Volume 137, Issue 11, 21 September 2012

In this work, a novel method to model offdiagonal disorder in organic materials has been developed. The offdiagonal disorder is taken directly from the geometry of the system, which includes both a distance and an orientational dependence on the constituent molecules, and does not rely on a parametric random distribution. The geometry of the system is generated by running molecular dynamics simulations on phenylenevinylene oligomers packed into boxes. The effect of the kind of randomness generated in this way is then investigated by means of Monte Carlo simulations of the charge transport in these boxes and a comparison is made to the commonly used model of offdiagonal disorder, where only the distance dependence is accounted for. It is shown that this new refined way of treating the disorder has a significant impact on the charge transport, while still being compliant with previously published and confirmed results.
 COMMUNICATIONS


Communication: Beyond the random phase approximation on the cheap: Improved correlation energies with the efficient “radial exchange hole” kernel
View Description Hide DescriptionThe “ACFDRPA” correlation energy functional has been widely applied to a variety of systems to successfully predict energy differences, and less successfully predict absolute correlation energies. Here, we present a parameterfree exchangecorrelation kernel that systematically improves absolute correlation energies, while maintaining most of the good numerical properties that make the ACFDRPA numerically tractable. The radial exchange hole kernel is constructed to approximate the true exchange kernel via a carefully weighted, easily computable radial averaging. Correlation energy errors of atoms with 2–18 electrons show a 13fold improvement over the RPA and a threefold improvement over the related Petersilka, Gossmann, and Gross kernel, for a mean absolute error of 13 mHa or 5%. The average error is small compared to all but the most difficult to evaluate kernels. van der Waals C _{6} coefficients are less well predicted, but still show improvements on the RPA, especially for highly polarisable Li and Na.
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 ARTICLES

 Theoretical Methods and Algorithms

JahnTeller, pseudoJahnTeller, and spinorbit coupling Hamiltonian of a d electron in an octahedral environment
View Description Hide DescriptionStarting from the model of a single delectron in an octahedral crystal environment, the Hamiltonian for linear and quadratic JahnTeller(JT) coupling and zeroth order as well as linear spinorbit (SO) coupling in the ^{2} T _{2g } + ^{2} E _{ g } electronic multiplet is derived. The SO coupling is described by the microscopic BreitPauli operator. The 10 × 10 Hamiltonian matrices are explicitly given for all linear and quadratic electrostatic couplings and all linear SOinduced couplings. It is shown that the ^{2} T _{2g }manifold exhibits, in addition to the wellknown electrostaticJTeffects, linear JT couplings which are of relativistic origin, that is, they arise from the SO operator. While only the e _{ g } mode is JTactive in the ^{2} E _{ g } state in the nonrelativistic approximation, the t _{2g } mode becomes JTactive through the SO operator. Both electrostatic as well as relativistic forces contribute to the ^{2} T _{2g } − ^{2} E _{ g } pseudoJT coupling via the t _{2g } mode. The relevance of these analytic results for the static and dynamic JTeffects in octahedral complexes containing heavy elements is discussed.

Molecular gradient for secondorder MøllerPlesset perturbation theory using the divideexpandconsolidate (DEC) scheme
View Description Hide DescriptionWe demonstrate that the divideexpandconsolidate (DEC) scheme – which has previously been used to determine the secondorder Møller–Plesset (MP2) correlation energy – can be applied to evaluate the MP2 molecular gradient in a linearscaling and embarrassingly parallel manner using a set of local Hartree–Fock orbitals. All manipulations of fourindex quantities (describing electron correlation effects) are carried out using small local orbital fragment spaces, whereas twoindex quantities are treated for the full molecular system. The sizes of the orbital fragment spaces are determined in a blackbox manner to ensure that the error in the DECMP2 correlation energy compared to a standard MP2 calculation is proportional to a single input threshold denoted the fragment optimization threshold (FOT). The FOT also implicitly controls the error in the DECMP2 molecular gradient as substantiated by a theoretical analysis and numerical results. The development of the DECMP2 molecular gradient is the initial step towards calculating higher order energy derivatives for large molecular systems using the DEC framework, both at the MP2 level of theory and for more accurate coupledcluster methods.

A fusion of the closedshell coupled cluster singles and doubles method and valencebond theory for bond breaking
View Description Hide DescriptionClosedshell coupled cluster singles and doubles (CCSD) is among the most important of electronicstructure methods. However, it fails qualitatively when applied to molecular systems with more than two strongly correlated electrons, such as those with stretched or broken covalent bonds. We show that it is possible to modify the doubles amplitudes to obtain a closedshell CCSD method that retains the computational cost and desirable features of standard closedshell CCSD, e.g., correct spin symmetry, size extensivity, orbital invariance, etc., but produces greatly improved energies upon bonddissociation of multiple electron pairs; indeed, under certain conditions the dissociation energies are exact.

Comparison of the performance of exactexchangebased density functional methods
View Description Hide DescriptionHow to describe nondynamic electron correlation is still a major challenge to density functional theory(DFT). Recent models designed particularly for this problem, such as Becke'05 (B05) and PerdewStaroverovTaoScuseria (PSTS) functionals employ the exactexchange density, the efficient calculation of which is technically quite challenging. We have recently implemented selfconsistently the B05 functional based on an efficient resolutionidentity (RI) technique. In this study, we report a selfconsistent RI implementation of the PSTS functional. In contrast to its original implementation, our version brings no limitation on the choice of the basis set. We have also implemented the MoriSanchezCohenYang2 (MCY2) functional, another recent DFT method that includes full exact exchange. The performance of PSTS, B05, and MCY2 is validated on thermochemistry,reaction barriers, and dissociation energy curves, with an emphasis on nondynamic correlation effects in the discussion. All three methods perform rather well in general, B05 and MCY2 being on average somewhat better than PSTS. We include also results with other functionals that represent various aspects of the development in this field in recent years, including B3LYP, M06HF, M062X, ωB97X, and TPSSh. The performance of the heavyparameterized functionals M062X and ωB97X is on average better than that of B05, MCY2, and PSTS for standard thermodynamic properties and reactions, while the latter functionals do better in hydrogen abstraction reactions and dissociation processes. In particular, B05 is found to be the only functional that yields qualitatively correct dissociation curves for twocenter symmetric radicals like . Finally, we compare the performance of all these functionals on a strongly correlated exemplary case system, the NO dimer. Only PSTS, B05, and MCY2 describe the system qualitatively correctly. Overall, this new type of functionals show good promise of overcoming some of the difficulties DFT encounters for systems with strong nondynamic correlation.

Assessment of ten DFT methods in predicting structures of sheet silicates: Importance of dispersion corrections
View Description Hide DescriptionThe performance of ten density functional theory(DFT) methods in a prediction of the structure of four clay minerals, in which nonbonding interactions dominate in the layer stacking (dispersive forces in talc and pyrophyllite, and hydrogen bonds in lizardite and kaolinite), is reported. In a set of DFT methods following functionals were included: standard local and semilocal (LDA, PW91, PBE, and RPBE), dispersion corrected (PW91D2, PBED2, RPBED2, and vdWTS), and functionals developed specifically for solids and solid surfaces (PBEsol and AM05). We have shown that the standard DFT functionals fail in the correct prediction of the structural parameters, for which nonbonding interactions are important. The remarkable improvement leading to very good agreement with experimental structures is achieved if the dispersion corrections are included in the DFT calculations. In such cases the relative error for the most sensitive lattice vector c dropped below 1%. Very good performance was also observed for both DFT functionals developed for solids. Especially, the results achieved with the PBEsol are qualitatively similar to those with DFTD2.

Analysis of the physical contributions to magnetic couplings in broken symmetry density functional theory approach
View Description Hide DescriptionWe present a new and simple scheme that aims to decompose into its main physical contributions the magnetic exchange interaction between two unpaired electrons. It is based on the popular brokensymmetry density functional theory (DFT) approach and relies on the frozen orbital capabilities of the local selfconsistent field method. Accordingly, the magnetic exchange interaction energy can be separated into three main contributions: the direct exchange between magnetic orbitals, the spin polarization of the core orbitals, and the relaxation of the magnetic orbitals (kinetic exchange). This decomposition scheme is applied to a series of binuclear inorganic magnetic compounds both ferromagnetic and antiferromagnetic. The direct exchange is determined from the restricted DFT description. On the one hand, starting from the restricted orbital set and relaxing only the magnetic orbitals provides the kinetic exchange contribution and an estimate of the t and U parameters of the generalized Anderson mechanism. On the other hand, relaxing the core orbitals only introduces the spin polarization contribution. The decomposition leads to almost additive contributions. The effect of the amount of HartreeFock exchange on the different contributions is analyzed.

Magnetic coupling constants and vibrational frequencies by extended broken symmetry approach with hybrid functionals
View Description Hide DescriptionThe description of the electronic structure and magnetic properties of multicenters transition metal complexes, especially of mixedvalence compounds, still represents a challenge for density functional theory(DFT) methods. The energies and the geometries of the correctly symmetrized lowspin ground state are estimated using the HeisenbergDiracvan Vleck spin Hamiltonian within the extended broken symmetry method introduced by Marx and coworkers [Nair et al., J. Chem. Theory Comput.4, 1174–1188 (2008)10.1021/ct800089x]. In the present work we extend the application of this technique, originally implemented using the DFT+U scheme, to the use of hybrid functionals, investigating the groundstate properties of diiron and dimanganese compounds. The calculated magnetic coupling and vibrational properties of ferredoxin molecular models are in good agreements with experimental results and DFT+U calculations. Six different mixedvalence Mn(III)–Mn(IV) compounds have been extensively studied optimizing the geometry in lowspin, highspin, and brokensymmetry states and with different functionals. The magnetic coupling constants calculated by the extended broken symmetry approach using B3LYP functional presents a remarkable agreement with the experimental results, revealing that the proposed methodology provides a consistent and accurate DFT approach to the electronic structure of multicenters transition metal complexes.

Vibrational multireference coupled cluster theory in bosonic representation
View Description Hide DescriptionThe vibrational multireference coupled cluster method is developed to calculate the vibrational excitation energies of polyatomic molecules. The method is implemented on ozone and formaldehyde molecules and the results are compared with full vibrational configuration interaction (FVCI) method. A good agreement is found between the vibrational multireference coupled cluster method and converged FVCI method for lower lying vibrational states.

The virial theorem for the smoothly and sharply, penetrably and impenetrably confined hydrogen atom
View Description Hide DescriptionConfinement of atoms by finite or infinite boxes containing sharp (discontinuous) jumps has been studied since the fourth decade of the previous century, modelling the effect of external pressure. Smooth (continuous) counterparts of such confining potentials, that depend on a parameter such that in an appropriate limit they coincide with the sharp confining potentials, are investigated, with an emphasis on deriving the corresponding virial and HellmannFeynman theorems.

Efficient computation of adiabatic electronic populations in multimode vibronic systems: Theory, implementation, and application
View Description Hide DescriptionThe effectivemode formalism developed earlier is applied to efficiently compute adiabatic electronic populations of multimode vibronic systems. Two different versions of the formalism are utilized. In the first one, the effective modes are used as new vibrational basis, and the timedependent wave function as well as populations are calculated numerically exactly. In the second variant, the hierarchyofmodes formalism is applied as an approximation scheme which leads to accurate results when including typically 7–10 members of the hierarchy. While in the first version, the propagation of the wave packet becomes numerically tedious, the computation of the adiabatic populations is rendered possible at all. Through the hierarchyofmodes formalism, both the propagation as well as computation of adiabatic populations are speeded up by 1–3 orders of magnitude in typical cases. The formalism is applied to study the dynamics of pyrazinetype models for varying vibronic coupling strength and a (very) large number of bath modes.

Van der Waals interactions between hydrocarbon molecules and zeolites: Periodic calculations at different levels of theory, from density functional theory to the random phase approximation and MøllerPlesset perturbation theory
View Description Hide DescriptionThe adsorption of small alkane molecules in purely siliceous and protonated chabazite has been investigated at different levels of theory: (i) densityfunctional (DFT) calculations with a gradientcorrected exchangecorrelation functional;DFT calculations using the PerdewBurkeErnzerhof (PBE) functional with corrections for the missing dispersion forces in the form of C _{6}/R ^{6} pair potentials with (ii) C _{6} parameters and vdW radii determined by fitting accurate energies for a large molecular data base (PBE−d) or (iii) derived from “atoms in a solid” calculations; (iv) DFT calculations using a nonlocal correlation functional constructed such as to account for dispersion forces (vdWDF); (v) calculations based on the random phase approximation (RPA) combined with the adiabaticcoupling fluctuationdissipation theorem; and (vi) using HartreeFock (HF) calculations together with correlation energies calculated using secondorder MøllerPlesset (MP2) perturbation theory. All calculations have been performed for periodic models of the zeolite and using a planewave basis and the projectoraugmented wave method. The simpler and computationally less demanding approaches (i)–(iv) permit a calculation of the forces acting on the atoms using the HellmannFeynman theorem and further a structural optimization of the adsorbatezeolite complex, while RPA and MP2 calculations can be performed only for a fixed geometry optimized at a lower level of theory. The influence of elevated temperature has been taken into account by averaging the adsorption energies calculated for purely siliceous and protonated chabazite, with weighting factors determined by molecular dynamics calculations with dispersioncorrected forces from DFT. Compared to experiment, the RPA underestimates the adsorption energies by about 5 kJ/mol while MP2 leads to an overestimation by about 6 kJ/Mol (averaged over methane, ethane, and propane). The most accurate results have been found for the “hybrid” RPAHF method with an average error of less than 2 kJ/mol only, while RPA underestimates the adsorption energies by about 8 kJ/mol on average. MP2 overestimates the adsorption energies slightly, with an average error of 5 kJ/mol. The more approximate and computationally less demanding methods such as the vdWDF density functional or the C _{6}/R ^{6} pair potentials with C _{6} parameters from “atoms in a solid” calculations overestimate the adsorption energies quite strongly. Relatively good agreement with experiment is achieved with the empirical PBE+d method with an average error of about 5 kJ/mol.

Variational fractionalspin densityfunctional theory for diradicals
View Description Hide DescriptionAccurate computation of singlettriplet energy gaps of diradicals remains a challenging problem in densityfunctional theory(DFT). In this work, we propose a variational extension of our previous work [D. H. Ess, E. R. Johnson, X. Q. Hu, and W. T. Yang, J. Phys. Chem. A115, 76 (2011)10.1021/jp109280y], which applied fractionalspin densityfunctional theory (FSDFT) to diradicals. The original FSDFT approach assumed equal spinorbital occupancies of 0.5 αspin and 0.5 βspin for the two degenerate, or nearly degenerate, frontier orbitals. In contrast, the variational approach (VFSDFT) optimizes the total energy of a singlet diradical with respect to the frontierorbital occupation numbers, based on a full configurationinteraction picture. It is found that the optimal occupation numbers are exactly 0.5 αspin and 0.5 βspin for diradicals such as O_{2}, where the frontier orbitals belong to the same multidimensional irreducible representation, and VFSDFT reduces to FSDFT for these cases. However, for diradicals where the frontier orbitals do not belong to the same irreducible representation, the optimal occupation numbers can vary between 0 and 1. Furthermore, analysis of CH_{2} by VFSDFT and FSDFT captures the ^{1} A _{1} and ^{1} B _{1} states, respectively. Finally, because of the static correlation error in commonly used density functional approximations, both VFSDFT and FSDFT calculations significantly overestimate the singlettriplet energy gaps for disjoint diradicals, such as cyclobutadiene, in which the frontier orbitals are confined to separate atomic centers.
 Advanced Experimental Techniques

High resolution ^{11}B NMR of magnesium diboride using cryogenic magic angle spinning
View Description Hide DescriptionStatic and magicangle spinning ^{11}B nuclear magnetic resonance(NMR) data at 4.7 T and 8.5 T have been obtained under cryogenic conditions on a diluted sample of magnesium diboride powder in the normal and superconducting state. The data provide accurate information on the magnetic shift and longitudinal relaxation time down to a temperature of 8 K, with a resolution improvement over the entire temperature range. The onset of superconductivity is unaffected by the sample rotation, as revealed by a steep variation of the magnetic shift just below the critical temperature.
 Atoms, Molecules, and Clusters

Vibrational effects on valence electron momentum distributions of ethylene
View Description Hide DescriptionWe report an electron momentum spectroscopy study of vibrational effects on the electron momentum distributions for the outer valence orbitals of ethylene (C_{2}H_{4}). The symmetric noncoplanar (e,2e) experiment has been conducted at an impact energy of 1.2 keV. Furthermore, a theoretical method of calculating electron momentum distributions for polyatomic molecules has been developed with vibrational effects being involved. It is shown from comparisons between experiment and theory that taking into account effects of the CH_{2} asymmetric stretching and CH_{2} rocking vibrational modes of C_{2}H_{4} is essential for a proper understanding of the electron momentum distribution of the 1b_{3g} molecular orbital.

Optical absorption spectra of gold clusters Au_{n} (n = 4, 6, 8,12, 20) from longrange corrected functionals with optimal tuning
View Description Hide DescriptionAbsorptionUV spectra of gold clusters Au_{n} (n = 4, 6, 8, 12, 20) are investigated using the timedependent density functional theory (TDDFT). The calculations employ several longrange corrected xc functionals: ωB97X, LCωPBEh, CAMB3LYP* (where * denotes a variant with corrected asymptote of CAMB3LYP), and LCωPBE. The latter two are subject to firstprinciple tuning according to a prescription of Stein et al. [Phys. Rev. Lett.105, 266802 (2010)10.1103/PhysRevLett.105.266802] by varying the range separation parameter. TDDFT results are validated for Au_{4} and Au_{8} against the equationofmotion coupled cluster singles and doubles results and the experiment. Both longrange correction and the inclusion of a fixed portion of the exact exchange in the shortrange are essential for the proper description of the optical spectra of gold. The ωB97X functional performs well across all studied cluster sizes. LCωPBEh, with parameters recommended by Rohrdanz et al. [J. Chem. Phys.130, 054112 (2009)10.1063/1.3073302], affords the best performance for clusters of n > 4. The optimally tuned CAMB3LYP* features the range separation parameter of 0.33 for Au_{4} and 0.25 for all the larger clusters. For LCωPBE the tuning procedure resulted in incorrect transition energies and oscillator strengths despite the fact that the optimized functional showed the accurate linear dependence on fractional electron numbers. Au_{n} (n = 4, 6, 8) feature optical gaps above of 3 eV and Au_{20} of ∼2.9 eV. In Au_{12} this gap narrows to ∼2.1 eV. The calculated spectrum for Au_{20} involves intensity being concentrated in only a few transitions with the absorption maximum at 3.5 eV. The intense 3.5 eV absorption is present in all cluster sizes of n > 4. The calculated HOMOLUMO gaps for all cluster sizes are within 0.5 eV of the difference between the vertical ionization potential and electron affinity. The reasons for this and for the failure of conventional xc functionals for optical spectra of gold are discussed.

Experimental and theoretical studies of the decomposition of new imidazole based energetic materials: Model systems
View Description Hide DescriptionDecomposition of three imidazole based model energetic systems (2nitroimidazole, 4nitroimidazole, and 1methyl5nitroimidazole) is investigated both experimentally and theoretically. The initial decomposition mechanism for these three nitroimidazoles is explored with nanosecond energy resolved spectroscopy, and quantum chemical theory at the complete active space selfconsistent field (CASSCF) level. The NO molecule is observed as an initial decomposition product from these three nitroimidazoles subsequent to UV excitation. A unique, excitation wavelength independent dissociation channel is observed for these three nitroimidazoles that generates the NO product with a rotationally cold (∼50 K) and a vibrationally mildly hot (∼800 K) distribution. Potential energy surface calculations at the CASSCF/631G(d) level of theory illustrate that conical intersections play an important and essential role in the decomposition mechanism. Electronically excited S_{2} nitroimidazole molecules relax to the S_{1} state through the (S_{2}/S_{1})_{CI} conical intersection, and undergo a nitronitrite isomerization to generate the NO product from the S_{1}potential energy surface. Nevertheless, NO_{2} elimination and nitronitrite isomerization are expected to be competitive reaction mechanisms for the decomposition of these molecules on the ground statepotential energy surface from the FranckCondon equilibrium geometry through thermal dissociation.

Ab initio rovibrational structure of the lowest singlet state of O_{2}O_{2}
View Description Hide DescriptionRovibrational bound states of the = 0)− = 0) dimer in its singlet electronic state have been obtained by solving the timeindependent Schrödinger equation for the nuclear degrees of freedom. We have employed two different ab initiopotential energy surfaces, based on high level multiconfigurational methods, which are expected to give upper and lower bounds for the real values of the interaction. Results are compared with spectroscopy experiments as well as with calculations using other semi ab initioand empirical interaction potentials. For the two ab initio potentials studied here, the ground vibrational state has a rectangular geometry and behaves as a semirigid molecule. The associated rotational constant is found in very good agreement with high resolution spectra. However, the computed dissociation energy and the frequency of the torsion mode are larger than previous experimental determinations, and possible reasons for these discrepancies are discussed. On the other hand, we have computed the splitting between the rovibrational states of the singlet and triplet electronic states and have found a fair agreement with measurements of the dimer spectra in a solid rare gas host.

Ab initio longrange interaction and adiabatic channel capture model for ultracold reactions between the KRb molecules
View Description Hide DescriptionThe coefficients at the lowestorder electrostatic, induction, and dispersion terms of the anisotropic longrange potential between the two KRb(^{1}Σ^{+}) molecules are evaluated through the static and dynamic molecular properties using the ab initio coupled cluster techniques. Adiabatic channel potentials for the groundstate molecules are obtained and used for the numerical quantum capture probability calculations in the spirit of the statistical adiabatic channel models. Capture rate coefficients for indistinguishable (polarized) and distinguishable (unpolarized) molecules at temperatures below 10 μK agree well with those computed with the simple isotropic dispersion R ^{−6} potential, but underestimate the measured ones [Ospelkaus et al., Science327, 853 (2010)10.1126/science.1184121] up to a factor of 3. Preliminary assessment of the effects of higherorder longrange terms, retardation of dispersion forces, and magnetic dipole–dipole interaction does not offer any clear perspectives for drastic improvement of the capture approximation for the reactions studied.

Fine and hyperfine excitation of NH and ND by He: On the importance of calculating rate coefficients of isotopologues
View Description Hide DescriptionThe NH and ND molecules play an important role in interstellar nitrogen chemistry. Accurate modeling of their abundance in space requires the calculation of rates for collisional excitation by the most abundant interstellar species. We calculate rate coefficients for the fine and hyperfine excitation of NH and ND by He. Statetostate rate coefficients between the first levels of NH and ND were obtained for temperatures ranging from 5 to 150 K. Fine structure resolved rate coefficients present a strong propensity rule in favor of Δj = ΔN transitions, as expected from theoretical considerations. The Δj = ΔF _{1} = ΔF propensity rule is observed for the hyperfine transitions of both isotopologues. The two sets of fine structure resolved rate coefficients are compared in detail and we find significant differences between the two isotopologues. This comparison shows that specific calculations are necessary for the deuterated isotopologues of any hydride. The new rate coefficients will help significantly in the interpretation of NH and ND terahertz spectra observed with current and future telescopes, and enable these molecules to become a powerful astrophysical tool for studying the nitrogen chemistry.