Volume 135, Issue 14, 14 October 2011

We present a method for selectively exciting nuclear magnetic resonances(NMRs) from welldefined subsets of crystallites from a powdered sample under magic angle spinning. Magic angle spinning induces a time dependence in the anisotropic interactions, which results in a time variation of the resonance frequencies which is different for different crystallite orientations. The proposed method exploits this by applying selective pulses, which we refer to as XS (for crystalliteselective) pulses, that follow the resonance frequencies of nuclear species within particular crystallites, resulting in the induced flip angle being orientation dependent. By selecting the radiofrequency field to deliver a 180^{ ○} pulse for the target orientation and employing a train of such pulses combined with cogwheel phase cycling, we obtain a high degree of orientational selectivity with the resulting spectrum containing only contributions from orientations close to the target. Typically, this leads to the selection of between 0.1% and 10% of the crystallites, and in extreme cases to the excitation of a single orientation resulting in single crystal spectra of spinning powders. Two formulations of this method are described and demonstrated with experimental examples on [1 − ^{13}C]alanine and the paramagnetic compound Sm_{2}Sn_{2}O_{7}.
 ARTICLES

 Theoretical Methods and Algorithms

The hierarchical expansion of the kinetic energy operator in curvilinear coordinates extended to the vibrational configuration interaction method
View Description Hide DescriptionThe hierarchical expansion of the kinetic energy operator in curvilinear coordinates presented earlier for the vibrational selfconsistent field technique is extended to the vibrational configuration interaction (VCI) method. The high accuracy of the modified VCI method is demonstrated by computing first excitation energies of the H_{2}O_{2} molecule using an analytic potential (PCPSDE) and showing convergence to accurate results from full dimensional discrete variable representation calculations.

Surface hopping with Ehrenfest excited potential
View Description Hide DescriptionGiven the exponentially scaling cost of full quantum calculations, approximations need to be employed for the simulation of the time evolution of chemical systems. We present a modified version of surface hopping that has the potential to treat larger systems. This is accomplished through an Ehrenfestlike treatment of the excited states, thereby reducing the dynamics to transitions between the ground state and a meanfieldexcited state. A simplified description of the excited states is achieved, while still allowing for an accurate description of disparate reaction channels. We test our meanfield approximation for the excited states on a series of model problems. Results are compared to the standard surface hopping procedure, with its explicit treatment of all excited states, and the traditional Ehrenfest approach, with its averaging together of all states.

Comparison of polarizable continuum model and quantum mechanics/molecular mechanics solute electronic polarization: Study of the optical and magnetic properties of diazines in water
View Description Hide DescriptionA combination of the polarizable continuum model (PCM) and the hybrid quantum mechanics/molecular mechanics (QM/MM) methodology, PCMMM/QM, is used to include the solute electronic polarization and then study the solvent effects on the lowlying n→π^{*} excitation energy and the ^{15}N nuclear magnetic shielding of pyrazine and pyridazine in aqueous environment. The results obtained with PCMMM/QM are compared with two other procedures, i.e., the conventional PCM and the iterative and sequential QM/MM (IQM/MM). The QM calculations are made using density functional theory in the three procedures. For the excitation energies, the timedependent B3LYP/6311+G(d) model is used. For the magnetic shielding, the B3LYP/augpcS2(N)/pcS2(C,O,H) is used with the gaugeincluding atomic orbitals. In both cases, i.e., PCMMM/QM and IQM/MM, that use a discrete model of the solvent, the solute is surrounded by a first shell of explicit water molecules embedded by an electrostatic field of point charges for the outer shells. The best results are obtained including 28 explicit water molecules for the spectral calculations and 9 explicit water molecules for the magnetic shielding. Using the PCMMM/QM methodology the results for the n→π^{*} excitation energies of pyridazine and pyrazine are 32 070 ± 80 cm^{−1} and 32 675 ± 60 cm^{−1}, respectively, in good agreement with the corresponding IMM/QM results of 32 540 ± 80 cm^{−1} and 32 710 ± 60 cm^{−1} and the experimental results of 33 450–33 580 cm^{−1} and 32 700–33 300 cm^{−1}. For the ^{15}N magnetic shielding, the corresponding numbers for the gaswater shifts obtained with PCMMM/QM are 47.4 ± 1.3 ppm for pyridazine and 19.7 ± 1.1 ppm for pyrazine, compared with the IQM/MM values of 53.4 ± 1.3 ppm and 19.5 ± 1.2 ppm and the experimental results of 42–54 ppm and 17–22 ppm, respectively. The agreement between the two procedures is found to be very good and both are in agreement with the experimental values. PCMMM/QM approach gives a good solute polarization and could be considered in obtaining reliable results within the expected QM/MM accuracy. With this electronic polarization, the solvent effects on the electronic absorption spectra and the ^{15}N magnetic shielding of the diazines in water are well described by using only an electrostatic approximation. Finally, it is remarked that the experimental and theoretical results suggest that the ^{15}N nuclear magnetic shielding of any diazine has a clear dependence with the solvent polarity but not directly with the solutesolvent hydrogen bonds.

Robust conductance of dumbbell molecular junctions with fullerene anchoring groups
View Description Hide DescriptionThe conductance of a molecular wire connected to metallic electrodes is known to be sensitive to the atomic structure of the moleculemetal contact. This contact is to a large extent determined by the anchoring group linking the molecular wire to the metal. It has been found experimentally that a dumbbell construction with C_{60} molecules acting as anchors yields more welldefined conductances as compared to the widely used thiol anchoring groups. Here, we use density functional theory to investigate the electronic properties of this dumbbell construction. The conductance is found to be stable against variations in the detailed bonding geometry and in good agreement with the experimental value of . Electron tunneling across the molecular bridge occurs via the lowest unoccupied orbitals of C_{60} which are pinned close to the Fermi energy due to partial charge transfer. Our findings support the original motivation to achieve conductance values more stable towards changes in the structure of the moleculemetal contact leading to larger reproducibility in experiments.

An overlap fitted chain of spheres exchange method
View Description Hide DescriptionThe “chain of spheres” (COS) algorithm, as part of the RIJCOSX SCF procedure, approximates the exchange term by performing analytic integration with respect to the coordinates of only one of the two electrons, whereas for the remaining coordinates, integration is carried out numerically. In the present work, we attempt to enhance the efficiency of the method by minimizing numerical errors in the COS procedure. The main idea is based on the work of Friesner and consists of finding a fitting matrix, , which leads the numerical and analytically evaluated overlap matrices to coincide. Using , the evaluation of exchange integrals can indeed be improved. Improved results and timings are obtained with the present default grid setup for both single point calculations and geometry optimizations. The fitting procedure results in a reduction of grid sizes necessary for achieving chemical accuracy. We demonstrate this by testing a number of grids and comparing results to the fully analytic and the earlier COS approximations. This turns out to be favourable for total and reaction energies, for which chemical accuracy can now be reached with a corresponding ∼30% speedup over the original RIJCOSX procedure for single point energies. Results are slightly less favourable for the accuracy of geometry optimizations, but the procedure is still shown to yield geometries with errors well below the method inherent errors of the employed theoretical framework.

The effects of shape and flexibility on bioengineered fdvirus suspensions
View Description Hide DescriptionWe present a theoretical model to describe binary mixtures of semiflexible rods, applied here to fdvirus suspensions. We investigate the effects of rod stiffness on both monodisperse and binary systems, studying thickthin and longshort mixtures. For monodisperse systems, we find that fdvirus particles have to be made extremely stiff to even approach the behavior of rigid rods. For thickthin mixtures, we find increasingly rich phase behavior as the rods are either made more flexible or if their diameter ratio is increased. For longshort rod mixtures we find that the phase behavior is controlled by the relative stiffness of the rods, with increasing the stiffness of the long rods or decreasing that of the short rods resulting in richer phase behavior. We also calculate the state point dependent effective shape of the rods. The flexible rods studied here always behave as shorter, thicker rigid rods, but with an effective shape that varies widely throughout the phase diagrams, and plays a key role in determining phase behavior.

Analytic energy gradients in combined second order MøllerPlesset perturbation theory and conductorlike polarizable continuum model calculation
View Description Hide DescriptionThe analytic energy gradients in combined second order MøllerPlesset perturbation theory and conductorlike polarizable continuum model calculations are derived and implemented for spinrestricted closed shell (RMP2), Zaveraged spinrestricted open shell (ZAPT2), and spinunrestricted open shell (UMP2) cases. Using these methods, the geometries of the S_{0}ground state and the T_{1} state of three nucleobase pairs (guaninecytosine, adeninethymine, and adenineuracil) in the gas phase and aqueous solution phase are optimized. It is found that in both the gas phase and the aqueous solution phase the hydrogen bonds in the T_{1} state pairs are weakened by ∼1 kcal/mol as compared to those in the S_{0} state pairs.

Virtual interface substructure synthesis method for normal mode analysis of superlarge molecular complexes at atomic resolution
View Description Hide DescriptionNormal mode analysis of large biomolecular complexes at atomic resolution remains challenging in computational structure biology due to the requirement of large amount of memory space and central processing unit time. In this paper, we present a method called virtual interface substructure synthesis method or VISSM to calculate approximate normal modes of large biomolecular complexes at atomic resolution. VISSM introduces the subunit interfaces as independent substructures that join contacting molecules so as to keep the integrity of the system. Compared with other approximate methods, VISSM delivers atomic modes with no need of a coarsegrainingthenprojection procedure. The method was examined for 54 proteincomplexes with the conventional allatom normal mode analysis using CHARMM simulation program and the overlap of the first 100 lowfrequency modes is greater than 0.7 for 49 complexes, indicating its accuracy and reliability. We then applied VISSM to the satellite panicum mosaic virus (SPMV, 78 300 atoms) and to Factin filament structures of up to 39mer, 228 813 atoms and found that VISSM calculations capture functionally important conformational changes accessible to these structures at atomic resolution. Our results support the idea that the dynamics of a large biomolecular complex might be understood based on the motions of its component subunits and the way in which subunits bind one another.

A new Monte Carlo method for getting the density of states of atomic cluster systems
View Description Hide DescriptionA novel Monte Carlo flat histogram algorithm is proposed to get the classical density of states in terms of the potential energy, g(E _{ p }), for systems with continuous variables such as atomic clusters. It aims at avoiding the long iterative process of the WangLandau method and controlling carefully the convergence, but keeping the ability to overcome energy barriers. Our algorithm is based on a preliminary mapping in a series of points (called a σmapping), obtained by a twoparameter local probing of g(E _{ p }), and it converges in only two subsequent reweighting iterations on large intervals. The method is illustrated on the model system of a 432 atom cluster bound by a Rydberg type potential. Convergence properties are first examined in detail, particularly in the phase transition zone. We get g(E _{ p }) varying by a factor 10^{3700} over the energy range [0.01 < E _{ p } < 6000 eV], covered by only eight overlapping intervals. Canonical quantities are derived, such as the internal energy U(T) and the heat capacity C_{V}(T). This reveals the solid to liquidphase transition, lying in our conditions at the triple point. This phase transition is further studied by computing a LindemannBerry index, the atomic cluster density n(r), and the pressure, demonstrating the progressive surface melting at this triple point. Some limited results are also given for 1224 and 4044 atom clusters.

Model for the fast estimation of basis set superposition error in biomolecular systems
View Description Hide DescriptionBasis set superposition error (BSSE) is a significant contributor to errors in quantumbased energy functions, especially for large chemical systems with many molecular contacts such as folded proteins and proteinligand complexes. While the counterpoise method has become a standard procedure for correcting intermolecular BSSE, most current approaches to correcting intramolecular BSSE are simply fragmentbased analogues of the counterpoise method which require many (two times the number of fragments) additional quantum calculations in their application. We propose that magnitudes of both forms of BSSE can be quickly estimated by dividing a system into interacting fragments, estimating each fragment's contribution to the overall BSSE with a simple statistical model, and then propagating these errors throughout the entire system. Such a method requires no additional quantum calculations, but rather only an analysis of the system's interacting fragments. The method is described herein and is applied to a proteinligand system, a small helical protein, and a set of native and decoy protein folds.

Ab initio investigation of titanium hydroxide isomers and their cations, TiOH^{0, +} and HTiO^{0, +}
View Description Hide DescriptionWe studied the electronic and geometrical structure of the [Ti, O, H]^{0, +} species, using large basis sets and both singlereference coupled cluster and multireference configuration interaction methodologies. The electronic structure of HTiO^{0, +} is interpreted qualitatively in terms of a hydrogen atom bonding to TiO^{0, +}, while the structure of TiOH^{0, +} is interpreted in terms of Ti^{+, 2 +} bonding to OH^{−}. Potential energy profiles are reported as functions of the Ti–OH and H–TiO bond lengths, and of the H–Ti–O angle. For a total of 33 stationary points on the potential energy surfaces, we report absolute energies, geometries, and harmonic frequencies. For the neutral species, dipole moments are also given.

Dynamics of interatomic Coulombic decay in quantum dots
View Description Hide DescriptionIn this work we demonstrate that the interatomic Coulombic decay (ICD), an ultrafast electron relaxation process known for atoms and molecules, is possible in general binding potentials. We used the multiconfiguration timedependent Hartree method for fermions to study ICD in real time in a twoelectron model system of two potential wells. Two decay channels were identified and analyzed by using the box stabilization analysis as well as by evaluating the autocorrelation function and measuring the outgoing electron flux during timepropagations. The total and partial ICD widths of an excited state localized in one potential well as a function of the distance between the two potentials was obtained. Finally, we discuss the results with a view to a possible application of ICD in quantum dot technology.

Effective Hamiltonian for femtosecond vibrational dynamics
View Description Hide DescriptionTime propagation of zeroorder states of an effective spectroscopic Hamiltonian is tested against femtosecond time dependent dynamics of adiabatic wavepackets evolving on a model potential energy surface for two coupled modes of the radical HO_{2} with multiple potential wells and above barrier motion. A generalized Hamiltonian which breaks the usual conserved polyad action by including extra resonance couplings (V _{2:1} and V _{3:1}) successfully describes the time evolution after the further addition of two “ultrafast” couplings. These new couplings are a nonresonant coupling and a resonant coupling V _{1:1} that functions as an ultrafast term because the system is far from 1:1 frequency resonance.

Allatom modeling of anisotropic atomic fluctuations in protein crystal structures
View Description Hide DescriptionThe accurate modeling of protein dynamics in crystalline states is essential for the development of computational techniques for simulating protein dynamics under physiological conditions. Following a previous coarsegrained modeling study of atomic fluctuations in proteincrystal structures, we have refined our modeling with allatom representation and force field. We have calculated the anisotropic atomic fluctuations of a proteinstructure interacting with its crystalline environment either explicitly (by including neighboring proteins into modeling) or implicitly (by adding harmonic restraints to surface atoms involved in crystal contacts). The modeling results are assessed in comparison with the experimental anisotropic displacement parameters (ADP) determined by Xray crystallography. For a list of 40 highresolution proteincrystal structures, we have found that the optimal modeling of ADPs is achieved when the proteinenvironmentinteractions are much weaker than the internal interactions within a proteinstructure. Therefore, the intrinsic dynamics of a proteinstructure is only weakly perturbed by crystal packing. We have also found no noticeable improvement in the accuracy of ADP modeling by using allatom over coarsegrained representation and force field, which justifies the use of coarsegrained modeling to investigate protein dynamics with both efficiency and accuracy.

Multidimensional treatment of stochastic solvent dynamics in photoinduced protoncoupled electron transfer processes: Sequential, concerted, and complex branching mechanisms
View Description Hide DescriptionA theoretical approach for the multidimensional treatment of photoinduced protoncoupled electron transfer (PCET) processes in solution is presented. This methodology is based on the multistate continuum theory with an arbitrary number of diabatic electronic states representing the relevant charge distributions in a general PCET system. The active electrons and transferring proton(s) are treated quantum mechanically, and the electronproton vibronic free energysurfaces are represented as functions of multiple scalar solvent coordinates corresponding to the single electron and proton transfer reactions involved in the PCET process. A dynamical formulation of the dielectric continuum theory is used to derive a set of coupled generalized Langevin equations of motion describing the time evolution of these collective solvent coordinates. The parameters in the Langevin equations depend on the solvent properties, such as the dielectric constants, relaxation time, and molecular moment of inertia, as well as the solute properties. The dynamics of selected intramolecular nuclear coordinates, such as the proton donoracceptor distance or a torsional angle within the PCET complex, may also be included in this formulation. A surface hopping method in conjunction with the Langevin equations of motion is used to simulate the nonadiabaticdynamics on the multidimensional electronproton vibronic free energysurfaces following photoexcitation. This theoretical treatment enables the description of both sequential and concerted mechanisms, as well as more complex processes involving a combination of these mechanisms. The application of this methodology to a series of model systems corresponding to collinear and orthogonal PCET illustrates fundamental aspects of these different mechanisms and elucidates the significance of proton vibrational relaxation and nonequilibrium solventdynamics.

An efficient local coupled cluster method for accurate thermochemistry of large systems
View Description Hide DescriptionAn efficient local coupled cluster method with single and double excitation operators and perturbative treatment of triple excitations [DFLCCSD(T)] is described. All required twoelectron integrals are evaluated using density fitting approximations. These have a negligible effect on the accuracy but reduce the computational effort by 1–2 orders of magnitude, as compared to standard integraldirect methods. Excitations are restricted to local subsets of nonorthogonal virtual orbitals (domain approximation). Depending on distance criteria, the correlated electron pairs are classified into strong, close, weak, and very distant pairs. Only strong pairs, which typically account for more than 90% of the correlation energy, are optimized in the LCCSD treatment. The remaining close and weak pairs are approximated by LMP2 (local secondorder MøllerPlesset perturbation theory); very distant pairs are neglected. It is demonstrated that the accuracy of this scheme can be significantly improved by including the close pair LMP2 amplitudes in the LCCSD equations, as well as in the perturbative treatment of the triples excitations. Using this ansatz for the wavefunction, the evaluation and transformation of the twoelectron integrals scale cubically with molecular size. If local density fitting approximations are activated, this is reduced to linear scaling. The LCCSD iterations scale quadratically, but linear scaling can be achieved by neglecting some terms involving contractions of single excitations. The accuracy and efficiency of the method is systematically tested using various approximations, and calculations for molecules with up to 90 atoms and 2636 basis functions are presented.

An explicitly correlated local coupled cluster method for calculations of large molecules close to the basis set limit
View Description Hide DescriptionA new explicitly correlated local coupledcluster method with single and double excitations and a perturbative treatment of triple excitations [DFLCCSD(T0)F12x (x = a,b)] is presented. By means of truncating the virtual orbital space to pairspecific local domains (domain approximation) and a simplified treatment of close, weak and distant pairs using LMP2F12 (pair approximation) the scaling of the computational cost with molecular size is strongly reduced. The basis set incompleteness errors as well as the errors due to the domain approximation are largely eliminated by the explicitly correlated terms. All integrals are computed using efficient density fitting (DF) approximations. The accuracy of the method is investigated for 52 reactions involving medium size molecules. A comparison of DFLCCSD(T0)F12xreaction energies with canonical CCSD(T)F12x calculations shows that the errors introduced by the domain approximation are indeed very small. Care must be taken to keep the errors due to the additional pair approximation equally small, and appropriate distance criteria are recommended. Using these parameters, the root mean square (RMS) deviations of DFLCCSD(T0)F12a calculations with tripleζ basis sets from estimated CCSD(T) complete basis set (CBS) limits and experimental data amount to only 1.5 kJ mol^{−1} and 2.9 kJ mol^{−1}, respectively. For comparison, the RMS deviation of the CCSD(T)/CBS values from the experimental values amounts to 3.0 kJ mol^{−1}. The potential of the method is demonstrated for five reactions of biochemical or pharmacological interest which include molecules with up to 61 atoms. These calculations show that molecules of this size can now be treated routinely and yield results that are close to the CCSD(T) complete basis set limits.

How to compare diffusion processes assessed by singleparticle tracking and pulsed field gradient nuclear magnetic resonance
View Description Hide DescriptionHeterogeneous diffusion processes occur in many different fields such as transport in living cells or diffusion in porous media. A characterization of the transport parameters of such processes can be achieved by ensemblebased methods, such as pulsed field gradient nuclear magnetic resonance (PFG NMR), or by trajectorybased methods obtained from singleparticle tracking (SPT) experiments. In this paper, we study the general relationship between both methods and its application to heterogeneous systems. We derive analytical expressions for the distribution of diffusivities from SPT and further relate it to NMRspinechodiffusion attenuation functions. To exemplify the applicability of this approach, we employ a wellestablished tworegion exchange model, which has widely been used in the context of PFG NMR studies of multiphase systems subjected to interphase molecular exchange processes. This type of systems, which can also describe a layered liquid with layerdependent selfdiffusion coefficients, has also recently gained attention in SPT experiments. We reformulate the results of the tworegion exchange model in terms of SPTobservables and compare its predictions to that obtained using the exact transformation which we derived.

Basis set convergence of explicitly correlated doublehybrid density functional theory calculations
View Description Hide DescriptionThe basis set convergence of explicitly correlated doublehybrid density functional theory(DFT) is investigated using the B2GPPLYP functional. As reference values, we use basis set limit B2GPPLYPF12 reaction energies extrapolated from the aug^{′}ccpV(Q+d)Z and aug^{′}ccpV(5+d)Z basis sets. Explicitly correlated doublehybrid DFT calculations converge significantly faster to the basis set limit than conventional calculations done with basis sets saturated up to the same angular momentum (typically, one “gains” one angular momentum in the explicitly correlated calculations). In explicitly correlated F12 calculations the VnZF12 basis sets converge faster than the orbital A^{′}VnZ basis sets. Furthermore, basis set convergence of the MP2F12 component is apparently faster than that of the underlying KohnSham calculation. Therefore, the most costeffective approach consists of combining the MP2F12 correlation energy from a comparatively small basis set such as VDZF12 with a DFT energy from a larger basis set such as aug^{′}ccpV(T+d)Z.
 Advanced Experimental Techniques

Single crystal nuclear magnetic resonance in spinning powders
View Description Hide DescriptionWe present a method for selectively exciting nuclear magnetic resonances(NMRs) from welldefined subsets of crystallites from a powdered sample under magic angle spinning. Magic angle spinning induces a time dependence in the anisotropic interactions, which results in a time variation of the resonance frequencies which is different for different crystallite orientations. The proposed method exploits this by applying selective pulses, which we refer to as XS (for crystalliteselective) pulses, that follow the resonance frequencies of nuclear species within particular crystallites, resulting in the induced flip angle being orientation dependent. By selecting the radiofrequency field to deliver a 180^{ ○} pulse for the target orientation and employing a train of such pulses combined with cogwheel phase cycling, we obtain a high degree of orientational selectivity with the resulting spectrum containing only contributions from orientations close to the target. Typically, this leads to the selection of between 0.1% and 10% of the crystallites, and in extreme cases to the excitation of a single orientation resulting in single crystal spectra of spinning powders. Two formulations of this method are described and demonstrated with experimental examples on [1 − ^{13}C]alanine and the paramagnetic compound Sm_{2}Sn_{2}O_{7}.