Correlation function transition dipole

All of these time correlation functions contain time dependences that arise from rotational motion of a dipole-related vector (i.e., the vibrationally averaged dipole P-avejv (t), the vibrational transition dipole itrans (t) or the electronic transition dipole ii f(Re,t)) and the latter two also contain oscillatory time dependences (i.e., exp(icofv,ivt) or exp(icOfvjvt + iAEi ft/h)) that arise from vibrational or electronic-vibrational energy level differences. In the treatments of the following sections, consideration is given to the rotational contributions under circumstances that characterize, for example, dilute gaseous samples where the collision frequency is low and liquid-phase samples where rotational motion is better described in terms of diffusional motion. 

If the rotational motion of the molecules is assumed to be entirely unhindered (e.g., by any environment or by collisions with other molecules), it is appropriate to express the time dependence of each of the dipole time correlation functions listed above in terms of a "free rotation" model. For example, when dealing with diatomic molecules, the electronic-vibrational-rotational C(t) appropriate to a specific electronic-vibrational transition becomes ... 

Taylor series 260 torque, correlation functions 28 transfer time, rotational relaxation 51 transitions dipole moment 30 forbidden 30 non-adiabatic 130 translational velocity v 6... 

Most FPA studies to date on DNA have lacked sufficient time resolution to observe directly the relaxation of the internal correlation functions. Instead, the initial anisotropy r0 is taken as an adjustable parameter. Equations (4.30) show that such a procedure is completely valid for anisotropic diffusors (i.e., (A ft)2 = (dx(t)2)), provided the rapid internal motion of the transition dipole is isotropic. It has not yet been ascertained whether the internal motion actually is isotropic, so this must be assumed.(83) A recent claim(86) that large amplitudes of polar wobble are required to fit both the small amplitude of initial FPA relaxation 87 and the linear dichroism88 has been refuted. 83j... 

It is well known that in n-body complexes rotational transitions of the order n may occur [400]. However, we will assume here that the interaction forces are pairwise additive and isotropic so that rotations and translations are uncorrelated. In this case, at most double transitions occur [400] and the correlation function of the total dipole moment can be written as... 

Kar and Ho [196] have estimated the oscillator strengths for different transitions, dipole and quadrupole polarizabilities of He for a wide range of the Debye screening parameters using explicitly correlated wavefunctions. Results presented by Kar and Ho [196] are very accurate and may be of substantial use for comparison with those from laser plasma experiments. The behavior of several singly and doubly excited states of He under screened potential was also accurately estimated by Kar and Ho [197] using correlated basis functions. Variation of the transition wavelength as a... 

When interpreting time-resolved mid-IR spectra, it is beneficial to consider the influence of rotational dynamics on the vibrational spectrum of a heteronuclear diatomic. It was shown more than 30 years ago that the vibrational absorption spectrum of a diatomic is related to its transition dipole correlation function (/z(0) /r(t)> through a Fourier transform (10) ... 

In a later paper McQung presents experimental evidence on the correlation function for the transition dipole of an i.r. band in methane. In pure liquid methane, mechanism (ir) above gives good approximation to the experimental results, and (0 is definitely unsatisfactory in solutions of methane in argon, xenon, and krypton, the reverse is the case. 

The electronic-transition dipole moment for the G E transition is defined by Mge = ( g A/ ge1 e> where the are the state wave functions and A/ ge is the dilference in dipole moment of the ground and excited states [22]. The intensity of the transition is proportional to Mge - The broad absorption bands usually observed in transition metal systems are composed of progressions in the vibrational modes that correlate with the differences in nuclear coordinates between the vibrationally equilibrated ground and excited state. Since the energy difference between the donor and acceptor is generally solvent-dependent, the distribution of solvent environments that is characteristic of solutions may also contribute to the bandwidth (see further discussion of this point in the sections below). If the validity of the Born Oppenheimer approximation is assumed, the intensity of each of these vibronic components is given by Eq. 11,... 

In this expression, P2 is the second Legendre polynomial and i(t) is a unit vector with the same orientation as the transition dipole at time t. The brackets indicate an ensemble average over all transition dipoles in the sample. The correlation function has a value of one at very short times when the orientation of y(t) has not changed from its initial orientation. At long times, the correlation function decays to zero because all memory of the initial orientation is lost. At intermediate times, the shape of the correlation function provides detailed information about the types of motions taking place. Table I shows the three theoretical models for the correlation function which we have compared with our experimental results. 

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