Computational Features

In order to evaluate the dipole moment, the finite-field method [see Eq. (2.3.2)] described by Cohen and Roothaan [1] is often employed. This approach is now implemented practically in all computational codes (Gaussian [2], Molpro [3] and others). One can propose several techniques to obtain the dipole moment in this way. The first technique is evident following the definition (2.3.2). In this case the dipole moment components can be determined easily as the first derivatives of the energy (F°) with respect to the external field using the most simple 2-point expression [with errors of order (F°) ]  

Cherepanov et al., Interaction-induced Electric Properties of van der Wools Complexes, SpringerBriefs in Electrical and Magnetic Properties of Atoms, Molecules, and Clusters, 

2 Long-Range Analytical Formalism. Induction and Dispersion Contributions 

To obtain the induced dipole moment of the molecule A being in the weak electric field of the molecule B one should calculate the first derivative of the energy with respect to the external field F. The electrostatic interactions (Eq. 2.3.3) give the permanent dipole moment the induction interactions 

For further consideration of the dipole moment, polarizability and hyperpolar-izabihty of a complex we need also some expressions for multipole moments (see 2.3.1-2.3.6)  

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The data for our analysis were collected from production runs of about 10000 steps, corresponding to a total simulation time of approximately 2 ps. The temperature for each simulation was chosen as that value for which experimental data are available. In general, the temperature lies about 50 K above the corresponding melting point. A detailed description of the computational features and the simulation procedure -including systems and temperatures - is given in [7]. 

In this section we report the most common formulations of the BEM equations for three different versions of PCM [1], namely IEFPCM (isotropic), CPCM and DPCM. The mathematical and physical significance of these equations are discussed in the contribution by Cances. Here we are interested only in the computational features. 

Next follows a series of reports on important developments in computational methods or program packages incorporating novel computational features. 

In order to illustrate some computational features of the response methods we show in this section convergence behavior of results for SOC with respect to correlating orbital spaces and basis sets. For this purpose we choose the particular case of the A 3Ej - b1 magnetic dipole transition in O2, partially presented in ref. [8]. 

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Table 5.11 Computed features of infinite chain of water molecules . ...

Gangestad To second Geoffrey Miller s point, we do have to be careful about the criteria we use to say that things are not modular, as well as that they are modular. If we find that two aspects of performance are correlated, we should not necessarily conclude that they rely on common computational features. In a sense, the software used to perform the two tasks may be distinct, with the correlation due to the fact that there is common hardware. 

The absolute accuracy of our FobIS measurement system is not comparable to commercial lab equipment, and there are important variations in SNR, depending on the impedance values and frequency measured. Nonetheless, we can use it to acquire impedance data in the field with good reproducibility. These data can be used to compute features for classification, i.e. gas discrimination. As usual in multivariate classification, features are derived from the measured raw data, e.g. mean values or slopes of the impedance spectrum or the resistance response curve in TCO [20]. 

Apropriately therefore, the present volume illustrates many of the mathematical and computational features of potential energy surfaces as well as their wide-spread conceptual utility in explaining chemical phenomena. 

Having outlined the basic points of DFT, we now discuss the computational features that characterize the methods most frequently used for the study of clusters, with special emphasis on the techniques underlying the ab initio MD introduced by Car and Parrinello [8]. 

A CRF is a discriminative probabilistic model. Van Kasteren et al. [32] compared CRF with HMMs and found that CRF outperformed HMMs in all cases with respect to time slice accuracy, but HMMs achieved the overall highest accuracy. This is due to the way both models maximize their parameters. HMMs make use of a Bayesian framework in which a separate model is learned for each class. A CRF uses a single model for all classes. A comparison of HMMs and CRF was also discussed by Hu et al. [33], who found that CRF is able to easily incorporate a wide variety of computed features, which allows domain knowledge to be added to the models. They also showed that due to the independence assumptions inherent in HMMs, such computed features are not nearly as effective in improving classification accuracy. Thus, CRF s classification accuracy has shown to be consistently higher than HMM s. 

Most of the computer features shown in the figure have already been touched upon. I only want to add the importance of using as exact as possible R s or, better, R s for a) further identification... 

Hartree-Fock theory and density functional theory are both SCF models and share many conceptual and computational features. Yet they are all too rarely presented together. This can be traced to the fact that, historically, they have not been studied by the same people and this dichotomy has been detrimental to the development of both. Fortunately, late in the 20th century, the two schools have recognized their common heritage and fruitfully liaised. 

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