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A variety of experiments for the N2O decomposition over Fe-ZSM-5 catalysts have been simulated in the presence and absence of small amounts of nitric oxide and water vapor. A comprehensive reaction mechanism over mononuclear iron sites was considered, and all elementary reaction rate constants were obtained from density functional theory and transition state theory. Various experimental observations, such as the acceleration of the N2O decomposition in the presence of nitric oxide at low temperatures, can be described with the studied reaction mechanism on mononuclear iron sites. No other iron species, such as binuclear iron, are necessary for explaining experimental observations. At high temperatures, Z−[FeO]+sites are active for N2O decomposition, forming either Z−[OFeO]+and Z−[FeO2]+sites on which a second N2O can decompose to form Z−[OFeO2]+sites from which O2can rapidly desorb. At low temperatures, nitric oxide activates water poisoned Z−[Fe(OH)2]+sites to form active Z−[FeOH]+species. The catalytic cycle on Z−[FeOH]+involves N2O dissociation to form Z−[OFeOH]+sites that are inactive for a second N2O decomposition. Instead, NO adsorbs and NO2desorbs in order to regenerate the Z−[FeOH]+sites. On all active iron sites, the first N2O dissociation step is the most critical rate-controlling step. The concentration of nitric oxide and water vapor together determine at which temperature the switch between the most dominant active site (hydroxo-versusoxo-iron species) occurs. Overall, this study motivates the investigation of Z−[OFeOH]+sites as potential α-oxygen species that can oxidize various hydrocarbons at low temperatures.

Quantum mechanics/molecular mechanics (QM/MM) models are applied to investigate the adsorption and cracking of n-hexane on ZSM-5 and Faujasite zeolite structures. These simulations account for the long-range electrostatic and midrange van-der-Waals interactions in the zeolite and provide energy barriers that are close to experimental data. The active acidic site was modeled by dispersion corrected density functional theory (DFT, ω B97X-D6-311/G∗). The long-range interactions were calculated by molecular mechanics (MM). The adsorbed molecules under investigation are characterized by their thermodynamic properties (adsorption energy and enthalpy). The influence of the zeolite type on the thermodynamic properties is also pointed out. The results reveal that the kinetics of cracking is insensitive to differences in acid strengths. The thermodynamic data obtained are mainly influenced by the adsorption energy of n-hexane on ZSM-5 and/or Faujasite (Y) structures. The pore sizes of the zeolite types can lead to a stronger or weaker adsorption energy. Except for the thermodynamic property investigations in this article, the quasi-classical trajectory method (QCT) is used for investigating the pathways along metastable intermediates toward various cracking products. Not only the reaction barriers but also the reaction dynamics determine the reaction selectivity.

Two-dimensional (2D) monolayer pristine MoS 2 transition metal dichalcogenide (TMD) is the most studied material because of its potential applications as nonprecious electrocatalyst for the hydrogen evolution reaction (HER). Previous studies have shown that the basal planes of 2D MoS 2 are catalytically inert, and hence it cannot be used directly in desired applications such as electrochemical HER in industry. Here, we thoroughly studied a defect-engineered Mn-doped 2D monolayer MoS 2 (Mn-MoS 2 ) material, where Mn was doped in pristine MoS 2 to activate its inert basal planes. Using the density functional theory (DFT) method, we performed rigorous inspection of the electronic structures and properties of the 2D monolayer Mn-MoS 2 as a promising alternative to noble metal-free catalyst for effective HER. A periodic 2D slab of monolayer Mn-MoS 2 was created to study the electronic properties (such as band gap, band structures and total density of states (DOS)) and the reaction pathways occurring on the surface of this material. The detailed HER mechanism was explored by creating an Mn 1 Mo 9 S 21 non-periodic finite molecular cluster model system using the M06-L DFT method including solvation effects to determine the reaction barriers and kinetics. Our study revealed that the 2D Mn-MoS 2 follows the most favorable Volmer-Heyrovsky reaction mechanism with a very low energy barrier during H 2 evolution. It was found that the change in the free energy barrier (Δ G ) during the H˙-migration ( i.e. , Volmer) and Heyrovsky reactions is about 10.34-10.79 kcal mol -1 (computed in the solvent phase), indicating that this material is an exceptional electrocatalyst for the HER. The Tafel slope ( y ) was lower in the case of the 2D monolayer Mn-MoS 2 material due to the overlap of the s-orbital of hydrogen and d-orbitals of the Mn atoms in the HOMO and LUMO transition states (TS1 and TS2) of both the Volmer and Heyrovsky reaction steps, respectively. The better stabilization of the atomic orbitals in the HER rate-limiting step Heyrovsky TS2 is the key for reducing the reaction barrier, and thus the overall catalysis, indicating a better electrocatalytic performance for H 2 evolution. This study focused on designing low-cost and efficient electrocatalysts for the HER using earth abundant transition metal dichalcogenides (TMDs) and decreasing the activation energy barriers by scrutinizing the kinetics of the reaction to achieve high reactivity.

Chemical reactor modelling based on insights and data on a molecular level has become reality over the last few years. Multiscale models describing elementary reaction steps and full microkinetic schemes, pore structures, multicomponent adsorption and diffusion inside pores, and entire reactors have been presented. Quantum mechanical (QM) approaches, molecular simulations (Monte Carlo and molecular dynamics), and continuum equations have been employed for this purpose. Some recent developments in these approaches are presented, in particular time-dependent QM methods, calculation of van der Waals forces, new approaches for force field generation, automatic setup of reaction schemes, and pore modelling. Multiscale simulations are discussed. Applications of these approaches to heterogeneous catalysis are demonstrated for examples that have found growing interest over the last few years, such as metal-support interactions, influence of pore geometry on reactions, noncovalent bonding, reaction dynamics, dynamic changes in catalyst nanoparticle structure, electrocatalysis, solvent effects in catalysis, and multiscale modelling.

Four metal-organic frameworks with similar topology but different chemical environment inside the pore structure, namely, IFP-1, IFP-3, IFP-5, and IFP-7, have been investigated with respect to the separation potential for olefin-paraffin mixtures as well as the influence of the different linkers on adsorption properties using experiments and Monte Carlo simulations. All IFP structures show a higher adsorption of ethane compared to ethene with the exception of IFP-7 which shows no selectivity in breakthrough experiments. For propane/propane separation, all adsorbents show a higher adsorption for the olefin. The experimental results agree quite well with the simulated values except for the IFP-7, which is presumably due to the flexibility of the structure. Moreover, the experimental and simulated isotherms were confirmed with breakthrough experiments that render IFP-1, IFP-3, and IFP-5 as suitable for the purification of ethene from ethane.

Diffusion in nanoporous host-guest systems is often considered to be too complicated to comply with such "simple" relationships as Fick's first and second law of diffusion. However, it is shown herein that the microscopic techniques of diffusion measurement, notably the pulsed field gradient (PFG) technique of NMR spectroscopy and microimaging by interference microscopy (IFM) and IR microscopy (IRM), provide direct experimental evidence of the applicability of Fick's laws to such systems. This remains true in many situations, even when the detailed mechanism is complex. The limitations of the diffusion model are also discussed with reference to the extensive literature on this subject., (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Quantitative predictions of biomembrane/water partition coefficients are important, as they are a key property in pharmaceutical applications and toxicological studies. Molecular dynamics (MD) simulations are used to calculate free energy profiles for different solutes in lipid bilayers. How to calculate partition coefficients from these profiles is discussed in detail and different definitions of partition coefficients are compared. Importantly, it is shown that the calculated coefficients are in quantitative agreement with experimental results. Furthermore, we compare free energy profiles from MD simulations to profiles obtained by the recent method COSMOmic, which is an extension of the conductor-like screening model for realistic solvation to micelles and biomembranes. The free energy profiles from these molecular methods are in good agreement. Additionally, solute orientations calculated with MD and COSMOmic are compared and again a good agreement is found. Four different solutes are investigated in detail: 4-ethylphenol, propanol, 5-phenylvaleric acid, and dibenz[a,h]anthracene, whereby the latter belongs to the class of polycyclic aromatic hydrocarbons. The convergence of the free energy profiles from biased MD simulations is discussed and the results are shown to be comparable to equilibrium MD simulations. For 5-phenylvaleric acid the influence of the carboxyl group dihedral angle on free energy profiles is analyzed with MD simulations.

The goal of multiscale modelling of heterogeneous catalytic reactors is the prediction of all steps, starting from the reaction mechanism at the active centre, the rates of reaction, adsorption and diffusion processes inside the porous system of the catalyst support, based on first principles, quantum chemistry, force field simulations and macroscopic differential equations. The progress in these fields of research will be presented, including linking models between the various levels of description. Alkylation of benzene will be used as an example to demonstrate the various approaches from the active centre to the reactor.

First-principles calculations within the density functional theory (DFT) framework have been performed in order to investigate various conformations of the 2,5-pyridine di-carboxylic acid (PDCA) molecule adsorbed onto the Cu(011) surface. By means of DFT calculations the adsorption geometry, the bond formation and the electronic properties of PDCA molecule conformations on the Cu(011) surface have been studied. The most important structural property is the orientation of the COOH H atom which can point either toward the aromatic ring or toward the vacuum. This H atom position determines the possible reactions in which the adsorbed molecule can get involved and also has a significant impact on the value of the Cu-molecule system work function. Thus, we find that simply by changing the H atom orientation (from up to down) the Cu-molecule system work function can be varied with more than 2.5 eV. This is a significant result as a lot of effort is put nowadays in finding efficient ways for the in situ variation of the systems work function. Scanning tunneling microscopy (STM) images, reflexion absorption infrared vibrational spectra (RAIRS) as well as various thermodynamic properties (adsorption entropies, enthalpies) have also been investigated in order to get a better insight into the system studied and to provide support to possible experimental studies (STM or RAIRS experiments).

The alkylation of benzene by ethene over H-ZSM-5 is analyzed by means of a hybrid MP2:DFT scheme. Density functional calculations applying periodic boundary conditions (PBE functional) are combined with MP2 energy calculations on a series of cluster models of increasing size which allows extrapolation to the periodic MP2 limit. Basis set truncation errors are estimated by extrapolation of the MP2 energy to the complete basis set limit. Contributions from higher-order correlation effects are accounted for by CCSD(T) coupled cluster calculations. The sum of all contributions provides the "final estimates" for adsorption energies and energy barriers. Dispersion contributes significantly to the potential energy surface. As a result, the MP2:DFT potential energy profile is shifted downward compared to the PBE profile. More importantly, this shift is not the same for reactants and transition structures due to different self-interaction correction errors. The final enthalpies for ethene, benzene, and ethylbenzene adsorption on the Brønsted acid site at 298 K are -46, -78, and -110 kJ/mol, respectively. The intrinsic enthalpy barriers at 653 K are 117 and 119/94 kJ/mol for the one- and two-step alkylation, respectively. Intrinsic rate coefficients calculated by means of transition state theory are converted to apparent Arrhenius parameters by means of the multicomponent adsorption equilibrium. The simulated apparent activation energy (66 kJ/mol) agrees with experimental data (58-76 kJ/mol) within the uncertainty limit of the calculations. Adsorption energies obtained by adding a damped dispersion term to the PBE energies (PBE+D), agree within +/-7 kJ/mol, with the "final estimates", except for physisorption (pi-complex formation) and chemisorption of ethene (ethoxide formation) for which the PBE+D energies are 12.4 and 26.0 kJ/mol, respectively larger than the "final estimates". For intrinsic energy barriers, the PBE+D approach does not improve pure PBE results.

Knowledge about the structural elements of skin and its appendices is an essential prerequisite for understanding their complex functions and interactions. The hence necessary morphological description across several orders of scale not only requires the investigation at the light microscopic level but also ultrastructural investigation, ideally on the identical sample. For a correlative and multimodal observation one unique preparation protocol is mandatory. As a compromise between sample sizes of >500 microm in diameter on the one hand and optimal preservation of antigenicity and morphology on the other, we developed a new preparation protocol that allows (i) 3D reconstruction of the resin-embedded sample by confocal light microscopy prior to (ii) direct immunolocalization of target proteins within selected sample planes by light and fluorescence microscopy or transmission electron microscopy. Alternatively, (iii) serial cryosections of the frozen sample can be taken for characterizing the sample in toto. With this unique approach we were able to fully demonstrate the structural complexity of axillary skin samples, increasing the structural resolution from 3D reconstruction of the whole gland up to ultrastructural investigations at the subcellular level. We could demonstrate that axillary sweat glands are not separately distributed, as has been assumed to date; instead, they seem to be intricately twisted into one another. This promotes the concept of a complex axillary sweat gland organ instead of single sweat gland entities.

A novel algorithm for modeling the influence of the host lattice flexibility in molecular dynamics simulations is extended to chain-like molecules and mixtures. This technique, based on a Lowe-Andersen thermostat, maintains the advantages of both simplicity and efficiency. The same diffusivities and other properties of the flexible framework system are reproduced. Advantageously, the computationally demanding flexible host lattice simulations can be avoided. Using this methodology we study the influence of flexibility on diffusion of n-alkanes inside single-walled carbon nanotubes. Furthermore, results are shown for diffusion of two mixtures (methane-helium and ethane-butane). Using these results we investigate the accuracy of theories describing diffusion in the Knudsen regime. For the dynamics in carbon nanotubes the Knudsen diffusivities are much too low. The Smoluchowski model gives better results. Interestingly, the extended Smoluchowski model can reproduce our simulation results obtained with a rigid host lattice. We modify this model to also treat collisions with a flexible interface correctly. As the tangential momentum accommodation coefficient is needed for the theoretical models, we introduce a simple concept to calculate it.

In order to efficiently calculate chemical equilibria of large molecules in a confined environment the reactive Monte Carlo technique is combined with the configurational-bias Monte Carlo approach. To prove that detailed balance is fulfilled the acceptance rule for this combination of particular Monte Carlo techniques is derived in detail. Notably, by using this derivation all other acceptance rules of any Monte Carlo trial moves usually carried out in combination with the configurational-bias Monte Carlo approach can be deduced from it. As an application of the combination of reactive and configurational-bias Monte Carlo the influence of different zeolitic confinements (MFI, TON, LTL, and FER) on the reaction equilibrium and the selectivity of the propene metathesis reaction system was investigated. Compared to the bulk phase the conversion is increased significantly. The authors study this reaction system in the temperature range between 300 and 600 K, and the pressure range from 1 to 7 bars. In contrast to the bulk phase, pressure and temperature have a strong influence on the composition of the reaction mixture in confinement. At low pressures and temperatures both conversion and selectivity are highest. Furthermore, the equilibrium composition is strongly dependent on the type of zeolite. This demonstrates the important role of the host structure in catalytic systems.

A number of experimental studies have shown recently that ppm-level additions of nitric oxide (NO) enhance the rate of nitrous oxide (N(2)O) decomposition catalyzed by Fe-ZSM-5 at low temperatures. In the present work, the NO-assisted N(2)O decomposition over mononuclear iron sites in Fe-ZSM-5 was studied on a molecular level using density functional theory (DFT) and transition-state theory. A reaction network consisting of over 100 elementary reactions was considered. The structure and energies of potential-energy minima were determined for all stable species, as were the structures and energies of all transition states. Reactions involving changes in spin potential-energy surfaces were also taken into account. In the absence of NO and at temperatures below 690 K, most active single iron sites (Z(-)[FeO](+)) are poisoned by small concentrations of water in the gas phase; however, in the presence of NO, these poisoned sites are converted into a novel active iron center (Z(-)[FeOH](+)). These latter sites are capable of promoting the dissociation of N(2)O into a surface oxygen atom and gas-phase N(2). The surface oxygen atom is removed by reaction with NO or nitrogen dioxide (NO(2)). N(2)O dissociation is the rate-limiting step in the reaction mechanism. At higher temperatures, water desorbs from inactive iron sites and the reaction mechanism for N(2)O decomposition becomes independent of NO, reverting to the reaction mechanism previously reported by Heyden et al. [J. Phys. Chem. B 2005, 109, 1857].

We study the self-diffusion of simple gases inside single-walled carbon nanotubes at the zero-loading limit by molecular dynamics simulations. The host-framework flexibility influence is taken into account. In particular, we study the influences of nanotube size and temperature. For the carbon-nanotube radius-dependent self-diffusivities, a maximum is observed, which resembles the so-called levitation effect. This occurs for pores having a radius comparable to the position of the interaction-energy minimum. Surprisingly, the temperature influence is not uniform throughout different pore sizes. Diffusivities are expected to increase with temperature. This effect is observed for carbon nanotubes distinctly larger than the guest molecules. Remarkably, for smaller pores, the self-diffusivities decrease with increasing temperature or exhibit a maximum in the temperature dependence. This effect is caused by competing influences of collision frequency and temperature.

Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.

We describe a novel algorithm that includes the effect of host lattice flexibility into molecular dynamics simulations that use rigid lattices. It uses a Lowe-Andersen thermostat for interface-fluid collisions to take the most important aspects of flexibility into account. The same diffusivities and other properties of the flexible framework system are reproduced at a small fraction of the computational cost of an explicit simulation. We study the influence of flexibility on the self-diffusion of simple gases inside single walled carbon nanotubes. Results are shown for different guest molecules (methane, helium, and sulfur hexafluoride), temperatures, and types of carbon nanotubes. We show, surprisingly, that at low loadings flexibility is always relevant. Notably, it has a crucial influence on the diffusive dynamics of the guest molecules.

To build an effective barrier against the penetration of extrinsic agents is one of the skin's main functions. The barrier properties of the stratum corneum and the epidermis have been subject to extensive studies in the past while the role of skin appendages as possible pathways of penetration are only rarely described. In order to study the possible penetration barriers in these complex appendages, a careful investigation of their morphology and ultrastructure has to be done. Studying the morphology of axillary skin appendages requires clear-cut criteria for the differentiation between eccrine, apocrine and apoeccrine glands. Therefore we studied the distribution of proteins described to be specific for either eccrine or apocrine glands (CD15, CD44, S-100 and milk fat globulin) on axillary skin samples from healthy young adults by immunofluorescence. Additionally, we examined the distribution of cytoskeletal proteins such as cytokeratins (1/10/11, 14, 18) and F-actin. For a more detailed understanding of the possible versatile barrier elements of the axillary sweat glands, we studied the distribution of tight-junction-associated proteins (occludin, claudin 1, claudin 4). The coils and the dermal duct may provide an active barrier built of tight junctions as occludin and claudin 4 are co-localized. However, the intra-epidermal duct did not show any co-localization of the investigated proteins. By combining morphological features as revealed by F-actin staining and the distribution of the above-mentioned proteins, immunocytochemical typing of eccrine and apocrine glands becomes possible. With this tool, we could also confirm the existence of apoeccrine glands and locate them in their 'natural environment'., ((c) 2006 S. Karger AG, Basel)

A combination of interpolation methods and local saddle-point search algorithms is probably the most efficient way of finding transition states in chemical reactions. Interpolation methods such as the growing-string method and the nudged-elastic band are able to find an approximation to the minimum-energy pathway and thereby provide a good initial guess for a transition state and imaginary mode connecting both reactant and product states. Since interpolation methods employ usually just a small number of configurations and converge slowly close to the minimum-energy pathway, local methods such as partitioned rational function optimization methods using either exact or approximate Hessians or minimum-mode-following methods such as the dimer or the Lanczos method have to be used to converge to the transition state. A modification to the original dimer method proposed by [Henkelman and Jonnson J. Chem. Phys. 111, 7010 (1999)] is presented, reducing the number of gradient calculations per cycle from six to four gradients or three gradients and one energy, and significantly improves the overall performance of the algorithm on quantum-chemical potential-energy surfaces, where forces are subject to numerical noise. A comparison is made between the dimer methods and the well-established partitioned rational function optimization methods for finding transition states after the use of interpolation methods. Results for 24 different small- to medium-sized chemical reactions covering a wide range of structural types demonstrate that the improved dimer method is an efficient alternative saddle-point search algorithm on medium-sized to large systems and is often even able to find transition states when partitioned rational function optimization methods fail to converge.

The influence of flexible walls on the self-diffusion of CH4 in an isolated single walled carbon nanotube, as an example, is studied by molecular dynamics simulations. By simulating the carbon nanotube as a flexible framework we demonstrate that the flexibility has a crucial influence on self-diffusion at low loadings. We show how this influence can be incorporated in a simulation of a rigid nanotube by using a Lowe-Andersen thermostat which works on interface-fluid collisions. The reproduction of the results of a flexible carbon nanotube by a rigid nanotube simulation is excellent.

The influence of silicalite-1 pores on the reaction equilibria and the selectivity of the propene metathesis reaction system in the temperature range between 300 and 600 K and the pressure range from 0.5 to 7 bars has been investigated with molecular simulations. The reactive Monte Carlo (RxMC) technique was applied for bulk-phase simulations in the isobaric-isothermal ensemble and for two phase systems in the Gibbs ensemble. Additionally, Monte Carlo simulations in the grand-canonical ensemble (GCMC) have been carried out with and without using the RxMC technique. The various simulation procedures were combined with the configurational-bias Monte Carlo approach. It was found that the GCMC simulations are superior to the Gibbs ensemble simulations for reactions where the bulk-phase equilibrium can be calculated in advance and does not have to be simulated simultaneously with the molecules inside the pore. The confined environment can increase the conversion significantly. A large change in selectivity between the bulk phase and the pore phase is observed. Pressure and temperature have strong influences on both conversion and selectivity. At low pressure and temperature both conversion and selectivity have the highest values. The effect of confinement decreases as the temperature increases.

The reaction mechanism for nitrous oxide decomposition has been studied on hydrated and dehydrated mononuclear iron sites in Fe-ZSM-5 using density functional theory. In total, 46 different surface species with different spin states (spin multiplicity M(S) = 4 or 6) and 63 elementary reactions were considered. Heats of adsorption, activation barriers, reaction rates, and minimum energy pathways were determined. The approximate minimum energy pathways and transition states were calculated using the "growing string method" and a modified "dimer method". Spin surface crossing (e.g., O(2) desorption) was considered. The minimum potential energy structure on the seam of two potential energy surfaces was determined with a multiplier penalty function algorithm by Powell and approximate rates of spin surface crossings were calculated. It was found that nitrous oxide decomposition is first order with respect to nitrous oxide concentration and zero order with respect to oxygen concentration. Water impurities in the gas stream have a strong inhibiting effect. In the concentration range of 1-100 ppb, the presence of water vapor influences the surface composition and the apparent rate coefficient. This is especially relevant in the temperature range of 600-700 K where most experimental kinetic studies are performed. Apparent activation barriers determined over this temperature range vary from 28.4 (1 ppb H(2)O) to 54.8 kcal/mol (100 ppb H(2)O). These results give an explanation why different research groups and different catalyst pretreatments often result in very different activation barriers and preexponential factors. Altogether perfect agreement with experimental results could be achieved.

The radiation force float technique is extended in the present investigation, for the determination of the total radiated low ultrasonic power in the milliwatt region. It is elucidated, experimentally, using floats having a conical reflecting target comprising of new material (teflon insulated copper wire) stems with smaller diameters (0.55 and 1 mm). The sensitivity is improved with these two stems and the ultrasonic power levels are measured in the range from 1.4 to 140 mW and 4.6 to 460 mW respectively and the results are reproducible within +/- 5%. Limitations of float technique and factors influencing the uncertainties involved for the high quality ultrasonic power measurements are discussed. The proposed method is simple, versatile and inexpensive and can be used as an interim standard.

In several branches of science and technology a gaseous phase is dispersed into a liquid in the form of bubbles, a gaseous component then dissolves into the liquid and subsequently undergoes chemical reaction. The overall process performance can be improved substantially when the area of gas-liquid contact is increased. By subjecting the liquid phase to low frequency vibrations, the bubbles are shown to suffer significant breakage, induced by resonance. When the vibration is properly tuned, the interfacial area is found to increase by a factor of 1.8-2.4, depending on the properties of the liquid. Resonance-induced bubble breakage phenomena have a great potential for improving the rates of chemical processes involving fast reactions, with minimal energy input.

During the last 50 years extensive experimental investigation has been carried out on the chemical effects of ultrasound, but limited work has been reported on modeling. This paper presents a new model in which a numerical calculation of the three-dimensional linear sound pressure field distribution in a commonly used sonoreactor containing three transducers is carried out. In this model the inhomogeneous three-dimensional time-dependent wave equation was solved using the finite difference approach. The modeled results are then compared with the experimentally measured values, and the agreement, in general, is found to be good. Further, our modeling studies have an advantage, since they clearly describe the continuous sound pressure field structure, unlike previously reported results in which some information is missing due to limited intermittent measured points.