Volume 134, Issue 11, 21 March 2011
Index of content:

Crystallization is observed during microsecond long molecular dynamics simulations of bent trimers, a molecular model proposed by Lewis and Wahnström for orthoterphenyl. In the crystal, the three spheres that make up the rigid molecule sit near sites of a body centered cubic lattice. The trimer bond angle is almost optimal for this structure. The crystal exhibits orientational disorder with the molecules aligned randomly along the three Cartesian axis, i.e., cubatic orientational order. The rotational and translational mobilities exhibit only modest decreases on crystallization, by factors of 10 and 3, respectively. The rotational relaxation does change from Debyelike in the liquid to large angle jumps in the crystal. We consider the origin of the superior glass forming ability of the trimer over the monatomic liquid.
 ARTICLES

 Theoretical Methods and Algorithms

Direct correlation function for complex square barriersquare well potentials in the firstorder mean spherical approximation
View Description Hide DescriptionThe direct correlation function of the complex discrete potential model fluids is obtained as a linear combination of the firstorder mean spherical approximation (FMSA) solution for the simple square well model that has been reported recently [Hlushak et al., J. Chem. Phys.130, 234511 (2009)]. The theory is employed to evaluate the structure and thermodynamics of complex fluids based on the square wellbarrier and square wellbarrierwell discrete potential models. Obtained results are compared with theoretical predictions of the hybrid mean spherical approximation, already reported in the literature [GuillenEscamilla et al., J. Phys.: Condens. Matter19, 086224 (2007)], and with computer simulation data of this study. The compressibility route to thermodynamics is then used to check whether the FMSA theory is able to predict multiple fluid–fluid transitions for the square barrierwell model fluids.

An orbitalinvariant internally contracted multireference coupled cluster approach
View Description Hide DescriptionWe have formulated and implemented an internally contracted multireference coupled cluster (icMRCC) approach aimed at solving two of the problems encountered in methods based on the Jeziorski–Monkhorst ansatz: (i) the scaling of the computational and memory costs with respect to the number of references, and (ii) the lack of invariance of the energy with respect to rotations among active orbitals. The icMRCC approach is based on a straightforward generalization of the singlereference coupled cluster ansatz in which an exponential operator is applied to a multiconfigurational wave function. The icMRCC method truncated to single and double excitations (icMRCCSD) yields very accurate potential energy curves in benchmark computations on the Be + H_{2} insertion reaction, the dissociation of hydrogen fluoride, and the symmetric double dissociation of water. Approximations of the icMRCC theory in which the Baker–Campbell–Hausdorff expansion is truncated up to a given number of commutators are found to converge quickly to the full theory. In our tests, two commutators are sufficient to recover a total energy within 0.5 mE _{ h } of the full icMRCCSD method along the entire potential energy curve. A formal analysis shows that the icMRCC method is invariant with respect to rotation among active orbitals, and that the orthogonalization procedure used to produce the set of linearly independent excitation operators plays a crucial role in guaranteeing the invariance properties. The orbital invariance was confirmed in numerical tests. Moreover, approximated versions of the icMRCC theory based on a truncated Baker–Campbell–Hausdorff expansion, preserve the orbital invariance properties of the full theory.

Semiclassical instanton approach to calculation of reaction rate constants in multidimensional chemical systems
View Description Hide DescriptionThe semiclassical instanton approximation is revisited in the context of its application to the calculation of chemical reactionrate constants. An analytical expression for the quantum canonical reaction rate constants of multidimensional systems is derived for all temperatures from the deep tunneling to hightemperature regimes. The connection of the derived semiclassical instanton theory with several previously developed reaction rate theories is shown and the numerical procedure for the search of instanton trajectories is provided. The theory is tested on seven different collinear symmetric and asymmetric atom transfer reactions including heavylightheavy, lightheavylight and lightlightheavy systems. The obtained thermal rate constants agree within a factor of 1.5–2 with the exact quantum results in the wide range of temperatures from 200 to 1500 K.

On the equivalence of two commonly used forms of semiclassical instanton theory
View Description Hide DescriptionSemiclassical instanton theory gives an approximate description of deep tunneling by means of periodic orbits on the inverted potential energy surface. There are two versions of the theory, one derived by taking a semiclassical limit of the exact fluxside timecorrelation function and the other by starting from the “Im F” premise, in which the partition function is analytically continued into the complex plane. Here, we provide a derivation showing that the two versions of the theory are exactly equivalent. Unlike a previous derivation (which was restricted to a systembath model), our derivation is completely general, and thus establishes that the “Im F” premise, which is behind such methods as quantum transitionstate theory and ring polymermolecular dynamics ratetheory, is correct in the steepestdescent limit.

Reducing experimental variability in variancebased sensitivity analysis of biochemical reaction systems
View Description Hide DescriptionSensitivity analysis is a valuable task for assessing the effects of biological variability on cellular behavior. Available techniques require knowledge of nominal parameter values, which cannot be determined accurately due to experimental uncertainty typical to problems of systems biology. As a consequence, the practical use of existing sensitivity analysis techniques may be seriously hampered by the effects of unpredictable experimental variability. To address this problem, we propose here a probabilistic approach to sensitivity analysis of biochemical reaction systems that explicitly models experimental variability and effectively reduces the impact of this type of uncertainty on the results. The proposed approach employs a recently introduced variancebased method to sensitivity analysis of biochemical reaction systems [Zhang et al., J. Chem. Phys.134, 094101 (2009)] and leads to a technique that can be effectively used to accommodate appreciable levels of experimental variability. We discuss three numerical techniques for evaluating the sensitivity indices associated with the new method, which include Monte Carlo estimation, derivative approximation, and dimensionality reduction based on orthonormal Hermite approximation. By employing a computational model of the epidermal growth factor receptor signaling pathway, we demonstrate that the proposed technique can greatly reduce the effect of experimental variability on variancebased sensitivity analysis results. We expect that, in cases of appreciable experimental variability, the new method can lead to substantial improvements over existing sensitivity analysis techniques.

Dispersion interaction in hydrogenchain models
View Description Hide DescriptionWe have investigated the dispersion interaction in hydrogen chain models via density functional theorybased symmetryadapted perturbation theory using the asymptotically corrected PBE0 energy functional. The quasimetallic and the insulating prototype systems were chosen to be hydrogen chains with equally and alternately spaced H_{2} units, respectively. The dependence of the dispersion energy on the chain length for quasimetallic and insulating cases has been determined for two chains arranged either in pointing or in parallel geometries. The results are compared with those previously calculated from a continuum coupledplasmon approach [Phys. Rev. B77, 075436 (2008)]. The interaction energy has also been modeled by pairwise summations over short fragments of the chains, demonstrating the failure of the additivity principle for the quasimetallic case, while confirming that the additivity is a qualitatively reasonable hypothesis for the insulating case.

Catalytic conversion reactions mediated by singlefile diffusion in linear nanopores: Hydrodynamic versus stochastic behavior
View Description Hide DescriptionWe analyze the spatiotemporal behavior of species concentrations in a diffusionmediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict singlefile (no passing) constraint. Both transient and steadystate behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice–gas model for this reaction–diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of meanfield type truncation approximations, produces discrete reaction–diffusion type equations (mfRDE). For slowly varying concentrations, we further develop coarsegrained continuum hydrodynamic reaction–diffusion equations (hRDE) incorporating a precise treatment of singlefile diffusion in this multispecies system. The hRDE successfully describe nontrivial aspects of transient behavior, in contrast to the mfRDE, and also correctly capture unreactive steadystate behavior in the pore interior. However, steadystate reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mfRDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

Multireference coupledcluster theory: The easy way
View Description Hide DescriptionThe multiionization equationofmotion coupledcluster (CC) method is developed for multireference (MR) problems. It is operationally single reference, depending upon a formal matrix diagonalization step to define the coefficients in the wavefunction in an unbiased way that allows for important MR character. The method is illustrated for the autoisomerization of cyclobutadiene, which has a very large multireference effect and compared to other MRCC results. The newly implemented methods are also used to obtain the vertical double ionization (DI) potentials of several small molecules (H_{2}O, CO, C_{2}H_{2}, C_{2}H_{4}). Also, the performance of the new methods is analyzed by plotting the potential energy curve for twisted ethylene as a function of a dihedral angle between two methylenes. Evaluation of the total molecular energy via MRDICC calculations makes it possible to avoid an unphysical cusp.

Interaction between LiH molecule and Li atom from stateoftheart electronic structure calculations
View Description Hide DescriptionStateoftheart ab initio techniques have been applied to compute the potential energy surface for the lithium atom interacting with the lithium hydride molecule in the Born–Oppenheimer approximation. The interaction potential was obtained using a combination of the explicitly correlated unrestricted coupledcluster method with single, double, and noniterative triple excitations [UCCSD(T)F12] for the core–core and core–valence correlation and full configuration interaction for the valence–valence correlation. The potential energy surface has a global minimum 8743 cm^{−1} deep if the Li–H bond length is held fixed at the monomer equilibrium distance or 8825 cm^{−1} deep if it is allowed to vary. In order to evaluate the performance of the conventional CCSD(T) approach, calculations were carried out using correlationconsistent polarized valence Xtuplezeta basis sets, with X ranging from 2 to 5, and a very large set of bond functions. Using simple twopoint extrapolations based on the singlepower laws X ^{−2} and X ^{−3} for the orbital basis sets, we were able to reproduce the CCSD(T)–F12 results for the characteristic points of the potential with an error of 0.49% at worst. The contribution beyond the CCSD(T)–F12 model, obtained from full configuration interaction calculations for the valence–valence correlation, was shown to be very small, and the error bars on the potential were estimated. At linear LiH–Li geometries, the groundstate potential shows an avoided crossing with an ionpair potential. The energy difference between the groundstate and excitedstate potentials at the avoided crossing is only 94 cm^{−1}. Using both adiabatic and diabatic pictures, we analyze the interaction between the two potential energy surfaces and its possible impact on the collisional dynamics. When the Li–H bond is allowed to vary, a seam of conical intersections appears at C _{2v} geometries. At the linear LiH–Li geometry, the conical intersection is at a Li–H distance which is only slightly larger than the monomer equilibrium distance, but for nonlinear geometries it quickly shifts to Li–H distances that are well outside the classical turning points of the groundstate potential of LiH. This suggests that the conical intersection will have little impact on the dynamics of Li–LiH collisions at ultralow temperatures. Finally, the reaction channels for the exchange and insertion reactions are also analyzed and found to be unimportant for the dynamics.

A simple but fully nonlocal correction to the random phase approximation
View Description Hide DescriptionThe random phase approximation (RPA) stands on the top rung of the ladder of groundstatedensity functional approximations. The simple or direct RPA has been found to predict accurately many isoelectronic energy differences. A nonempirical local or semilocal correction to this direct RPA leaves isoelectronic energy differences almost unchanged, while improving total energies, ionization energies, etc., but fails to correct the RPA underestimation of molecular atomization energies. Direct RPA and its semilocal correction may miss part of the middlerange multicenter nonlocality of the correlation energy in a molecule. Here we propose a fully nonlocal, hybridfunctionallike addition to the semilocal correction. The added full nonlocality is important in molecules, but not in atoms. Under uniformdensity scaling, this fully nonlocal correction scales like the secondorderexchange contribution to the correlation energy, an important part of the correction to direct RPA, and like the semilocal correction itself. For the atomization energies of ten molecules, and with the help of one fit parameter, it performs much better than the elaborate secondorder screened exchange correction.

The two faces of static correlation
View Description Hide DescriptionRestricted Hartree–Fock (RHF) and UHF wavefunctions for berylliumlike ions with nuclear charge 3 ⩽ Z ⩽ 5 are found using a nearcomplete Slater basis set. The triplet (RHF → UHF) instability and correlation energy are investigated as a function of Z and we find that the instability vanishes for Z > 4.5. We reproduce this surprising behavior using a minimalbasis model and, by comparing with the stretched H_{2} molecule, conclude that “static” (also known as nondynamical, neardegeneracy, firstorder, or strong) correlation comes in two flavors: one that can be captured by UHF and another that cannot. In the former (Type A), there is an “absolute neardegeneracy”; in the latter (Type B), there is a “relative neardegeneracy.” This dichotomy clarifies discussions of static correlation effects.

Planar mixed flow and chaos: Lyapunov exponents and the conjugatepairing rule
View Description Hide DescriptionIn this work we characterize the chaotic properties of atomic fluids subjected to planar mixed flow, which is a linear combination of planar shear and elongational flows, in a constant temperature thermodynamic ensemble. With the use of a recently developed nonequilibrium molecular dynamics algorithm, compatible and reproducible periodic boundary conditions are realized so that Lyapunov spectra analysis can be carried out for the first time. Previous studies on planar shear and elongational flows have shown that Lyapunov spectra organize in different ways, depending on the character of the defining equations of the system. Interestingly, planar mixed flow gives rise to chaotic spectra that, on one hand, contain elements common to those of shear and elongational flows but also show peculiar, unique traits. In particular, the influence of the constituent flows in regards to the conjugatepairing rule (CPR) is analyzed. CPR is observed in homogeneously thermostated systems whose adiabatic (or unthermostated) equations of motion are symplectic. We show that the component associated with the shear tends to selectively excite some of those degrees, and is responsible for violations in the rule.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

New ab initio potential energy surface for BrH_{2} and rate constants for the H + HBr → H_{2} + Br abstraction reaction
View Description Hide DescriptionA global potential energy surface (PES) for the electronic ground state of the BrH_{2} system was constructed based on the multireference configuration interaction (MRCI) method including the Davidson's correction using a large basis set. In addition, the spin–orbit correction were computed using the Breit–Pauli Hamiltonian and the unperturbed MRCI wavefunctions in the Br + H_{2} channel and the transition state region. Adding the correction to the ground state potential, the lowest spin–orbit correlated adiabatic potential was obtained. The characters of the new potential are discussed. Accurate initial state specified rate constants for the H + HBr → H_{2} + Br abstraction reaction were calculated using a timedependent wave packet method. The predicted rate constants were found to be in excellent agreement with the available experimental values and much better than those obtained from a previous PES.

Unusual mechanism for H_{3} ^{+} formation from ethane as obtained by femtosecond laser pulse ionization and quantum chemical calculations
View Description Hide DescriptionThe formation of H_{3} ^{+} from saturated hydrocarbon molecules represents a prototype of a complex chemical process, involving the breaking and the making of chemical bonds. We present a combined theoretical and experimental investigation providing for the first time an understanding of the mechanism of H_{3} ^{+}formation at the molecular level. The experimental approach involves femtosecond laser pulse ionization of ethane leading to H_{3} ^{+} ions with kinetic energies on the order of 4 to 6.5 eV. The theoretical approach involves highlevel quantum chemical calculation of the complete reaction path. The calculations confirm that the process takes place on the potential energy surface of the ethane dication. A surprising result of the theoretical investigation is, that the transition state of the process can be formally regarded as a H_{2} molecule attached to a C_{2}H_{4} ^{2+} entity but IRC calculations show that it belongs to the reaction channel yielding C_{2}H_{3} ^{+} + H_{3} ^{+}. Experimentally measured kinetic energies of the correlated H_{3} ^{+} and C_{2}H_{3} ^{+} ions confirm the reaction path suggested by theory.

Relativistic multireference calculation of photodissociation of o, m, and pbromofluorobenzene
View Description Hide DescriptionQuantum chemical calculations with relativistic effects were performed on the photodissociation of o, m, and pbromofluorobenzene (o, m, and pBrFPh) at 266 nm. The method of multistate secondorder multiconfigurational perturbation theory in conjunction with spin–orbit interaction through complete active space state interaction was employed to calculate the potential energy curves for the ground and lowlying excited states of o, m, and pBrFPh along their photodissociation reaction coordinates. The dissociation mechanisms with products of Br(^{2}P_{3/2}) and Br^{*}(^{2}P_{1/2}) states were clarified with the computed potential energy curves and the surface crossings. The current calculations augmented previous theoretical investigations by including relativistic effects and resolved some differences of experimental assignment regarding the dissociation channels of o, m, and pBrFPh.

Flickering dipoles in the gas phase: Structures, internal dynamics, and dipole moments of βnaphtholH_{2}O in its ground and excited electronic states
View Description Hide DescriptionDescribed here are the rotationally resolved S_{1} –S_{0} electronic spectra of the acid–base complex cisβnaphtholH_{2}O in the gas phase, both in the presence and absence of an applied electric field. The data show that the complex has a translinear O − H⋅⋅⋅O hydrogen bond configuration involving the −OH group of cisβnaphthol and the oxygen lone pairs of the attached water molecule in both electronic states. The measured permanent electric dipole moments of the complex are 4.00 and 4.66 D in the S_{0} and S_{1} states, respectively. These reveal a small amount of photoinduced charge transfer between solute and solvent, as supported by density functional theory calculations and an energy decomposition analysis. The water molecule also was found to tunnel through a barrier to internal motion nearly equal in energy to kT at room temperature. The resulting large angular jumps in solvent orientation produce “flickering dipoles” that are recognized as being important to the dynamics of bulk water.

Perturbation theory treatment of pseudorotation in cyclicN_{3}
View Description Hide DescriptionA relatively simple treatment using perturbation theory is proposed to describe spectrum of pseudorotational states in cyclicN_{3}. The purpose is to develop an analytical expression that could be used to fit the experimentally determined spectrum of cyclicN_{3}, with purpose of identifying this molecule in the laboratory and deriving parameters of its potential energy surface directly from the experimental data. The perturbation theory expression derived in this work is used to fit the spectrum calculated numerically in the previous work [D. Babikov and B. Kendrick, J. Chem. Phys.133, 174310 (2010)]. It is found that the second order of perturbation theory works well, giving a very good fit of the spectrum, with the rms deviation of only 0.26 cm^{−1}. Analysis reveals that important characteristics of the potential energy surface, such as equilibrium geometry and pseudorotation barriers, are directly related to the features of spectrum, such as splittings, and can be readily derived from experimental data, when those become available.

Rotationally correlated reactivity in the CH (v = 0, J, F_{i}) + O_{2} → OH (A) + CO reaction
View Description Hide DescriptionThe rotationalstateselected CH (v = 0, J, F_{i}) beam has been prepared by using an electric hexapole and applied to the crossed beamreaction of CH (v = 0, J, F_{i}) + O_{2} → OH (A) + CO at different O_{2}beam conditions. The rotational state selected reactive cross sections of CH (RSSRCSCH) turn out to depend remarkably on the rotational state distribution of O_{2} molecules at a collision energy of ∼ 0.19 eV. The reactivity of CH molecules in the N = 1 rotational states (namely J = 1/2, F_{2}〉 and J = 3/2, F_{1}〉 states, N designates the angular momentum excluding spin) becomes strongly enhanced upon a lowering of the rotational temperature of the O_{2}beam. The RSSRCSCH in these two rotational states correlate linearly with the population of O_{2} molecule in the specific frame rotation number states: These linear correlations mean that the rotationalstateselected CH molecules are selectively reactive upon the incoming O_{2} molecules in a specific rotational state; here, we use the term “rotationally correlated reactivity” to such specific reactivity depending on the combination of the rotational states between two molecular reactants. In addition, the steric asymmetry in the oriented CH (J = 1/2, F_{2}, M = 1/2〉) + O_{2} () reaction turns out to be negligible (< ±1%). This observation supports the reaction mechanism as theoretically predicted by Huang et al. [J. Phys. Chem. A 106, 5490 (2002)] that the first step is an intermediate formation with no energy barrier in which Catom of CH molecule attacks on one Oatom of O_{2} molecule at a sideways configuration.

Lowlying excited states and nonradiative processes of the adenine analogues 7H and 9H2aminopurine
View Description Hide DescriptionWe have investigated the UV vibronic spectra and excitedstate nonradiative processes of the 7H and 9Htautomers of jetcooled 2aminopurine (2AP) and of the 9H2APd _{4} and d _{5} isotopomers, using twocolor resonant twophoton ionization spectroscopy at 0.3 and 0.045 cm^{−1} resolution. The S _{1} ← S _{0} transition of 7H2AP was observed for the first time. It lies ∼ 1600 cm^{−1} below that of 9H2AP, is ∼1000 times weaker and exhibits only inplane vibronic excitations. In contrast, the S _{1} ← S _{0} spectra of 9H2AP, 9H2APd _{4}, and 9H2APd _{5} show numerous lowfrequency bands that can be systematically assigned to overtone and combinations of the outofplane vibrations ν_{1}′, ν_{2}′, and ν_{3}′. The intensity of these outofplane bands reflects an outofplane deformation in the ^{1}ππ*(L _{ a }) state. Approximate secondorder coupledcluster theory also predicts that 2aminopurine undergoes a “butterfly” deformation in its lowest ^{1}ππ* state. The rotational contours of the 9H2AP, 9H2APd _{4}, and 9H2APd _{5} bands and of eight vibronic bands of 9H2AP up to cm^{−1} exhibit 75%–80% inplane (a/b) polarization, which is characteristic for a ^{1}ππ* excitation. A 20%–25% caxis (perpendicular) transition dipole moment component may indicate coupling of the ^{1}ππ* bright state to the closelying ^{1} nπ* dark state. However, no ^{1} nπ* vibronic bands were detected below or up to 500 cm^{−1} above the ^{1}ππ* band. Following ^{1}ππ* excitation, 9H2AP undergoes a rapid nonradiative transition to a lowerlying longlived state with a lifetime ⩾5μs. The ionization potential of 9H2AP was measured via the ^{1}ππ* state (IP = 8.020 eV) and the longlived state (IP 9.10 eV). The difference shows that the longlived state lies ⩾1.08 eV below the ^{1}ππ* state. Timedependent B3LYP calculations predict the ^{3}ππ* (T _{1}) state 1.12 eV below the ^{1}ππ* state, but place the ^{1} nπ* (S _{1}) state close to the ^{1}ππ* state, implying that the longlived state is the lowest triplet (T _{1}) and not the ^{1} nπ* state.

Sequential bond energies and barrier heights for the water loss and charge separation dissociation pathways of Cd^{2+}(H_{2}O)_{ n }, n = 3–11
View Description Hide DescriptionThe bond dissociation energies for losing one water from Cd^{2+}(H_{2}O)_{ n } complexes, n = 3–11, are measured using threshold collisioninduced dissociation in a guided ion beam tandem mass spectrometer coupled with a thermal electrospray ionization source. Kinetic energy dependent cross sections are obtained for n = 4–11 complexes and analyzed to yield 0 K threshold measurements for loss of one, two, and three water ligands after accounting for multiple collisions, kinetic shifts, and energy distributions. The threshold measurements are converted from 0 to 298 K values to give the hydration enthalpies and free energies for sequentially losing one water from each complex. Theoretical geometry optimizations and single point energy calculations are performed on reactant and product complexes using several levels of theory and basis sets to obtain thermochemistry for comparison to experiment. The charge separation process, Cd^{2+}(H_{2}O)_{ n } → CdOH^{+}(H_{2}O)_{ m } + H^{+}(H_{2}O)_{ n−m− } _{1}, is also observed for n = 4 and 5 and the competition between this process and water loss is analyzed. Ratelimiting transition states for the charge separation process at n = 3–6 are calculated and compared to experimental threshold measurements resulting in the conclusion that the critical size for this dissociation pathway of hydrated cadmium is n _{crit} = 4.