Self-consistent reaction field calculation of solvent reorganization energy in electron transfer: a dipole-reaction field interaction model

Based on the continuum dielectric model, this work has established the relationship between the solvent reorganization energy of electron transfer (ET) and the equilibrium solvation free energy. The dipole-reaction field interaction model has been proposed to describe the electrostatic solute-solvent interaction. The self-consistent reaction field (SCRF) approach has been applied to the calculation of the solvent reorganization energy in self-exchange reactions. A series of redox couples, O₂/O⁻ ₂, NO/NO⁺, O₃/O⁻ ₃, N₃/N⁻ ₃, NO₂/NO⁺ ₂, CO₂/CO⁻ ₂, SO₂/SO⁻ ₂, and ClO₂/ClO⁻ ₂, as well as (CH₂)₂C-(-CH₂-) _n -C(CH₂)₂ (n=1 ∼ 3) model systems have been investigated using ab initio calculation. For these ET systems, solvent reorganization energies have been estimated. Comparisons between our single-sphere approximation and the Marcus two-sphere model have also been made. For the inner reorganization energies of inorganic redox couples, errors are found not larger than 15% when comparing our SCRF results with those obtained from the experimental estimation. While for the (CH₂)₂C–(–CH₂–) _n –C(CH₂)₂ (n=1 ∼ 3) systems, the results reveal that the solvent reorganization energy strongly depends on the bridge length due to the variation of the dipole moment of the ionic solute, and that solvent reorganization energies for different systems lead to slightly different two-sphere radii. Received: 19 April 2000 / Accepted: 6 July 2000 / Published online: 27 September 2000     

Crystallographic and theoretical studies of 4,4′-dimethyl-7,7′-bi([1,2,5]thiadiazolo[3,4-b]pyridylidene)–chloranilic acid (1/1) with intermolecular O–H···N hydrogen bonds and S···O heteroatom interactions

Abstract  The molecular and crystal structure of a 1:1 co-crystal of 4,4′-dimethyl-7,7′-bi([1,2,5]thiadiazolo[3,4-b]pyridylidene)–chloranilic acid, (1), has been determined by X-ray diffraction at the monoclinic space group P2₁/c with cell parameters of a = 8.422(6), b = 7.343(4), c = 16.112(7) ?, β = 104.988(8)°, V = 962.5(10) ?³ and Z = 2. In the crystal structure, two components connect via the intermolecular O–H···N hydrogen bonds [2.804(4) ?] and S···O heteroatom interaction [2.945(3) ?] with R ₂ ²(7) couplings to form a unique and infinite one-dimensional supramolecular tape structure. The calculations of (1) at the HF/6-31G(d), MP2/6-31G(d), and B3LYP/6-31G(d) levels can almost reproduce X-ray geometry. In addition, the distances of the intermolecular O–H···N and S···O interactions by MP2/6-31G(d) and B3LYP/6-31G(d) levels agree well with those in the crystal. The calculated binding energies corrected BSSE and ZPE are −4.487 (HF), −7.473 (MP2), and −5.640 (B3LYP) kcal/mol. The results suggest that the complex (1) is very stable and the dispersion interaction is significantly important for the attractive intermolecular interaction in (1). The NBO analysis has revealed that the n(N) → σ*(O–H) interaction gives the strongest stabilization to the system and the major interaction for the intermolecular S···O contact is n(O) → σ*(S–N). Index Abstract  In the crystal structure of the title compound, the molecules are linked by intermolecular O–H···N hydrogen bonds and short S···O heteroatom interactions with R ₂ ²(7) couplings to construct a unique and infinite one-dimensional supramolecular tape structure.      

The effect of basis set superposition error on the convergence of intermolecular interaction energies for deprotonated complexes

The intermolecular interaction energies of the deprotonated hydrogen-bonded complexes F(-)(HF), F(-)(H(2)O), F(-)(NH(3)), Cl(-)(HF), SH(-)(HF), H(2)P(-)(HF), OH(-)(H(2)O), OH(-)(H(2)O)(2), OH(-)(NH(3)), Cl(-)(H(2)O), SH(-)(H(2)O), H(2)P(-)(H(2)O), Cl(-)(NH(3)), SH(-)(NH(3)), H(2)P(-)(NH(3)), Cl(-)(HCl), Cl(-)(H(2)S), Cl(-)(PH(3)), SH(-)(H(2)S), SH(-)(PH(3)), and H(2)P(-)(PH(3)) were calculated with correlation consistent basis sets at the MP2, MP4, QCISD(T), and CCSD(T) levels. When the basis set is smaller, the counterpoise-uncorrected intermolecular interaction energies are closer to the complete basis set limit than the counterpoise-corrected intermolecular interaction energies. The counterpoise-uncorrected intermolecular interaction energies obtained at the MP2/aug-cc-pVDZ level of theory are close to the interaction energies obtained at the extrapolated complete basis set limit in most of the complexes. Also, we investigate the accuracy of the other levels.     

Modeling the H5+ potential-energy surface: a first attempt

 Ab initio molecular electronic structure calculations are performed for H₅ ⁺ at the QCISD(T) level of theory, using a correlation-consistent quadruple-zeta basis set. Structures, vibrational frequencies and thermochemical properties are evaluated for ten stationary points of the H₅ ⁺ hypersurface and are compared with previous calculations. The features of the H₃ ⁺…H₂ interaction at intermediate and large intermolecular distances are also investigated. Furthermore, an analytical functional form for the potential-energy surface of H₅ ⁺ is derived using a first-order diatomics-in-molecule perturbation theory approach. Its topology is found to be qualitatively correct for the short-range interaction region. Received: 15 March 2001 / Accepted: 5 July 2001 / Published online: 11 October 2001     

An atom-in-molecules and electron-localization-function study of the interaction between O2 and VxOy+/VxOy (x = 1, 2, y = 1–5) clusters

 The most stable structures of V _x O _y ⁺/V _x O _y (x=1, 2, y=1–5) clusters and their interaction with O₂ are determined by density functional calculations, the B3LYP functional with the 6-31G* basis set. The nature of the bonding of these clusters and the interaction with O₂ have been studied by topological analysis in the framework of both the atoms-in-molecules theory of Bader and the Becke–Edgecombe electron localization function. Bond critical points are localized by means of the analysis of the electron density gradient field, ∇ρ(r), and the electron localization function gradient field, ∇η(r). The values of the electron density properties, i.e., electron density, ρ(r), Laplacian of the electron density, ∇²ρ(r), and electron localization function, η(r), allow the nature of the bonds to be characterized, and linear correlation is found for the results obtained in both gradient fields. Vanadium-oxygen interactions are characterized as unshared-electron interactions, and linear correlation is observed between the electron density properties and the V–O bond length. In contrast, O₂ units involve typical shared-electron interactions, as for the dioxygen molecule. Four different vanadium–oxygen interactions are found and characterized: a molecular O₂ interaction, a peroxo O₂ ²⁻ interaction, a superoxo O₂ ⁻ interaction and a side-on O₂ ⁻ interaction. Received: 15 October 2001 / Accepted: 30 January 2002 / Published online: 24 June 2002     

Ab initio study of bonding trends for f0 actinide oxyfluoride species

 Fully relativistic, four-component Dirac–Fock calculations and quasirelativistic pseudopotential calculations at different ab initio levels are used to study the bonding trends among the naked, triatomic [OAnO] ^q+ groups or the oxyfluorides [AnO _n F _m ] ^q with f ⁰ configurations. The triatomic f ⁰ series is suggested to range from the bent ThO₂ via the linear OPaO⁺ to at least NpO₂ ³⁺, a possible new gas-phase species. The neutral oxyfluoride molecules include the experimentally unknown NpO₂F₃ and PuO₂F₄. The latter is a candidate for the so far unknown oxidation state Pu(VIII), which is found to lie considerably above Pu(VI), but to be locally stable. Their all-oxygen isoelectronic analogues are NpO₅ ³⁻, known in the solid state, and the unknown PuO₆ ⁴⁻. Further possible candidates for Pu(VIII) are PuO₄(D _4h ) and the cube-shaped PuF₈(O _h ). Isoelectronic UF₈ ²⁻ is calculated to be D _4d , in agreement with experiment. Received: 18 May 2001 / Accepted: 21 June 2001 / Published online: 11 October 2001     

A proposed modification of CBS-4M model chemistry for application to molecules of increasing molecular size

 In order to calculate more accurately the enthalpies of formation, ΔH _f°(298 K), for large molecules using the CBS-4M method, a new formulation of the empirical higher-level correction to the energy is proposed: ΔE=a|S|² _{i i} I _{i i} +b(n _α+n _β)+cΔ<S ²>+Σn _i d _{i .} The new methodology (CBS-4MB) applied to a set of 114 molecules of different size significantly decreases the mean absolute deviation from 3.78 to 2.06 kcal/mol. Received: 7 February 2001 / Accepted: 5 April 2001 / Published online: 13 June 2001     

Structure and stability of hypervalent NLi n Na2 (n = 1–4) and related species at density functional theory level

A number of configurations of NLi _n Na₂ (n = 1–4) species were optimized using the B3LYP–density functional theory method; the 6-31G^* basis set was used in this calculation. In order to study all possible dissociation energies, some related species such as NLi₂Na, NLi _n (n = 1–4), Li _n (n = 1, 2) and Na _n (n = 1, 2) were also considered. Optimizations of these species were followed by fundamental frequency calculations at the same level. Global minima of these species were shown to adopt C _{2 v} (NLi₄Na₂, NLi₂Na₂), D _{3 h} (NLi₃Na₂) and C _s (NLiNa₂ and NLi₂Na) configurations. All possible dissociation energies were obtained. Received: 30 November 1998 / Accepted: 15 October 1999 / Published online: 14 March 2000     

Theoretical predictions of the structure, gas-phase acidity and aromaticity of 1,2-diseleno-3,4-dithiosquaric acid

Results of ab initio self-consistent-field (SCF) and density functional theory (DFT) calculations of the gas-phase structure, acidity (free energy of deprotonation, ΔG^o), and aromaticity of 1,2-diseleno-3,4-dithiosquaric acid (3,4-dithiohydroxy-3-cyclobutene-1,2-diselenone, H₂C₄Se₂S₂) are reported. The global minimum found on the potential energy surface of 1,2-diseleno-3,4-dithiosquaric acid presents a planar conformation. The ZZ isomer was found to have the lowest energy among the three planar conformers and the ZZ and ZE isomers are very close in energy. The optimized geometric parameters exhibit a bond length equalization relative to reference compounds, cyclobutanediselenone, and cyclobutenedithiol. The computed aromatic stabilization energy (ASE) by homodesmotic reaction (Eq 1) is −20.1 kcal/mol (MP2(fu)/6-311+G** //RHF/6-311+G**) and −14.9 kcal/mol (B3LYP//6-311+G**//B3LYP/6-311+G**). The aromaticity of 1,2-diseleno-3,4-dithiosquaric acid is indicated by the calculated diamagnetic susceptibility exaltation (Λ) −17.91 (CSGT(IGAIM)-RHF/6-311+G**//RHF/6-311+G**) and −31.01 (CSGT(IGAIM)-B3LYP/6-311+G**//B3LYP/6-311+G**). Thus, 1,2-diseleno-3,4-dithiosquaric acid fulfils the geometric, energetic and magnetic criteria of aromaticity. The calculated theoretical gas-phase acidity is ΔG^o _1(298K)=302.7 kcal/mol and ΔG^o _2(298K)=388.4 kcal/mol. Hence, 1,2-diseleno-3,4-dithiosquaric acid is a stronger acid than squaric acid(3,4-dihydroxy-3-cyclobutene-1,2-dione, H₂C₄O₄). Received: 11 April 2000 / Accepted: 7 July 2000 / Published online: 27 September 2000     

Theoretical study of bifurcated bent blue-shifted hydrogen bonds CH<Subscript>2</Subscript>···Y

Ab initio quantum chemistry methods were applied to study the bifurcated bent hydrogen bonds Y··· H₂CZ (Z = O, S, Se) and Y···H₂CZ₂ (Z = F, Cl, Br) (Y = Cl⁻, Br⁻) at the MP2/6-311++G(d,p) and MP2/6-311++G(2df,2p) levels. The results show that in each complex there are two equivalent blue-shifted H-bonds Y···H-C, and that the interaction energies and blue shifts are large, the energy of each Y···H-C H-bond is 15–27 kJ/mol, and Δr(CH) = −0.1 − −0.5 pm and Δv(CH) = 30 − 80 cm⁻¹. The natural bond orbital analysis shows that these blue-shifted H-bonds are caused by three factors: large rehybridization; small direct intermolecular hyperconjugation and larger indirect intermolecular hyperconjugation; large decrease of intramolecular hyperconjugation. The topological analysis of electron density shows that in each complex there are three intermolecular critical points: there is one bond critical point between the acceptor atom Y and each hydrogen, and there is a ring critical point inside the tetragon YHCH, so these interactions are exactly H-bonding.     

Binding energies of hydrogen-bonded clusters from extrapolation-oriented basis sets

The MP2 and CCSD(T) basis set limit binding energies of various hydrogen-bonded clusters were estimated via basis set extrapolation employing the correlation consistent aug-cc-pVDZ and modified aug-cc-pVDZ set containing extra polarization functions from cc-pVTZ set. By adopting the optimal interval for the difference between the cardinal numbers (X) corresponding to two basis sets in the X ⁻³ type extrapolation scheme the estimated binding energies for (H₂O)_n and (HF)_n (n=3−5) are shown to be close to the reference basis set limit values within the error bounds in many cases, manifesting the significance of these basis sets in studying the structures and binding of large hydrogen-bonded clusters.     

Structures and stability of N7+ and N7− clusters

Ab initio molecular orbital theory and density functional theory have been used to study nine isomers of N₇ ionic clusters with low spin at the HF/6-31G*, MP2/6-31G*, B3LYP/6-31G*, and B3LYP/6-311(+)G* levels of theory. All stationary points are examined with harmonic vibrational frequency analyses. Four N₇ ⁺ isomers and five N₇ ⁻ isomers are determined to be local minima or very close to the minima on their potential-energy hypersurfaces, respectively. For N₇ ⁺ and N₇ ⁻, the energetically low lying isomers are open-chain structures (C _{2 v} and C _{2 v} or C₂). The results are very similar to those of other known odd-number nitrogen ions, such as N₅ ⁺, N₉ ⁺, and N₉ ⁻, for which the open-chain structures are also the global minima. This research suggests that the N₇ ionic clusters are likely to be stable and to be potential high-energy-density materials if they could be synthesized. Received: 16 July 2001 / Accepted: 8 October 2001 / Published online: 21 January 2002     

Dipole–reaction field interaction model for the solvent reorganization energy and its application to the benzoquinone–benzoquinone anion radical system

 Based on the spherical cavity approximation and the Onsager model, a dipole–reaction field interaction model has been proposed to elucidate the solvent reorganization energy of electron transfer (ET). This treatment only needs the cavity radius and the solute dipole moment in the evaluation of the solvent reorganization energy, and fits spherelike systems well. As an application, the ET reaction between p-benzoquinone and its anion radical has been investigated. The inner reorganization energy has been calculated at the level of MP2/6–31+G, and the solvent reorganization energies of different conformations have been evaluated by using the self-consistent reaction field approach at the HF/6–31+G level. Discussions have been made on the cavity radii and the values are found to be reasonable when compared with the experimental ones of some analogous intramolecular ET reactions. The ET matrix element has been determined on the basis of the two-state model. The fact that the value of the ET matrix element is about 10 times larger than RT indicates that this ET reaction can be treated as an adiabatic one. By invoking the classical Marcus ET model, a value of 4.9 × 10⁷M⁻¹s⁻¹ was obtained for the second-order rate constant, and it agrees quite well with the experimental one. Received: 19 October 2001 / Accepted: 17 January 2002 / Published online: 3 May 2002     

Density functional computation of 55Mn NMR parameters

Gradient-corrected (GGA) and hybrid variants of density functional theory are used to compute geometries and ⁵⁵Mn chemical shifts of MnO₄ ⁻, Mn(CO)₆ ⁺, Mn₂(CO)₁₀, Mn(CO)₅ X [X=H, Cl, C(O)Me], Mn(CO)₅ ⁻, Mn(NO)₃(CO), and Mn(C₅H₅)L _x [L _x =(CO)₃, C₆H₆, C₇H₈]. For this set of compounds, substituent effects on δ(⁵⁵Mn) are significantly underestimated with the pure GGA functional BPW91 and are well described with hybrid functionals such as mPW1PW91 and, in particular, B3LYP. The computed data provide evidence for solvent and counterion effects on δ(⁵⁵Mn) of MnO₄ ⁻ and Mn(CO)₆ ⁺, respectively. The latter, in the presence of Cl⁻, may be described as highly fluxional Mn(CO)₅C(O)Cl. Electric field gradients computed with the B3LYP functional can be used for a qualitative rationalization of observed trends in ⁵⁵Mn NMR line widths. Electronic supplementary material to this paper can be obtained by using the Springer LINK server located at http://dx.doi.org/10.1007/s002140020338x Received: 17 January 2002 / Accepted: 13 March 2002 / Published online: 3 June 2002     

Synthesis,spectroscopic, thermal and biological aspect of mixed ligand copper(II) complexes

Derivative of 8-hydroxyquinoline i.e. Clioquinol is well known for its antibiotic properties, drug design and coordinating ability towards metal ion such as Copper(II). The structure of mixed ligand complexes has been investigated using spectral, elemental and thermal analysis. In vitro anti microbial activity against four bacterial species were performed i.e. Escherichia coli, Pseudomonas aeruginosa, Serratia marcescens, Bacillus substilis and found that synthesized complexes (15–37 mm) were found to be significant potent compared to standard drugs (clioquinol i.e. 10–26 mm), parental ligands and metal salts employed for complexation. The kinetic parameters such as order of reaction (n = 0.96–1.49), and the energy of activation (E _a = 3.065–142.9 kJ mol⁻¹), have been calculated using Freeman–Carroll method. The range found for the pre-exponential factor (A), the activation entropy (S* = −91.03 to−102.6 JK⁻¹ mol⁻¹), the activation enthalpy (H* = 0.380–135.15 kJ mol⁻¹), and the free energy (G* = 33.52–222.4 kJ mol⁻¹) of activation reveals that the complexes are more stable. Order of stability of complexes were found to be [Cu(A⁴)(CQ)OH] · 4H₂O > [Cu(A³)(CQ)OH] · 5H₂O > [Cu(A¹)(CQ)OH] · H₂O > [Cu(A²)(CQ)OH] · 3H₂O     

A correlation-consistent basis set for Fe

 A series of correlation-consistent basis sets are developed for Fe. Our best computed ⁵F–⁵D separation in the Fe atom is in excellent agreement with experiment. Our best estimate for the FeCO D ₀ value is in good agreement with experiment. The ⁵Σ⁻–³Σ⁻ separation in FeCO has an error of 3.6 kcal/mol; while the origin of this error is not clear, it is probably not due to the basis set. Received: 5 March 2001 / Accepted: 2 May 2001 / Published online: 9 August 2001     

Synthesis, structure and spectroscopic characterization of a new organic cation diphosphate: [2,6-(C2H5)2C6H3NH3]2H2P2O7?·?2H2O

The chemical preparation, crystal structure and spectroscopic characterization of [2,6-(C₂H₅)₂C₆H₃NH₃]₂H₂P₂O₇ · 2H₂O have been reported. The compound crystallizes in the monoclinic system in space group P2₁/c and cell parameters a = 14.323(2), b = 11.158(3), c = 16.387(2) ? and β = 96.34(3)°; V = 2602.8(9) ?³ and Z = 4. Crystal structure has been determined and refined to R = 0.044, using 3528 independent reflections. The atomic arrangement of the title compound shows anionic layer of formulae [H₂P₂O₇(H₂O)₂] _n ²ⁿ⁻ stacked along the c-axis. The 2,6-diethylanilinium cations establish on both sides of these inorganic layer hydrogen bonds so as to contribute to the intralayer cohesion in the network. The different building species are held together by means of O–H···O and N–H···O intermolecular hydrogen bonds in addition to electrostatic and van der Waals interactions.     

A B3LYP study on counterpoise-corrected geometry optimizations for hydrated complexes of [K(H2O)n] and [Na(H2O)n]

We report the basis set dependencies and the basis set superposition errors for the hydrated complexes of K⁺ and Na⁺ ions in relation to the recent studies of the KcsA potassium channel. The basis set superposition errors are estimated by the geometry optimizations at the counterpoise-corrected B3LYP level. The counterpoise optimizations alter the hydration distances by about 0.02–0.03 Å. The enthalpies and free energies for K⁺ + n(H₂O) → [K(H₂O)_n]⁺ and Na⁺ + n(H₂O) → [Na(H₂O)_n]⁺ (n = 1–6) are compared between the theoretical and experimental values. The results show that the addition of diffuse functions to K, Na, and O species are effective. However, it is also found that the counterpoise corrections using diffuse functions work so as to underestimate the free energies for the complexes with increasing the hydration number. The stabilization energies in aqueous solution are larger for a Na⁺ ion than for a K⁺ ion, suggesting the contributions of their dehydration processes to the ion selectivity of the KcsA potassium channel. The changes in coordination distance between the isolated [K(H₂O)₈]⁺ and the [K(H₂O)₈]⁺ in the KcsA potassium channel indicate the importance of hydrogen bondings between the first hydration shell and the outer hydration shells.     

Theoretical studies on anionic clusters of sulfate anions and carbon dioxide, SO 4?1/?2 (CO2)n, n?=?1?4

Geometry optimizations were performed on monoanionic and dianionic clusters of sulfate anions with carbon dioxide, SO₄^−1/−2(CO₂) _n , for n = 1–4, using the B3PW91 density functional method with the 6-311 + G(3df) basis set. Limited calculations were carried out with the CCSD(T) and MP2 methods. Binding energies, as well as adiabatic and vertical electron detachment energies, were calculated. No covalent bonding is seen for monoanionic clusters, with O₃SO–CO₂ bond distances between 2.8 and 3.0 ?. Dianionic clusters show covalent bonding of type [O₃S–O–CO₂]⁻², [O₃S–O–C(O)O–CO₂]⁻², and [O₂C–O–S(O₂)–O–CO₂]⁻², where one or two oxygens of SO₄⁻² are shared with CO₂. Starting with n = 2, the dianionic clusters become adiabatically more stable than the corresponding monoanionic ones. Comparison with SO₄^−1/−2(SO₂) _n and CO₃^−1/−2(SO₂) _n clusters, the binding energies are smaller for the present SO₄^−1/−2(CO₂) _n systems, while stabilization of the dianion occurs at n = 2 for both SO₄⁻²(CO₂) _n and SO₄⁻²(SO₂) _n , but only at n = 3 for CO₃⁻²(SO₂) _n .