Perturbative approaches

In most cases of chemical and physical interest the property X is incorporated perturbatively by means of the linear response expression given by Eq. (15.7). 

The four-component reference value has to be reproduced by the infinite-order two-component DKH scheme, and any finite-order DKH approximation should converge toward this reference with increasing order of decoupling. 

We emphasize that it is not the exact variational energy ej (A) discussed above which has to be reproduced by the DKH linear response treatment but the first-order correction 

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Since shallow-level impurities have energy eigenvalues very near Arose of tire perfect crystal, tliey can be described using a perturbative approach first developed in tire 1950s and known as effective mass theoiy (EMT). The idea is to approximate tire band nearest to tire shallow level by a parabola, tire curvature of which is characterized by an effective mass parameter m. ... 

Yarkoni [108] developed a computational method based on a perturbative approach [109,110], He showed that in the near vicinity of a conical intersection, the Hamiltonian operator may be written as the sum a nonperturbed Hamiltonian Hq and a linear perturbative temr. The expansion is made around a nuclear configuration Q, at which an intersection between two electronic wave functions takes place. The task is to find out under what conditions there can be a crossing at a neighboring nuclear configuration Qy. The diagonal Hamiltonian matrix elements at Qy may be written as... 

The first theoretical handling of the weak R-T combined with the spin-orbit coupling was carried out by Pople [71]. It represents a generalization of the perturbative approaches by Renner and PL-H. The basis functions are assumed as products of (42) with the eigenfunctions of the spin operator conesponding to values E = 1/2. The spin-orbit contribution to the model Hamiltonian was taken in the phenomenological form (16). It was assumed that both interactions are small compared to the bending vibrational frequency and that both the... 

S. Miyamoto and P. A. Kollman. Absolute and relative binding free energy calculations of the interaction of biotin and its analogs with streptavidin using molecular dynamics/free energy perturbation approaches. Proteins, 16 226-245, 1993. 

Miyamoto S and P A Kollman 1993a. Absolute and Relative Binding Tree Energy Calculations of the Interaction of Biotin and its Analogues with Streptavidin Using Molecular Dynamics/Free Energy Perturbation Approaches. Proteins Structure, Function and Genetics 16 226-245. 

The solution of equation 16 is a decreasing, simple exponential where = k ([A ] + [P ]) + k. The perturbation approach generates small deviations in concentrations that permit use of the linearized differential equation and is another instance of pseudo-first-order behavior. Measurements over a range of [A ] + [T ] allow the kineticist to plot against that quantity and determine / ftom the slope and from the intercept. 

S Hirono, PA Kollman. Calculation of the relative binding free energy of 2 -GMP and 2 -AMP to ribonuclease T1 using molecular dynamics/free energy perturbation approaches. J Mol Biol 212 197-209, 1990. 

Some methods of describing electron correlation are compared from the point of view of requirements for theoretical chemical models. The perturbation approach originally introduced by Mpller and Plesset, terminated at finite order, is found to satisfy most of these requirements. It is size consistent, that is applicable to an ensemble of isolated systems in an additive manner. On the other hand, it does not provide an upper bound for the electronic energy. ... 

Although eq. (10.103) for the propagator appears to involve the same effort as the perturbation approach (sum over all excited states, eq. (10.18)), the actual calculation of the propagator is somewhat different. Returning to the time representation of the polarization propagator, it may be written in terms of a commutator. 

The vibrational spectrum of 1,4-dioxin was studied at the MP2 and B3-LYP levels in combination with the 6-3IG basis set [98JST265]. The DPT results tend to be more accurate than those obtained by the perturbational approach. The half-chair conformation of 4//-1,3-dioxin 164 was found to be more stable than the corresponding conformations of 3,4-dihydro-1,2-dioxin 165,3,6-dihydro-1,2-dioxin 166, and of 2,3-dihydro-1,4-dioxin 167 (Scheme 114) [98JCC1064, 00JST145]. The calculations indicate that hyperconjugative orbital interactions contribute to its stability. 

Correlation diagrams include the product orbitals while perturbation approaches require knowledge of the empty orbitals of the reactant. However, the occupied molecular orbitals of diazirine (II), compared with those of cyclopropene (I), do seem to give some indication of a preferred thermal decomposition of (II) compared with the rearrangement of (I). Moreover these molecular orbitals are a typical illustration of the localization obtained in the presence of an electronegativity perturbation. 

A perturbative approach to Eq. (12) has recently been developed by Gomez-Monivas et al. [37]. For a dielectric film on top of a flat metallic surface, these authors find that the electrostatic force is a convolution of the instrumental resolution with an effective profile... 

Cycloadditions of nitrones, nitrile oxides or diazo compounds to thiete dioxides do not show the high stereoselectivity observed with acyclic vinyl sulfones, and mixtures of the two possible adducts are formed . The charge-transfer stabilization energy calculated according to the Klopman-Salem perturbational approach is able to account for the experimental trends of the isomer ratio in terms of the major stereochemical structural differences between the acyclic vinyl sulfones and the four-membered ring sulfones (see Section IV.B.3). 

Truong, T. N. and E. Stefanovich. 1996. Development of a perturbative approach for Monte Carlo simulations using hybrid ab initio QM/MM method. Chem. Phys. Lett. 256, 348. 

The basic FEP algorithm for ligand binding can be improved in several ways. One method is to use a nonphysical ligand that serves as the common reference state for a variety of ligands of interest [25]. This method, referred to as the one-step perturbation approach, appears to be quite successful even for complex and fairly diverse ligands [26],... 

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