thakur, 1968). The structures of these molecules in the ground electronic state have been determined from either microwave or X-ray diffraction measurements, and the high-resolution studies have helped in estimating the shape and size of the molecules in the excited electronic state, using a symmetric rotor approximation. We have performed Pariser-Parr-Pople (PPP) calculations for a number of substituted benzenes in which both 7r-electron charge densities at different atoms and the bond orders for different bonds in the ground and the excited electronic states are obtained as by-products. I t is found that the bond lengths obtained from the self-consistent field (SCF) bond orders can be used successfully to discuss the effect of electronic excitation on the molecular geometry, at least qualitatively, and in the present note we report these results for a number of molecules for which the experimental data are available. The PPP method (Pariser & Parr, 1953; Pople, 1953) has been employed to determine the selfconsistent molecular orbitals, fl~Z~ integrals (ev) have been determined from overlap using the Wolfsberg-Helmholtz formula (Wolfsberg & Helmholtz, 1952). The one-centre and the two-centre repulsion integrals have been determined from the (I.P.-E.A.) approximation and the NishimotoMataga formula (Nishimoto & Mataga, 1957), respectively. The parameters used in these calculations are listed in Table 1, and the 7r-electron bond orders obtained from the SCF C I calculations are given in Table 2. These bond orders have been used to calculate the bond engths using the Coulson formula (Coulson, 1939)

Approximate Self-Consistent Molecular Orbital Theory. I. Invariant Procedures

A general discussion of approximate methods for obtaining self-consistent molecular orbitals for all valence electrons of large molecules is presented. It is shown that the procedure of neglecting differential overlap in electron-interaction integrals (familiar in π-electron theory) without further adjustment may lead to results which are not invariant to simple transformations of the atomic orbital basis set such as rotation of axes or replacement of s, p orbitals by hybrids. The behavior of approximate methods in this context is examined in detail and two schemes are found which are invariant to transformations among atomic orbitals on a given atom. One of these (the simpler but more approximate) involves the complete neglect of differential overlap (CNDO) in all basis sets connected by such transformations. The other involves the neglect of diatomic differential overlap (NDDO) only, that is only products of orbitals on different atoms being neglected in the electron-repulsion integrals.

Electronic Structures and Spectra of Nitromethane and Nitrogen Dioxide

The electronic structures and spectra of nitromethane and nitrogen dioxide have been calculated by a semiempirical method. The self-consistent molecular orbitals and energies of the π-electron system have been calculated; however, for the nonbonding σ-electron system Hückel-type molecular orbitals are used. The nonbonding 2p oxygen orbitals of nitromethane are very slightly modified by mixing with the σ-electron system; in nitrogen dioxide, on the other hand, the totally symmetric combination of 2p oxygen orbitals and the sp2 nonbonding nitrogen orbital mix strongly to form slightly bonding and slightly antibonding molecular orbitals. The calculated transition energies of nitromethane are in reasonable agreement with experiment. For nitrogen dioxide a series of transition energies are obtained which may illuminate experimental results; the complexity of the empirical data, however, and the multitude of calculated low-energy excited states, preclude definite assignment of the observed band systems at this stage.

The Electronic Spectra of Aromatic Molecules II: A Theoretical Treatment of Excited States of Alternant Hydrocarbon Molecules based on Self-Consistent Molecular Orbitals

The theoretical treatment of the electronic spectrum of benzenoid hydrocarbons recently given by Dewar and Longuet-Higgins (Part I) is generalized so that full account is taken of electron interaction. The method is based on the use of a self-consistent molecular orbital function for the ground state and corresponding functions for excited states. It is found that all the general features of the method of Part I carry over, although certain accidental degeneracies are removed. Approximate numerical calculations based on the new method give support to the assignments made by Dewar and Longuet-Higgins.

A Semi-empirical Approach to the Self-consistent Molecular Orbitals

A Semi-empirical Approach to the Self-consistent Molecular Orbitals