Vibrational Entropy Term Research Articles

Modelling the impact of configurational entropy on the stability of amorphous SiO2

Configurational entropy has been computed to assess its impact on stabilizing the amorphous structure of SiO2. Using a range of atomic scale modelling methods, the structure of crystalline and amorphous SiO2 has been assessed and the configurational entropy associated with the structures observed at varying temperatures has allowed computation of the associated Shannon entropy. Combined with the enthalpy terms generated from density functional theory, a robust method for assessing the stability of crystalline and amorphous structures has been presented that can be used in future work assessing the role of dopants, glass forming additions and radiation damage. Future work will include the vibrational entropy term, to capture the full entropic contribution to amorphisation.

Hydrogen accommodation in the TiZrNbHfTa high entropy alloy

The equiatomic TiZrNbHfTa high entropy alloy (HEA) and its hydrides (TiZrNbHfTaH0.4- 2.0) have been modelled at the atomic scale and the phase transformations that occur during hydrogen absorption have been simulated. The thermodynamics of vacancy formation, hydrogen accommodation and hydride decomposition have been examined using density functional theory, linking results to experimental investigations. A model predicting the decomposition of the TiZrNbHfTaH system is proposed based on the temperature dependence of configurational and vibrational entropy terms and the hydrogen solution energies of individual interstitials. The presence of hydrogen in the HEA structure was shown to promote the formation of vacancies due to a 0.21 eV reduction of the energy barrier for vacancy formation. Interstitials placed around vacancies were observed to relax onto octahedral sites from initial tetrahedral positions, while interstitials placed in the same environment, without the vacancy present, were observed to relax onto tetrahedral sites from initial octahedral positions. This provides a mechanistic basis for experimentally observed behaviour. The phase stabilities of each arrangement of the TiZrNbHfTaH structure were explored, identifying that the FCC arrangement of the dihydride at the hydrogen to metal atom ratio (H/M) = 2.0, is more stable than the BCT arrangement at 550 K. The spontaneous BCC to BCT transformation, observed in the H/M range 1.2 – 1.6, and the thermodynamically favourable BCT to FCC phase transformation at H/M = 2.0, provides a comprehensive depiction of the mechanistic behaviour of the TiZrNbHfTa HEA during hydrogen absorption.

Computational study (MM and DFT) on the conformations of some aromatic crown ether rotaxane macrocycles

We examined the preferred conformations of several aromatic crown ether macrocycles containing dibenzo (DB24C8 (1), BMP25C8 (2), BPP34C10 (3)), dinaphtho (2/3DN30C10 (4), 1/5DN38C10 (5)), diphenyl phenanthroline (6) or isophthalamide (7) groups in order to elucidate their preferred conformations and to test the performance of computational methods (molecular mechanics and DFT) in the description of the building blocks of some mechanically interlocked molecules. An exhaustive search for low energy conformations was carried out. The analyses of the geometries of the low-energy conformations of 1–7 revealed that all they have either preformed cavities for adopting substrates, or due to the high flexibility and easy deformability of the macrorings, they have the potential to allow threading of an axle-like molecular component as a slippage step in the formation of a rotaxane structure. Unexpectedly, for one of the macrorings, 4, the geometries of the low-energy conformations differ significantly from the representative conformations of prima facie conformationally similar macrocycles. Contributions from the vibrational entropy term reorder the steric energy lists of conformations in some cases (1, 2, 4, 6), compensating relative steric energies up to 0.9 kcal mol−1. Cluster analysis of the molecular conformations was performed with examining the dependence of the results on the number of torsions for the clustering and the characteristic threshold distances, defining the clustering. All conformations with relative steric energies not exceeding 2.0 kcal mol−1 were examined also with the DFT method (M06-2X functional). In some cases (1 and 2) conformations with relative steric energies ca. 2.0 kcal mol−1 are with the lowest total energies in the corresponding DFT energy lists. These are conformations where the aromatic fragments are facing each other at short distance, ca. 5 Å. We are inclined to conclude that in such cases the DFT models used enhance the dispersion interactions at short distances.

Thermodynamic and structural aspects of molecular recognition in mannose-binding protein complexes: a theoretical study over HRP-ArtinM association.

The biomolecular recognition of D-mannose-binding lectin from Artocarpus heterophyllus (ArtinM) by Horseradish Peroxidase (HRP) mediated by glycosylation allows their application in a multitude of biological systems. The present work describes the use of molecular dynamics (MD) to assess the Gibbs free energy associated with the formation of a ArtinM-HRP conjugate mediated by a glycosylation molecule. For the enthalpy term, we applied the molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) method and for the vibrational entropy term, we use the quasi-harmonic approximation. Our results show that, even without glycosylation, the binding free energy between ArtinM and HRP is - 196.154 kJmol- 1, an extremely high affinity with low selectivity, originated mainly through the van der Waals energy terms. The binding free energy between ArtinM and the glycosylated HRP (gHRP) was calculated at - 66.156 kJmol- 1, an absolute and considerably lower value, however, originated from electrostatic energy terms, which increases the selectivity of molecular recognition. Our work has shown that the HRP active site region has a high affinity and low selectivity for other biomolecules. The presence of glycosylation plays a role in increasing this selectivity for this region. Thus, we conclude that performing mutagenesis of amino acid residues near the entrance of the catalytic site, can improve the activity of non-glycosylated HRPs. This illustrates new insights that can be applied to carbohydrate-based immunochemistry.

A vibrational entropy term for DNA docking with autodock

DNA interacts with small molecules, from water to endogenous reactive oxygen and nitrogen species, environmental mutagens and carcinogens, and pharmaceutical anticancer molecules. Understanding and predicting the physical interactions of small molecules with DNA via docking is key not only for the comprehension of molecular-level events that lead to carcinogenesis and other diseases, but also for the rational design of drugs that target DNA. We recently validated AutoDock, a popular docking method that includes a physics-based scoring function and a Lamarckian Genetic Algorithm, for the prediction of small molecule geometries upon physical binding to DNA. In this work, we added a vibrational entropy term based on the docking frequency to the scoring function in order to improve the accuracy of the best (lowest) score geometry. We found that in four small molecule–DNA systems the inclusion of the vibrational entropy term decreased the root-mean-square-deviation from the experimental crystallographic structure. Including the entropy term also preserved the successful prediction of the binding geometry compared to the crystallographic structure for the rest of the small molecule–DNA systems. We also improved the method of creating clusters of docking geometries and emphasized the importance of the length of the search process for similar vibrational entropy terms.

Elastic Properties of DNA as the Entropic Driving Force for Dehybridization Transitions

Through the use of a coarse-grained lattice model informed from all-atomic simulations near equilibrium, we obtain a theoretical estimate of the sequence-dependent slow melting rates (> nanoseconds) of DNA duplexes with activation free energies accurate within 3kT. We show that the change in elastic properties of short DNAs is the key entropic driving force for DNA melting and hybridization. Using a vibration and torsional continuum model, we relate this entropy to the bending and torsional persistence lengths captured from the phonon spectra in all-atomic simulations, near equilibrium, by capturing both the momentum and configuration degrees of freedom simultaneously. A key to the theory is the cooperative melting of all but one base pair at the transition state. This hinge transition state allows us to replace the hydrogen bond vibration modes with a set of out/of-phase bending modes with a much higher vibration entropy (lower phonon frequencies). A multidimensional version of Kramers transition state theory allows us to assign this change to an effective vibrational entropy term that counters the enthalpic gain required to break the hydrogen bonds, leading to an elastic theory for the melting rate of short DNAs. As the hydrogen bond enthalpies are thermodynamic quantities, we estimate them from the classical nearest-neighbor theory. The vibration entropy of the hinge transition state is strictly kinetic but, as it relates only to the persistence lengths, we are able to capture it from near-equilibrium simulations of the duplex. This theory allows us both to make quantitative estimates of the melting rates of short DNAs as well as to differentiate between unzipping and other reaction pathways that may be followed in the presence of secondary structures or mismatches. It represents the first theory for DNA melting with quantitative accuracy.

Giant direct and inverse magnetocaloric effect linked to the same forward martensitic transformation

Metamagnetic shape memory alloys have aroused considerable attraction as potential magnetic refrigerants due to the large inverse magnetocaloric effect associated to the magnetic-field-induction of a reverse martensitic transformation (martensite to austenite). In some of these alloys, the austenite phase can be retained on cooling under high magnetic fields, being the retained phase metastable after field removing. Here, we report a giant direct magnetocaloric effect linked to the anomalous forward martensitic transformation (austenite to martensite) that the retained austenite undergoes on heating. Under moderate fields of 10 kOe, an estimated adiabatic temperature change of 9 K has been obtained, which is (in absolute value) almost twice that obtained in the conventional transformation under higher applied fields. The observation of a different sign on the temperature change associated to the same austenite to martensite transformation depending on whether it occurs on heating (retained) or on cooling is attributed to the predominance of the magnetic or the vibrational entropy terms, respectively.

Calculation of conformational energies and optical rotation of the most simple chiral alkane

Quantum chemical calculations have been performed to investigate the conformer distribution of 4-ethyl-4-methyloctane and its optical rotation. With the reference methods MP2 and SCS-MP2, the energies of seven conformers are found within a range of about 1.5 kcal mol(-1). It is demonstrated that the relative energies cannot be reliably predicted with conventional GGA or hybrid density functionals, Hartree-Fock, semiempirical AM1, and classical force field (MM3) calculations. An empirical dispersion correction to GGA (PBE-D), hybrid (B3LYP-D), or double hybrid (B2PLYP-D) functionals corrects these errors and results in very good agreement with the reference energies. Optical rotations have been calculated for all seven conformers at the TDDFT(BHLYP/aTZV2P) level. The computed macroscopic rotation is derived from a classical Boltzmann average. The result (1.9-3.2 deg dm(-1) (g/mL)(-1)) is very close to the experimental value of 0.2 deg dm(-1) (g/mL)(-1) for the (R)-enantiomer and has the right sign. Because six conformers are significantly populated at room temperature and the rotations of individual conformers differ in sign and magnitude, the calculated average rotation is rather sensitive to the conformer population used. From the electronic structure point of view, this example emphasizes the effect of long-range dispersion effects for the evaluation of population averaged quantities in large molecules. Computations based on free enthalpies are in worse agreement with experiment that is attributed to artefacts of the harmonic approximation used to compute the vibrational entropy terms.

Comparison between computational alanine scanning and per‐residue binding free energy decomposition for protein–protein association using MM‐GBSA: Application to the TCR‐p‐MHC complex

Recognition by the T-cell receptor (TCR) of immunogenic peptides (p) presented by Class I major histocompatibility complexes (MHC) is the key event in the immune response against virus-infected cells or tumor cells. A study of the 2C TCR/SIYR/H-2K(b) system using a computational alanine scanning and a much faster binding free energy decomposition based on the Molecular Mechanics-Generalized Born Surface Area (MM-GBSA) method is presented. The results show that the TCR-p-MHC binding free energy decomposition using this approach and including entropic terms provides a detailed and reliable description of the interactions between the molecules at an atomistic level. Comparison of the decomposition results with experimentally determined activity differences for alanine mutants yields a correlation of 0.67 when the entropy is neglected and 0.72 when the entropy is taken into account. Similarly, comparison of experimental activities with variations in binding free energies determined by computational alanine scanning yields correlations of 0.72 and 0.74 when the entropy is neglected or taken into account, respectively. Some key interactions for the TCR-p-MHC binding are analyzed and some possible side chains replacements are proposed in the context of TCR protein engineering. In addition, a comparison of the two theoretical approaches for estimating the role of each side chain in the complexation is given, and a new ad hoc approach to decompose the vibrational entropy term into atomic contributions, the linear decomposition of the vibrational entropy (LDVE), is introduced. The latter allows the rapid calculation of the entropic contribution of interesting side chains to the binding. This new method is based on the idea that the most important contributions to the vibrational entropy of a molecule originate from residues that contribute most to the vibrational amplitude of the normal modes. The LDVE approach is shown to provide results very similar to those of the exact but highly computationally demanding method.

A computational analysis of the binding affinities of FKBP12 inhibitors using the MM‐PB/SA method

The FK506-binding proteins have been targets of pharmaceutical interests over years. We have studied the binding of a set of 12 nonimmunosuppressive small-molecule inhibitors to FKBP12 through molecular dynamics simulations. Each complex was subjected to 1-ns MD simulation conducted in an explicit solvent environment under constant temperature and pressure. The binding free energy of each complex was then computed by the MM-PB/SA method in the AMBER program. Our MM-PB/SA computation produced a good correlation between the experimentally determined and the computed binding free energies with a correlation coefficient (R(2)) of 0.93 and a standard deviation as low as 0.30 kcal/mol. The vibrational entropy term given by the normal mode analysis was found to be helpful for achieving this correlation. Moreover, an adjustment to one weight factor in the PB/SA model was essential to correct the absolute values of the final binding free energies to a reasonable range. A head-to-head comparison of our MM-PB/SA model with a previously reported Linear Response Approximation (LRA) model suggested that the MM-PB/SA method is more robust in binding affinity prediction for this class of compounds.

Defects in silicon: the role of vibrational entropy

Vibrational free energies are calculated from first-principles in the same Si periodic supercells routinely used to perform defect calculations. The specific heat, vibrational entropy, and zero-point energy obtained in defect-free cells are very close to the measured values. The importance of the vibrational part of the free energy is studied in the case of two defect problems: the relative energies of the H 2 and H 2 ∗ dimers and the binding energy of a copper pair. In both cases, the vibrational entropy term causes total energy differences to change by about 0.2 eV between 0 and 800 K. We also comment on the rotational entropy in the case of H 2 and the configurational entropy in the case of the Cu pair. These examples illustrate the importance of extending first-principles calculations of defects in semiconductors to include free energy contributions.

Two-dimensional equilibrium island shape and step free energies of Cu(001)

We have derived expressions for the free energies of the densely packed [110] and 100% kinked [010] step edges of Cu(001), including both meandering and vibrational entropy terms. The meandering entropy is calculated by taking into account nearest-neighbor and next-nearest-neighbor interactions between the Cu atoms. The vibrational entropy is determined within the framework of an isotropic Einstein oscillator. By using the earlier obtained kink creation energy by Giesen, Steimer, and Ibach [Surf. Sci. 471, 80 (2001)] and taking the strength of the next-nearest-neighbor interaction as the only fitting parameter, we obtain perfect agreement between the ratio of the calculated and experimentally determined ratio of the step free energies (i.e., ${F}_{[010]}{/F}_{[110]}).$ Moreover, in contrast to the Ising model we predict that the two-dimensional equilibrium Cu(001) island shape at $T=0\mathrm{K}$ is not a perfect square.

Temperature dependence of the step free energy

We have derived an expression for the step free energy that includes the usual thermally induced step meandering term and a vibrational entropy term related to the step edge atoms. The latter term results from the reduced local coordination of the step atoms with respect to the terrace atoms and was introduced recently by Frenken and Stoltze as well as by Bonzel and Emundts. Additionally, we have added third and fourth terms that deal with the vibrational entropy contribution of the thermally generated step and kink atoms. At elevated temperatures the two latter vibrational entropy terms are of the same order of magnitude. Incorporation of these vibrational entropy terms results in a faster decrease of the step free energy with increasing temperature than anticipated previously. This enhanced temperature dependence of the step free energy results in a lower thermal roughening temperature of the facet.

Surface diffusion potential energy surfaces from first principles: CO chemisorbed on Pt{110}

Lateral potential energy curves for the chemisorption of CO on Pt{110} (1×1) and (1×2) along different azimuthal directions have been calculated using density functional theory slab calculations. In contrast to the simple models almost universally used, the results along 〈11̄0〉 show that there is a barrier of ∼0.15 eV between bridge and atop sites. Both bridge and atop sites are local minima. Diffusion along 〈100〉 on the (1×1) surface is strongly inhibited by a barrier ⩾1.2 eV. Quasielastic helium atom scattering data require reanalysis in the light of these results. The free energy, determining the most stable site at finite temperatures, includes a significant vibrational entropy term in the atop site.

Simulation of surface segregation free energies.

The effects of different assumptions made in the simulation of surface segregation free energies are considered. Thirty face-centered-cubic dilute binary alloys are investigated using embedded-atom method potentials. First, it is demonstrated that the inclusion of local atomic relaxations in lattice statics simulations strongly affects the segregation free energy at (111) free surfaces in over half of the alloys. Second, a Monte Carlo technique, namely, the overlapping distributions method (ODMC), is used to determine the effect of the vibrational entropy term on the surface segregation Helmholtz free energy for simulations at elevated temperatures (1000 K). It is determined that the vibrational entropy term is important for a quarter of the alloys. We conclude that for accurate calculations of surface segregation free energies, both local atomic relaxations and the vibrational entropy must be included in nearly all cases. Since the ODMC method is very computer-time intensive, a technique based on a simplification of the quasiharmonic approximation for calculating free energies is investigated. Results from this free-energy minimization (FEM) method using the local harmonic approximation are compared to results from the ODMC method. It is found that the FEM method calculates the segregation free energies at (111) free surfaces accurately for most of the 30 alloys. Segregation free energy profiles are also calculated as a function of distance from (111) free surfaces employing both methodologies. The agreement is found to be poor for alloys that have a large solvent atom and a small solute atom. Other problems and sources of error with the FEM method are also discussed.

On the role of the vibrational entropy in phase transitions at surfaces

For many chemisorption systems several different substrate binding sites (e.g., on-top and bridge sites) can be occupied simultaneously. The resonance frequencies of the low-frequency adsorbate vibrational modes (frustrated translations and rotations) may differ strongly between the different symmetry sites and this introduces an important vibrational entropy term in the free energy for the adsorbate system which at high temperature tends to favour occupation of the sites with the lowest vibrational frequencies. In this letter it is argued that this is a strong driving force for phase transitions in many adsorbate systems and in particular for the order-disorder transition of CO on Pt(1 1 1).

Thermochemistry of binary liquid gold alloys: The systems Au-Ni, Au-Co, Au-Fe, and Au-Mn

In this paper we report enthalpy of mixing data for the liquid alloys of gold with manganese, iron, cobalt, and nickel obtained by a Calvet-type calorimeter at 1378 K. The enthalpies of mixing are compared with Gibbs energies calculated from earlier emf and vapor pressure studies to yield information on the excess entropies of mixing. The limiting enthalpies of solution of the liquid transition metals in liquid gold are compared with values predicted from the semi-empirical model of Miedemaet al. and with earlier data for the same transition metals in liquid copper. The calculated values of the excess entropy of solution in liquid gold are compared with the corresponding values in liquid copper near 1400 K. For Ni, Co, and Fe as solutes we observepositive shifts of 5 to 9 J K−1 mol−1 which are attributed to vibrational entropy terms. For Mn there is a strongnegative shift of about 35 J K−1 mol−1. This shift probably is due to “complex” or “associate” formation between gold and manganese atoms.