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** Intermolecular interaction energy perturbation-theory approach **

** Perturbation theory - slightly different approach **

In the perturbation theory approach a similar vector is obtained by operating with the perturbation operator V on the vector of the previous order (=iteration). Since the matrix H and the matrix V differ only in trivial diagonal terms the work in the two approaches is nearly identical in each iteration. [Pg.278]

This same perturbation theory approach is capable of describing both inter- and intra-molecular interactions. [Pg.419]

A symmetry-adapted perturbation theory approach for the calculation of the Hartree-Fock interaction energies has been proposed by Jeziorska et al.105 for the helium dimer, and generalized to the many-electron case in Ref. (106). The authors of Refs. (105-106) developed a basis-set independent perturbation scheme to solve the Hartree-Fock equations for the dimer, and analyzed the Hartree-Fock interaction energy in terms of contributions related to many-electron SAPT reviewed in Section 7. Specifically, they proposed to replace the Hartree-Fock equations for the [Pg.56]

FIGURE 7.3 Breakdown of perturbation-theory approach for Cun(H20)6 in L-band. The spectrum of the elongated CuOs octahedron (upper trace) is simulated (lower trace) with the approximative resonance condition defined in Equation 5.18. There is no fit of the first hyper-fine line at low field (Hagen 1982a). [Pg.133]

A DFT-based third order perturbation theory approach includes the FC term by FPT. Based on the perturbed nonrelativistic Kohn-Sham orbitals spin polarized by the FC operator, a sum over states treatment (SOS-DFPT) calculates the spin orbit corrections (35-37). This approach, in contrast to that of Nakatsuji et al., includes both electron correlation and local origins in the calculations of spin orbit effects on chemical shifts. In contrast to these approaches that employed the finite perturbation method the SO corrections to NMR properties can be calculated analytically from [Pg.5]

Notice finally that the perturbation theory approach for calculating NAC corrections has been developed in Ref. [58]. [Pg.124]

B. Jeziorski, R. Moszynski, K. Szalewicz, Perturbation theory approach to intermolecular potential energy surfaces of van der Waals complexes. Chem. Rev. 94, 1887-1930 (1994) [Pg.396]

Jeziorski B, Moszynski R, Szalewicz K (1994) Perturbation-theory approach to intermolecular [Pg.253]

In this section, we shall use the degenerate perturbation theory approach to derive the form of the effective Hamiltonian for a diatomic molecule in a given electronic state. Exactly the same result can be obtained by use of the Van Vleck or contact transformations [12, 13]. The general expression for the operator up to fourth order in perturbation theory is given in equation (7.43). Fourth order can be considered as the practical limit to this type of approach. Indeed, even its implementation is very laborious and has only been used to investigate the form of certain special terms in the effective Hamiltonian. We shall consider some of these terms later in this chapter. For the moment we confine our attention to first- and second-order effects only. [Pg.316]

Cybulski SM, Scheiner S (1990) Comparison of Morokuma and perturbation theory approaches to decomposition of interaction energy. (NH4+). .. NH3. Chem. Phys Lett 166 57-64 [Pg.142]

Uncoupled methods [sometimes called the sum over states (SOS) methods] do not include the field in the Hamiltonian but use a time-dependent perturbation theory approach.38-56 A sum over all excited states is used that requires values for dipole moments in ground and excited states and excitation energies to be evaluated. One must choose the number of states at which to terminate the series. It has been shown in several studies of second-order nonlinearities38 that the /8 values converge after a finite number of states are chosen. Furthermore, this approach intrinsically accounts for frequency dependence. [Pg.313]

A. Fiethen, G. Jansen, A. Hesselmann, M. Schiitz, Stacking energies for average B-DNA structures from the combined density functional theory and symmetry-adapted perturbation theory approach. J. Am. Chem. Soc. 130, 1802-1803 (2008) [Pg.398]

Y.. Dappe, M.A. Basanta, F. Flores, J. Ortega, Weak chemical interaction and van der Waals forces between graphene layers A combined density functional and intermolecular perturbation theory approach, vol. 74, p. 205434-9, 2006. [Pg.110]

In summary, density functional theory provides a natural framework to discuss solvent effects in the context of RF theory. A general expression giving the insertion energy of an atom or molecule into a polarizable medium was derived. This expression given in Eq (83), when treated within a first order perturbation theory approach (i.e. when the solute self-polarization [Pg.119]

** Intermolecular interaction energy perturbation-theory approach **

** Perturbation theory - slightly different approach **

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