Volume 133, Issue 6, 14 August 2010

We have determined the full crystal structure of the highpressure phase methane A. Xray singlecrystaldiffraction data were used to determine the carbonatom arrangement, and neutronpowderdiffraction data from a deuterated sample allowed the deuterium atoms to be located. It was then possible to refine all the hydrogen positions from the singlecrystal xray data. The structure has 21 molecules in a rhombohedral unit cell, and is quite strongly distorted from the cubic closepacked structure of methane I, although some structural similarities remain. Full knowledge of this structure is important for modeling of methane at higher pressures, including in relation to the mineralogy of the outer solar system. We discuss interesting structural parallels with the carbon tetrahalides.
 ARTICLES

 Theoretical Methods and Algorithms

A density functional theory study of the zerofield splitting in highspin nitrenes
View Description Hide DescriptionThis work presents a detailed evaluation of the performance of density functional theory(DFT) for the prediction of zerofield splittings (ZFSs) in highspin nitrenes. A number of well experimentally characterized triplet mononitrenes, quartet nitrenoradicals, quintet dinitrenes, and septet trinitrenes have been considered. Several DFTbased approaches for the prediction of ZFSs have been compared. It is shown that the unrestricted Kohn–Sham and the Pederson–Khanna approaches are the most successful for the estimation of the direct spinspin (SS) interaction and the spinorbit coupling(SOC) parts, respectively, to the final ZFS parameters. The most accurate theoretical predictions (within 10%) are achieved by using the PBE density functional in combination with the DZ, EPRII, and TZV basis sets. For highspin nitrenes constituted from light atoms, the contribution of the SOC part to ZFS parameters is quite small (7%–12%). By contrast, for chlorinesubstituted septet trinitrenes, the contribution of the SOC part is small only to value but, in the case of value, it is as large as the SS part and has opposite sign. Due to this partial cancellation of two different contributions, SS and SOC, the resulting values of in heavy molecules are almost two times smaller than those predicted by analysis of the widely used semiempirical onecenter spinspin interaction model. The decomposition of into center interactions shows that the major contribution to results from the onecenter spinspin interactions. This fact indicates that the semiempirical SS interaction model accurately predicts the ZFS parameters for all types of highspin nitrenes with total spin and 3, if their molecules are constructed from the firstrow atoms.

Quantum Monte Carlo ground state energies for the singly charged ions from Li through Ar
View Description Hide DescriptionNonrelativistic frozen nucleus allelectron Quantum Monte Carloground state energies of positive and negative ions to and to , respectively, are reported. Explicitly correlated wave functions with a single configuration model function times a Jastrow factor are employed for all of the systems studied. The accuracy obtained for the ions in the third period is similar to that reached for the ions in the second one. For those ions with a stronger multiconfiguration nature a restricted multiconfiguration expansion has been employed. The ground state energy here obtained for the charged species shows a similar quality to that reached for neutral atoms. Starting from those results, ionization potentials and electron affinities are calculated.

Free energy calculations using duallevel Born–Oppenheimer molecular dynamics
View Description Hide DescriptionWe describe an efficient and accurate method to compute free energy changes in complex chemical systems that cannot be described through classical molecular dynamics simulations, examples of which are chemical and photochemical reactions in solution, enzymes, interfaces, etc. It is based on the use of duallevel Born–Oppenheimer molecular dynamics simulations. A lowlevel quantum mechanical method is employed to calculate the potential of mean force through the umbrella sampling technique. Then, a highlevel quantum mechanical method is used to estimate a free energy correction on selected points of the reaction coordinate using perturbation theory. The precision of the results is comparable to that of ab initiomolecular dynamics methods such as the Car–Parrinello approach but the computational cost is much lower, roughly by two to three orders of magnitude. The method is illustrated by discussing the association free energy of simple organometallic compounds, although the field of application is very broad.

Spincomponentscaling secondorder Møller–Plesset theory and its variants for economical correlation energies: Unified theoretical interpretation and use for quartet
View Description Hide DescriptionThe spincomponentscaling secondorder Møller–Plesset theory proposed by Grimme, the scaled oppositespin variant of HeadGordon and coworkers, and other variants of the theory to treat the electron correlationenergy are examined. A refinement of scaled oppositespin theory for strong chemical interactions is suggested where the scaled correlation contribution is chosen such as to mimic closely the one obtained by more sophisticated methods of the coupled cluster type. With the scaling factor chosen to vary in a simple statistical manner with the number of oppositespin electron pairs of the system, the parameters have been calibrated from standard coupled cluster type calculations for a chosen ab initio test data set. The new approach, termed as variablescaling opposite spin, aims to be applicable at any regions of the molecule configuration space where secondorder Møller–Plesset perturbation theory converges. It thus benefits of all advantages inherent to the original theory, which makes it an attractive approach on a computational cost basis. Because the method in one of its formats fails sizeextensivity, the consequences and remedies of this are analyzed. Illustrations are presented for many molecules utilizing Dunningtype basis sets, in particular, for a detailed analysis of in its lowest quartet state, which does not belong to the test set. Extrapolations of the calculated raw energies to the complete oneelectron basis set limit are also reported, giving the most reliable estimates available thus far of the energetics for the exchange reaction. All spincomponentscaling schemes are known to show difficulties in dealing with weak interactions of the van der Waals type, which has justified the design of specific variants of the theory according to the property and regime of interactions. Several variants of the theory are then examined using a second test set of molecules, and shown to be linked via a coordinate that evolves gradually between two known extreme regimes. It is further shown that such a coordinate can be specified via a constrained Feenbergtype scaling approach, a theory whose merits are also explored.

Linear complex polarization propagator in a fourcomponent Kohn–Sham framework
View Description Hide DescriptionAn algorithm for the solution of the linear response equation in the random phase approximation is presented. All entities including frequency arguments, matrices, and vectors, are assumed to be complex, and it represents the core equation solver needed in complex polarization propagator approaches where nonstimulated relaxation channels are taken into account. Stability and robustness of the algorithm are demonstrated in applications regarding visible, ultraviolet, and xray spectroscopies. An implementation of the algorithm at the level of fourcomponent relativistic, noncollinear, density functional theory for imaginary (but not complex) frequency arguments has been achieved and is used to determine the electric dipole dispersion interaction coefficients for the rubidium and cesium dimers. Our best estimates for the coefficients of and are equal to and , respectively.

Spinadapted openshell random phase approximation and timedependent density functional theory. I. Theory
View Description Hide DescriptionThe spinadaptation of singlereference quantum chemical methods for excited states of openshell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spinincomplete. Those “missing” configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., timedependent density functional theory (TDDFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensorcoupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spinadapted tuply excited configuration space can readily be constructed by tensor products between the tuple tensorexcitation operators and the chosen tensor reference. Further combined with the tensor equationofmotion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spinadapted openshell random phase approximation is first developed. The socalled “translation rule” is then adopted to formulate a spinadapted, restricted openshell Kohn–Sham (ROKS)based TDDFT (ROKSTDDFT). Here, a particular symmetry structure has to be imposed on the exchangecorrelation kernel. While the standard ROKSTDDFT can access only excited states due to singletcoupled single excitations, i.e., only some of the singly excited states of the same spin as the reference, the new scheme can capture all the excited states of spin , , or due to both singlet and tripletcoupled single excitations. The actual implementation and computation are very much like the (spincontaminated) unrestricted Kohn–Shambased TDDFT. It is also shown that spincontaminated spinflip configuration interaction approaches can easily be spinadapted via the tensorcoupling scheme.

Conical intersections of free energy surfaces in solution: Effect of electron correlation on a protonated Schiff base in methanol solution
View Description Hide DescriptionThe minimum energy conical intersection (MECI) optimization method with taking account of the dynamic electron correlation effect [T. Mori and S. Kato, Chem. Phys. Lett.476, 97 (2009)] is extended to locate the MECI of nonequilibrium free energysurfaces in solution. A multistate electronic perturbation theory is introduced into the nonequilibrium free energy formula, which is defined as a function of solute and solvation coordinates. The analytical free energy gradient and interstate coupling vectors are derived, and are applied to locate MECIs in solution. The present method is applied to study the cistrans photoisomerization reaction of a protonated Schiff base molecule (PSB3) in methanol (MeOH) solution. It is found that the effect of dynamic electron correlation largely lowers the energy of state. We also show that the solvation effect strongly stabilizes the MECI obtained by twisting the terminal bond to become accessible in MeOH solution, whereas the conical intersection is found to be unstable in gas phase. The present study indicates that both electron correlation and solvation effects are important in the photoisomerization reaction of PSB3. The effect of counterion is also examined, and seems to be rather small in solution. The structures of free energysurfaces around MECIs are also discussed.

An efficient matrixmatrix multiplication based antisymmetric tensor contraction engine for general order coupled cluster
View Description Hide DescriptionIn this paper, we present an efficient implementation of general tensor contractions, which is part of a new coupledcluster program. The tensor contractions, used to evaluate the residuals in each coupledcluster iteration are particularly important for the performance of the program. We developed a generic procedure, which carries out contractions of two tensors irrespective of their explicit structure. It can handle coupledclustertype expressions of arbitrary excitation level. To make the contraction efficient without loosing flexibility, we use a threestep procedure. First, the data contained in the tensors are rearranged into matrices, then a matrixmatrix multiplication is performed, and finally the result is backtransformed to a tensor. The current implementation is significantly more efficient than previous ones capable of treating arbitrary high excitations.

The multiscale coarsegraining method: Assessing its accuracy and introducing density dependent coarsegrain potentials
View Description Hide DescriptionThe ability of particlebased coarsegrain potentials, derived using the recently proposed multiscale coarsegraining (MSCG) methodology [S. Izvekov and G. A. Voth, J. Phys. Chem. B109, 2469 (2005); J. Chem. Phys.123, 134105 (2005)] to reconstruct atomistic freeenergy surfaces in coarsegrain coordinates is discussed. The MSCG method is based on forcematching generalized forces associated with the coarsegrain coordinates. In this work, we show that the MSCG method recovers only part of the atomistic freeenergy landscape in the coarsegrain coordinates (termed the potential of mean force contribution). The portion of the atomistic freeenergy landscape that is left out in the MSCG procedure contributes to a pressure difference between atomistic and coarsegrain ensembles. Employing one and twosite coarsegraining of nitromethane as worked examples, we discuss the virial and compressibility constraints to incorporate a pressure correction interaction into the MSCG potentials and improve performance at different densities. The nature of the pressure correction interaction is elucidated and compared with those used in structurebased coarsegraining. As pairwise approximations to the atomistic freeenergy, the MSCG potentials naturally depend on the variables describing a thermodynamic state, such as temperature and density. Such dependencies limit statepoint transferability. For nitromethane, the one and twosite MSCG potentials appear to be transferable across a broad range of temperatures. In particular, the twosite models, which are matched to low and ambient temperature liquid states, perform well in simulations of the ambient crystal structure. In contrast, the transferability of the MSCG models of nitromethane across different densities is found to be problematic. To achieve better statepoint transferability, density dependent MSCG potentials are introduced and their performance is examined in simulations of nitromethane under various thermodynamic conditions, including shocked states.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Lifetimes of heavyRydberg ionpair states formed through Rydberg electron transfer
View Description Hide DescriptionThe lifetimes of , , and heavyRydberg ionpair states produced through Rydbergelectron transferreactions are measured directly as a function of binding energy using electric field induced detachment and the ionpair decay channels discussed. The data are interpreted using a Monte Carlo collision code that models the detailed kinematics of electron transferreactions. The lifetimes of ionpair states are observed to be very long, , and independent of binding energy. The lifetimes of strongly bound ion pairs are found to be similarly long but begin to decrease markedly as the binding energy is reduced below this value. This behavior is attributed to conversion of rotational energy in the ion into translational energy of the ion pair. No longlived ion pairs are observed, their lifetimes decreasing with increasing binding energy. This behavior suggests that ionpair loss is associated with mutual neutralization as a result of charge transfer.

Ultrafast deactivation processes in the 2aminopyridine dimer and the adeninethymine base pair: Similarities and differences
View Description Hide Description2aminopyridine dimer has frequently been used as a model system for studying photochemistry of DNA base pairs. We examine here the relevance of 2aminopyridine dimer for a Watson–Crick adeninethymine base pair by studying UVlight induced photodynamics along two main hydrogen bridges after the excitation to the localized excitedstate. The respective twodimensional potentialenergysurfaces have been determined by timedependent density functional theory with Coulombattenuated hybrid exchangecorrelation functional (CAMB3LYP). Different mechanistic aspects of the deactivation pathway have been analyzed and compared in detail for both systems, while the related reaction rates have also be obtained from Monte Carlo kinetic simulations. The limitations of the 2aminopyridine dimer as a model system for the adeninethymine base pair are discussed.

Imaging the radical channel in acetaldehyde photodissociation: Competing mechanisms at energies close to the triplet exit barrier
View Description Hide DescriptionThe photodissociation of acetaldehyde in the radical channel has been studied at wavelengths between 315 and 325 nm using the velocitymap imaging technique. Upon onephoton absorption at 315 nm, the molecule is excited to the first singlet excited state, which, in turn, undergoes intersystem crossing to the first excited triplet state . On the triplet surface, the molecule dissociates into and HCO radicals with large kinetic energy release (KER), in accordance with the well characterized exit barrier on . However, at longer wavelengths , which correspond to excitation energies just below the triplet barrier, a sudden change in KER is observed. At these photolysis wavelengths, there is not enough energy to surpass the exit barrier on the triplet state, which leaves the possibility of unimolecular dissociation on after internal conversion from . We have characterized the fragments’ KER at these wavelengths, as well as determined the energy partitioning for the radical fragments. A new accurate estimate of the barrier height on is presented.

Giant Renner–Teller vibronic coupling in the radical: An ab initio study of the and electronic states
View Description Hide DescriptionThe potential energy surfaces (PESs) of the ground and the first excited electronic states of the radical have been studied ab initio, using a large basis set and CCSD(T) and EOMCCSD techniques. The calculated PESs were used to variationally calculate the energy levels up to above the ground state. The Renner–Teller splitting parameter found for the state of this radical is very large which results in an unusual excited stateenergy level structure.

The electronic structure of the triiodide ion from relativistic correlated calculations: A comparison of different methodologies
View Description Hide DescriptionThe triiodide ion exhibits a complex photodissociation behavior, the dynamics of which are not yet fully understood. As a first step toward determining the full potential energy surfaces of this species for subsequent simulations of its dissociation processes, we investigate the performance of different electronic structure methods [timedependent density functional theory, complete active space perturbation theory to second order (CASPT2), Fockspace coupled cluster and multireference configuration interaction] in describing the ground and excited states of the triiodide ion along the symmetrical dissociation path. All methods apart from CASPT2 include scalar relativity and spinorbit coupling in the orbital optimization, providing useful benchmark data for the more common twostep approaches in which spinorbit coupling is introduced in the configuration interaction. Timedependent density functional theory with the statistical averaging of model orbital potential functional is off the mark for this system. Another choice of functional may improve performance with respect to vertical excitation energies and spectroscopic constants, but all functionals are likely to face instability problems away from the equilibrium region. The Fockspace coupled cluster method was shown to perform clearly best in regions not too far from equilibrium but is plagued by convergence problems toward the dissociation limit due to intruder states. CASPT2 shows good performance at significantly lower computational cost, but is quite sensitive to symmetry breaking. We furthermore observe spikes in the CASPT2 potential curves away from equilibrium, signaling intruder state problems that we were unable to curb through the use of level shifts. Multireference configuration interaction is, in principle, a viable option, but its computational cost in the present case prohibits use other than for benchmarking purposes.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Recoupling of native homonuclear dipolar couplings in magicanglespinning solidstate NMR by the doubleoscillating field technique
View Description Hide DescriptionA new solidstate NMR method, the doubleoscillating field technique (DUO), that under magicanglespinning conditions produces an effective Hamiltonian proportional to the native highfield homonuclear dipoledipole coupling operator is presented. The method exploits one part of the radio frequency (rf) field to recouple the dipolar coupling interaction with a relatively high scaling factor and to eliminate offset effects over a reasonable bandwidth while in the recoupling frame, the other part gives rise to a sufficiently large longitudinal component of the residual rf field that averages nonsecular terms and in addition ensures stability toward rf inhomogeneity and rf miscalibration. The capability of the DUO experiment to mediate transfer of polarization is described theoretically and compared numerically and experimentally with finite pulse rf driven recoupling and experimentally with dipolarassisted rotational resonance. Twodimensional recoupling experiments were performed on antiparallel amyloidfibrils of the decapeptide SNNFGAILSS with the FGAIL fragment uniformly labeled with and .

Monte Carlo study of structural ordering of LennardJones fluids confined in nanochannels
View Description Hide DescriptionWe investigate quantitatively the ordering of LennardJones fluids confined in a thin and infinitely long nanochannel with square cross section. The most probable spatial configurations of the atoms were examined by Monte Carlo simulations, and the order parameter was calculated. The effect of the various parameters, such as the wallfluid attractive interaction, the size of constriction, and the temperature, was studied. The results indicate that for strong wallfluid interactions and small constrictions, the ordering of the fluid particles is almost perfect. Geometrical mismatch, as well as increasing the system’s temperature, deteriorates the ordering phenomenon, even for very small openings. We observe a nontrivial trend in the dependence of the order parameter on the size of the opening of the channel with a linear size smaller than five atomic layers. We also examined the rearrangements of the fluid’s atoms in more symmetrical pores—slitlike pores and cylindrical nanopores—and discuss their similarities and differences with the square channels.

A generalized reactive force field for nonlinear hydrogen bonds: Hydrogen dynamics and transfer in malonaldehyde
View Description Hide DescriptionUsing molecular dynamics (MD) simulations, the spectroscopy and dynamics of malonaldehyde is investigated. To this end, the recently proposed molecular mechanics with proton transfer (MMPT) potential is generalized to nonlinear hydrogen bonds. The calculated properties for malonaldehyde in both gas and condensed phases, including equilibrium geometries, infrared spectra,tunneling splittings, and hydrogen transfer rates, compare well with previous experimental and computational works. In particular, by using a harmonic bath averaged (HBA) Hamiltonian, which is based on a reaction path Hamiltonian, it is possible to estimate the tunneling splitting in an efficient manner. It is found that a zero point corrected barrier of 6.7 kcal/mol and effective masses of 1.234 (i.e., 23.4% larger than the mass of a physical Hatom) and 1.117 (for the physical Datom) are consistent with the measured splittings of 21.6 and , respectively. The HBA Hamiltonian also yields a pair of hydrogen transfer fundamentals at 1573 and , similar to results obtained with a reaction surface Hamiltonian on a MP2/ potential energy surface. This amounts to a substantial redshift of more than which can be rationalized by comparison with weakly (: rare gas) and strongly protonbound systems. Hydrogen transfer rates in vacuum and water were determined from the validated MMPT potential and it is found that the solvent enhances the rate by a factor of 5 at 300 K. The rates of 2.4/ns and 10/ns are commensurate with previous density functional tight binding ab initio MD studies.

The distorted closepacked crystal structure of methane A
View Description Hide DescriptionWe have determined the full crystal structure of the highpressure phase methane A. Xray singlecrystaldiffraction data were used to determine the carbonatom arrangement, and neutronpowderdiffraction data from a deuterated sample allowed the deuterium atoms to be located. It was then possible to refine all the hydrogen positions from the singlecrystal xray data. The structure has 21 molecules in a rhombohedral unit cell, and is quite strongly distorted from the cubic closepacked structure of methane I, although some structural similarities remain. Full knowledge of this structure is important for modeling of methane at higher pressures, including in relation to the mineralogy of the outer solar system. We discuss interesting structural parallels with the carbon tetrahalides.

Why are parahydrogen clusters superfluid? A quantum theorem of corresponding states study
View Description Hide DescriptionThe quantum theorem of corresponding states is applied to and cold quantum fluid clusters to establish where parahydrogen clusters lie in relation to more and less quantum delocalized systems. Path integral Monte Carlo calculations of the energies, densities, radial and pair distributions, and superfluid fractions are reported at for a LennardJones (LJ) (12,6) potential using six different de Boer parameters including the accepted value for hydrogen. The results indicate that the hydrogen clusters are on the borderline to being a nonsuperfluid solid but that the molecules are sufficiently delocalized to be superfluid. A general phase diagram for the total and kinetic energies of LJ (12,6) clusters encompassing all sizes from to and for the entire range of de Boer parameters is presented. Finally the limiting de Boer parameters for quantum delocalization induced unbinding (“quantum unbinding”) are estimated and the new results are found to agree with previous calculations for the bulk and smaller clusters.

Three pulse UV photon echo studies of molecules in solution: Effect of the chirp
View Description Hide DescriptionWe report on the electronic dephasing times of the nonpolar chromophore diphenylacetylene (DPA) in ethanol and in cyclohexane (polar and nonpolar solvents respectively) by photon echo measurements in the ultraviolet. Contrary to previous reports, we observed sub100fs electronic dephasing times for DPA in both solvents. We identify fast dynamics of on the photon echo peak shift (PEPS) traces of DPA in ethanol. In addition, we observed a dependence of the PEPS asymptotic value on the temporal chirp of the pulses. We propose a model to describe it in terms of phasematching condition and beam geometry.