Semiclassical treatment of reactions at surfaces with electronic transitions

The semiclassical treatment of reactions at surfaces with electronic transitions based on the fewest-switches algorithm is compared with full quantum mechanical results. As a model system the ionization probability in I2 scattering from a diamond surface is chosen. In the calculations we treat the molecular distance from the surface and one surface oscillator coordinate explicitly. Furthermore, we also consider molecular rotation in the semiclassical calculations. The semiclassical results agree with the quantum results although some discrepancies remain, as far as the phase coherence is concerned. We identify energy transfer to molecular and surface degrees of freedom as a possible mechanism that could explain the experimental dependence of the ionization probability on the incident kinetic energy of the molecule.     

Semiclassical simulation of electronic spectra in aniline-Arn clusters

We present results of semiclassical simulations of the electronic spectra and dynamics of aniline-Ar_n (1≤n≤3) clusters. The spectral density formalism of Mukamel [3] is used to generate the spectra from the time dependent energy difference of the S₀ and S₁ states of aniline solvated by the argon atoms. A repulsive Ar-N interaction is incorporated in the Hamiltonian of the S₁ state; this term permits a quantitative prediction of the origin shifts of the S₁<--S₀ transition (both red and blue shifts) for all the clusters studied. The temperature dependence of the spectrum of aniline-Ar₂ is correlated with the underlying dynamics of this cluster.     

Communication: A simple method for simulation of freezing transitions

Despite recent advances, precise simulation of freezing transitions continues to be a challenging task. In this work, a simulation method for fluid-solid transitions is developed. The method is based on a modification of the constrained cell model which was proposed by Hoover and Ree [J. Chem. Phys. 47, 4873 (1967)]. In the constrained cell model, each particle is confined in a single Wigner-Seitz cell. Hoover and Ree pointed out that the fluid and solid phases can be linked together by adding an external field of variable strength. High values of the external field favor single occupancy configurations and thus stabilize the solid phase. In the present work, the modified cell model is simulated in the constant-pressure ensemble using tempering and histogram reweighting techniques. Simulation results on a system of hard spheres indicate that as the strength of the external field is reduced, the transition from solid to fluid is continuous at low and intermediate pressures and discontinuous at high pressures. Fluid-solid coexistence for the hard-sphere model is established by analyzing the phase transition of the modified model in the limit in which the external field vanishes. The coexistence pressure and densities are in excellent agreement with current state-of-the-art techniques.     

A wave-packet simulation of the low-lying singlet electronic transitions of acetylene

The vibronic structure of the S0 --> S1 and the S0 --> S2 electronic transitions of acetylene is studied theoretically based on an ab initio quantum-dynamical approach. The underlying potential-energy surfaces and transition dipole moment functions are obtained from high-level multireference calculations, including the Davidson correction. Ensuing quantum-dynamical simulations rely on the wave-packet propagation method, using grid techniques, and including three nuclear degrees of freedom (C-C stretching and both HCC bending modes for J = 0). The importance of strong anharmonicity is assessed, especially for the S2 excited state with its unusual potential-energy surface. Good overall agreement with the experimental UV absorption spectrum of acetylene is achieved in the range of 6-8 eV.     

Couplings between electronic transitions in a subsystem formulation of time-dependent density functional theory

A subsystem formulation of time-dependent density functional theory (TDDFT) within the frozen-density embedding (FDE) framework and its practical implementation are presented, based on the formal TDDFT generalization of the FDE approach by Casida and Wesolowski [Int. J. Quantum Chem. 96, 577 (2004)]. It is shown how couplings between electronic transitions on different subsystems can be seamlessly incorporated into the formalism to overcome some of the shortcomings of the approximate TDDFT-FDE approach in use so far, which was only applicable for local subsystem excitations. In contrast to that, the approach presented here allows to include couplings between excitations on different subsystems, which become very important in aggregates composed of several similar chromophores, e.g., in biological or biomimetic light-harvesting systems. A connection to Forster- and Dexter-type excitation energy coupling expressions is established. A hybrid approach is presented and tested, in which excitation energy couplings are selectively included between different chromophore fragments, but neglected for inactive parts of the environment. It is furthermore demonstrated that the coupled TDDFT-FDE approach can cure the inability of the uncoupled FDE approach to describe induced circular dichroism in dimeric chromophores, a feature known as a "couplet," which is also related to couplings between (nearly) degenerate electronic transitions.     

A new grand canonical ensemble method to calculate first-order phase transitions

A theory about first-order phase transition of pure fluids is proposed. The theory is developed by combining grand canonical ensemble with density functional for homogeneous fluids. It is based on the fact that the grand partition function of one macroscopic volume is the product of the grand partition functions of its subvolumes. Density fluctuations of molecules determine the relation between the grand partition function and the free energy density. By combining pairs of subvolumes successively, the free energy density is transformed and rapidly becomes stationary. The stationary curve versus molecule density is convex and its linear segments represent phase transitions. The transform leads to the new grand canonical method to calculate phase equilibrium, which is more robust than classic ones. The transform suggests that classical van der Waals loop is physical and essential to phase transition.     

A new method of semigrand canonical ensemble to calculate first-order phase transitions for binary mixtures

First-order phase transitions of binary mixtures at the given pressure (P) and temperature (T) are studied by taking into account the composition fluctuations. Isothermal-isobaric semigrand canonical ensemble is adopted to find the relations among the total number of molecules, the composition fluctuations and Gibbs free energy density. By combining two identical subsystems of mixtures successively, the free energy density is transformed until being stable and its linear segments represent phase transitions. A new method is developed to calculate the phase equilibriums of binary mixtures. The method handles multiple types and number of phase equilibriums at single time and its solutions are physically justified. One example is shown for calculating the phase diagram of binary Lennard-Jones mixture. It demonstrates that the fluctuations of the total number of molecules in mixtures are fundamental behind phase transitions and the van der Waals loops in Gibbs free energy are reasonable.     

Dense orientationally ordered states of a single semiflexible macromolecule: an expanded ensemble Monte Carlo simulation

Using a coarse-grained model we perform a Monte Carlo simulation of the state behavior of an individual semiflexible macromolecule. Chains consisting of N = 256 and 512 monomer units have been investigated. A recently proposed enhanced sampling Monte Carlo technique for the bond fluctuation model in an expanded ensemble in four-dimensional coordinate space was applied. The algorithm allows one to accelerate the sampling of statistically independent three-dimensional conformations in a dense globular state. We found that the temperature of the intraglobular liquid-solid transition decreases with increasing chain stiffness. We have investigated the possible intraglobular orientationally ordered (i.e., liquid-crystalline) structures and obtained a diagram of states for chains consisting of N = 256 monomer units. This diagram contains regions of stability of coil, two spherical globules (liquid and solid), and rod-like globule conformations. Transitions between the globular states are rounded first-order ones since the states of liquid, solid, and cylinder-like globules do have different internal symmetry.     

Determination of fluid--solid transitions in model protein solutions using the histogram reweighting method and expanded ensemble simulations

Protein crystallization conditions are usually identified by empirical screening methods because of the complexity of the process, such as the existence of nonequilibrium phases and the different crystal forms that may result from changes in solution conditions. Here the crystallization of a model protein is studied using computer simulation. The model consists of spheres that have both an isotropic interaction of short range and anisotropic interactions between patch-antipatch pairs. The free energy of a protein crystal is calculated using expanded ensemble simulations of the Einstein crystal, and NpT-Monte Carlo simulations with histogram reweighting are used to determine the fluid-solid coexistence. The histogram reweighting method is also used to trace out the complete coexistence curve, including multiple crystal phases, with varying reduced temperature, which corresponds to changing solution conditions. At a patch-antipatch interaction strength five times that of the isotropic interaction, the protein molecules form a stable simple cubic structure near room temperature, whereas an orientationally disordered face-centered-cubic structure is favored at higher temperatures. The anisotropic attractions also lead to a weak first-order transition between orientationally disordered and ordered face-centered-cubic structures at low temperature, although this transition is metastable. A complete phase diagram, including a fluid phase, three solid phases, and two triple points, is found for the six-patch protein model. A 12-patch protein model, consistent with the face-centered-cubic structure, leads to greater thermodynamic stability of the ordered phase. Metastable liquid-liquid phase equilibria for isotropic models with varying attraction tails are also predicted from Gibbs ensemble simulations.     

Assignment of the electronic transitions in benzene

The problem of the assignment of π-electronic transitions in benzene is discussed using all criteria presently available. It is shown that based on this information a few different assignments are impossible to exclude. The correct assignment ³B_1u < ³E_1u < ¹B_2u < ³B_2u < ¹B_1u < ³E⁺_2g < ¹E_1u < ¹E^?_2g < ³E^?_2g has been selected as result of theoretical considerations based on a new approach to the semi-empirical π-electron theory. The results confirm the adequacy of the π-electron model for energy level calculations, and emphasise the fundamental importance of multi-excited configurations.     

Rate of radiationless electronic transitions for molecules in the condensed phase

Rate constants of radiationless electronic transitions in a diatomic molecule in a crystal at non-zero temperature are calculated. The electronic terms of the molecule are simulated by the Morse potential. The crystal vibrations are assumed to be harmonic. The calculations are done under the assumption that perturbation theory is applicable to the operator inducing the electronic transitions. The vibrational interaction of the molecule with the medium is not supposed to be small. The results explain certain experimental data on the radiationless electronic transitions in aromatic hydrocarbons.     

The calculation of Franck-Condon factors for the electronic transitions of the polyacenes

Progressional intensities have been calculated for the ¹ L _a band of the polyacenes which give good agreement with experiment. The Franck-Condon factors are calculated on the assumption that the frequencies and normal modes in the ground and excited states are identical. Our results, based on a simple force field, also show that the assumption (by McCoy and Ross) that the C-C stretching frequencies are degenerate is satisfactory as far as the calculation of the shape of the overall vibrational envelope is concerned.

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Zusammenfassung Wir berechneten die Intensitäten der ¹ L _a-Progressionen von Acenen, in guter Übereinstimmung mit dem Experiment. Die Franck-Condon-Faktoren werden unter der Annahme bestimmt, daß Frequenzen und Normalschwingungen im Grund- und angeregten Zustand gleich sind. Unsere mit einem einfachen Kraftansatz erhaltenen Ergebnisse zeigen weiter, daß die Annahme (von McCoy und Ross) entarteter C-C-Valenzschwingungen ausreicht, um die allgemeine Schwingungsstruktur der Bandenenveloppe zu berechnen.

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Résumé Nous avons calculé les intensités de progression de la bande ¹ L _a des acènes, en bon accord avec l'expérience. Les facteurs de Franck-Condon sont déterminés, en admettant des fréquences et vibrations normales identiques pour les états fondamental et excité. Nos résultats, sur base d'un champ de force simple, montrent de plus que l'hypothèse (de McCoy et Ross) des vibrations de valence C-C dégénérées est satisfaisant pour le calcul de la forme générale de l'enveloppe vibrationelle des bandes.

     

Calculated electronic transitions of the water ammonia complex

We have calculated vertical excitation energies and oscillator strengths of the low lying electronic transitions in H2O, NH3, and H2ONH3 using a hierarchy of coupled cluster response functions [coupled cluster singles (CCS), second order approximate coupled cluster singles and doubles (CC2), coupled cluster singles and doubles (CCSD), and third order approximate coupled cluster singles, doubles, and triples (CC3)] and correlation consistent basis functions (n-aug-cc-pVXZ, where n=s,d,t and X=D,T,Q). Our calculations indicate that significant changes in the absorption spectra of the photodissociative states of H2O and NH3 monomers occur upon complexation. In particular, we find that the electronic transitions originating from NH3 are blueshifted, whereas the electronic transitions originating from H2O are redshifted.     

A general simulation method for computing conformational properties of single polymer chains

Rotational isomeric state (RIS) theory is the standard method for computing the conformational statistics of polymer chains. It applies to chains under theta conditions, either in the melt or in theta solution. RIS statistical weights can also be used in a Monte Carlo scheme for generating independent chain conformations with the correct statistics. One practical drawback of RIS methods is that statistical weights must be derived before any chain properties can be calculated. This can be tedious for all but relatively simple chains. Here, an efficient method is presented for computing the properties of theta chains without the intermediate step of deriving statistical weights. The method—‘RIS’ Metropolis Monte Carlo (RMMC) simulation-allows computation of the same type of properties as does RIS theory. It shares certain approximations with RIS theory but is not, strictly speaking, a rotational isomeric state method, as it allows bond torsion angles to vary continuously.     

Molecular dynamics simulation in the grand canonical ensemble

An extended system Hamiltonian is proposed to perform molecular dynamics (MD) simulation in the grand canonical ensemble. The Hamiltonian is similar to the one proposed by Lynch and Pettitt (Lynch and Pettitt, J Chem Phys 1997, 107, 8594), which consists of the kinetic and potential energies for real and fractional particles as well as the kinetic and potential energy terms for material and heat reservoirs interacting with the system. We perform a nonlinear scaling of the potential energy parameters of the fractional particle, as well as its mass to vary the number of particles dynamically. On the basis of the equations of motion derived from this Hamiltonian, an algorithm has been proposed for MD simulation at constant chemical potential. The algorithm has been tested for the ideal gas, for the Lennard-Jones fluid over a wide range of temperatures and densities, and for water. The results for the low-density Lennard-Jones fluid are compared with the predictions from a truncated virial equation of state. In the case of the dense Lennard-Jones fluid and water our predicted results are compared with the results reported using other available methods for the calculation of the chemical potential. The method is also applied to the case of vapor-liquid coexistence point predictions.     

Topological implications of Y-conjugation for electronic transitions of cyanine dyes

To understand connections between electronic transitions of dyes having related conjugated systems, topological arguments from graph theory are often helpful. Using the Chebyshev expansion of the characteristic polynomials of cyanines, it is shown that the two possible structures of tribranched cyanines, i.e., a strongly out-of-plane orientation of one of the conjugated branches or a Y-conjugation of the entire unsaturated system, are both consistent with the similarities between visible absorption of these compounds and of simple chains. To choose between these two structures, evidence from other sources should be added.