Volume 134, Issue 21, 07 June 2011

We investigate atomistic mechanisms governing hydrogen release and uptake processes in ammonia borane (AB) within the framework of the density functional theory. In order to determine the most favorable pathways for the thermal interconversion between AB and polyaminoborane plus H_{2}, we calculate potential energy surfaces for the corresponding reactions. We explore the possibility of enclosing AB in narrow carbon nanotubes to limit the formation of undesirable sideproducts such as the cyclic compound borazine, which hinder subsequent rehydrogenation of the system. We also explore the effects of nanoconfinement on the possible rehydrogenation pathways of AB and suggest the use of photoexcitation as a means to achieve dehydrogenation of AB at low temperatures.
 COMMUNICATIONS


Communication: Determination of the bond dissociation energy (D _{0}) of the water dimer, (H_{2}O)_{2}, by velocity map imaging
View Description Hide DescriptionThe bond dissociation energy (D _{0}) of the water dimer is determined by using statetostate vibrational predissociationmeasurements following excitation of the bound OH stretch fundamental of the donor unit of the dimer. Velocity map imaging and resonanceenhanced multiphoton ionization (REMPI) are used to determine paircorrelated product velocity and translational energy distributions. H_{2}O fragments are detected in the ground vibrational (000) and the first excited bending (010) states by 2 + 1 REMPI via the ^{1}B_{1} (000) ← ^{1}A_{1} (000 and 010) transitions. The fragments’ velocity and centerofmass translational energy distributions are determined from images of selected rovibrational levels of H_{2}O. An accurate value for D _{0} is obtained by fitting both the structure in the images and the maximum velocity of the fragments. This value, D _{0} = 1105 ± 10 cm^{−1} (13.2 ± 0.12 kJ/mol), is in excellent agreement with the recent theoretical value of D _{0} = 1103 ± 4 cm^{−1} (13.2 ± 0.05 kJ/mol) suggested as a benchmark by Shank et al. [J. Chem. Phys. 130, 144314 (2009)].
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 ARTICLES

 Theoretical Methods and Algorithms

Magnetic exchange couplings evaluated with Rung 3.5 density functionals
View Description Hide DescriptionRung 3.5 exchangecorrelation functionals are assessed for the calculation of magnetic exchange coupling parameters and atomic spin populations for a variety of inorganic and organic magnetic systems. Density functional theory calculations of exchange couplings sensitively depend on nonlocal contributions to the exchangecorrelation functional. Semilocal functionals, Rungs 13 on “Jacob's Ladder” of density functional approximations, yield excessively delocalized electrons and overestimated absolute exchange couplings. Fourthrung hybrid functionals admixing nonlocal exchange improve the results. We show that new “Rung 3.5” functionals give magnetic properties intermediate between semilocal and hybrid functionals, providing additional evidence that these functionals incorporate some desirable aspects of nonlocal exchange. Results for ferromagnetic complexes indicate areas for future improvement.

Two and fourcomponent relativistic generalizedactivespace coupled cluster method: Implementation and application to BiH
View Description Hide DescriptionA stringbased coupledcluster method of general excitation rank and with optimal scaling which accounts for special relativity within the fourcomponent framework is presented. The method opens the way for the treatment of multireference problems through an activespace inspired singlereference based stateselective expansion of the model space. The evaluation of the coupledclustervector function is implemented by considering contractions of elementary secondquantized operators without setting up the amplitude equations explicitly. The capabilities of the new method are demonstrated in application to the electronic ground state of the bismuth monohydride molecule. In these calculations simulated multireference expansions with both doubles and triples excitations into the external space as well as the regular coupledcluster hierarchy up to full quadruples excitations are compared. The importance of atomic outer corecorrelation for obtaining accurate results is shown. Comparison to the nonrelativistic framework is performed throughout to illustrate the additional work of the transition to the fourcomponent relativistic framework both in implementation and application. Furthermore, an evaluation of the highest order scaling for generalorder expansions is presented.

A smoothly decoupled particle interface: New methods for coupling explicit and implicit solvent
View Description Hide DescriptionA common theme of studies using molecular simulation is a necessary compromise between computational efficiency and resolution of the forcefield that is used. Significant efforts have been directed at combining multiple levels of granularity within a single simulation in order to maintain the efficiency of coarsegrained models, while using finer resolution in regions where such details are expected to play an important role. A specific example of this paradigm is the development of hybrid solventmodels, which explicitly sample the solvent degrees of freedom within a specified domain while utilizing a continuum description elsewhere. Unfortunately, these models are complicated by the presence of structural artifacts at or near the explicit/implicit boundary. The presence of these artifacts significantly complicates the use of such models, both undermining the accuracy obtained and necessitating the parameterization of effective potentials to counteract the artificial interactions. In this work, we introduce a novel hybrid solventmodel that employs a smoothly decoupled particle interface (SDPI), a switching region that gradually transitions from fully interacting particles to a continuum solvent. The resulting SDPI model allows for the use of an implicit solventmodel based on a simple theory that needs to only reproduce the behavior of bulk solvent rather than the more complex features of local interactions. In this study, the SDPI model is tested on spherical hybrid domains using a coarsegrained representation of water that includes only LennardJones interactions. The results demonstrate that this model is capable of reproducing solvent configurations absent of boundary artifacts, as if they were taken from full explicit simulations.

Damped response theory description of twophoton absorption
View Description Hide DescriptionDamped response theory is applied to the calculation of twophoton absorption(TPA)spectra, which are determined directly, at each frequency, from a modified damped cubic response function. The TPAspectrum may therefore be evaluated for selected frequency ranges, making the damped TPA approach attractive for calculations on large molecules with a high density of states, where the calculation of TPA using standard theory is more problematic. Damped response theory can also be applied to the case of intermediate state resonances, where the standard TPA expression is divergent. Both exact damped response theory and its application within density functional theory are discussed. The latter is implemented using an atomicorbital based density matrix formulation, which makes the approach especially suitable for studies on large systems. A test preliminary study is presented for the TPAspectrum of R(+)1,1′bi(2naphtol).

Approaching the theoretical limit in periodic local MP2 calculations with atomicorbital basis sets: The case of LiH
View Description Hide DescriptionThe atomic orbital basis set limit is approached in periodic correlated calculations for solid LiH. The valence correlation energy is evaluated at the level of the local periodic second order MøllerPlesset perturbation theory (MP2), using basis sets of progressively increasing size, and also employing “bond”centered basis functions in addition to the standard atomcentered ones. Extended basis sets, which contain linear dependencies, are processed only at the MP2 stage via a dual basis set scheme. The local approximation (domain) error has been consistently eliminated by expanding the orbital excitation domains. As a final result, it is demonstrated that the complete basis set limit can be reached for both HF and local MP2 periodic calculations, and a general scheme is outlined for the definition of highquality atomicorbital basis sets for solids.

A fluctuating quantum model of the CO vibration in carboxyhemoglobin
View Description Hide DescriptionIn this paper, we present a theoretical approach to construct a fluctuating quantum model of the CO vibration in hemeCO proteins and its interaction with external laser fields. The methodology consists of mixed quantumclassical calculations for a restricted number of snapshots, which are then used to construct a parametrized quantum model. As an example, we calculate the infrared absorption spectrum of carboxyhemoglobin, based on a simplified protein model, and found the absorption linewidth in good agreement with the experimental results.

Twocomponent natural spinors from twostep spinorbit coupled wave functions
View Description Hide DescriptionWe developed an algorithm to obtain the natural orbitals (natural spinors) from the twostep spinorbit coupled wave functions. These natural spinors are generally complexvalued, mixing two spin components, and they can have similar symmetry properties as the jj spinors from the onestep spinorbit coupling calculations, if the reduced density equally averages all the components of a multidimensional irreducible representation. Therefore, the natural spinors can serve as an approximation to the jj spinors and any wave function analysis based on the jj spinors can also be performed based on them. The comparison between the natural spinors and the jj spinors of three representative atoms, Tl, At, and Lu, shows their close similarity and demonstrates the ability of the natural spinors to approximate the jj spinors.

Correcting model energies by numerically integrating along an adiabatic connection and a link to density functional approximations
View Description Hide DescriptionModel Hamiltonians are considered for which electrons interact via longrange forces. It is assumed that their eigenvalues can be obtained with satisfying accuracy. Extrapolation techniques using asymptotic behavior considerations provide estimates for the energy of the physical system. Results for the uniform electron gas and some twoelectron systems show that very few quadrature points can already produce good quality results. Connections to the density functional theory are discussed.

A novel interpretation of reduced density matrix and cumulant for electronic structure theories
View Description Hide DescriptionWe propose a novel interpretation of the reduced density matrix (RDM) and its cumulant that combines linear and exponential parametrizations of the wavefunction. Any nparticle RDM can be written as a weighted average of “configuration interaction” amplitudes. The corresponding nparticle cumulant is represented in terms of two types of contributions: “connected” (statistical averages of substitution amplitudes) and “disconnected” (crosscorrelations of substitution amplitudes). A diagonal element of nRDM represents the average occupation number of the orbital ntuple. The diagonal elements of 2 and 3cumulants take particularly elegant forms in the natural spinorbital basis: they represent the covariances (correlated fluctuations) of the occupation numbers of the orbital pair and triples, respectively. Thus, the diagonal elements of the cumulants quantify the correlation between the orbital occupation numbers. Our interpretation is used to examine the weak to strong correlation transition in the “two electrons in two orbitals” problem.

Development of a new variational approach for thermal density matrices
View Description Hide DescriptionA McLachlantype variational principle is derived for thermal density matrices. In this approach, the trace of the mean square of the differences between the derivatives of the exact and model density matrices is minimized with respect to the parameters in the model Hamiltonian. Applications to model anharmonic systems in the independent particle model show that the method can provide thermodynamic state functions accurately (within 5% of the converged basis set results) and at the same level of accuracy as the results using FeynmanGibbsBogoliubov variational principle at this level of approximation.

Transferable model of water with variable molecular size
View Description Hide DescriptionBy decreasing the steepness of the repulsive wing in the intermolecular potential, one can extend the applicability of a watermodel to the high pressure region. Exploiting this trivial possibility, we published a polarizable model of water which provided good estimations not only of gas clusters, ambient liquid, hexagonal ice, but ice VII at very high pressures as well [A. Baranyai and P. Kiss, J. Chem. Phys.133, 144109 (2010)10.1063/1.3490660]. This straightforward method works well provided the closest O–O distance is reasonably shorter in the high pressure phase than in hexagonal ice. If these O–O distances are close to each other and we fit the interactions to obtain an accurate picture of hexagonal ice, we underestimate the density of the highpressure phases. This can be overcome if models use contracted molecules under high external pressure.In this paper we present a method, which is capable to describe the contraction of water molecules under high pressure by using two simple repulsionattraction functions. These functions represent the dispersion interaction under low pressure and high pressure. The switch function varies between 0 and 1 and portions the two repulsions among the individual particles. The argument of the switch function is a virialtype expression, which can be interpreted as a net force compressing the molecule. We calculated the properties of gas clusters, densities, and internal energies of ambient water, hexagonal ice,ice III, ice VI, and ice VII phases and obtained excellent match of experimental data.

Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics
View Description Hide DescriptionStochastic thermodynamics of chemical reactionsystems has recently gained much attention. In the present paper, we consider such an issue for a system with both oscillatory and excitable dynamics, using catalyticoxidation of carbon monoxide on the surface of platinum crystal as an example. Starting from the chemical Langevin equations, we are able to calculate the stochastic entropy production P along a random trajectory in the concentration state space. Particular attention is paid to the dependence of the timeaveraged entropy production P on the system size N in a parameter region close to the deterministic Hopf bifurcation (HB). In the large system size (weak noise) limit, we find that P ∼ N ^{β} with β = 0 or 1, when the system is below or above the HB, respectively. In the small system size (strong noise) limit, P always increases linearly with N regardless of the bifurcation parameter. More interestingly, P could even reach a maximum for some intermediate system size in a parameter region where the corresponding deterministic system shows steady state or small amplitude oscillation. The maximum value of P decreases as the system parameter approaches the socalled CANARD point where the maximum disappears. This phenomenon could be qualitatively understood by partitioning the total entropy production into the contributions of spikes and of small amplitude oscillations.

Extended multiconfiguration quasidegenerate perturbation theory: The new approach to multistate multireference perturbation theory
View Description Hide DescriptionThe distinctive desirable features, both mathematically and physically meaningful, for all partially contracted multistate multireference perturbation theories (MSMRPT) are explicitly formulated. The original approach to MSMRPT theory, called extended multiconfiguration quasidegenerate perturbation theory (XMCQDPT), having most, if not all, of the desirable properties is introduced. The new method is applied at the second order of perturbation theory (XMCQDPT2) to the 1^{1}A^{′} – 2^{1}A^{′} conical intersection in allene molecule, the avoided crossing in LiF molecule, and the 1^{1}A_{1} to 2^{1}A_{1} electronic transition in cis1,3butadiene. The new theory has several advantages compared to those of wellestablished approaches, such as second order multiconfiguration quasidegenerate perturbation theory and multistatesecond order complete active space perturbation theory. The analysis of the prevalent approaches to the MSMRPT theory performed within the framework of the XMCQDPT theory unveils the origin of their common inherent problems. We describe the efficient implementation strategy that makes XMCQDPT2 an especially useful generalpurpose tool in the highlevel modeling of small to large molecular systems.

Reduction of the virtual space for coupledcluster excitation energies of large molecules and embedded systems
View Description Hide DescriptionWe investigate how the reduction of the virtual space affects coupledclusterexcitation energies at the approximate singles and doubles coupledcluster level (CC2). In this reducedvirtualspace (RVS) approach, all virtual orbitals above a certain energy threshold are omitted in the correlation calculation. The effects of the RVS approach are assessed by calculations on the two lowest excitation energies of 11 biochromophores using different sizes of the virtual space. Our set of biochromophores consists of common model systems for the chromophores of the photoactive yellow protein, the green fluorescent protein, and rhodopsin. The RVS calculations show that most of the highlying virtual orbitals can be neglected without significantly affecting the accuracy of the obtained excitation energies. Omitting all virtual orbitals above in the correlation calculation introduces errors in the excitation energies that are smaller than . By using a RVS energy threshold of , the CC2 calculations using tripleζ basis sets (TZVP) on protonated Schiff base retinal are accelerated by a factor of 6. We demonstrate the applicability of the RVS approach by performing CC2/TZVP calculations on the lowest singlet excitation energy of a rhodopsin model consisting of 165 atoms using RVS thresholds between 20 eV and 120 eV. The calculations on the rhodopsin model show that the RVS errors determined in the gasphase are a very good approximation to the RVS errors in the protein environment. The RVS approach thus renders purely quantum mechanical treatments of chromophores in protein environments feasible and offers an ab initio alternative to quantum mechanics/molecular mechanics separation schemes.

A graphtheoretical kinetic Monte Carlo framework for onlattice chemical kinetics
View Description Hide DescriptionExisting kinetic Monte Carlo(KMC) frameworks for the simulation of adsorption, desorption,diffusion, and reaction on a lattice often assume that each participating species occupies a single site and represent elementary events involving a maximum of two sites. However, these assumptions may be inadequate, especially in the case of complex chemistries, involving multidentate species or complex coverage and neighboring patterns between several lattice sites. We have developed a novel approach that employs graphtheoretical ideas to overcome these challenges and treat easily complex chemistries. As a benchmark, the ZiffGulariBarshad system is simulated and comparisons of the computational times of the graphtheoretical KMC and a simpler KMC approach are made. Further, to demonstrate the capabilities of our framework, the watergas shift chemistry on Pt(111) is simulated.

A statespecific partially internally contracted multireference coupled cluster approach
View Description Hide DescriptionA statespecific partially internally contracted multireference coupled cluster approach is presented for general complete active spaces with arbitrary number of active electrons. The dominant dynamical correlation is included via an exponential parametrization of internally contracted cluster operators () which excite electrons from a multideterminantal reference function. The remaining dynamical correlation and relaxation effects are included via a diagonalization of the transformed Hamiltonian in the multireference configuration interaction singles space in an uncontracted fashion. A new set of residual equations for determining the internally contracted cluster amplitudes is proposed. The second quantized matrix elements of , expressed using the extended normal ordering of Kutzelnigg and Mukherjee, are used as the residual equations without projection onto the excited configurations. These residual equations, referred to as the manybody residuals, do not have any nearsingularity and thus, should allow one to solve all the amplitudes without discarding any. There are some relatively minor remaining convergence issues that may arise from an attempt to solve all the amplitudes and an initial analysis is provided in this paper. Applications to the bondstretching potential energy surfaces for N_{2}, CO, and the lowlying electronic states of C_{2} indicate clear improvements of the results using the manybody residuals over the conventional projected residual equations.

Phonostat: Thermostatting phonons in molecular dynamics simulations
View Description Hide DescriptionThermostat algorithms in a molecular dynamics simulation maintain an average temperature of a system by regulating the atomic velocities rather than the internal degrees of freedom. Herein, we present a “phonostat” algorithm that can regulate the total energy in a given internal degree of freedom. In this algorithm, the modal energies are computed at each time step using a modetracking scheme and then the system is driven by an external driving force of desired frequency and amplitude. The rate and amount of energy exchange between the phonostat and the system is controlled by two distinct damping parameters. Two different schemes for controlling the external driving force amplitude are also presented. In order to test our algorithm, the method is applied initially to a simple anharmonic oscillator for which the role of various phonostat parameters can be carefully tested. We then apply the phonostat to a more realistic (10,0) carbon nanotubesystem and show how such an approach can be used to regulate energy of highly anharmonic modes.

Multireference stateuniversal coupledcluster approaches to electronically excited states
View Description Hide DescriptionThe multireference (MR), general model space (GMS), stateuniversal (SU),coupledcluster (CC) method with singles and doubles (GMSSUCCSD), as well as its triplecorrected versions GMSSUCCSD(T), are employed to assess their ability to describe lowlying excited states of various molecules, with an emphasis on a simultaneous handling of several states of the same symmetry species. A special attention is given to the role of the socalled Cconditions that account for nonvanishing internal cluster amplitudes when relying on an incomplete GMS, as well as to the choice of suitable model spaces and a perturbative account of secondary triples. The ambiguities arising when using large basis sets are also pointed out. To achieve a general assessment of the potential of the GMStype SUCC approaches, the vertical excitation energies of several species, including the challenging BN diatomic as well as larger systems, namely formaldehyde, transbutadiene, formamide, and benzene are considered. These results are compared with those provided by the equationofmotion EOMCCSD method and, whenever available, the density functional theory results and experimental data. These comparisons clearly demonstrate the usefulness of GMStype MRCC approaches.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

I^{−}·(CH_{3}I)_{2} photoexcitation: The influence of dipole bound states on detachment and fragmentation
View Description Hide DescriptionWe present the results of a photoelectron imaging study of the I^{−}·(CH_{3}I)_{2} cluster anion over excitation wavelengths 355–260 nm. The resulting spectra and photoelectron angular distributions (PADs) suggest extensive electronmolecule interaction following photoexcitation. Fragmentation channels are observed subsequent to excitation between 355 and 330 nm. The origin of these features, which begin 200 meV and peak 70 meV below the X band direct detachment threshold, is described in terms of a predissociative dipole bound state. The nature of the fragments detected and the energetics of the channel opening argue strongly in favor of an asymmetric, head to tail cluster anion geometry posited by Dessent et al. [Acc. Chem. Res.31, 527 (1998)]10.1021/ar950061f. Above the direct detachment threshold, PADs display evidence of phenomena akin to electronmolecule scattering. The fragment anions disappear above the X band threshold but reappear some distance below the second (A) direct detachment band. At these energies there is also rapid variation of the X band PAD, an observation attributed to autodetachment via spinorbit relaxation of the iodine core of the cluster.