Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Perturbation theory overview

This Introductory Section was intended to provide the reader with an overview of the structure of quantum mechanics and to illustrate its application to several exactly solvable model problems. The model problems analyzed play especially important roles in chemistry because they form the basis upon which more sophisticated descriptions of the electronic structure and rotational-vibrational motions of molecules are built. The variational method and perturbation theory constitute the tools needed to make use of solutions of... [Pg.73]

Ab initio calculations at the CIS, CASSCF and MRMP2 (second-order multireference Mpller-Plesset perturbation theory) levels have revealed that the reaction proceeds by H atom transfer via a series of Grotthus-type translocation steps [15]. Figure 3.35 gives an overview of these computational results. [Pg.423]

We are not going into details of the above groups of procedures and shall limit ourselves to an overview of the main results of ordinary Rayleigh-Schroedinger perturbation theory for long range interactions first, and then of the methods developed in [40,41] to deal with short range interactions. [Pg.372]

In order to improve on the Hartree-Fock model, the use of perturbation theory is common. The first energy correction is obtained at second order and the corresponding method is calles second-order Moller-Plesset perturbation theory (MP2). MP2 calculations provide a first estimate for the correlation energy SE, which turned out to be also useful for estimates of the interaction energy in cases dominated by dispersive interactions (see the next section for an overview on how interaction energies can be calculated from total electronic energy estimates). [Pg.426]

In this paper we have given a short overview of the application of symmetry-adapted perturbation theory to intermolecular potentials and interaction-induced properties, and of the methods going directly from these intermolecular properties to experimentally measurable quantities such as collision-induced Raman spectra, rovibrational spectra, and second (pressure and dielectric) virial coefficients. The results presented in this paper show that intermolecular potentials and dipole/polarizability surfaces obtained from ab initio SAPT calculations can be used to correctly describe the spectroscopic and dynamical processes involving weakly bound complexes. [Pg.138]

The plan of this chapter is as follows. In the next section an overview of the history of the weak interactions in general, and atomic PNC in particular, is given. In section 3, Furry representation is introduced and applied to a calculation of a transition energy of a highly charged ion, Bi ". Section 4 describes the theory of cesium PNC, starting with low-order many-body perturbation theory (MBPT) methods, and then generalizing to all-orders methods based on coupled cluster theory. Section 5 closes the chapter with a brief description of the closely related field of atomic electric dipole moments. [Pg.471]

The plan of this report is as follows in Section 2 an overview of the theoretical apparatus of the many-body perturbation theory is presented together a discussion of practical algorithms. A review of some of the more important applications made during the period covered by this report will be given in Section 3. Finally, in Section 4, future directions for research on the electron correlation problem in general and the many-body perturbation theory expansion in particular will be given. [Pg.368]

An overview of the salient features of the relativistic many-body perturbation theory is given here concentrating on those features which differ from the familiar non-relativistic formulation and to its relation with quantum electrodynamics. Three aspects of the relativistic many-body perturbation theory are considered in more detail below the representation of the Dirac spectrum in the algebraic approximation is discussed the non-additivity of relativistic and electron correlation effects is considered and the use of the Dirac-Hartree-Fock-Coulomb-Breit reference Hamiltonian demonstrated effects which go beyond the no virtual pair approximation and the contribution made by the negative energy states are discussed. [Pg.401]

This is not the place for a full overview of the wave function based post Hartree-Fock methods currently applied for the calculation of intermolecular interactions and in particular molecule/surface interactions. Table 3 contains a brief characterization of the most widely applied schemes. The two most popular methods are MP2 (second order Moller-Plesset perturbation theory), because it covers large part of electronic correlation at comparably low ex-... [Pg.238]

In order to stndy the short time vibrational energy transfer behavior of a vibra-tionally excited system, we employ a non-Markovian time-dependent perturbation theory [83]. Onr approach builds on the successful application of Markovian time-dependent pertnrbation theory by Leitner and coworkers to explore heat flow in proteins and glasses, and Tokmakoff, Payer, and others, in modeling vibrational population relaxation of selected modes in larger molecules. In a separate chapter in this volnme, Leitner provides an overview of the development of normal mode-based methods, snch as the one employed here, for the study of energy flow in solids and larger molecnlar systems. [Pg.211]

The plan of this report is as follows in Section 2 an overview of the most important theoretical aspects of the second-order many-body perturbation theory is given. Section 3 contains a review of the numerous applications of the second-order theory in its MP2 form which were published during the period Jime 1999 to May 2001. The final section then contains a brief summary and a discussion of prospects. [Pg.331]

In summary, we have made an attempt to classify existing MQC strategies in formulations resulting from (i) a partial classical limit, (ii) a connection ansatz, and (iii) a mapping formalism. In this overview, we shall focus on essentially classical formulations that may be relatively easily applied to multidimensional surface-crossing problems. On the other hand, it should be noted that there also exists a number of essentially quantum-mechanical formulations which at some point use classical ideas. A well-known example are formulations that combine quantum-mechanical time-dependent perturbation theory with a classical evaluation of the resulting correlation functions, e.g. Golden Rule type formulations.Furthermore, several... [Pg.623]

As an alternative for the variational methods, one can also apply multireference perturbation theory (MRPT) to calculate magnetic interactions. In principle, this type of calculations makes it possible to treat larger systems with more unpaired electrons. Among the many different implementations, two schemes are especially popular in the field of magnetic interactions CASPT2 [13] and NEVPT2 [14, 15], which will be shortly overviewed here. [Pg.127]

For a recent overview of the [lOjannulene problem see King, R. A., Crawford, D., Stanton, J. F., and Schaefer 111, H. F. "Conformations of [10] Annulene More Bad News for Density Functional Theory and Second-Order Perturbation Theory." /. Am. Chem. Soc., 121,10788 (1999), and references therein. [Pg.875]


See other pages where Perturbation theory overview is mentioned: [Pg.533]    [Pg.443]    [Pg.173]    [Pg.255]    [Pg.641]    [Pg.53]    [Pg.15]    [Pg.157]    [Pg.241]    [Pg.38]    [Pg.50]    [Pg.13]    [Pg.5]    [Pg.84]    [Pg.181]    [Pg.578]    [Pg.40]    [Pg.443]    [Pg.132]    [Pg.172]    [Pg.455]    [Pg.527]    [Pg.725]    [Pg.44]    [Pg.641]    [Pg.203]    [Pg.131]    [Pg.617]    [Pg.40]    [Pg.441]    [Pg.315]    [Pg.74]   
See also in sourсe #XX -- [ Pg.391 ]




SEARCH



Theories overview

© 2024 chempedia.info