Energy Decomposition Scheme Research Articles

Bonding in Ammonia Borane: An Analysis Based on the Natural Orbitals for Chemical Valence and the Extended Transition State Method (ETS-NOCV)

In the present study the natural orbitals for chemical valence (NOCVs) combined with the energy decomposition scheme (ETS) were used to characterize bonding in various clusters of ammonia borane (borazane): dimer D, trimer TR, tetramer TE, and the crystal based models: nonamer N and tetrakaidecamer TD. ETS-NOCV results have shown that shortening of the B-N bond (by ~0.1 Å) in ammonia borane crystal (as compared to isolated borazane molecule) is related to the enhancement of donation (by 6.5 kcal/mol) and electrostatic (by 11.3 kcal/mol) contributions. This, in turn, is caused solely by the electrostatic dipole-dipole interaction between ammonia borane units; dihydrogen bonding, BH···HN, formed between borazane units exhibits no direct impact on B-N bond contraction. On the other hand, formation of dihydrogen bonding appeared to be very important in the total stabilization of single borazane unit, namely, ETS-based data indicated that it leads to significant electronic stabilization ΔE(orb) = -17.5 kcal/mol, which is only slightly less important than the electrostatic term, ΔE(elstat) = -19.4 kcal/mol. Thus, both factors contribute to relatively high melting point of the borazane crystal. Deformation density contributions (Δρ(i)) obtained from NOCVs allowed to conclude that dihydrogen bonding is primarily based on outflow of electron density from B-H bonding orbitals to the empty σ*(N-H) (charge transfer component). Equally important is the covalent contribution resulting from the shift of the electron density from hydrogen atoms of both NH and BH groups to the interatomic regions of NH···HB. Quantitatively, averaged electronic strength of dihydrogen bond per one BH···HN link varies from 1.95 kcal/mol (for the crystal structure model, N), 2.47 kcal/mol (for trimer TR), through 2.65 kcal/mol (for tetramer TE), up to 3.95 kcal/mol (for dimer D).

Bond energy analysis revisited and designed toward a rigorous methodology

The present study theoretically revisits and numerically assesses two-body energy decomposition schemes including a newly proposed one. The new decomposition scheme is designed to make the equilibrium bond distance equivalent with the minimum point of bond energies. Although the other decomposition schemes generally predict the wrong order of the C-C bond strengths of C(2)H(2), C(2)H(4), and C(2)H(6), the new decomposition scheme is capable of reproducing the C-C bond strengths. Numerical assessment on a training set of molecules demonstrates that the present scheme exhibits a stronger correlation with bond dissociation energies than the other decomposition schemes do, which suggests that the new decomposition scheme is a reliable and powerful analysis methodology.

Large Changes of Static Electric Properties Induced by Hydrogen Bonding: An ab Initio Study of Linear HCN Oligomers

We report the partitioning of the interaction-induced static electronic dipole (hyper)polarizabilities for linear hydrogen cyanide complexes into contributions arising from various interaction energy terms. We analyzed the nonadditivities of the studied properties and used these data to predict the electric properties of an infinite chain. The interaction-induced static electric dipole properties and their nonadditivities were analyzed using an approach based on numerical differentiation of the interaction energy components estimated in an external electric field. These were obtained using the hybrid variational-perturbational interaction energy decomposition scheme, augmented with coupled-cluster calculations, with singles, doubles, and noniterative triples. Our results indicate that the interaction-induced dipole moments and polarizabilities are primarily electrostatic in nature; however, the composition of the interaction hyperpolarizabilities is much more complex. The overlap effects substantially quench the contributions due to electrostatic interactions, and therefore, the major components are due to the induction and exchange-induction terms, as well as the intramolecular electron-correlation corrections. A particularly intriguing observation is that the interaction first hyperpolarizability in the studied systems not only is much larger than the corresponding sum of monomer properties, but also has the opposite sign. We show that this effect can be viewed as a direct consequence of hydrogen-bonding interactions that lead to a decrease of the hyperpolarizability of the proton acceptor and an increase of the hyperpolarizability of the proton donor. In the case of the first hyperpolarizability, we also observed the largest nonadditivity of interaction properties (nearly 17%) which further enhances the effects of pairwise interactions.

Applications of the ETS-NOCV method in descriptions of chemical reactions

The present study characterizes changes in the electronic structure of reactants during chemical reactions based on the combined charge and energy decomposition scheme, ETS-NOCV (extended transition state-natural orbitals for chemical valence). Decomposition of the activation barrier, ΔE (#), into stabilizing (orbital interaction, ΔE (orb), and electrostatic, ΔE (elstat)) and destabilizing (Pauli repulsion, ΔE (Pauli), and geometry distortion energy, ΔE (dist)) factors is discussed in detail for the following reactions: (I) hydrogen cyanide to hydrogen isocyanide, HCN → CNH isomerization; (II) Diels-Alder cycloaddition of ethene to 1,3-butadiene; and two catalytic processes, i.e., (III) insertion of ethylene into the metal-alkyl bond using half-titanocene with phenyl-phenoxy ligand catalyst; and (IV) B-H bond activation catalyzed by an Ir-containing catalyst. Various reference states for fragments were applied in ETS-NOCV analysis. We found that NOCV-based deformation densities (Δρ (i)) and the corresponding energies ΔE (orb)(i) obtained from the ETS-NOCV scheme provide a very useful picture, both qualitatively and quantitatively, of electronic density reorganization along the considered reaction pathways. Decomposition of the barrier ΔE(#) into stabilizing and destabilizing contributions allowed us to conclude that the main factor responsible for the existence of positive values of ΔE (#) for all processes (I, II, III and IV) is Pauli interaction, which is the origin of steric repulsion. In addition, in the case of reactions II, III and IV, a significant degree of structural deformation of the reactants, as measured by the geometry distortion energy, plays an important role. Depending on the reaction type, stabilization of the transition state (relatively to the reactants) originating either from the orbital interaction term or from electrostatic attraction can be of vital importance. Finally, use of the ETS-NOCV method to describe catalytic reactions allows extraction of information on the role of catalysts in determination of ΔE (#).

Electronic excitation and ionization of hydrogen peroxide–water clusters: Comparison with water clusters

AbstractElectronic properties of H2O2(H2O)1–6 and (H2O)1–7 clusters are reported. Emphasis was placed on the changes induced by the presence of hydrogen peroxide on the electronic properties of water aggregates. Theoretical results for excitation energies as well as vertical and adiabatic ionization energies are reported. Excitation energies were calculated with time‐dependent density functional theory and equation‐of‐motion coupled cluster with single and double excitations (EOM‐CCSD). A many‐body energy decomposition scheme recently proposed was coupled to the EOM‐CCSD method making possible an accurate prediction of the first vertical excitation energy of peroxide–water clusters. In comparison with water clusters, our results show that the presence of hydrogen peroxide in water clusters is characterized by a [1.5–1.8] eV red‐shift of the first excitation energy. The first excitation is localized on the HOOH moiety, and no significant dependence of the first excitation energy on the cluster size is observed. The differences between vertical and adiabatic ionization energies for both water and hydrogen peroxide–water clusters reflect the feature that ionization leads to proton transfer and to a significant structural and electronic density reorganization. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Nonadditivity in the alpha‐helix to coil transition

The Lifson-Roig Model (LRM) and all its variants describe the α-helix to coil transition in terms of additive component-free energies within a free energy decomposition scheme, and these contributions are interpreted through sequence-context dependent nucleation and propagation parameters. Although this phenomenological approach is able to adequately fit experimental data on helix content and heat capacity, the number of required parameters increases dramatically with additional sequence variation. Moreover, due to nonadditive competing microscopic effects that are difficult to disentangle within a LRM, large uncertainties within the parameters emerge. We offer an alternative view that removes the need for sequence-context parameterization by focusing on individual microsopic interactions within a free energy decomposition and explicitly account for nonadditivity in conformational entropy through network rigidity using a Distance Constraint Model (DCM). We apply a LRM and a DCM to previously published experimental heat capacity and helix content data for a series of heterogeneous polypeptides. Both models describe the experimental data well, and the parameters from both models are consistent with prior work. However, the number of DCM parameters is independent of sequence-variability, the parameter values exhibit better transferability, and the helix nucleation is predicted by the DCM explicitly through the nonadditive nature of conformational entropy. The importance of these results is that the DCM offers a system-independent approach for modeling stability within polypeptides and proteins, where the demonstrated accuracy for the α-helix to coil transition over a series of heterogeneous polypeptides described here is one case in point.

Structural Variability and the Nature of Intermolecular Interactions in Watson−Crick B-DNA Base Pairs

A set of nearly 100 crystallographic structures was analyzed using ab initio methods in order to verify the effect of the conformational variability of Watson-Crick guanine-cytosine and adenine-thymine base pairs on the intermolecular interaction energy and its components. Furthermore, for the representative structures, a potential energy scan of the structural parameters describing mutual orientation of the base pairs was carried out. The results were obtained using the hybrid variational-perturbational interaction energy decomposition scheme. The electron correlation effects were estimated by means of the second-order Møller-Plesset perturbation theory and coupled clusters with singles and doubles method adopting AUG-cc-pVDZ basis set. Moreover, the characteristics of hydrogen bonds in complexes, mimicking those appearing in B-DNA, were evaluated using topological analysis of the electron density. Although the first-order electrostatic energy is usually the largest stabilizing component, it is canceled out by the associated exchange repulsion in majority of the studied crystallographic structures. Therefore, the analyzed complexes of the nucleic acid bases appeared to be stabilized mainly by the delocalization component of the intermolecular interaction energy which, in terms of symmetry adapted perturbation theory, encompasses the second- and higher-order induction and exchange-induction terms. Furthermore, it was found that the dispersion contribution, albeit much smaller in terms of magnitude, is also a vital stabilizing factor. It was also revealed that the intermolecular interaction energy and its components are strongly influenced by four (out of six) structural parameters describing mutual orientation of bases in Watson-Crick pairs, namely shear, stagger, stretch, and opening. Finally, as a part of a model study, much of the effort was devoted to an extensive testing of the UBDB databank. It was shown that the databank quite successfully reproduces the electrostatic energy determined with the aid of ab initio methods.

Theoretical description of hydrogen bonding in oxalic acid dimer and trimer based on the combined extended-transition-state energy decomposition analysis and natural orbitals for chemical valence (ETS-NOCV)

In the present study we have analyzed hydrogen bonding in dimer and trimer of oxalic acid, based on a recently proposed charge and energy decomposition scheme (ETS-NOCV). In the case of a dimer, two conformations, α and β, were considered. The deformation density contributions originating from NOCV’s revealed that the formation of hydrogen bonding is associated with the electronic charge deformation in both the σ—(Δρσ) and π-networks (Δρπ). It was demonstrated that σ-donation is realized by electron transfer from the lone pair of oxygen on one monomer into the empty rho_{H - O}^* orbital of the second oxalic acid fragment. In addition, a covalent contribution is observed by the density transfer from hydrogen of H-O group in one oxalic acid monomer to the oxygen atom of the second fragment. The resonance assisted component (Δρπ), is based on the transfer of electron density from the π—orbital localized on the oxygen of OH on one oxalic acid monomer to the oxygen atom of the other fragment. ETS-NOCV allowed to conclude that the σ(O---HO) component is roughly eight times as important as π (RAHB) contribution in terms of energetic estimation. The electrostatic factor (ΔEelstat) is equally as important as orbital interaction term (ΔEorb). Finally, comparing β-dimer of oxalic acid with trimer we found practically no difference concerning each of the O---HO bonds, neither qualitative nor quantitative. FigureThe contours of deformation density σ- and π-contributions describing the hydrogen bonding between the monomers in the oxalic acid dimer, together with the corresponding ETS-NOCV-based orbital-interaction energies (in kcal/mol).

New Insights into Charge Flow Processes and Their Impact on the Activation of Ethene and Ethyne by Cu(I) and Ag(I) Sites in MFI

This paper concerns the activation of ethene and ethyne molecules on two cationic sites (Cu(I) and Ag(I)) in ZSM-5 zeolite. QM/MM calculations were carried out to obtain geometric structure and vibrational frequencies. A novel analysis tool, NOCV (natural orbitals for chemical valence) supported by an ETS energy decomposition scheme, was applied to characterize charge flow between adsorbed molecules and the cationic site in ZSM-5 zeolite. The ETS-NOCV method allows for separating independent components of differential electron density into donation and backdonation channels, responsible for the substrate activation. It also helps to evaluate the importance of particular density transfer channels in the activation process. Two partition schemes into two subsystems are proposed here to extract complete information on the electronic balance between the molecule, the cation, and the zeolite framework. Both cationic sites (Cu(I) and Ag(I)) and both molecules (ethene and ethyne) are compared and the differences in the red-shift of CC stretching frequency are rationalized in terms of donation and backdonation charge transfer processes. They are shown to depend as well on metal specific properties as on the interaction between the metal and the framework.

Ab initio study of the cooperativity between NH···N and NH···C hydrogen bonds in H3N–HNC–HNC complex

Ab initio calculations at the MP2/aug-cc-pVTZ level have been performed to study the cooperativity of hydrogen bonds in homoclusters (HNC–HNC–HNC and HNC–HNC–HNC–HNC) and heteroclusters (H3N–HNC–HNC and H3N–HNC–HNC–HNC). The cooperative energies in the HNC–HNC–HNC and H3N–HNC–HNC trimers are –2.05 and –2.56 kcal/mol, respectively. The result shows that the cooperativity in the heterotrimer is larger than that in the homotrimer. A similar result also happens in the tetramers. The energy decomposition scheme indicates that orbital interaction is a major contribution to the cooperative energy of N···HN hydrogen bond, whereas the electrostatic and orbital interactions to that of C···HN hydrogen bond. The effect of HNC chain length on the strength of N···HN hydrogen bond has also been considered at the MP2/aug-cc-pVDZ level. It is indicated that the interaction energy of N···HN hydrogen bond trends to be a fixed value when the HNC number tends to be infinite, and the strength of N···HN hydrogen bond is regulated mainly through the electrostatic and polarization interactions although the charge transfer interaction also has an effect on it.

Binding of polar monomers in the complexes with organometallic ethylene polymerization catalysts — Natural orbitals for chemical valence and energy decomposition analysis

The binding mode of polar monomers in complexes with late-transition-metal catalysts for ethylene polymerization was studied by density functional theory (DFT) calculations. The Ziegler–Rauk energy decomposition scheme was used to characterize the geometry distortion and steric and orbital-interaction terms in the bonding energy, while Natural Orbitals for Chemical Valence (NOCV) were applied to describe the donation and back-bonding components of the bond between the monomer and the catalyst. The NOCV analysis allowed for comparison of the donor–acceptor properties of different monomers in the σ- and π-complexes. The complexes with the model, cationic Ni– or Pd–diimine catalysts, N^N–Ni(H)+ and N^N–Pd(H)+, and the neutral Ni–anilinotropone system, N^O–Ni(H), were investigated. The monomers studied included: simple olefins (Et and Pr); examples of oxygen- and nitrogen-containing polar monomers (methyl acrylate (MA), vinyl acetate (VAc), their fluorinated derivatives (FMA, FVAc), vinyl ether (VE), acrylonitrile (AN), and β-butenoic nitrile (BN); vinyl and allyl amines (VAm, PrAm); and a tertiary dimethyl vinyl amine (MVAm). The results demonstrate that the metal-based fragment has a significant influence on the relative stability of the σ- and π-complexes; the π-binding mode increases in the following order: N^N–Ni(H)+ < N^N–Pd(H)+ < N^O–Ni(H). The results of the Ziegler–Rauk bond-energy decomposition indicate that for some monomers (MA, FMA, VAc, AN, VAm, MVAm) the preference of the coordination mode has a steric (electrostatic and Pauli) origin. For other monomers (VE, FVAc, BN, PrAm) the changes in the orbital-interaction terms are important as well. The results of the NOCV analysis indicate that for both, σ- and π-coordination modes there exist components describing σ-donation and π-back-bonding. The sequences of σ-donor and π-acceptor properties of monomers in the π-complexes as well as σ-complexes are similar for the considered catalysts.

On the Nature of the Agostic Bond between Metal Centers and β-Hydrogen Atoms in Alkyl Complexes. An Analysis Based on the Extended Transition State Method and the Natural Orbitals for Chemical Valence Scheme (ETS-NOCV)

We have in the present account analyzed the bonding in β-agostic alkyl complexes between the carbon chain (R) and the transition metal center. The analysis is based on a recently proposed energy decomposition scheme (ETS-NOCV). We have considered R = Et, n-Pr, i-Pr, n-Bu, attached to the cationic Ni(II)- and Pd(II)-bis-diimine Brookhart complexes (1), the cationic Ti(IV)- or Zr(IV)-metallocenes (2), and the neutral Pd(II) Drent (3) complexes. We find for a given metal that the total M−R dissociation energy −ΔEtotal follows the order n-Bu > n-Pr > Et ≫ i-Pr. For the same R-group (n-Pr), −ΔEtotal for second-row metals is larger than for first-row, as 4d forms better overlaps with the alkyl orbitals than 3d. The major stabilizing contribution to −ΔEtotal is the σ-bond between the α-carbon and the metal. It is augmented by smaller contributions from the Cβ−M σ-interaction as well as the hyperconjugation of charge into the σCC* and σCH* alkyl orbitals. We finally have the β-agostic contribution from the interaction between a hydrogen atom on the β-carbon and the metal center. The strength of this bond is rather constant for the cationic species 1 and 2. It can be considered as originating from a (largely) Coulombic interaction between the metal center and the electron pair in the Cβ−H bond, where the density of the pair has been polarized by the positive metal charge. The neutral Drent system (3) exhibits a weaker β-agostic interaction, as the net charge on the metal center is less positive.

Role of Ancillary Ligands in a Description of Copper(I)−Bis(trimethylsilyl)acetylene bonding. A Theoretical Study

The bonding between bis(trimethylsilyl)acetylene (BTMSA) and the Cu(I) cation in complexes containing ligands originating from β-diketimine and β-diketone has been analyzed with the help of the extended transition state (ETS) energy decomposition scheme as well as the natural orbitals for chemical valence (NOCV) method. The results demonstrate that the copper−BTMSA bond predominantly involves π back-donation: i.e., electron transfer from the occupied copper d orbital into the empty π* orbital of BTMSA. The strength of π-bonding decreases with the subsequent replacement of nitrogen/oxygen by phosphorus/sulfur, while the changes in the substituents on the main chain of both the β-diketimine and β-diketone ligands were found not to affect the π back-donation significantly. In spite of the similarities in the qualitative picture of the Cu−BTMSA bonding, its quantitative energy descriptions are very different for the β-diketimine- and β-diketone-based series. Namely, for 1-N2, 1-PN, and 1-P2, the Cu−BTMSA bond...

A Combined Charge and Energy Decomposition Scheme for Bond Analysis.

In the present study we have introduced a new scheme for chemical bond analysis by combining the Extended Transition State (ETS) method [ Theor. Chim. Acta 1977, 46, 1 ] with the Natural Orbitals for Chemical Valence (NOCV) theory [ J. Phys. Chem. A 2008, 112, 1933 ; J. Mol. 2007, 13, 347 ]. The ETS-NOCV charge and energy decomposition scheme based on the Kohn-Sham approach makes it not only possible to decompose the deformation density, Δρ, into the different components (such as σ, π, δ, etc.) of the chemical bond, but it also provides the corresponding energy contributions to the total bond energy. Thus, the ETS-NOCV scheme offers a compact, qualitative, and quantitative picture of the chemical bond formation within one common theoretical framework. Although, the ETS-NOCV approach contains a certain arbitrariness in the definition of the molecular subsystems that constitute the whole molecule, it can be widely used for the description of different types of chemical bonds. The applicability of the ETS-NOCV scheme is demonstrated for single (H3X-XH3, for X = C, Si, Ge, Sn) and multiple (H2X═XH2, H3CX≡XCH3, for X = C, Ge) covalent bonds between main group elements, for sextuple and quadruple bonds between metal centers (Cr2, Mo2, W2, [Cl4CrCrCl4](4-)), and for double bonds between a metal and a main group element ((CO)5Cr═XH2, for X = C, Si, Ge, Sn). We include finally two applications involving hydrogen bonding. The first covers the adenine-thymine base pair and the second the interaction between C-H bonds and the metal center in the alkyl complex.

Effect of Methoxy Substituents on the Structural and Electronic Properties of Fluorinated Cyclobutenes: A Study of Hexafluorocyclobutene and Its Vinyl Methoxy Derivatives by XRD and Periodic DFT Calculations

The effect of the methoxy substituent on the structure, crystal packing, and electrostatic properties of hexafluorocyclobutene (C(4)F(6)) was investigated in the solid-state with DFT-B3LYP calculations. Full geometry optimizations were done for the parent compound and its two vinyl methoxy derivatives C(4)F(5)OCH(3) and C(4)F(4)(OCH(3))(2), starting from the structures obtained by single-crystal X-ray diffraction at low temperature. A full topological analysis, followed by the calculation of several electrostatic properties, was performed on the periodic electron density using the quantum theory of atoms in molecules. Eventually, the cohesive energies of the three crystals were estimated. In the cyclobutene plane, the methoxy substitution yields a significant electronic rearrangement involving the pi-electrons. The solid-state (periodic) results agree with those obtained by gas-phase calculations on C(4)F(6) and its derivatives at a comparable level of theory. It was found that the substitution of one or two vinylic fluorine atoms with the OCH(3) group considerably influences the molecular dipole moment, which undergoes an enhancement in both the solid and the gas phase as large as 200% and 235% for C(4)F(5)OCH(3) and C(4)F(4)(OCH(3))(2), respectively, with respect to that calculated for C(4)F(6). The charge rearrangement due to the substituents provides a significant electrostatic contribution to the lattice energy, and in turn it can be related to the change in the observed crystal packing on going from C(4)F(6) (space group P2(1)/c) to both of its derivatives (space group P1). It is also shown that the dispersion energy significantly contributes to the lattice stability in all three compounds. Since the DFT calculations, in the limit of large separations, entirely miss the dispersion term, this was estimated by applying a recently proposed dampening function to the semiempirical atom-atom C(6) R(-6) potentials in the mainframe of Spackman's energy decomposition scheme for Mulliken multipoles.

Synthesis and structures of cationic μ-diborolyl triple-decker complexes [CpCo(1,3-C3B2Me5)M(C5R5)]+ (M = Rh or Ir)

The cationic triple-decker complexes [CpCo(1,3-C3B2Me5)M(C5R5)]+ (M = Rh (2), Ir (3), R = H (a), Me (b)) with the bridging diborolyl ligand were synthesized by the reaction of the sandwich anion [CpCo(1,3-C3B2Me5)]- (1) with the halide complexes [CpMI2]2 or [Cp*MCl2]2 (Cp* = C5Me5). The structures of [2b]PF6 and [3b]PF6 were established by X-ray diffraction. The nature of the metal—diborolyl bond in these complexes was analyzed using the energy decomposition scheme.

One‐body energy decomposition schemes revisited: Assessment of Mulliken‐, Grid‐, and conventional energy density analyses

AbstractWe propose a new energy density analysis (EDA) that evaluates atomic contributions of all energy terms, i.e., the kinetic, nuclear‐attraction, Coulomb, and Hartree–Fock (HF) exchange and density functional theory (DFT) exchange‐correlation energies using the Mulliken‐type partitioning. Although widely used DFT exchange‐correlation functionals are nonlinear expressions in terms of density, they are decomposed into atomic contributions by focusing the linear part of the density. Numerical assessment on Mulliken‐EDA, Grid‐EDA, and conventional EDA has been carried out for the G2‐1 set. Correlations between HF and DFT exchanges demonstrate that a consistent partitioning of all energy terms is essential for EDA. These numerical results confirm that the present Mulliken‐EDA offers a more reasonable picture for the atomization process. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

π‐Electronic communication through mono and multinuclear gold(I) complexes

AbstractWe have theoretically studied gold(I) complexes of the type L1‐AuI‐L2 and HCN‐[AuI‐CN]n (n = 1–8) using relativistic density functional theory at ZORA‐BP86/TZ2P. Our purpose, besides determining structure and stability, is to analyze the bonding in our model systems in the conceptual framework of Kohn–Sham molecular orbital theory in combination with a quantitative bond energy decomposition scheme and analysis of the charge distribution. We focus on the π‐bonding interaction for a given ligand‐gold coordination bond and how this is affected by the presence of the other ligand. We find pronounced π‐electronic communication through the gold(I) valence shell in complexes that involve a π‐donor as well as a π‐acceptor ligand. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Kinetic and theoretical study of the reaction of Cl atoms with a series of linear thiols

The reactions of Cl with a series of linear thiols: 1-propanethiol (k(1)), 1-butanethiol (k(2)), and 1-pentanethiol (k(3)) were investigated as a function of temperature (in the range of 268-379 K) and pressure (in the range of 50-200 Torr) by laser photolysis-resonance fluorescence. Only 1-propanethiol has previously been studied, but at 1 Torr of total pressure. The derived Arrhenius expressions obtained using our kinetic data were as follows: k(1)=(3.97+/-0.44)x10(-11) exp[(410+/-36)T], k(2)=(1.01+/-0.16)x10(-10) exp[(146+/-23)T], and k(3)=(1.28+/-0.10)x10(-10) exp[(129+/-25)T] (in units of cm(3) molecule(-1) s(-1)). Moreover, a theoretical insight into mechanisms of these reactions has also been pursued through ab initio Moller-Plesset second-order perturbation treatment calculations with 6-311G(**) basis set. Optimized geometries have been obtained for transition states and molecular complexes appearing along the different reaction pathways. Furthermore, molecular energies have been calculated at QCISD(T) level in order to get an estimation of the activation energies. Finally, the nature of the molecular complexes and transitions states is analyzed by using kinetic-potential and natural bond orbital total energy decomposition schemes.

Unifying mechanical and thermodynamic descriptions across the thioredoxin protein family

We compare various predicted mechanical and thermodynamic properties of nine oxidized thioredoxins (TRX) using a Distance Constraint Model (DCM). The DCM is based on a nonadditive free energy decomposition scheme, where entropic contributions are determined from rigidity and flexibility of structure based on distance constraints. We perform averages over an ensemble of constraint topologies to calculate several thermodynamic and mechanical response functions that together yield quantitative stability/flexibility relationships (QSFR). Applied to the TRX protein family, QSFR metrics display a rich variety of similarities and differences. In particular, backbone flexibility is well conserved across the family, whereas cooperativity correlation describing mechanical and thermodynamic couplings between the residue pairs exhibit distinctive features that readily standout. The diversity in predicted QSFR metrics that describe cooperativity correlation between pairs of residues is largely explained by a global flexibility order parameter describing the amount of intrinsic flexibility within the protein. A free energy landscape is calculated as a function of the flexibility order parameter, and key values are determined where the native-state, transition-state, and unfolded-state are located. Another key value identifies a mechanical transition where the global nature of the protein changes from flexible to rigid. The key values of the flexibility order parameter help characterize how mechanical and thermodynamic response is linked. Variation in QSFR metrics and key characteristics of global flexibility are related to the native state X-ray crystal structure primarily through the hydrogen bond network. Furthermore, comparison of three TRX redox pairs reveals differences in thermodynamic response (i.e., relative melting point) and mechanical properties (i.e., backbone flexibility and cooperativity correlation) that are consistent with experimental data on thermal stabilities and NMR dynamical profiles. The results taken together demonstrate that small-scale structural variations are amplified into discernible global differences by propagating mechanical couplings through the H-bond network.