First-principles perturbative approach

At this point the first-principles perturbative (FP) approach becomes valuable. The same kinds of perturbative models are used to describe the vibrational-rotational motions as in the SP approach. However, data from electronic structure theory computations or potential energy functions are used to parameterize the formulas instead of spectroscopically obtained data. The FP approach has for example, been pursued by Martin et al. [16-18] and by Isaacson, Truhlar, and co-workers [19-25]. This avenue is especially valuable when spectroscopic data are not available for a molecule of interest. Codes are available that can carry out vibrational perturbation theory computations, using a grid of ab initio data as input SURVIBTM... 

The problems that occur when one tries to estimate affinity in terms of component terms do not arise when perturbation methods are used with simulations in order to compute potentials of mean force or free energies for molecular transformations simulations use a simple physical force field and thereby implicitly include all component terms discussed earlier. We have used the molecular transformation approach to compute binding affinities from these first principles [14]. The basic approach had been introduced in early work, in which we studied the affinity of xenon for myoglobin [11]. The procedure was to gradually decrease the interactions between xenon atom and protein, and compute the free energy change by standard perturbation methods, cf. (10). An (issential component is to impose a restraint on the... 

Lattice vibrations are calculated by applying the second order perturbation theory approach of Varma and Weber , thereby combining first principles short range force constants with the electron-phonon coupling matrix arising from a tight-binding theory. 

In this chapter we will focus on one particular, recently developed DFT-based approach, namely on first-principles (Car-Parri-nello) molecular dynamics (CP-MD) [9] and its latest advancements into a mixed quantum mechanical/molecular mechanical (QM/MM) scheme [10-12] in combination with the calculation of various response properties [13-18] within DFT perturbation theory (DFTPT) and time-dependent DFT theory (TDDFT) [19]. 

The Pauli operator of equations 2 to 5 has serious stability problems so that it should not, at least in principle, be used beyond first order perturbation theory (20). These problems are circumvented in the QR approach where the frozen core approximation (21) is used to exclude the highly relativistic core electrons from the variational treatment in molecular calculations. Thus, the core electronic density along with the respective potential are extracted from fully relativistic atomic Dirac-Slater calculations, and the core orbitals are kept frozen in subsequent molecular calculations. 

Despite the big advance in various experimental techniques used to study the JT effect, it is not sufficient to understand the latter based only on experimental data. Computational methods are, thus, necessary to get deeper insight into the system under study and to predict the properties of unknown ones. Traditional first principles methods can still be used even where non-adiabatic effects are important, if the BO approximation is reintroduced by the perturbation approach. Density... 

Electron tunneling was first analyzed by Bardeen [12] and Cohen et al. [13] using the perturbative transfer Hamiltonian (TH) approach and more recently by many other authors [14-16]. Although the TH gives, in many cases, a good description of the observed effects, it lacks a firm first principles theoretical basis and does not account properly for many-body effects [17]. An improved form of TH [18] that involved energy dependent transfer matrix elements was used to incorporate many-body effects. However, this model does not describe the electron-phonon interaction properly [19]. 

In principle, surface atomic and electronic structures are both available from self-consistent calculations of the electronic energy and surface potential. Until recently, however, such calculations were rather unrealistic, being based on a one-dimensional model using a square well crystal potential, with a semi-infinite lattice of pseudo-ions added by first-order perturbation theory. This treatment could not adequately describe dangling bond surface bands. Fortunately, the situation has improved enormously as the result of an approach due to Appelbaum and Hamann (see ref. 70 and references cited therein), which is based on the following concepts. 

Theoretical models allow us to better understand the relationship between the spectroscopic parameters and the structure of the samples and they are indispensable for a realistic modeling of the parameters as a function of structure. Therefore, we present here the essential features of the theory underlying the calculations of VCD spectra. The first principle calculations of the chiroptic spectroscopic parameters have appeared over the years. Theoretical foundations of the models including their mathematical formulation and numerical implementation have been discussed in the articles [30-32], while the ab initio most successful - in terms of its applications-the perturbative approaches by Stephens calculations are presented in Refs. 81-87. We shall refer to some of them in what follows. However, we directing the reader to the review articles for a more detailed description [81-83]. 

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