Volume 138, Issue 19, 21 May 2013
 ARTICLES

 Theoretical Methods and Algorithms

Nonlinear eigensolverbased alternative to traditional SCF methods
View Description Hide DescriptionThe selfconsistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the nonlinear eigenvector problem, i.e., H({ψ})ψ = Eψ. This new scheme is derived from a generalization of the FEAST eigenvalue algorithm to account for the nonlinearity of the Hamiltonian with the occupied eigenvectors. Using a series of numerical examples and the density functional theoryKohn/Sham model, it will be shown that our approach can outperform the traditional SCF mixingscheme techniques by providing a higher converge rate, convergence to the correct solution regardless of the choice of the initial guess, and a significant reduction of the eigenvalue solve time in simulations.

Doubly electronattached and doubly ionized equationofmotion coupledcluster methods with 4particle–2hole and 4hole–2particle excitations and their activespace extensions
View Description Hide DescriptionThe full and activespace doubly electronattached (DEA) and doubly ionized (DIP) equationofmotion coupledcluster (EOMCC) methods with up to 4particle–2hole (4p2h) and 4hole–2particle (4h2p) excitations are developed. By examining bond breaking in F2 and lowlying singlet and triplet states in the methylene, (HFH)−, and trimethylenemethane biradicals, we demonstrate that the DEA and DIPEOMCC methods with an activespace treatment of 4p2h and 4h2p excitations reproduce the results of the analogous full calculations at the small fraction of the computer effort, while improving the DEA/DIPEOMCC theories truncated at 3p1h/3h1p excitations.

Potential energy curves via double electronattachment calculations: Dissociation of alkali metal dimers
View Description Hide DescriptionThe recently developed method [M. Musiał, J. Chem. Phys.136, 134111 (2012)] to study double electron attached states has been applied to the description of the ground and excited state potential energy curves of the alkali metal dimers. The method is based on the multireference coupled cluster scheme formulated within the Fock space formalism for the (2,0) sector. Due to the use of the efficient intermediate Hamiltonian formulation, the approach is free from the intruder states problem. The description of the neutral alkali metal dimers is accomplished via attaching two electrons to the corresponding doubly ionized system. This way is particularly advantageous when a closed shell molecule dissociates into open shell subunits while its doubly positive cation generates the closed shell fragments. In the current work, we generate the potential energy curves for the ground and multiple excited states of the Li2 and Na 2 molecules. In all cases the potential energy curves are smooth for the entire range of interatomic distances (from the equilibrium point to the dissociation limit). Based on the calculated potential energy curves, we are able to compute spectroscopic parameters of the systems studied.

Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. I. Sensitivity to physical parameters of the pore
View Description Hide DescriptionIn this article, uncertainty quantification is applied to molecular dynamics (MD) simulations of concentration driven ionic flow through a silica nanopore. We consider a silica pore model connecting two reservoirs containing a solution of sodium (Na +) and chloride (Cl−) ions in water. An ad hoc concentration control algorithm is developed to simulate a concentration driven counter flow of ions through the pore, with the ionic flux being the main observable extracted from the MD system. We explore the sensitivity of the system to two physical parameters of the pore, namely, the pore diameter and the gating charge. First we conduct a quantitative analysis of the impact of the pore diameter on the ionic flux, and interpret the results in terms of the interplay between size effects and ion mobility. Second, we analyze the effect of gating charge by treating the charge density over the pore surface as an uncertain parameter in a forward propagation study. Polynomial chaos expansions and Bayesian inference are exploited to isolate the effect of intrinsic noise and quantify the impact of parametric uncertainty on the MD predictions. We highlight the challenges arising from the heterogeneous nature of the system, given the several components involved, and from the substantial effect of the intrinsic thermal noise.

Uncertainty quantification in MD simulations of concentration driven ionic flow through a silica nanopore. II. Uncertain potential parameters
View Description Hide DescriptionThis article extends the uncertainty quantification analysis introduced in Paper I for molecular dynamics (MD) simulations of concentration driven ionic flow through a silica nanopore. Attention is now focused on characterizing, for a fixed pore diameter of D = 21 Å, the sensitivity of the system to the LennardJones energy parameters, and , defining the depth of the potential well for the two ions Na + and Cl−, respectively. A forward propagation analysis is applied to map the uncertainty in these parameters to the MD predictions of the ionic fluxes. Polynomial chaos expansions and Bayesian inference are exploited to isolate the effect of the intrinsic noise, stemming from thermal fluctuations of the atoms, and properly quantify the impact of parametric uncertainty on the target MD predictions. A Bayes factor analysis is then used to determine the most suitable regression model to represent the MD noisy data. The study shows that the response surface of the Na + conductance can be effectively inferred despite the substantial noise level, whereas the noise partially hides the underlying trend in the Cl− conductance data over the studied range. Finally, the dependence of the conductances on the uncertain potential parameters is analyzed in terms of correlations with key bulk transport coefficients, namely, viscosity and collective diffusivities, computed using GreenKubo time correlations.

Assessment of rangeseparated timedependent densityfunctional theory for calculating C _{6} dispersion coefficients
View Description Hide DescriptionWe assess a variant of linearresponse rangeseparated timedependent densityfunctional theory (TDDFT), combining a longrange HartreeFock (HF) exchange kernel with a shortrange adiabatic exchangecorrelation kernel in the localdensity approximation (LDA) for calculating isotropic C 6 dispersion coefficients of homodimers of a number of closedshell atoms and small molecules. This rangeseparated TDDFT tends to give underestimated C 6 coefficients of small molecules with a mean absolute percentage error of about 5%, a slight improvement over standard TDDFT in the adiabatic LDA which tends to overestimate them with a mean absolute percentage error of 8%, but close to timedependent HartreeFock which has a mean absolute percentage error of about 6%. These results thus show that introduction of longrange HF exchange in TDDFT has a small but beneficial impact on the values of C 6 coefficients. It also confirms that the present variant of rangeseparated TDDFT is a reasonably accurate method even using only a LDAtype density functional and without adding an explicit treatment of longrange correlation.

Discrete variable representation in electronic structure theory: Quadrature grids for leastsquares tensor hypercontraction
View Description Hide DescriptionWe investigate the application of molecular quadratures obtained from either standard Becketype grids or discrete variable representation (DVR) techniques to the recently developed leastsquares tensor hypercontraction (LSTHC) representation of the electron repulsion integral (ERI) tensor. LSTHC uses leastsquares fitting to renormalize a twosided pseudospectral decomposition of the ERI, over a physicalspace quadrature grid. While this procedure is technically applicable with any choice of grid, the best efficiency is obtained when the quadrature is tuned to accurately reproduce the overlap metric for quadratic products of the primary orbital basis. Properly selected Becke DFT grids can roughly attain this property. Additionally, we provide algorithms for adopting the DVR techniques of the dynamics community to produce two different classes of grids which approximately attain this property. The simplest algorithm is radial discrete variable representation (RDVR), which diagonalizes the finite auxiliarybasis representation of the radial coordinate for each atom, and then combines LebedevLaikov spherical quadratures and Becke atomic partitioning to produce the full molecular quadrature grid. The other algorithm is full discrete variable representation (FDVR), which uses approximate simultaneous diagonalization of the finite auxiliarybasis representation of the full position operator to produce nondirectproduct quadrature grids. The qualitative features of all three grid classes are discussed, and then the relative efficiencies of these grids are compared in the context of LSTHCDFMP2. Coarse Becke grids are found to give essentially the same accuracy and efficiency as RDVR grids; however, the latter are built from explicit knowledge of the basis set and may guide future development of atomcentered grids. FDVR is found to provide reasonable accuracy with markedly fewer points than either Becke or RDVR schemes.

A generalized anyparticle propagator theory: Prediction of proton affinities and acidity properties with the proton propagator
View Description Hide DescriptionWe have recently extended the electron propagator theory to the treatment of any type of particle using an AnyParticle Molecular Orbital (APMO) wavefunction as reference state. This approach, called APMO/PT, has been implemented in the LOWDIN code to calculate correlated binding energies, for any type of particle in molecular systems. In this work, we present the application of the APMO/PT approach to study proton detachment processes. We employed this method to calculate proton binding energies and proton affinities for a set of inorganic and organic molecules. Our results reveal that the secondorder proton propagator (APMO/PP2) quantitatively reproduces experimental trends with an average deviation of less than 0.41 eV. We also estimated proton affinities with an average deviation of 0.14 eV and the proton hydration free energy using APMO/PP2 with a resulting value of −270.2 kcal/mol, in agreement with other results reported in the literature. Results presented in this work suggest that the APMO/PP2 approach is a promising tool for studying proton acid/base properties.

Anharmonic state counts and partition functions for molecules via classical phase space integrals in curvilinear coordinates
View Description Hide DescriptionAn algorithm is presented for calculating fully anharmonic vibrational state counts, state densities, and partition functions for molecules using Monte Carlo integration of classical phase space. The algorithm includes numerical evaluations of the elements of the Jacobian and is general enough to allow for sampling in arbitrary curvilinear or rectilinear coordinate systems. Invariance to the choice of coordinate system is demonstrated for vibrational state densities of methane, where we find comparable sampling efficiency when using curvilinear zmatrix and rectilinear Cartesian normal mode coordinates. In agreement with past work, we find that anharmonicity increases the vibrational state density of methane by a factor of ∼2 at its dissociation threshold. For the vinyl radical, we find a significant (∼10×) improvement in sampling efficiency when using curvilinear zmatrix coordinates relative to Cartesian normal mode coordinates. We attribute this improved efficiency, in part, to a more natural curvilinear coordinate description of the double well associated with the H2C–C–H wagging motion. The anharmonicity correction for the vinyl radical state density is ∼1.4 at its dissociation threshold. Finally, we demonstrate that with trivial parallelizations of the Monte Carlo step, tractable calculations can be made for the vinyl radical using direct ab initio potential energy surface evaluations and a composite QCISD(T)/MP2 method.
 Atoms, Molecules, and Clusters

The structures of neutral transition metal doped silicon clusters, Si_{ n } X (n = 6−9; X = V, Mn)
View Description Hide DescriptionWe present a combined experimental and theoretical investigation of small neutral vanadium and manganese doped silicon clusters Si n X (n = 6−9, X = V, Mn). These species are studied by infrared multiple photon dissociation and mass spectrometry. Structural identification is achieved by comparison of the experimental data with computed infrared spectra of lowlying isomers using density functional theory at the B3P86/6311+G(d) level. The assigned structures of the neutral vanadium and manganese doped silicon clusters are compared with their cationic counterparts. In general, the neutral and cationic Si n V0,+ and Si n Mn0,+ clusters have similar structures, although the position of the capping atoms depends for certain sizes on the charge state. The influence of the charge state on the electronic properties of the clusters is also investigated by analysis of the density of states, the shapes of the molecular orbitals, and NBO charge analysis of the dopant atom.

Water nanodroplets: Predictions of five model potentials
View Description Hide DescriptionPutative global minima for five intermolecular potential energy models are reported for water clusters (H2O) n with n ⩽ 55. The models studied include three empirical, pairwiseadditive potential energy surfaces, TIP4P, TIP4PEw, and TIP4P/2005, which use fixed point charges and rigid monomers. The other two, TTM2.1F and AMOEBA, are polarizable, include nonadditive inductive effects, have flexible monomers, and were parametrized, at least partially, using ab initio data. The n = 51 cluster has the same structure and is exceptionally stable for all five potentials. A structured inner core can be seen in cage clusters with n > 37. Periplanar rings, branched rings, and coils are among the structural motifs of the inner core.

The ethyl radical in superfluid helium nanodroplets: Rovibrational spectroscopy and ab initio computations
View Description Hide DescriptionThe ethyl radical has been isolated and spectroscopically characterized in 4He nanodroplets. The band origins of the five CH stretch fundamentals are shifted by < 2 cm−1 from those reported for the gas phase species [S. Davis, D. Uy, and D. J. Nesbitt, J. Chem. Phys.112, 1823 (Year: 2000)10.1063/1.480746; T. Häber, A. C. Blair, D. J. Nesbitt, and M. D. Schuder, J. Chem. Phys.124, 054316 (Year: 2006)10.1063/1.2140740]. The symmetric CH2 stretching band (v 1) is rotationally resolved, revealing nuclear spin statistical weights predicted by G 12 permutationinversion group theory. A permanent electric dipole moment of 0.28 (2) D is obtained via the Stark spectrum of the v 1 band. The four other CH stretch fundamental bands are significantly broadened in He droplets and lack rotational fine structure. This broadening is attributed to symmetry dependent vibrationtovibration relaxation facilitated by the He droplet environment. In addition to the five fundamentals, three a 1′ overtone/combination bands are observed, and each of these have resolved rotational substructure. These are assigned to the 2v 12, v 4 + v 6, and 2v 6 bands through comparisons to anharmonic frequency computations at the CCSD(T)/ccpVTZ level of theory.

A new ab initio based global HOOH(1^{3}A″) potential energy surface for the O(^{3}P) + H_{2}O(X^{1}A_{1}) ↔ OH(X^{2}Π) + OH(X^{2}Π) reaction
View Description Hide DescriptionAn accurate global potential energy surface is developed for the title reaction by fitting more than 36 000 of ab initio points at the CCSD(T)/AVTZ level using the permutation invariant polynomial method. The canonical rate constants for both the forward and reverse directions of the title reaction are determined on the new potential energy surface and the agreement with experiment is satisfactory. In addition, the dynamics of the forward reaction is investigated with the quasiclassical trajectory method. It is found that this direct abstraction reaction has a backward bias in its product angular distribution, consistent with a direct rebound mechanism. The OH product newly formed by the reaction exhibits a bimodal rotational state distribution, due apparently to secondary collisions with the slowly recoiling spectator OH product.

Directdynamics VTST study of hydrogen or deuterium abstraction and C–C bond formation or dissociation in the reactions of CH_{3} + CH_{4}, CH_{3} + CD_{4}, CH_{3}D + CD_{3}, CH_{3}CH_{3} + H, and CH_{3}CD_{3} + D
View Description Hide DescriptionDirectdynamics variational transitionstate theory calculations are studied at the MPWB1K/6311++G(d,p) level for the four parts of reactions. The first part is hydrogen or deuterium abstraction in the reactions of CH3 + CH4, CH3 + CD4, and CH3D + CH3. The second part involves C–C bond formation in these reactions. The third one is the reactions of CH3CH3 + H and CH3CD3 + D to form of H2, HD, and D2. The last one is the dissociation of C–C bonds in the last group of reactions. The groundstate vibrational adiabatic potential is plotted for all channels. We have carried out directdynamics calculations of the rate constants, including multidimensional tunneling in the temperature range T = 200–2200 K. The results of CVT/μOMT rate constants were in good agreement with the experimental data which were available for some reactions. Smallcurvature tunneling and Largecurvature tunneling with the LCG4 version were used to include the quantum effects in calculation of the rate constants. To try to find the region of formation and dissociation of bounds we have also reported the variations of harmonic vibrational frequencies along the reaction path. The thermally averaged transmission probability (P(E)exp (−ΔE/RT)) and representative tunneling energy at 298 K are reported for the reactions in which tunneling is important. We have calculated kinetic isotope effect which shows tunneling and vibrational contributions are noticeable to determine the rate constant. Nonlinear leastsquares fitting is used to calculate rate constant expressions in the temperature range 200–2200 K. These expressions revealed that preexponential factor includes two parts; the first part is a constant number which is important at low temperatures while the second part is temperature dependent which is significant at high temperatures.

Lowenergy electron collisions with thiophene
View Description Hide DescriptionWe report on elastic integral, momentum transfer, and differential cross sections for collisions of lowenergy electrons with thiophene molecules. The scattering calculations presented here used the Schwinger multichannel method and were carried out in the staticexchange and staticexchange plus polarization approximations for energies ranging from 0.5 eV to 6 eV. We found shape resonances related to the formation of two longlived π* anion states. These resonant structures are centered at the energies of 1.00 eV (2.85 eV) and 2.82 eV (5.00 eV) in the staticexchange plus polarization (staticexchange) approximation and belong to the B 1 and A 2 symmetries of the C 2v point group, respectively. Our results also suggest the existence of a σ* shape resonance in the B 2 symmetry with a strong dwave character, located at around 2.78 eV (5.50 eV) as obtained in the staticexchange plus polarization (staticexchange) calculation. It is worth to mention that the results obtained at the staticexchange plus polarization level of approximation for the two π* resonances are in good agreement with the electron transmission spectroscopy results of 1.15 eV and 2.63 eV measured by Modelli and Burrow [J. Phys. Chem. A108, 5721 (Year: 2004)10.1021/jp048759a]. The existence of the σ* shape resonance is in agreement with the observations of DezarnaudDandiney et al. [J. Phys. B31, L497 (Year: 1998)10.1088/09534075/31/11/004] based on the electron transmission spectra of dimethyl(poly)sulphides. A comparison among the resonances of thiophene with those of pyrrole and furan is also performed and, altogether, the resonance spectra obtained for these molecules point out that electron attachment to π* molecular orbitals is a general feature displayed by these fivemembered heterocyclic compounds.

Ab initio study of ground and excited states of ^{6}Li^{40}Ca and ^{6}Li^{88}Sr molecules
View Description Hide DescriptionWe present quantumchemical calculations for the ground and some lowlying excited states of isolated LiCa and LiSr molecules using multistate complete active space secondorder perturbation theory (MSCASPT2). The potential energy curves (PECs) and their corresponding spectroscopic constants, obtained at the spinfree (SF) and spinorbit (SO) levels, agree well with available experimental values. Our SOMSCASPT2 calculation at the atomic limit (R = 100 a.u.) with the largest basis set reproduces experimental atomic excitation energies within 3% for both LiCa and LiSr. In addition, permanent dipole moments and transition dipole moments at the SF level are also obtained. Rovibrational calculations of the ground and selected excited states, together with the spontaneous emission rates, demonstrate that the formation of ultracold LiCa and LiSr molecules in lowlying vibrational levels of the electronic ground state may be possible.

Theoretical prediction of rare gas inserted hydronium ions: HRgOH_{2} ^{+}
View Description Hide DescriptionA possibility of existence of new species through insertion of a rare gas atom in hydronium ion resulting into HRgOH2 + cation (Rg = He, Ar, Kr, and Xe) has been explored by using various ab initio quantum chemical techniques. Structure, harmonic vibrational frequencies, stability, and charge distribution of HRgOH2 + species as obtained using density functional theory, second order MøllerPlesset perturbation theory, and coupledcluster theory based methods are reported in this work. All the calculated results suggest that the HRgOH2 + species are stable enough with respect to all the dissociation channels, except the 2body dissociation path (H3O+ + Rg). Nevertheless, this 2body dissociation channel connected through the relevant transition state is associated with a finite barrier, which in turn would prevent the metastable species in transforming to global minimum products. The calculated values of topological properties within the framework of quantum theory of atomsinmolecules are found to be consistent with the bond length values. Structural and energetic parameters clearly suggest that it might be possible to prepare and characterize the HRgOH2 + species (except HHeOH2 +) using electron bombardment matrix isolation technique in a way similar to that of the preparation of (Rg2H)+ or mixed (RgHRg′)+ cations.

Water clusters adsorbed on polycyclic aromatic hydrocarbons: Energetics and conformational dynamics
View Description Hide DescriptionIn this work, we present some classical molecular dynamics (MD) simulations and finite temperature infrared (IR) spectra of water clusters adsorbed on coronene (C24H12), a compact polycyclic aromatic hydrocarbon (PAH). The potential energy surface is obtained within the selfconsistentcharge densityfunctional based tightbinding approach with modifications insuring the correct description of waterwater and waterPAH interactions. This scheme is benchmarked for the minimal energy structures of (C24H12)(H2O) n (n = 3–10) against densityfunctional theory (DFT) calculations and for the lowenergy isomers of (H2O)6 and (C6H6)(H2O)3 against correlated wavefunction and DFT calculations. A detailed study of the low energy isomers of (C24H12)(H2O)3, 6 complexes is then provided. Onthefly BornOppenheimer MD simulations are performed in the temperature T range 10–350 K for (C24H12)(H2O) n (n = 3–7) complexes. The description of the evolution of the systems with T is provided with emphasis on (C24H12)(H2O) n (n = 3,6). For T in the range 50–150 K, isomerisation processes are observed and when T increases, a solidtoliquid phasechange like behavior is shown. The desorption of one water molecule is frequently observed at 300 K. The isomerisation processes are evidenced on the finite temperature IR spectra and the results are presented for (C24H12)(H2O) n (n = 3,6). A signature for the edgecoordination of the water cluster on the PAH is also proposed.

Vibrational overtone spectroscopy and intramolecular dynamics of C–H stretches in pyrrole
View Description Hide DescriptionRoomtemperature photoacoustic spectra and jetcooled action spectra of the regions of the first and second C–H stretch overtones of pyrrole were measured with the goal of gaining new insight on the vibrational patterns and the intramolecular energy flow out of the initially excited vibrational states. The rotational cooling of the action spectra helped in observing hitherto unresolved features, assisting determination of the existing multiple bands and their positions in each region. These bands were analyzed by building vibrational Hamiltonian matrices related to a simplified joint localmode/normalmode (LM/NM) model, accounting for two types of C–H stretches and their Fermi resonances with the CCH deformation modes. The diagonalization of the LM/NM vibrational Hamiltonians and the fitting of the eigenvalues to the band positions revealed model parameters, enabling assignment of the observed bands. The time dependences of the survival probabilities of the C–H stretches in the region of the first and second overtones, deduced from the vibrational Hamiltonian, show quantum beats due to the couplings to the deformations and decays driven by weaker interactions to the bath states. The C–H stretches, although somewhat lower in energy, show stronger coupling than the N–H stretches.
 Liquids, Glasses, and Crystals

Structure of kaolinite and influence of stacking faults: Reconciling theory and experiment using inelastic neutron scattering analysis
View Description Hide DescriptionThe structure of kaolinite at the atomic level, including the effect of stacking faults, is investigated using inelastic neutron scattering (INS) spectroscopy and density functional theory (DFT) calculations. The vibrational dynamics of the standard crystal structure of kaolinite, calculated using DFT (VASP) with normal mode analysis, gives good agreement with the experimental INS data except for distinct discrepancies, especially for the low frequency modes (200 – 400 cm−1). By generating several types of stacking faults (shifts in the a , b plane for one kaolinite layer relative to the adjacent layer), it is seen that these low frequency modes are affected, specifically through the emergence of longer hydrogen bonds (O–H⋯O) in one of the models corresponding to a stacking fault of −0.3151 a − 0.3151 b . The small residual disagreement between observed and calculated INS is assigned to quantum effects (which are not taken into account in the DFT calculations), in the form of translational tunneling of the proton in the hydrogen bonds, which lead to a softening of the low frequency modes. DFTbased molecular dynamics simulations show that anharmonicity does not play an important role in the structural dynamics of kaolinite.