Model Potential Energy Surfaces Research Articles

The sticking of H and D atoms on a graphite (0001) surface: The effects of coverage and energy dissipation

Classical trajectory methods are used to examine the trapping and sticking of H and D atoms on the graphite (0001) surface. Total energy calculations based on density functional theory are used to construct the model potential energy surface, and graphite clusters of up to 121 atoms are considered. For hydrogen to chemisorb, the bonding carbon must pucker out of the surface plane by roughly 0.4 A. For incident energies above the 0.2 eV barrier, any trapped H atoms must rapidly dissipate their excess energy into the surrounding lattice within a few vibrations of the C-H stretch in order to remain bound. For sufficiently large clusters, the C-H bond stabilizes within about 0.1 ps. The sticking probability for D at 150 K is in the range of 5%-10%, more-or-less consistent with the most recent measurements in the limit of zero coverge. Variation with isotope and substrate temperature is weak. We estimate that the sticking cross section for adsorption at the para site, directly across the sixfold carbon ring from an already adsorbed H atom, can be four or more times larger that the zero coverage sticking cross section.

MODEL REAL-TIME QUANTUM DYNAMICAL SIMULATIONS OF PROTON TRANSFER IN THE GREEN FLUORESCENT PROTEIN (GFP)

In this paper, we present the results from model real-time quantum dynamical calculations of the proton transfer in green fluorescent protein (GFP) regarding four electronic states (labeled A, A*, I, I*). A coupled-states quantum wavepacket method has been used, which involves split-operator and fast FFT algorithms. The model potential energy surfaces are based upon data derived from experimental results with some modifications. Several important processes in GFP have been simulated, which include the photo-absorption and proton transfer in the excited state, the isotope effect and the recurrence time for proton motion in the excited state. The origin of the early-time (prompt) stimulated emission is tentatively explained in terms of off-resonance excitation as well as the contribution from the fastest component for proton transfer in GFP.

Excited-State Structure and Dynamics of cis- and trans-Azobenzene from Resonance Raman Intensity Analysis

Resonance Raman intensity analysis was used to investigate the initial excited-state nuclear dynamics of cis- and trans-azobenzene following S1 (npi*) excitation, and fluorescence quantum yield measurements were used to estimate the excited-state lifetimes. trans-Azobenzene exhibits the strongest Raman intensities in its skeletal stretching and bending modes, while torsional motions dominate the nuclear relaxation of cis-azobenzene as indicated by intense Raman lines at 275, 542, 594, and 778 cm(-1). The very weak fluorescence quantum yield for cis-azobenzene is consistent with its approximately 100 fs electronic lifetime while trans-azobenzene, with a fluorescence quantum yield of 1.1 x 10(-5), has an estimated S1 lifetime of approximately 3 ps. The absorption and Raman cross-sections of both isomers were modeled to produce a harmonic displaced excited-state potential energy surface model revealing the initial nuclear motions on the reactive surface, as well as values for the homogeneous and inhomogeneous linewidths. For cis-azobenzene, this modeling predicts slopes on the S1 potential energy surface that when extrapolated to the position of the harmonic minimum give excited-state changes of approximately 6-20 degrees in the CNNC torsion angle and a < or =3 degrees change in the CNN bending angle. The relatively large excited-state displacements along these torsional degrees of freedom provide the driving force for ultrafast isomerization. In contrast, the excited-state geometry changes of trans-azobenzene are primarily focused on the CNN bend and CN and NN stretches. These results support the idea that cis-azobenzene isomerizes rapidly via rotation about the NN bond, while isomerization proceeds via inversion for trans-azobenzene.

On the Chaperon Mechanism: Application to ClO + ClO (+N2) → ClOOCl (+N2)

The dynamics of the ClO + ClO (+N(2)) radical complex (or chaperon) mechanism is studied by electronic structure methods and quasi-classical trajectory calculations. The geometries and frequencies of the stationary points on the potential energy surface (PES) are optimized at the B3LYP/6-311+G(3df) level of theory, and the energies are refined at the CCSD(T)/6-311+G(3df) (single-point) level of theory. Basis set superposition error (BSSE) corrections are applied to obtain 1.5 kcal mol(-1) for the binding energy of the ClO.N(2) van der Waals (VDW) complex. A model PES is developed and used in quasi-classical trajectory calculations to obtain the capture rate constant and nascent energy distributions of ClOOCl* produced via the chaperon mechanism. A range of VDW binding energies from 1.5 to 9.0 kcal mol(-1) are investigated. The anisotropic PES for the ClO.N(2) complex and a separable anharmonic oscillator approximation are used to estimate the equilibrium constant for formation of the VDW complex. Rate constants, branching ratios to produce ClOOCl, and nascent energy distributions of excited ClOOCl* are discussed with respect to the VDW binding energy and temperature. Interestingly, even for weak VDW binding energies, the N(2) usually carries away enough energy to stabilize the nascent ClOOCl*, although the VDW equilibrium constant is small. For stronger binding energies, the stabilization efficiency is reduced, but the capture rate constant is increased commensurately. The resulting rate constants for forming ClOOCl* from the title reaction are only weakly dependent on the VDW binding energy and temperature. As a result, the relative importance of the chaperon mechanism is mostly dependent on the VDW equilibrium constant. For the calculated ClO.N(2) binding energy of 1.5 kcal mol(-1), the VDW equilibrium constant is small, and the chaperon mechanism is only important at very high pressures.

Accuracy of recent potential energy surfaces for the He–N2 interaction. I. Virial and bulk transport coefficients

A new exchange-Coulomb semiempirical model potential energy surface for the He-N2 interaction has been developed. Together with two recent high-level ab initio potential energy surfaces, it has been tested for the reliability of its predictions of second-virial coefficients and bulk transport phenomena in binary mixtures of He and N2. The agreement with the relevant available measurements is generally within experimental uncertainty for the exchange-Coulomb surface and the ab initio surface of Patel et al. [J. Chem. Phys. 119, 909 (2003)], but with slightly poorer agreement for the earlier ab initio surface of Hu and Thakkar [J. Chem. Phys. 104, 2541 (1996)].

Cluster-enhanced X–O2 photochemistry (X=CH3I, C3H6, C6H12, and Xe)

The effect of a local environment on the photodissociation of molecular oxygen is investigated in the van der Waals complex X-O(2) (X=CH(3)I, C(3)H(6), C(6)H(12), and Xe). A single laser operating at wavelengths around 226 nm is used for both photodissociation of the van der Waals complex and simultaneous detection of the O((3)P(J),J=2,1,0) atom photoproduct via (2+1) resonance enhanced multiphoton ionization. The kinetic energy distribution (KED) and angular anisotropy of the product O atom recoil in this dissociation are measured using the velocity map imaging technique configured for either full ("crush") or partial ("slice") detection of the three-dimensional O((3)P(J)) atom product Newton sphere. The measured KED and angular anisotropy reveal a distinct difference in the mechanism of O atom generation from an X-O(2) complex compared to a free O(2) molecule. The authors identify two one-photon excitation pathways, the relative importance of which depends on IPx, the ionization potential of the X partner. One pathway, observed for all complexes independent of IPx, involves a direct transition to the perturbed covalent state X-O(2)(A'(3)Delta(u)) with excitation localized on the O(2) subunit. The predominantly perpendicular character of this channel relative to the laser polarization detection, together with data on the structure of the complex, allows us to confirm that X partner induced admixing of an X(+)-O(2) (-) charge transfer (CT) state is the perturbing factor resulting in the well-known enhancement of photoabsorption within the Herzberg continuum of molecular oxygen. The second excitation pathway, observed for X-O(2) complexes with X=CH(3)I and C(3)H(6), involves direct excitation into the (3)(X(+)-O(2) (-)) CT state of the complex. The subsequent photodissociation of this CT state by the same laser pulse gives rise to the superoxide anion O(2) (-), which then photodissociates, providing fast (0.69 eV) O atoms with a parallel image pattern. Products from the photodissociation of singlet oxygen O(2)(b (1)Sigma(g) (+)) are also observed when the CH(3)I-O(2) complex was irradiated. Potential energy surfaces (PES) for the ground and relevant excited states of the X-O(2) complex have been constructed for CH(3)I-O(2) using the results of CASSCF calculations for the ground and CT states of the complex as well as literature data on PES of the subunits. These model potential energy surfaces allowed us to interpret all of the observed O((3)P(J)) atom production channels.

Watching Atoms Move

The X-ray free-electron laser has made possible a direct test of potential energy surface models for highly excited states of bismuth.

Deriving a mechanistic model for potential energy surface of coordination compounds of nontransition elements

AbstractMolecules of coordination compounds (those formed by a central atom—largely by a transition or non‐transition metal ion, but also by non‐transition elements like sulfur, phosphorus, etc., and by atoms or groups surrounding it—the ligands) for decades represent a significant problem for any “classical” description given in terms of empirical force fields of molecular mechanics (MM) due to diversity of coordination polyhedra resulting in the numerosity of the parameters necessary to describe the objects of interest within such a setting. This situation is further toughened by the specific collection of effects known as mutual influence of ligands, of which the trans‐effect in transition metal complexes is the most known. A feature particularly complicating understanding the ligand influence is its qualitative dependence on the nature of the central atom. The real source of these problems is of course the specificity of the electronic structure of the coordination compounds. If compared with usual organic molecules for which the MM in its classical form is rather successful the major distinction characteristic for coordination compounds is the absence of fairly distinguishable two‐center two‐electron bonds incident to its central atom (ion). Using a methodology called deductive molecular mechanics (DMM) we have recently shown that for “organic” molecules it is possible to sequentially derive the form of the MM force field departing from a simple but intuitively transparent model of electronic structure of a single chemical bond. Here we present an analogous derivation for the force fields describing coordination compounds. It is based on the analysis of electronic structure of the closest ligand shell of coordination compounds and on that of its relation with the geometry changes induced by chemical substitution (ligand influence) performed recently by Levin and Dyachkov. By using the elements of the one‐electron density matrix as an economical set of electronic structure variables for the closest ligand shell, the DMM model of coordination compounds is constructed. Next, by excluding the electronic structure variables the effective elastic elements describing the force fields concordant with the mutual ligands' influence in coordination compounds are constructed and their dependence on the state of the central ion is established. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

Isomerization dynamics and thermodynamics of ionic argon clusters

The dynamics and thermodynamics of small Ar(n) (+) clusters, n=3, 6, and 9, are investigated using molecular dynamics (MD) and exchange Monte Carlo (MC) simulations. A diatomic-in-molecule Hamiltonian provides an accurate model for the electronic ground state potential energy surface. The microcanonical caloric curves calculated from MD and MC methods are shown to agree with each other, provided that the rigorous conservation of angular momentum is accounted for in the phase space density of the MC simulations. The previously proposed projective partition of the kinetic energy is used to assist MD simulations in interpreting the cluster dynamics in terms of inertial, internal, and external modes. The thermal behavior is correlated with the nature of the charged core in the cluster by computing a dedicated charge localization order parameter. We also perform systematic quenches to establish a connection with the various isomers. We find that the Ar(3) (+) cluster is very stable in its linear ground state geometry up to about 300 K, and then isomerizes to a T-shaped isomer in which a quasineutral atom lies around a charged dimer. In Ar(6) (+) and Ar(9) (+), the covalent trimer core is solvated by neutral atoms, and the weakly bound solvent shell melts at much lower energies, occasionally leading to a tetramer or pentamer core with weakly charged extremities. At high energies the core itself becomes metastable and the cluster transforms into Ar(2) (+) solvated by a fluid of neutral argon atoms.

Obtaining reaction coordinates by likelihood maximization

We present a new approach for calculating reaction coordinates in complex systems. The new method is based on transition path sampling and likelihood maximization. It requires fewer trajectories than a single iteration of existing procedures, and it applies to both low and high friction dynamics. The new method screens a set of candidate collective variables for a good reaction coordinate that depends on a few relevant variables. The Bayesian information criterion determines whether additional variables significantly improve the reaction coordinate. Additionally, we present an advantageous transition path sampling algorithm and an algorithm to generate the most likely transition path in the space of collective variables. The method is demonstrated on two systems: a bistable model potential energy surface and nucleation in the Ising model. For the Ising model of nucleation, we quantify for the first time the role of nuclei surface area in the nucleation reaction coordinate. Surprisingly, increased surface area increases the stability of nuclei in two dimensions but decreases nuclei stability in three dimensions.

Exploring Model Energy and Geometry Surfaces Using Sum of Squares Decompositions.

The difficulty in exploring potential energy surfaces, which are nonconvex, stems from the presence of many local minima, typically separated by high barriers and often disconnected in configurational space. We obtain the global minimum on model potential energy surfaces without sampling any minima a priori. Instead, a different problem is derived, which is convex and hence easy to solve, but which is guaranteed to either have the same solution or to be a lower bound to the true solution. A systematic way for improving the latter solutions is also given. Because many nonconvex problems are projections of higher dimensional convex problems, Parrilo has recently shown that by obtaining a sum of squares decomposition of the original problem, which can be subsequently transformed to a semidefinite program, a large class of nonconvex problems can be solved efficiently. The semidefinite duality formulation also provides a proof that the global minimum of the energy surface has either been found exactly or has been bounded from below. It additionally provides physical insight into the problem through a geometric interpretation. The sum of squares polynomial representation of the potential energy surface may further reveal information about the nature of the potential energy surface. We demonstrate the applicability of this approach to low-dimensional potential energy landscapes and discuss its merits and shortcomings. We further show how to apply it to geometric problems by obtaining the exact distance of closest approach of anisotropic particles. Efficient molecular dynamics simulations of mixtures of ellipsoids are illustrated.

Complex Dynamics of a Pyranose Ring Structure Molecule Attached to an Atomic Force Microscope

Dynamic numerical simulations were performed for a pyranose ring structure molecule attached to an Atomic Force Microscope (AFM) using a standard semiempirical potential energy surface model. The fundamental static force-extension behavior was first determined using a slow pulling base excitation at the AFM probe. The static force-extension curve displays a stiffness nonlinearity, both softening and hardening, that depends upon level of the pulling force. For the dynamic analysis, a single harmonic base excitation is applied to the AFM probe. A typical evolution process from periodic to aperiodic or chaotic motion obtained by varying the excitation frequency and amplitude is discussed. A strong chaotic response motion was generated for certain system parameters. The numerical analysis shows this chaotic response arises from a molecular structure conformational change.

Hydrogen atom quantum migration on platinum

We have reexamined hydrogen-platinum systems, giving emphasis on the atomic migration on the metal surface. The ideal (111) surface was firstly revisited, with the model potential energy surface for the motion of hydrogen created from calculations using a slab of platinum atoms fixed at the bulk separation obtained from experimental measurements. Calculated hydrogen hopping states in an adiabatic approximation are presented, with the lowest of these found at only 30 meV above the ground state. Effects of the presence of vacancies on the atomic migration are discussed from a potential energy surface constructed using a similar model. [DOI: 10.1380/ejssnt.2006.619]

Photochemistry of pyrrole: Time-dependent quantum wave-packet description of the dynamics at the π1σ*-S conical intersections

The photoinduced hydrogen-elimination reaction in pyrrole via the conical intersections of the two (1)pi sigma(*) excited states with the electronic ground states [(1)B(1)(pi sigma(*))-S(0) and (1)A(2)(pi sigma(*))-S(0)] have been investigated by time-dependent quantum wave-packet calculations. Model potential-energy surfaces of reduced dimensionality have been constructed on the basis of accurate multireference ab initio electronic-structure calculations. For the (1)B(1)-S(0) conical intersection, the model includes the NH stretching coordinate as the tuning mode and the hydrogen out-of-plane bending coordinate as the coupling mode. For the (1)A(2)-S(0) conical intersection, the NH stretching coordinate and the screwing coordinate of the ring hydrogens are taken into account. The latter is the dominant coupling mode of this conical intersection. The electronic population-transfer processes at the conical intersections, the branching ratio between the dissociation channels, and their dependence on the initial preparation of the system have been investigated for pyrrole and deuterated pyrrole. It is shown that the excitation of the NH stretching mode strongly enhances the reaction rate, while the excitation of the coupling mode influences the branching ratio of different dissociation channels. The results suggest that laser control of the photodissociation of pyrrole via mode-specific vibrational excitation should be possible. The calculations provide insight into the microscopic details of ultrafast internal-conversion processes in pyrrole via hydrogen-detachment processes, which are aborted at the (1)pi sigma(*)-S(0) conical intersections. These mechanisms are of relevance for the photostability of the building blocks of life (e.g., the DNA bases).

A new algorithm for predicting triplet-triplet energy-transfer activated complex coordinate in terms of accurate potential-energy surfaces

The new algorithm presented here allows, for the first time, the determination of the optimal geometrical distortions that an acceptor molecule in the triplet-triplet energy-transfer process undergoes, as well as the dependence of the activation energy of the process on the triplet energy difference of donor and acceptor molecules. This algorithm makes use of the complete potential-energy surfaces (singlet and triplet states), and contrasts with the first-order approximation already published [L. M. Frutos, O. Castano, J. L. Andres, M. Merchan, and A. U. Acuna, J. Chem. Phys. 120, 1208 (2004)] in which an expansion of the potential-energy surfaces was used. This algorithm is gradient based and finds the best trajectory for the acceptor molecule, starting from S(0) ground-state equilibrium geometry, to achieve the maximum variation of the singlet-triplet energy gap with the minimum energy of activation on S(0). Therefore, the algorithm allows the determination of a "reaction path" for the triplet-triplet energy-transfer processes. Also, the algorithm could also serve eventually to find minimum-energy crossing (singlet-triplet) points on the potential-energy surface, which can play an important role in the intersystem crossing process for the acceptor molecules to recover their initial capacity as acceptors. Also addressed is the misleading use of minimum-energy paths in T(1) to describe the energy-transfer process by comparing these results with those obtained using the new algorithm. The implementation of the algorithm is illustrated with different potential-energy surface models and it is discussed in the frame of nonvertical behavior.

Low temperature quantum rate coefficient of the H + CH+ reaction

In this paper we report the first theoretical study of the title reaction. A global, single-valued model of the ground-state potential energy surface has been obtained by fitting to an extensive set of high-level ab initio calculations. The surface is found to be attractive apart from linear geometries where energy barriers appear due to conical intersections. This model was then used to calculate the reactive reactant state selected cross sections for collision energies ranging from threshold up to 4000 cm(-1). These calculations were performed using our version of the Baer's approach of the RIOSA-NIP method which is based on the use of a negative imaginary potential. We find that the reaction probability is extremely oscillatory as a function of kinetic energy as it is a case for insertion reactions with a low exoergicity. The resulting reaction rate coefficient is found to first increase slowly as a function of temperature up to a broad maximum around 20 K and then to decrease slowly when temperature keeps increasing.

Intramolecular anharmonicity in the naphthalene molecule: thermodynamics and spectral effects

The anharmonicity of the ground electronic state of the naphthalene molecule has been investigated using a tight-binding potential energy surface model. The vibrational density of states is calculated from a mixed classical quantum theoretical approach. The primary assumption of this model is that the evolution of the mean anharmonic quantum energy as a function of temperature follows the classical evolution. From the thermal expansion of the classical free energy obtained using a reversible-scaling method, the mean vibrational frequency has also been determined as a function of temperature.

The reaction pathway of a potential energy surface as curve with induced tangent

The reaction path is an important concept of theoretical chemistry. We employ the definitions of the Newton trajectory (NT) and of the gradient extremal (GE). An NT follows a curve where the gradient is always a pointer to a fixed direction. A GE is a curve where the gradient of the potential energy surfaces (PES) is eigenvector of the Hessian. Examples are given with the Müller–Brown potential and further model PESs. An induced tangent opens the possibility to follow the curve by a predictor–corrector method. We show that the two kinds of curves can be treated as curves with induced tangent, however, the gradient descent, or intrinsic reaction coordinate not.

A PM3-SRP + Analytic Function Potential Energy Surface Model for O(3P) Reactions with Alkanes. Application to O(3P) + Ethane

The PM3 semiempirical electronic structure theory is reparametrized with specific reaction parameters (SRPs) to develop a potential energy surface (PES) for O(3P) processing of alkanes. The results of high-level ab initio calculations for the O(3P) + C2H6 primary reactions, yielding OH + C2H5, C2H5O + H, and CH3O + CH3, 11 ensuing secondary and unimolecular dissociation reactions involving products of these primary reactions, and additional reactions were used to develop two PM3-SRP models for the PES. The ab initio results used for this fitting were taken from previous multiconfiguration calculations and additional PMP2/cc-pVTZ calculations reported here. Even though these two PM3-SRP models are unable to quantitatively represent the many reactions that occur in high-energy collisions of O(3P) with alkanes, they are vast improvements over the PES of PM3 theory. These models are used in direct dynamics classical trajectory simulations of the O(3P) + C2H6 reaction at a 5 eV collision energy. The results of the simulations show that the products of the three primary reactions are highly excited and are able to undergo a large number of ensuing secondary and unimolecular dissociation reactions, and long-time trajectory integrations are required to study these many product channels. The large internal excitations of the primary reactions' products agree with results of a previous MSINDO direct dynamics trajectory study. Reaction cross sections calculated for the primary reaction channels are also in good agreement with the MSINDO results. Velocity scattering angles, calculated for products of the secondary and unimolecular dissociation channels, provide detailed information concerning the molecular dynamics of these products. They are formed directly and also via long-lived intermediates.

Intramolecular vibrational energy redistribution in toluene: a nine-dimensional quantum mechanical study using the MCTDH algorithm

Abstract The intramolecular vibrational energy redistribution within the methyl group of toluene is investigated. A nine-dimensional model potential energy surface in curvilinear coordinates, derived by Cavagnat and Lespade, is adopted along with an exact nine-dimensional kinetic operator in polyspherical coordinates. The quantum calculations are performed with the multiconfiguration time-dependent Hartree (MCTDH) method. MCTDH and some recent extensions of the algorithm are briefly reviewed. We investigate the vibrational energy transfer which is initiated by a local CH-stretch excitation of 1–5 quanta. The redistribution of vibrational energy strongly depends on the initial excitation, being most efficient for the vCH=3 excitation. Selected energy levels are also computed, using a recently developed relaxation scheme as well as the filter-diagonalisation approach.