Nonlocal density functional theory

Fan, L., Ziegler, T., 1991, Optimization of Molecular Structures by Self-Consistent and Nonlocal Density-Functional Theory , J. Chem. Phys., 95, 7401. 

Fan, L. and T. Ziegler. 1992. Nonlocal Density Functional Theory as a Practical Tool in Calculations on Transition States and Activation Energies. Applications to Elementary Reaction Steps in Organic Chemistry. J. Am. Chem. Soc. 114, 10890. 

Physical properties of calcined catalysts were investigated by N2 adsorption at 77 K with an AUTOSORB-l-C analyzer (Quantachrome Instruments). Before the measurements, the samples were degassed at 523 K for 5 h. Specific surface areas (,S BEX) of the samples were calculated by multiplot BET method. Total pore volume (Vtot) was calculated by the Barrett-Joyner-Halenda (BJH) method from the desorption isotherm. The average pore diameter (Dave) was then calculated by assuming cylindrical pore structure. Nonlocal density functional theory (NL-DFT) analysis was also carried out to evaluate the distribution of micro- and mesopores. 

Thus, either type I or type IV isotherms are obtained in sorption experiments on microporous or mesoporous materials. Of course, a material may contain both types of pores. In this case, a convolution of a type I and type IV isotherm is observed. From the amount of gas that is adsorbed in the micropores of a material, the micropore volume is directly accessible (e.g., from t plot of as plot [1]). The low-pressure part of the isotherm also contains information on the pore size distribution of a given material. Several methods have been proposed for this purpose (e.g., Horvath-Kawazoe method) but most of them give only rough estimates of the real pore sizes. Recently, nonlocal density functional theory (NLDFT) was employed to calculate model isotherms for specific materials with defined pore geometries. From such model isotherms, the calculation of more realistic pore size distributions seems to be feasible provided that appropriate model isotherms are available. The mesopore volume of a mesoporous material is also rather easy accessible. Barrett, Joyner, and Halenda (BJH) developed a method based on the Kelvin equation which allows the calculation of the mesopore size distribution and respective pore volume. Unfortunately, the BJH algorithm underestimates pore diameters, especially at... 

NONLOCAL DENSITY FUNCTIONAL THEORY OF ADSORPTION HYSTERESIS... 

The Ne adsorption isotherms on model AIPO4-5 micropores were calculated from the Tarazona s version of the nonlocal density functional theory [34,35] which has beer actually applied to the study on micropore filling [36,37]. The necessary parameters were obtained fram the adsorption isotherms of Ne on AIPO4-S at 27K and 30K in a lov pressure range. 

The nonlocal density functional theory (NLDFT) has been used to characterize mesocaged structures.[164] NLDFT analysis gives accurate information about the cage size, the total meso- and micropore volumes and surface area, and the pore-wall thickness in combination with XRD measurements. Argon- and nitrogen-desorption data on FDU-1 provided evidence that there are two major populations of pore entrances. Argon desorption was superior in providing information about pore connectivity in FDU-1 samples. 

Pan et al. [34] used the nonlocal density functional theory (DFT) [35] and the three-process Langmuir model (TPLM) [36] to predict the adsorption heats of propane and butane on carbon and compared these results with experimental data determined from isotherms measured on BAX-activated carbon (Westvaco) in the 297—333 K temperature interval. Both models agreed in showing that the adsorption heat for butane was c. 10 kj/mol higher than that of propane at the same loading. The satisfactory agreement found prompted the authors to propose the use of the DFT method as it requires only one experimental isotherm in contrast with the numerous isotherms required by the classic technique. 

Figure 7.5 (a) A comparison of experimental data for nitrogen adsorbed at 77 K on Vulcan 3-G(2700) (points) with the fit given by the modified nonlocal density functional theory (MNLDFT) models (line), (b) The adsorptive potential distribution for the Vulcan 3 graphite. 

Figure 7.10 The average pore fluid density in pores of various widths as calculated hy nonlocal density functional theory (NLDFT). Note the periodic nature of the density, with density maxima near the positions of the minima in the distrihutions shown in Figs 7.8(h) and 7.9(h).

The solid line is calculated by the nonlocal density functional theory (NLDFT), which will be described to some detail in Section 11.4. As seen in the figure, the curve obtained with the HK method (dashed fine) correlates with NLDFT much better than that calculated with the Kelvin equation (dash-dotted line). 

Nonlocal density functional theory is an effective means for determining the energetics and elucidating the mechanisms of the decomposition processes of molecules of real chemical interest and significance. It should be viewed as another practical tool that is available for this purpose, a useful addition to existing experimental techniques, but with the extremely important advantage that it can be applied to proposed molecules that may not yet have been synthesized or isolated. 

This would allow performing accurate PSD calculations using these simple algorithms. Theoretical considerations [13], nonlocal density functional theory (NLDFT) calculations [62, 146], computer simulations [147], and studies of the model adsorbents [63, 88] strongly suggested that the Kelvin equation commonly used to provide a relation between the capillary condensation or evaporation pressure and the pore size underestimates the pore size. 

Beside classical methods of pore size analysis, there are many advanced methods. Seaton et al. [161] proposed a method based on the mean field theory. Initially this method was less accurate in the range of small pore sizes, but even so it g ve a more realistic -way for evaluation of the pore size distribution than the classical methods based on the Kelvin equation [162]. More rigorous methods based on molecular approaches such as grand canonical Monte Carlo (GCMC) simulations [147, 163-165] and nonlocal density functional theory (NLDFT) [86, 146, 147, 161, 163-169] have been developed and their use for pore size analysis of active carbons is continuously growing. 

Neimark et al. [102] also studied the problem of adsorption-desorption hysteresis with the nonlocal density functional theory (NLFT). They compared NLFT results with Monte Carlo (MC) simulations. Their main conclusion is that both methods, NLFT and MC, can quantitatively predict the adsorption and desorption branches of the isotherm provided that the fluid—fluid and fluid-solid interaction parameters are adequate. 

While good descriptions of adsorption on uniform surfaces in the submonolayer region are available, only recently has accurate calculation of the whole isotherm, including the multilayer region, been demonstrated [19]. These calculations use a modified nonlocal density functional theory (MDFT). The first use of multilayer local isotherms calculated by MDFT in obtaining a measure of surface energetic heterogeneity for several solid adsorbents was reported in 1996 [20]. 

Finn and Monson [139] first tested the predictability of IAS theory for binary systems using the isothermal isobaric Monte Carlo simulation on a single surface. However, this system does not represent real adsorption systems. Tan and Gubbins [140,141] conducted detailed studies on the binary equilibria of the methane-ethane system in slit-shaped micropores using the nonlocal density function theory (NLDFT). The selectivity of ethane to methane was studied in terms of pore width, temperature, pressure, and molar fractions. 

HCP-l,4-benzenedimethanol (HCP-BDM) and HCP-ben l alcohol (HCP-BA) networks synthesized by the Friedel-Crafts self-condensation method have shown high selectivity for CO2 over N2, measured by nitrogen adsorption isotherm at two different temperatures, 273 and 298 Nonlocal density functional theory (NLDFT) calculations confirmed the pore sizes to be below 2 nm for both of the networks. Such small pore sizes, as well as the high ojq gen content in both the polymers, is most probably tbe reason for the strong interactions with polar CO2 rather than N2, making these good candidates for the selective separation of CO2 from N2. 

The electronic structure of [MoCl3(T 3-cyclopiopenyl)] complexes was studied using nonlocal density functional theory as part of a study of acetylene metathesis catalysed by high-oxidation state molybdenum complexes3. ... 

Note that several variants of the above functional (i.e., Eq. 41) exist. Instead of using WDA for treating as shown in Eq. (43), the EDA can also be appHed which provides comparable accuracy as discussed by Fu et al. (2015a). In addition, if we simply ignore this correlation term F ot and apply WCA scheme for the decomposition of repulsion and attraction in the LJ potential, the above combined functional recovers to the so-called nonlocal density functional theory (NLDFT) initiated by Balbuena and Gubbins (1993) and extensively appfred by Neimark et al. (Landers et al., 2013 Olivier et al., 1994). 

Douglas Frink LJ, Salinger AG Two- and three-dimensional nonlocal density functional theory for inhomogeneous fluids I. Algorithms and parallelization, J Comput Phys 159(2) 407 24, 2000. 

The use of nonlocal density functional theory (NLDFT) for modeling adsorption isotherms of Lennard-Jones (LJ) fluids in porous materials is now well-established [1-5], and is central to modem characterization of nanoporous carbons as well as a variety of other adsorbent materials [1-3]. The principal concept here is that in confined spaces the potential energy is related to the size of the pore [6], thereby permitting a pore size distribution (PSD) to be extracted by fitting adsorption isotherm data. For carbons the slit pore model is now well established, and known to be applicable to a variety of nanoporous carbon forms, where the underlying micro structure comprises a disordered aggregate of crystallites. Such slit width distributions are then useful in predicting the equilibrium [1-5] and transport behavior [7,8] of other fluids in the same carbon. 

Interaction Energies of Monosubstituted Benzene Dimers via Nonlocal Density Functional Theory. 

Seaton et al. [16] used a multilinear least-squares fitting of the parameters of the assumed PSD function so as to match measured isotherm data. A similar method was employed by Lastoskie et al. [18] in their analysis using the nonlocal density functional theory (NL-DFT). Later, an important contribution toward the numerical deconvolution of the distribution result was made by Olivier et al. [35]. They developed a program based on the regularization method [65], in which no restrictions were imposed on the form of PSD. Moreover, this method was found to be numerically robust. Also, a simpler optimization technique has recently been suggested by Nguyen and Do [66]. 

A different and more sophisticated approach to the theory of the nematic-smectic A transition is based on the nonlocal density functional theory developed for inhomogeneous hard-core fluids [68]. The nonlocal free energy functional is defined in the following way [69-71] ... 

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