Article

Effective Hamiltonian approach to catalytic activity of transition metal complexes

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

The application of an effective electron Hamiltonian approach to the description of the electronic structure of transition metal complexes with chemically active ligands is analyzed. This approach is implemented in a computational code. The evolution of the electronic structure along a path of isomerization of quadricyclane to norbornadiene in the coordination sphere of Co-tetraphenylporphyrin is considered. In addition, the electronic states of atomic oxygen coordinated to transition metal oxides and metal porphyrins are studied. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 84: 99–109, 2001

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

Chapter
Full-text available
Hybrid QM/MM methods are widely used for describing diierent as-pects of behavior of complex molecular systems. The key problem when applying the QM/MM methodology is a substantiated construc-tion/selection of the junction between the parts of the system described at the QM and MM levels, respectively. It is especially important in the case of covalently bound QM and MM subsystems. We pursue here a general approach based on a sequential separation of electronic variables in order to develop a fundamental form of the intersubsys-tem junction. Special attention is given to construction of frontier one-electron states and renormalization of QM Hamiltonian parameters and MM force elds. From this point of view we consider a series of the junction forms present in the literature and in some cases suggest theo-retically more reliable alternatives. General theoretical conclusions are supported by data of numerical experiments.
Article
The theory of catalytic activity of transition-metal compounds is a fascinating problem especially if a comparison of different catalysts is necessary. The isomerization of quadricyclane (QC) to norbornadiene (NB) catalyzed by transition-metal porphyrins is a challenge and incidentally a suitable benchmark for various theories of catalysis. We analyze this process in detail using a valence bond-like scheme adjusted for the description of reaction centers containing transition-metal atoms. A qualitative explanation of contrasting catalytic behavior of Mn-phthalocyanine and Co-tetraphenylporphyrin is obtained from the analysis of the spectra of local many electron states of free catalysts and their complexes with the reactant/product. This picture is supported by the numerical analysis of potential energy profiles for the QC to NB isomerization in the presence of a catalyst performed in the effective Hamiltonian approximation. This exemplary reaction is put in a more general perspective of theories of catalytic activity of transition-metal complexes and in relation with oxygenation reactions. V C 2013 Wiley Periodicals, Inc.
Article
Molecular mechanics (MM) is now widely used for modeling potential energy surfaces of large organic molecules. All MM schemes use ad hoc forms for the potential functions and parameters specially adjusted to fit experimental or quantum chemical data. In this work we attempt to deduce a generic MM scheme starting from a local quantum mechanical description of molecular electronic structure. The basis for this derivation is the trial electronic wave function in the form of antisymmetrized product of strictly localized geminals. The MM scheme obtained does not require adjusting any parameters. The quality of numerical estimates obtained by this scheme is analyzed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002
Article
A short summary of the n-electron valence state perturbation theory (NEVPT) is provided, and the defects inherent in cases of quasi-degeneration are underscored. A new version of the theory, called QD-NEVPT, based on quasi-degenerate perturbation theory, is presented. The new theory introduces an effective interaction among the zero-order wave functions and overcomes the difficulties of state-specific NEVPT. An application concerning the interaction among the pi->pi* and Rydberg singlets of formaldehyde is presented.
Article
The local many-electron states in transition metal oxides (TMOs) are considered in the framework of the effective Hamiltonian of the crystal field (EHCF) method. The calculations are performed with use of the 5×5×5 clusters modeling TMOs with the rock salt crystal structure. The d–d excitation spectra are calculated and discussed with the aim of interpreting the experimental data on optical adsorption and electron energy loss spectra. The EHCF method is extended to account for the electron correlation in the d-shell and some electronic variables of ligands simultaneously. This approach is used to calculate the states of atomic and molecular oxygen on the surfaces of the TMOs. The possible role of geometric parameters of the adsorption complex is evaluated. The metal–oxygen distance and the exit of the metal ion from the surface plane are varied in a wide range. In the case of molecular oxygen different coordination forms are considered and for all adsorption systems the weights of different oxygen states (triplet, singlet, and charge transfer) are estimated.
Article
Full-text available
Well decorated maghemite-supported ultra-fine Pd (1-3 nm) nanoparticles, prepared by a simple co-precipitation method, find application in the catalytic continuous flow hydrogenation of nitroarenes, azides, and alkenes wherein they play an important role in reduction of various functional groups on the surface of maghemite with low catalyst loading (~6 wt%). The salient features of the protocol include expeditious formation of reduced products in high yields at near ambient conditions with recycling of the catalyst (up to 12 cycles) without any loss in selectivity and yield; barely noticeable Pd metal leaching was detected after the reactions.
Book
Full-text available
The structure and application of a new unitary operator calculus for atomic and molecular electronic states are outlined. A complete background of this new calculus is given along with new results which describe common types of shell structure, their mixtures, and spin or orbit dependent operators. The presentation in part I includes some review of the important ingredients of the pattern theory, some of which are more or less well known, but which the non-specialist might otherwise find difficult to assemble. In part II the pattern calculus is applied to complex atomic and molecular configurations. In particular, atomic configurations involving pure and mixed subshells are treated with an analysis of more than half-filled shells and the jj-coupling approximation. Finally, a general mathematical analyis of unitary tableau bases is given with discussions of the parentage and shell structure of these states. (GHT)
Article
Full-text available
The authors applied general quantum mechanical ideas in order to establish the form of the many electron wave functions suitable for analysis of catalytic processes. This led us to the conclusion that the relevant wave functions for the electrons of the catalytic complexes must be taken as superpositions of the antisymmetrized products of the wave functions of electrons in excited and ionized states of the catalyst and reactants. With the use of the trial wave function for the electrons of the catalytic complex in such a form, it becomes possible to construct model potential energy surfaces of catalytic reactions as a superposition of the potential energy surfaces of the reactants in different electronic states. The authors formulate the criteria which when satisfied make it possible to implement a catalytic version of a desired chemical transformation. The authors also propose an approach to the explanation of the frequently observed correlations between the catalytic activity and other physical properties of a catalyst. 16 refs., 4 figs.
Article
Full-text available
The method of an effective crystalline field (ECF) suggested previously to assess magnetic and optical properties of transition metal complexes is realized with INDO parametrization of ligand atoms and applied to calculate the ground state and spectrum of low-energy excitations of the central ion in aquo-, amino, and fluoro-complexes of transition metals of the first transition row and of some metalloporphyrins and chlorine-copper complexes.
Article
Full-text available
The effective crystal field method for calculating the magnetic and optical properties of transition metal complexes is extended to take into account the electrons that fill the ligand molecular orbitals whose occupancy changes during chemical transformations. An effective Hamiltonian is constructed for a system of strongly correlating d-shell electrons and electrons on ligand orbitals that intersect each other during a reaction. Taking into account complete configuration interaction for this subsystem makes it possible to determine the structure of the ground and excited electronic states. The suggested calculation procedure is applied to isomerization of quadricyclane to norbornadiene in the coordination sphere of Co-tetraphenylporphyrin.
Article
Full-text available
The atomic angular-factor calculation methods given in a previous work are simplified and extended to include a treatment of spin-orbit operators and multiple shell configuration. A tableau formula is given for the matrix between Slater states and states of definite total spin.
Article
Full-text available
A semiempirical effective Hamiltonian treatment is proposed for transition metal complexes, taking into accountd-electron correlations, weak covalency of the metal-ligand bonds and the electronic structure of the ligand sphere. The technique uses the variation wave function which differs from the usual Hartree-Fock antisymmetrized product of molecular orbitals extended over the whole complex. The scheme is implemented and parameters describing the metal-ligand interactions are adjusted to reproduced-d-excitation spectra of a number of octahedral MF 64− (M=Mn, Fe, Co, Ni) anions, Mn(FH) 62+ cation, CoCl 64− anion, and a tetrahedral CoCl 42− anion. The values of the parameters are reasonable, thus confirming the validity of the proposed scheme.
Article
Publisher Summary This chapter presents the specific catalytic functions of the transition metal in the various types of transformations, and discusses the associated chemistry. Molecular orbital symmetry conservation constrains all molecular systems to specific paths of transformation. Symmetry conservation principles have proven to be powerful tools for understanding a large body of complex organic chemistry. These concepts further bear on molecular stability. A molecule in one bonding configuration transforms into other configurations primarily through allowed paths. The thermal stability enjoyed by simple olefins to a certain extent rests on orbital symmetry restraints. Both olefin cyclobutanation and double-bond isomerization (through a 1,3-hydrogen shift), involving forbidden passages, are not observed at moderate temperatures. Simple olefins are fixed in their bonding configurations and cannot interconvert through the sterically-preferred paths. The thermal interconversion of olefins is necessarily a high-temperature process involving predominantly the higher energy, allowed transformations incorporating free radical intermediates.
Article
An ab initio investigation of a model heme prosthetic group based on the carbon monoxy myoglobin (MbCO) IMBC X-ray structure reproduces the large off-perpendicular distortions of the Fe-C-O unit reported for the protein. The distortion is mainly caused by the nonequilibrium orientation of the proximal residue and not by the distal residue: inclusion of the distal residue in a supermolecule calculation has a smaller effect on the Fe-C-O geometry. If such a mechanism primarily determines the Fe-C-O distortion in the protein itself, then the large strain energies implied by the Fe-C-O geometries in the X-ray structures are delivered by the protein tertiary structure, via the proximal residue, and not by the mobile distal side chain, as had been previously proposed. The structure-function relationship, as revealed by the X-ray structure, would then be clarified. Distortion of the Fe-C-O geometry is largely determined by the proximal residue, and so Fe-C-O is nonperpendicular even in the His64Gly mutant. The distal residue is not subject to a large repulsive interaction with the carbonyl ligand; thus, its orientation in the solvated protein can be determined by weaker attractive electrostatic interactions, as inferred from recent experimental studies of distal residue mutant myoglobins. This result removes the need to invoke a large stabilization of the distal side chain orientation by a rigid hydrogen-bonding network, an interpretation of the physiological structure-function relationship that was at odds with the X-ray B factors and the mobility of surface residue side chains expected under physiological conditions.
Article
We applied general quantum mechanical ideas in order to establish the form of the many-electron wave functions suitable for analysis of catalytic processes. This led us to the conclusion that the relevant wave functions for the electrons of the catalytic complexes must be taken as superpositions of the antisymmetrized products of the wave functions of electrons in excited and ionized states of the catalyst and reactants. With use of the trial wave function for the electrons of the catalytic complex in such a form, it becomes possible to construct model potential energy surfaces of catalytic reactions as a superposition of the potential energy surfaces of the reactants in different electronic states. We formulate the criteria which when satisfied make it possible to implement a catalytic version of a desired chemical transformation. We also propose an approach to the explanation of the frequently observed correlations between the catalytic activity and other physical properties of a catalyst.
Article
By ESR technique the formation of adsorbed O2− and O− on , , , , , , has been studied. The properties of adsorbed radicals are determined by valence state and coordination of surface transition metal ions. The very high reactivity of adsorbed O− is discovered.
Article
The fundamentals of molecular quantum mechanics have changed remarkably little since the 1930’s: the most commonly used methods of constructing molecular wave functions are still dominated by expansions in terms of Slater determinants, in which individual electrons are described by spin-orbitals; the spin-orbitals (one-electron wavefunctions) still usually refer to an independent-particle model (IPM) in which each electron ‘sees’ an average field due to the nuclei and to all its companion electrons — in the spirit of Hartree and Fock; and simple first approximations, in which the wavefunction is built up from a few configurations of ‘occupied’ orbitals, are still systematically refined by adding more and more configurational functions (CFs) in a typical configuration interaction (CI) calculation. It is true that the techniques have changed: Fock space, for example, is now more familiar to quantum chemists than it used to be; the simple self-consistent field (SCF) of Hartree and Fock is nowadays often replaced by its multi-configuration counterpart; and CI may be admitted by diagrammatic perturbation theory or by unitary group methods. But, beautiful as some of these techniques may be, they are simply sophisticated and clever ways of doing the same old things!
Article
This paper reviews the work carried out by the authors' research groups on the forms of adsorbed oxygen and the role of oxygen in processes of catalytic oxidation on transition metal oxides. The discussion covers the following topics - species of oxygen adsorbed at the surface of transition metal oxides and their identification; thermodynamic stability of adsorbed oxygen species; oxides which adsorb oxygen in the form of electron-rich species; oxides which adsorb oxygen as species less rich in electrons; stoichiometric oxides which do not adsorb oxygen. Results are summarized and some conclusions drawn regarding oxygen adsorption mechanisms.
Article
Aus den nach bekannten Verfahren hergestellten Quadricyclanen (I), (III), (V) und (VII) entstehen bei der Behandlung mit Rhodium(I)-Komplexen in einer thermodynamisch kontrollierten Reaktion die Norbornadien-Derivate (II), (IV), (VI) bzw. (VIII), während aus dem Oxa-quadricyclan (IX) in einer kinetisch kontrollierten Reaktion das thermodynamisch stabilere Hydroxyfulven (X) erhalten wird.
Article
A method for the determination of the mean number of elementary electric charges acquired by one oxygen atom adsorbed on the surface of such oxides as NiO, CoO, MnO is proposed. It consists of the determination of the volume of oxygen gas adsorbed on a high surface area sample of strictly stoichiometric oxide and the subsequent analytical determination of the number of metal ions promoted to a higher oxidation state as the result of electron transfer from the adsorbent to the adsorbate. Using this method it has been shown that, in the case of high surface area nickel oxide, oxygen is chemisorbed at room temperature predominantly in the form of O− ions (irreversible adsorption). The percentage of reversibly adsorbed oxygen decreases with the time of contact. At 150 °C only the O− form was observed after a short period of adsorption. Slow formation of O2− could be subsequently observed. The velocity of this latter process increases with an increase in temperature. In the case of high surface area cobalt oxide, the O2− form predominates even at room temperature.
Article
The ultrafast release of O2 from the O2 adduct of picket-fence cobalt porphyrin (see picture) has been probed in real time, and has a total reaction time of 2 ps, without subsequent recombination over several nanoseconds. The dynamics of this ultrafast release of O2 shows that relaxation within the porphyrin system (200 fs) precedes porphyrin-to-metal electron transfer, but the latter occurs at an enhanced rate (500 fs as opposed to the more usual 1 – 2 ps) because of the dative bonding of cobalt and O2, which gives the adduct ground state significant CoIII−O2− character.
Article
The mechanism of the catalytic activity of transition metal complexes is discussed in terms of an effective Hamiltonian of a reactant-catalyst system. The potential energy surface has been constructed for the reaction of catalytic isomerization of quadricyclane to nonbornadiene. The properties of the catalyst are found to affect strongly the activation energy of the reaction.
Article
A general scheme for theoretical treatment of organometallic reactivity is proposed. It is based upon the notion that the reactivity of a molecule is strongly affected by its coordination to metal-containing fragments. Based upon this idea we describe the large-scale organometallic reactions as reactions of the ligands in the coordination spheres of transition metal complexes. We propose here a quantum mechanical framework for analysis of effects of coordination on the reactivity and give several examples of qualitative energy profiles for reactions in the ligand spheres of transition metal complexes. © 1996 John Wiley & Sons, Inc.
Article
A theorem is proven for quantum information theory that is analogous to the noiseless coding theorem of classical information theory. In the quantum result, the von Neumann entropy S of the density operator describing an ensemble of pure quantum signal states is equal to the number of spin-1/2 systems (‘‘quantum bits’’ or ‘‘qubits’’) necessary to represent the signal faithfully. The theorem holds whether or not the signal states are orthogonal. Related results are also presented about the fidelity of quantum coding and about representing entangled quantum states.
Article
The partitioning technique for solving secular equations is briefly reviewed. It is then reformulated in terms of an operator language in order to permit a discussion of the various methods of solving the Schrödinger equation. The total space is divided into two parts by means of a self‐adjoint projection operator O. Introducing the symbolic inverse T = (1—O)/(E—H), one can show that there exists an operator Ω = O + THO, which is an indempotent eigenoperator to H and satisfies the relations HΩ = EΩ and Ω2 = Ω. This operator is not normal but has a form which directly corresponds to infinite‐order perturbation theory. Both the Brillouin‐ and Schrödinger‐type formulas may be derived by power series expansion of T, even if other forms are perhaps more natural. The concept of the reaction operator is discussed, and upper and lower bounds for the true eigenvalues are finally derived.
Article
We have investigated the 57Fe Mössbauer quadrupole splittings in the following compounds by using density functional theory, and in some cases via experiment:  Fe(CO)3(cyclo-butadiene), Fe(CO)5, Fe(CO)3(1,4−butadiene), CpFe(CO)2Me, Fe(CO)3(propenal), CpFe(CO)2Cl, (CO)(pyridine)(DMGBPh2)2Fe(II) (DMG = dimethylglyoximato), (CO)(pyridine)(DMGBBN)2Fe(II) (BBN = 9-borabicyclo[3.3.1]nonane), (CO)(1-methylimidazole)(5,10,15,20-tetraphenylporphinato)Fe(II), (CO)(pyridine)(5,10,15,20-tetraphenyl-porphinato)Fe(II), (nitrosobenzene)(pyridine)(5,10,15,20-tetraphenylporphinato)Fe(II), (pyridine)2(5,10,15,20-tetraphenylporphinato)Fe(II), (1-methylimidazole)2(5,10,15,20-tetramesitylporphinato)Fe(II), and (trimethylphosphine)2(2,3,7,8,12,13,17,18-octaethylporphinato)Fe(II). The electric field gradients at iron were evaluated by using a locally dense basis approach:  a Wachters' all electron representation for iron, a 6-311++G2d basis for all atoms directly bonded to iron, and either a 6-31G* basis for all other atoms or, in the case of the metalloporphyrins, a 6-31G*/3-21G* or 4-31G* basis, with the smaller basis being used on the peripheral atoms. Using a value of 0.16 × 10-28 m2 for the quadrupole moment of 57Fem, we find good agreement between theoretical and experimental quadrupole splittings:  a slope of 1.04, an R2 value of 0.975, and a root-mean-square error of 0.18 mm s-1, for the 14 compounds examined. We have also investigated the effects of the CO ligand tilt and bend on the 57Fe quadrupole splittings in several heme models. The theoretical results provide no support for the very large (40°) Fe−C−O bond angles suggested by several diffraction studies on Physeter catodon carbonmonoxymyoglobin (P21 crystals). In contrast, the experimental results for (CO)(1-MeIm)(5,10,15,20-tetraphenylporphinato)Fe(II), which contains a linear and untilted Fe−CO, are in very close accord with the experimental values for CO-myoglobin:  0.35 mm s-1 for the model system versus 0.363−0.373 mm s-1 for MbCO, with Vzz oriented perpendicular to the porphyrin plane, as found experimentally. Calculations on metalloporphyrins at the more distorted X-ray geometries yield quadrupole splittings around 2 mm s-1, inconsistent with experiment.
Article
When crystals of (2-methylimidazole)-meso-tetra(α,α,α,α-o- pivalamidophenyl)porphyrinatoiron(II)-ethanol, Fe(TpivPP)(2-Melm)·EtOH, are exposed to dioxygen, the crystals of the resultant dioxygen adduct are still suitable for diffraction studies. The direct, precise determination of the stereochemical changes accompanying oxygenation of an iron(II)-(porphyrinato)(base) complex has been carried out using conventional X-ray diffraction methods. The structures have been refined by full-matrix, least-squares methods, using 4176 and 5183 reflections for the deoxy and oxy complexes, respectively, to R indices on F2 of 0.162 and 0.120. For the portion of data where Fo2 > 3σ(Fo2) the respective indices on F are 0.086 and 0.083. Crystal data for the deoxy compound follow: space group C2h6-C2/c, Z = 4, molecular symmetry C2, a = 18.871 (11) Å, b = 19.425 (13) Å, c = 18.434 (11) Å, β = 91.48 (3)°, V = 6755.0 Å3. The oxy complex is nearly isomorphic with Z = 4 in space group C2/c with a cell of dimensions a = 18.864 (5) Å, b = 19.451 (5) Å, c = 18.287 (5) Å, β = 91.45 (2)°, V = 6707.0 Å3. Some selected parameters for the coordination spheres, with those in square brackets pertaining to the dioxygen adduct, follow: Fe-Nporph = 2.068 (5), 2.075 (5) [1.997 (4), 1.995 (4)] Å; Fe-N1m = 2.095 (6) [2.107 (4)] Å. The iron atom is displaced 0.399 [0.086] Å from the least-squares plane of the porphinato nitrogen atoms toward the imidazole ligand. The Fe-O separation is 1.898 (7) Å. The average O-O separation is 1.22 (2) Å and the Fe-O-O angle is 129 (1)°. In the presence of ethanol the deoxy complex binds dioxygen reversibly, noncooperatively, and with lower affinity than when the sample is desolvated - in the latter case dioxygen uptake has been found to be cooperative. The structure and properties of these possible models for T-state deoxy- and oxyhemoglobin are correlated and then compared with the 1-methylimidazole analogue. The sterically active 2-methyl substituent appears to perturb the Fe-O bond but not the Fe-N1m bond.
Article
Magnetic and optical properties of transition-metal complexes are governed by the ground state and the low-energy excitation spectrum of the d-shell of the central transition metal ion. These spectra are successfully fit to the crystal field theory. We present here an account of the effective Hamiltonian method recently developed to calculate the ground state and the excitations of the d-shells of transition-metal complexes and report the results of its application to some complexes of particular interest. © 1996 John Wiley & Sons, Inc.
Article
A quantitative study of the interplay between the structure, energy, and dynamics of heme models is presented. Our calculations are based on density functional theory (DFT) combined with molecular dynamics (MD), within the Car–Parrinello scheme. The systems analyzed are the five-coordinated FeP–AB (FeP = iron–porphyrin, AB = CO, NO, O2) and Fe(Heme)–O2, the six-coordinated FeP(Im)–AB (Im = imidazole), and the picket fence–oxygen complex, Fe(TpivP)(2me–Im)–O2. Starting from the optimized structures of these systems, we analyze the trends in their ligand binding properties. Our calculations show the peculiar trans repulsive effect of the NO ligand when binding to iron–porphyrin (it elongates and weakens the trans axial ligand bond), in contrast with the synergistic effect of CO and O2. Energy variations associated to the rotation of the O2 molecule around the Fe–O bond in Fe(TpivP)(2me–Im)–O2 are analyzed, in comparison with that of a simpler FeP(Im)–O2 model. A small energy barrier (<2 kcal/mol) is found in both cases. Room temperature molecular dynamics simulations reveal how the O2 ligand overcomes this barrier at room temperature: It undergoes large-amplitude oscillations within one porphyrin quadrant, jumping to another one in the picosecond timescale. In contrast, the CO dynamics is characterized by small, albeit extremely complex, displacements around its equilibrium position. Small fluctuations of the FeCO tilt (δ) and bend (θ) angles (δ≤8°, θ≤13°) are observed. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 1172–1180, 2000
Article
The valence isomerization of quadricyclene to norbornadiene is catalyzed by certain transition metal complexes of phthalocyanine and tetraphenyl porphyrin. To explore the dependence of catalytic activity on the number of d-electrons in the metal ion, complexes having a number of d-electrons from 5 to 10 were studied. Most of the d6, d7 and d8 ions were active whereas the d9 and d10 ions were inactive. The influence of the stereochemistry of the ligand was studied using cobalt (II) complexes with certain quadridentate Schiff bases whose stereochemistry could be changed by small modifications in structure. Square planarity of the complex appeared to be a condition for catalytic activity. The catalytic reaction could be inhibited by the addition of pyridine bases. 4-Picoline was more effective than pyridine, but 2-picoline did not poison the reaction at all. These results could be explained within the framework of existing theories dealing with this form of catalysis.
Article
When N2O reacts with irradiated MgO, an ESR signal due to O− is found. This species is highly reactive and when molecular oxygen, carbon monoxide and ethylene are adsorbed at 77°K on O−, new signals are found due to the formation of O3−, CO2− and C2H4O− radicals.
  • B Meunier
Meunier, B. Chem Rev 1992, 92, 1411.
  • A V Soudackov
  • A L Tchougréeff
  • I A Misurkin
Soudackov, A. V.; Tchougréeff, A. L.; Misurkin, I. A. Int J Quantum Chem 1996, 58, 161.
  • K Ruedenberg
Ruedenberg, K. Rev Mod Phys 1962, 34.
Advances and Perspectives
  • J Paldus
Paldus, J. In Theoretical Chemistry, Advances and Perspectives ; Eyring, H.; Henderson, D., Eds.; Academic Press: New York, 1976; Vol. 2.
  • A M Tokmachev
  • A L Tchougréeff
  • Russ
Tokmachev, A. M.; Tchougréeff, A. L. Russ J Phys Chem 2000, 74, 58.
  • C Rovira
  • M Parrinello
Rovira, C.; Parrinello, M. Int J Quantum Chem 2000, 80, 1172.
  • A Bielanski
  • Haber
Bielanski, A.; Haber, J. Catal Rev 1979, 19, 1.
  • B Steiger
  • J S Baskin
  • F C Anson
  • A H Zewail
Steiger, B.; Baskin, J. S.; Anson, F. C.; Zewail, A. H. Angew Chem Int Ed 2000, 39, 257.
  • A L Tchougréeff
  • I A Misurkin
Tchougréeff, A. L.; Misurkin, I. A. Dokl Akad Nauk USSR 1986, 291, 1177.
  • A Bielanski
  • M Najbar
Bielanski, A.; Najbar, M. J Catal 1972, 25, 398.
  • V A Shwets
  • V B Kazanskii
Shwets, V. A.; Kazanskii, V. B. J Catal 1972, 25, 123.