Simultaneous single excitations

Here a and b are occupied MO s of systems A and B. Equation (6,32) is easily expressible in terms of integrals over atomic basis functions and elements of the density matrix. In eqn. (5.31) two terms may be distinguished. The first one is due to single electron excitations of the type a r") and (b —->s"), where a and r", respectively, are occupied and virtual MO s in the system A, and b and s" are occupied and virtual MO s in the system B, Contribution of these terms corresponds to the classical polarization interaction energy, Ep, Two-electron excitations (a r", b — s"), i.e. simultaneous single excitations of either subsystem, may be taken as contributions to the second term - the classical London dispersion energy, Ep, If the Mjiller-Ples-set partitioning of the Hamiltonian is used, Ep may be expressed in... 

Interpair terms consist of simultaneous single excitations between pairs of electrons for example, (0 a ) x (02 cr ) j which allows... 

Niino Y, Hotta K, OkA K (2009) Simultaneous live cell imaging using dual FRET sensors with a single excitation light. PLoS One 4 e6036... 

A tentative explanation for the importance of connected triple excitations for the inner-shell contribution to TAE can be found in the need to account for simultaneously correlating a valence orbital and relaxing an inner-shell orbital, or conversely, requiring a double and a single excitation simultaneously. 

Similarity transformation, 87, 92,101,412 Similar matrices, 87,101-102 Simultaneous linear equations, 15-16, 87 Singlet, 58,310-311 Singly excited function, 311 Singularity, 17 SI units, 23... 

Fig. 15.8. Schematic one-dimensional illustration of electronic predissociation. The photon is assumed to excite simultaneously both excited states, leading to a structureless absorption spectrum for state 1 and a discrete spectrum for state 2, provided there is no coupling between these states. The resultant is a broad spectrum with sharp superimposed spikes. However, if state 2 is coupled to the dissociative state, the discrete absorption lines turn into resonances with lineshapes that depend on the strength of the coupling between the two excited electronic states. Two examples are schematically drawn on the right-hand side (weak and strong coupling). Due to interference between the non-resonant and the resonant contributions to the spectrum the resonance lineshapes can have a more complicated appearance than shown here (Lefebvre-Brion and Field 1986 ch.6). In the first case, the autocorrelation function S(t) shows a long sequence of recurrences, while in the second case only a single recurrence with small amplitude is developed. The diffuseness of the resonances or vibrational structures is a direct measure of the electronic coupling strength.

For a single excitation path (i.e., one or three photons), the only possibility for controlling the outcome of the reaction is to select the excited eigenstate by varying E, as is normally done in mode-selective processes. A completely new form of control becomes possible, however, if both excitation paths are simultaneously available. In that case, the reaction probability is... 

In the fluorescence microscope, careful consideration of the sample and system components is necessary to specify the correct filters for probe detection. Use of multiband dichroics and emission filters in a stationary turret with single exciters in an external slider or filter wheel can give near simultaneous probe detection with no registration shift, but there are likely compromises in overall brightness, color balance difficulty, and reduced resolution of the color CCD camera. 

The first term generates the reference HF and the second all singly excited states. The first parenthesis generates all doubly excited states, which may be considered as connected (T2) or disconnected (Tj). The second parenthesis generates all triply excited states, which again may be either true (T3) or product triples (T2T1, Tj). The quadruply excited states can similarly be viewed as composed of five terms, a true quadruple and four product terms. Physically a connected type such as T4 corresponds to four electrons interacting simultaneously, while a disconnected term such as T2 corresponds to two... 

Standard CC methods, which have been termed plain old CC (POCC) in the literature [231], are those in which the orbital optimization and correlation steps of the calculation are performed separately. POCC calculations therefore suffer from instability poles in addition to the appropriately located EOM poles, but the width of the former are quite small because of the approximate orbital invariance of CC methods that include single excitations [243]. These methods offer some advantages in treating PJT effects relative to CC approaches in which orbitals and cluster amplitudes are determined simultaneously, as discussed briefly in the next section. 

Since Eq. (224) shows that an arbitrary two-electron singlet wavefunction may be expanded in terms of only n CSFs, a possible solution to this problem may lie in the particular choice of these n expansion terms. If there are alternate n-term expansions for the general wavefunction, these might then be used to advantage in the simultaneous descriptions of several states since different CSF expansion spaces would produce different approximations to the other states. It is instructive to consider a possible -term expansion in terms of i i and its single excitations. This -term wavefunction expansion consists of a symmetric C matrix of the form... 

After a single excitation pulse or a series of pulses the signal detection period begins where the response of the spin system to the pulse sequence is recorded. The basic configuration for quadrature detection [2.32, 2.33] is two detectors in the x,y-plane with a 90° phase difference where each detector may be assigned to the x- or y-axis. As illustrated in Fig. 2.6 there are two detection methods, in simultaneous detection both detectors are sampled at the same time whilst in sequential detection the detectors are sampled alternatively. 

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