Comparison of ab Initio and DFT Electronic Structure Methods for Peptides Containing an Aromatic Ring: Effect of Dispersion and BSSE

Basis Set Superposition Errors Are Partly Basis Set Imbalances

When calculating fragment interaction energies by electronic structure methods employing medium-sized atom-centered basis sets, it is often observed that the effect is systematically overestimated. The common interpretation is that the systematic error arises because the basis set for the complex is more complete than for the isolated fragments, and this is denoted basis set superposition errors. It has been observed, however, that the interaction energy in some cases is underestimated, which defies the interpretation in terms of basis set completeness, and instead suggests that the effect partly is due to basis set imbalance. The imbalance can be removed by explicit optimization of the basis sets for each structure, and it is shown that this to a significant extent reduces the systematic overestimation attributed to basis set superposition error.

The Role of Water in the Adsorption of Nitro-Organic Pollutants on Activated Carbon

The density functional theory (DFT) is applied to theoretically study the capture and storage of three different nitro polycyclic aromatic hydrocarbons, 4-nitrophenol, 2-nitrophenol, and 9-nitroanthracene by activated carbon, with and without the presence of water. These species are pollutants derived from vehicle and industry emissions. The modeling of adsorption is carried out at the molecular level using a high-level density functional theory with the B3LYP-GD(BJ)/6-31+G(d,p) level of theory. The adsorption energies of polluting gases considered isolated and in a humid environment are compared to better understand the role of water. The calculations reveal different possible pathways involving the formation of chemical bonds between adsorbent and adsorbate on the formation of intermolecular van der Waals interactions. The negative adsorption energy on AC for the three species is obtained when they are treated individually and in mixture with H2O. The basis-set superposition error, estimated using the counterpoise correction, varies the adsorption energies by 2-13%. Dispersion effects were also taken into account. The adsorption energy ranges from -10 to -414 kJ/mol suggesting a diversity of pathways. The resulting analysis suggests three preferred pathways for capture. The main pathway is physical interaction due to π-π stacking. Other means are capture due to the formation of hydrogen bonds resulting from water adsorbed on the surface and the simultaneous adsorption of pollutant and water where water can act as a link that promotes adsorption. The thermodynamic properties give a clue to the most eco-friendly approaches for molecular adsorption.

Quantifying Intramolecular Basis Set Superposition Errors

We show that medium-sized Gaussian basis sets lead to significant intramolecular basis set superposition errors at Hartree-Fock and density functional levels of theory, with artificial stabilization of compact over extended conformations for a 186 atom deca-peptide. Errors of ∼80 and ∼10 kJ/mol are observed, with polarized double zeta and polarized triple zeta quality basis sets, respectively. Two different procedures for taking the basis set superposition error into account are tested. While both reduce the error, it appears that polarized quadruple zeta basis sets are required to reduce the error below a few kJ/mol. Alternatively, the basis set superposition error can be eliminated using multiresolution methods based on Multiwavelets.

High-temperature reactivity of vanadium oxide clusters in methane activation: Vibrational degrees of freedom matter

Understanding the properties of small particles working under high-temperature conditions at the atomistic scale is imperative for exact control of related processes, but it is quite challenging to achieve experimentally. Herein, benefitting from state-of-the-art mass spectrometry and by using our newly designed high-temperature reactor, the activity of atomically precise particles of negatively charged vanadium oxide clusters toward hydrogen atom abstraction (HAA) from methane, the most stable alkane molecule, has been measured at elevated temperatures up to 873 K. We discovered the positive correlation between the reaction rate and cluster size that larger clusters possessing greater vibrational degrees of freedom can carry more vibrational energies to enhance the HAA reactivity at high temperature, in contrast with the electronic and geometric issues that control the activity at room temperature. This finding opens up a new dimension, vibrational degrees of freedom, for the simulation or design of particle reactions under high-temperature conditions.

Fantasy versus reality in fragment-based quantum chemistry

Since the introduction of the fragment molecular orbital method 20 years ago, fragment-based approaches have occupied a small but growing niche in quantum chemistry. These methods decompose a large molecular system into subsystems small enough to be amenable to electronic structure calculations, following which the subsystem information is reassembled in order to approximate an otherwise intractable supersystem calculation. Fragmentation sidesteps the steep rise (with respect to system size) in the cost of ab initio calculations, replacing it with a distributed cost across numerous computer processors. Such methods are attractive, in part, because they are easily parallelizable and therefore readily amenable to exascale computing. As such, there has been hope that distributed computing might offer the proverbial "free lunch" in quantum chemistry, with the entrée being high-level calculations on very large systems. While fragment-based quantum chemistry can count many success stories, there also exists a seedy underbelly of rarely acknowledged problems. As these methods begin to mature, it is time to have a serious conversation about what they can and cannot be expected to accomplish in the near future. Both successes and challenges are highlighted in this Perspective.

Direct hydroxylation of benzene to phenol mediated by nanosized vanadium oxide cluster ions at room temperature

Gas-phase vanadium oxide cluster cations and anions are prepared by laser ablation. The small cluster ions (<1000 amu) are mass-selected using a quadrupole mass filter and reacted with benzene in a linear ion trap reactor; large clusters (>1000 amu) with no mass selection are reacted with C₆H₆ in a fast flow reactor. Rich product variety is encountered in these reactions, and the reaction channels for small cationic and anionic systems are different. For large clusters, the reactivity patterns of (V₂O₅) _n⁺ (n = 6-25) and (V₂O₅) _n O^- (n = 6-24) cluster series are very similar to each other, indicating that the charge state has little influence on the oxidation of benzene. In sharp contrast to the dramatic changes of reactivity of small clusters, a weakly size dependent reaction behavior of large (V₂O₅)_6-25⁺ and (V₂O₅)_6-24O^- clusters is observed. Therefore, the charge state and the size are not the major factors influencing the reactivity of nanosized vanadium oxide cluster ions toward C₆H₆, which is not common in cluster science. In the reactions with benzene, the small and large reactive vanadium oxide cations show similar reactivity of hydroxyl radicals (OH^•) toward C₆H₆ at higher and lower temperatures, respectively; different numbers of vibrational degrees of freedom and the released energy during the formation of adduct complexes can explain this intriguing correlation. The reactions investigated herein might be used as the models of how to realize the partial oxidation of benzene to phenol in a single step, and the observed mechanisms are helpful to understand the corresponding heterogeneous reactions, such as those over vanadium oxide aerosols and vanadium oxide catalysts.

Fe2 O+ Cation Mediated Propane Oxidation by Dioxygen in the Gas Phase

The mass-selected Fe₂ O⁺ cation mediated propane oxidation by O₂ was investigated by mass spectrometry and density functional theory calculations. In the reaction of Fe₂ O⁺ with C₃ H₈ , H₂ was liberated by C-H bond activation to give Fe₂ OC₃ H₆⁺ . Interestingly, when a mixture of C₃ H₈ /O₂ was introduced into the reactor, an intense signal that corresponded to the Fe₂ O₂⁺ cation was present; the experiments indicated that O₂ was activated in its reaction with Fe₂ O(C₃ H₆ )⁺ to give Fe₂ O₂⁺ and C₃ H₆ O (acetone or propanal). A Langmuir-Hinshelwood-like mechanism was adopted in the propane oxidation reaction by O₂ on gas-phase Fe₂ O⁺ cations. In comparison with the absence of Fe₂ O₂⁺ in the reaction of Fe₂ O⁺ with O₂ , the ligand effect of C₃ H₆ on Fe₂ OC₃ H₆⁺ is important in the oxygen activation reaction. The theoretical results are consistent with the experimental observations. The propane oxidation by O₂ in the presence of Fe₂ O⁺ might be applied as a model for alkane and O₂ activations over iron oxide catalysts, and the mechanisms and kinetic data are useful for understanding corresponding heterogeneous reactions.

A DFT study of 2-aminopurine-containing dinucleotides: prediction of stacked conformations with B-DNA structure

The fluorescence properties of dinucleotides incorporating 2-aminopurine (2AP) suggest that the simplest oligonucleotides adopt conformations similar to those found in duplex DNA. However, there is a lack of structural data for these systems. We report a density functional theory (DFT) study of the structures of 2AP-containing dinucleotides (deoxydinucleoside monophosphates), including full geometry optimisation of the sugar-phosphate backbone. Our DFT calculations employ the M06-2X functional for reliable treatment of dispersion interactions and include implicit aqueous solvation. Dinucleotides with 2AP in the 5'-position and each of the natural bases in the 3'-position are examined, together with the analogous 5'-adenine-containing systems. Computed structures are compared in detail with typical B-DNA base-step parameters, backbone torsional angles and sugar pucker, derived from crystallographic data. We find that 2AP-containing dinucleotides adopt structures that closely conform to B-DNA in all characteristic parameters. The structures of 2AP-containing dinucleotides closely resemble those of their adenine-containing counterparts, demonstrating the fidelity of 2AP as a mimic of the natural base. As a first step towards exploring the conformational heterogeneity of dinucleotides, we also characterise an imperfectly stacked conformation and one in which the bases are completely unstacked.

N-Protonated Isomers and Coulombic Barriers to Dissociation of Doubly Protonated Ala8Arg

Collision-induced dissociation (or tandem mass spectrometry, MS/MS) of a protonated peptide results in a spectrum of fragment ions that is useful for inferring amino acid sequence. This is now commonplace and a foundation of proteomics. The underlying chemical and physical processes are believed to be those familiar from physical organic chemistry and chemical kinetics. However, first-principles predictions remain intractable because of the conflicting necessities for high accuracy (to achieve qualitatively correct kinetics) and computational speed (to compensate for the high cost of reliable calculations on such large molecules). To make progress, shortcuts are needed. Inspired by the popular mobile proton model, we have previously proposed a simplified theoretical model in which the gas-phase fragmentation pattern of protonated peptides reflects the relative stabilities of N-protonated isomers, thus avoiding the need for transition-state information. For singly protonated Ala _n (n = 3-11), the resulting predictions were in qualitative agreement with the results from low-energy MS/MS experiments. Here, the comparison is extended to a model tryptic peptide, doubly protonated Ala₈Arg. This is of interest because doubly protonated tryptic peptides are the most important in proteomics. In comparison with experimental results, our model seriously overpredicts the degree of backbone fragmentation at N₉. We offer an improved model that corrects this deficiency. The principal change is to include Coulombic barriers, which hinder the separation of the product cations from each other. Coulombic barriers may be equally important in MS/MS of all multiply charged peptide ions. Graphical Abstract ᅟ.

Exploring short intramolecular interactions in alkylaromatic substrates

From proteins and peptides to semiconducting polymers, aliphatic chains on aromatic groups are recurring motifs in macromolecules from very diverse application fields. Fields in which molecular folding and packing determine the macroscopic physical properties that make such advanced materials appealing in the first place. Within each macromolecule, the intrinsic structure of each unit defines how it interacts with its neighbours, ultimately opening up or denying certain backbone conformations. This eventually also determines how macromolecules interact with each other. This account deals specifically with the conformational problem of many common alkylaromatic units, examining the features of an intramolecular interaction involving a side chain with as few as three methylene groups. A set of 23 model compounds featuring an intramolecular interaction between an aliphatic X-H (X = C, N, O, and S) bond and an aromatic ring was considered. Quantitative computational analysis was made possible, thanks to complete basis set extrapolated CCSD(T) calculations and NCI topological analysis, the latter of which revealed an elaborate network of dispersive and steric interactions leading to somewhat unintuitive and unexpected results, such as the higher energetic stability of certain twisted conformational isomers over those with extended side chains. Vicinal covalent effects from polarizing groups and various heteroatoms, along with the occurrence of non-dispersive phenomena, were also investigated. The conclusions drawn from the investigation include a comprehensive set of guidelines intended to aid in the prediction of the most stable conformation for this class of building blocks. Our findings affect a variety of different research fields, including the tailoring of functional materials for organic electronics and photovoltaics, with insights into a rational treatment of conformational disorder, and the study of protein- and peptide-folding preferences, putting an emphasis on peculiar interactions between the backbone and aromatic residues.

Study on the inter- and intra-peptide salt-bridge mechanism of Aβ23-28 oligomer interaction with small molecules: QM/MM method

Amyloid β (Aβ) peptides have long been known to be a potential candidate for the onset of Alzheimer's disease (AD). The biophysical properties of Aβ42 peptide aggregates are of significant importance for the amyloid cascade mechanism of AD. It is necessary to design an inhibitor using small molecules to reduce the aggregation process in Aβ42 peptides. Attention has been given to use the natural products as anti-aggregation compounds, directly targeting Aβ peptides. Polyphenols have been extensively studied as a class of amyloid inhibitors. 9,10-Anthraquinone (AQ) is present in abundance in medicinal plants (rhubarb), the Trp-Pro-Tyr (TPT) peptide has been found in the venom of the black mamba snake, and the morin molecule is naturally present in wine and green tea; several other polyphenol derivatives are under clinical trials to develop anti-neurodegenerative drugs. In vitro and in vivo results strongly suggest that AQ and morin molecules are potential inhibitors of Aβ aggregation; however, the detailed understanding of the inhibition mechanism remains largely unknown. The formation of Aβ fibrils and oligomers requires a conformational change from α-helix to β-sheet, which occurs due to the formation of a salt-bridge between Asp(23) and Lys(28) residues. The present study focused on investigating the salt-bridge mechanism in the monomer, dimer and oligomer of the Aβ23-28 peptide during the interaction with TPT, morin and AQ molecules. Interaction energy and natural bond orbital analyses have been carried out using the ONIOM(M05-2X/6-31++G(d,p):UFF) method. The QM/MM studies have been performed to study the mechanism of salt-bridge formation during the inhibition process of amyloid β protein aggregation. The TPT molecule, which binds with the Asp(23) and Lys(28) residues of Aβ, prevents the salt-bridge formation between Asp(23) and Lys(28) residues and consequently the probability of the formation of Aβ fibrils is reduced.

Local NH–π interactions involving aromatic residues of proteins: influence of backbone conformation and ππ* excitation on the π H-bond strength, as revealed from studies of isolated model peptides

Gas phase conformer-selective IR spectroscopy combined and relevant quantum chemistry methods document the NH–π interactions in Phe residues.

Exploring the Limit of Accuracy of the Global Hybrid Meta Density Functional for Main-Group Thermochemistry, Kinetics, and Noncovalent Interactions

The hybrid meta density functionals M05-2X and M06-2X have been shown to provide broad accuracy for main group chemistry. In the present article we make the functional form more flexible and improve the self-interaction term in the correlation functional to improve its self-consistent-field convergence. We also explore the constraint of enforcing the exact forms of the exchange and correlation functionals through second order (SO) in the reduced density gradient. This yields two new functionals called M08-HX and M08-SO, with different exact constraints. The new functionals are optimized against 267 diverse main-group energetic data consisting of atomization energies, ionization potentials, electron affinities, proton affinities, dissociation energies, isomerization energies, barrier heights, noncovalent complexation energies, and atomic energies. Then the M08-HX, M08-SO, M05-2X, and M06-2X functionals and the popular B3LYP functional are tested against 250 data that were not part of the original training data for any of the functionals, in particular 164 main-group energetic data in 7 databases, 39 bond lengths, 38 vibrational frequencies, and 9 multiplicity-changing electronic transition energies. These tests include a variety of new challenges for complex systems, including large-molecule atomization energies, organic isomerization energies, interaction energies in uracil trimers, and bond distances in crowded molecules (in particular, cyclophanes). The M08-HX functional performs slightly better than M08-SO and M06-2X on average, significantly better than M05-2X, and much better than B3LYP for a combination of main-group thermochemistry, kinetics, noncovalent interactions, and electronic spectroscopy. More important than the slight improvement in accuracy afforded by M08-HX is the conformation that the optimization procedure works well for data outside the training set. Problems for which the accuracy is especially improved by the new M08-HX functional include large-molecule atomization energies, noncovalent interaction energies, conformational energies in aromatic peptides, barrier heights, multiplicity-changing excitation energies, and bond lengths in crowded molecules.

An Atomic Counterpoise Method for Estimating Inter- and Intramolecular Basis Set Superposition Errors

An atomic counterpoise method is proposed to calculate estimates of inter- and intramolecular basis set superposition errors. The method estimates the basis set superposition error as a sum of atomic contributions and can be applied for both independent particle and electron correlation models. It is shown that the atomic counterpoise method provides results very similar to the molecular counterpoise method for intermolecular basis set superposition errors at both the HF and MP2 levels of theory with a sequence of increasingly larger basis sets. The advantage of the atomic counterpoise method is that it can be applied with equal ease to estimate intramolecular basis set superposition errors, for which few other methods exist. The atomic counterpoise method is computationally quite efficient, requiring typically double the amount of computer time as required for calculating the uncorrected energy.

Charge transfer and first hyperpolarizability: cage-like radicals C59X and lithium encapsulated Li@C59X (X=B, N)

Very recently, two new cage-like radicals (C59B and C59N) formed by a boron or nitrogen atom substituting one carbon atom of C60 were synthesized and characterized. In order to explore the structure-property relationships of combination the cage-like radical and alkali metal, the endohedral Li@C59B and Li@C59N are designed by lithium (Li) atom encapsulated into the cage-like radicals C59B and C59N. Further, the structures, natural bond orbital (NBO) charges, and nonlinear optical (NLO) responses of C59B, C59N, Li@C59B, and Li@C59N were investigated by quantum chemical method. Three density functional methods (BHandHLYP, CAM-B3LYP, and M05-2X) were employed to estimate their first hyperpolarizabilities (β tot) and obtained the same trend in the β tot value. The β tot values by BHandHLYP functional of the pure cage-like radicals C59B (1.30 × 10(3) au) and C59N (1.70 × 10(3) au) are close to each other. Interestingly, when one Li atom encapsulated into the electron-rich radical C59N, the β tot value of the Li@C59N increases to 2.46 × 10(3) au. However, when one Li atom encapsulated into the electron-deficient radical C59B, the β tot value of the Li@C59B sharply decreases to 1.54 × 10(2) au. The natural bond orbital analysis indicates that the encapsulated Li atom leads to an obvious charge transfer and valence electrons distribution plays a significant role in the β tot value. Further, frontier molecular orbital explains that the interesting charge transfer between the encapsulated Li atom and cage-like radicals (C59B and C59N) leads to differences in the β tot value. It is our expectation that this work will provide useful information for the design of high-performance NLO materials.

Isolated neutral peptides

This chapter examines the structural characterisation of isolated neutral amino-acids and peptides. After a presentation of the experimental and theoretical state-of-the-art in the field, a review of the major structures and shaping interactions is presented. Special focus is made on conformationally-resolved studies which enable one to go beyond simple structural characterisation; probing flexibility and excited-state photophysics are given as examples of promising future directions.

Separate electronic attenuation allowing a spin-component-scaled second-order Møller-Plesset theory to be effective for both thermochemistry and noncovalent interactions

Spin-component-scaled (SCS) second-order Møller-Plesset perturbation theory (MP2) improves the treatment of thermochemistry and noncovalent interactions relative to MP2, although the optimal scaling coefficients are quite different for thermochemistry versus noncovalent interactions. This work reconciles these two different scaling regimes for SCS-MP2 by using two different length scales for electronic attenuation of the two spin components. The attenuation parameters and scaling coefficients are optimized in the aug-cc-pVTZ (aTZ) basis using the S66 database of intermolecular interactions and the W4-11 database of thermochemistry. Transferability tests are performed for atomization energies and barrier heights, as well as on further test sets for inter- and intramolecular interactions. SCS dual-attenuated MP2 in the aTZ basis, SCS-MP2(2terfc, aTZ), performs similarly to SCS-MP2/aTZ for thermochemistry while frequently outperforming MP2 at the complete basis set limit (CBS) for nonbonded interactions.

Achieving the CCSD(T) Basis-Set Limit in Sizable Molecular Clusters: Counterpoise Corrections for the Many-Body Expansion

An efficient procedure is introduced to obtain the basis-set limit in electronic structure calculations of large molecular and ionic clusters. This approach is based on a Boys-Bernardi-style counterpoise correction for clusters containing arbitrarily many monomer units, which is rendered computationally feasible by means of a truncated many-body expansion. This affords a tractable way to apply the sequence of correlation-consistent basis sets (aug-cc-pVXZ) to large systems and thereby obtain energies extrapolated to the complete basis set (CBS) limit. A three-body expansion with three-body counterpoise corrections is shown to afford errors of ≲0.1-0.2 kcal/mol with respect to traditional MP2/CBS results, even for challenging systems such as fluoride-water clusters. A triples correction, δCCSD(T) = ECCSD(T) - EMP2, can be estimated accurately and efficiently as well. Because the procedure is embarrassingly parallelizable and requires no electronic structure calculations in systems larger than trimers, it is extendible to very large clusters. As compared to traditional CBS extrapolations, computational time is dramatically reduced even without parallelization.

Analysis of the basis set superposition error in molecular dynamics of hydrogen-bonded liquids: application to methanol

An efficient protocol is presented to compensate for the basis set superposition error (BSSE) in DFT molecular dynamics (MD) simulations using localized Gaussian basis sets. We propose a classical correction term that can be added a posteriori to account for BSSE. It is tested to what extension this term will improve radial distribution functions (RDFs). The proposed term is pairwise between certain atoms in different molecules and was calibrated by fitting reference BSSE data points computed with the counterpoise method. It is verified that the proposed exponential decaying functional form of the model is valid. This work focuses on hydrogen-bonded liquids, i.e., methanol, and more specific on the intermolecular hydrogen bond, but in principle the method is generally applicable on any type of interaction where BSSE is significant. We evaluated the relative importance of the Grimme-dispersion versus BSSE and found that they are of the same order of magnitude, but with an opposite sign. Upon introduction of the correction, the relevant RDFs, obtained from MD, have amplitudes equal to experiment.

Modeling the interactions between peptide functions and Sr2+: formamide-Sr2+ reactions in the gas phase

The interactions between formamide, which can be considered a prototype of a peptide function, and Sr(2+) have been investigated by combining nanoelectrospray ionization/mass spectrometry techniques and G96LYP DFT calculations. For Sr an extended LANL2DZ basis set was employed, together with a 6-311+G(3df,2p) basis set expansion for the remaining atoms of the system. The observed reactivity seems to be dominated by the Coulomb explosion process yielding [SrOH](+) + [HNCH](+), which are the most intense peaks in the MS/MS spectra. Nevertheless, additional peaks corresponding to the loss of HNC and CO indicate that the association of Sr(2+) to water or to ammonia leads to long-lived doubly charged species detectable in the timescale of these experimental techniques. The topology of the calculated potential energy surface permits us to establish the mechanisms behind these processes. Although the interaction between the neutral base and Sr(2+) is essentially electrostatic, the polarization triggered by the doubly charged metal ion results in the activation of several bonds, and favors different proton transfer mechanisms required for the formation of the [SrOH](+), [SrOH(2)](2+) and [SrNH(3)](2+) products.

Mechanistic insight into stereoselective carbolithiation

This article addresses the mechanistic features of asymmetric carbolithiation of β-methylstyrenes. While often the presence of functional groups is required to obtain high enantioselectivities in carbolithiation reactions, simple β-methylstyrene also gives high selectivities in (-)-sparteine-mediated addition of alkyl lithium compounds. Computational studies on the carbolithiation of β-methylstyrene with (-)-sparteine show that the observed selectivities are the result of repulsion effects in the diastereomeric transition states between the (-)-sparteine⋅alkyl lithium adduct and the β-methylstyrene, upon approximation of the two reactants. In contrast, for the ortho-amino β-methylstyrene (E)-benzyl(2-propenylphenyl)amine (4) X-ray structure analyses of intermediate lithium amides indicate a carbolithiation mechanism in which one side of the double bond is shielded by the amide moiety, leaving only one side free for approach of the chiral alkyl lithium adduct.

Methane activation by V3PO10(˙+) and V4O10(˙+) clusters: a comparative study

A series of vanadium and phosphorus heteronuclear oxide cluster cations (V(x)P(y)O(z)(+)) are prepared by laser ablation and the reactions of V(3)PO(10)˙(+) and V(4)O(10)˙(+) with methane in a fast flow reactor under the same conditions are studied. A time of flight mass spectrometer is used to detect the cluster distribution before and after reactions. In addition to previously identified reaction of V(4)O(10)˙(+) + CH(4)→ V(4)O(10)H(+) + CH(3)˙, the observation of hydrogen atom pickup cluster V(3)PO(10)H(+) suggests the reaction: V(3)PO(10)˙(+) + CH(4)→ V(3)PO(10)H(+) + CH(3)˙. The rate of the reaction of V(4)O(10)˙(+) with CH(4) is approximately 2.5 times faster than that of V(3)PO(10)˙(+) with CH(4). Density functional theory (DFT) calculations predict that structure of V(3)PO(10)˙(+) is topologically similar to that of V(4)O(10)˙(+), as well as that of P(4)O(10)˙(+), which is very similar to V(4)O(10)˙(+) in terms of methane activation in previous studies. The facile methane activation by the homo- and hetero-nuclear oxide clusters can all be attributed to the presence of an oxygen-centered radical (O˙) in these clusters. Further theoretical study indicates that the O˙ radical (or spin density of the cluster) can transfer within the high symmetry V(4)O(10)˙(+) and P(4)O(10)˙(+) clusters quite easily, and CH(4) molecule further enhances the rate of intra-cluster spin density transfer. In contrast, the intra-cluster spin density transfer within low symmetry V(3)PO(10)˙(+) is thermodynamically forbidden. The experimentally observed reactivity difference is consistent with the theoretical consideration of the intra-cluster spin density transfer.