Vibrational eigenstates

An alternative perspective is as follows. A 5-frmction pulse in time has an infinitely broad frequency range. Thus, the pulse promotes transitions to all the excited-state vibrational eigenstates having good overlap (Franck-Condon factors) with the initial vibrational state. The pulse, by virtue of its coherence, in fact prepares a coherent superposition of all these excited-state vibrational eigenstates. From the earlier sections, we know that each of these eigenstates evolves with a different time-dependent phase factor, leading to coherent spatial translation of the wavepacket. 

Since the vibrational eigenstates of the ground electronic state constitute an orthonomial basis set, tire off-diagonal matrix elements in equation (B 1.3.14) will vanish unless the ground state electronic polarizability depends on nuclear coordinates. (This is the Raman analogue of the requirement in infrared spectroscopy that, to observe a transition, the electronic dipole moment in the ground electronic state must properly vary with nuclear displacements from... 

Fig. 3 Probability density for the Fig. 4 Probability density for the vibrational eigenstates (/>o, and (j)2 optimal superpositions and tp ...

Figure 39. Pump-dump control of NaK molecule by using two quadratically chirped pulses. The initial state taken as the ground vibrational eigenstate of the ground state X is excited by a quadratically chirped pulse to the excited state A. This excited wavepacket is dumped at the outer turning point at t 230 fs by the second quadratically chirped pulse. The laser parameters used are = 2.75(1.972) X 10-2 eVfs- 1.441(1.031) eV, and / = 0.15(0.10)TWcm-2 for the first (second) pulse. The two pulses are centered at t = 14.5 fs and t2 = 235.8 fs, respectively. Both of them have a temporal width i = 20 fs. (See color insert.) Taken from Ref. [37].

The extension of Eqs. (12)—(16) to a standard pump-probe experiment, where the final state is a (dissociation or ionization) continuum is straightforward. It requires only that we replace the pulse that spans two vibrational eigenstates by a shorter one that spans several eigenstates. 

Triatomic Vibrational Eigenstates Product or Contracted Basis Sets, Lanczos or Conventional Eigensolvers What Is the Most Efficient Combination ... 

Vibrational Eigenstates of Four-Atom Molecules A Parallel Strategy Employing the Implicitly Restarted Lanczos Method. 

A. Back,/. Chem. Phys., 117, 8314 (2002). Vibrational Eigenstates ofN02 by a Chebyshev-... 

The spectra being discussed here are C2H2 A-X DF spectra, and the initial state created on the So surface corresponds to a perfectly known vibrational eigenstate of the A state (Si) surface transferred onto the X state (So) surface. However, any conceivable initial state could be expressed as a superposition of independently evolving polyads, each initially illuminated via one or more a priori known bright zero-order states. 

A rotation-vibration eigenstate is typically sensitive to the global potential-energy surface. In time-dependent language, in order to resolve individual... 

The SEP spectra sample a large set of completely assignable vibrational eigenstates as well as some partially assignable interlopers, which are also vibrational levels of the HCP X state, made observable either by perturba-... 

The energies of the vibrational eigenstates in the electronic ground state, which are related to the frequencies of the emitted photons by E% T hu> — Ef T Tuo. ... 

Using the basic rationale of EMA theory [267], the parametric function e(q) becomes p q) = E—Hn when the kinetic energy of nuclear motion cannot be neglected. However, the operator (erflS(q) — op(q)) has a well-defined c-number value in vibrational eigenstates determined by the eigenvalue equation... 

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