Six-dimensional quantum dynamics of H2 dissociative adsorption on the Pt(211) stepped surface

Results of experimental studies, and theoretical calculations utilizing classical trajectories, have shown that dissociation of H2 on the Pt(211) stepped surface is enhanced at low energies by a molecular trapping mechanism. Because quantum effects can play a large role at the low energies and long lifetimes that characterize molecular trapping, we have undertaken quantum dynamics calculations for this system, the first to treat all molecular degrees of freedom of a gas molecule reacting on a stepped metallic surface. The calculations show that molecular trapping persists in the quantum system, but only at much lower energies than experimentally seen, pointing to possible deficiencies in the potential energy surface. Classical and quasiclassical trajectory calculations on the same potential provide a reasonable picture of reaction overall, but many of the finer details are inaccurate, and certain classical reaction mechanisms are entirely invalid. We conclude that some skepticism should be shown toward any classical study for which long-lived trapping states play a role.     

Quantum wave packet ab initio molecular dynamics: an approach to study quantum dynamics in large systems

A methodology to efficiently conduct simultaneous dynamics of electrons and nuclei is presented. The approach involves quantum wave packet dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator, in conjunction with ab initio molecular dynamics treatment of the electronic and classical nuclear degree of freedom. The latter may be achieved either by using atom-centered density-matrix propagation or by using Born-Oppenheimer dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. The quantum wave packet dynamics is made computationally robust by using adaptive grids to achieve optimized sampling. One notable feature of the approach is that important quantum dynamical effects including zero-point effects, tunneling, as well as over-barrier reflections are treated accurately. The electronic degrees of freedom are simultaneously handled at accurate levels of density functional theory, including hybrid or gradient corrected approximations. Benchmark calculations are provided for proton transfer systems and the dynamics results are compared with exact calculations to determine the accuracy of the approach.     

Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations

Combined ab initio quantum mechanical and molecular mechanical calculations have been widely used for modeling chemical reactions in complex systems such as enzymes, with most applications being based on the determination of a minimum energy path connecting the reactant through the transition state to the product in the enzyme environment. However, statistical mechanics sampling and reaction dynamics calculations with a combined ab initio quantum mechanical (QM) and molecular mechanical (MM) potential are still not feasible because of the computational costs associated mainly with the ab initio quantum mechanical calculations for the QM subsystem. To address this issue, a reaction path potential energy surface is developed here for statistical mechanics and dynamics simulation of chemical reactions in enzymes and other complex systems. The reaction path potential follows the ideas from the reaction path Hamiltonian of Miller, Handy and Adams for gas phase chemical reactions but is designed specifically for large systems that are described with combined ab initio quantum mechanical and molecular mechanical methods. The reaction path potential is an analytical energy expression of the combined quantum mechanical and molecular mechanical potential energy along the minimum energy path. An expansion around the minimum energy path is made in both the nuclear and the electronic degrees of freedom for the QM subsystem internal energy, while the energy of the subsystem described with MM remains unchanged from that in the combined quantum mechanical and molecular mechanical expression and the electrostatic interaction between the QM and MM subsystems is described as the interaction of the MM charges with the QM charges. The QM charges are polarizable in response to the changes in both the MM and the QM degrees of freedom through a new response kernel developed in the present work. The input data for constructing the reaction path potential are energies, vibrational frequencies, and electron density response properties of the QM subsystem along the minimum energy path, all of which can be obtained from the combined quantum mechanical and molecular mechanical calculations. Once constructed, it costs much less for its evaluation. Thus, the reaction path potential provides a potential energy surface for rigorous statistical mechanics and reaction dynamics calculations of complex systems. As an example, the method is applied to the statistical mechanical calculations for the potential of mean force of the chemical reaction in triosephosphate isomerase.     

Influence of Intermolecular Vibrations on the Electronic Coupling in Organic Semiconductors: The Case of Anthracene and Perfluoropentacene

We have performed classical molecular dynamics simulations and quantum‐chemical calculations on molecular crystals of anthracene and perfluoropentacene. Our goal is to characterize the amplitudes of the room‐temperature molecular displacements and the corresponding thermal fluctuations in electronic transfer integrals, which constitute a key parameter for charge transport in organic semiconductors. Our calculations show that the thermal fluctuations lead to Gaussian‐like distributions of the transfer integrals centered around the values obtained for the equilibrium crystal geometry. The calculated distributions have been plugged into Monte‐Carlo simulations of hopping transport, which show that lattice vibrations impact charge transport properties to various degrees depending on the actual crystal structure.     

Mixed time slicing in path integral simulations

A simple and efficient scheme is presented for using different time slices for different degrees of freedom in path integral calculations. This method bridges the gap between full quantization and the standard mixed quantum-classical (MQC) scheme and, therefore, still provides quantum mechanical effects in the less-quantized variables. Underlying the algorithm is the notion that time slices (beads) may be "collapsed" in a manner that preserves quantization in the less quantum mechanical degrees of freedom. The method is shown to be analogous to multiple-time step integration techniques in classical molecular dynamics. The algorithm and its associated error are demonstrated on model systems containing coupled high- and low-frequency modes; results indicate that convergence of quantum mechanical observables can be achieved with disparate bead numbers in the different modes. Cost estimates indicate that this procedure, much like the MQC method, is most efficient for only a relatively few quantum mechanical degrees of freedom, such as proton transfer. In this regime, however, the cost of a fully quantum mechanical simulation is determined by the quantization of the least quantum mechanical degrees of freedom.     

Internal rotation and equilibrium structure of the 2-methyl-2-nitropropane molecule from joint processing of gas phase electron diffraction data,vibrational and microwave spectroscopy data,and quantum chemical calculation results

The structure and internal rotation of the 2-methyl-2-nitropropane molecule is studied by electron diffraction and quantum chemical calculations with the use of microwave and vibrational spectroscopy data. The electron diffraction data are analyzed within the general intramolecular anharmonic force field model and the quantum chemical pseudoconformer model, considering the adiabatic separation of the degree of freedom of large amplitude motion, i.e., the internal rotation of the NO₂ group. The equilibrium eclipsed configuration of the C _s symmetry molecule has the following experimental bond lengths and valence angles: r _e(N=O) = 1.226//1.226(8) Å, r _e(C–N)//r _e(C–C) = 1.520//1.515/1,521(4) Å, ∠_еC–C–N = = 109.1/106,1(8)°, ∠_еO=N=O = 124.2(6)°, ∠_eC–C–H_avg = 110(3)°. The equilibrium geometry parameters are well consistent with MP2/cc-pVTZ quantum chemical calculations and microwave spectroscopy data. The thermally average parameters previously obtained within the small vibration model show a satisfactory agreement with the new results. The electron diffraction data used in this work do not allow a reliable determination of the barrier to internal rotation. However, at a barrier of 203(2) cal/mol, which is derived from the microwave study, it follows from the electron diffraction data that the equilibrium configuration must correspond to an eclipsed arrangement of C–C and N=O bonds, which is also consistent with the results of quantum chemical calculations of various levels.     

Insight into Local Structure and Molecular Dynamics in Organic Solid‐State Ionic Conductors

Elucidating the rate and geometry of molecular dynamics is particularly important for unravelling ion‐conduction mechanisms in electrochemical materials. The local molecular motions in the plastic crystal 1‐ethyl‐1‐methylpyrrolidinium tetrafluoroborate ([C₂mpyr][BF₄]) are studied by a combination of quantum chemical calculations and advanced solid‐state nuclear magnetic resonance spectroscopy. For the first time, a restricted puckering motion with a small fluctuation angle of 25° in the pyrrolidinium ring has been observed, even in the low‐temperature phase (?45 °C). This local molecular motion is deemed to be particularly important for the material to maintain its plasticity, and hence, its ion mobility at low temperatures.     

Adapting the nudged elastic band method for determining minimum-energy paths of chemical reactions in enzymes

Optimization of reaction paths for enzymatic systems is a challenging problem because such systems have a very large number of degrees of freedom and many of these degrees are flexible. To meet this challenge, an efficient, robust and general approach is presented based on the well-known nudged elastic band reaction path optimization method with the following extensions: (1) soft spectator degrees of freedom are excluded from path definitions by using only inter-atomic distances corresponding to forming/breaking bonds in a reaction; (2) a general transformation of the distances is defined to treat multistep reactions without knowing the partitioning of steps in advance; (3) a multistage strategy, in which path optimizations are carried out for reference systems with gradually decreasing rigidity, is developed to maximize the opportunity of obtaining continuously changing environments along the path. We demonstrate the applicability of the approach using the acylation reaction of type A beta-lactamase as an example. The reaction mechanism investigated involves four elementary reaction steps, eight forming/breaking bonds. We obtained a continuous minimum energy path without any assumption on reaction coordinates, or on the possible sequence or the concertedness of chemical events. We expect our approach to have general applicability in the modeling of enzymatic reactions with quantum mechanical/molecular mechanical models.     

Ab initio dynamics with wave-packets and density matrices

Efficient methodologies to conduct simultaneous dynamics of electrons and nuclei are discussed. Particularly, attention is directed to a recent development that combines quantum dynamics with ab initio molecular dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. An approach to conduct quantum dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator is highlighted with suitable review of other related approaches. One notable feature of the method is that all important quantum dynamical effects including zero-point effects, tunneling as well as over-barrier reflections are accurately treated. Computational methodologies for improved efficiency of the quantum dynamics are also discussed. There exists a number of ways to carry out simultaneous ab initio molecular dynamics (such as Born–Oppenheimer dynamics and extended Lagrangian dynamics, Car–Parrinello dynamics being a prime example of the latter); our prime focus remains on atom-centered density-matrix propagation and Born–Oppenheimer dynamics. The electronic degrees of freedom are handled at accurate levels of density functional theory, using hybrid or gradient corrected approximations. Benchmark calculations are provided for a prototypical proton transfer system. Future generalizations and goals are discussed.     

The Scent of Maibowle – π Electron Localization in Coumarin from Its Microwave-Determined Structure

The microwave spectra of the natural substance coumarin, a planar aromatic molecule with the specific scent of maibowle, a popular fruit punch served in spring and early summer, were recorded using a molecular jet Fourier transform microwave spectrometer working in the frequency range from 4.0 to 26.5 GHz. The rotational constants and centrifugal distortion constants were determined with high precision, reproducing the spectra to experimental accuracy. The spectra of all singly-substituted ¹³C and ¹⁸O isotopologues were observed in their natural abundances to determine the experimental heavy atom substitution r_s and semi-experimental equilibrium r_e^SE structures. The experimental bond lengths and bond angles were compared to those obtained from quantum chemical calculations and those of related molecules reported in the literature with benzene as the prototype. The alternation of the C−C bond lengths to the value of 1.39 Å found for benzene reflects the localization of π electrons in coumarin, where the benzene ring and the lactone-like chain −CH=CH−(C=O)−O− are fused. The large, negative inertial defect of coumarin is consistent with out-of-plane vibrations of the fused rings.     

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Spin-inversion dynamics in O₂ binding to a model heme complex, which consisted of Fe(II)-porphyrin and imidazole, were studied using nonadiabatic wave packet dynamics calculations. We considered three active nuclear degrees of freedom in the dynamics, including the motions along the Fe–O distance, Fe–O–O angle, and Fe out-of-plane distance. Spin-free potential energy surfaces for the singlet, triplet, quintet, and septet states were developed using density functional theory calculations, and spin–orbit coupling elements were obtained from CASSCF-level electronic structure calculations. The spin-inversion mainly occurred between the singlet state and one of the triplet states due to large spin–orbit couplings and the contributions of other states were extremely small. The present quantum dynamics calculations suggested that the narrow crossing region model plays a dominant role in the O₂ binding dynamics. In addition, the one-dimensional Landau–Zener model underestimated the nonadiabatic transition probability.     

A structurally driven spectral transform Lanczos method for mixed quantum—classical canonical simulations (MQCC): the thermodynamics of Kr10–H and the energies of Krn–H, (n:1→9)

We develop and test an approximate approach for canonical simulations of weakly bound atomic or molecular systems for which some degrees of freedom can be treated separately by quantum mechanics. The system chosen for testing is Kr₁₀–H, for which the adiabatic approximation applied to separate the hydrogen degrees of freedom works reasonably well. The hydrogen atom is bound to the Kr clusters at cold temperatures and we calculate several bound states for clusters in the n=1–9 range, in the global minimum configuration. The structural character of the mixed quantum classical simulation is substantially different than the classical simulation for Kr₁₀–H as a result of zero point energy effects. When quantum effects are included, the low temperature dynamics of Kr₁₀–H are dominated by a significant well to well hopping about an incomplete icosahedral krypton core.     

Two Equivalent Internal Rotations in the Microwave Spectrum of 2,6-Dimethylfluorobenzene

Large amplitude motion of methyl groups in isolated molecules is a fundamental phenomenon in molecular physics. The methyl torsional barrier is sensitive to the steric and electronic environment in the surrounding of the methyl group, making the methyl group a detector of the molecular structure. To probe this effect, the microwave spectrum of 2,6-dimethylfluorobenzene, one of the six isomers of dimethylfluorobenzene, was measured using two pulsed molecular jet Fourier transform microwave spectrometers operating in the frequency range from 2 to 40 GHz. Due to internal rotations of two equivalent methyl groups with relatively low torsional barriers, all rotational transitions split into quartets with separations of up to several hundreds of MHz. The splittings were analyzed and modeled to deduce a torsional barrier of 236.7922 (21) cm⁻¹. The results are compared to those obtained from quantum chemical calculations and with other fluorine substituted toluene derivatives of the current literature where the methyl group is adjacent to a fluorine atom.     

Multiply Twisted Chiral Macrocycles Clamped by Tethered Binaphthyls Exhibiting High Circularly Polarized Luminescence Brightness

Chiral macrocyclic dimers, trimers, and tetramers composed of paraphenylene and tethered binaphthyl were synthesized, and their molecular structures and chiroptical properties were investigated. X-ray analysis and theoretical calculations revealed that multiple twisted molecular structures – dimers, trimers, and tetramers – adopt figure-of-eight, Möbius triangle, and concave rectangle structures, respectively. These homologues have large ϵ values in their UV-vis absorption spectra because of the π-conjugation of the naphthalene-phenylene-naphthalene frameworks. Owing to the shape-persistent ring structure and tethering with −OCH₂CH₂O−, high fluorescence quantum yields and a relatively high dissymmetry factor g_CPL in circularly polarized luminescence (CPL) spectra were achieved. This results in CPL brightness (B_CPL) of over 100, which is greater than that of the conventional organic CPL dye.     

Translational to rotational energy transfer in molecule-surface collisions

A theoretical approach that combines classical mechanics for treating translational and rotational degrees of freedom and quantum mechanics for describing the excitation of internal molecular modes is applied to the scattering of diatomic molecules from metal surfaces. Calculations are carried out for determining the extent of energy transfer to the rotational degrees of freedom of the projectile molecule. For the case of observed spectra of intensity versus final rotational energy, quantitative agreement with available experimental data for the scattering of NO and N(2) from close packed metal surfaces is obtained. It is shown that such measurements can be used to determine the average rotational energy of the incident molecular beam. Measurements of the exchange of energy between translational and rotational degrees of freedom upon collision are also described by calculations for these same systems.     

Incorporation of quantum effects for selected degrees of freedom into the trajectory-based dynamics using spatial domains

The approach of defining quantum corrections on nuclear dynamics of molecular systems incorporated approximately into selected degrees of freedom, is described. The approach is based on the Madelung-de-Broglie-Bohm formulation of time-dependent quantum mechanics which represents a wavefunction in terms of an ensemble of trajectories. The trajectories follow classical laws of motion except that the quantum potential, dependent on the wavefunction amplitude and its derivatives, is added to the external, classical potential. In this framework the quantum potential, determined approximately for practical reasons, is included only into the "quantum" degrees of freedom describing light particles such as protons, while neglecting with the quantum force for the heavy, nearly classical nuclei. The entire system comprised of light and heavy particles is described by a single wavefunction of full dimensionality. The coordinate space of heavy particles is divided into spatial domains or subspaces. The quantum force acting on the light particles is determined for each domain of similar configurations of the heavy nuclei. This approach effectively introduces parametric dependence of the reduced dimensionality quantum force, on classical degrees of freedom. This strategy improves accuracy of the quantum force and does not restrict interaction between the domains. The concept is illustrated for two-dimensional scattering systems, where the quantum force is required to reproduce vibrational energy of the quantum degree of freedom.     

Theoretical studies of some sulphonamides as corrosion inhibitors for mild steel in acidic medium

Density functional theory (DFT) at the B3LYP/6‐31G (d,p) and BP86/CEP‐31G* basis set levels and ab initio calculations using the RHF/6‐31G (d,p) methods were performed on four sulfonamides (namely sulfaacetamide (SAM), sulfapyridine (SPY), sulfamerazine (SMR), and sulfathiazole (STI)) used as corrosion inhibitors for mild steel in acidic medium to determine the relationship between molecular structure and their inhibition efficiencies (%IE). The order of inhibition efficiency obtained was SMR > SPY > STI > SAM which corresponded with the order of most of the calculated quantum chemical parameters namely E_HOMO (highest occupied molecular orbital energy), E_LUMO (lowest unoccupied molecular orbital energy), the energy gap (ΔE), the Mulliken charges on the C, O, N, S atoms, hardness (η), softness (S), polarizability (α), dipole moment (μ), total energy change (ΔE_T), electrophilicity (ω), electron affinity (A), ionization potential (I), the absolute electronegativity (χ), and the fraction of electrons transferred (ΔN). Quantitative structure activity relationship (QSAR) approach has been used and a correlation of the composite index of some of the quantum chemical parameters was performed to characterize the inhibition performance of the sulfonamides studied. The results showed that the %IE of the sulfonamides was closely related to some of the quantum chemical parameters but with varying degrees/order. The calculated %IE of the sulfonamides studied was found to be close to their experimental corrosion inhibition efficiencies. The experimental data obtained fits the Langmuir adsorption isotherm. The negative sign of the E_HOMO values and other thermodynamic parameters obtained indicates that the data obtained supports physical adsorption mechanism. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Proton transfer in ammonia cluster cations: molecular dynamics in a self consistent field

A theoretical study of the energetics and intramolecular dynamics for ammonia cluster cations (NH₃) ₂ ⁺ and (NH₃) ₃ ⁺ is presented. The proton transfer mechanism after a vertical ionisation is followed in detail. Structural and energetic calculations are performed near the Hartree-Fock self consistent field (HF-SCF) limit; all open shell calculations are spin restricted (RHF). The calculations reconcile experimental results from thermochemical and photoionisation measurements: discrepancies in the energetics are shown to be due to the probing of different regions of the potential energy surface (PES). For the dynamics calculations, it is impractical to determine a large region of the multidimensional PES and then integrate Newton's equations. The calculations therefore incorporate a quantum mechanical determination of the electronic energy of the system after each time increment while nuclear degrees of freedom are handled classically. In this way, the classical reaction path across the Born-Oppenheimer surface is obtained.     

Reversibility and diffusion in mandelythiamin decarboxylation. Searching dynamical effects in decarboxylation reactions

Decarboxylation of mandelylthiamin in aqueous solution is analyzed by means of quantum mechanics/molecular mechanics simulations including solvent effects. The free energy profile for the decarboxylation reaction was traced, assuming equilibrium solvation, while reaction trajectories allowed us to incorporate nonequilibrium effects due to the solvent degrees of freedom as well as to evaluate the rate of the diffusion process in competition with the backward reaction. Our calculations that reproduce the experimental rate constant show that decarboxylation takes place with a non-negligible free energy barrier for the backward reaction and that diffusion of carbon dioxide is very fast compared to the chemical step. According to these findings catalysts would not act by preventing the backward reaction.