Volume 139, Issue 17, 07 November 2013

Neutron scattering experiments directly probe the dynamics of complex molecules on the sub pico to microsecond time scales. However, the assignment of the relaxations seen experimentally to specific structural rearrangements is difficult, since many of the underlying dynamical processes may exist on similar timescales. In an accompanying article, we present a theoretical approach to the analysis of molecular dynamics simulations with a Markov State Model (MSM) that permits the direct identification of structural transitions leading to each contributing relaxation process. Here, we demonstrate the use of the method by applying it to the configurational dynamics of the wellcharacterized alanine dipeptide. A practical procedure for deriving the MSM from an MD is introduced. The result is a 9state MSM in the space of the backbone dihedral angles and the sidechain methyl group. The agreement between the quasielastic spectrum calculated directly from the atomic trajectories and that derived from the Markov state model is excellent. The dependence on the wavevector of the individual Markov processes is described. The procedure means that it is now practicable to interpret quasielastic scattering spectra in terms of welldefined intramolecular transitions with minimal a priori assumptions as to the nature of the dynamics taking place.
 COMMUNICATIONS


Communication: The RosenfeldTarazona expression for liquids’ specific heat: A numerical investigation of eighteen systems
View Description Hide DescriptionWe investigate the accuracy of the expression of Rosenfeld and Tarazona (RT) for the excess isochoric heat capacity, , for 18 model liquids. Previous investigations have reported no unifying features of breakdown for the RT expression. Here, liquids with different stoichiometric composition, molecular topology, chemical interactions, degree of undercooling, and environment are investigated. The RT expression is a better approximation for liquids with strong correlations between equilibrium fluctuations of virial and potential energy, i.e., “Roskildesimple” liquids[T. S. Ingebrigtsen, T. B. Schrøder, and J. C. Dyre, Phys. Rev. X2, 011011 (2012)]. This observation holds even for molecular liquids under severe nanoscale confinement which does not follow from the original RT bulk hardsphere fluid perturbation theory arguments. The density dependence of the specific heat is predicted from the isomorph theory for Roskildesimple liquids, which in combination with the RT expression provides a complete description of the specific heat's density and temperature dependence.

Communication: Transfer ionization in a thermal reaction of a cation and anion: Ar^{+} with Br^{−} and I^{−}
View Description Hide DescriptionWe present experimental evidence that reactions of argon cations Ar^{+} with the halogen anions Br^{−} and I^{−} do not occur exclusively by mutual neutralization, but also produce the cations Br^{+} or I^{+} ions by transfer ionization (TI). The experiments were carried out in flowingafterglow plasmas at gas temperatures between and 300 and 500 K, and employed a variant of the Variable Electron and Neutral Density Attachment Mass Spectrometry method. The measured TI rate coefficients are 1.9 ± 0.6 × 10^{−9} cm^{3} s^{−1} and × 10^{−9} cm^{3} s^{−1} for the Br^{−} and I^{−} reactions, respectively. We find that the TI rate coefficients decline with temperature as T^{−0.5} to T^{−1}. No indication of TI was found in the reaction with Cl^{−}, where it is endoergic.

Communication: Random phase approximation renormalized manybody perturbation theory
View Description Hide DescriptionWe derive a renormalized manybody perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPArenormalized perturbation theory extends the scope of singlereference MBPT methods to smallgap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than secondorder screened exchange [A. Grüneis et al. , J. Chem. Phys.131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of secondorder MøllerPlesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, nonempirical, and robust tool to assess and improve semilocal density functional theory for a wide range of systems previously inaccessible to firstprinciples electronic structure calculations.
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 ARTICLES

 Theoretical Methods and Algorithms

A simple monomerbased modelHamiltonian approach to combine excitonic coupling and JahnTeller theory
View Description Hide DescriptionThe interplay of excitonic and vibronic coupling in coupled chromophores determines the efficiency of exciton localization vs delocalization, or in other words, coherent excitation energy transfer vs exciton hopping. For the investigation of exciton localization in large coupled dimers, a model Hamiltonian approach is derived, the ingredients of which can all be obtained from monomer ab initio calculations alone avoiding costly ab initio computation of the full dimer. The accuracy and applicability of this model are exemplified for the benzene dimer by rigorous comparison to ab initio results.

Tractability gains in symmetryadapted perturbation theory including coupled double excitations: CCD+ST(CCD) dispersion with natural orbital truncations
View Description Hide DescriptionThis work focuses on efficient and accurate treatment of the intermolecular dispersion interaction using the CCD+ST(CCD) dispersion approach formulated by Williams et al. [J. Chem. Phys.103, 4586 (1995)]. We apply natural orbital truncation techniques to the solution of the monomer coupledcluster double (CCD) equations, yielding substantial accelerations in this computationally demanding portion of the SAPT2+(CCD), SAPT2+(3)(CCD), and SAPT2+3(CCD) analyses. It is shown that the wholly ratelimiting dimerbasis particleparticle ladder term can be computed in a reduced natural virtual space which is essentially the same size as the monomerbasis virtual space, with an error on the order of a few thousandths of 1 kcal mol^{−1}. Coupled with our existing natural orbital techniques for the perturbative triple excitation contributions [E. G. Hohenstein and C. D. Sherrill, J. Chem. Phys.133, 104107 (2010)], this technique provides speedups of greater than an order of magnitude for the evaluation of the complete SAPT2+3(CCD) decomposition, with a total error of a few hundredths of 1 kcal mol^{−1}. The combined approach yields tractability gains of almost 2× in the system size, allowing for SAPT2+3(CCD)/augccpVTZ analysis to be performed for systems such as adeninethymine for the first time. Natural orbital based SAPT2+3(CCD)/augccpVTZ results are presented for stacked and hydrogenbonded configurations of uracil dimer and the adeninethymine dimer.

Massively parallel implementations of coupledcluster methods for electron spin resonance spectra. I. Isotropic hyperfine coupling tensors in large radicals
View Description Hide DescriptionCoupled cluster (CC) methods provide highly accurate predictions of molecular properties, but their high computational cost has precluded their routine application to large systems. Fortunately, recent computational developments in the ACES III program by the Bartlett group [the OED/ERD atomic integral package, the super instruction processor, and the super instruction architecture language] permit overcoming that limitation by providing a framework for massively parallel CC implementations. In that scheme, we are further extending those parallel CC efforts to systematically predict the three main electron spin resonance (ESR) tensors (A, g, and Dtensors) to be reported in a series of papers. In this paper inaugurating that series, we report our new ACES III parallel capabilities that calculate isotropic hyperfine coupling constants in 38 neutral, cationic, and anionic radicals that include the ^{11}B, ^{17}O, ^{9}Be, ^{19}F, ^{1}H, ^{13}C, ^{35}Cl, ^{33}S,^{14}N, ^{31}P, and ^{67}Zn nuclei. Present parallel calculations are conducted at the HartreeFock (HF), secondorder manybody perturbation theory [MBPT(2)], CC singles and doubles (CCSD), and CCSD with perturbative triples [CCSD(T)] levels using Roos augmented double and triplezeta atomic natural orbitals basis sets. HF results consistently overestimate isotropic hyperfine coupling constants. However, inclusion of electron correlation effects in the simplest way via MBPT(2) provides significant improvements in the predictions, but not without occasional failures. In contrast, CCSD results are consistently in very good agreement with experimental results. Inclusion of perturbative triples to CCSD via CCSD(T) leads to small improvements in the predictions, which might not compensate for the extra computational effort at a noniterative N^{7}scaling in CCSD(T). The importance of these accurate computations of isotropic hyperfine coupling constants to elucidate experimental ESR spectra, to interpret spindensity distributions, and to characterize and identify radical species is illustrated with our results from large organic radicals. Those include species relevant for organic chemistry, petroleum industry, and biochemistry, such as the cyclohexyl, 1adamatyl, and Znporphycene anion radicals, inter alia.

A multireference perturbation method using nonorthogonal HartreeFock determinants for ground and excited states
View Description Hide DescriptionIn this article we propose the ΔSCF(2) framework, a multireference strategy based on secondorder perturbation theory, for ground and excited electronic states. Unlike the complete active space family of methods, ΔSCF(2) employs a set of selfconsistent HartreeFock determinants, also known as ΔSCF states. Each ΔSCF electronic state is modified by a firstorder correction from MøllerPlesset perturbation theory and used to construct a Hamiltonian in a configuration interactions like framework. We present formulas for the resulting matrix elements between nonorthogonal states that scale as . Unlike most active space methods, ΔSCF(2) treats the ground and excited state determinants evenhandedly. We apply ΔSCF(2) to the H2, hydrogen fluoride, and H4 systems and show that the method provides accurate descriptions of ground and excitedstate potential energy surfaces with no single active space containing more than 10 ΔSCF states.

Analyzing milestoning networks for molecular kinetics: Definitions, algorithms, and examples
View Description Hide DescriptionNetwork representations are becoming increasingly popular for analyzing kinetic data from techniques like Milestoning, Markov State Models, and Transition Path Theory. Mapping continuous phase space trajectories into a relatively small number of discrete states helps in visualization of the data and in dissecting complex dynamics to concrete mechanisms. However, not only are molecular networks derived from molecular dynamics simulations growing in number, they are also getting increasingly complex, owing partly to the growth in computer power that allows us to generate longer and better converged trajectories. The increased complexity of the networks makes simple interpretation and qualitative insight of the molecular systems more difficult to achieve. In this paper, we focus on various network representations of kinetic data and algorithms to identify important edges and pathways in these networks. The kinetic data can be local and partial (such as the value of rate coefficients between states) or an exact solution to kinetic equations for the entire system (such as the stationary flux between vertices). In particular, we focus on the Milestoning method that provides fluxes as the main output. We proposed Global Maximum Weight Pathways as a useful tool for analyzing molecular mechanism in Milestoning networks. A closely related definition was made in the context of Transition Path Theory. We consider three algorithms to find Global Maximum Weight Pathways: Recursive Dijkstra's, EdgeElimination, and EdgeList Bisection. The asymptotic efficiency of the algorithms is analyzed and numerical tests on finite networks show that EdgeList Bisection and Recursive Dijkstra's algorithms are most efficient for sparse and dense networks, respectively. Pathways are illustrated for two examples: helix unfolding and membrane permeation. Finally, we illustrate that networks based on local kinetic information can lead to incorrect interpretation of molecular mechanisms.

A comparison of geometric parameters from PBEbased doubly hybrid density functionals PBE0DH, PBE02, and xDHPBE0
View Description Hide DescriptionWe present a systematic investigation on the optimized geometric parameters for covalently bonded molecules, nonbonded intermolecular complexes, and transition state structures from three PBE (PerdewBurkeErnzerhof)based doubly hybrid (DH) density functionals, namely PBE0DH, PBE02, and xDHPBE0. While the former two are the B2PLYPtype of DH functionals with no fit parameters, the latter is the XYG3type of DH functional (xDH for short) with three fit parameters, whose energy expression is constructed by using density and orbital information from another standard (general) KohnSham functional (i.e., PBE0) for doing the selfconsistent field calculations. Generally good performances have been obtained with all three DH functionals, in particular, with xDHPBE0.

Zeromultipole summation method for efficiently estimating electrostatic interactions in molecular system
View Description Hide DescriptionThe zeromultipole summation method has been developed to efficiently evaluate the electrostatic Coulombic interactions of a point charge system. This summation prevents the electrically nonneutral multipole states that may artificially be generated by a simple cutoff truncation, which often causes large amounts of energetic noise and significant artifacts. The resulting energy function is represented by a constant term plus a simple pairwise summation, using a damped or undamped Coulombic pair potential function along with a polynomial of the distance between each particle pair. Thus, the implementation is straightforward and enables facile applications to highperformance computations. Any higherorder multipole moment can be taken into account in the neutrality principle, and it only affects the degree and coefficients of the polynomial and the constant term. The lowest and second moments correspond respectively to the Wolf zerocharge scheme and the zerodipole summation scheme, which was previously proposed. Relationships with other nonEwald methods are discussed, to validate the current method in their contexts. Good numerical efficiencies were easily obtained in the evaluation of Madelung constants of sodium chloride and cesium chloride crystals.

Mixed quantum/classical theory of rotationally and vibrationally inelastic scattering in spacefixed and bodyfixed reference frames
View Description Hide DescriptionWe formulated the mixed quantum/classical theory for rotationally and vibrationally inelastic scattering process in the diatomic molecule + atom system. Two versions of theory are presented, first in the spacefixed and second in the bodyfixed reference frame. First version is easy to derive and the resultant equations of motion are transparent, but the statetostate transition matrix is complexvalued and dense. Such calculations may be computationally demanding for heavier molecules and/or higher temperatures, when the number of accessible channels becomes large. In contrast, the second version of theory requires some tedious derivations and the final equations of motion are rather complicated (not particularly intuitive). However, the statetostate transitions are driven by realvalued sparse matrixes of much smaller size. Thus, this formulation is the method of choice from the computational point of view, while the spacefixed formulation can serve as a test of the bodyfixed equations of motion, and the code. Rigorous numerical tests were carried out for a model system to ensure that all equations, matrixes, and computer codes in both formulations are correct.

Quantized Hamiltonian dynamics captures the lowtemperature regime of charge transport in molecular crystals
View Description Hide DescriptionThe quantized Hamiltonian dynamics (QHD) theory provides a hierarchy of approximations to quantum dynamics in the Heisenberg representation. We apply the firstorder QHD to study charge transport in molecular crystals and find that the obtained equations of motion coincide with the Ehrenfest theory, which is the most widely used mixed quantumclassical approach. Quantum initial conditions required for the QHD variables make the dynamics surpass Ehrenfest. Most importantly, the firstorder QHD already captures the lowtemperature regime of charge transport, as observed experimentally. We expect that simple extensions to higherorder QHDs can efficiently represent other quantum effects, such as phonon zeropoint energy and loss of coherence in the electronic subsystem caused by phonons.

Benchmark tests and spin adaptation for the particleparticle random phase approximation
View Description Hide DescriptionThe particleparticle random phase approximation (ppRPA) provides an approximation to the correlation energy in density functional theory via the adiabatic connection [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A88, 030501 (2013)]. It has virtually no delocalization error nor static correlation error for singlebond systems. However, with its formal O(N ^{6}) scaling, the ppRPA is computationally expensive. In this paper, we implement a spinseparated and spinadapted ppRPA algorithm, which reduces the computational cost by a substantial factor. We then perform benchmark tests on the G2/97 enthalpies of formation database, DBH24 reaction barrier database, and four test sets for nonbonded interactions (HB6/04, CT7/04, DI6/04, and WI9/04). For the G2/97 database, the ppRPA gives a significantly smaller mean absolute error (8.3 kcal/mol) than the direct particlehole RPA (phRPA) (22.7 kcal/mol). Furthermore, the error in the ppRPA is nearly constant with the number of atoms in a molecule, while the error in the phRPA increases. For chemical reactions involving typical organic closedshell molecules, pp and phRPA both give accurate reaction energies. Similarly, both RPAs perform well for reaction barriers and nonbonded interactions. These results suggest that the ppRPA gives reliable energies in chemical applications. The adiabatic connection formalism based on pairing matrix fluctuation is therefore expected to lead to widely applicable and accurate density functionals.

Block correlated second order perturbation theory with a generalized valence bond reference function
View Description Hide DescriptionThe block correlated secondorder perturbation theory with a generalized valence bond (GVB) reference (GVBBCPT2) is proposed. In this approach, each geminal in the GVB reference is considered as a “multiorbital” block (a subset of spin orbitals), and each occupied or virtual spin orbital is also taken as a single block. The zerothorder Hamiltonian is set to be the summation of the individual Hamiltonians of all blocks (with explicit twoelectron operators within each geminal) so that the GVB reference function and all excited configuration functions are its eigenfunctions. The GVBBCPT2 energy can be directly obtained without iteration, just like the second order Møller–Plesset perturbation method (MP2), both of which are size consistent. We have applied this GVBBCPT2 method to investigate the equilibrium distances and spectroscopic constants of 7 diatomic molecules, conformational energy differences of 8 small molecules, and bondbreaking potential energy profiles in 3 systems. GVBBCPT2 is demonstrated to have noticeably better performance than MP2 for systems with significant multireference character, and provide reasonably accurate results for some systems with large active spaces, which are beyond the capability of all CASSCFbased methods.
 Atoms, Molecules, and Clusters

Pi and sigma double conjugations in boronyl polyboroene nanoribbons: B_{ n }(BO)_{2} ^{−} and B_{ n }(BO)_{2} (n = 5−12)
View Description Hide DescriptionA series of boron dioxide clusters, B x O2 ^{−} (x = 7−14), have been produced and investigated using photoelectron spectroscopy and quantum chemical calculations. The dioxide clusters are shown to possess elongated ladderlike structures with two terminal boronyl (BO) groups, forming an extensive series of boron nanoribbons, B n (BO)2 ^{−} (n = 5−12). The electron affinities of B n (BO)2 exhibit a 4n periodicity, indicating that the rhombic B4 unit is the fundamental building block in the nanoribbons. Both π and σ conjugations are found to be important in the unique bonding patterns of the boron nanoribbons. The π conjugation in these clusters is analogous to the polyenes (aka polyboroenes), while the σ conjugation plays an equally important role in rendering the stability of the nanoribbons. The concept of σ conjugation established here has no analogues in hydrocarbons. Calculations suggest the viability of even larger boronyl polyboroenes, B16(BO)2 and B20(BO)2, extending the boron nanoribbons to ∼1.5 nm in length or possibly even longer. The nanoribbons form a new class of nanowires and may serve as precursors for a variety of boron nanostructures.

Relative energies, structures, vibrational frequencies, and electronic spectra of pyrylium cation, an oxygencontaining carbocyclic ring isoelectronic with benzene, and its isomers
View Description Hide DescriptionWe have studied relative energies, structures, rotational, vibrational, and electronic spectra of the pyrylium cation, an oxygencontaining sixmembered carbocyclic ring, and its six isomers, using ab initio quantum chemical methods. Isoelectronic with benzene, the pyrylium cation has a benzenoid structure and is the global minimum on the singlet potential energy surface of C5H5O^{+}. The second lowest energy isomer, the furfuryl cation, has a five membered backbone akin to a sugar, and is only 16 kcal mol^{−1} above the global minimum computed using coupled cluster theory with singles, doubles, and perturbative triple excitations (CCSD(T)) with the correlation consistent ccpVTZ basis set. Other isomers are 25, 26, 37, 60, and 65 kcal mol^{−1} above the global minimum, respectively, at the same level of theory. Lower level methods such as density functional theory (B3LYP) and second order MøllerPlesset perturbation theory performed well when tested against the CCSD(T) results. The pyrylium and furfuryl cations, although separated by only 16 kcal mol^{−1}, are not easily interconverted, as multiple bonds must be broken and formed, and the existence of more than one transition state is likely. Additionally, we have also investigated the asymptotes for the barrierless ionmolecule association of molecules known to exist in the interstellar medium that may lead to formation of the pyrylium cation.

Time domain simulations of chemical bonding effects in surfaceenhanced spectroscopy
View Description Hide DescriptionThe atomcentered densitymatrix propagation method is used to illustrate how timedependent conformational changes affect the electronic structure and derived spectroscopic properties of a prototypical finite metal clusterbound πconjugated organic complex, Ag 7benzenethiol. We establish that there is considerable conformational flexibility to the model structure, even at relatively low temperatures, which influences the predicted spectroscopic properties. Namely, the computed electron densities, dipoles, and polarizabilities are all dictated by torsional motion which controls the coupling between the πframework of the chemisorbed molecular system and the cluster.

Massresolved twophoton and photoelectron spectra of ArXe in the region of Xe^{*} 7p, 6p′, 6d
View Description Hide DescriptionThe two photon resonant, three photon ionization spectra of ArXe were recorded in the spectral region of 88 500–90 100 cm^{−1}. Seven new molecular band progressions dissociating to ArXe^{*} → Ar^{1}S0 + Xe^{*} 7p[1/2]0, Xe^{*} 7p[3/2]2, Xe^{*} 6p′[3/2]2, Xe^{*} 6p′[1/2]1, Xe^{*} 6p′[1/2]0 have been selected and analyzed. The molecular constants for the excited states of ArXe^{*} of these vibrational progressions were determined in the approximation of the anharmonic oscillator, the Morse potential and the FranckCondon principle. The photoelectron spectra were recorded by several excited electronicvibrational transitions of ArXe, the dissociation channels of the excited molecules were determined and extra information about the electron structure of the excited molecular states was obtained.

Photodissociation mechanisms of the CO_{2} ^{2+} dication studied using multistate multiconfiguration secondorder perturbation theory
View Description Hide DescriptionEmploying the multistate multiconfiguration secondorder perturbation theory (MSCASPT2) and complete active space selfconsistent field (CASSCF) methods, the geometries, relative energies (T v′) to the ground state (X^{3}Σg ^{−}), adiabatic excited energies, and photodissociation mechanisms and corresponding kinetic energy releases for the lowerlying 14 electronic states of the CO2 ^{2+} ion are studied. The T v′ values are calculated at the experimental geometry of the ground state CO2 molecule using MSCASPT2 method and highly close to the latest threshold photoelectrons coincidence and timeofflight photoelectron photoelectron coincidence spectrum observations. The Oloss dissociation potential energy curves (PECs) for these 14 states are drawn using MSCASPT2 partial optimization method at C∞v symmetry with one C–O bond length ranging from 1.05 to 8.0 Å. Those 14 states are confirmed to be correlated to the lowest four dissociation limits [CO^{+}(X^{2}Σ^{+}) + O^{+}(^{4}Su), CO^{+}(A^{2}Π) + O^{+}(^{4}Su), CO^{+}(X^{2}Σ^{+}) + O^{+}(^{2}Du), and CO^{+}(X^{2}Σ^{+}) + O^{+}(^{2}Pu)] by analyzing Coulomb interaction energies, charges, spin densities, and bond lengths for the geometries at the C–O bond length of 8.0 Å. On the basis of these 14 MSCASPT2 PECs, several state/state pairs are selected to optimize the minimum energy crossing points (MECPs) at the CASSCF level. And then the CASSCF spinorbit couplings and CASPT2 state/state energies are calculated at these located MECPs. Based on all of the computational results, the photodissociation mechanisms of CO2 ^{2+} are proposed. The relationships between the present theoretical studies and the previous experiments are discussed.

An experimental and theoretical study of the electronic spectrum of HPS, a second row HNO analog
View Description Hide DescriptionThe ^{1} A″ ‑ ^{1} A′ electronic spectra of jetcooled HPS and DPS have been observed for the first time, using a pulsed discharge jet source. Laser induced fluorescence spectra were obtained in the 850–650 nm region. Although the band was not observed, strong and progressions and 31 hot bands could be assigned in the HPS LIF spectrum. Single vibronic level emission spectra were also recorded, resulting in the determination of all three HPS ground state vibrational frequencies. High level ab initio calculations were used to help confirm the vibronic assignments by calculation of transition energies, anharmonic vibrational frequencies, and anharmonic FranckCondon factors. Ab initio potential energy surfaces gave an equilibrium structure for the ^{1} A′ state of r″ PH = 1.4334 Å, r″ PS = 1.9373 Å, θ″ = 101.77° and for the ^{1} A″ state of r′ PH = 1.4290 Å, r′ PS = 2.0635 Å, and θ′ = 91.74°. The rotational contours observed are consistent with these structures, confirming that the bond angle of HPS decreases on electronic excitation. Although the bond angles of HNO and HNS open in the excited state, in accord with the Walsh predictions for 12 valence electron HAB molecules, HPO, HAsO and now HPS all show the opposite behavior.