Molecular systems, component amplitude

Component amplitudes, molecular systems analytic theory, 214-233... 

Fourier transform, molecular systems, component amplitude analysis cyclic wave functions, 224-228 reciprocal relations, 216-217 Four-state system loop construction ... 

Gaussian wavepackets multiple spawning, 402 propagation, 380-381 molecular systems, component amplitude analysis, wave packet construction, 229-230... 

Restriction equations, molecular systems, component amplitude analysis, reciprocal relations, 215-217 Robb, Bemardi, and Olivucci (RBO) method, conical intersection location, 489—490 Rotational couplings ... 

Wigner rotation/adiabatic-to-diabatic transformation matrices, 92 Time-dependent ground state (TDGS), molecular systems, component amplitude analysis, near-adiabatic limit, 220-224... 

The cartesian components of the TPA transition amplitude tensor, T f, between the ground state 0)0 and the excited state 0)/ of an isolated molecular system are defined as... 

Molecular machines can be defined as a subset of molecular devices (functional molecular systems) in which some stimulus triggers the controlled, large amplitude mechanical motion of one component relative to another (or of a substrate relative to the machine) which results in a net task being performed [9]. Since chirality is a direct consequence of the relative position of the different parts of a molecule, the intimate relationship between mechanical motion in molecular machines and chirality is self-evident. 

The presence of /,/ and components requires an iterative solution of this equation—an approach that necessitates storage of the T3 amplitudes in each iteration This scheme is unreasonable because the number of such amplitudes would rapidly become the computational bottleneck as the size of the molecular system increased. This problem may be circumvented, however, by utilizing the so-called semicanonical molecular orbital basis in which the occupied-occupied and virtual-virtual blocks of the Fock matrix are diagonal. In this basis, the two final terms in the T3 equation above vanish, and the conventional noniterative computational procedure described earlier in the chapter may be employed. 

These definitions are similar to Wilson s3, but more general. The usual s-vectors, here written S(°a, have special properties because they are formed from derivatives evaluated in the equilibrium configuration. The constant 5-elements in the treatment of small amplitude vibrations are their components in a molecular system fixed to this equilibrium configuration,... 

Terahertz (THz) spectroscopy systems utilize far-infrared radiation to extract molecular spectral information in an otherwise inaccessible region of the electromagnetic spectrum where various rotational, vibrational, and translational modes of molecules are located, 0.1-10 THz (Fig. 1). As the wavenumber range is narrowed, THz-radiation can yield more specific information about a particular chemical component within the system. Unlike most spectroscopic techniques, THz instrument measures the wave temporal electric field, which can be Fourier transformed to yield THz pulse amplitude and phase. This added capability allows precise... 

Because in H, the two spin energy levels are separated by KHz frequency (rather than MHz frequency as in Hq), it is fluctuating local (dipolar) fields with components in this frequency regime that induce the necessary spin transitions for relaxation. Measurement of the spin-lattice relaxation time in H thus allows information to be obtained on the density and amplitude of motions of the molecular system in the KHz range. 

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