Density functional theory condensed results

Lewis et al.106 calculated four possible decomposition pathways of the ot-HMX polymorph N-N02 bond dissociation, HONO elimination, C-N bond scission, and concerted ring fission. Based on energetics, it was determined that N-N02 dissociation was the initial mechanism of decomposition in the gas phase, whereas they proposed HONO elimination and C-N bond scission to be favorable in the condensed phase. The more recent study of Chakraborty et al.42 using density functional theory (DFT), reported detailed decomposition pathways of p-HMX, which is the stable polymorph at room temperature. It was concluded that consecutive HONO elimination (4 HONO) and subsequent decomposition into HCN, OH, and NO are the most energetically favorable pathways in the gas phase. The results also showed that the formation of CH20 and N20 could occur preferably from secondary decomposition of methylenenitramine. 

The Horvath-Kawazoe (HK) method is capable of generating model isotherms more efficiently than either molecular simulation (MS) or density functional theory (DFT) to characterize the pore size distribution (PSD) of microporous solids. A two-stage HK method is introduced that accounts for monolayer adsorption in mesopores prior to capillary condensation. PSD analysis results from the original and two-stage HK models are evaluated. 

The inclusion of the solvent surrounding would be desirable in all cases to obtain reliable results for reactions in enzymes active sites. However, the most reliable methods are computationally expensive and the direct application of e.g. ab initio QM methods to model condensed-phase systems is presently impractical. Accurate ab initio methods [295] are only viable in the study of small to medium-sized molecules whereas density functional theory [296] and semiempirical methods [297] although computationally more versatile are still very much limited considering the fact that we are dealing with thousands of atoms. However, in any approach to studying a particular subject, the quality of the model used should be paramount in the mind of the researcher and therefore any method that could succeed in providing a computationally feasible shape of reality is worth investigating. 

Density functional theory (DFT) or molecular simulation offer a much more accurate theory for the local isotherm. For simple adsorbates (near-spherical nonpolar molecules) and simple pore geometries (slits, cylinders), DFT is easy to apply, and the results for capillary condensation pressures, and for the remainder of the isotherm, are in... 

As one moves towards the realm of condensed matter physics, the hope of a wavefunction-based theory involving an exact treatment of spin-jK>larisation and exchange fades. Most modem work in this field is carried out within the density functional theory (DFT) introduced by Hohenbei, Kohn and Sham [1,2], in which the electron density tak i on the role of the primary variable. This allows scope for any number of s roximate treatments of electronic exchange and correlation, so that calculations for even the largest s> tems become tractable. Insofar as spin-polarisation is included, it is tinted in a parametric maimer, making use of exact results obtained for the homogeneous electron gas. 

Although ab initio molecular orbital theory and density functional theory can be used to systematically improve the accuracy of X-Pol results for large systems, it is still impractical to use these methods to perform molecular dynamics simulations for an extended period of time. With increased computing power, this will become feasible in the future however, at present, it is desirable to use semiempirical molecular orbital models such as the popular approaches based on neglect of diatomic differential overlap (NDDO) or the more recent self-consistent-charge tight-binding density functional (SCC-method to model condensed-phase and biomacromolecules. 

The classical models of adsorption processes like Langmuir, BET, DR or Kelvin treatments and their numerous variations and extensions, contain several uncontrolled approximations. However, the classical theories are convenient and their usage is very widespread. On the other hand, the aforementioned classical theories do not start from a well - defined molecular model, and the result is that the link between the molecular behaviour and the macroscopic properties of the systems studied are blurred. The more developed and notable descriptions of the condensed systems include lattice models [408] which are solved by means of the mean - field or other non-classical techniques [409]. The virial formalism of low -pressure adsorption discussed above, integral equation method and perturbation theory are also useful approaches. However, the state of the art technique is the density functional theory (DFT) introduced by Evans [410] and Tarazona [411]. The DFT method enables calculating the equilibrium density profile, p (r), of the fluid which is in contact with the solid phase. The main idea of the DFT approach is that the free energy of inhomogeneous fluid which is a function of p (r), can be... 

A. Schreiber, H. Bock, M. Schoen, G. H. Findenegg, Effect of surface modification on the pore condensation of fluids Experimental results and density functional theory. Mol. Phys. 100 (2002) 2097-2107. 

We test three theories for adsorption and capillary condensation in pores against computer simulation results. They are the Kelvin equation, and two forms of density functional theory, the local density approximation (LDA) and the (nonlocal) smoothed density approximation (SDA) all three theories are of potential use in determining pore size distributions for raesoporous solids, while the LDA and SDA can also be applied to mlcroporous materials and to surface area determination. The SDA is found to be the most accurate theory, and has a much wider range of validity than the other two. The SDA is used to study the adsorption of methane and methane-ethane mixtures on models of porous carbon in which the pores are slit-shaped. We find that an optimum pore size and gas pressure exists that maximizes the excess adsorption for methane. For methane-ethane mixtures we show the variation of selectivity with pore size and temperature. 

Molecular polarizabilities and hyperpolarizabilities are now routinely calculated in many computational packages and reported in publications that are not primarily concerned with these properties. Very often the calculated values are not likely to be of quantitative accuracy when compared with experimental data. One difficulty is that, except in the case of very small molecules, gas phase data is unobtainable and some allowance has to be made for the effect of the molecular environment in a condensed phase. Another is that the accurate determination of the nonlinear response functions requires that electron correlation should be treated accurately and this is not easy to achieve for the molecules that are of greatest interest. Very often the higher-level calculation is confined to zero frequency and the results scaled by using a less complete theory for the frequency dependence. Typically, ab initio studies use coupled-cluster methods for the static values scaled to frequencies where the effects are observable with time-dependent Hartree-Fock theory. Density functional methods require the introduction of specialized functions before they can cope with the hyperpolarizabilities and higher order magnetic effects. 

The presently available explicit approximations for the relativistic xc-energy functional are presented in Section 4. Both implicit functionals (as the exact exchange) and explicit density functionals (as the RLDA and RGGA) are discussed (on the basis of the information on the RHEG in Appendix C and that on the relativistic gradient expansion in Appendix E). Section 4 also contains a number of illustrative results obtained with the various functionals. However, no attempt is made to review the wealth of RDFT applications in quantum chemistry (see e.g.[74-88]) and condensed matter theory (see e.g.[89-l(X)]) as well as the substantial literature on nonrelativistic xc-functionals (see e.g.[l]). In this respect the reader is referred to the original literature. The review is concluded by a brief summary in Section 5. 

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