Mechanism of the oxidation reaction of Cu with N2O via nonadiabatic electron transfer

We treat the present work as an attempt to elucidate the mechanism of the oxidation reaction of the Cu atom by nitrous oxide based on our recent work (Kryachko, E. S.; Vinckier, C.; Nguyen, M. T. J Chem Phys 2001, 114, 7911) on the electron attachment to this molecule. We suggest that the title reaction in its Arrhenius regime occurs via the nonadiabatic electron transfer from Cu to the oxygen atom at the crossing of the potential energy surfaces Cu(4s ²S_1/2) + N₂O(X ¹Σ⁺) and Cu⁺ + N₂O^?, where the latter is linked to the complex N₂O^? originated from the higher‐energy T‐shape N₂O molecule and discovered in the aforementioned work. The calculations performed in the present work using a variety of quantum chemical methods support the proposed model. We also show the existence of other reaction pathways of the title reaction that, we believe, contribute to its non‐Arrhenius behavior observed experimentally at T > 1190 K. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Synthesis, crystal and electronic structures, and magnetic properties of LiLn9Mo16O35 (Ln = La, Ce, Pr, and Nd) compounds containing the original cluster Mo16O36

The new compounds LiLn(9)Mo(16)O(35) (Ln=La, Ce, Pr, and Nd) were synthesized from stoichiometric mixtures of Li(2)MoO(4), Ln(2)O(3), Pr(6)O(11) or CeO(2), MoO(3), and Mo heated at 1600 °C for 48 h in a molybdenum crucible sealed under a low argon pressure. The crystal structure, determined from a single crystal of the Nd member, showed that the main building block is the Mo(16)O(36) unit, the Mo(16) core of which is totally new and results from the fusion of two bioctahedral Mo(10) clusters. It can also be viewed as a fragment of an infinite twin chain of edge-sharing Mo(6) octahedra. The Mo(16)O(36) cluster units share some oxygen atoms to form infinite chains running parallel to the b axis, which are separated by the rare-earth and lithium cations. (7)Li-NMR experiments, carried out at high field on the nonmagnetic LiLa(9)Mo(16)O(35), provided insights into the local environment of the lithium ions. Magnetic susceptibility measurements confirmed the trivalent oxidation state of the magnetic rare-earth cations and indicated the absence of localized moments on the Mo(16) clusters. The electronic structure of the LiLn(9)Mo(16)O(35) compounds was analyzed using molecular and periodic quantum calculations. The study of the molecular orbital diagrams of isolated Mo(16)O(36) models allowed the understanding of this unique metallic architecture. Periodic density functional theory calculations demonstrated that few interactions occur between the Mo(16) clusters, and predicted semiconducting properties for LiLn(9)Mo(16)O(35) as a band gap of 0.57 eV was computed for the lanthanum phase.     

Density Functional Theory for the Investigation of Catalytic Activity of X@Cu12 (X =Cu,Ni, Co,or Fe) for N2O Decomposition

We have investigated the reaction mechanism for N2 O decomposition on Cu13 via density functional theory. It is found that N2 O decomposition on the cluster is more prone to be along the Eley-Rideal(ER) pathway in comparison with the Langmuir-Hinshelwood(LH) channel. There exists structural relaxation for Cu13 cluster in the reaction, which may influence the catalytic activity of cluster for the subsequent N2 O decomposition. The core atom in the Cu13 cluster is substituted with the Fe, Co, or Ni to enhance structural stability and prevent from the obvious configuration relaxation in the reaction. Note that these bimetallic clusters are of icosahedra as the Cu13. They have activities for N2 O dissociation along ER pathway and the heteroatom in the cluster can prevent configuration from relaxation. Finally, the Ni@Cu12 cluster can be as a superior catalyst in a complete catalytic cycle via comparison in this study.     

Synthesis and Characterization of Surfactant‐encapsulated Polyoxoanions: [(CnH2n + 1)2N(CH3)2]12[Mo36(NO)4Om(H2O)16] (n = 12, 18)

By employing electrostatic interaction as driving force, an organic/inorganic composite with positively charged dimethyl dialkyl‐chain ammonium surfactants encapsulating negatively charged (NH₄)12[Mo₃₆(NO)₄O₁₀₈(H₂O)₁₆]. 33H₂O polyoxoanion was prepared. The structure of the novel organic/inorganic hybrid particle with hydrophilic core and hydrophobic shell in a defined stoichiometric ratio was confirmed by element analysis, ¹H NMR and FT‐IR spectra. The property of the polyoxoanion was changed due to the encapsulation and it can be dissolved in organic solvent such as chloroform, benzene and toluene, but not dissolved in water.     

Bismuth(III) Complexes with N,N‐Di(2‐hydroxylethyl)aminodithiocarboxylate: Synthesis and Crystal Structure of {Bi[S2CN(C2H4OH)2]2[1, 10‐Phen]2(NO3)}·3H2O and (Bi[S2CN(C2H4OH)2]3}2

Two novel one‐ and two‐dimensional network structure bismuth(III) complexes with N, N‐di(2‐hydroxylethyl)‐aminodithiocarboxylate, {Bi[S₂CN(C₂H₄OH)₂]₂[1, 10‐Phen]₂(NO₃)}·3H₂O (1) and (Bi[S₂CN(C₂H₄OH)₂]₃)₂ (2) were synthesized. Their crystal and molecular structures were determined by X‐ray single crystal diffraction analysis. The crystal 1 belongs to monoclinic system with space group C2/c, a=1.6431(7) nm, b=2.4323(10) nm, c= 1.2646(5) nm, β=126. 237(5), Z=4, V=4.076(3) nm³, D_c=1.757 Mg/m^3, μ=4.598 mm^?1, F(000)=2156, R= 0.0211, wR=0.0369. The structure shows a distorted square antiprism configuration with eight‐coordination for the central Bi atom. The one‐dimensional chain structure was formed by H‐bonding interaction between hydroxyl group of N, N‐di(2‐hydroxylethyl)aminodithiocarboxylate ligands and crystal water. The crystal 2 belongs to monoclinic system with space group p2(1)/c, a= 1.1149(4) nm, b=2.1274(8) nrn, c=2.2107(8) nm, β=98.325(8)°, 2=4, V=5. 188(3) nm³, Dc=1.920 Mg/m³, μ=7.315 mm^?1, F(000)=2944, R=0.0565, wR=0.0772. The structure shows a distorted square antiprism configuration with eight‐coordination for the central Bi atoms. The two‐dimensional network structure was formed by H‐bonding interaction between adjacent molecules.     

Density functional theory study of trans-dioxo complexes of iron, ruthenium, and osmium with saturated amine ligands, trans-[M(O)2(NH3)2(NMeH2)2]2+ (M=Fe, Ru, Os), and detection of [Fe(qpy)(O)2]n+ (n=1, 2) by high-resolution ESI mass spectrometry

Density functional theory (DFT) calculations on trans-dioxo metal complexes containing saturated amine ligands, trans-[M(O)2(NH3)2(NMeH2)2]2+ (M=Fe, Ru, Os), were performed with different types of density functionals (DFs): 1) pure generalized gradient approximations (pure GGAs): PW91, BP86, and OLYP; 2) meta-GGAs: VSXC and HCTH407; and 3) hybrid DFs: B3LYP and PBE1PBE. With pure GGAs and meta-GGAs, a singlet d2 ground state for trans-[Fe(O)2(NH3)2(NMeH2)2]2+ was obtained, but a quintet ground state was predicted by the hybrid DFs B3LYP and PBE1PBE. The lowest transition energies in water were calculated to be at lambda approximately 509 and 515 nm in the respective ground-state geometries from PW91 and B3LYP calculations. The nature of this transition is dependent on the DFs used: a ligand-to-metal charge-transfer (LMCT) transition with PW91, but a pi(Fe-O)-->pi*(Fe-O) transition with B3LYP, in which pi and pi* are the bonding and antibonding combinations between the dpi(Fe) and ppi(O(2-)) orbitals. The FeVI/V reduction potential of trans-[Fe(O)2(NH3)2NMeH2)2]2+ was estimated to be +1.30 V versus NHE based on PW91 results. The [Fe(qpy)(O)2](n+) (qpy=2,2':6',2':6',2':6',2'-quinquepyridine; n=1 and 2) ions, tentatively assigned to dioxo iron(V) and dioxo iron(VI), respectively, were detected in the gas phase by high-resolution ESI-MS spectroscopy.     

六聚同多酸阴离子M_6O_(19)~(n-)(M=Mo,W,n=2;M=Nb,Ta,n=8)电子结构和化学性质的密度泛函理论研究

采用B3LYP方法在LanL2DZ水平上计算了六聚同多阴离子 (M6On-19,M =Mo和W ,n =2 ;M =Nb和Ta ,n =8)的电子结构 ,分析了它们的前线轨道、分子静电势 (MEP) .计算结果表明 ,Nb6O8-19和Ta6O8-19是电子给体 ,而Mo6O2 -19和W6O2 -19则是电子受体 ,这与它们在溶液中具有不同的化学性质是一致的     

A comparative study on the reaction mechanisms of Cp2MH2 (M = Cr,Mo, W) with HBF4

The reaction mechanisms of group 6 transition metal dihydride complexes, Cp₂MH₂ (M = Cr, Mo, and W), and HBF₄ were studied using M06‐L density functional theory. The chemical bond changes along the reaction pathway are analyzed by the topological analysis of electron density. The calculated results show that the interactions between the H atom of HBF₄ and Cp₂MH₂ are stronger than those between Cp₂MH₂ and BF₃; additionally, due to the low energy barriers in the subsequent reaction, all the title reactions can occur easily, and the yield rates of the Cp₂MH₂ + HBF₄ reactions are high. For M = Cr and Mo, the [Cp₂MH₃]⁺ in the product Cp₂MH₃·BF₄ is in the nonclassic dihydrogen‐hydride form ([Cp₂M(η²‐H₂)H]⁺). [Cp₂CrH₃]⁺ and [Cp₂MoH₃]⁺are unstable, and H₂ can be easily liberated from them. For M = W, the final product is Cp₂WH₃·BF₄, and [Cp₂WH₃]⁺ is stable in the classic trihydride form.     

Synthesis,Crystal Structure,and Bonding of (PCl4)2[Mo2Cl10], the First Compound in Mo–P–Cl System

An ampule reaction between Mo and PCl₅ at 200 °C yielded (PCl₄)₂[Mo₂Cl₁₀], the first ternary compound in Mo–P–Cl system. Single crystal X-ray diffraction gave a triclinic unit cell: a = 6.870(1), b = 8.892(2), c = 9.423(2) Å, α = 100.24(2), β = 95.55(2), γ = 96.12(2)° (V = 559.3(2) ų, Z = 1, sp. gr. P1, wR₂ = 0.0575 and R₁ = 0.0279. The ionic compound is built from edge sharing bioctahedra [Mo₂Cl₁₀]^2– and two tetrahedra PCl₄⁺. The averaged Mo–Cl_b distance, 2.503(1) Å, is longer than the Mo–Cl_t distance, 2.33(2) Å. The Mo … Mo distance, 3.77 Å, indicates the absence of a direct Mo–Mo interaction. Semiempirical and ab initio calculations showed the possibility for [Mo₂Cl₁₀]^2– to exist with long and short Mo to Mo distances, the letter corresponding to the Mo–Mo bond.     

Structures and electron affinities of the di-arsenic fluorides As2Fn/As2Fn- (n=1-8)

Developments in the preparation of new materials for microelectronics are focusing new attention on molecular systems incorporating several arsenic atoms. A systematic investigation of the As2Fn/As2Fn- systems was carried out using Density Functional Theory methods and a DZP++ quality basis set. Global and low-lying local geometric minima and relative energies are discussed and compared. The three types of neutral-anion separations reported in this work are: the adiabatic electron affinity (EAad), the vertical electron affinity (EAvert), and the vertical detachment energy (VDE). Harmonic vibrational frequencies pertaining to the global minimum for each compound are reported. From the first four studied species (As2Fn, n=1-4), all neutral molecules and their anions are shown to be stable with respect to As-As bond breaking. The neutral As2F molecule and its anion are predicted to have Cs symmetry. We find the trans F-As-As-F isomer of C2h symmetry and a pyramidalized vinylidene-like As-As-F2- isomer of Cs symmetry to be the global minima for the As2F2 and As2F2- species, respectively. The lowest lying minima of As2F3 and As2F3- are vinyl radical-like structures F-As-As-F2 of Cs symmetry. The neutral As2F4 global minimum is a trans-bent (like Si2H4) F2-As-As-F2 isomer of C2 symmetry, while its anion is predicted to have an unusual fluorine-bridged (C(1)) structure. The global minima of the neutral As2Fn species, n=5-8, are weakly bound complexes, held together by dipole-dipole interactions. All such structures have the AsFm-AsFn form, where (m,n) is (2,3) for As2F5, (3,3) for As2F6, (4,3) for As2F7), and (5,3) for As2F8. For As2F8 the beautiful pentavalent F4As-AsF4 structure (analogous to the stable AsF5 molecule) lies about 30 kcal/mol above the AsF3 . . . AsF5 complex. The stability of AsF(5) depends crucially on the strong As-F bonds, and replacing one of these with an As-As bond (in F4As-AsF4) has a very negative impact on the molecule's stability. The anions As2Fn-, n=5-8, are shown to be stable with respect to the As-As bond breaking, and we predict that all of them have fluorine-bridged or fluorine-linked structures. The zero-point vibrational energy corrected adiabatic electron affinities are predicted to be 2.28 eV (As2F), 1.95 eV (As2F2), 2.39 eV (As2F3), 1.71 eV (As2F4), 2.72 eV (As2F5), 1.79 eV (As2F6), 5.26 eV (As2F7), and 3.40 eV (As2F8) from the BHLYP method. Vertical detachment energies are rather large, especially for species with fluorine-bridged global minima, having values up to 6.45 eV (As2F7, BHLYP).     

Theoretical study of bifurcated hydrogen bonding effects on the 1J(N,H), 1hJ(N,H), 2hJ(N,N) couplings and 1H, 15N shieldings in model pyrroles

According to the density functional theory calculations, the X···H···N (X?N, O) intramolecular bifurcated (three‐centered) hydrogen bond with one hydrogen donor and two hydrogen acceptors causes a significant decrease of the ^1hJ(N,H) and ^2hJ(N,N) coupling constants across the N? H···N hydrogen bond and an increase of the ¹J(N,H) coupling constant across the N? H covalent bond in the 2,5‐disubsituted pyrroles. This occurs due to a weakening of the N? H···N hydrogen bridge resulting in a lengthening of the N···H distance and a decrease of the hydrogen bond angle at the bifurcated hydrogen bond formation. The gauge‐independent atomic orbital calculations of the shielding constants suggest that a weakening of the N? H···N hydrogen bridge in case of the three‐centered hydrogen bond yields a shielding of the bridge proton and deshielding of the acceptor nitrogen atom. The atoms‐in‐molecules analysis shows that an attenuation of the ^1hJ(N,H) and ^2hJ(N,N) couplings in the compounds with bifurcated hydrogen bond is connected with a decrease of the electron density ρ_H···N at the hydrogen bond critical point and Laplacian of this electron density ?²ρ_H···N. The natural bond orbital analysis suggests that the additional N? H···X interaction partly inhibits the charge transfer from the nitrogen lone pair to the σ*_{N? H} antibonding orbital across hydrogen bond weakening of the ^1hJ(N,H) and ^2hJ(N,N) trans‐hydrogen bond couplings through Fermi‐contact mechanism. An increase of the nitrogen s‐character percentage of the N? H bond in consequence of the bifurcated hydrogen bonding leads to an increase of the ¹J(N,H) coupling constant across the N? H covalent bond and deshielding of the hydrogen donor nitrogen atom. Copyright © 2010 John Wiley & Sons, Ltd.     

钼(钨)/铜/硫三核簇合物[A]2[MS4(CuCN)2] (M=Mo,W;A=Et4N,PPh4)的合成及晶体结构

合成了四个三核簇合物[A]2[MS4(CuCN)2](1A＝Et4N,M＝Mo;2A＝PPh4,M＝W;3A＝Et4N,M＝W;4A＝PPh4,M＝Mo),测定了[Et4N]2[MoS4(CuCN)2]*H2O(1*H2O)和[PPh4]2[WS4(CuCN)2]*0.5DMF*H2O(2*0.5DMF*H2O)的晶体结构.1和2的簇阴离子[MS4(CuCN)2]2-(M＝Mo,W)均具有一个双齿配体MS42-和两个CuCN形成的近似D2d对称性结构.     

Synthesis and Structural Characterization of a Salt{[Co(Phen)3][Mo2S2(μ-S)2(edt)2]}2·(DMSO)2·(Et2O)(Phen = 1,10-Phenanthroline,edt = Ethane-1,2-dithiolate)

Reaction of [Et4N]2[Mo2S2(μ-S)2(edt)2] with CoCl2(6H2O and Phen in MeCN followed by recrystallization in DMSO/Et2O gave rise to dark-red block crystals of {[Co(Phen)3]- [Mo2S2(μ-S)2(edt)2]}2·(DMSO)2·(Et2O) 1 (C88H86Co2Mo4N12O3S18). 1 crystallizes in the monoclinic system, space group P21/c with a = 24.631(4), b = 16.117(3), c = 24.791(4) (A), β = 92.835°, V = 9829.3(3) (A)3, Z = 4, Mr = 2438.57, Dc = 1.648 g/cm3, F(000) = 4928, μ = 12.61 cm-1, R = 0.0936 and wR = 0.1682 for 12998 observed reflections with I > 2.0σ(I). In the structure of 1, the Co atom of the [Co(Phen)3]2+ dication is octahedrally coordinated by three Phen ligands. The Mo atom of the [Mo2S2(μ-S)2(edt)2]2- dianion is coordinated by two μ-S, one terminal S and two S atoms from edt, forming a distorted square pyramidal geometry. The mean Co-N and Mo…Mo bond distances are 2.139 and 2.872 (A), respectively.     

双帽Keggin型杂多阴离子[PM12O40(VO)2]n-(M=Mo,n=5; M=V,n=9)的离散变分方法研究

使用密度泛函理论的离散变分方法(DFT-DVM)研究了双帽Keggin型杂多阴离子[PM₁₂O₄₀(VO)₂]^n--(M=Mo,n=5; M=V,n=9),即[PMo₁₂O₄₀(VO)₂]^5- (a)和[PV₁₂O₄₀(VO)₂]^9- (b)的电子结构,讨论了双帽的形成对Keggin型杂多阴离子的电子结构和催化性质的影响,并与其Keggin型杂多阴离子(PM₁₂O₄₀)_n-(M=Mo,n=3; M=V,n=15)的计算结果进行了对比分析,计算结果表明,双帽的形成对Keggin型杂多阴离子的电子结构产生了很大的影响,因而它们在催化活性上可能会表现出较大的差异.     

双帽Keggin型杂多阴离子[PM12O40(VO)2]n-(M=Mo,n=5; M=V, n=9)的离散变分方法研究

使用密度泛函理论的离散变分方法(DFT-DVM)研究了双帽Keggin型杂多阴离子[PM12O40(VO)2]n-(M=Mo, n=5; M=V, n=9),即[PMo12O40(VO)2]5- (a)和[PV12O40(VO)2]9- (b)的电子结构,讨论了双帽的形成对Keggin型杂多阴离子的电子结构和催化性质的影响,并与其Keggin型杂多阴离子(PM12O40)n-(M=Mo, n=3; M=V, n=15)的计算结果进行了对比分析,计算结果表明,双帽的形成对Keggin型杂多阴离子的电子结构产生了很大的影响,因而它们在催化活性上可能会表现出较大的差异.     

Structural and Spectroscopic Properties of Linear Carbon Chains NC2nN and HC2n+1N (n = 1～10)

Using density functional theory, geometries and vibrational frequencies of linear chains NC2nN and HC2n+1N (n = 1～ 10) have been investigated.Time-dependent density functional theory (TD-DFT) has been used to calculate the vertical transition energies and oscillator strengths for the X 1∑+k → 11∑+u transition in NC2nN (n = 1 ～10) and X1∑+ → 11∑+ transition in HC2n+1N (n =1 ～7).On the basis of present calculations, the explicit expressions for the size dependence of the excitation energy and the first adiabatic ionization energy in both carbon chains have been suggested.     

Formation of abundant [Pb(H2O)]2+ by ligand-exchange reaction between [Pb(N2)n]2+ (n = 1-3) and H2O

Doubly charged lead monohydrate, [Pb(H2O)]2+, was predicted to be unstable in the gas phase, but it has recently been observed to form in low yield via ligand change between [Pb(CH3CN)]2+ and H2O [Shi, T.; Orlova, G.; Guo, J.; Bohme, D. K.; Hopkinson, A. C.; Siu, K. W. M. J. Am. Chem. Soc. 2004, 126, 7975-7980]. Here we report that abundant [Pb(H2O)]2+ is formed in the gas phase by ligand-exchange reaction between [Pb(N2)n]2+ (n = 1-3) and water after collisional activation. Density functional theory has been used to examine the ligand-exchange reaction profile. A comparison of the potential-energy surfaces between [Pb(N2)]2+ and [Pb(CH3CN)]2+ reacting with H2O provides strong evidence that the ligand-exchange reaction of [Pb(N2)]2+ with H2O to form [Pb(H2O)]2+ is more efficient than that of [Pb(CH3CN)]2+ with H2O.     

Synthesis and structures of silicon-, germanium-, and tin-containing imido-alkyl molybdenum complexes (ArN)2Mo(CH2EMe3)2 (E = Si, Ge, Sn)

New silicon-, germanium-, and tin-containing imido-alkyl molybdenum complexes (ArN)₂Mo(CH₂EMe₃)₂ (Ar is 2,6-diisopropylphenyl; E = Si (1), Ge (2), Sn (3)) were prepared in the crystalline state in 58–66% yields by the reactions of the (ArN)₂MoCl₂(DME) complex with alkyllithium derivatives Me₃ECH₂Li (E = Si or Ge) or the Grignard reagents Me₃ECH₂MgCl (E = Ge or Sn). The structures of complexes 1–3 and the known analog (ArN)₂Mo(CH₂Bu^t)₂ (4) were established by X-ray diffraction analysis. Complexes 1–3 were found to be isostructural. The coordination environment about the Mo atom can be described as a distorted tetrahedron. Complex 4 has a similar structure. The Mo-C distance tends to decrease with increasing electron donating ability of the EMe₃ group.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 597–600, March, 2005.     

Synthesis,Characterization, and Catalytic Exploration of Mononuclear Mo(VI) Dioxido Complexes of (Z)-1-R-2-(4′,4′-Dimethyl-2′-oxazolin-2′-yl)-eth-1-en-1-ates

The coordination chemistry of the title ligands with Mo metal centers was investigated. Thus, the synthesis and characterization (NMR, X-ray diffraction) of four mononuclear formally Mo(6+) complexes of (Z)-1-R-2-(4′,4′-dimethyl-2′-oxazolin-2′-yl)-eth-1-en-1-ates (L: R = –Ph, –Ph-p-NO₂, –Ph-p-OMe and –t-Bu), derived from the part enols (LH), is described. The resulting air-stable MoO₂L₂ complexes (1–4) exist, as shown by single-crystal X-ray diffraction experiments, in the cis-dioxido-trans(N)-κ²-N,O-L conformation in the solid state for all four examples. This situation was further probed using semi-empirical PM6(tm) calculations. Complexes 1–4 represent the first Mo complexes of this ligand class and, indeed, of Group 6 metals in general. Structural and spectroscopic comparisons were made between these and related Mo(6+) compounds. Complex 1 (R = –Ph) was studied for its ability to selectively catalyze the production of poly-norbornene from the monomer in the presence of MAO. This, unfortunately, only resulted in the synthesis of insoluble, presumably highly cross-linked, polymeric and/or oligomeric materials. However, complexes 1–4 were demonstrated to be highly effective for catalyzing benzoin to benzil conversion using DMSO as the O-transfer agent. This catalysis work is likewise put into perspective with respect to analogous Mo(6+) complexes.     

An ab initio study of water clusters in gas phase and bulk aqueous media: (H2O)n,n=1–12

Geometries of several clusters of water molecules including single minimum energy structures of n‐mers (n=1–5), several hexamers and two structures of each of heptamer to decamer derived from hexamer cage and hexamer prism were optimized. One structural form of each of 11‐mer and 12‐mer were also studied. The geometry optimization calculations were performed at the RHF/6‐311G* level for all the cases and at the MP2/6‐311++G** level for some selected cases. The optimized cluster geometries were used to calculate total energies of the clusters in gas phase employing the B3LYP density functional method and the 6‐311G* basis set. Frequency analysis was carried out in all the cases to ensure that the optimized geometries corresponded to total energy minima. Zero‐point and thermal free energy corrections were applied for comparison of energies of certain hexamers. The optimized cluster geometries were used to solvate the clusters in bulk water using the polarized continuum model (PCM) of the self‐consistent reaction field (SCRF) theory, the 6‐311G* basis set, and the B3LYP density functional method. For the cases for which MP2/6‐311++G** geometry optimization was performed, solvation calculations in water were also carried out using the B3LYP density functional method, the 6‐311++G** basis set, and the PCM model of SCRF theory, besides the corresponding gas‐phase calculations. It is found that the cage form of water hexamer cluster is most stable in gas phase among the different hexamers, which is in agreement with the earlier theoretical and experimental results. Further, use of a newly defined relative population index (RPI) in terms of successive total energy differences per water molecule for different cluster sizes suggests that stabilities of trimers, hexamers, and nonamers in gas phase and those of hexamers and nonamers in bulk water would be favored while those of pentamer and decamer in both the phases would be relatively disfavored. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 90–104, 2001