States Of Different Symmetry Research Articles

Electronic structure of compounds with Fe-C bonds

We present an ab initio study of the electronic structure of three compounds containing Fe-C bonds: CH 3FeH, FeCH 2 and HFeCH. The geometries of several electronic states were optimised at the SCF or CASSCF level, with triple-zeta basis sets. Single point CI calculations allow the energy ordering of states of different symmetry and spin multiplicity to be assessed. The nature of bonding in the three compounds is discussed.

One- and two-photon spectra of some selected molecules: A comparative study

The complementarity of one- and two-photon spectroscopy has been utilised for throwing light on the following problems of chemical interest: (1) Weak interaction between identical chromophores separated by insulating bridges gives rise to split states of different symmetries. Two-photon spectroscopy (TPA), in conjunction with one-photon absorption (OPA), has been used to identify the states and hence to estimate the magnitude of interaction in bimolecules and trimolecules. From the shifts between the one- and the two-photon spectra, the splittings have been estimated. Calculations confirm that the dominant interaction is the through-bond one. (2) The second type of problem is the identification ofg andu vibrations in molecules. We have initiated studies on three molecules in jet-cooled conditions: 9,10-dihydro-anthracene (DHA). 9,10-dihydro-phenanthrene (DHP) and octa-fluoronaph-thalene (OFN). Only the one-photon fluorescence excitation spectra have so far been obtained by us and the TPA spectra are under investigation. (3) The third class of molecules discussed here are the Ln3+ complexes wheref n⇒ fn transitions are intrinsically two-photon allowed. We have studied two GD3+ single crystals. The CF-splittings, observed clearly in TPA, have been fitted with a parametric model. Some of our observations on the variations of TPA intensity patterns from crystal to crystal, such as circular:linear polarisation ratios, relative intensities of transitions to differentJ-states, do not quite fit in with the Axe-Judd-Downer model. The discrepancies call for a reappraisal of the role of ligand in the TPA process.

Vortex states in an unconventional superconductor and the mixed phases of UPt3.

Recent experiments on ${\mathrm{UPt}}_{3}$ indicate the existence of more than one superconducting phase and an associated unconventional order parameter belonging to a nontrivial representation of the crystal point group ${\mathit{D}}_{6\mathit{h}}$. In this article we consider the Ginzburg-Landau (GL) theory for the vortex states in the two-dimensional ${\mathit{E}}_{1}$ representation for the order parameter, the representation believed to describe the phases of ${\mathrm{UPt}}_{3}$. One of the zero-field superconducting phases is predicted to break time-reversal symmetry. We show that the lower critical field for vortex nucleation in a ground state with broken time-reversal symmetry exhibits a novel asymmetry. Observation of this asymmetry in any superconductor would provide clear evidence for an unconventional order parameter. We present solutions to the GL equations for singly quantized vortices. For rectilinear vortices along the c axis two classes of solutions are found: (i) axially symmetric vortices and (ii) nonaxisymmetric vortices which spontaneously break the axial symmetry of the condensate density. We discuss the structure of these vortices, their relation to the asymmetry of ${\mathit{H}}_{\mathit{c}1}$, the possibility of phase transitions between vortex states of different symmetry, and the phase diagram of ${\mathrm{UPt}}_{3}$ in the H-T plane.

Calculation of the potentials for ionization into various states of the cation for a series of polyacenes by the ?SCF method

The Fock equations for orbitals of systems with an open shell featuring a single matrix variable (density) are applicable for the excited states of the ion. The calculated potentials for the ionization to cation states of different symmetry obtained by removal of an electron from the inner orbitals for a series of polyacenes provide for the same precision (∼0.1 eV) in the π-electron approximation as for the electronic spectra and lower ionization potentials.

Pairing instabilities of the extended Hubbard model for Cu-O-based superconductors.

We use weak-coupling methods to calculate the effective interaction between quasiparticles induced by charge and spin fluctuations in a three-band model for the copper-oxide superconductors with both intersite and intrasite repulsion. The instabilities to superconducting states of different symmetries are calculated; besides the d-wave superconductivity near the antiferromagnetic instability, we find that extended s-wave superconductivity is favored by a charge transfer resonance close to a valence instability. A phase diagram similar to experiments is obtained.

Photofragmentation in non-symmetric carbonyl compounds

The energy profiles for radical dissociation of the lowest triplet state of some non-symmetric carbonyls have been examined using the MINDO/3 method and employing configuration interaction. The activation barriers in the cleavage process arise from an avoided crossing between two states of different symmetries. Our analysis reveals that the perpendicular motion of carbonyl carbon is an important component in the reaction coordinate. Selectivity of the cleavage of a σ bond adjacent to the chromophore is determined by the third derivative of energy with respect to the reaction coordinate at the starting point of reaction.

Semiempirical MNDOC—CI calculations on photochemical reactions: Criteria for selecting configurations

To make the semiempirical MNDOC—CI method applicable to photochemical reactions, various criteria for selecting configurations are tested in order to truncate the CI space in such a way, that potential energy surfaces of states of different symmetry and multiplicity can be described adequately using a fixed maximum number of configurations (limit ca. 100–200) and taking care of the fact, that the number of singly and doubly excited configurations is different for different states. Reliable results for the relative energies of excited states are obtained, if the same set of excitation indices is used for all states under consideration and if these indices are chosen such that the maximum number of resulting configurations is close to the limit. Applications to the α-cleavage reaction of carbonyl compounds demonstrate the usefulness of the MNDOC—CI method for treating photochemical problems.

Activation barrier for the .alpha.-cleavage process in thiones

The Occurrence of the Norrish type I a-cleavage process in some thio compounds has been examined by using the MIND013 method and employing the configuration interaction. Results reveal that where the radiationless process is not efficient, thio compounds can undergo photodissociation into radicals in their lowest triplet and singlet excited states. The activation barriers in all these cases arise from an avoided crossing between two states of different symmetries. The calculations of activation barriers by the CNDO-CI and MINDO-CI procedures reveal that the MINDO-CI method leads to realistic values of the activation energies.

A theoretical study of the photochemical α-cleavage processes in symmetric and non-symmetric ketones

The energy profiles for radical dissociation of the lowest triplet state of various symmetric and non-symmetric ketones have been computed using the MINDO/3 method and employing configuration interaction. The results of radical dissociation of thioformaldehyde were also examined. In each case, the activation barrier arises from an avoided crossing between two states of different symmetry. Our analysis reveals that the perpendicular motion of the carbonyl carbon is an important component in the reaction coordinate.

New coherence effects in the polarization of light emitted by photofragments: Theory.

A quantum-mechanical treatment of the degree of polarization of photofragment fluorescence in the case where two dissociative electronic states of different symmetry with the same limit are excited coherently is presented. This results in an interference effect which depends both on the photoabsorption probability amplitudes in the different excited states as well as on the phase differences of their vibrational wave functions at large distances. Oscillations of the polarization ratio as a function of the photon energy are predicted. Applications to some simple cases involving a diatomic molecule initially in a $^{1}\mathrm{\ensuremath{\Sigma}}$ state are presented. The case of ${\mathrm{Ca}}_{2}$ is discussed. The role of fine (or hyperfine) structure, and in particular the case of unresolved fluorescence is treated. The classical model in terms of oscillating electric dipole moments properly averaged over the initial orientations of the molecule is presented and allows the interpretation of the quantum results.

Quantitative analysis of third harmonic generation of XUV radiation in a cell and a cw free jet of carbon monoxide

In the theory, the two-photon resonant third-order nonlinear susceptibility of a molecular gas is calculated. The variations of this susceptibility, with the rotational quantum numbers of the resonant states, are given in the case of two singlet states of different symmetries, Σ and Π. In the experiment, third harmonic generation of XUV light (94.5–97.5 nm) is obtained with and without two-photon resonance. The gaseous nonlinear medium is formed by CO as used either in a cell, or in a continuous supersonic free jet zone of silence. The intensity of the third harmonic wave generated is well related to the laser power, phase-matching conditions, two-photon resonances, and rotational temperature, through the nonlinear susceptibility, as described theoretically.

Polarisation-dependent two-photon spectra of triptycene

Two-photon excitation spectra of a methylcyclohexane solution of triptycene using linearly and circularly polarized light are recorded. It is concluded from the polarisation dependence of the spectra that there exist two electronic states of different symmetry ≈2500 cm −1 apart.

Electronics states of a surface nickel atom on the nickel (001) surface

Electronic states of a Ni(001) surface atom, corresponding to different d-occupations, are calculated for a 49 atom cluster model of the surface. SCF and CI calculations on a variety of low lying states are reported. Strong mixing between d 9 and d 10 configurations is found for the lowest states of different symmetries with the splitting between the states ranging from 1.7 to 2.0 eV. In contrast, the d 8 configurations do not interact strongly with other d configurations and lie energetically much higher at ∼3.0 eV. Thus, the splitting between d 9 and d 10 configurations is comparable to that of the isolated atom whereas the d 8 configuration is greatly destabilized. The cluster produces a manifold of closely spaced electronic states above the ground state thus modeling the density of unoccupied states above the Fermi level.

Effective masses for impurity states in anisotropic crystals

Spherically averaged effective masses for donor states of different symmetry in Si and Ge are obtained following the methods of Tefft (1969) and Lee and co-workers (1982). The presence of equivalent conduction band minima in these semiconductors is taken into account following a many-valley formalism developed by Twose. The results, failing to satisfy symmetry requirements, indicate the inadequacy of the Twose equation.

The polarization dependence of two-photon absorption rates for randomly oriented molecules

The method and results are presented for the analysis of the two-photon absorption experiment for randomly oriented molecules (in a single-beam regime) that can be easily extended to higher-order processes without any assumption regarding the nature of the initial state. Some known results were recovered and some new ones presented. The ratio of the averaged transition rate for circularly polarized light to the one for linearly polarized light, Ω, can be obtained from the following rules: (a) for any transition involving two states of the same symmetry (on any point group), Ω < 1: (b) exceptions to rule (a) are found in T, T h, T d, O and O h groups for which A ↔ A transitions give Ω = 0 and E ↔ E gives Ω = 24 31 : and (c) for any transition involving two states of different symmetry, Ω = 3 2 . The results of these predictions are in excellent agreement with the available experimental data.

The decoupling of electronic orbital angular momentum from the molecular axis in a1S+1P atom-atom collision

The decoupling of electronic orbital angular momentum from the molecular axis in atom-atom collisions is described as a case of rotational coupling between molecular states of different symmetry. For a system A(1S)+B(1P) with not too large an impact parameter, the corresponding semiclassical equations are solved. Explicit predictions are made about the polarisation of the 1P wavefunction from a typical inelastic collision process, that is a process which proceeds through a single molecular state, Sigma or Pi , at small internuclear distance.

D—s, p Resonance and Electronic Structure of Compounds, Alloys, and Solid Solutions

AbstractOn the basis of the valence band structure regularities, obtained from combined X‐ray spectral and X‐ray photoelectron studies of electron energy spectra, a model is suggested for the interaction between valence electrons of s, p‐elements and d‐electrons of IIIA, IIB, IB, and transition metals under the formation of compounds, alloys, and solid solutions, the so called d—s, p resonance. The model qualitatively explains different observed manifestations of state interaction: the energy displacements, subband splitting, mixing of states of different symmetry or, vice versa, pushing of s, p‐states out of the energy interval, occupied by d‐band, due to the mutual energy arrangement of d‐ and s, p‐subbands.

Observation of —100% Spin-Polarized Photoelectrons from a Transversely Magnetized Ni(110) Single Crystal

We have measured for the first time the electron spin polarization $P$ of photoelectrons emitted from a transversely magnetized sample in the absence of an externally applied magnetic field. With this photoemission geometry, use has been made of optical selection rules for selectively exciting spin-polarized electron states of different symmetry as illustrated for emission from the ${\ensuremath{\Sigma}}_{3}$ and ${\ensuremath{\Sigma}}_{4}$ bands of Ni(110), where values of $P$ up to ---100% have been observed.

Orbital angular momentum in triatomic molecules

The effects of electronic angular momentum in triatomic linear molecules are considered. An effective vibronic hamiltonian is derived and second order energy level expressions are obtained for the bending levels in an electronic Π state. The formulae allow for the anharmonicity of the bending potentials and for the variation of the expectation value <Lz > with bond angle; effects of electron spins are also included. The vibronic levels predicted by the analytic expressions are compared with those calculated using a full matrix treatment of the orbital angular momentum; it is shown that they are far more accurate than the levels predicted by the formulae currently available in the literature. The relationship between the anharmonic corrections and the deviation of <Lz > from unity is discussed in terms of an electrostatic interaction between linear molecule states of different symmetry.

Electronic structure investigation of metallic vanadium by XS and XPS

AbstractThe valence band of vanadium is investigated using X‐ray and X‐ray photoelectron spectro‐scopy. By XPS core level measurements the several spectra are correlated and drawn in unitary energy scale for comparison purpose. The spectra are compared with density‐of‐states functions from the literature and discussed in terms of electron states of different symmetry (s‐, p‐, d‐like). From the experimental spectra the widths of the occupied d‐band and s‐d band are estimated to 4.0 and 6.8 eV, respectively. The experimental results confirm the general accepted picture of the electron structure of 3d metals.