Description of state

Fane U 1957 Description of states in quantum mechanics by density matrix and operator techniques Rev. Mod. Phys. 29 74-93... 

The description of states participating in a spin-state transition as electronic isomers with discrete nuclear configurations, in particular different metal-ligand distances, requires that separate electronic and vibrational spectra of the two spin states exist. Indeed, a superposition of the individual vibrational spectra of the two states is in general observed, the relative contribution of the states being a function of temperature [41, 139, 140, 141, 142]. This observation sets a lower limit for the spin-state lifetime longer than the nuclear vibrational period, i.e.,... 

Gas sensors are a new type of sensor for which there is an increasing demand. We include a description of state-of-the-art-gas sensors in Chapter 5.3. 

This description of these two states, as resonance hybrids of the two states Pi and lD is arbitrary, but it is useful, inasmuch as the Russell-Saunders structures correspond closely to the actual properties for many atomic states, and it is convenient to continue to use these structures in the description of states for which no single Russell-Saunders structure provides a completely satisfactory representation of the observed properties. 

Note that each state factor can influence soil carbon storage in two ways by influencing the quantity and quality of plant inputs and by influencing the residence time of organic matter in the soil. Figures 6.2-6.4 show the influence of three state factors on soil C storage. Many of the descriptions of state factors below touch upon the importance of controls on SOM stabilization, and these controls are discussed further in a following section. 

Calculated even- and odd-parity levels are compared with experiment in Becker, et al. [BEC84] An adequate description of states with J > 10 requires contributions from Models II and III. Technically, Model II and ill calculations require a shift in main frame computers and are not complete. 

Complex molecules may not possess any symmetry elements, or if they do, the localizations of the electrons can so distort the electron cloud that its symmetry bears little relation to the molecular symmetry. In such cases it may be best to revert to a description of states in terms of the individual orbitals. As an example, we will consider formaldehyde, although a molecule as simple as this is probably best described by the group-theoretical term symbol of the last paragraph. The last filled orbitals in H2CO can easily be shown to be. ..(jtco)2 (no)2, where no represents the nonbonding orbital on the O atom and the two electrons in it are the lone pair. The first unfilled orbitals in formaldehyde are the tt 0 and rr o antibonding orbitals. Promotion of one... 

About the earliest days of the Soviet state, Borrero writes that Although Lenin complained of the excessively negative descriptions of state cafeterias in the Soviet press, the truth was that few cafeterias actually lived up to basic health and culinary standards 1997 168). 

Detailed descriptions of state-of-the-art apparatus and experimental procedures can be found in the literature for D.C. [124] and A.C. [133] conductivity detection. 

Single letters are used to denote the three basic states of aggregation, gas, liquid, and solid, while combinations of letters are used for more subtle descriptions of states. 

U. FanO Description of States in Quantum Mec hanics by Density Matrix and Operator Techniques, Rev. Mod. Phys., 29, p. 74 93, (1957). 

Figure 3, Absorption spectrum of hematin si-globin complex at state VIL See Figure 1 for description of states...

This chapter deals with the discussion and interpretation of approximate molecular electronic structure methods in terms of propagator concepts. Only situations with fixed nuclear frameworks are considered, and the discussion is limited to the description of states that are close in energy to the normal state of the system. We adopt the view that the main features of the electronic structure of such states can be developed in terms of atomic orbital representations of operators and that only valence shell orbitals need be considered. 

The macroscopic, thermodynamic description of states is achieved through their major functions and variables of state listed in Fig. 2.116. One can deduce from the microscopic picture of the states of matter that the enthalpy of the gas must be largest, and of the solid, smallest. The larger the packing density, the stronger are the interactions between the motifs decreasing the enthalpy. On transition to a new, higher-temperature phase, this interaction must be overcome by an endothermic heat of transition. 

Some of the above components might be omitted and others added. The description of states and different criteria for evaluations can be regarded... 

The description of state behaviour of real gases and their mixtures is an extensive branch of thermodynamics. It is not practically possible (neither would it be purposeful) to attempt a detailed discussion of the topic, the more as it has been treated in several outstanding publications in great detail. Since highly complex, multi-component systems must be expected to originate in calculations of chemical equilibria, where the state behaviour in dependence on composition of the mixture usually is not known, it seems to be useful to limit the discussion to the determination of the real behaviour of mixtures from the known properties of their pure constituents. 

The experimental spectra of DTD " have been recorded in hexane. Keeping in mind the above described diffuse character of all excited states in DTD, an unbalanced theoretical description of states with stronger Rydberg character is to be expected when gas-phase data are compared with those from the condensed phase (Pauli-repulsion between the Rydberg state and solvent molecule wave functions). Figure 19, however, shows an almost perfect match between the theoretical gas-phase and experimental CD spectrum in the entire energy range. Even band C, which is theoretically predicted to have almost... 

The macroscopic, thermodynamic description of states is achieved through their major functions and variables of state listed in the center of Fig. 3.6. The... 

The CIS approach to excited state calculations may also be applied at the ab initio level. However it was recognized that CIS often fails dramatically for radicals. ° This failure is due to the neglect of certain configurations, such as Xz ill Figure 7, which arise by promotion of the a electron from the SOMO to a virtual MO coupled with excitation of a P electron from a doubly occupied MO to the SOMO. Such configurations are, at least formally, doubly excited and their neglect in CIS makes even a qualitatively correct description of states that involve this type of excitation impossible. 

For the description of state space models two common notations are used the state space or Output-Error form is defined as ... 

ONIOM based approaches employing QM/QM or QM/MM schemes were used to describe the vibrational spectra of some molecules of biological interest [841] and of boldine hydrochloride [842], Further examples of the computation of vibrational spectra with QM/MM approaches are reviewed in recent overviews of Barone and co-worker [541, 544], A description of state-of-the-art modeling of IR spectra to elucidate secondary-structure information of peptides and proteins is provided by Amadei et al. [843, 844],... 

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