Transition moment functions

There are other measurable physical properties which reflect the change of electronic character as a function of the inter-nuclear distance R in the avoided crossing region. Examples can be found in the measurements of the vibrationally resolved dipole moments of the A E" state of LiH and NaH ( ) to complement earlier X Z results (35). Also, measurements on the lifetimes (36, 37) and the fluorescence intensity patterns (, M) provide information about the transition moment functions. Further experimental measurements when coupled with the theoretical calculations of the dipole moments and the transition moments (25, 26) and the radiative lifetimes (40) will eventually give a more detailed picture of the ionic-covalent interactions, and should also more clearly establish the limitations of a two-state model. 

In order to compute or interpret photodissociation a(E) functions, it is necessary to know (i) the potential energy curve of the initial state (ii) the potential energy curves of all energetically accessible excited electronic states (both purely repulsive states and the above dissociation repulsive region of bound states) (iii) the electric dipole transition moment function between the initial and final state (iv) the (R- dependent) interactions among the set of electronic... 

Using highly correlated MCSCF-Cl wave functions for the A rij and X states, the transition moment function for the A - X transition has been calculated which in turn allowed the evaluation of Einstein coefficients of spontaneous emission A, (v = 0,1 v" = 0,1,2), absorption oscillator strengths f v (v = 0,1 v" = 0,1), and radiative lifetimes for A Ili, v = 0,1 of PH and PD. The v = 0 lifetime Xrad = 399 ns for PH (390 ns for PD) is shorter than the experimental value, probably because the large correlation energy contributions to the transition moment have not been sufficiently accounted for in the calculation [32]. 

The dipole transition moment function fiij between the ground state and the B state... 

Hattig, C., Christiansen, O., 8c Jorgensen, P. (1998a). Multiphoton transition moments and absorption cross sections in coupled cluster response theory employing variational transition moment functionals. Journal of Chemical Physics, 10, 331. 

Hollenstein H, Marquardt R, Quack M and Suhm M A 1994 Dipole moment function and equilibrium structure of methane In an analytical, anharmonic nine-dimenslonal potential surface related to experimental rotational constants and transition moments by quantum Monte Carlo calculations J. Chem. Phys. 101 3588-602... 

The Einstein coefficients are related to the wave functions j/ and of the combining states through the transition moment R , a vector quantity given by... 

The transition moment (Equation 2.13) for a transition between lower and upper states with vibrational wave functions and j/[ respectively is given by... 

Linear response function approaches were introduced into the chemistry literature about thirty years ago Ref. [1,2]. At that time they were referred to as Green functions or propagator approaches. Soon after the introduction it became apparent that they offered a viable and attractive alternative to the state specific approaches for obtaining molecular properties as excitation energies, transition moments and second order molecular properties. 

In these dye-functionalized dendrimers, light absorbed by the numerous peripheral coumarin-2 units is funneled to the coumarin-343 core with remarkably high efficiency (toluene solution 98% for the first three generations 93% for compound 8). Given the large transition moments and the good overlap between donor emission and acceptor absorption, energy transfer takes place by Forster mechanism [34]. 

All three states were described by a single set of SCF molecular orbitals based on the occupied canonical orbitals of the X Z- state and a transformation of the canonical virtual space known as "K-orbitals" [10] which, among other properties, approximate the set of natural orbitals. Transition moments within orthogonal basis functions are easier to derive. For the X state the composition of the reference space was obtained by performing two Hartree-Fock single and double excitations (HFSD-CI) calculations at two typical intemuclear distances, i.e. R. (equilibrium geometry) and about 3Re,and adding to the HF... 

In order for a transition to occur, the transition moment integral must be an even function. This integral is the product of the wave function corresponding to the ground state Tff, an operator R, and the wave function of the excited state Ye. Since R is antisymmetric, the product of the wave... 

Spectral shift (in wave number Av) of the azobenzene chromophore caused by intermolecular interaction can be estimated by using Kasha s equation (2), which is a function of the transition moment (n), distance between dipoles (r), and number of interacting molecules in bilayer assemblics(V). 

For a rod-like probe with its absorption transition moment direction coinciding with the long molecular axis, the rotational motion in this potential well is described by the diffusion coefficient D. The decay of the autocorrelation functions is then shown to be an infinite sum of exponential terms ... 

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