https://web.iitd.ac.in/~arunku/files/CEL311_Y13/Adsorption%20Theory%20to%20practice_Dabrowski.pdf

Adsorption — from theory to practice

A grid-based real-space implementation of the projector augmented wave (PAW) method of Bl\"ochl [Phys. Rev. B 50, 17953 (1994)] for density functional theory (DFT) calculations is presented. The use of uniform three-dimensional (3D) real-space grids for representing wave functions, densities, and potentials allows for flexible boundary conditions, efficient multigrid algorithms for solving Poisson and Kohn-Sham equations, and efficient parallelization using simple real-space domain-decomposition. We use the PAW method to perform all-electron calculations in the frozen core approximation, with smooth valence wave functions that can be represented on relatively coarse grids. We demonstrate the accuracy of the method by calculating the atomization energies of 20 small molecules, and the bulk modulus and lattice constants of bulk aluminum. We show that the approach in terms of computational efficiency is comparable to standard plane-wave methods, but the memory requirements are higher.

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Real-space grid implementation of the projector augmented wave method

High-pressure adsorption of methane, carbon dioxide, and nitrogen on zeolite 13X was measured in the pressure range (0 to 5) MPa at (298, 308, and 323) K and fitted with the Toth and multisite Langmuir models. Isosteric heats of adsorption were (12.8, 15.3, and 37.2) kJ/mol for nitrogen, methane, and carbon dioxide respectively, which indicate a very strong adsorption of carbon dioxide. The preferential adsorption capacity of CO2 on zeolite 13X was much higher than for the other gases, indicating that zeolite 13X can be used for methane purification from natural gas or for carbon dioxide sequestration from flue gas.

Adsorption Equilibrium of Methane, Carbon Dioxide, and Nitrogen on Zeolite 13X at High Pressures

Theoretical models of sorption kinetics including a surface reaction mechanism: A review

We report the creation of thermal, Fock, coherent, and squeezed states of motion of a harmonically bound {sup 9}Be{sup +} ion. The last three states are coherently prepared from an ion which has been initially laser cooled to the zero point of motion. The ion is trapped in the regime where the coupling between its motional and internal states, due to applied (classical) radiation, can be described by a Jaynes-Cummings-type interaction. With this coupling, the evolution of the internal atomic state provides a signature of the number state distribution of the motion. {copyright} {ital 1996 The American Physical Society.}

Generation of Non-classical Motional States of a Trapped Atom

An adsorption isotherm for a heterogeneous surface is described on the basis of a multi-site occupancy model followed by a group-contribution assumption. Equations of single- and multi-component adsorptions are derived for systems of molecules consisting of several functional groups and a surface composed of active sites of different energies interacting with the groups independently. The isotherm equation reduces to the expression derived by Sparnaay in the special case where a molecule occupies one site of the surface. The theory is applied to adsorption equilibria for systems of oxygen, nitrogen, and carbon monoxide on Molecular Sieves 5A and 10X. Correlations of single-component isotherms are excellent for nitrogen and oxygen and fairly good for carbon monoxide; predictions of adsorption isotherms of binary gas mixtures are made satisfactorily by means of parameters determined from the best fit to each single-component isotherm.

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An adsorption isotherm of multi-site occupancy model for homogeneous surface

The basis set and electron correlation effects on the static polarizability (alpha) and second hyperpolarizability (gamma) are investigated ab initio for two model open-shell pi-conjugated systems, the C(5)H(7) radical and the C(6)H(8) radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C(6)H(8) whereas diffuse functions are compulsory for C(5)H(7), in particular, p diffuse functions. In addition to the 6-31G(*)+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for alpha and gamma of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order Moller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order Moller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree-Fock results. Moreover, the differences between the restricted open-shell Hartree-Fock and restricted open-shell second-order Moller-Plesset methods are small. In what concerns the second hyperpolarizability, the unrestricted Hartree-Fock and unrestricted second-order Moller-Plesset values remain of similar quality while using spin-projected schemes fails for the charged system but performs nicely for the neutral one. The restricted open-shell schemes, and especially the restricted open-shell second-order Moller-Plesset method, provide for both compounds gamma values close to the results obtained at the unrestricted coupled cluster level including singles and doubles with a perturbative inclusion of the triples. Thus, to obtain well-converged alpha and gamma values at low-order electron correlation levels, the removal of spin contamination is a necessary but not a sufficient condition. Density-functional theory calculations of alpha and gamma have also been carried out using several exchange-correlation functionals. Those employing hybrid exchange-correlation functionals have been shown to reproduce fairly well the reference coupled cluster polarizability and second hyperpolarizability values. In addition, inclusion of Hartree-Fock exchange is of major importance for determining accurate polarizability whereas for the second hyperpolarizability the gradient corrections are large.

Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell π-conjugated systems

Solubilities of hydrogen and nitrogen in alcohols and n-hexane

A methodology has been proposed to compute the solvation free energy of a molecule described quantum chemically by means of quantum mechanical/molecular mechanical method combined with the theory of energy representation (QM/MM-ER). The present approximate approach is quite simple to implement and requires much less computational cost as compared with the free energy perturbation or thermodynamic integration. Furthermore, the electron distribution can be treated faithfully as a quantum chemical object, and it is no longer needed to employ the artificial interaction site model, a reduced form of the realistic electron distribution, which is commonly used in the conventional solution theory. The point of the present approach is to employ the QM solute with electron density fixed at its average distribution in order to make the solute-solvent interaction pairwise. Then, the solvation free energy can be computed within the standard framework of the energy representation. The remaining minor contribution originating from the many-body effect inherent in the quantum mechanical description can be evaluated separately within a similar framework if necessary. As a test calculation, the method has been applied to a QM water solute solvated by MM water solvent in ambient and supercritical states. The results of the QM/MM-ER simulations have been in excellent agreement with the experimental values.

A quantum chemical approach to the free energy calculations in condensed systems: the QM/MM method combined with the theory of energy representation.

A novel hybrid quantum mechanical (QM)/molecular mechanical (MM) approach that employs the real-space grids for the QM subsystem is proposed for investigating chemical reactions in an aqueous condensed phase. All of the Hamiltonian matrix elements including electric fields formed by the point charges on MM waters is represented in the real space. Details of the practical implementations are presented. The solute polarization, solvation structure, and the solvation energy of a water are computed, and the results are compared with those obtained by experiments and other QM/MM approaches that used the LCAO basis. It is shown that the real-space grid QM/MM method is adequate and superior for the description of the polarization of QM water in a water solution as well as in the gas phase. Solvation structures of classical water solvents are also properly reproduced by this method. Further, parallelization of the code is implemented on a distributed memory architecture, and it is demonstrated that the real-space grid approach is suitable for the high-performance parallel computing due to the localization of Hamiltonian operations in the real space. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1252–1261, 2001

Tomoshige Nitta

Papers

An adsorption isotherm of multi-site occupancy model for homogeneous surface

Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell π-conjugated systems

Solubilities of hydrogen and nitrogen in alcohols and n-hexane

A quantum chemical approach to the free energy calculations in condensed systems: the QM/MM method combined with the theory of energy representation.

A hybrid QM/MM method employing real space grids for QM water in the TIP4P water solvents