Volume 135, Issue 1, 07 July 2011

Nuclear resonance vibrational spectroscopy (NRVS) reveals the vibrational dynamics of a Mössbauer probe nucleus. Here, ^{57}Fe NRVS measurements yield the complete spectrum of Fe vibrations in halide complexes of ironporphyrins.Iron porphine serves as a useful symmetric model for the more complex spectrum of asymmetric heme molecules that contribute to numerous essential biological processes. Quantitative comparison with the vibrational density of states (VDOS) predicted for the Fe atom by density functional theory calculations unambiguously identifies the correct sextet ground state in each case. These experimentally authenticated calculations then provide detailed normal mode descriptions for each observed vibration. All Feligand vibrations are clearly identified despite the high symmetry of the Fe environment. Low frequency molecular distortions and acoustic lattice modes also contribute to the experimental signal. Correlation matrices compare vibrations between different molecules and yield a detailed picture of how heme vibrations evolve in response to (a) halide binding and (b) asymmetric placement of porphyrin side chains. The side chains strongly influence the energetics of heme doming motions that control Fe reactivity, which are easily observed in the experimental signal.
 ARTICLES

 Theoretical Methods and Algorithms

Direct selected multireference configuration interaction calculations for large systems using localized orbitals
View Description Hide DescriptionA selected multireference configuration interaction (CI) method and the corresponding code are presented. It is based on a procedure of localization that permits to obtain well localized occupied and virtual orbitals. Due to the local character of the electron correlation, using local orbitals allows one to neglect long range interactions. In a first step, three topological matrices are constructed, which determine whether two orbitals must be considered as interacting or not. Two of them concern the truncation of the determinant basis, one for occupied/virtual, the second one for dispersive interactions. The third one concerns the truncation of the list of two electron integrals. This approach permits a fine analysis of each kind of approximation and induces a huge reduction of the CI size and of the computational time. The procedure is tested on linear polyene aldehyde chains, dissociation potential energy curve, and reaction energy of a pesticideCa^{2+} complex and finally on transition energies of a large iron system presenting a lightinduced excited spinstate trapping effect.

Selfassembly behavior of ABA coilrodcoil triblock copolymers: A Brownian dynamics simulation approach
View Description Hide DescriptionThe selfassembly behavior of ABA coilrodcoil triblock copolymers in a selective solvent was studied by a Brownian molecular dynamics simulation method. It was found that the rod midblock plays an important role in the selfassembly of the copolymers. With a decrease in the segregation strength, ɛ _{ RR }, of rod pairs, the aggregate structure first varies from a smecticlike disk shape to a long twisted string micelle and then to small aggregates. The influence of the block length and the asymmetry of the triblock copolymer on the phase behavior were studied and the corresponding phase diagrams were mapped. It was revealed that the variation of these parameters has a profound effect on microstructure. The simulation results are consistent with experimental results. Compared to rodcoil diblock copolymers, the coilrodcoil triblock copolymers has a larger entropy penalty associated with the interfacial grafting density of the aggregate, leading to a higher ɛ _{ RR } value for structural transitions.

Simple preconditioning for timedependent density functional perturbation theory
View Description Hide DescriptionBy far, the most common use of timedependent density functional theory is in the linearreponse regime, where it provides information about electronic excitations. Ideally, the linearresponse equations should be solved by a method that avoids the use of the unoccupied KohnSham states — such as the Sternheimer method — as this reduces the complexity and increases the precision of the calculation. However, the Sternheimer equation becomes illconditioned near and indefinite above the first resonant frequency, seriously hindering the use of efficient iterative solution methods. To overcome this serious limitation, and to improve the general convergence properties of the iterative techniques, we propose a simple preconditioning strategy. In our method, the Sternheimer equation is solved directly as a linear equation using an iterative Krylov subspace method, i.e., no selfconsistent cycle is required. Furthermore, the preconditioner uses the information of just a few unoccupied states and requires simple and minimal modifications to existing implementations. In this way, convergence can be reached faster and in a considerably wider frequency range than the traditional approach.

Simple orbital theory for the molecular electrician
View Description Hide DescriptionTheories of molecular electronic devices (MEDs) are quite involved in general. However, various prominent features of MEDs can be understood drawing only on elementary quantum theory. To support this point of view, we provide a two component orbital theory that enables one to reproduce various important features of MEDs. In this theory, the device orbitals are divided into two components, each of which is obtained from simple rules. To illustrate our twocomponent model, we apply it to explain, among other things, the conductance suppression in crossconjugated systems and the dependence of the conductance on the contact position in aromatic systems.

QM:QM embedding using electronic densities within an ONIOM framework: Energies and analytic gradients
View Description Hide DescriptionAccurate calculations of large systems remain a challenge in electronic structuretheory. Hybrid energy techniques are a promising family of methods for treating such systems. Expanding on previous developments, we present a QM:QM electronic embedding model whereby the highlevel region is polarized by the electron density of the lowlevel region within an ONIOM framework. A direct Coulomb embedding model as well a more computationally efficient model involving a density fitting expansion are considered. We also develop a generalized theory for the first derivatives of these classes of QM:QM electronic embedding schemes, which requires solution of a single set of selfconsistent field response equations. Two initial test cases are presented and discussed.

Accurate explicitly correlated wave functions for two electrons in a square
View Description Hide DescriptionAn explicitly correlated linearr _{12}variational method is developed for a system of two electrons confined to a twodimensional square well with infinite walls. The wave function is written as an expansion in products of nonnegative integer powers of the relative and centerofmass electronic coordinates and powers of r _{12} restricted to 0 and 1. This form indirectly includes higher powers of the interelectronic distance and exhibits a much faster convergence than a similar expansion without r _{12}dependent terms. The method is implemented using highprecision floatingpoint arithmetic. Groundstate total energies are reported with at least 12 accurate significant figures for squares with sides from 1 to 50 bohrs. The method can be used “as is” for excited states and for twodimensional rectangular wells. We also show that wave functions for two electrons in a square and in a rectangle have a higher symmetry than can be accounted for by the point group of the system.

Condensed phase molecular dynamics using interpolated potential energy surfaces with application to the resolvation process of coumarin 153
View Description Hide DescriptionInterpolatedpotential energy surfaces (PESs) have been used for performing reliable molecular dynamics (MD) simulations of small molecular reactions. In this article, we extend this method to MD simulations in condensed phase and show that the same scheme can also be feasibly used when it is supplemented with additional terms for describing intermolecular interactions. We then apply the approach for studying the resolvation process of coumarin 153 in a number of polar solvents. We find that the interpolatedsurface actually reproduces experimentally found features much better than the conventional force field based potential especially in terms of both dynamics Stokes shift in the short time limit and solute vibrational decoherence. This shows that the solute vibrational effect is important to some degree along the resolvation and should be modeled properly for accurate description of the related dynamics. The stability issue of trajectories on the interpolated PESs is also discussed, in regard to the goal of reliably performing long time simulations. Operational limitations of the present scheme are also discussed.

An enhanced splined saddle method
View Description Hide DescriptionWe present modifications for the method recently developed by Granot and Baer [J. Chem. Phys.128, 184111 (2008)]10.1063/1.2916716. These modifications significantly enhance the efficiency and reliability of the method. In addition, we discuss some specific features of this method. These features provide important flexibilities which are crucial for a doubleended saddle point search method in order to be applicable to complex reaction mechanisms. Furthermore, it is discussed under what circumstances this methods might fail to find the transition state and remedies to avoid such situations are provided. We demonstrate the performance of the enhanced splined saddle method on several examples with increasing complexity, isomerization of ammonia, ethane and cyclopropane molecules, tautomerization of cytosine, the ring opening of cyclobutene, the StoneWales transformation of the C _{60}fullerene, and finally rolling a small NaCl cube on NaCl(001) surface. All of these calculations are based on density functional theory. The efficiency of the method is remarkable in regard to the reduction of the total computational time.

Polarization justified Fukui functions: The theory and applications for molecules
View Description Hide DescriptionThe Fukui functions based on the computable local polarizability vector have been presented for a group of simple molecules. The necessary approximation for the density functional theory softness kernel has been supported by a theoreticalanalysis unifying and generalizing early concepts produced by the several authors. The exact relation between local polarizability vector and the derivative of the nonlocal part of the electronic potential over the electric field has been demonstrated. The resulting Fukui functions are unique and represent a reasonable refinement when compared to the classical ones that are calculated as the finite difference of the density in molecular ions. The new Fukui functions are strongly validated by their direct link to electron dipole polarizabilities that are reported experimentally and by other computational methods.

Bifurcations of dividing surfaces in chemical reactions
View Description Hide DescriptionWe study the dynamical behavior of the unstable periodic orbit (NHIM) associated to the nonreturn transition state (TS) of the H_{2} + H collinear exchange reaction and their effects on the reaction probability. By means of the normal form of the Hamiltonian in the vicinity of the phase space saddle point, we obtain explicit expressions of the dynamical structures that rule the reaction. Taking advantage of the straightforward identification of the TS in normal form coordinates, we calculate the reaction probability as a function of the system energy in a more efficient way than the standard Monte Carlo method. The reaction probability values computed by both methods are not in agreement for high energies. We study by numerical continuation the bifurcations experienced by the NHIM as the energy increases. We find that the occurrence of new periodic orbits emanated from these bifurcations prevents the existence of a unique nonreturn TS, so that for high energies, the transition state theory cannot be longer applied to calculate the reaction probability.

On the effect of electron correlation on the static second hyperpolarizability of π conjugated oligomer chains
View Description Hide DescriptionIn this article, we report on the ab initio calculation of the static longitudinal second hyperpolarizability (γ) of π conjugated unsaturated oligomer chains using polyacetylene and polyyne as model compounds. The common observation is that the electron correlation enhances γ in these systems. The present study reveals that for extended chain lengths the opposite appears to be true: Electron correlation may have a damping effect on this property. For doublezeta basis sets, a negative contribution from electron correlation to γ is found within the range of chain lengths investigated. For triplezeta basis sets, the same behavior must be anticipated at larger chain lengths based on extrapolation schemes. The analysis of the excitation energies and transition moments shows that transition moments between excited states as predicted by the HartreeFock and coupled cluster methods have a different response to chain length extension. There also are indications that higher order correlation effects will enhance γ.

Dimension reduction by balanced truncation: Application to lightinduced control of open quantum systems
View Description Hide DescriptionIn linear control, balanced truncation is known as a powerful technique to reduce the statespace dimension of a system. Its basic principle is to identify a subspace of jointly easily controllable and observable states and then to restrict the dynamics to this subspace without changing the overall response of the system. This work deals with a first application of balanced truncation to the control of open quantum systems which are modeled by the Liouvillevon Neumann equation within the Lindblad formalism. Generalization of the linear theory has been proposed to cope with the bilinear terms arising from the coupling between the control field and the quantum system. As an example we choose the dissipative quantum dynamics of a particle in an asymmetric double well potential driven by an external control field, monitoring population transfer between the potential wells as a control target. The accuracy of dimension reduction is investigated by comparing the populations obtained for the truncated system versus those for the original system. The dimension of the model system can be reduced very efficiently where the degree of reduction depends on temperature and relaxation rate.

Analytical Hessian of electronic excited states in timedependent density functional theory with TammDancoff approximation
View Description Hide DescriptionWe present the analytical expression and computer implementation for the secondorder energy derivatives of the electronic excited state with respect to the nuclear coordinates in the timedependent density functional theory (TDDFT) with Gaussian atomic orbital basis sets. Here, the TammDancoff approximation to the full TDDFT is adopted, and therefore the formulation process of TDDFT excitedstate Hessian is similar to that of configuration interaction singles (CIS) Hessian. However, due to the replacement of the HartreeFock exchange integrals in CIS with the exchangecorrelation kernels in TDDFT, many quantitative changes in the derived equations are arisen. The replacement also causes additional technical difficulties associated with the calculation of a large number of multipleorder functional derivatives with respect to the density variables and the nuclear coordinates. Numerical tests on a set of test molecules are performed. The simulated excitedstate vibrational frequencies by the analytical Hessian approach are compared with those computed by CIS and the finitedifference method. It is found that the analytical Hessian method is superior to the finitedifference method in terms of the computational accuracy and efficiency. The numerical differentiation can be difficult due to root flipping for excited states that are close in energy. TDDFT yields more exact excitedstate vibrational frequencies than CIS, which usually overestimates the values.

A multigrid method for Ncomponent nucleation
View Description Hide DescriptionA multigrid algorithm has been developed enabling more efficient solution of the cluster size distribution for Ncomponent nucleation from the BeckerDöring equations. The theoretical derivation is valid for an arbitrary number of condensing components, making the simulation of manycomponent nucleating systems feasible. A steady state ternary nucleation problem is defined to demonstrate its efficiency. The results are used as a validation for existing nucleation theories. The nonsteady state ternary problem provides useful insight into the initial stages of the nucleation process. We observe that for the ideal mixture the main nucleation flux bypasses the saddle point.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Collisioninduced dipole polarizability of helium dimer from explicitly correlated calculations
View Description Hide DescriptionLarge expansions in basis sets of explicitly correlated Gaussian functions and the variationperturbation technique were used to calculate the static dipole polarizability of the helium dimer at 16 different internuclear separations from 1.0 to 9.0 bohrs. The convergence towards the complete basis set limit was analyzed in order to estimate uncertainties of all the calculated values. The results are significantly more accurate than literature data. Asymptotically correct analytic fits for the trace and anisotropy of collisioninduced polarizability were obtained.

The binding energies of NO–Rg (Rg = He, Ne, Ar) determined by velocity map imaging
View Description Hide DescriptionWe report velocity map imaging measurements of the binding energies,D _{0}, of NO–Rg (Rg = He, Ne, Ar) complexes. The state binding energies determined are 3.0 ± 1.8, 28.6 ± 1.7, and 93.5 ± 0.9 cm^{−1} for NO–He, –Ne, and –Ar, respectively. These values compare reasonably well with ab initio calculations. Because the – transitions were unable to be observed for NO–He and NO–Ne, values for the binding energies in the state of these complexes have not been determined. Based on our state value and the reported – origin band position, the state binding energy for NO–Ar was determined to be 50.6 ± 0.9 cm^{−1}.

Kinetics and dynamics of the NH_{3} + H → NH_{2} + H_{2} reaction using transition state methods, quasiclassical trajectories, and quantummechanical scattering
View Description Hide DescriptionOn a recent analytical potential energy surface developed by two of the authors, an exhaustive kinetics study, using variational transition state theory with multidimensional tunneling effect, and dynamics study, using both quasiclassical trajectory and fulldimensional quantum scattering methods, was carried out to understand the reactivity of the NH_{3} + H → NH_{2} + H_{2} gasphase reaction. Initial stateselected timedependent wave packet calculations using a fulldimensional model were performed, where the total reaction probabilities were calculated for the initial ground vibrational state and for four excited vibrational states of ammonia. Thermal rate constants were calculated for the temperature range 200–2000 K using the three methods and compared with available experimental data. We found that (a) the total reaction probabilities are very small, (b) the symmetric and asymmetric N–H stretch excitations enhance the reactivity, (c) the quantummechanical calculated thermal rate constants are about one order of magnitude smaller than the transition state theory results, which reproduce the experimental evidence, and (d) quasiclassical trajectory calculations, which were performed with the main goal of analyzing the influence of the zeropoint energy problem on the final dynamics results, reproduce the quantum scattering calculations on the same surface.

Theoretical study of radiative and nonradiative decay processes in pyrazine derivatives
View Description Hide DescriptionAggregationinduced emission (AIE) phenomenon has attracted much attention in recent years due to its potential applications in optoelectronic devices, fluorescence sensors, and biological probes. Restriction of intramolecular rotation has been proposed as the cause of this unusual phenomenon. Rational design of AIE luminogens requires quantitative descriptions of its mechanism. 2,3dicyano5,6diphenylpyrazine (DCDPP) with “free” phenyl rings is an AIE active compound, whereas 2,3dicyanopyrazino [5,69,10] phenanthrene (DCPP) with “locked” phenyl rings is not. Quantum chemistry calculations coupled with our thermal vibration correlation function formalism for the radiative and nonradiative decay rates reveal that the radiative decay rates for both DCPP and DCDPP are close to each other for all the temperatures, but the nonradiative decay processes are very different. For DCDPP, the lowfrequency modes originated from the phenyl ring twisting motions are strongly coupled with the electronic excited state, which dissipate the electronic excitation energy through modemixing (Duschinsky rotation effect), and the nonradiative decay rate strongly increases with temperature. For DCPP, however, such modemixing effect is weak and the nonradiative decay rate is insensitive to temperature. These findings rationalize the fact that DCDPP is AIE active but DCPP is not, and are instructive to further development of AIE luminogens.

Fulldimensional timedependent wave packet dynamics of H_{2} + D_{2} reaction
View Description Hide DescriptionCollision induced dissociation (CID), four center reaction (4C), and single exchange reaction (SE) in H_{2} (v _{1} = high) + D_{2} (v _{2} = low) were studied by means of timedependent wave packet approach within a fulldimensional model. Initial stateselected total reaction probabilities for the three competitive processes have been computed on two realistic global potential energy surfaces of AguadoSuárezPaniagua and BoothroydMartinKeoghPeterson (BMKP) with the total angular momentum J = 0. The role of both vibrationally excited and rotationally excited reagents was examined by varying the initial vibrational and rotational states. The vibrational excitation of the hot diatom gives an enhancement effect on the CID process, while the vibrational excitation of the cold diatom gives an inhibition effect. The rotational excitation of both reagents has a significant effect on the reaction process. The 4C and SE probabilities are at least one order of magnitude smaller than the CID probabilities over the energy range considered. Isotope substitution effects were also studied by substituting the collider D_{2} by H_{2} and HD on the BMKP potential energy surfaces. The CID process is most efficient for the H_{2} + D_{2} combination and least efficient for the H_{2} + H_{2} combination and is different for the 4C and SE processes.

The products of the thermal decomposition of CH_{3}CHO
View Description Hide DescriptionWe have used a heated 2 cm × 1 mm SiC microtubular (μtubular) reactor to decompose acetaldehyde: CH_{3}CHO + Δ → products. Thermal decomposition is followed at pressures of 75–150 Torr and at temperatures up to 1675 K, conditions that correspond to residence times of roughly 50–100 μs in the μtubular reactor. The acetaldehyde decomposition products are identified by two independent techniques: vacuum ultraviolet photoionization mass spectroscopy (PIMS) and infrared (IR) absorption spectroscopy after isolation in a cryogenic matrix. Besides CH_{3}CHO, we have studied three isotopologues, CH_{3}CDO, CD_{3}CHO, and CD_{3}CDO. We have identified the thermal decomposition products CH_{3} (PIMS), CO (IR, PIMS), H (PIMS), H_{2} (PIMS), CH_{2}CO (IR, PIMS), CH_{2}=CHOH (IR, PIMS), H_{2}O (IR, PIMS), and HC≡CH (IR, PIMS). Plausible evidence has been found to support the idea that there are at least three different thermal decomposition pathways for CH_{3}CHO; namely, radical decomposition: CH_{3}CHO + Δ → CH_{3} + [HCO] → CH_{3} + H + CO; elimination: CH_{3}CHO + Δ → H_{2} + CH_{2}=C=O; isomerization/elimination: CH_{3}CHO + Δ → [CH_{2}=CH–OH] → HC≡CH + H_{2}O. An interesting result is that both PIMS and IR spectroscopy show compelling evidence for the participation of vinylidene, CH_{2}=C:, as an intermediate in the decomposition of vinyl alcohol: CH_{2}=CH–OH + Δ → [CH_{2}=C:] + H_{2}O → HC≡CH + H_{2}O.