Specific state theories

The essence of the above argument permeates much of our work since the early 1970s, for example, [7-10, 17, 20-22, 26a-26c, 34], a basic element of which, namely the utility of the proper choice of the zero-order model, Fermi-sea zero-order function space, is reviewed here. Here, I use the generic name SPSA (also called state-specific theory (SST)) because of the special attention that is given to the nature of each state and property of interest and to the related theoretical and computational requirements of optimized function spaces. 

C.A. Nicolaides, State-specific theory of quantum chemistry, in R. Carb (Ed)., Quantum Chemistry- Basic Aspects, Actual Trends", Elsevier, Amsterdam, 1989, p. 343. 

N.C. Bacalis, Y. Komninos, C.A. Nicolaides, State-specific theory and method for the computation of diatomic molecules Application to E+, Phys. Rev. A 45 (1992) 2701. 

C.A. Nicolaides, The state-specific theory of atomic structure and aspects of the dynamics of photoabsorption, in Connerade J.P., Esteva J.R, Kamatak R.C. (Eds.), Giant Resonances in Atoms, Molecules and Solids, Plenum Publishing, New York, 1987, p. 213. 

M. Bylicki, S.l. Themelis, C.A. Nicolaides, State-specific theory and computation of a polyelectronic atomic state in a magnetic field. Application to doubly excited states of H-, J. Phys. B 27 (1994) 2741. 

An alternative to the conventional methods of quanfum chemistry is the state-specific theory, useful especially for excited states [1,42,131,132]. Such a theory is based on the choice and optimization of the function spaces for each excited state of interest, both at the zeroth-order and at the correlation level. This allows the systematic inclusion of relaxation and correlation effects to a very good degree of accuracy and the reliable description of phenomena and calculation of properties with small wavefunctions. Furthermore, physical and chemical concepts become more transparent while aspects of transferability of parfs of fhe energy or of the wavefunctions and their distinct effects on spectroscopy, on properties, and on chemical bonding in excited states may be systematized. 

For atoms and diatomics, the 4)]] for a state that is treated as isolated (e.g., a multiply excited valence state) can be obtained for the root labeled by the configuration(s) of interest. In cases of strong configurational mixing, the rate of convergence of the overall calculation is sensitive to the radial details of the FS orbitals. This is why in the state-specific theory these are obtained numerically when possible. When configurations in 4) ... 

We note that eq (4) involves the coefficients and c explicitly, indicating that the cluster amphtudes depend on them, as is expected of a state-specific theory. We also note that the sets T and c are coupled through eq (4) and eq (7). Solving these coupled set of equation we obtain both the cluster amplitudes and the converged coefficients from the diagonalization. The number of unknowns in this formalism is exactly the same as in the effective hamiltonian based SU-MRCC theory [12]. 

Hase W L, Cho S-W, Lu D-H and Swamy K N 1989 The role of state specificity in unimolecular rate theory Chem. Phys. 139 1-13... 

These predicates are clearly dependent on the specific problem. We will assume that they are available as basic facts, but we could continue to analyze them using the specific theory of the problem, to turn the start-and end-times of one state into constraints on processing times, and start-and end-times of other states. 

Experimental probes of Born-Oppenheimer breakdown under conditions where large amplitude vibrational motion can occur are now becoming available. One approach to this problem is to compare theoretical predictions and experimental observations for reactive properties that are sensitive to the Born-Oppenheimer potential energy surface. Particularly useful for this endeavor are recombinative desorption and Eley-Rideal reactions. In both cases, gas-phase reaction products may be probed by modern state-specific detection methods, providing detailed characterization of the product reaction dynamics. Theoretical predictions based on Born-Oppenheimer potential energy surfaces should be capable of reproducing experiment. Observed deviations between experiment and theory may be attributed to Born-Oppenheimer breakdown. 

Consequently, we can carry out the BCH expansion to arbitrarily high order without any increase in the complexity of the terms in the effective Hamiltonian. In practice, the expansion is carried out until convergence in a suitable norm of the operator coefficients is achieved, as illustrated in Table I. Rapid convergence is usually observed. Note that through the decomposition (23), the effective Hamiltonian depends on the one- and two-particle density matrices and therefore becomes state specific, much like the Fock operator in Hartree-Fock theory. 

The first part of the review deals with aspects of photodissociation theory and the second, with reactive scattering theory. Three appendix sections are devoted to important technical details of photodissociation theory, namely, the detailed form of the parity-adapted body-fixed scattering wavefunction needed to analyze the asymptotic wavefunction in photodissociation theory, the definition of the initial wavepacket in photodissociation theory and its relationship to the initial bound-state wavepacket, and finally the theory of differential state-specific photo-fragmentation cross sections. Many of the details developed in these appendix sections are also relevant to the theory of reactive scattering. 

Most of the experimental results on CJTE can be explained on the basis of molecular field theory. This is because the interaction between the electron strain and elastic strain is fairly long-range. Employing simple molecular field theory, expressions have been derived for the order parameter, transverse susceptibility, vibronic states, specific heat, and elastic constants. A detailed discussion of the theory and its applications may be found in the excellent review by Gehring Gehring (1975). In Fig. 4.23 various possible situations of different degrees of complexity that can arise in JT systems are presented. 

W. H. Miller I would like to ask Prof. Schinke the following question. Regarding the state-specific unimolecular decay rates for HO2 — H + O2, you observe that the average rate (as a function of energy) is well-described by standard statistical theory (as one expects). My question has to do with the distribution of the individual rates about die average since there is no tunneling involved in this reaction, the TST/Random Matrix Model used by Polik, Moore and me predicts this distribution to be x-square, with the number of decay channels being the cumulative reaction probability [the numerator of the TST expression for k(E)] how well does this model fit the results of your calculations ... 

Prof. Troe has presented to us the capture cross sections for two colliding particles, for example, an induced dipole with a permanent dipole interacting via the potential V(r,0) = ctq/2rA - ocos 0/r2 (see Recent Advances in Statistical Adiabatic Channel Calculations of State-Specific Dissociation Dynamics, this volume). The results have been evaluated using classical trajectories or SAC theory. But quantum mechanically, a colliding pair of an induced dipole and a permanent dipole could never be captured because ultimately they have to dissociate after forming some sort of a collision complex. I would therefore like to ask for the definition of the capture cross section. ... 

There are four basic rules of scientific method to which an investigator is committed (1) good observation, (2) the public nature of observation, (3) the necessity to theorize logically, and (4) the testing of theory by observable consequences. These constitute the scientific enterprise. I consider below the wider application of each rule to d-ASCs and indicate how unnecessary physicaliStic restrictions may be dropped. I also show that all these commitments or rules can be accommodated in the development of state-specific sciences. 

Any (state-specific) science may be considered as consisting of two parts observations and theories. The observations are what can be experienced relatively directly the theories are the inferences about what nonobservable factors account for the observations. For example, the phenomenon of synesthesia (seeing colors as a result of hearing sounds) is a theoretical proposition for me in my ordinary d-SoC I do not experience it and can only generate theories about what other people report about it. if I were under the influence of psychedelic drug such as LSD or marijuana 105, I could probably experience synesthesia directly, and my descriptions of the experience would become data. 

Area TlT2 permits theoretical inferences about common subject matter from the two perspectives, in area OlT2, by contrast, the theoretical propositions of state-specific science 2 are matters of direct observation for the scientist in d-SoC 1, and vice versa for the area Tlo2. State-specific science 3 consists of a body of observation and theory exclusive to that science and has no overlap with the two other sciences it does not confirm, contradict, or complement them. 

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