Spin-orbit Coupling Matrix Elements Research Articles

Collisional quenching of O(1 D) by rare gas atoms

Off-diagonal spin–orbit coupling matrix elements are calculated for the lowest 1Σ+, 3Π and 3Σ– states of the rare-gas oxides from SCF wave functions in a double-zeta basis. From the resulting parameters and calculated potential energy curves of Dunning and Hay, estimates of the O(1D) collisional quenching rate constant at 300 K have been made. Calculated values are in good agreement with experiment for Ar and a little too low for Kr and Xe; this may be due to an under-estimation of the spin–orbit parameter. For Ne the calculated value is too low by a factor 104. Reduction of the calculated crossing point by a factor of three would be needed to give agreement with experiment, suggesting that latter may be in error. Experimental data at other temperatures is needed unambiguously to decide the source of error.

Mechanisms of intersystem crossing in aromatic hydrocarbons

A rate expression for intersystem crossings S-T in aromatic hydrocarbons is formulated by means of a Green’s function technique. The rate constant involves not only diagonal terms of spin–orbit coupling and nonadiabatically induced spin–orbit coupling but also cross terms between them that are usually neglected. It is shown that promoting modes for intersystem crossings can be classified into two groups according to the perturbations causing intersystem crossings. One group is governed by vibronic spin–orbit coupling matrix elements and the other by vibronic coupling matrix elements which involve the nuclear momentum operator. An approximate calculation of vibronic spin–orbit coupling matrix elements is carried out for the S1(1B2u) -T intersystem crossing in benzene. The results indicate that C–H out-of-plane vibration ν10 acts as a dominant promoting mode for both S1-T1 direct and S1-T2-T1 indirect mechanisms.

The phosphorescence of hindered aminopyrimidines

The spectra quantum yields, lifetimes and polarizations of phosphorescence of 4- and 5-aminopyrimidines and their hindered alkyl derivatives were measured in solvents of different polarity at 90 K. The model presented for interpretation of these data allows us to determine the matrix elements of spin-orbit coupling between the emitting singlet and triplet states. These elements are 0.2-0.8 cm -1 in aminopyrimidines and increase as the amino group becomes more twisted relative to the ring. Spin-orbit coupling of higher 1(n,π ∗) states with emitting triplets is about 10 times stronger than that of the lowest 1( l , a π ∗ ).

Theoretical Interpretation of Luminescent Properties of Nitroanilines

Abstract The energies of low-lying singlet and triplet ππ∗-, and nπ∗- states of nitroanilines and their methylated derivatives have been calculated with the aid of the PPP-method including the superposition of singly excited configurations. For these systems the spin-orbit coupling matrix elements between the ππ∗- and nπ∗- states of different multiplicities were estimated using one-electron and one-center approximations. The interpretation of the luminescent properties of nitroanilines in a dense medium is given. The dependence of the luminescence on temperature is predicted for molecules having the Tnπ∗- state located somewhat above the lowest Sππ∗- state.

On the interaction of O( 1S) with O( 3P)

The quenching rate for O( 1S) by O( 3P) into the O( 1D) + O( 1D) channel is calculated using a theoretically calculated spin-orbit coupling matrix element. An upper bound to the rate is found to be 2.0 × 10 −14 cm 3 s −1 which is much smaller than the experimental value. The low value of the rate constant is the result of a spin-orbit coupling matrix element of about 3 cm −1 at the relevant curve corssing.

Semiempirical Molecular Orbital Calculations. II. The Nonbonding Orbital, the Electronic Spectrum, and the Spin—Orbit Coupling in X2CO Molecules

Phosphorescence lifetimes have been calculated for the T1→S0(π*→n) transition in formaldehyde and some of its halogen substituents. The wavefunctions used were obtained by a charge self-consistent Wolfsberg—Helmholz method. The so-called n orbital on the oxygen atom is mixed with carbon and halogen p orbitals to a considerable extent. As a consequence, one-center terms on the halogens have to be considered in the evaluation of spin—orbit coupling matrix elements. The results indicate a considerable internal heavy-atom effect on the (π*→n) phosphorescence lifetimes of formaldehyde derivatives. The available experimental evidence agrees with this conclusion.