Volume 137, Issue 12, 28 September 2012

Electron dispersion forces play a crucial role in determining the structure and properties of biomolecules, molecular crystals, and many other systems. However, an accurate description of dispersion is highly challenging, with the most widely used electronic structure technique, density functional theory (DFT), failing to describe them with standard approximations. Therefore, applications of DFT to systems where dispersion is important have traditionally been of questionable accuracy. However, the last decade has seen a surge of enthusiasm in the DFT community to tackle this problem and in sodoing to extend the applicability of DFTbased methods. Here we discuss, classify, and evaluate some of the promising schemes to emerge in recent years. A brief perspective on the outstanding issues that remain to be resolved and some directions for future research are also provided.
 PERSPECTIVES


Perspective: Advances and challenges in treating van der Waals dispersion forces in density functional theory
View Description Hide DescriptionElectron dispersion forces play a crucial role in determining the structure and properties of biomolecules, molecular crystals, and many other systems. However, an accurate description of dispersion is highly challenging, with the most widely used electronic structure technique, density functional theory (DFT), failing to describe them with standard approximations. Therefore, applications of DFT to systems where dispersion is important have traditionally been of questionable accuracy. However, the last decade has seen a surge of enthusiasm in the DFT community to tackle this problem and in sodoing to extend the applicability of DFTbased methods. Here we discuss, classify, and evaluate some of the promising schemes to emerge in recent years. A brief perspective on the outstanding issues that remain to be resolved and some directions for future research are also provided.
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 ARTICLES

 Theoretical Methods and Algorithms

Affineresponse model of molecular solvation of ions: Accurate predictions of asymmetric charging free energies
View Description Hide DescriptionTwo mechanisms have been proposed to drive asymmetric solvent response to a solute charge: a static potential contribution similar to the liquidvapor potential, and a steric contribution associated with a water molecule's structure and charge distribution. In this work, we use freeenergy perturbation moleculardynamics calculations in explicit water to show that these mechanisms act in complementary regimes; the large static potential (∼44 kJ/mol/e) dominates asymmetric response for deeply buried charges, and the steric contribution dominates for charges near the solutesolvent interface. Therefore, both mechanisms must be included in order to fully account for asymmetric solvation in general. Our calculations suggest that the steric contribution leads to a remarkable deviation from the popular “linear response” model in which the reaction potential changes linearly as a function of charge. In fact, the potential varies in a piecewiselinear fashion, i.e., with different proportionality constants depending on the sign of the charge. This discrepancy is significant even when the charge is completely buried, and holds for solutes larger than single atoms. Together, these mechanisms suggest that implicitsolvent models can be improved using a combination of affine response (an offset due to the static potential) and piecewiselinear response (due to the steric contribution).

The effect of the PerdewZunger selfinteraction correction to density functionals on the energetics of small molecules
View Description Hide DescriptionSelfconsistent calculations using the PerdewZunger selfinteraction correction (PZSIC) to local density and gradient dependent energyfunctionals are presented for the binding energy and equilibrium geometry of small molecules as well as energy barriers of reactions. The effect of the correction is to reduce binding energy and bond lengths and increase activation energy barriers when bond breaking is involved. The accuracy of the corrected functionals varies strongly, the correction to the binding energy being too weak for the local density approximation but too strong for the gradient dependent functionals considered. For the Perdew, Burke, and Ernzerhof (PBE) functional, a scaling of the PZSIC by one half gives improved results on average for both binding energy and bond lengths. The PZSIC does not necessarily give more accurate total energy, but it can result in a better cancellation of errors. An essential aspect of these calculations is the use of complex orbitals. A restriction to real orbitals leads to less accurate results as was recently shown for atoms [S. Klüpfel, P. Klüpfel, and H. Jónsson, Phys. Rev. A84, 050501 (2011)10.1103/PhysRevA.84.050501]. The molecular geometry of radicals can be strongly affected by PZSIC. An incorrect, nonlinear structure of the C_{2}H radical predicted by PBE is corrected by PZSIC. The CH_{3} radical is correctly predicted to be planar when complex orbitals are used, while it is nonplanar when the PZSIC calculation is restricted to real orbitals.

Electron scattering cross sections from HCN over a broad energy range (0.1–10 000 eV): Influence of the permanent dipole moment on the scattering process
View Description Hide DescriptionWe report theoretical integral and differential cross sections for electron scattering from hydrogen cyanide derived from two ab initioscattering potential methods. For low energies (0.1–100 eV), we have used the symmetry adaptedsingle centre expansion method using a multichannel scattering formulation of the problem. For intermediate and high energies (10–10 000 eV), we have applied an optical potential method based on a screening corrected independent atom representation. Since HCN is a strong polar molecule, further dipoleinduced excitations have been calculated in the framework of the first Born approximation and employing a transformation to a spacefixed reference frame of the calculated Kmatrix elements. Results are compared with experimental data available in the literature and a complete set of recommended integral elastic, inelastic, and total scattering cross sections is provided from 0.1 to 10 000 eV.

Mean firstpassage time for random walks in general graphs with a deep trap
View Description Hide DescriptionWe provide an explicit formula for the global mean firstpassage time (GMFPT) for random walks in a general graph with a perfect trap fixed at an arbitrary node, where GMFPT is the average of mean firstpassage time to the trap over all starting nodes in the whole graph. The formula is expressed in terms of eigenvalues and eigenvectors of Laplacian matrix for the graph. We then use the formula to deduce a tight lower bound for the GMFPT in terms of only the numbers of nodes and edges, as well as the degree of the trap, which can be achieved in both complete graphs and star graphs. We show that for a large sparse graph, the leading scaling for this lower bound is proportional to the system size and the reciprocal of the degree for the trap node. Particularly, we demonstrate that for a scalefree graph of size N with a degree distribution P(d) ∼ d ^{−γ} characterized by γ, when the trap is placed on a most connected node, the dominating scaling of the lower bound becomes N ^{1−1/γ}, which can be reached in some scalefree graphs. Finally, we prove that the leading behavior of upper bounds for GMFPT on any graph is at most N ^{3} that can be reached in the barbell graphs. This work provides a comprehensive understanding of previous results about trapping in various special graphs with a trap located at a specific location.

Timedependent importance sampling in semiclassical initial value representation calculations for time correlation functions. II. A simplified implementation
View Description Hide DescriptionAn efficient timedependent (TD) Monte Carlo(MC) importance sampling method has recently been developed [G. Tao and W. H. Miller, J. Chem. Phys.135, 024104 (2011)10.1063/1.3600656] for the evaluation of time correlation functions using the semiclassical (SC) initial value representation (IVR) methodology. In this TDSCIVR method, the MC sampling uses information from both timeevolved phase points as well as their initial values, and only the “important” trajectories are sampled frequently. Even though the TDSCIVR was shown in some benchmark examples to be much more efficient than the traditional timeindependent sampling method (which uses only initial conditions), the calculation of the SC prefactor—which is computationally expensive, especially for large systems—is still required for accepted trajectories. In the present work, we present an approximate implementation of the TDSCIVR method that is completely prefactorfree; it gives the time correlation function as a classicallike magnitude function multiplied by a phase function. Application of this approach to fluxflux correlation functions (which yield reaction rate constants) for the benchmark H + H_{2} system shows very good agreement with exact quantum results. Limitations of the approximate approach are also discussed.

Extension of local response dispersion method to excitedstate calculation based on timedependent density functional theory
View Description Hide DescriptionWe report the extension of the local response dispersion (LRD) method to the excitedstate calculation based on timedependent density functional theory. The difference density matrix, which is usually used for excitedstate response properties, enables a statespecific dispersion correction. The numerical assessment proves that interactionenergies of excitonlocalized molecular complexes and their shifts from the ground state are accurately reproduced by the LRD method. Furthermore, we find that the dispersion correction is important in reproducing binding energies of aromatic excimers, despite the existence of other attractive forces such as exciton delocalization and chargetransferinteraction.

On the stability of ion water clusters at atmospheric conditions: Open system Monte Carlo simulation
View Description Hide DescriptionThe formation of water clusters on Li^{+}, Na^{+}, K^{+}, Cl^{−}, and I^{−} ions from water vapor at atmospheric conditions have been studied using Monte Carlo simulations. The extended simple point charge model has been employed for water molecules. The polarization of ions in the field of molecules and the polarization of molecules in the field of ions have been considered explicitly in the total Hamiltonian of the molecular system. The cluster formation work and the Gibbs free energy and enthalpy of attachment reactions of one water molecule to the cluster have been calculated via the bicanonical ensemble method. Our results reveal the formation of stable clusters in equilibrium with the moist atmosphere in a wide range of vapor pressure values, with largest clusters are formed around cations. Decreasing the temperature, from 293 K to 253 K, leads to the formation of larger equilibrium clusters, and enhances the stability of systems as whole. According to clusters’ molecular structures, negative ions are expected to be more active in atmospheric processes, including chemical reactions and cloud formation, than positive ones.
 Atoms, Molecules, and Clusters

Interaction between coinage metal cations M(II) and Xe: CCSD(T) study of MXe_{n} ^{2+}(M = Cu, Ag, and Au, n = 1–6)
View Description Hide DescriptionQuantum chemical calculations of the structures, stabilities, and interactions of the title series at the coupledcluster single double triple theoretical level are performed. The n = 2 systems are more stable than its neighbors. Topological analysis of the Laplacian, electron density deformation, electron localization function, bond critical point properties, and reduced density gradient analysis are performed to explore the nature of the interaction. The results show that a covalent contribution occurs in the Xe–M^{2+} intermediate interaction.

Electronic transitions of platinum monoboride
View Description Hide DescriptionThe electronic transition spectrum of platinum monoboride (PtB) radical has been observed for the first time. Using laser vaporization/reaction free jet expansion and laser induced fluorescencespectroscopy, the optical spectrum of PtB in the visible region between 455 and 520 nm has been studied. Gasphase PtB molecule was produced by the reaction of diborane (B_{2}H_{6}) seeded in argon and laser ablated platinum atom. Seven vibrational bands of the Pt^{11}B radical have been recorded and analyzed. The observation of Pt isotopic molecules and the Pt^{10}B isotope confirmed the carrier of the bands. Two different transition systems, namely: the [20.2]3/2–X^{2}Σ^{+} and the [21.2]1/2–X^{2}Σ^{+} systems were identified. PtB was determined to have an X^{2}Σ^{+}ground state and the bond length, r_{e}, was determined to be 1.741 Å.

Assessment of density functional theory for iron(II) molecules across the spincrossover transition
View Description Hide DescriptionOctahedral Fe^{2+} molecules are particularly interesting as they often exhibit a spincrossover transition. In spite of the many efforts aimed at assessing the performances of density functional theory for such systems, an exchangecorrelation functional able to account accurately for the energetic of the various possible spinstates has not been identified yet. Here, we critically discuss the issues related to the theoretical description of this class of molecules from first principles. In particular, we present a comparison between different density functionals for four ions, namely, [Fe(H_{2}O)_{6}]^{2+}, [Fe(NH_{3})_{6}]^{2+}, [Fe(NCH)_{6}]^{2+}, and [Fe(CO)_{6}]^{2+}. These are characterized by different ligandfield splittings and ground state spin multiplicities. Since no experimental data are available for the gas phase, the density functional theory results are benchmarked against those obtained with diffusion Monte Carlo, one of the most accurate methods available to compute ground state total energies of quantum systems. On the one hand, we show that most of the functionals considered provide a good description of the geometry and of the shape of the potential energy surfaces. On the other hand, the same functionals fail badly in predicting the energy differences between the various spin states. In the case of [Fe(H_{2}O)_{6}]^{2+}, [Fe(NH_{3})_{6}]^{2+}, [Fe(NCH)_{6}]^{2+}, this failure is related to the drastic underestimation of the exchange energy. Therefore, quite accurate results can be achieved with hybrid functionals including about 50% of HartreeFock exchange. In contrast, in the case of [Fe(CO)_{6}]^{2+}, the failure is likely to be caused by the multiconfigurational character of the ground state wavefunction and no suitable exchange and correlation functional has been identified.

Experimental and theoretical studies of ammonia generation: Reactions of H_{2} with neutral cobalt nitride clusters
View Description Hide DescriptionAmmonia generation through reaction of H_{2} with neutral cobalt nitride clusters in a fast flow reactor is investigated both experimentally and theoretically. Single photon ionization at 193 nm is used to detect neutral cluster distributions through timeofflight mass spectrometry. Co_{ m }N_{ n }clusters are generated through laser ablation of Co foil into N_{2}/He expansion gas. Mass peaks Co_{ m }NH_{2} (m = 6, 10) and Co_{ m }NH_{3} (m = 7, 8, 9) are observed for reactions of H_{2} with the Co_{ m }N_{ n }clusters. Observation of these products indicates that clusters Co_{ m }N (m = 7, 8, 9) have high reactivity with H_{2} for ammonia generation. Density functional theory(DFT) calculations are performed to explore the potential energy surface for the reaction Co_{7}N + 3/2H_{2} → Co_{7}NH_{3}, and a barrierless, thermodynamically favorable pathway is obtained. An odd number of hydrogen atoms in Co_{ m }NH_{3} (m = 7, 8, 9) probably come from the hydrogen molecule dissociation on two active cobalt nitride clusters based on the DFT calculations. Both experimental observations and theoretical calculations suggest that hydrogen dissociation on two active cobalt nitride clusters is the key step to form NH_{3} in a gas phase reaction. A catalytic cycle for ammonia generation from N_{2} and H_{2} on a cobalt metal catalyst surface is proposed based on our experimental and theoretical investigations.

On the relationship between bondlength alternation and manyelectron selfinteraction error
View Description Hide DescriptionPredicting accurate bondlength alternations (BLAs) in long conjugated molecular chains has been a major challenge for electronicstructure theory for many decades. While HartreeFock (HF) overestimates BLA significantly, secondorder perturbation theory and commonly used density functional theory(DFT) approaches typically underestimate it. Here, we discuss how this failure is related to the manyelectron selfinteraction error (MSIE), which is inherent to both HF and DFT approaches. We use tuned longrange corrected hybrids to minimize the MSIE for a series of polyenes. The key result is that the minimization of the MSIE alone does not yield accurate BLAs. On the other hand, if the rangeseparation parameter is tuned to yield accurate BLAs, we obtain a significant MSIE that grows with chain length. Our findings demonstrate that reducing the MSIE is one but not the only important aspect necessary to obtain accurate BLAs from density functional theory.

Symmetry interplay in Brownian photomotors: From a singlemolecule device to ensemble transport
View Description Hide DescriptionUnlike most of Brownian motor models in which the state of a point particle is described by a single scalar fluctuating parameter, we consider lightinduced dichotomic fluctuations of electron density distributions in an extended molecule moving in the electrostatic periodic potential of a polar substrate. This model implies that the potential energy profiles of two motor states differ substantially and their symmetry is dictated by the interplay between the symmetries of the substrate potential and of molecular electronic states. As shown, a necessary condition for the occurrence of directed motion, the asymmetry of the potential energy profiles, is satisfied for (i) symmetric electron density distributions in molecules on asymmetric substrates and (ii) asymmetric electron density distributions in molecules on symmetric substrates. In the former case, the average velocity of directed motion is independent of molecular orientations and the ensemble of molecules moves as a whole, whereas in the latter case, oppositely oriented molecules move counterdirectionally thus causing the ensemble to diffuse. Using quantum chemical data for a specific organicbased photomotor as an example, we demonstrate that the behavior of molecular ensembles is controllable by switching on/off resonance laser radiation: they can be transported as a whole or separated into differently oriented molecules depending on the ratio of symmetric and antisymmetric contributions to the substrate electrostatic potential and to the molecular electron density distributions.

First principle evaluation of the chiroptical activity of the diphenyldiazene derivatives
View Description Hide DescriptionAzobenzene (diphenyldiazene) is wellknown as a photoisomerisable molecule and has been widely studied as a molecular photoswitcher. Molecular rods, where diphenyl arms are bound to the diazene moiety, have been also synthesized. In this article we explore by first principle density functional theory calculations the chiroptical properties (electronic circular dichroism spectra, ECD) of azobenzene and its homologues with polyphenyl arms. In particular, we demonstrate that for molecules in the cis configuration the intrinsic chirality of the distorted cis diazene group dominates the ECD response, while for trans species the nonplanarity of the polyphenyl arms induces peaks in the ECD spectrum. Finally, the possibility of obtaining a lightcontrolled chiral switch by proper functionalization is also speculated.

Competitive fragmentation pathways of acetic acid dimer explored by synchrotron VUV photoionization mass spectrometry and electronic structure calculations
View Description Hide DescriptionIn present study, photoionization and dissociation of acetic acid dimers have been studied with the synchrotron vacuum ultraviolet photoionization mass spectrometry and theoretical calculations. Besides the intense signal corresponding to protonated cluster ions (CH_{3}COOH)_{n}·H^{+}, the feature related to the fragment ions (CH_{3}COOH)H^{+}·COO (105 amu) via βcarboncarbon bond cleavage is observed. By scanning photoionization efficiency spectra, appearance energies of the fragments (CH_{3}COOH)·H^{+} and (CH_{3}COOH)H^{+}·COO are obtained. With the aid of theoretical calculations, seven fragmentation channels of acetic acid dimer cations were discussed, where five cation isomers of acetic acid dimer are involved. While four of them are found to generate the protonated species, only one of them can dissociate into a C–C bond cleavage product (CH_{3}COOH)H^{+}·COO. After surmounting the methyl hydrogentransfer barrier 10.84 ± 0.05 eV, the opening of dissociative channel to produce ions (CH_{3}COOH)^{+} becomes the most competitive path. When photonenergy increases to 12.4 eV, we also found dimer cations can be fragmented and generate new cations (CH_{3}COOH)·CH_{3}CO^{+}. Kinetics, thermodynamics, and entropy factors for these competitive dissociation pathways are discussed. The present report provides a clear picture of the photoionization and dissociation processes of the acetic acid dimer in the range of the photonenergy 9–15 eV.

Short and longrange binding of Be with Mg in the X ^{1}Σ^{+} ground state and in the A ^{1}Π excited state
View Description Hide DescriptionWe present results of configurationinteraction (CI) computations of wavefunctions and of properties of the first two singlet states, X ^{1}Σ^{+} and A ^{1}Π, of the, as yet unobserved, BeMg polar molecule, for internuclear distances in the range [2.5–1000] Å. The X ^{1}Σ^{+} state is very weakly bound, (D _{ e } = 469.4 cm^{−1} at R _{ e } = 3.241 Å), whereas the A ^{1}Π state, which correlates with the excited dissociation channel [MgKL3s3p ^{1} P ^{ o } + Be 1s ^{2}2s ^{2} ^{1} S], is bound rather strongly (D _{ e } = 19 394 cm^{−1} (55.5 kcal/mol) at R _{ e } = 2.385 Å). The X ^{1}Σ^{+} state supports 12 vibrational levels, for which vibrationally averaged dipole moments, ⟨μ⟩_{υ}, were obtained, while 71 vibrational levels were found for A ^{1}Π. For the level (X ^{1}Σ^{+}), ⟨μ⟩_{0} = 0.213 D. The υ^{″} = 7 and 8 X ^{1}Σ^{+} vibrational levels are found to have the highest probability to be reached via emission from the lowest lying vibrational levels of A ^{1}Π. The work had a dual outcome: First, it explored consequences of different choices of the statespecific reference “Fermisea” space (“active” space), which is required for the construction and execution of the multiconfigurational “complete active space selfconsistent field” calculations and the subsequent multireference CI calculations. In this context, comparisons with results on the weakly bound ground states of the homonuclear Be_{2} and Mg_{2} molecules were made. Second, it produced reliable data for the short as well as the longrange parts of the potential energy curve (PEC). Such information is relevant to analyses concerning cold and ultracold Physics and Chemistry. For example, accurate fits to the X ^{1}Σ^{+} PEC, which was computed to nanoHartree accuracy, with account for basissetsuperposition error, produced the C _{6} and C _{8} dispersion coefficients as 364.3 ± 1.1 a.u. and 28 000 ± 500 a.u., respectively. The result for C _{6} is in excellent agreement with that of Derevianko et al. [At. Data Nucl. Data Tables96, 323 (2010)10.1016/j.adt.2009.12.002], (364 ± 4 a.u.), that was obtained in the framework of the theory of longrange interactions and manybody calculations on the constituent atoms. On the other hand, our result for C _{8} differs from that of Standard and Certain [J. Chem. Phys.83, 3002 (1985)10.1063/1.449203] by about 7000 a.u.

The vibrationally mediated photodissociation of Cl_{2}
View Description Hide DescriptionThe photodissociation of vibrationally excited Cl_{2}(v = 1) has been investigated experimentally using the velocity mapped ion imaging technique. The experimental measurements presented here are compared with the results of timedependent wavepacket calculations performed on a set of ab initio potential energy curves. The high level calculations allow prediction of all the dynamical information regarding the dissociation, including electronic polarization effects. Using a combination of theory and experiment it was found that there was negligible cooling of the vibrational degree of freedom of the parent molecule in the molecular beam. The results presented are compared with those following the photodissociation of Cl_{2}(v = 0). Although the same electronic states are found to be important for Cl_{2}(v = 1) as for Cl_{2}(v = 0), significant differences were found regarding many of the observables. The overall level of agreement between theory and experiment was found to be reasonable and confirms previous assignments of the photodissociation mechanism.

A GGA+U approach to effective electronic correlations in thiolateligated ironoxo (IV) porphyrin
View Description Hide DescriptionHighvalent oxometal complexes exhibit correlated electronic behavior on dense, lowlying electronic state manifolds, presenting challenging systems for electronic structure methods. Among these species, the ironoxo (IV) porphyrin denoted Compound I occupies a privileged position, serving a broad spectrum of catalytic roles. The most reactive members of this family bear a thiolate axial ligand, exhibiting high activity toward molecular oxygen activation and substrate oxidation. The default approach to such systems has entailed the use of hybrid density functionals or multiconfigurational/multireference methods to treat electronic correlation. An alternative approach is presented based on the GGA+U approximation to density functional theory, in which a generalized gradient approximation (GGA) functional is supplemented with a localization correction to treat onsite correlation as inspired by the Hubbard model. The electronic structure of thiolateligated ironoxo (IV) porphyrin and corresponding Coulomb repulsion U are determined both empirically and selfconsistently, yielding spindistributions, state level splittings, and electronic densities of states consistent with prior hybrid functional calculations. Comparison of this detailed electronic structure with model Hamiltonian calculations suggests that the localized 3d iron moments induce correlation in the surrounding electron gas, strengthening local moment formation. This behavior is analogous to strongly correlated electronic systems such as Mott insulators, in which the GGA+U scheme serves as an effective singleparticle representation for the full, correlated manybody problem.

Properties of the B^{+}H_{2} and B^{+}D_{2} complexes: A theoretical and spectroscopic study
View Description Hide DescriptionThe rotationally resolved infrared spectrum of the B^{+}D_{2} ionneutral complex is recorded in the DD stretch vibration region (2805–2875 cm^{−1}) by detecting B^{+} photofragments. Analysis of the spectrum confirms a Tshaped equilibrium geometry for the B^{+}D_{2} complex with a vibrationally averaged intermolecular bond length of 2.247 Å, around 0.02 Å shorter than for the previously characterised B^{+}H_{2} complex [V. Dryza, B. L. J. Poad, and E. J. Bieske, J. Am. Chem. Soc.130, 12986 (2008)10.1021/ja8018302]. The DD stretch band centre occurs at 2839.76 ± 0.10 cm^{−1}, representing a −153.8 cm^{−1} shift from the Q _{1}(0) transition of the free D_{2} molecule. A new three dimensional ab initiopotential energy surface for the B^{+}+H_{2}interaction is calculated using the coupled cluster RCCSD(T) method and is used in variational calculations for the rovibrational energies of B^{+}H_{2} and B^{+}D_{2}. The calculations predict dissociation energies of 1254 cm^{−1} for B^{+}H_{2} with respect to the B^{+}+H_{2} (j = 0) limit, and 1313 cm^{−1} for B^{+}D_{2} with respect to the B^{+}+D_{2} (j = 0) limit. The theoretical approach reproduces the rotational and centrifugal constants of the B^{+}H_{2} and B^{+}D_{2} complexes to within 3%, and the magnitude of the contraction of the intermolecular bond accompanying excitation of the H_{2} or D_{2} subunit, but underestimates the HH and DD vibrational band shifts by 7%–8%. Combining the theoretical and experimental results allows a new, more accurate estimation for the B^{+}H_{2} band origin (3939.64 ± 0.10 cm^{−1}).