Theoretical investigation of hyperthermal reactions at the gas-liquid interface: O (3P) and squalane

Hyperthermal collisions (5 eV) of ground-state atomic oxygen [O ((3)P)] with a liquid-saturated hydrocarbon, squalane (C(30)H(62)), have been studied using QM/MM hybrid "on-the-fly" direct dynamics. The surface structure of the liquid squalane is obtained from a classical molecular dynamics simulation using the OPLS-AA force field. The MSINDO semiempirical Hamiltonian is combined with OPLS-AA for the QM/MM calculations. In order to achieve a more consistent and efficient simulation of the collisions, we implemented a dynamic partitioning of the QM and MM atoms in which atoms are assigned to QM or MM regions based on their proximity to "seed" (open-shell) atoms that determine where bond making/breaking can occur. In addition, the number of seed atoms is allowed to increase or decrease as time evolves so that multiple reactive events can be described. The results show that H abstraction is the most important process for all incident angles, with H elimination, double H abstraction, and C-C bond cleavage also being important. A number of properties of these reactive channels, as well as inelastic nonreactive scattering, are investigated, including angular and translational energy distributions, the effect of incident collision angle, variation with depth of the reactive event within the liquid, with the reaction site on the hydrocarbon, and the effect of dynamics before and after reaction (direct reaction versus trapping reaction-desorption).     

Hyperthermal reactions of O and O2 with a hydrocarbon surface: direct C-C bond breakage by O and H-atom abstraction by O2

A C-C bond-breaking reaction has been observed when a beam containing hyperthermal oxygen was directed at a continuously refreshed saturated hydrocarbon liquid (squalane) surface. The dynamics of this C-C bond-breaking reaction have been investigated by monitoring time-of-flight and angular distributions of the volatile product, OCH3 or H2CO. The primary product is believed to be the methoxy radical, OCH3, but if this radical is highly internally excited, then it may undergo secondary dissociation to form formaldehyde, H2CO. Either the primary or the secondary product may scatter directly into the gas phase before thermal equilibrium with the surface is reached, or they may become trapped on the surface and desorb in thermal equilibrium with the surface. Direct, single-collision scattering events that produce a C-C bond-breaking product are described with a kinematic picture that allows the determination of the effective surface mass encountered by an incident O atom, the atom-surface collision energy in the center-of-mass frame, and the fraction of the center-of-mass collision energy that goes into translation of the scattered gaseous product and the recoiling surface fragment. The dynamical behavior of the C-C bond-breaking reaction is compared with that of the H-atom abstraction reaction, which was the subject of an earlier study. Another reaction, H-atom abstraction by O2 (which is present in the hyperthermal beam), has also been observed, and the dynamics of this reaction are compared with the inelastic scattering dynamics of O2 and the dynamics of H-atom abstraction by O. The dynamics involving direct inelastic and reactive scattering of O2 are also described in terms of a kinematic picture where the incident O2 molecule is viewed as interacting with a local region of the surface.     

Combined valence bond-molecular mechanics potential-energy surface and direct dynamics study of rate constants and kinetic isotope effects for the H + C2H6 reaction

This article presents a multifaceted study of the reaction H+C(2)H(6)-->H(2)+C(2)H(5) and three of its deuterium-substituted isotopologs. First we present high-level electronic structure calculations by the W1, G3SX, MCG3-MPWB, CBS-APNO, and MC-QCISD/3 methods that lead to a best estimate of the barrier height of 11.8+/-0.5 kcal/mol. Then we obtain a specific reaction parameter for the MPW density functional in order that it reproduces the best estimate of the barrier height; this yields the MPW54 functional. The MPW54 functional, as well as the MPW60 functional that was previously parametrized for the H+CH(4) reaction, is used with canonical variational theory with small-curvature tunneling to calculate the rate constants for all four ethane reactions from 200 to 2000 K. The final MPW54 calculations are based on curvilinear-coordinate generalized-normal-mode analysis along the reaction path, and they include scaled frequencies and an anharmonic C-C bond torsion. They agree with experiment within 31% for 467-826 K except for a 38% deviation at 748 K; the results for the isotopologs are predictions since these rate constants have never been measured. The kinetic isotope effects (KIEs) are analyzed to reveal the contributions from subsets of vibrational partition functions and from tunneling, which conspire to yield a nonmonotonic temperature dependence for one of the KIEs. The stationary points and reaction-path potential of the MPW54 potential-energy surface are then used to parametrize a new kind of analytical potential-energy surface that combines a semiempirical valence bond formalism for the reactive part of the molecule with a standard molecular mechanics force field for the rest; this may be considered to be either an extension of molecular mechanics to treat a reactive potential-energy surface or a new kind of combined quantum-mechanical/molecular mechanical (QM/MM) method in which the QM part is semiempirical valence bond theory; that is, the new potential-energy surface is a combined valence bond molecular mechanics (CVBMM) surface. Rate constants calculated with the CVBMM surface agree with the MPW54 rate constants within 12% for 534-2000 K and within 23% for 200-491 K. The full CVBMM potential-energy surface is now available for use in variety of dynamics calculations, and it provides a prototype for developing CVBMM potential-energy surfaces for other reactions.     

Convergence in the QM‐only and QM/MM modeling of enzymatic reactions: A case study for acetylene hydratase

We report systematic quantum mechanics‐only (QM‐only) and QM/molecular mechanics (MM) calculations on an enzyme‐catalyzed reaction to assess the convergence behavior of QM‐only and QM/MM energies with respect to the size of the chosen QM region. The QM and MM parts are described by density functional theory (typically B3LYP/def2‐SVP) and the CHARMM force field, respectively. Extending our previous work on acetylene hydratase with QM regions up to 157 atoms (Liao and Thiel, J. Chem. Theory Comput. 2012, 8, 3793), we performed QM/MM geometry optimizations with a QM region M4 composed of 408 atoms, as well as further QM/MM single‐point calculations with even larger QM regions up to 657 atoms. A charge deletion analysis was conducted for the previously used QM/MM model ( M3a , with a QM region of 157 atoms) to identify all MM residues with strong electrostatic contributions to the reaction energetics (typically more than 2 kcal/mol), which were then included in M4 . QM/MM calculations with this large QM region M4 lead to the same overall mechanism as the previous QM/MM calculations with M3a , but there are some variations in the relative energies of the stationary points, with a mean absolute deviation (MAD) of 2.7 kcal/mol. The energies of the two relevant transition states are close to each other at all levels applied (typically within 2 kcal/mol), with the first (second) one being rate‐limiting in the QM/MM calculations with M3a ( M4 ). QM‐only gas‐phase calculations give a very similar energy profile for QM region M4 (MAD of 1.7 kcal/mol), contrary to the situation for M3a where we had previously found significant discrepancies between the QM‐only and QM/MM results (MAD of 7.9 kcal/mol). Extension of the QM region beyond M4 up to M7 (657 atoms) leads to only rather small variations in the relative energies from single‐point QM‐only and QM/MM calculations (MAD typically about 1–2 kcal/mol). In the case of acetylene hydratase, a model with 408 QM atoms thus seems sufficient to achieve convergence in the computed relative energies to within 1–2 kcal/mol.Copyright © 2013 Wiley Periodicals, Inc.     

Correlation effects on the structure and dynamics of the H3O+ hydrate: B3LYP/MM and MP2/MM MD simulations

Two combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations, namely B3LYP/MM and MP2/MM, have been performed to investigate the possible influence of electron correlation on the structure and dynamics of the H(3)O(+) hydrate. In comparison to the previously published HF/MM results, both B3LYP/MM and MP2/MM simulations clearly reveal stronger H(3)O(+)-water hydrogen bond interactions, which are reflected in a slightly greater compactness of the H(3)O(+) hydrate. However, the B3LYP/MM simulation, although providing structural details very close to the MP2/MM data, shows an artificially slow dynamic nature of some first shell water molecules as a consequence of the formation of a long-lived H(3)O(+)···H(2)O hydrogen bonding structure.     

Studies of carbon incorporation on the diamond [100] surface during chemical vapor deposition using density functional theory

Accurate potential energy surface calculations are presented for many of the key steps involved in diamond chemical vapor deposition on the [100] surface (in its 2 x 1 reconstructed and hydrogenated form). The growing diamond surface was described by using a large (approximately 1500 atoms) cluster model, with the key atoms involved in chemical steps being described by using a quantum mechanical (QM, density functional theory, DFT) method and the bulk of the atoms being described by molecular mechanics (MM). The resulting hybrid QM/MM calculations are more systematic and/or at a higher level of theory than previous work on this growth process. The dominant process for carbon addition, in the form of methyl radicals, is predicted to be addition to a surface radical site, opening of the adjacent C-C dimer bond, insertion, and ultimate ring closure. Other steps such as insertion across the trough between rows of dimer bonds or addition to a neighboring dimer leading to formation of a reconstruction on the next layer may also contribute. Etching of carbon can also occur; the most likely mechanism involves loss of a two-carbon moiety in the form of ethene. The present higher-level calculations confirm that migration of inserted carbon along both dimer rows and chains should be relatively facile, with barriers of approximately 150 kJ mol (-1) when starting from suitable diradical species, and that this step should play an important role in establishing growth of smooth surfaces.     

Quantum mechanics/molecular mechanics electrostatic embedding with continuous and discrete functions

A quantum mechanics/molecular mechanics (QM/MM) implementation that uses the Gaussian electrostatic model (GEM) as the MM force field is presented. GEM relies on the reproduction of electronic density by using auxiliary basis sets to calculate each component of the intermolecular interaction. This hybrid method has been used, along with a conventional QM/MM (point charges) method, to determine the polarization on the QM subsystem by the MM environment in QM/MM calculations on 10 individual H(2)O dimers and a Mg(2+)-H(2)O dimer. We observe that GEM gives the correct polarization response in cases when the MM fragment has a small charge, while the point charges produce significant over-polarization of the QM subsystem and in several cases present an opposite sign for the polarization contribution. In the case when a large charge is located in the MM subsystem, for example, the Mg(2+) ion, the opposite is observed at small distances. However, this is overcome by the use of a damped Hermite charge, which provides the correct polarization response.     

CPMD/GULP QM/MM interface for modeling periodic solids: Implementation and its application in the study of Y‐zeolite supported Rhn clusters

We report here the development of hybrid quantum mechanics/molecular mechanics (QM/MM) interface between the plane‐wave density functional theory based CPMD code and the empirical force‐field based GULP code for modeling periodic solids and surfaces. The hybrid QM/MM interface is based on the electrostatic coupling between QM and MM regions. The interface is designed for carrying out full relaxation of all the QM and MM atoms during geometry optimizations and molecular dynamics simulations, including the boundary atoms. Both Born–Oppenheimer and Car–Parrinello molecular dynamics schemes are enabled for the QM part during the QM/MM calculations. This interface has the advantage of parallelization of both the programs such that the QM and MM force evaluations can be carried out in parallel to model large systems. The interface program is first validated for total energy conservation and parallel scaling performance is benchmarked. Oxygen vacancy in α‐cristobalite is then studied in detail and the results are compared with a fully QM calculation and experimental data. Subsequently, we use our implementation to investigate the structure of rhodium cluster (Rh_n; n = 2 to 6) formed from Rh(C₂H₄)₂ complex adsorbed within a cavity of Y‐zeolite in a reducible atmosphere of H₂ gas. © 2016 Wiley Periodicals, Inc.     

Fragmentation and reactivity in collisions of protonated diglycine with chemically modified perfluorinated alkylthiolate-self-assembled monolayer surfaces

Direct dynamics simulations are reported for quantum mechanical (QM)/molecular mechanical (MM) trajectories of N-protonated diglycine (gly(2)-H(+)) colliding with chemically modified perfluorinated octanethiolate self-assembled monolayer (SAM) surfaces. The RM1 semiempirical theory is used for the QM component of the trajectories. RM1 activation and reaction energies were compared with those determined from higher-level ab initio theories. Two chemical modifications are considered in which a head group (-COCl or -CHO) is substituted on the terminal carbon of a single chain of the SAM. These surfaces are designated as the COCl-SAM and CHO-SAM, respectively. Fragmentation, peptide reaction with the SAM, and covalent linkage of the peptide or its fragments with the SAM surface are observed. Peptide fragmentation via concerted CH(2)-CO bond breakage is the dominant pathway for both surfaces. HCl formation is the dominant species produced by reaction with the COCl-SAM, while for the CHO-SAM a concerted H-atom transfer from the CHO-SAM to the peptide combined with either a H-atom or radical transfer from the peptide to the surface to form singlet reaction products is the dominant pathway. A strong collision energy dependence is found for the probability of peptide fragmentation, its reactivity, and linkage with the SAM. Surface deposition, i.e., covalent linkage between the surface and the peptide, is compared to recent experimental observations of such bonding by Laskin and co-workers [Phys. Chem. Chem. Phys. 10, 1512 (2008)]. Qualitative differences in reactivity are seen between the COCl-SAM and CHO-SAM showing that chemical identity is important for surface reactivity. The probability of reactive surface deposition, which is most closely analogous to experimental observables, peaks at a value of around 20% for a collision energy of 50 eV.     

QM/MM-PBSA method to estimate free energies for reactions in proteins

We have developed a method to estimate free energies of reactions in proteins, called QM/MM-PBSA. It estimates the internal energy of the reactive site by quantum mechanical (QM) calculations, whereas bonded, electrostatic, and van der Waals interactions with the surrounding protein are calculated at the molecular mechanics (MM) level. The electrostatic part of the solvation energy of the reactant and the product is estimated by solving the Poisson-Boltzmann (PB) equation, and the nonpolar part of the solvation energy is estimated from the change in solvent-accessible surface area (SA). Finally, the change in entropy is estimated from the vibrational frequencies. We test this method for five proton-transfer reactions in the active sites of [Ni,Fe] hydrogenase and copper nitrite reductase. We show that QM/MM-PBSA reproduces the results of a strict QM/MM free-energy perturbation method with a mean absolute deviation (MAD) of 8-10 kJ/mol if snapshots from molecular dynamics simulations are used and 4-14 kJ/mol if a single QM/MM structure is used. This is appreciably better than the original QM/MM results or if the QM energies are supplemented with a point-charge model, a self-consistent reaction field, or a PB model of the protein and the solvent, which give MADs of 22-36 kJ/mol for the same test set.     

Application of the ONIOM-molecular dynamics method to the organometallic reaction cis-(H)2Pt(PR3)2 --> H2 + Pt(PR3)2 (R=H, Me, Ph, and t-Bu). An insight into the dynamical environmental effects

The ONIOM-molecular dynamics (MD) method, which we recently developed, is applied to one of representative organometallic reactions, cis-(H)2Pt(PR3)2 --> H2 + Pt(PR3)2(R=H, Me, Ph, and t-Bu) to give an insight into the dynamical effects of the environment on the reaction. We adopted the two-layered ONIOMmethodology and divided the system into the inner part of cis-(H)2Pt(PH3)2 and the outer part of the others.The inner and outer parts are treated by the quantum mechanics (QM) method at the HF level of theory and the molecular mechanics (MM) method with the MM3 force field, respectively. The ONIOM-MD simulations how that the thermal motion of the outer part increases the magnitude of the energy fluctuations of the inner part and promotes the H2 elimination reaction. These dynamical environmental effects increase in the order,t-Bu > Ph > Me > H, indicating that the reactivity of cis-(H)2Pt(PR3)2 increases in the same order. These results are also supported by an equation derived from the Arrhenius' equation (Matsubara's equation). The snapshots of the reaction for R=t-Bu clearly indicate the new feature of the H2 elimination process     

Ab initio QM/MM dynamics of H3O+ in water

A molecular dynamics (MD) simulation based on a combined ab initio quantum mechanics/molecular mechanics (QM/MM) method has been performed to investigate the solvation structure and dynamics of H3O+ in water. The QM region is a sphere around the central H3O+ ion, and contains about 6-8 water molecules. It is treated at the Hartree-Fock (HF) level, while the rest of the system is described by means of classical pair potentials. The Eigen complex (H9O4+) is found to be the most prevalent species in the aqueous solution, partly due to the selection scheme of the center of the QM region. The QM/MM results show that the Eigen complex frequently converts back and forth into the Zundel (H5O2+) structure. Besides the three nearest-neighbor water molecules directly hydrogen-bonded to H3O+, other neighbor waters, such as a fourth water molecule which interacts preferentially with the oxygen atom of the hydronium ion, are found occasionally near the ion. Analyses of the water exchange processes and the mean residence times of water molecules in the ion's hydration shell indicate that such next-nearest neighbor water molecules participate in the rearrangement of the hydrogen bond network during fluctuative formation of the Zundel ion and, thus, contribute to the Grotthuss transport of the proton.     

Geometry optimization using tuned and balanced redistributed charge schemes for combined quantum mechanical and molecular mechanical calculations

We performed geometry optimizations using the tuned and balanced redistributed charge algorithms to treat the QM-MM boundary in combined quantum mechanical and molecular mechanical (QM/MM) methods. In the tuned and balanced redistributed charge (TBRC) scheme, the QM boundary atom is terminated by a tuned F link atom, and the charge of the MM boundary atom is properly adjusted to conserve the total charge of the entire QM/MM system; then the adjusted MM boundary charge is moved evenly to the midpoints of the bonds between the MM boundary atom and its neighboring MM atoms. In the tuned and balanced redistributed charge-2 (TBRC2) scheme, the adjusted MM boundary charge is moved evenly to all MM atoms that are attached to the MM boundary atom. A new option, namely charge smearing, has been added to the TBRC scheme, yielding the tuned and balanced smeared redistributed charge (TBSRC) scheme. In the new scheme, the redistributed charges near the QM-MM boundary are smeared to make the electrostatic interactions between the QM region and the redistributed charges more realistic. The TBRC2 scheme and new TBSRC scheme have been tested for various kinds of bonds at a QM-MM boundary, including C-C, C-N, C-O, O-C, N-C, C-S, S-S, S-C, C-Si, and O-N bonds. Charge smearing is necessary if the redistributed charges are close to the QM region, as in the TBSRC scheme, but not if the redistributed charge is farther from the QM region, as in the TBRC2 scheme. We found that QM/MM results using either the TBRC2 scheme or the TBSRC scheme agree well with full QM results; the mean unsigned error (MUE) of the QM/MM deprotonation energy is 1.6 kcal/mol in both cases, and the MUE of QM/MM optimized bond lengths over the three bonds closest to the QM-MM boundary, with errors averaged over the protonated forms and unprotonated forms, is 0.015 ? for TBRC2 and 0.021 ? for TBSRC. The improvements in the new scheme are essential for QM-MM boundaries that pass through a polar bond, but even for boundaries that pass through C-C bonds, the improvement can be quite significant.     

Crossed-beams studies of the dynamics of the H-atom abstraction reaction, O(3P) + CH4 → OH + CH3, at hyperthermal collision energies

The H-atom abstraction reaction, O((3)P) + CH(4) → OH + CH(3), has been studied at a hyperthermal collision energy of 64 kcal mol(-1) by two crossed-molecular-beams techniques. The OH products were detected with a rotatable mass spectrometer employing electron-impact ionization, and the CH(3) products were detected with the combination of resonance-enhanced multiphoton ionization (REMPI) and time-sliced ion velocity-map imaging. The OH products are mainly formed through a stripping mechanism, in which the reagent O atom approaches the CH(4) molecule at large impact parameters and the OH product is scattered in the forward direction: roughly the same direction as the reagent O atoms. Most of the available energy is partitioned into product translation. The dominance of the stripping mechanism is a unique feature of such H-atom abstraction reactions at hyperthermal collision energies. In the hyperthermal reaction of O((3)P) with CH(4), the H-atom abstraction reaction pathway accounts for 70% of the reactive collisions, while the H-atom elimination pathway to produce OCH(3) + H accounts for the other 30%.     

Dynamic structures of phosphodiesterase-5 active site by combined molecular dynamics simulations and hybrid quantum mechanical/molecular mechanical calculations

Various quantum mechanical/molecular mechanical (QM/MM) geometry optimizations starting from an x-ray crystal structure and from the snapshot structures of constrained molecular dynamics (MD) simulations have been performed to characterize two dynamically stable active site structures of phosphodiesterase-5 (PDE5) in solution. The only difference between the two PDE5 structures exists in the catalytic, second bridging ligand (BL2) which is HO- or H2O. It has been shown that, whereas BL2 (i.e. HO-) in the PDE5(BL2 = HO-) structure can really bridge the two positively charged metal ions (Zn2+ and Mg2+), BL2 (i.e. H2O) in the PDE5(BL2 = H2O) structure can only coordinate Mg2+. It has been demonstrated that the results of the QM/MM geometry optimizations are remarkably affected by the solvent water molecules, the dynamics of the protein environment, and the electronic embedding charges of the MM region in the QM part of the QMM/MM calculation. The PDE5(BL2 = H2O) geometries optimized by using the QM/MM method in different ways show strong couplings between these important factors. It is interesting to note that the PDE5(BL2 = HO-) and PDE5(BL2 = H2O) geometries determined by the QM/MM calculations neglecting these three factors are all consistent with the corresponding geometries determined by the QM/MM calculations that account for all of these three factors. These results suggest the overall effects of these three important factors on the optimized geometries can roughly cancel out. However, the QM/MM calculations that only account for some of these factors could lead to considerably different geometries. These results might be useful also in guiding future QM/MM geometry optimizations on other enzymes.     

Fragmentation-based QM/MM simulations: length dependence of chain dynamics and hydrogen bonding of polyethylene oxide and polyethylene in aqueous solutions

Molecular fragmentation quantum mechanics (QM) calculations have been combined with molecular mechanics (MM) to construct the fragmentation QM/MM method for simulations of dilute solutions of macromolecules. We adopt the electrostatics embedding QM/MM model, where the low-cost generalized energy-based fragmentation calculations are employed for the QM part. Conformation energy calculations, geometry optimizations, and Born-Oppenheimer molecular dynamics simulations of poly(ethylene oxide), PEO(n) (n = 6-20), and polyethylene, PE(n) ( n = 9-30), in aqueous solution have been performed within the framework of both fragmentation and conventional QM/MM methods. The intermolecular hydrogen bonding and chain configurations obtained from the fragmentation QM/MM simulations are consistent with the conventional QM/MM method. The length dependence of chain conformations and dynamics of PEO and PE oligomers in aqueous solutions is also investigated through the fragmentation QM/MM molecular dynamics simulations.     

Hydrogenation of CO on a silica surface: an embedded cluster approach

The sequential addition of H atoms to CO adsorbed on a siliceous edingtonite surface is studied with an embedded cluster approach, using density functional theory for the quantum mechanical (QM) cluster and a molecular force field for the molecular mechanical (MM) cluster. With this setup, calculated QM/MM adsorption energies are in agreement with previous calculations employing periodic boundary conditions. The catalytic effect of the siliceous edingtonite (100) surface on CO hydrogenation is assessed because of its relevance to astrochemistry. While adsorption of CO on a silanol group on the hydroxylated surface did not reduce the activation energy for the reaction with a H atom, a negatively charged defect on the surface is found to reduce the gas phase barriers for the hydrogenation of both CO and H2C=O. The embedded cluster approach is shown to be a useful and flexible tool for studying reactions on (semi-)ionic surfaces and specific defects thereon. The methodology presented here could easily be applied to study reactions on silica surfaces that are of relevance to other scientific areas, such as biotoxicity of silica dust and geochemistry.     

An embedded QM/MM study for different SiO2/Al2O3 ratios of the HZSM‐5 zeolite and for their interaction with n‐heptane

We carried out a theoretical study of the HZSM‐5 zeolite, for different SiO₂/Al₂O₃ ratios, that interacts with the n‐heptane molecule. The study was performed using a QM/MM (quantum mechanics/molecular mechanics) methodology. For the QM part, we have chosen a hybrid Hartree‐Fock density functional theory (DFT). The hybrid ACM/DZP approach, as implemented in Turbomole, was used for the treatment of the QM cluster containing 84 atoms that represents a ring structure model of the zeolite‐n‐heptane interacting system. The MM part was represented by means of an electrostatic forcefield (ESFF), which assesses the electronic embedding. The chosen QM/MM silicalite base model contains 3862 atoms. The studied SiO₂/Al₂O₃ ratios were 2300, 573.5, 287.7, and 189.83, containing 1, 4, 8, and 12 Al atoms, respectively. For the first ratio, the site for the substitution of Al for Si was that of minimum QM total energy value, because this replacement was done in the QM region. For the other SiO₂/Al₂O₃ ratios, the Al atoms were randomly spread through the MM region in accordance with the Lowenstein substitution rule. These results show the importance of the environment on the electronic properties in the QM region, where the active site lies, and their effects on the earlier steps on the activation experienced by the n‐heptane moiety. A minimal content of 12 Al atoms produces significant effects of the environment on the electronic structure of the QM region. Moreover, the carbocationic character of n‐heptane increases with the aluminum content. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002