Langevin dynamics simulations of polymer translocation through nanopores

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of an external driving force, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau(e) required for the polymer to completely exit the pore on either side. The distribution of the escape times is wide and has a long tail. We find that tau(e) scales with the chain length N as tau(e) approximately N(1+2nu), where nu is the Flory exponent. For driven translocation, we concentrate on the influence of the friction coefficient xi, the driving force E, and the length of the chain N on the translocation time tau, which is defined as the time duration between the first monomer entering the pore and the last monomer leaving the pore. For strong driving forces, the distribution of translocation times is symmetric and narrow without a long tail and tau approximately E(-1). The influence of xi depends on the ratio between the driving and frictional forces. For intermediate xi, we find a crossover scaling for tau with N from tau approximately N(2nu) for relatively short chains to tau approximately N(1+nu) for longer chains. However, for higher xi, only tau approximately N(1+nu) is observed even for short chains, and there is no crossover behavior. This result can be explained by the fact that increasing xi increases the Rouse relaxation time of the chain, in which case even relatively short chains have no time to relax during translocation. Our results are in good agreement with previous simulations based on the fluctuating bond lattice model of polymers at intermediate friction values, but reveal additional features of dependency on friction.     

Stretching semiflexible polymer chains: evidence for the importance of excluded volume effects from Monte Carlo simulation

Semiflexible macromolecules in dilute solution under very good solvent conditions are modeled by self-avoiding walks on the simple cubic lattice (d = 3 dimensions) and square lattice (d = 2 dimensions), varying chain stiffness by an energy penalty ε(b) for chain bending. In the absence of excluded volume interactions, the persistence length l(p) of the polymers would then simply be l(p) = l(b)(2d - 2)(-1)q(b) (-1) with q(b) = exp(-ε(b)/k(B)T), the bond length l(b) being the lattice spacing, and k(B)T is the thermal energy. Using Monte Carlo simulations applying the pruned-enriched Rosenbluth method (PERM), both q(b) and the chain length N are varied over a wide range (0.005 ≤ q(b) ≤ 1, N ≤ 50,000), and also a stretching force f is applied to one chain end (fixing the other end at the origin). In the absence of this force, in d = 2 a single crossover from rod-like behavior (for contour lengths less than l(p)) to swollen coils occurs, invalidating the Kratky-Porod model, while in d = 3 a double crossover occurs, from rods to Gaussian coils (as implied by the Kratky-Porod model) and then to coils that are swollen due to the excluded volume interaction. If the stretching force is applied, excluded volume interactions matter for the force versus extension relation irrespective of chain stiffness in d = 2, while theories based on the Kratky-Porod model are found to work in d = 3 for stiff chains in an intermediate regime of chain extensions. While for q(b) ? 1 in this model a persistence length can be estimated from the initial decay of bond-orientational correlations, it is argued that this is not possible for more complex wormlike chains (e.g., bottle-brush polymers). Consequences for the proper interpretation of experiments are briefly discussed.     

Influence of substitution on kinetics and mechanism of ring transformation of substituted S-[1-phenylpyrrolidin-2-on-3-yl]isothiuronium salts

Twelve new substituted S-(1-phenylpyrrolidin-2-on-3-yl)isothiuronium bromides and twelve corresponding 2-imino-5-(2-phenylaminoethyl)thiazolidin-4-ones have been prepared and characterised. Kinetics and mechanism of transformation reaction of S-[1-(4-methoxyphenyl)pyrrolidin-2-on-3-yl]isothiuronium bromide and its N,N-dimethyl derivative 5a into corresponding substituted thiazolidin-4-ones 2a and 6a have been studied in aqueous solutions of amine buffers (pH 8.1-11.5) and sodium hydroxide solutions (0.005-0.5 mol l(-1)) at 25 degrees C and at I= 1 mol l(-1) under pseudo-first-order reaction conditions. The kinetics observed show that the transformation reaction is subject to general acid-base, and hydroxide ion catalyses. Acid catalysis does not operate in the transformation of 1a; the rate-limiting step of the base-catalysed transformation is the decomposition of bicyclic tetrahedral intermediate In(+/-) and the Br?nsted dependence is non-linear (pK(a) approximately 9.8). In the case of derivative 5a both base and acid catalyses make themselves felt. In the base catalysis, the rate-limiting step consists of the decomposition of bicyclic intermediate In, and the Br?nsted dependence is linear (beta = 0.9; pK(a) > 11.5). The acid-catalysed transformation of 5a also proceeds via the intermediate In, and the reaction is controlled by diffusion (alpha approximately equal to 0). With compound 5a in triethylamine and butylamine buffers, the general base catalysis changes into specific base catalysis. The effect of substitution in aromatic moiety of compounds 1a-h and 3a-h on the course of the transformation reaction has been studied in solutions of sodium hydroxide (0.005-0.5 mol l(-1)) at 25 degrees C by the stopped-flow method. The electron-acceptor substituents 4-NO(2) and 4-CN do not obey the Hammett correlation, which is due to a suppression of cross-conjugation in the ring-closure step of the transformation reaction.     

Gas-phase protonation thermochemistry of adenosine

The goal of this work was to obtain a detailed insight on the gas-phase protonation energetic of adenosine using both mass spectrometric experiments and quantum chemical calculations. The experimental approach used the extended kinetic method with nanoelectrospray ionization and collision-induced dissociation tandem mass spectrometry. This method provides experimental values for proton affinity, PA(adenosine) = 979 +/- 1 kJ.mol (-1), and for the "protonation entropy", Delta p S degrees (adenosine) = S degrees (adenosineH (+)) - S degrees (adenosine) = -5 +/- 5 J.mol (-1).K (-1). The corresponding gas-phase basicity is consequently equal to: GB(adenosine) = 945 +/- 2 kJ.mol (-1) at 298K. Theoretical calculations conducted at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31+G(d,p) level, including 298 K enthalpy correction, predict a proton affinity value of 974 kJ.mol (-1) after consideration of isodesmic proton transfer reactions with pyridine as the reference base. Moreover, computations clearly showed that N3 is the most favorable protonation site for adenosine, due to a strong internal hydrogen bond involving the hydroxyl group at the 2' position of the ribose sugar moiety, unlike observations for adenine and 2'-deoxyadenosine, where protonation occurs on N1. The existence of negligible protonation entropy is confirmed by calculations (theoretical Delta p S degrees (adenosine) approximately -2/-3 J.mol (-1).K (-1)) including conformational analysis and entropy of hindered rotations. Thus, the calculated protonation thermochemical properties are in good agreement with our experimental measurements. It may be noted that the new PA value is approximately 10 kJ.mol (-1) lower than the one reported in the National Institute of Standards and Technology (NIST) database, thus pointing to a correction of the tabulated protonation thermochemistry of adenosine.     

Kinetics of loop formation in polymer chains

We investigate the kinetics of loop formation in ideal flexible polymer chains (the Rouse model), and polymers in good and poor solvents. We show for the Rouse model, using a modification of the theory of Szabo, Schulten, and Schulten, that the time scale for cyclization is tau(c) approximately tau(0)N(2) (where tau(0) is a microscopic time scale and N is the number of monomers), provided the coupling between the relaxation dynamics of the end-to-end vector and the looping dynamics is taken into account. The resulting analytic expression fits the simulation results accurately when a, the capture radius for contact formation, exceeds b, the average distance between two connected beads. Simulations also show that when a < b, tau(c) approximately N(alpha)(tau), where 1.5 < alpha(tau) < or = 2 in the range 7 < N < 200 used in the simulations. By using a diffusion coefficient that is dependent on the length scales a and b (with a < b), which captures the two-stage mechanism by which looping occurs when a < b, we obtain an analytic expression for tauc that fits the simulation results well. The kinetics of contact formation between the ends of the chain are profoundly effected when interactions between monomers are taken into account. Remarkably, for N < 100, the values of tau(c) decrease by more than 2 orders of magnitude when the solvent quality changes from good to poor. Fits of the simulation data for tau(c) to a power law in N (tau(c) approximately N(alpha)(tau)) show that alpha(tau) varies from about 2.4 in a good solvent to about 1.0 in poor solvents. The effective exponent alpha(tau) decreases as the strength of the attractive monomer-monomer interactions increases. Loop formation in poor solvents, in which the polymer adopts dense, compact globular conformations, occurs by a reptation-like mechanism of the ends of the chain. The time for contact formation between beads that are interior to the chain in good solvents changes nonmonotonically as the loop length varies. In contrast, the variation in interior loop closure time is monotonic in poor solvents. The implications of our results for contact formation in polypeptide chains, RNA, and single-stranded DNA are briefly outlined.     

Nature of the entropy versus self-diffusivity plot for simple liquids

The empirical relation (D(*))(alpha) = a exp[S] between the self-diffusion coefficient D(*) and the excess entropy S of a liquid is studied here in the context of theoretical model calculation. The coefficient alpha is dependent on the interaction potential and shows a crossover at an intermediate density, where cooperative dynamics become more important. Around this density a departure from the Stokes-Einstein relation is also observed. The above relation between entropy and diffusion is also tested for the scaled total diffusion coefficient in a binary mixture.     

Self-diffusion coefficient of the hard-sphere fluid: system size dependence and empirical correlations

Molecular dynamics simulations have been used to calculate the self-diffusion coefficient, D, of the hard sphere fluid over a wide density range and for different numbers of particles, N, between 32 and 10 976. These data are fitted to the relationship D = D(infinity) - AN(-alpha) where the parameters D(infinity), A, and alpha are all density-dependent (the temperature dependence of D can be trivially scaled out in all cases). The value alpha = 1/3 has been predicted on the basis of hydrodynamic arguments. In the studied system size range, the best value of alpha is approximately 1/3 at intermediate packing fractions of approximately 0.35, but increases in the low- and high-density extremes. At high density, the scaling follows more closely that of the thermodynamic properties, that is, with an exponent of order unity. At low packing fractions (less than approximately 0.1), the exponent increases again, appearing to approach a limiting value of unity in the zero-density limit. The origin of this strong N dependence at low density probably lies in the divergence in the mean path between collisions, as compared with the dimensions of the simulation cell. A new simple analytical fit formula based on fitting to previous simulation data is proposed for the density dependence of the shear viscosity. The Stokes-Einstein relationship and the dependence of D on the excess entropy were also explored. The product Deta(s)p with p = 0.975 was found to be approximately constant, with a value of 0.15 in the packing fraction range between 0.2 and 0.5.     

Intermediates trapped during nitrogenase reduction of N triple bond N, CH3-N=NH, and H2N-NH2

A high population intermediate has been trapped on the nitrogenase active site FeMo cofactor during reduction of N2. In addition, intermediates have been trapped during reduction of CH3-N=NH by the alpha-195Gln variant and during reduction of H2N-NH2 by the alpha-70Ala/alpha-195Gln variant. Each of these trapped states shows an EPR signal arising from an S = 1/2 state of the FeMo cofactor. 15N ENDOR shows that each intermediate has a nitrogenous species bound to the FeMo cofactor, with a single type of N seen for each bound intermediate. The g tensors are unique to each intermediate, g(e) = [2.084, 1.993, 1.969], g(m) = [2.083, 2.021, 1.993], g(l) = [2.082, 2.015, 1.987], as are the 15N hyperfine couplings at g1, which suggests that three distinct stages of NN reduction may have been trapped. The 1H ENDOR spectra show that the N2 intermediate is at a distinct and earlier stage of reduction from the other two, so at least two stages of NN reduction have been trapped. Some possible structures of the hydrazine intermediate are presented.     

Charge transport in DNA via thermally induced hopping.

In this contribution we advance and explore the thermally induced hopping (TIH) mechanism for long-range charge transport (CT) in DNA and in large-scale chemical systems. TIH occurs in donor-bridge-acceptor systems, which are characterized by off-resonance donor-bridge interactions (energy gap DeltaE > 0), involving thermally activated donor-bridge charge injection followed by intrabridge charge hopping. We observe a "transition" from superexchange to TIH with increasing the bridge length (i.e., the number N of the bridge constituents), which is manifested by crossing from the exponential N-dependent donor-acceptor CT rate at low N (< N(X)) to a weakly (algebraic) N-dependent CT rate at high N (>N(X)). The "critical" bridge size N(X) is determined by the energy gap, the nearest-neighbor electronic couplings, and the temperature. Experimental evidence for the TIH mechanism was inferred from our analysis of the chemical yields for the distal/proximal guanine (G) triplets in the (GGG)(+)TTXTT(GGG) duplex (X = G, azadine (zA), and adenine (A)) studied by Nakatani, Dohno and Saito [J. Am. Chem. Soc. 2000, 122, 5893]. The TIH sequential model, which involves hole hopping between (GGG) and X, is analyzed in terms of a sequential process in conjunction with parallel reactions of (GGG)(+) with water, and provides a scale of (free) energy gaps (relative to (GGG)(+)) of Delta = 0.21-0.24 eV for X = A, Delta = 0.10-0.14 eV for X = zA, and Delta = 0.05-0.10 eV for X = G. We further investigated the chemical yields for long-range TIH in (G)l(+)Xn(G)l (l = 1-3) duplexes, establishing the energetic constraints (i.e., the donor - bridge base (X) energy gap Delta), the bridge structural constraints (i.e., the intrabridge X-X hopping rates k(m)), and the kinetic constraints (i.e., the rate k(d) for the reaction of with water). Effective TIH is expected to prevail for Delta less than or approximately equal to 0.20 eV with a "fast" water reaction (k(d)/k(m) approximately 10(-3)) and for Delta < 0.30 eV with a "slow" water reaction (k(d)/k(m) approximately 10(-5)). We conclude that (T)n bridges (for which Delta approximately equals 0.6 eV) cannot act in TIH of holes. From an analysis based on the energetics of the electronic coupling matrix elements in G(+)(T-A)n(GGG) duplexes we conclude that the superexchange mechanism is expected to dominate for n = 1-4. For long (A)n bridges (n > or approximately equal to 4) the TIH prevails, provided that the water side reaction is slow, raising the issue of chemical control of TIH through long (A)n bridges in DNA attained by changing the solution composition.     

Folding and unfolding of helix-turn-helix motifs in the gas phase

Ion mobility measurements and molecular dynamic simulations have been performed for a series of peptides designed to have helix-turn-helix motifs. For peptides with two helical sections linked by a short loop region: AcA(14)KG(3)A(14)K+2H(+), AcA(14)KG(5)A(14)K+2H(+), AcA(14)KG(7)A(14)K+2H(+), and AcA(14)KSar(3)A(14)K+2H(+) (Ac = acetyl, A = alanine, G = glycine, Sar = sarcosine and K = lysine); a coiled-coil geometry with two anti-parallel helices is the lowest energy conformation. The helices uncouple and the coiled-coil unfolds as the temperature is raised. Equilibrium constants determined as a function of temperature yield enthalpy and entropy changes for the unfolding of the coiled-coil. The enthalpy and entropy changes depend on the length and nature of the loop region. For a peptide with three helical sections: protonated AcA(14)KG(3)A(14)KG(3)A(14)K; a coiled-coil bundle with three helices side-by-side is substantially less stable than a geometry with two helices in an antiparallel coiled-coil and the third helix collinear with one of the other two.     

S = (3)/(2) <= => S = (1)/(2) spin crossover behavior in five-coordinate halido- and pseudohalido-bis(o-iminobenzosemiquinonato)iron(III) complexes

Five-coordinate halido- and pseudohalido-bis(o-iminobenzosemiquinonato)iron(III) complexes [Fe(III)X(L(ISQ))(2)] (X = Cl(-) (1), Br(-) (2a, 2b), I(-) (3), N(3)(-) (4), and NCS(-) (5)) have been synthesized where (L(ISQ))(1)(*)(-) represents the pi radical anion N-phenyl-o-imino(4,6-di-tert-butyl)benzosemiquinonate(1-). The molecular structures of the two polymorphs 2a and 2b have been determined at 100, 220, and 295 K, respectively, by single crystal X-ray crystallography. Variable temperature magnetic susceptibility data reveal the following electronic ground states, S(t): For 1, it is (3)/(2). Polymorph 2a contains a 1:1 mixture of (3)/(2) and (1)/(2) forms in the range 4.2 to approximately 150 K; above 150 K the latter form undergoes a spin crossover (1)/(2) --> (3)/(2). Polymorph 2b contains only the S(t) = (3)/(2) form (4-300 K). Complex 3 contains the S(t) = (1)/(2) form in the range 4-130 K, but above 130 K, a spin crossover to the (3)/(2) form is observed which is confirmed by three crystal structure determinations at 100, 220, and 295 K. Complex 4 possesses an S(t) = (1)/(2) ground state at 80 K and undergoes a spin crossover at higher temperatures. Complex 5 has a temperature-independent S(t) = (3)/(2) ground state. All crystal structures of 1, 2a, 2b, 3, 4, and 5, regardless at which temperature the data sets have been measured, show that two o-iminobenzosemiquinonate(1-) pi radical anions are N,O-coordinated in all of these neutral iron complexes. The Fe-N and Fe-O bond distances are longer in the S(t) = (3)/(2) and shorter in the S(t) = (1)/(2) forms. The S(t) = (3)/(2) ground state is attained via intramolecular antiferromagnetic coupling between a high spin ferric ion (S(Fe) = (5)/(2)) and two ligand pi radicals whereas the S(t) = (1)/(2) form is generated from exchange coupling between an intermediate spin ferric ion (S(Fe) = (3)/(2)) and two ligand radicals.     

Helix-turn-helix motifs in unsolvated peptides

The conformations of unsolvated Ac-A14KG3A14K + 2H+ (Ac = acetyl, A = alanine, K = lysine, G = glycine) have been examined by ion mobility measurements and molecular dynamics simulations. This peptide was designed as a model helix-turn-helix motif. It was found to adopt three distinct geometries which were assigned to an extended helical conformation which is only stable at low temperatures (<230 K), a relatively high energy but metastable structure with exchanged lysines, and a coiled-coil. The coiled coil (which consists of an antiparallel arrangement of two helical alanine sections linked by a flexible glycine loop) is the dominant conformation. For temperatures >350 K, the experimental results indicate the helices uncouple and the loop randomizes. From equilibrium constants determined for this helix coupling right arrow over left arrow uncoupling transition, we found DeltaH degrees = -45 kJ mol-1 and DeltaS degrees = 114 J K-1 mol-1. -DeltaH degrees is essentially the enthalpy change for docking the two helices together while DeltaS degrees is essentially the entropy change for freeing up the glycine loop.     

Unforced translocation of a polymer chain through a nanopore: the solvent effect

The authors have performed the Langevin dynamics simulation to investigate the unforced polymer translocation through a narrow nanopore in an impermeable membrane. The effects of solvent quality controlled by the attraction strength lambda of the Lennard-Jones cosine potential between polymer beads and beads on two sides of the membrane on the translocation processes are extensively examined. For polymer translocation under the same solvent quality on both sides of the membrane, the two-dimensional and three-dimensional simulations confirm the scaling law of tautrans approximately N1+2upsilon for the translocation in the good solvent, where tautrans is the translocation time, N is the chain length, and upsilon is the Flory exponent. For the three-dimensional polymer translocation under different solvent qualities on two sides of the membrane, the translocation efficiency may be notably improved. The scaling law between tautrans and N varies from tautrans approximately N1+2upsilon to tautrans approximately N with the increase of the difference of solvent qualities, and the crossover occurs at the theta temperature point, where a scaling law of tautrans approximately N1.27 is found. The simulation results here also show that the translocation time changes from a wide and asymmetric distribution with a long tail to a narrow and symmetric distribution with the increase of the difference of the solvent qualities.     

Physical origin of peak tailing on C18-bonded silica in reversed-phase liquid chromatography

Single component isotherm data of caffeine and phenol were acquired on two different stationary phases for RPLC, using a methanol/water solution (25%, v/v, methanol) as the mobile phase. The columns were the non-endcapped Waters Resolve-C18, and the Waters XTerra MS C18. Both columns exhibit similar C18 -chain densities (2.45 and 2.50 micromol/m2) and differ essentially by the nature of the underivatized solid support (a conventional, highly polar silica made from water glass, hence containing metal impurities, versus a silica-methylsilane hybrid surface with a lower density of less acidic free silanols). Thirty-two adsorption data points were acquired by FA, for caffeine, between 10(-3) and 24 g/l, a dynamic range of 24,000. Twenty-eigth adsorption data points were acquired for phenol, from 0.025 to 75 g/l, a dynamic range of 3000. The expectation-maximization procedure was used to derive the affinity energy distribution (AED) from the raw FA data points, assuming a local Langmuir isotherm. For caffeine, the AEDs converge to a bimodal and a quadrimodal distribution on XTerra MS-C18 and Resolve-C18, respectively. The values of the saturation capacity (q(s,1) approximately equal to 0.80 mol/l and q(s,2) approximately equal to 0.10 mol/l) and the adsorption constant (b1 approximately equal to 3.11/mol and b2 approximately equal to 29.1 l/mol) measured on the two columns for the lowest two energy modes 1 and 2, are comparable. These data are consistent with those previously measured on an endcapped Kromasil-C18 in a 30/70 (v/v), methanol/water solution (q(s,1) = 0.9 mol/l and q(s,2) = 0.10 mol/l, b1 = 2.4 l/mol and b2 = 16.1 l/mol). The presence of two higher energy modes on the Waters Resolve-C18 column (q(s,3) approximately equal to 0.013 mol/l and q(s,4) approximately equal to 2.6 10(-4) mol/l, b3 approximately equal to 252 l/mol and b4 = 13,200 l/mol) and the strong peak tailing of caffeine are explained by the existence of adsorption sites buried inside the C18-bonded layer. It is demonstrated that strong interactions between caffeine and the water protected bare silica surface cannot explain these high-energy sites because the retention of caffeine on an underivatized Resolve silica column is almost zero. Possible hydrogen-bond interactions between caffeine and the non-protected isolated silanol groups remaining after synthesis amidst the C18-chain network cannot explain these high energy interactions because, then, the smaller phenol molecule should exhibit similarly strong interactions with these isolated silanols on the same Resolve-C18 column and, yet, the consequences of such interactions are not observed. These sites are more consistent with the heterogeneity of the local structure of the C18-bonded layer. Regarding the adsorption of phenol, no matter whether the column is endcapped or not, its molecular interactions with the bare silica were negligible. For both columns, the best adsorption isotherm was the Bilangmuir model (with q(s,1) approximately equal to 2 and q(s,2) approximately equal to 0.67 mol/l, b1 0.61 and b2 approximately equal to 10.3 l/mol). These parameters are consistent with those measured previously on an endcapped Kromasil-C18 column under the same conditions (q(s,1) = 1.5 and q(s,2) = 0.71 mol/l, b1 = 1.4 l/mol and b2 = 11.3 l/mol). As for caffeine, the high-energy sites are definitely located within the C18-bonded layer, not on the bare surface of the adsorbent.     

SEGMENT DENSITY PROFILES OF COMPACT POLYMER CHAINS CONFINED BETWEEN TWO PARALLEL PLANE WALLS

We use the pruned-enriched Rosenbluth method to investigate systematically the segment density profiles of compact polymer chains confined between two parallel plane walls.The non-adsorption case of adsorption interaction energyε=0 and the weak adsorption case ofε=-1 are considered for the compact polymer chains with different chain lengths N and different separation distances between two walls D.Several special entropy effects on the confined compact polymer chains,such as a damped oscillation in the segment density profile for the large separation distance D,are observed and discussed for different separation distances D in the non-adsorption case.In the weak adsorption case,investigations on the segment density profiles indicate that the competition between the entropy and adsorption effects results in an obvious depletion layer.Moreover,the scaling laws of the damped oscillation period T_d and the depletion layer width L_d are obtained for the confined compact chains.Most of these results are obtained for the first time so far as we know,which are expected to understand the properties of the confined compact polymer chains more completely.     

Thermodynamic analysis of decomposition of thiourea and thiourea oxides

Thiourea has exhibited extremely rich dynamical behavior when being oxidized either through a chemical approach or via an electrochemical method. In this study, thermodynamic properties of thiourea and its oxides are investigated by measuring their thermogravimetry (TG), differential thermogravimetry (DTG), and differential scanning calorimetry (DSC) simultaneously. Online FT-IR measurements show that products of the thermal decomposition vary significantly with the reaction temperature. In addition to the determination of their apparent activation energy (E), preexponential factor (A), and entropy (DeltaS++), enthalpy (DeltaH++), and Gibbs energy (DeltaG++) of thermal decomposition, our investigation further illustrates that the decomposition kinetics of thiourea and thiourea oxides follows the Johnson-Mehl-Avrami Equation, f (alpha) = n(1 - alpha)[-ln(1 - alpha)](1-1/n) and G(alpha) = [-ln(1 - alpha)](1/n) with n equal to 2, 3.43, and 3, respectively.     

Factors influencing conformer equilibria in retro models of cisplatin-DNA adducts as revealed by moderately dynamic (N,N'-dimethyl-2,3-diaminobutane)PtG(2) retro models (G = a guanine derivative)

Typical cis-PtA(2)G(2) models of key DNA lesions formed by cis-type Pt anticancer drugs are very dynamic and difficult to characterize (A(2) = diamine or two amines; G = guanine derivative). Retro models have A(2) carrier ligands designed to decrease dynamic motion without eliminating any of three possible conformers with bases oriented head-to-tail (two: DeltaHT and LambdaHT) or head-to-head (one: HH). All three were found in NMR studies of eight Me(2)DABPtG(2) retro models (Me(2)DAB = N,N'-dimethyl-2,3-diaminobutane with S,R,R,S and R,S,S,R configurations at the chelate ring N, C, C, and N atoms, respectively; G = 5'-GMP, 3'-GMP, 5'-IMP, and 3'-IMP). The bases cant to the left (L) in (S,R,R,S)-Me(2)DABPtG(2) adducts and to the right (R) in (R,S,S,R)-Me(2)DABPtG(2) adducts. Relative to the case in which the bases are both not canted, canting will move the six-membered rings closer in to each other ("6-in" form) or farther out from each other ("6-out" form). Interligand interactions between ligand components near to Pt (first-first sphere communication = FFC) or far from Pt (second-sphere communication = SSC) influence stability. In typical cases at pH < 8, the "6-in" form is favored, although the larger six-membered rings of the bases are close. In minor "6-out" HT forms, the proximity of the smaller five-membered rings could be sterically favorable. Also, G O6 is closer to the sterically less demanding NH part of the Me(2)DAB ligand, possibly allowing G O6-NH hydrogen bonding. These favorable FFC effects do not fully compensate for possibly stronger FFC dipole effects in the "6-in" form. SSC, phosphate-N1H cis G interactions favor LambdaHT forms in 5'-GMP and 5'-IMP complexes and DeltaHT forms in 3'-GMP and 3'-IMP complexes. When SSC and FFC favor the same HT conformer, it is present at >90% abundance. In six adducts [four (S,R,R,S)-Me(2)DABPtG(2) and (R,S,S,R)-Me(2)DABPtG(2) (G = 3'-GMP and 3'-IMP)], the minor "6-out" HT form at pH approximately 7 becomes the major form at pH approximately 10, where G N1H is deprotonated, because the large distance between the negatively charged N1 atoms minimizes electrostatic repulsion and probably because the G O6-(NH)Me(2)DAB H-bond (FFC) is strengthened by N1H deprotonation. At pH approximately 10, phosphate-negative N1 repulsion is an unfavorable SSC term. This factor disfavors the LambdaHT R form of two (R,S,S,R)-Me(2)DABPtG(2) (G = 5'-GMP and 5'-IMP) adducts to such an extent that the "6-in" DeltaHT R form remains the dominant form even at pH approximately 10.     

Tetrazol-2-yl as a donor group for incorporation of a spin-crossover function based on Fe(II) ions into a coordination network

The coordination polymer {[Fe(pbtz)3](ClO4)2 . 2EtOH}infinity (1) has been prepared in a reaction between Fe(ClO4)2 . 6H2O and 1,3-di(tetrazol-2-yl)propane (pbtz). The formation of the second product {[Fe(pbtz)3](ClO4)2}infinity (2) was also noticed. Both complexes crystallize in the R3 space group. The single-crystal X-ray diffraction study of 1 (295, 90 and 230 K) revealed that the 2-substituted tetrazole rings (2tz) coordinate monodentately to the metal ions, forming Fe(2tz)6 cores. There are two crystallographically independent iron(II) ions in 1. At 295 K the Fe-N4 bond lengths are equal to 2.173(5) and 2.196(5) A for Fe1 and 2.176(5) and 2.190(4) A for Fe2. The pbtz ligand molecules act as N4,N4' connectors, bridging central atoms in the three directions, which leads to the formation of the 3D network. The crystal lattice of 1 is solvated by ethanol molecules. At 295 K the solvent and ligand molecules are disordered. The results of temperature-dependent magnetic susceptibility measurements (5-300 K), and the single-crystal X-ray diffraction studies (90 K) have exhibited that 1 undergoes the thermally induced spin transition HS<-->LS (SCO). The chiMT(T) dependence shows in the range 200-75 K gradual SCO. Below 75 K the transition is finished and approximately 20% of the HS fraction is present in the sample. The HS-->LS transition is accompanied by a shortening of the Fe-N bonds of 0.15 A. At 90 K the ligand molecules are ordered. The presence of 2 in the reaction product was disclosed accidentally, and only the X-ray diffraction studies (250, 90 K) were performed. Also in 2 iron(II) ions serve as topological nodes of the 3D network. Despite the same network topology, 2 crystallizes without ethanol molecules solvating the crystal lattice. The pbtz molecules bridge the neighboring iron(II) ions, coordinating through N4,N4' atoms of the 2-substituted tetrazole rings forming the Fe(2tz)6 cores. At 250 K the Fe-N bond lengths are equal to 2.208(5) and 2.218(5) A. In contrast to 1, the cooling of the crystal of 2 from 250 to 90 K does not involve the shortening of the Fe-N bond lengths. At this temperature, the Fe-N distances remain characteristic for the HS form of the complex and are equal to 2.203(3) and 2.208(3) A.     

Mechanism of the addition reaction of alkyl azides to [60]fullerene and the subsequent N2 extrusion to form monoimino-[60]fullerenes.

The 1,3-dipolar cycloaddition of methyl azide to C60 and the subsequent nitrogen elimination from the formed triazoline intermediate to yield the aziridine adduct have been studied using semiempirical and density functional methods. The results obtained show that the addition of methyl azide to C60 takes place in the ring junction between two six-membered rings leading to a closed [6,6]-trizoline intermediate with an energy barrier of about 20 kcal mol-1 and an exothermicity of ca. 2 kcal mol-1 at the B3LYP/6-31G**//AM1 level of theory. The subsequent thermal loss of N2 takes place through a stepwise mechanism in which the cleavage of the N-N single bond precedes the breaking of the N-C bond, with a total activation energy of approximately 45 kcal mol-1. The N2 loss occurs simultaneously with the formation of the new N-C bond. During the process, the steric effects of the leaving N2 molecule prevent the addition of the nitrene substituent to the [6,6]-ring junction attacked initially and force the addition to an adjacent [5,6]-ring junction.     

Finite size scaling for the atomic Shannon-information entropy

We have developed the finite size scaling method to treat the criticality of Shannon-information entropy for any given quantum Hamiltonian. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. To illustrate this approach we present a study to estimate the critical exponents of the Shannon-information entropy S approximately (lambda-lambda(c))(alpha(S) ), the electronic energy E approximately (lambda-lambda(c))(alpha(E) ), and the correlation length xi approximately mid R:lambda-lambda(c)mid R:(-nu) for atoms with the variable lambda=1/Z, which is the inverse of the nuclear charge Z. This was realized by approximating the multielectron atomic Hamiltonian with a one-electron model Hamiltonian. This model is very accurate for describing the electronic structure of the atoms near their critical points. For several atoms in their ground electronic states, we have found that the critical exponents (alpha(E),nu,alpha(S)) for He (Z=2), C (Z=6), N (Z=7), F (Z=9), and Ne (Z=10), respectively, are (1, 0, 0). At the critical points lambda(c)=1/Z(c), the bound state energies become absorbed or degenerate with continuum states and the entropies reach their maximum values, indicating a maximal delocalization of the electronic wave function.